Water at Molecular Interfaces: Structure and Dynamics Near Biomolecules and Amorphous Silica

Home , Orthosilicic acid, Properties of water

WATER AT MOLECULAR INTERFACES: STRUCTURE AND DYNAMICS NEAR BIOMOLECULES AND AMORPHOUS SILICA

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

Ali A. Hassanali, M.S.

Biophysics Graduate Program

The Ohio State University

2010

Dissertation Committee:

Professor Sherwin J. Singer, Adviser Professor Dongping Zhong Professor Terrence Conlisk Professor Justin Wu ABSTRACT

Water, the fundamental constituent of life, has been found to have a critical role at both organic and inorganic surfaces. The properties of water near surfaces, is known to be diﬀerent from water far away from the interface. This dissertation explores the degree to which inorganic materials such as amorphous silica (glass) and biomolecular surfaces change the properties of water. Of particular interest is the interplay between biological molecules - proteins and nucleic acids - and their aqueous environment, and how this determines biological function.

The mobility of water near protein surfaces has been of considerable recent in-

terest. There have been many reports in the literature postulating that interfacial

water is incapable of undergoing rapid rotational motions due to strong electrostatic

forces from the protein surface. This has led to confusing and conﬂicting interpre-

tations on the molecular origin of the slow features observed in certain experiments

that probe protein surfaces. Our theoretical studies resolve the conﬂicts and show

that the slow dynamics observed, originates from the protein and water jostling in a

concerted fashion. Our studies support a change in the paradigm for the function of

proteins to include both the protein and the surrounding water as active participants

in biological function.

ii For 80 years, scientists have employed models in which ions and water near the silica surface form a stagnant layer called the Stern layer. To account for all experimental features, these models invoke puzzling properties such as the transport of ions through immobile water. In this dissertation, we develop a realistic theoretical description of the water-amorphous silica interface. We have successfully constructed and validated a model for the water-amorphous silica interface and have begun to examine the fate of biomolecules near this important interface. Our simulations challenge the classical textbook Stern layer model. Both ions and water exhibit a substantial degree of mobility, yet the phenomena the Stern layer was originally invoked to explain, are reproduced by our calculations.

Theoretical studies for the repair of DNA bases damaged by sunlight demonstrate that fast water motions are critical in ensuring the rapid repair of the bases. We have constructed a simple model using our ground state calculations that provides new insights into the mechanisms of efficient DNA repair that might be deployed in the active site of the DNA repair protein. The splitting energetics during DNA repair is shown to modulate the charge recombination process and can significantly affect the quantum repair yields.

iii Dedicated to humanity, in the quest for the search of truth and purpose in this

universe

iv ACKNOWLEDGMENTS

I have always been fascinated and some might say, obsessed with epistemological methods that we think help us understand more about our purpose and role in this complex universe - that is of course, if there is any purpose at all! The original motivation for pursuing a PhD in the sciences was and still is motivated by philosophical interests in the scientiﬁc method and its intimate connections with other methods of discovery. The journey has been extremely rewarding and in many ways very hum- bling. The beauty of knowledge, is that it manifests itself in an inﬁnite manner in both breadth and depth...and hence I see this milestone as simply the beginning of unending journey.

I feel very humbled to be in this position of privilege writing an acknowledgment for my PhD dissertation. I interpret it as a privileged position because circumstances in my life have shaped and facilitated my choices to be where I am. While the PhD degree can often give you an elevated position amongst the academic elite, the “ivory tower” can also be very indiﬀerent to issues of socio-economic justice. Approximately

1 billion people entered the 21st century unable to read or sign their names. I put this fact out as a call for all of us in this privileged position, including myself, to think about and hopefully render progressive responses.

I was extremely lucky to have my PhD co-advised by a theoretician and experi- mentalist. The collaboration was very enjoyable and allowed me to get involved in

v several projects that were intellectually rewarding. Since this is an acknowledgment,

it would be prudent to share some personal experiences about the people you spend

so much time with in the oﬃce and on email.

I’d like to begin by thanking Sherwin for being a phenomenal adviser and more importantly a patient teacher throughout my tenure in the PhD program. Sherwin was always ready to explain things repeatedly to me with a smile on his face. I was always fascinated by his unique skill of taking verbal arguments and expressing them in terms of mathematical equations. He is a very careful scientist (and that’s rare to ﬁnd these days) who pays close attention to detail that others often neglect.

Anyone who spends enough time with Sherwin knows that he has an interesting sense of humor and always lightens the often scientifically intense moments. His intellectual and moral support throughout my PhD was invaluable. I was lucky to have an adviser like Sherwin who loved to argue and debate and who was perfectly comfortable with his students challenging his scientific opinions. Beyond his scientific mentoring, Sherwin always showed a genuine interest and concern in my personal development. Sherwin, I look forward to receiving many more emails from you in the future at 4.30 AM! I’d also like to specifically thank you for taking the time to carefully read, edit and re-write my lousy first drafts of manuscripts.

I’d like to thank Dongping for providing fertile ground for a healthy and productive collaboration between theory and experiment on several projects and for being a great co-adviser. Dongping always set the bar very high for both scientiﬁc productivity and work ethic. His enthusiasm and excitement for science can often be very contagious!

I’ve always been intrigued by Dongping’s ability to choose biological systems that are rich in fundamental physical and chemical problems that in turn provide a lot of room

vi for the development of interesting theory and computational work. Dongping has a

unique skill of ﬁnding voids in scientiﬁc arguments, when you think you completely

understand all the issues. I am anxious to see what new biological problems you

aim to to tackle in the future, for inspiration perhaps, on the development of new

computational methods.

A special thanks goes to the members of my thesis committee, Terry Conlisk and

Justin Wu for carefully reading my thesis and providing insightful comments.

I’ve been blessed with a beautiful family who have supported me in a multitude

of ways throughout my life. My parents, for giving me the opportunity to pursue

further education in the United States, much to the concerns of my darling mother

who wanted me much closer to home! My mom and dad provided an environment

that allowed for creative exploration of intellectual thought but more importantly,

taught me that this must always be accompanied by a profound sense of humility and

responsibility. I’d like to thank my sisters Rumina and Raabia for setting the bar

pretty high right from the beginning. You left big shoes to ﬁll. Rumina, I guess you

will always be the doctor who actually makes a diﬀerence! I’d like to thank my three

little nieces Imaan, Sahar and Layla for making my Saturday and Sunday mornings

entertaining with their singing during many many skype conversations! I’d like to

thank my inlaws for all their support in the last 2 years.

Living far away from family, friends often become an intricate part of your support system and in many ways take the role as surrogate family members. I’d like to begin my thanking Daniel for being an awesome ﬂatmate for my ﬁrst two years at OSU.

I worked extremely hard my ﬁrst two years, probably the hardest throughout my

PhD, and Daniel was extremely patient with me. I will always have fond memories

vii of our philosophical exchanges. Its been a real pleasure sharing diﬀerent parts of the

evolution of my existential identity with you.

I’d like to thank Kashif for really being like an older brother to me and looking after me like one of his own family members. I’ve thoroughly enjoyed all our conversations on numerous topics and look forward to many more in the future. I will always remember feeling a sense of relief, every time I’d get a phonecall from you in the evenings after being in the oﬃce for over 12 hours. I will also miss our racquetball games...its been a lot of fun! Thanks to Taqdees for playing a motherly role and feeding a hungry and tired graduate student on too many occasions!

Laura, I’d like to thank you for not giving up on me, earlier on in our friendship and for dealing with my social idiosyncrasies in a way that was nurturing. I have fond memories of our jogging sessions late at night and the few racquetball games that I destroyed you on! I am really excited about hearing and listening to the unfolding of the bright future that I think lies ahead for you. You are one of the smartest kids that I know.

It would be impossible to run through all the people who have played an instrumental role in helping me understand and think about knowledge in diﬀerent ways, but I am thankful to all the following people who have contributed to my development both academically and personally: Rajeev, Dhananjay, Laura Beth, Rizwan,

Cristen, Renata, Mayank, Sachin, Kaushal, Ian, Yu-Kay, Carol, Bhavin, Andrea,

Kassie, Roshni, Mayuri, Carrie, Mark, Reshma, Shweta, Shouvik, Amjad...and I am probably missing a whole bunch of other people.

viii I’d like to thank all the members of the theory group: Tanping, Yun, Hui, Corey and Chris (when he was in the group) for all the fun times and healthy scientiﬁc debates at various points during the last six years.

Finally, I’d like to end by thanking two very important people who keep me motivated in my faith in a purposeful existence, Rubab and Bilal. Rubab, I am so glad that we found each other when we did. Through you I discover the essence of my being and strive to achieve a higher state of ethical reality. Rubab, no words can express my gratitude for your patience during the last 2 years as you put your career on hold. And my son Bilal, the new addition...you’ve brought me an enormous amount of joy and contentment and I am so excited to play an instrumental role in guiding the emergence and expression of your identity as a human being in this complex universe.

ix VITA

December 29, 1979 ...... Born - Dar-es-Salaam, Tanzania

2002 ...... B.S., Purdue University

2004 ...... M.S., Purdue University

2004-2009 ...... Graduate Teaching and Research Asso- ciate, The Ohio State University 2009-present ...... Presidential Fellow, The Ohio State University

PUBLICATIONS

Research Publications

1. Ali A. Hassanali, Tanping Li, Dongping Zhong and Sherwin J. Singer “A Molecular Dynamics Study of Lys-Trp-Lys: Structure and Dynamics in Solution Fol- lowing Photoexcitation”, J.Phys. Chem. B110(21):10497 (2006)

2. Ali A. Hassanali and Sherwin J. Singer “Static and dynamic properties of the water/amorphous silica interface: a model for the undissociated surface”, J. Computer-Aided Materials Design. 14(1):53 (2007)

3. Tanping Li, Ali A. Hassanali, Ya-Ting Kao, Dongping Zhong and Sherwin J. Singer “Hydration Dynamics and Time Scales of Coupled Water-Protein Fluctua- tions”, J. Amer. Chem. Soc. 129(11):3376 (2007)

4. Ali A. Hassanali and Sherwin J. Singer “Model for the Water-Amorphous Silica Interface: The Undissociated Surface”, J. Phys. Chem. B111(38):11181 (2007)

x 5. Tanping Li, Ali A. Hassanali and Sherwin J. Singer “Origin of Slow Relaxation Following Photoexcitation of W7 in Myoglobin and the Dynamics of its Hydration Layer”, J. Phys. Chem. B112(50):16121 (2008)

6. Hui Zhang, Ali A. Hassanali, Yun Kyung Shin, Chris Knight and Sher- win J. Singer “The Water-Amorphous Silica Surface: What is the Stern Layer?”, (manuscript in preparation)

7. Ali A. Hassanali, Dongping Zhong and Sherwin J. Singer “Molecular mechanisms in the repair of cyclobutane pyrimidine dimer:the C5-C5′ bond”, (manuscript in preparation)

8. Ali A. Hassanali, Dongping Zhong and Sherwin J. Singer “Molecular mechanisms in the repair of cyclobutane pyrimidine dimer:the C6-C6′ bond”, (manuscript in preparation)

9. Ali A. Hassanali, Hui Zhang, Yun Kyung Shin, Chris Knight and Sherwin J. Singer “The dissociated amorphous silica surface: model development and validation”, (submitted to J. Chem. Theory. and Comput.)

FIELDS OF STUDY

Major Field: Biophysics

xi TABLE OF CONTENTS

Page

Abstract...... ii

Dedication...... iv

Acknowledgments...... v

Vita...... x

ListofFigures ...... xv

ListofTables ...... xxx

Chapters:

1. Introduction...... 1

2. A molecular dynamics simulation of the tripeptide KWK: Structure and dynamics following photoexcitation in solution ...... 10

2.1 Introduction ...... 10 2.2 Simulationmethods ...... 13 2.3 Lys-Trp-Lys isomers and the π-cation eﬀect: static properties . . . 16 2.4 Dynamics in solution following photoexcitation ...... 23 2.4.1 Fluorescence anisotropy decay ...... 24 2.4.2 Stokesshift ...... 26 2.5 Conclusions...... 38

xii 3. Protein hydration dynamics in myoglobin ...... 41

3.1 Introduction ...... 41 3.2 Simulationmethods ...... 45 3.3 Analysisofastructuraltransition...... 46 3.4 Dynamics of ﬂexible and frozen myoglobin following photoexcitation 50 3.4.1 Fluorescence Stokes shift ...... 52 3.4.2 Fluorescence anisotropy ...... 62 3.5 Water residence time and protein-water coupling in the hydration shell 64 3.6 Conclusions ...... 68

4. A model for the water amorphous silica interface: the undissociated surface 72

4.1 Introduction ...... 72 4.2 Development of a model for hydrated amorphous silica ...... 76 4.2.1 Formulation of the potential ...... 76 4.2.2 Adjustment to match ab initio data ...... 80 4.2.3 Silanolgroups...... 83 4.2.4 Water-hydroxylated silica interactions ...... 86 4.2.5 Orthosilicicacid ...... 91 4.3 SlabStudies...... 92 4.3.1 SlabGeneration ...... 92 4.3.2 HeatofImmersion ...... 98 4.3.3 Structural features of the hydroxylated silica-water interface 100 4.4 Conclusions...... 103

5. The dissociated amorphous silica surface: Model development and evaluation106

5.1 Introduction ...... 106 5.2 Development of a model for dissociated amorphous silica ...... 111 5.2.1 Formulation of the potential ...... 111 5.2.2 Parameter adjustment to match ab initio data...... 114 5.3 Comparison of ab initio and empirical results ...... 123 5.3.1 Simulationmethods ...... 123 5.3.2 Radial densities near silanol groups of silica and orthosilicic acid ...... 126 5.3.3 Description of surface chemistry in AIMD simulations . . . 132 5.4 Conclusions...... 137

xiii 6. Applications of the model: Stern Layer Physics and Biomolecules near Silica139

6.1 Introduction ...... 139 6.2 Sternlayerphysics ...... 140 6.3 Biomolecules near silica ...... 151 6.3.1 Parameters for protein-silica interactions ...... 151 6.3.2 Tri-peptides near amorphous silica surface ...... 153 6.4 Conclusions...... 158

7. AtheoreticalstudyofCPDdimerrepairI ...... 160

7.1 Introduction ...... 160 7.2 Computationalmethods ...... 165 7.2.1 Electronic structure methods for ab initio simulation . . . . 165 7.2.2 Molecular dynamics, umbrella sampling, and WHAM . . . . 167 7.3 Freeenergysurfaces ...... 171 7.3.1 Anion: C5-C5′ and C6-C6′ ...... 172 7.3.2 Estimates of ksplit ...... 176 7.3.3 Neutral ...... 178 7.4 Back electron transfer (BET) from Anion Dimer ...... 180 7.5 Conﬁgurationalproperties ...... 185 7.6 A framework for understanding the competition between bond split- tingandchargerecombination...... 189 7.7 Conclusions...... 198

8. AtheoreticalpictureofCPDdimerrepair: II ...... 201

8.1 Introduction ...... 201 8.2 Multidimensional and possible non-equilibrium eﬀects during C5-C5′ bondsplitting...... 204 8.3 Methodological issues regarding charge delocalization ...... 218 8.4 Evolution of molecular properties during splitting ...... 223 8.5 Molecular mechanisms of C6-C6′ Splitting ...... 229 8.6 Conclusions...... 237

9. Summary ...... 243

Bibliography ...... 248

xiv LIST OF FIGURES

Figure Page

1.1 Hydrophobic patches (white outlines) on silica surface, with fewer nearby watermolecules(right)...... 2

1.2 Water and sodium ion (Na+) densities (bottom) and velocities (middle) nearasilicasurfacepicturedatthetop...... 5

1.3 Binding of small peptide to the silica surface...... 7

1.4 DNAbasesundergoingrepairinourstudies...... 9

2.1 The ground state dipole moment of the indole chromophore from the partial charges of the Amber-7 and GROMACS force ﬁelds (1.30 and 2.41 Debye, respectively) and the La excited state dipole moment (4.96 Debye) constructed for our simulations as described in the text are depicted on the left. The right hand image indicates the atom labels which are used inTable2.1andelsewhereinthetext...... 14

2.2 Three isomers of the KWK peptide, the a) KN ,b)N,andc)KC complexes, in order of decreasing stability in the ground state...... 16

2.3 Snapshot of the sandwich structure created using modiﬁed Lennard-Jones potentials...... 20

2.4 Snapshot of the reference structure used to determine the free energy difference of the three lys-trp-lys isomers in the ground state...... 21

xv 2.5 Time evolution of the fluorescence anisotropy [Eq. (2.8)] following excitation from the S0 to the La state. Results for each of the isomers predicted by non-equilibrium molecular dynamics simulation of 300 trajectories is shown, as well as experimental results which are affected to some extent by internal conversion from the Lb to the La state during the first 100fs following photoexcitation. For clarity the KN isomer data is shifted up by 0.2, and the KC data by 0.1. The molecular dynamics results for each of the isomers can be fit to a double exponential of −t/τ1 −t/τ2 the form c1e + c2e , the solid lines in the figure. The fitting results are (c1,τ1,τ2) = (0.15, 6.5, 114), (0.11, 4.7, 135), (0.10, 3.2, 94) for the N, KN and KC isomers, respectively. In these fits, the coefficients were constrained so that c1 + c2 = 0.4. All the the time constants are in ps. The values of τ2, the long time delay are also indicated in the figure. The experiment could be described with a double exponential as well, with τ1 = 7,τ2 = 130. Internal conversion causes the initial very rapid decay of the fluorescence anisotropy in the experiment, so the data do not extrapolate at short times to the theoretical anisotropy maximum of 0.4. 25

2.6 Scatter plot of the indole-protein and indole-water contribution to the stabilization energy of each of the isomers of the excited state, as indicated by the plot labels, and of the N isomer in the ground state (lower right panel). The scatter plots were accumulated over runs of duration 2-3ns in which transitions between diﬀerent excited state isomers did not occur. In all cases we used the gmx force ﬁeld1, 2 and the SPC/E water model.3 In addition, we recalculated the distribution of interaction energies using the 4 SPC water model for the KN isomer, shown as the lighter-colored dots in theupperleftpanel...... 28

2.7 Time dependent Stokes shift for the lys-trp-lys peptide photoexcited from the KN, N, and KC isomers are shown in the top, middle and bottom panels, respectively. The behavior during the ﬁrst picosecond following photoexcitation is shown in the small panels on the left. Errors bars for the KN and N isomers were calculated by dividing the total data set into three blocks.5 Onestandarddeviationisshown...... 30

xvi 2.8 Open circles are the experimental Stokes shift as reported in Ref.6 The fit 2 − t − t − t “ τg ” τ τ that goes through these points is of the form cge + c1e 1 + c2e 2 + − t τ3 kJ c3e + S∞, where cg = 9.15,c1 = 12.24,c2 = 7.87 and c3 = 1.96 mol , and τg = 590fs,τ1 = .613,τ2 = 3.3 and τ3 = 23.3ps. The other curve shows the Stokes shift calculated in molecular dynamics simulations for the N isomer, and the fit given in Eqs. (2.11-2.14). The inset provides a magnified view of the experimental and simulation data at short times. From this comparison, we see that the molecular dynamics data decays faster on the ∼ 1ps time scale, but slower on longer times scales compared toexperiment...... 32

2.9 Total stabilization energy of the indole group following photoexcitation (upper curve, left axis), and the water and protein contributions to the interaction energy (bottom two curves, right axis). At the instant of photoexcitation, the interaction energy contribution from water and protein kJ are −46.8 and −53.3 mol ,respectively...... 34

2.10 For the N isomer, distance between the CE3 carbon of the indole ring and N-terminal amino group (middle curve, referred to left-hand axis), amino group of the remote C- and proximal N-terminal lysines (top and bottom curve, respectively, referred to right-hand axis). The data shown in this ﬁgure represent averages over 300 non-equilibrium trajectories, as describedinsection2.2...... 35

2.11 a) Distance between the CE3 carbon of the indole ring and the proximal lysine amino groups in the KC isomer, and KN isomer. b) Distance between the CE3 carbon of the indole ring and the remote lysine N or C-terminus for KC and KN isomersrespectively...... 36

2.12 a) Degree of lysine side-chain extension, as measured by the distance from + the β-carbon to the -NH3 group, and π-cation distance, tracked by the + distance from the CE3 carbon of the indole to the lysine -NH3 group. The chain extension and π-cation plots are referred to the right- and left-hand axes, respectively. In the single trajectory shown here, and in many others, chain extension is correlated with breaking the π-cation complex. b) progress of isomerization in the KC and KN isomers, as measured by the average distance from the N-terminal amino group to the indole. The data shown in this ﬁgure represent averages over 300 non-equilibrium trajectories,asdescribedinsection2.2...... 37

xvii 3.1 Various energetic and structural features related to the indole group of tryptophan residue 7 during a 30ns trajectory in which the indole charges were that of the S0 ground state. Properties were calculated every 200fs. a) Indole-protein and indole-water interaction energy differences, upper and lower curves, respectively, between the excited La and ground state S0 potential energy surfaces. The indole-protein and indole-water energies were close to each other during the first 10ns, but are shifted and referred to different axis (note left- and right-hand scales) in the plot for clarity. b) Most of the jump of the indole-protein La-S0 interaction energy difference is accounted for by the interaction between the indole and the protein backbone between residues 77 and 86. c) Dot product of a unit vector along the dipole moment of the peptide bond between residues 78 and 79 with that of the indole group. d) Similar to previous plot for the peptide bondbetweenresidues80and81...... 47

3.2 Representative snapshots of tryptophan W7 and the loop region consisting of residues 77-86 that portray the structural transition quantified in Fig. 3.1. On the left, the E and F helices, the tryptophan W7, and some waters of hydration are shown. The proximity of the loop joining helices E and F is evident. On the right, snapshots from the isomer 1 and 2 sub- states are shown. The atoms of the peptide bonds connecting residues 78 and 79, and 80 and 81 are explicitly shown, reflecting the shift in angles relative to W7 which is quantified in Figs. 3.1c and d...... 49

3.3 Fluorescence Stokes shift for isomer 1. a) Linear response theory estimate for the total Stokes shift, and the contributions from indole-water and indole-protein interactions. The time interval used to calculate the linear response correlation functions, Eqs. (3.1) and (3.2), and sampled for initial conditions of the non-equilibrium trajectories is indicated in Fig. 3.1a. b) Total Stokes shift, and the contributions from indole-water and indole-protein interactions calculated from 360 non-equilibrium molecular dynamics trajectories. Error bars represent one standard deviation as estimated from block averages obtained by breaking the total data set into three parts.5 c) Comparison of the Stokes shift calculated with full protein dynamics, as in (b), or from 120 trajectories propagated with the protein coordinates frozen following photo-excitation. When the protein is frozen, the water response is the total response. d) Contribution of the loop region (residues 77-86) to the Stokes shift, and the contribution that arisesfromthebackboneatomsoftheloop...... 51

xviii 3.4 Same as Fig. 3.3 but for isomer 2. The time interval used to calculate the the linear response correlation functions for isomer 2 and sampled for initial conditions of the non-equilibrium trajectories is indicated in Fig. 3.1a. 100 trajectories were used to calculate non-equilibrium response with full protein dynamics, and 200 trajectories with the protein frozen. In panel (d), the protein backbone response is compared with the total protein response, indicating that backbone dynamics dominates the protein response. 53

3.5 The actual Stokes shift calculated from non-equilibrium trajectories for isomer 1 with the protein frozen at the moment of photo-excitation is −t/τ2 compared with curves that contain a slow component c2e where τ2 = −1 120ps. Several diﬀerent values of c2 are explored: c2 = 2, 3 and 6kJmol . 56

3.6 Top panels: Time evolution of the distance of two nearby charged residues, Lys79 and Glu4, the indole chromophore in isomer 1 (left) and isomer 2 (right) following photo-excitation. Distances are measured from the center of mass of the indole chromophore to the center of masses of the side chain amino and carboxylic acid groups of the lysine and glutamic acid, respectively. In isomer 1 the distance both become smaller, while in isomer 2 they become larger. Bottom panels: The energetic response of the positively and negatively charged residues shows opposite trends for both isomer 1 and 2, and they roughly cancel. For comparison with data in Figs. 3.3 and 3.4 the interaction energy diﬀerence between La and S0 statesareplottedinthebottompanels...... 58

3.7 Interaction energy of the indole chromophore with water within 5A˚ of the indole, backbone dipoles of the loop connecting helices E and F, and the interaction with the total protein. The average was accumulated for non-equilibrium trajectories sampled for isomer 2...... 60

3.8 Comparison of calculated and experimental Stokes shift...... 61

3.9 Anisotropy calculated from non-equilibrium molecular dynamics simulations and from experiment.7 Least-squared ﬁts are shown in addition to the simulation and experimental data. The parameters extracted from the ﬁt to simulation data are given in Table 3.2. The long-time behavior of the experimental data, characterized by a time constant of 6.6ns, is shown intheinset...... 63

xix 3.10 Residence time correlation function for waters within 5A˚ of Trp7 in the excited La electronic state for isomer 1 (solid curves) and isomer 2 (dashed curves). The correlation functions for frozen protein simulations lie above thosewithfulldynamics...... 64

3.11 Cross-correlation of the normalized displacements of the indole nitrogen atom with those of the waters hydrating the indole group. The correlation is accumulated separately for waters with residence times 20ps < tres < 30ps and tres > 50...... 67

4.1 Ab initio calculations were performed for the single-silanol (left) and geminal (right) clusters shown here to determine parameters for our empirical potential. A subset of the capping hydrogens are indicated...... 82

4.2 Fitted vs. ab initio energies for a) OH stretches of a geminal fragment, and b) SiOH angle. In the left-hand plot, points that agree perfectly would lie onthelinewithunitslope...... 84

4.3 A conﬁguration in which a hydrogen atom is simultaneously within covalent bonding distance of two oxygens. Such divalent hydrogen conﬁgura- tions, as well as spurious -SiOH2 groups, are eliminated by the HOH and OHO blocking potentials, Eqs. (4.2-4.3)...... 84

4.4 Paths of approach for water near silanols ...... 87

4.5 Paths of approach for water near siloxanes ...... 87

4.6 Fitted (open symbols) vs. ab initio (ﬁlled symbols) energies for the paths of approach shown in Fig. 4.4, and for approach of a water to a geminal fragment along the path shown in Fig. 4.7. The four paths are vertically oﬀset from each other on the graph for clarity...... 89

4.7 Path of approach of water to a geminal silanol fragment...... 90

4.8 Fitted empirical (open symbols) and ab initio energies (filled symbols) for water approaches to siloxane fragments. Our model was designed to match the more important interactions with silanol groups (see Fig. 4.6) and, as shown here, is not sufficiently flexible to also match ab initio data for approach of waters to this siloxane fragment...... 91

xx 4.9 Rare defects taken from the amorphous silica surface with a silanol density of 6.4nm−2. a) NBO, b) 3-coordinated oxygen, and c) silicon with three hydroxyl groups. Defects are indicated with arrows...... 97

4.10 Hydrogen bonded silanol chain on our silica surface...... 100

4.11 Number densities for water and siloxane oxygens (solid curve and long dash curves, referred to left axis) and silanol oxygens (short dash curve, referred to right axis) along a direction perpendicular to a silica slab with surface silanol density of 6.4nm−2...... 101

4.12 Figure showing aﬃnity of water for hydrophilic regions on the silica surface.Seediscussionintext...... 102

4.13 Radial density of water molecules surrounding silanol oxygens (solid curve) and surface siloxane oxygens (dashed curve). Siloxane oxygens were iden- tiﬁed as surface siloxanes if they were at least 12.5A˚ from the center of the slab. (See Fig. 4.11.) Asymptotically, the density of water oxygens is 1 ˚−3 approaching one half the bulk water density ( 2 0.0335A ) because there are no water molecules in the half space below the surface...... 103

5.1 Fitted (solid line) vs. ab initio energies (solid black circles) for b) Si-O− stretchforfragmentshownina)...... 116

5.2 Left panel shows the formation of a 2-membered ring involving a dissociated oxygen that is divalently bonded to two silicons. The dotted white arrow points in both cases to the dissociated oxygen involved in the interaction. In the right panel, the dotted yellow arrow shows the hydrogen that originates from a one of the hydroxyl groups of a geminal silanol. . . 117

5.3 Paths of approach for water near a dissociated silanol ...... 118

5.4 Fitted (solid line) vs. ab initio (ﬁlled symbols) energies for the paths of approach shown in Fig. 5.3. On the left are path 1 energies and on the rightpath2energies...... 119

xxi 5.5 Distribution of the dot product between unit vectors linking water oxygens to a dissociated surface oxygen (OW − OD) within a distance of 3.5A˚, and vectors along each of the two hydrogen bonds. The data conﬁrms that in the thermal simulations, path 1 (Fig. 5.3) is favored over path 2. Inset shows a small peak near the cosine of half the tetrahedral angle, the angle ofthebifurcatedstructureofpath2...... 120

5.6 The three fragments used for silica-sodium interactions labeled a) with a single OD, b) with a single OD and silanol OH and c) with three silanol OH’s. Unlabeled red-spheres correspond to siloxane oxygens in our empirical potential. The blue sphere is the sodium ion...... 121

5.7 Radial density of water (top row), and cumulative number of neighboring waters (bottom row) near silanol (solid line) and siloxanes (thick dashed lines) for empirical model shown in left panel, AIMD simulation with proton in middle panel and AIMD simulation with Na+ shown in right panel. The green and red thick lines are radial densities near siloxanes in only hydrophilic and only hydrophobic regions respectively...... 127

5.8 Radial density of water (top row), and cumulative number of neighboring waters (bottom row) near four individual silanol groups from empirical potentialsimulations...... 128

+ − − 5.9 Radial density of Na ions near O groups (solid thick line), OW near O + groups (solid dashed lines) and Na near OW (solid dotted line) for our empirical model in the left panel and AIMD simulations in the right panel. 130

5.10 Radial density of water (top row) and cumulative number of neighboring waters (bottom row) near silicon, oxygen and hydrogen atoms of orthosilicic acid shown for DZVP (solid black), TZVP (solid dashed) and empirical model(soliddotted)...... 131

5.11 Three different chemical processes that occur within the first 3ps of our AIMD simulations labeled 1-3. The first shows the conversion of an isolated silanol to a geminal silanol an another isolated silanol. The second shows the formation of an isolated silanol and a hydronium ion and the third shows a single water molecule sticking to an exposed silicon atom on ourhydrophobicsurface...... 133

xxii 5.12 Steps in the formation of a geminal and isolated silanol from an initial single silanol, process (1) in Fig. 5.11. The atoms of the water molecule that reacts with the surface are shown in blue in all four frames. i) Arrows point to water that attacks silicon atom and Si-O bond that begins to break. ii) Arrows point to the non bridging oxygen formed after the Si-O bond breaks and the hydronium ion transiently formed. iii) Arrow points to the proton transferred from the newly formed silanol to the NBO. iv) Final products are a geminal and a single silanol...... 134

5.13 The left and middle frames illustrate steps in the formation of an isolated silanol from an under-coordinated silicon, scheme 2 of Fig. 5.11. The atoms of the water molecule that reacts with the surface are shown in blue in these frames. i) Water attacks an undercoordinated silicon atom. ii) An OH group is added to silicon and hydronium ion formed. iii) The frame on the right shows a water molecule on the hydrophobic surface that binds to an exposed silicon atom without further reaction during the length of theAIMDsimulation...... 135

6.1 Current concepts of the Stern layer: a) A recent review article by Yuan 8 et al., showing the electroosmotic velocity veo(x) vanishing at a plane outside the Stern layer, and b) a popular text book on electrochemistry by Bockris, Reddy, and Galdoa-Aldeco9 (page 883) depicting ions of the Sternlayeras“stuck”...... 142

6.2 Scatter plots showing the eﬀect of the number of siloxanes surrounding each O− group and its correlations with number of waters around dissociated oxygens and the associated residence time of the Na+ counter-ions. 144

6.3 (a) Configuration taken from a typical non-equilibrium molecular dynamics simulation used to generate data in Figs. 6.3. The O− atoms of dissociated silanol groups are the large red spheres of the (centered) silica slab. Na+ and Cl− ions are visible in solution. (b) Average velocities of Na+ ions and water with a surface charge density of 12.7µC cm−2 = 0.795e nm−2, no ions except the Na+ ions needed to neutralize the silica, and an applied electric field of 7 × 108V m−1. Meaningless velocity spikes appear inside the silica slab where fluid rarely penetrates, and sampling is insufficient to m average normal thermal motion (∼ 400 s ) to zero. (c) Densities of water, Na+ions and O− groups of dissociated silanols. The vertical dashed lines are guides for the eye to facilitate comparison of the velocity and density profiles...... 145

xxiii 6.4 Comparison of velocity profiles from simulations with solutions to the Navier-Stokes equation (solid smooth curves). Stick boundary conditions are enforced at points that generated the best agreement with the molecular dynamics velocity profile across the channel. The velocity profiles are µC e for a surface charge of 12.7 cm2 = 0.795 nm2 , and for zero salt concentration. The two extra continuum hydrodynamics curves were calculated by enforcing stick boundary conditions at successive points 1A˚ closer to the point where the actual molecular dynamics velocity profile approached zero.147

6.5 Densities (top) and flow velocities (bottom) near an almost completely µC e dissociated silica surface with a large surface charge of 58.7 cm2 = 3.67 nm2 in the limit of low salt concentration. Because of the extremely large surface charge, the fluid is less mobile near the surface, which is apparent comparing the location of the dotted lines in this figure and Fig. 6.3. The

+ local ion mobility of sodium ions is proportional to (vNa − vH2O). . . . . 149

6.6 Paths of approach showing methane molecule near a) silanol, b) siloxane and c) dissociated oxygen. For visual clarity the rest of the silica cluster isnotshown...... 151

+ 6.7 Paths of approach showing an ammonium cation (NH4 ) molecule near a) silanol and b) dissociated oxygen. For visual clarity the rest of the silica clusterisnotshown...... 153

6.8 Paths of approach showing a single methanol molecule near a) silanol and b) dissociated oxygen. For visual clarity the rest of the silica cluster is not shown...... 154

6.9 Path of approach showing an acetate anion on the left panel and a benzene molecule on the right panel near a silica cluster...... 154

6.10 Left and right panels show snapshots of a single KWK tripeptide bound to the silica surface. Diﬀerent regions of the tripeptide can bind to the surface. Numbers on the ﬁgures are described in the text. For visual claritythesolventisnotshown...... 156

6.11 Left and right panels show snapshots of a single EWE tripeptide bound to the silica surface. Diﬀerent regions of the tripeptide can bind to the surface. Numbers on the ﬁgures are described in the text. For visual claritythesolventisnotshown...... 158

xxiv 7.1 Thyminecyclobutanedimer...... 163

7.2 Comparison of DZVP, TZV2P and DZVP-MOLOPT energies in a box of length 9.8A˚ with 32 waters. The solid line in both panels indicates a linear ﬁtwithslope1.0006 ...... 166

7.3 Free energy surface for lengthening the C5-C5′ bond in thymine CPD anion. The solid curve was obtained from 4-5ps trajectories in each umbrella sampling window, the dashed curve from 9-10ps trajectories...... 171

7.4 Free energy surface for lengthening the C6-C6′ bond in thymine CPD anion. The solid curve was obtained from 4-5ps trajectories in each umbrella sampling window, the dashed curve from 9-10ps trajectories...... 172

7.5 Overall reaction free energy surface for thymine CPD anion repair (kcalmol−1). The free energy well in which the C5-C5′ bond is broken and the C6-C6′ bond is intact (rC5−C5′ = 2.57A,˚ rC6−C6′ = 1.61A˚) is assigned as the zero of energy. The energy value on several contours is labeled...... 174

7.6 Free energy surface for lengthening the C5-C5′ bond in neutral thymine dimer...... 178

7.7 Distribution of C5-C5′ (solid) and C6-C6′ (dashed curves) distances before and after back ET on anion and neutral surfaces. In each case, the distribution on the neutral surface lies at larger distances compared to the neutral...... 181

7.8 Dynamics of a) C5-C5′ or b) C6-C6′ bond length afer back ET leading to either ring closure (gray curves) or ring splitting (black curves) ...... 183

7.9 Overall free energy surface with open white circles for trajectories that split after back ET and solid black circles for trajectories that close after back ET. 184

7.10 Potential energies on the neutral surface at time t=0 after back ET for splitting trajectories (solid grey circles) and trajectories undergoing ring closure (solid black circles). The vertical solid line is the position of the TST on the anion surface. The solid red line is a 4th order polynomial ﬁt through the simulation data of the shifted potential energies...... 186

7.11 Conﬁgurational changes during the splitting of the dimer...... 187

xxv 7.12 C5-C6 (solid curve) and C5′-C6′ (dashed curve) bond lengths over time for four splitting trajectories. The sharp decrease in bond length reﬂects formation of double bond character, which is seen to be simultaneous in both bases, as splitting of the C6-C6′ bond occurs. The circled regions indicate where the C6-C6′ bondsplits...... 189

7.13 Snapshots of typical conﬁgurations analyzed along umbrella sampling C6- C6′ coordinate...... 190

7.14 Schematic showing placement of a neutral ground state and CT state with respecttothedimersplittingcoordinate...... 191

7.15 Schematic showing placement of a neutral ground state and CT state with respect to the dimer splitting and solvent polarization coordinates. The white curve is the minimum free energy path from dimer to split products on the CT surface. The red curve above the white curve is the intersection between the anion and neutral surfaces. Decreasing solvent polarity will raise a zwitterionic CT state surface, as shown in the ﬁgure, and increase theactivationenergyforBET...... 193

7.16 Schematic showing placement of neutral ground state (white) and CT state (blue) with respect to the dimer splitting and solvent polarization coordinates in a non-polar solvent. The activation barrier for BET is very large throughout the splitting process and a short-circuiting channel would have signiﬁcant eﬀect only if the activation barrier for splitting was large. 194

7.17 Schematic showing placement of neutral ground state (white) and CT state (blue) with respect to the dimer splitting and solvent polarization coordinates for a situation in a highly polar solvent. In this scenario the CT surface is lowered to a point where there are two regions along the splitting coordinate where activation barrier for BET is zero. The BET in this situation can occur in the normal region near the TST although the barrierisstillsmall...... 196

8.1 Non-equilibrium dynamics of C5-C5′ bond after electron injection leading to splitting and unsplitting populations. Also shown are trajectories from the splitting population that split within 50 fs and between 200-500 fs. . 204

8.2 Snapshot showing location of single water molecule near the O4 carbonyl oxygen...... 205

xxvi 8.3 2D Surface for potential of mean force between C5 and HW of all waters with distances in Angstroms and free energy in kcal mol−1 ...... 207

8.4 Distribution of the distance of the closest water hydrogen to the C5 atom on the neutral surface and the ﬁrst two umbrella windows on the anion surface...... 208

8.5 Non-equilibrium swarm of trajectories in left panel a) that split within 50fs and right panel b) that split between 200 − 500fs...... 210

8.6 Non-equilibrium swarm of trajectories showing evolution of charge on C5 carbon atom for splitting and unsplitting populations ...... 211

8.7 Isosurfaces showing location of diﬀerence in electron density between anion and neutral systems. The isosurface on the left represents a positive isovalue while that on the left represents a negative isovalue. Solid yellow arrow on the left points to the C4-O4σ orbital while the dashed yellow arrow on the left points to the C5-C5′σ∗ orbital. The solid yellow arrows on the right point to the C4-O4π∗ and C2-O2π∗ orbitals...... 212

8.8 On the left is the 2D free energy surface for the C4-O4-C5-C5′ dihedral angle and C5-C5′ bond. On the right the path of a swarm of non-equilibrium trajectories over these two coordinates is shown. The trajectories that split are black (top right), while those that do not split within the observation window of 0.5 − 1psareshowninred(bottomright)...... 214

8.9 Distribution of splitting times for C5-C5′ bond...... 217

8.10 Electron charge partitioning between water and two thymine bases during splitting of the C6-C6′ bond at 4 points along the splitting of the C6-C6′ bondasdescribedinthetext...... 225

8.11 Charge coupling between carbonyl oxygens and solvent. The individual plots are discussed in the text. The degree of coupling of charge ﬂuctua- tions is assessed using a linear ﬁt to the data, which is indicated with a dashed line for O2/O2’ and a solid line for O4/O4’...... 230

8.12 Distribution of splitting times for C6-C6′ bond for groups of non-equilibrium trajectories ...... 231

xxvii 8.13 Left panel shows the evolution of the C6-C6′ distance with the closest water distance to the C6 atom for splitting trajectories while right panel shows the same for trajectories that do not split within the timescale of oursimulationruns...... 232

8.14 Distribution of charge on C6 atom and closest water distance to C6 for both splitting and unsplitting trajectories. On the left, the red labels parts

of the trajectory where rC6-C6′ > 1.85A˚, while the black labels portions where rC6-C6′ < 1.85A˚. The data in black on the right is for trajectories that remain unsplit during the 4.5ps run time. The data in red is the same inbothpanels...... 234

8.15 Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′...... 235

8.16 Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. As the C6-C6′ bond splits at about 2ps a water molecule moves closer toward the C6(C6′) carbon atom. For this trajectory we ﬁnd that the charge on both the C6 and C6′ carbon atoms transitions from less negative to more negative at the same time, when the C6-C6′ bondsplits...... 236

8.17 Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. The splitting of the C6-C6′ bond for this trajectory occurs at about 900fs. However for this trajectory we ﬁnd that the charge on the C6 carbon atom gradually decreases between 400 − 1000fs (the decrease begins before the split of the C6-C6′ bond) while the charge on the C6′ carbon atom decreases over a shortertimeintervalatabout900fs...... 238

8.18 Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. For this trajectory, the splitting of the C6-C6′ bond occurs at 250fs. The charge on the C6 and C6′ carbon atoms and the movement of a water molecule closer to these atoms for this trajectory, transitions on a similar timescale as the splitting of the C6-C6′ bond...... 239

xxviii 9.1 Nanonozzle made of silica walls with our empirical model ...... 246

xxix LIST OF TABLES

Table Page

2.1 Charges used for the indole group in the La state...... 15

−1 3.1 Stokes shift data. All energies (S∞’s and c’s) are in units of kJmol and all times (τ’s) in unit of ps...... 54

3.2 Parameters obtained by fitting the calculated fluorescence anisotropy, using the functional form specified in Eq. (3.5). The weights (c’s) are dimensionless and the time constants are in units of ps...... 64

4.1 Pairwise potential Buckingham parameters ...... 81

4.2 Three-body potential parameters. The Si-O-H parameters control the truncated Vessal angle potential of Eq. (4.1), and the H-O-H, O-H-O and Si-O-Si parameters are for the blocking potentials of Eqs. (4.2-4.4). . . . 81

4.3 Structural properties of gas phase orthosilicic acid. Angles are in degrees and distances in A...... ˚ 92

4.4 Population of NBO’s, 2M-rings, and 3-coordinated silicons on silica surface as a function of annealing time of a freshly cleaved surface at 300K. . . . 93

4.5 Average potential energy for systems consisting of 3220 water molecules used to calculate the heat of immersion. Error bars for each run are estimated by the blocking method5 by partitioning each run into 4 blocks. The combined surface area of the two sides of the silica slab is 2.16 × 10−17m2. The two sets of data are for surfaces containing silanol densities of 4.0nm−2 and 6.4nm−2...... 100

5.1 Pairwise potential Buckingham parameters ...... 115

xxx 5.2 3-bodyinteractionsparameters ...... 115

5.3 Pairwise potential Leonard Jones parameters ...... 115

5.4 Fitted and ab initio binding energies for silica-Na+ fragments...... 122

5.5 Average charges of species in AIMD simulations. Charges were obtained according to the DDAP10 charge partitioning scheme, which is based on theelectrondensity...... 135

8.1 Total T<>T anion charge delocalized on water molecules according to DDAP10 (CP2K) or CHELP11, 12 (Gaussian) density-based charge partitioning. The number of water molecules from the original simulation configuration is indicated. The CP2K calculations were performed in a cubic periodic cell of side length 9.8A˚ except for two values, indicated with a dagger (†), in which a cell dimension of 14.8A˚ was used and double dagger (‡) in which a cell dimension of 20.8 was used. The last 6 rows are CP2K and Gaussian (ROHF and LC-BLYP) calculations performed with different configurations as described in the text...... 220

8.2 Total T<>T anion charge delocalized on water molecules according to severalchargepartitioningschemes...... 223

8.3 Charge on carbon atoms: C5,C5′,C6,C6′ ...... 228

8.4 Average number of water hydrogens near C5,C5′,C6 and C6′ carbons. Er- ror bars for each data set are estimated by the blocking method5 by par- titioningeachruninto4blocks...... 229

xxxi CHAPTER 1

Introduction

In the 16th century Paracelsus the medieval physician said that “water was the matrix of the world and all its creatures”.13 Paracelsus’s view of the role of water in the matrix, as an active participant in biological function, that engages and interacts with biomolecules, is quite different from the naive approach adopted by many molecular biologists to date who usually discuss the function of biomolecules in the absence of the surrounding solvent. This is aptly summarized by Gerstein and Levitt14 who stated ten years ago, “When scientists publish models of biological molecules in jour- nals, they usually draw their models in bright colors and paint them against a plain, black background”, thus ignoring the water that surrounds the biomolecules. The role of water as a matrix, instead of a “black background”, is a central theme in the three projects that form my dissertation. These projects examine the dynamics of water near the surface of amorphous silica (glass), the water dynamics near the surface of proteins (known as hydration dynamics) and finally the role of water dynamics in DNA repair. In all these topics, involving widely different fields, similar issues arise. How mobile or immobile is the water near the surface? Is the water an active participant or a passive background in biomolecular function and in important cellular reactions like DNA repair?

1 Figure 1.1: Hydrophobic patches (white outlines) on silica surface, with fewer nearby water molecules (right).

Water molecules are held together by strong attractive interactions called hydro-

gen bonds (H-bonds). However water molecules that are in close proximity to surfaces

such as biomolecules or inorganic materials like glass, surfaces on which many elec-

trical charges reside, experience a disturbance in their ability to form H-bonds with

other water molecules and instead feel strong interactions with the charged surfaces.

Scientists have long debated the degree to which water near interfaces retains its bulk

properties, and have reached very diﬀerent opinions on the response properties of

water near surfaces.

We begin by examining the hydration layer near a peptide and protein in chapters 2, and 3 respectively. Proteins communicate with other proteins and with small molecules, mediated by the water between them, although a molecular understanding of the role of water in this process has been lacking. The cross-talk between biomolecules is critical for many biological processes.15 Recent time dependent ﬂuo- rescence Stokes shift experiments (TDFSS), probe the dynamics of water near proteins.16 In these experiments, an ultrafast laser pulse promotes the intrinsic amino acid tryptophan from its ground state into an excited state (photoexcitation). The

2 electrical charge distribution in the excited state is very diﬀerent than the ground

state. As a result, the surrounding protein and water starts to rearrange to stabilize

the excited state dipole. The wavelength of light emitted from the excited tryptophan

(ﬂuorescence) during this process continually changes as the environment adjusts to,

and stabilizes the excited tryptophan. These experiments can then probe the time it

takes for the tryptophan and the surrounding environment to slide back to equilib-

rium (relaxation dynamics). The relaxation dynamics of small molecules in water is

complete within several picoseconds, while near proteins the dynamics can take tens

of picoseconds or even much longer.

While these experiments show that the hydration layer is dynamic there have been some hotly debated issues concerning the molecular origin of the observed dynamics.

Several very diﬀerent explanations have been put forward in the literature. The

ﬁrst model proposes that water near the protein is rotationally immobilized and attributes the slow dynamics observed in the experiments to the occasional exchange of “bound” water molecules near the protein with those in the bulk.17 This model treats the protein as a static entity that does not contribute to the slow relaxation dynamics. On the other hand, the second model proposes that the slow relaxation dynamics speciﬁcally originates from protein dynamics.18 More recently some newer but rather ambiguous explanations have also been put forth that include features of both models15 where the slow component is attributed to water relaxation and the protein motions simply facilitate the process without contributing energetically to the stabilization of the tryptophan. Our calculations on various systems have resolved these discrepancies.

3 We have examined the relaxation dynamics of several protein systems, comparing the dynamics of a fully ﬂexible protein with a system in which the protein is artiﬁcially frozen at the instant of photoexcitation. Our simulations19–21 show unequivocally that the molecular origin of the slow dynamics emerges from coupled energetics of protein- water motions, and that the protein cannot be treated as static. Coupled motions imply that relaxation of the protein and the water in a concerted fashion account for the slow dynamics that is observed in the experiments. Both the protein and water environment energetically stabilize the altered charge distribution of a photo-excited tryptophan. These slow dynamics occur on the same timescale as important biological processes such as enzyme catalysis, an important protein function for speeding biological chemical reactions. Thus, the motions of the protein cannot be treated in isolation from the surrounding water.

We now turn our attention now to the amorphous silica surface. The surface of silica has been intensively studied for many years. Our interest in the silica surface stems from its wide use in biomedical engineering devices for the transport of biomolecules. Recently, silica has also become of interest in understanding the chemical reactions that resulted in the appearance of life (prebiotic chemistry). Minerals such as silica could have played an important role in organizing and concentrating organic molecules to convert them into essential large molecules for life22 such as proteins and DNA, which are essential for all biological function. Our work also makes important fundamental contributions to physical chemistry. In 1924 Stern invoked the presence of an immobile layer to explain why surfaces act like they have less surface charge than they really do:23 Ions trapped in the immobile layer partially neutralize the surface charge. This model has been used for the last 80 years in

4 Figure 1.2: Water and sodium ion (Na+) densities (bottom) and velocities (middle) near a silica surface pictured at the top.

numerous publications and textbooks although its validity has never been examined carefully to date.

We have successfully constructed and validated a realistic model for the water- amorphous silica interface.24–26 The model development and its evaluation are reported in chapters 4 and 5. The application of our model to examine the validity of the Stern layer is reported in chapter 6. Our surface is characterized by hydrophilic

(attracts water) and hydrophobic (repels water) regions (Fig. 1.1). This property has been validated by comparison with accurate periodic electronic density functional simulations. Our model also quantitatively reproduces some important energetic and structural features25 that have been determined experimentally such as the heat of immersion and surface silanol density. Our studies show that both ions and water

5 near the surface are quite mobile right up to the surface (Fig. 1.2). This result chal-

lenges the classical view of a stagnant layer of zero-velocity water extending 3-10A˚

from the surface. The stagnant layer was invoked to explain why the eﬀective surface

charge is less than the actual surface charge. An exciting aspect of our results is that

this behavior is reproduced by our model, only the physical mechanism is not the

same.

With a validated model, we can investigate the fate of biomolecules near the silica surface. The need for such theory has been recently expressed by Cruz-Chu et al. who comment, “Until recently, atomic scale simulations of inorganic and biomolecular materials, such as silica and DNA, have mostly evolved independently from each other and the consolidation of expertise from both areas demands now a great effort”.27 Using accurate electronic structure calculations, we have extended our model to interface with well established biomolecular force ﬁelds to build simulations involving proteins, DNA and lipids. We have begun to look at the binding properties of model peptides, such as the tri-peptide lysine-tryptophan-lysine (KWK), because experiments on the binding properties of this system to silica nanoparticles have been reported.28 Our models will help clarify the mechanism by which biomolecules interact with the surface. For example in a recent experimental work Tleugabulova et al.

speculate the absorption of KWK onto silica is dominated by the interaction between

oppositely charged chemical groups. Our preliminary results for this system, shown in

Fig. 1.3 indicate that the binding mechanisms are more complicated and can involve

negatively charged groups and/or the tryptophan as well. Preliminary results of the

binding of peptides to the silica surface are reported in chapter 6.

6 Figure 1.3: Binding of small peptide to the silica surface.

Finally, we have examined the role of hydration water in the repair of damaged

DNA bases. The theoretical study of DNA repair is reported in chapters 7 and 8.

Without DNA repair, cells are susceptible to mutations and ultimately death.29 The repair of the most common form of damaged DNA bases involves the breaking of two of the covalent bonds of the 4-membered ring visible in the center of the left- hand image in Fig. 1.4, initiated by the injection of an electron. Because we are modeling the cleavage and/or possibly the formation of chemical bonds, much more accurate (and expensive) methods, periodic electronic density functional simulations, are used. Our studies are the ﬁrst in the literature that treat the electronic degrees of freedom for all 128 atoms in the system. Our simulations show that there is a substantial amount of excess electron density that leaks out from the DNA bases to the water, giving the water molecules in the hydration water pocket of the DNA

7 bases, a net partial negative charge. The simulations show that fast water motions, on the timescale of picoseconds, are crucial in the splitting mechanism and are an essential part of the reaction coordinate. To put it into perspective, our calculations show that without the presence of the electron on the DNA bases, it would take over

30,000 years for the two bonds to split!

An important contribution of our work, is the mechanistic role of the process of the return of the electron to the donor (back electron transfer) in dimer repair. We have used our ground state calculations to advance a simple generic model that shows that in the Marcus inverted region, the back electron transfer rate will ﬁrst increase, pass through a maximum near the transition state region for dimer splitting, and then later decrease as the system reaches the split product well as seen in the right panel of Fig. 1.4. The exact details of the magnitude of change in the back electron transfer rate as a function of splitting and the location of the region where the back

ET rate is maximized, will be sensitive to the solvent environment. These results provide a potential mechanism for explaining eﬃcient repair of CPDs in the active site of the protein photolyase.29 Our model also provides a molecular framework for understanding numerous experiments conducted on this system.

8 Figure 1.4: DNA bases undergoing repair in our studies.

9 CHAPTER 2

A molecular dynamics simulation of the tripeptide KWK: Structure and dynamics following photoexcitation in solution

2.1 Introduction

The understanding of peptide dynamics in aqueous solution is critical in many biological processes such as protein folding,30–33 protein hydration16, 34, 35 and protein- peptide recognition.16, 36–39 Peptides are usually ﬂexible and heterogeneous in solution. In this chapter we focus on the interplay between peptide and solvent structural

ﬂuctuations. The time scales of these dynamical processes characterize the structural

ﬂexibility and conformational adaptability of the solvated complex. To understand these interactions on the atomic scale, we need to address several important questions.

How heterogeneous is a peptide structure, and what is the time scale of its conformational ﬂuctuations? How fast is the water motion around a speciﬁc side chain, and what is the nature of the dynamic peptide-solvent interaction? Currently, there is considerable interest and discussion concerning the nature of water in the immediate vicinity of proteins,35, 40–45 both with regard to the underlying physical phenomena and how to interpret experimental results in light of these phenomena.16, 18, 41, 46–48

10 We choose a small tripeptide, Lys-Trp-Lys (KWK), as a model system. In chap-

ter 3 we examine the hydration dynamics of a larger protein system. This tripeptide

has been widely used to recognize the DNA double helix49, 50 and is also an ideal mo-

tif to mimic ubiquitous π-cation interactions in proteins.51, 52 With several possible

π-cation interactions between protonated amino groups and the indole moiety, the

peptide ﬂexibility is reduced and the conformational isomers are minimized. This

peptide consists of four hydrophilic charged groups at neutral pH, the lysine amino

groups and the terminal amino and carboxylic acid groups, as well as several hy-

drophobic regions, namely the aliphatic portion of the lysine side chains and the

indole ring system. This is signiﬁcant because Russo et al. have recently found that

mixed hydrophilic/hydrophobic character is a predictor of slow solvent dynamics in

small oligopeptides,53–55 albeit in more concentrated solutions.

Fairly recently, time dependent ﬂuorescence spectroscopy experiments (TDFSS) have been reported for the solvation dynamics of the KWK tripeptide6 using intrinsic

tryptophan as a local optical probe.42, 46, 56 These experiments have observed that the

response following photoexcitation, occurs on time scales ranging from femtoseconds

to tens of picoseconds. The origin of the slow component in KWK was attributed

to slow motions of local water molecules6 around the tryptophan. There is a lot of

controversy in the literature on the molecular origins of the slow component from

TDFSS experiments, particularly for larger proteins. In the next chapter we examine

this issue in greater detail for the protein myoglobin. To interpret the experimental

observations and elucidate the molecular mechanism of peptide-water dynamic inter-

actions, we have studied the structure and dynamics of the same tripeptide in aqueous

solution by molecular dynamics (MD) simulations. The process of ultimate interest

11 is the relaxation of an ensemble of photoexcited KWK peptides which is initially in conﬁgurations representative of the electronic ground state. In the experiments, absorption of a photon at 290nm induces an electronic transition from the ground S0

57–60 electronic state to two excited states, La and Lb, that are closely spaced in energy.

59, 61, 62 Research has shown that the indole in polar solvents relaxes to the La state,

46, 63 which is more stable than the Lb state in polar media, on a time scale of 100fs.

Except for less than ∼ 100fs following photo-excitation, the ﬂuorescence detected from the photo-excited indole chromophore provides information on the solution dynamics of the La state which we interpret in this work. We have not attempted to model the rapid internal conversion dynamics from the Lb to the La state because this would require modeling a non-adiabatic process and is beyond the scope of this dissertation.

We begin this chapter in section 2.2 with a description of the MD methods that were used. As a prelude to understanding the dynamics, we describe the major conformational isomers in the ground and excited state, both in terms of structure and thermodynamic stability in section 2.3. Simulations inevitably depend on the quality of the force ﬁeld governing the dynamics of the system. We attempted to separate the qualitative conclusions that we can distill from our study, from what is highly model-dependent by comparing selected results with more than one peptide force ﬁeld and water model. Thereafter, relaxation dynamics results from our simulations are presented in section 2.4, revealing strong, long-lived correlations between peptide and water motion following photo-excitation. We then conclude in section 2.5 with an analysis of our results.

12 2.2 Simulation methods

Simulations were conducted using a double precision version of the GROMACS package.1, 64 Most of our studies were performed with the GROMACS (“gmx”)2 force field. To gauge the dependence of our results on the choice of force field, we recalculated selected results using the GROMOS96 force field65 which is also available in the GROMACS package. Since we were interested in solvent dynamics, we used the SPC/E water model3 because dynamical properties like the diffusion constant are in good agreement with experiment for this model. We note that even though the

GROMOS96 force ﬁeld was parametrized with the SPC water model, van Gunsteren and co-workers obtained better agreement with experimental reorientation times for the tryptophan monopeptide using GROMOS96 in combination with the SPC/E model.66 Solvation energies, described below in section 2.3, were also calculated with the SPC water model4 to gauge the sensitivity of our results to the potential model. Standard united atom parameters were used for the peptide atoms. The N-

+ terminus was protonated as an -NH3 group and the C-terminus was deprotonated as a -COO− group. The non-bonded pair list was produced using a cut-off of 11A.˚ Long range electrostatic interactions were handled using SPME67, 68 with a real space cutoff length of 9A.˚ A shifted Lennard-Jones potential for non-bonded pairwise interactions with a cutoff length at 9A˚ was used. All bond lengths were constrained using the

LINCS algorithm.69 Periodic boundary conditions were implemented using a cubic box of side length 32A˚ and solvated with 1040 water molecules using SPC/E as a water model. The number density of water far from the peptide was 0.0325A˚−3.

The solvated starting structure was subjected to a series of steepest descent energy minimizations and short MD runs to remove possible unfavorable interactions between

13 S0 (GROMACS) HZ2 S (AMBER) 0 HE1 HH2 CZ2 CE2 NE1 La HD1

CZ3 CD2 CD1 CG HZ3 CE3 CB HE3

Figure 2.1: The ground state dipole moment of the indole chromophore from the partial charges of the Amber-7 and GROMACS force ﬁelds (1.30 and 2.41 Debye, respectively) and the La excited state dipole moment (4.96 Debye) constructed for our simulations as described in the text are depicted on the left. The right hand image indicates the atom labels which are used in Table 2.1 and elsewhere in the text.

solute and solvent. During the initial equilibration period of the system, the Nos´e-

Hoover thermostat70, 71 was used to maintain the system at 300 K.

From the CASSCF calculations of Sobolewski and Domcke,60 partial charges, cal-

culated as Mulliken charges, are available for the S0 ground state and various excited

states, including the La state. The Mulliken charges qualitatively agree with the partial charges found in the Amber-7 and the default GROMACS force field available in the GROMACS package1, 64 (Fig. 2.1). We would not expect quantitative agreement because the Mulliken charges reflect artifacts of the basis set and do not necessarily reproduce the actual molecular charge distribution. Since the partial charges are chosen in each force field to optimize the overall accuracy of the force field, we chose not to re-adjust the charges in the ground state. For the excited state, we modified the partial charges of the indole chromophore by applying the ab initio charge density differences to the partial charges of the ground state GROMACS force field. The charge

14 density diﬀerence between La and S0 state actually dominates the S0 charges, so the precise nature of the ground state charges does not greatly aﬀect the La state dipole.

Therefore our La state dipole moment actually agrees well with the one reported by

60 Sobolewski and Domcke in both magnitude and direction. The charges on the La state indole are reported in Table 2.1. In our model, the ground state dipole moment

atom charge atom charge CB 0.00 CE3 −0.27 CG 0.01 HE3 0.14 CD1 −0.09 CZ2 −0.27 HD1 0.14 HZ2 0.14 CD2 −0.07 CZ3 −0.13 NE1 0.12 HZ3 0.14 HE1 0.19 CH2 −0.20 CE2 0.01 HH2 0.14

Table 2.1: Charges used for the indole group in the La state.

is 2.41D and that of the excited La state was 4.96D.

Excited state trajectories were run for a period of 400ps without any temperature or pressure coupling using NVE dynamics to determine tryptophan dynamics following photoexcitation for comparison with experiment. The degree of energy drift during these NVE simulations was very small. The average temperature, as calculated from the kinetic energy, drifted by approximately 0.4%. The starting conﬁgurations of the excited state trajectories were sampled from simulations run on the ground state using NVT dynamics by selecting conﬁgurations spaced by intervals of at least

3 ps.

15 a) b) c)

Figure 2.2: Three isomers of the KWK peptide, the a) KN ,b)N,andc)KC complexes, in order of decreasing stability in the ground state.

2.3 Lys-Trp-Lys isomers and the π-cation eﬀect: static properties

The starting structure of the tripeptide was obtained by cutting out the coordinates of the KWK segment from a nucleopeptide that contains this sequence72 (PDB identifier is 1J9N). Since extensive equilibration, as well as searches for alternate stable conformations of lys-trp-lys were performed, the particulars of the original starting configuration is of little significance. The starting structure of the tripeptide as extracted from the PDB file after solvation and equilibration took on a stable conformation with the indole group interacting with the side chain of the N-terminus lysine which was named the KN complex (Fig. 2.2a).

We suspected that the C-terminus lysine could also bind strongly to the indole ring. To search for that isomer, a gas phase simulation of the tripeptide with per- turbed charges was then conducted to facilitate the formation of an isomer with the indole group now interacting with the side-chain of the C-terminus lysine which we named as the KC complex (Fig. 2.2c). The perturbation entailed an inverse scaling of the weight of the charges on the ammonium group and hydrocarbon side chains of the

16 two lysines. This procedure facilitates easier dissociation of the indole from one lysine

while encouraging its intimacy with the other lysine. The structure obtained through

the gas phase simulation was then equilibrated with the unperturbed force ﬁeld in

aqueous solution. It was found to maintain its KC conformation hence conﬁrming the existence of the KC isomer.

A third isomer was later observed in simulations of the excited tripeptide. The

N-terminus can swing over and bind to the indole ring. This N isomer was then simulated with ground state charges and was found to maintain its N conformation

(Fig. 2.2b) which confirmed the existence of a third isomer of the tripeptide in the ground state as well. The existence of the three isomers is essentially driven by strong attraction between the three ammonium groups and the indole in the force field. The physical origin of this attraction is a π-cation interaction,51, 52, 73 although the degree to which commonly used force fields capture the π-cation interaction is a matter of some current discussion.74–81 It is also important to note that while the lysine ammonium groups can interact with the indole in a π-cation interaction, the ammonium group

was often not directly neighboring the indole ring system (Fig. 2.2). Instead, the

hydrocarbon side chain often aligns against the aromatic ring in a conﬁguration that

might be stabilized by hydrophobic interactions.

In the ground state, interconversion between the KN, N, and KC complexes was

virtually non-existent. In the many nanoseconds of total simulation time performed

for this project, we only witnessed one near barrier crossing between the KN and

KC complexes in the ground state, and never observed a successful barrier crossing.

However in the excited state we identiﬁed interconversion between KN and N, and

17 between KC and N complexes. The time scale for interconversion was hundreds of

picoseconds and this will be addressed in more detail later.

By this point, we discovered three stable isomers corresponding to each of the cationic groups binding to the indole rings. We tested whether a floppy conformer in which no group was bound to the indole was stable, and found that in all cases an initial configuration of this type reverted to one of the three stable isomers already identified. We also tested whether a “sandwich” structure was stable, one where amino groups from both lysine chains were bound on either side of the indole. (See

Fig. 2.3 below.) It was possible to stabilize an initial configuration with artificial interactions, but in all cases as soon as the force field parameters returned to gmx or GROMOS96 values, the sandwich fell apart. Despite the fact that the sandwich structure was not stable, there was reason to suspect that the force fields we were using, underestimated the binding of cationic groups to the indole, and that the sandwich would be more stable using a more accurate force field. To explain further, we have to provide some background on the π-cation effect.

Dougherty and co-workers have pointed out that an unusually strong attraction

exists between π-electron systems and cations,51, 73 a combination of mostly electrostatic attractions with some electronic polarization effects. Since that time, several groups have sought to address whether, and by how much, commonly used force fields should be revised to account for π-cation effects. Chipot et al.82 found that binding

kcal between ammonium and toluene in the gas phase was underestimated by 5.7 mol by the AMBER 4.1 force ﬁeld compared to ab initio MP2 level83–87 calculations. They

devised a modiﬁed force ﬁeld to increase the ammonium-toluene binding, and found

that the change in binding free energy in water was less pronounced than in the gas

18 kcal phase, by about 3.0-4.7 mol depending on how the free energy was calculated. Other workers have found similar results.74, 75, 77, 78, 88 There has been continuing discussion in the literature as to the degree to which water counteracts the π-cation interaction,79 how current force fields should be modified,75, 78, 88 and the ultimate relevance to biological systems.76, 80, 89 Some workers, such as Aliste et al.90 conducted their analysis of π-cation interactions without making any modifications to the GROMACS96 force

ﬁeld in their calculations.

Resolving how force fields should be modified to account for π-cation effects is beyond the scope of this work. However, we wanted to gauge the degree to which additional attractive interactions between the indole and cationic group would be needed to stabilize a sandwich structure. To this end, we incorporated an enhanced attraction of variable strength between the indole and ammonium groups to account for a possible underestimated π-cation interaction in the original force field. We added two dummy atoms to the indole group at the centers of the benzene and pyrrole rings. Another pair of dummy atoms was put on each lysine side chain at the location of the amino group. All dummy atoms had zero charge. A pair interaction between the dummy atoms of the indole and that of the lysine side chain was modeled with a Lennard-Jones potential. The Lennard-Jones diameter σ was maintained at

2−1/63.5A˚ to situate the well minimum at 3.54A˚ and the well depth ǫ was varied.

In order for the sandwich structure (Fig. 2.3) to be stable for at least 400 ps in the

kcal ground state, the Lennard-Jones ǫ parameter had to be at least 10 mol . This well depth exceeds that of any previous estimates for the amount of additional attraction

that should be added to empirical force ﬁelds to account for the π-cation eﬀect. The

results of this exercise indicate that the sandwich structure is unlikely to form in the

19 Figure 2.3: Snapshot of the sandwich structure created using modiﬁed Lennard-Jones potentials.

ground state. It should be noted that this π-cation model is rather crude. However, using a more realistic π-cation interaction model would infact make the sandwich structure less likely for the following reason. An effective π-cation model should account for the non-additive effect of bringing two cations to the π-ring and is best modeled with a polarizable forcefield.75 While the electrostatic component of the

π-cation interaction is approximately additive, the same is not true of the induced polarization. As pointed out by Minoux and Chipot,75 when cationic groups are on both sides of a π-ring system, the ring system cannot simultaneously polarize to accommodate both charges. Hence the binding energy for cations on both sides of the ring is expected to be less than twice the binding energy of a single cation. A similar argument applies for a sandwich type structure formed between the ammonium of the N-terminus and the lysine side-chain near the C-terminus.

Since KN , KC and N isomers were indeﬁnitely stable in the ground state and interconversion was not observed even in runs lasting several nanoseconds, we could determine their relative populations by free energy integration techniques. We created

20 a convenient reference structure (Fig. 2.4) with modiﬁed charges. Each of the isomers

smoothly transformed to the reference structure as the charges were modiﬁed from

the original force ﬁeld charges to the charges of the reference structure. By standard

free energy integration techniques,91 the free energy diﬀerence between each isomer

and the reference structure is obtained by,

1 ∂V (λ) ∆A = h idλ (2.1) Z0 ∂λ where V (λ) is a function that interpolates the potential energy of the system from one thermodynamic state to another. A “ﬂapped out” structure was generated by equally distributing a net charge of +0.9e on the carbon atoms of the hydrocarbon side chains.

Furthermore a similar magnitude of positive charge was distributed equally on the atoms of the indole ring. This has the eﬀect of inducing repulsive forces between the indole and side-chain thereby breaking the π-cation and potentially hydrophobic interactions.

Figure 2.4: Snapshot of the reference structure used to determine the free energy diﬀerence of the three lys-trp-lys isomers in the ground state.

21 The thermodynamic integration from the actual force ﬁeld to the potential governing the reference structure was achieved by linear interpolation of the potential using a parameter ranging between 0 ≤ λ ≤ 1. For each of the isomers, nine points were taken along the integration path using the free energy directive of the GROMACS

package.2 The diﬀerence in the Helmholtz free energy of the isomers in aqueous

solution relative to the KN complex, the most stable isomer, are as follows:

kJ ∆A = 3.15 (S state, gmx force ﬁeld) (2.2) N−KN mol 0 kJ ∆A = 5.11 (S state, gmx force ﬁeld) (2.3) KC −KN mol 0

This suggests the qualitative conclusion that at room temperature, each of the isomers has appreciable representation. Quantitatively, the results of Eqs. (2.2-2.3) indicate that an equilibrium mixture of the lys-trp-lys tripeptide is 71% KN, 20% N, and

9% KC complex. However, such quantitative predictions are probably beyond the

predictive capability of the force ﬁeld. To obtain some “theoretical error bars” on the

results, we repeated the free energy calculation using the GROMOS96 force ﬁeld65

for the peptide. Using the GROMOS96 force ﬁeld, we found the following free energy

diﬀerences.

kJ ∆A = 1.38 (S state, GROMOS96 force ﬁeld) (2.4) N−KN mol 0 kJ ∆A = 1.41 (S state, GROMOS96 force ﬁeld) (2.5) KC −KN mol 0

First, it is noteworthy that each of the isomers is stable in the alternative force ﬁeld.

Second, the free energy ordering of the most stable KN isomer is preserved. This is unlikely to change the qualitative results that we present in this work with the choice of the “gmx” forceﬁeld. Quantitatively, the populations under the GROMOS96 force

ﬁeld are 46.7% KN, 26.8% N, and 26.5% KC complex.

22 The free energy calculation was repeated in a similar fashion for the excited state charge distribution. The reference structure was similar to that of the ground state.

Because of the large La state dipole, a stronger modification of the charges was required to ensure dissociation of the ammonium groups from the indole so the “flapped out” reference structure could be reached specifically for KC. This modification entailed increasing the charge on the C-terminus lysine by +0.1e . The results from this calculation indicates that the relative stability of the KN and N complexes is reversed in the excited state. Specifically, the free energy differences in the La state relative to the N isomer are as follows,

kJ ∆A = 0.85 (L state, gmx force ﬁeld) (2.6) KN −N mol a kJ ∆A = 3.2 (L state, gmx force ﬁeld) (2.7) KC −N mol a leading to equilibrium populations in the La state of 50.2% for the N isomer, 35.8% for the KN isomer, and 13.9% for the KC isomer. Below in section 2.4 we report that the KN and KC isomers in the excited state are found to transform to the N complex, in agreement with these free energy calculations.

2.4 Dynamics in solution following photoexcitation

We now describe the relaxation of photoexcited lys-trp-lys which comes from the analysis of an ensemble of 300 trajectories for each of the KN, N, and KC isomers evolving on the excited state potential surface. Each of these trajectories began with statistically independent conﬁgurations sampled from a simulation of the ground state, as described in section 2.2. The accumulated evidence from calculations of the

ﬂuorescence anisotropy decay [Eq. (2.8)] and time-dependent Stokes shift [Eq. (2.10)] will point to three important time scales: 1) the sub-picosecond time regime of inertial

23 dynamics,92–96 2) a period of 10-20ps in which the peptide and water re-equilibrate to the altered charge distribution of the excited state, and 3) a long time scale of hundreds of picoseconds in which the relative populations of the three isomers shift in the excited state. While we expect the quantitative details to be dependent on the quality of the force ﬁeld, the qualitative picture of three diﬀerent time scales should be more robust.

2.4.1 Fluorescence anisotropy decay

The ﬂuorescence anisotropy decay is tracked by the following correlation function,97 2 µ(t) · µ(0) r(t)= P . (2.8) 5 2 hµ(0) · µ(0)i

The dipole µ(t) used in Eq. (2.8) is that of the indole chromophore, described in sec-

tion 2.2. The ﬂuorescence anisotropy of individual trajectories exhibited oscillatory,

highly non-exponential behavior. The emergence of a smooth decay curve, as shown

in Fig. 2.5, reﬂects ensemble averaging over initial conditions at excitation, as realized

by 300 non-equilibrium trajectories. Each of the isomers exhibited the same qualita-

tive pattern, a double exponential decay, as shown and described in the caption to

Fig. 2.5. In each case, 10-15% of the anistropy decay arose from a fast component

with a time constant of several picoseconds, and a much longer component with time

constant ranging from 94 to 135ps. We attribute the short time behavior to local wob-

bling motion of the tryptophan residue, and the long time decay to overall tumbling

of the tripeptide. To compare the ﬂuorescence anisotropy decay with experiment, we

have to bear in mind that the initial drop occurring over ∼ 100fs is due to internal

1 1 conversion between La and Lb following simultaneous photoexcitation of two states

24 0.5

0.4 (135 ps) KN + 0.2

0.3

K + 0.1(94 ps) 0.2 C fluorescence anisotropy N (114 ps)

0.1 experiment (130 ps) 0 0 100 200 300 400 time (ps)

Figure 2.5: Time evolution of the fluorescence anisotropy [Eq. (2.8)] following excitation from the S0 to the La state. Results for each of the isomers predicted by non-equilibrium molecular dynamics simulation of 300 trajectories is shown, as well as experimental results which are affected to some extent by internal conversion from the Lb to the La state during the first 100fs following photoexcitation. For clarity the KN isomer data is shifted up by 0.2, and the KC data by 0.1. The molecular dynamics results for each of the isomers can be fit to a double exponential −t/τ1 −t/τ2 of the form c1e + c2e , the solid lines in the figure. The fitting results are (c1,τ1,τ2) = (0.15, 6.5, 114), (0.11, 4.7, 135), (0.10, 3.2, 94) for the N, KN and KC isomers, respectively. In these fits, the coefficients were constrained so that c1 +c2 = 0.4. All the the time constants are in ps. The values of τ2, the long time delay are also indicated in the figure. The experiment could be described with a double exponential as well, with τ1 = 7,τ2 = 130. Internal conversion causes the initial very rapid decay of the fluorescence anisotropy in the experiment, so the data do not extrapolate at short times to the theoretical anisotropy maximum of 0.4.

in the experiments.46, 63 Therefore, it is only valid to compare the time constants. If our force ﬁelds are of suﬃcient accuracy, then according to the free energy calculations of section 2.3, the KN isomer is most prevalent in the sample before photoexcitation, and would be the most appropriate comparison with experiment. The KN isomer time constants do indeed compare well with experiment. Actually, the behavior of all the

25 isomers is qualitatively similar. In part, this reﬂects that the long time component

describes rotational diﬀusion of the tripeptide. In hydrodynamic models, using either

stick or slip boundary conditions,98 the diﬀusion time is controlled by the size of the isomer and solvent viscosity. Hence, the similar long time constant and agreement

with experiment indicates that the force ﬁelds give a reasonable description of the

tripeptide size and the SPC/E model yields a reasonable solvent viscosity.

2.4.2 Stokes shift

The time-dependent Stokes shift is a central quantity by which dynamics following

photoexcitation is tracked. The Stokes shift (see e.g. Ref.96) is the average of a double

diﬀerence that is measured experimentally by the diﬀerence between absorbed and

emitted light. The first difference is the energy difference between the excited and

ground state of the indole chromophore as a function of time following excitation.

∆Eindole(t)= Eindole,La (t) − Eindole,S0 (t) (2.9)

The energy diﬀerence ∆Eindole(t) depends upon the electronic excitation energy of the indole chromophore, and the interaction of the chromophore with the rest of

the peptide and the solvent. The energies Eindole,La (t) and Eindole,S0 (t) depend upon the instantaneous configuration of peptide and solvent. In our model, the energy difference ∆Eindole(t) arising from indole-protein and indole-water interactions is a difference of Coulomb interactions stemming from the different charges on the indole group in the La and S0 state, although all parts of the force field affect the position of the charges and are ultimately reflected in ∆Eindole(t). There is also a contribution to

∆Eindole(t) which is the gas phase excitation energy of the indole chromophore. This

26 need not be speciﬁed here since it cancels in the calculation of the Stokes shift,

∆EStokes(t)= h∆Eindole(t) − ∆Eindole(0)i . (2.10)

The average indicated by angle brackets in the above equation is over initial conditions sampled from an equilibrium distribution in the ground state. The dynamics indicated by the explicit dependence on time is governed by the La excited state potential surface since the Stokes shift represents relaxation in the excited state following photo-excitation. Like ∆Eindole(t), ∆EStokes(t) can also be decomposed into protein and water contributions by replacing ∆Eindole(t) in two places on the right

x side of Eq. (2.10) by ∆Eindole(t), where x can be p(protein) or w(water). We begin our discussion of the time-dependent Stokes shifts by showing how water and the protein compete to solvate the indole group. This eﬀect occurs in all isomers, and in both the ground and excited state. Although this is an equilibrium, and not a dynamic eﬀect, we postponed the discussion to this section because it is essential to understanding our non-equilibrium time-dependent Stokes shift data.

Competitive Stabilization

Our analysis shows that the peptide and solvent compete to solvate the chromophore in the sense that the protein and water interaction energies are inversely correlated. The scatter plots in Fig. 2.6 depict samples from long-time equilibrium runs – long after photoexcitation but before isomerization takes place, as noted above

– for each of the isomers in the excited state and for the N isomer in the ground state.

There is a clear inverse relationship between the indole-water and indole-protein interaction energies. In the excited La state the individual water and protein contributions to the indole stabilization energy typically ﬂuctuate over a very large range, roughly

27 Figure 2.6: Scatter plot of the indole-protein and indole-water contribution to the stabilization energy of each of the isomers of the excited state, as indicated by the plot labels, and of the N isomer in the ground state (lower right panel). The scatter plots were accumulated over runs of duration 2-3ns in which transitions between diﬀerent excited state isomers did not occur. In all cases we used the gmx force ﬁeld1, 2 and the SPC/E water model.3 In addition, we recalculated the distribution 4 of interaction energies using the SPC water model for the KN isomer, shown as the lighter-colored dots in the upper left panel.

kJ 150 mol , although their sum ﬂuctuates by a smaller amount. Later on, we will see that the increase in total interaction energy following photoexcitation is on the order

kJ of 23 mol (Fig. 2.9), much smaller than the individual range of ﬂuctuations for the water and protein contributions. In the ground state (lower right panel of Fig. 2.6) the range of ﬂuctuations is considerably smaller, but still larger than the response following photoexcitation.

28 We checked whether the inverse correlation between water and protein contributions to indole interactions was a particular feature of the water model by repeating the calculation with the SPC water model.4 The data (upper left panel of Fig. 2.6) suggest no qualitative diﬀerence. The data in Fig. 2.6 also have a particular feature which has important consequences for the time evolution of the Stokes shift. The points in Fig. 2.6 lie along a line whose slope is close to −1. This implies that as one contribution (indole-protein or indole-water) rises, the other contribution tends to fall by the same amount. On account of this, even as the relative contributions from protein and solvent ﬂuctuate, the total interaction energy of the chromophore tends to remain constant.

Evidence for a negative correlation between protein and water interactions has also been reported by Bandyopadhyay et al. in their simulations of the HP-36 fragment.45

In Fig. 3 of their work, the cross-correlation between water and protein interaction contributions is negative for all three helices of the protein. Nilsson and Halle18

have explained this behavior in terms of a simple dielectric model. Our ﬁndings are

consistent with these earlier results.

Time dependent Stokes shift

We now turn our attention to the time dependent relaxation dynamics as described

by the time dependent Stokes shifts ∆EStokes [Eq. (2.10)]. The total Stokes shift

for the three isomers compare well to those obtained from experiment within the

time frame measured by experiment. The total Stokes shift can be decomposed into

contributions from solvent and the rest of the tripeptide excluding the excited indole.

The total Stokes shifts curves (Fig. 2.7) suggest at least three, possibly four time

components for the solvation process. The ﬁrst is the inertial fast component at the

29 Figure 2.7: Time dependent Stokes shift for the lys-trp-lys peptide photoexcited from the KN, N, and KC isomers are shown in the top, middle and bottom panels, respectively. The behavior during the ﬁrst picosecond following photoexcitation is shown in the small panels on the left. Errors bars for the KN and N isomers were calculated by dividing the total data set into three blocks.5 One standard deviation is shown.

sub-picosecond scale (left hand panels of Fig. 2.7). Both experimental and simulation data from the Stokes shifts indicate a fast inertial component at the sub-picosecond time scale which has been well characterized in previous work.92, 93, 96 In this system, the inertial response is dominated by the water contribution to the Stokes shift. Since the N isomer is most stable in our excited state model, it is a good place to begin the analysis of dynamics following the inertial period because, unlike the other two isomers, isomerization does not complicate the calculated Stokes shift. The total

Stokes shift S(t) for the N isomer can be ﬁt well by a sum of a Gaussian for the fast

30 inertial response and two exponentials.

2 − t − t − t “ τg ” τ τ S(t) = cge + c1e 1 + c2e 2 + S∞ , (2.11) kJ where c = 18.85 ,τ = 47fs (2.12) g mol g kJ c = 9.49 ,τ = 0.79ps (2.13) 1 mol 1 kJ c = 4.98 ,τ = 52.5ps (2.14) 2 mol 2 kJ and S = −33.32 , the total Stokes shift. (2.15) ∞ mol

The quality of the fit provided by Eqs. (2.11-2.15) for the N isomer is depicted in Fig. 2.8. In that figure, the experimental data6 is also shown. The overall Stokes shift, S∞, for all the isomers is quite similar, and agrees almost quantitatively with experiment. However, there are several aspects where the agreement between theory and experiment is only qualitative. Firstly, the inertial decay found in experiments is quite a bit longer: the τg that fits experiment is an order of magnitude larger than from simulations. This discrepancy could be the result of the lack of resolution in the experiments to probe fast dynamics on the sub-fs timescale. On the other hand, the discrepancy might also be due to the fact that our theoretical model does not account for the non-adiabatic dynamics occurring between the two low lying excited states of tryptophan during the first ∼ 100fs. Both theory and experiment show a fast decay component on the order of picoseconds. As can be seen in Fig. 2.9, this component is slower in the experimental data. The best fit of the experimental data is obtained using two exponentials with time constants of 0.61ps and 3.3ps. The simulation data is noisier than the experimental data, and requires just one exponential with a time constant of 0.79ps. The long time decay is faster in experiments than in simulations, exhibiting a 23.3ps time constant as opposed to 52.5 from Eq. (2.14). Recently Xu et

31 0 0

) -10 -10 -1

-20

Stokes shift (kJ mol -30 0 2 4 6 8

-30

0 20 40 60 80 100 time (ps)

Figure 2.8: Open circles are the experimental Stokes shift as reported in Ref.6 The fit 2 − t − t − t − t “ τg ” τ τ τ that goes through these points is of the form cge +c1e 1 +c2e 2 +c3e 3 +S∞, kJ where cg = 9.15,c1 = 12.24,c2 = 7.87 and c3 = 1.96 mol , and τg = 590fs,τ1 = .613,τ2 = 3.3 and τ3 = 23.3ps. The other curve shows the Stokes shift calculated in molecular dynamics simulations for the N isomer, and the fit given in Eqs. (2.11-2.14). The inset provides a magnified view of the experimental and simulation data at short times. From this comparison, we see that the molecular dynamics data decays faster on the ∼ 1ps time scale, but slower on longer times scales compared to experiment.

al.,48 have emphasized that part of the experimental ﬂuorescence decays can reﬂect

quenching of the indole chromophore via electron transfer to neighboring residues.

We know fast quenching does not occur in the lys-trp-lys experiments, at least, on

the time scale of less than 400ps because we did not observe any fast decay component

at the red-side of the ﬂuorescence emission. For those transients gated at longer than

the 350nm emission peak, we observed a ultrafast rise component (< 1ps) and two

long decay components with 400ps and 2.5ns lifetimes.6

32 There is no evidence for isomerization in the experimental data. The average lifetime of tryptophan ﬂuorescence in the experiments is approximately 1 ns, which

falls within the timescale of the isomerization process observed in our simulations.

Since dynamics on the 102-103ps time scales is likely to reﬂect activated processes

and will depend sensitively on free energy barriers, quantitative agreement between

experiment and simulation will be particularly diﬃcult to achieve for this process.

In Fig. 2.7, only the N isomer Stokes shift is stable at long times. Following

the inertial decay, the dominant feature of the Stokes shift is a dramatic, and com-

pensating shift in Stokes shift contributions from indole-water and indole-protein

interactions. Within ∼ 3ps after dynamics begins in the La state, the water contribu-

kJ tion to the Stokes shift reaches −23 mol while the protein contribution is quite small.

Subsequently, with a time scale of τ1 = 52.5ps [Eq. (2.13)], the water contribution

decreases and the protein contribution increases until they stabilize at a point where

the indole-protein interactions account for roughly two-thirds of the Stokes shift. Be-

cause of competition between these two contributions and the fact that the scatter

plots of Fig. 2.6 lie along a line of slope −1 , the eﬀect of the 52.5ps process on the

total Stokes shift is quite small, although still visible in Fig. 2.7b.

The actual change in interaction energy in the excited state, not the Stokes shift,

for the N isomer is shown in Fig. 2.9. A steady lowering of the total interaction energy

of the indole with its peptide and water environment drives the overall process. The

inertial energy drop arises almost entirely from the water contribution to the solvation

of the indole. After 1ps, the indole-water solvation energy becomes more negative by

kJ 26.6 mol while the corresponding quantity for the indole-protein interaction is only

kJ 5.3 mol . This magnitude of the initial drop over ∼ 1ps duration is roughly two-thirds

33 0 -100

-20 -120 ) ) -1 -1

-40 -140 total

indole-water -60 solvation energy (kJ mol -160 solvation energy (kJ mol

indole-protein -80 -180

0 50 100 150 200 time (ps)

Figure 2.9: Total stabilization energy of the indole group following photoexcitation (upper curve, left axis), and the water and protein contributions to the interaction energy (bottom two curves, right axis). At the instant of photoexcitation, the interac- kJ tion energy contribution from water and protein are −46.8 and −53.3 mol , respectively.

of the total, long-time stabilization energy (Fig. 2.9). The remainder of the relaxation dynamics takes place on the slower, 0.79ps and 52.5ps time scales. During this later stage, the change in the water and protein contributions to the interaction energy are roughly compensating, as suggested by their competing stabilization at equilibrium

(Fig. 2.6). However, the indole-protein interaction energy becomes more negative while the indole-water energy becomes more positive, leading to the long term overall stabilization on the 52.5ps time scale. The competition between water and protein stabilization of the indole is even more pronounced for the KN isomer, but barely discernible for the KC isomer, although in both those isomers it is not completely separable from isomerization dynamics.

The 52.5ps component of the N isomer Stokes shift is characterized by local motions of the side chains. As shown in Fig. 2.10, the distance from the indole to the

34 0.55

+ remote lysine NH3 -indole 0.5 1.15

0.45 N terminus-indole 1.1 lys-indole distance (nm)

N terminus-indole distance (nm) 0.4 1.05

+ proximal lysine NH3 -indole

0.35 1 0 50 100 150 200 time (ps)

Figure 2.10: For the N isomer, distance between the CE3 carbon of the indole ring and N-terminal amino group (middle curve, referred to left-hand axis), amino group of the remote C- and proximal N-terminal lysines (top and bottom curve, respectively, referred to right-hand axis). The data shown in this ﬁgure represent averages over 300 non-equilibrium trajectories, as described in section 2.2.

N-terminal amino group decreases by about 0.8A˚ on this time scale, strengthening

the π-cation interaction. The amino group of the C-terminal lysine also approaches the indole by almost the same distance, although it is still over 10A˚ from the indole which is not surprising given our discussion of the sandwich structure analysis

(section 2.3). Similar conformational change of the KC isomer was observed following

photoexcitation, with change of the KN isomer occurring to a lesser extent. In the KC

isomer, Fig. 2.11a shows that the π-cation interaction was strengthened by a decrease

of the distance from the indole to the amino group of the C-terminal lysine, while the

distance to the amino group of the N-terminal lysine increased (Fig. 2.11b). While

the KN isomer shows a much weaker conformation response along these coordinates

than either the N or KC isomers, it is possible that there is a similar response in the

KN complex along diﬀerent coordinates.

35 + + b) remote lys-NH -indole distance a) proximal lys-NH3 -indole distance 3 0.8

K C-indole

K N-indole 0.7 1

0.6

K N-indole indole-lys (nm) K -indole indole-lys (nm) 0.5 C 0.95

0.4 0 100 200 300 400 0 100 200 300 400 time (ps) time (ps)

Figure 2.11: a) Distance between the CE3 carbon of the indole ring and the proximal lysine amino groups in the KC isomer, and KN isomer. b) Distance between the CE3 carbon of the indole ring and the remote lysine N or C-terminus for KC and KN isomers respectively.

The change in cation-indole distance is also accompanied by a bending of the

lysine side chain to facilitate the formation of the π-cation complex in the excited

state. The bending of the lysine side-chain was monitored by the distance between

+ the CB carbon atom (β-carbon) and nitrogen atom of the -NH3 group on the side

chain. This coordinate monitors the degree of extension of the side chain. When the

side chain extends, it breaks the classical π-cation complex. In such structures, the

aliphatic side chain of the lysine lies against the indole rings forming a complex that

appears to be stabilized by hydrophobic interactions between chain and the indole.

This process is clearly seen in Fig. 2.12 which shows an increase in the π-cation

distance coordinate as described earlier in this section, occurring concurrently with

chain extension. In the many nanoseconds of simulation performed for this project

we also witnessed situations where both hydrophobic and π-cation interactions break,

and the lysine side-chain and indole groups are relatively free from each other. While

36 this behavior may be the onset of isomerization, it might also be a typical ﬂuctuation

that contributes to the longer component of solvation.

1.5 a) side chain motion

+ NH3 (nm)

chain extension + 0.7 3 1 indole-lys (nm)

0.5 0.6 carbon - NH β π-cation distance 0 25 50 75 100 time (ps)

0.85 b) isomerization KC -indole (nm) + 3 0.8

K 0.75 N

N-terminal -NH 0 100 200 300 400 time (ps)

Figure 2.12: a) Degree of lysine side-chain extension, as measured by the distance + from the β-carbon to the -NH3 group, and π-cation distance, tracked by the distance + from the CE3 carbon of the indole to the lysine -NH3 group. The chain extension and π-cation plots are referred to the right- and left-hand axes, respectively. In the single trajectory shown here, and in many others, chain extension is correlated with breaking the π-cation complex. b) progress of isomerization in the KC and KN isomers, as measured by the average distance from the N-terminal amino group to the indole. The data shown in this ﬁgure represent averages over 300 non-equilibrium trajectories, as described in section 2.2.

The long term process occurring over hundreds of picoseconds evident in Fig. 2.7 is conﬁrmed as isomerization in Fig. 2.12b. In this plot, the distance between the amino group of the N-terminus and the CE3 carbon atom of the indole, averaged over non- equilibrium trajectories, is plotted as a function of time for the KC and KN isomers.

The data shows that this average distance is decreasing on a long timescale indicating that the KC and KN isomers are isomerizing into the N isomer. Even though the KC isomer lies higher in energy than the KN isomer, the isomerization rate to the N

37 complex is lower, indicating that this process is under kinetic control. The barrier

for dissociation of the indole from the lysine amino group is evidently larger for the

KC complex, and may be linked to the closer association of the lysine amino group to the indole in the KC complex (Fig. 2.10a), or the larger distance from the indole to the N-terminus in that isomer. Since 36% of the excited tripeptide at equilibrium in the excited state should be in the KN complex, we should observe transitions from the N to the KN complex in our simulations. This process presumably occurs on a time scale much longer than the 400ps length of our simulations. Any process with a

time scale much longer than 400ps will be missed in the calculations.

2.5 Conclusions

During folding and normal biological activity, typical proteins access a huge num-

ber of structures,33 which can be quantiﬁed in terms of basins of attraction to locally

stable minima on a potential energy surface.99 The scientiﬁc and medical relevance

of large proteins make them vital objects of study. However, it is also worthwhile to

examine the same forces that control folding and activity in large proteins at work in

a smaller, more easily studied, system. For that reason, in this chapter, we chose a

small lys-trp-lys tripeptide for study, one for which experimental data is available for

comparison6 and which exhibits internal π-cation51, 73 interactions. This tripeptide

is small enough for detailed simulation, and for cataloging all of the major struc-

tures (i.e. local potential energy minima) of the potential surface. The surface is

indeed rugged, just as it is for large proteins,33 but it is more amenable to detailed

investigation.

38 We showed in this chapter that the three major isomers of the lys-trp-lys tripeptide are accessible at 300K according to both the GROMACS1, 2, 64 (“gmx”) and GRO-

MOS9665 force ﬁelds. Three isomers arise from π-cation binding of either the protonated amino group of either the N-terminal lysine, C-terminal lysine or N-terminal amino group to the indole ring of the tryptophan. These isomers were designated as KN, KC and N isomers, respectively, in this work. In both force ﬁelds that we investigated, the KN isomer was most stable in the ground state. In the excited state the order of stability changes, leading to isomerization dynamics on a long time scale.

Our model of the excited state is based on the electronic structure calculations of

Sobolewski and Domcke.60 It qualitatively reproduces the ﬂuorescence depolarization dynamics and Stokes shifts measured experimentally. We expect that the force

ﬁelds we used underestimate the binding of cationic groups to the indole ring.75, 82

We do not expect this to change the qualitative behavior we observe in simulations because the π-cation binding was already suﬃciently strong in the current force ﬁelds to stabilize the isomers. We were concerned that increasing π-cation binding to more realistic levels would stabilize an additional “sandwich” isomer in which both lysine amino groups were bound to the indole. However, we found that an unreasonable increase in the indole-cation interaction was needed to stabilize the sandwich structure.

There has been recent discussion concerning the relative contribution of water and protein energetics to the Stokes shift, and of their relative time scales.18, 45, 47 These phenomena, which we can study in detail for the tripeptide, are actually quite rich for this simple system. We ﬁnd that the initial (∼ 1ps) relaxation dynamics are dominated by the interaction between the indole chromophore and aqueous solvent.

39 After the inertial period92–96 and picosecond time scale dynamics are complete, conformational changes occurs on an intermediate, ∼ 50ps time scale. The intermediate time dynamics is characterized by peptide and solvent establishing a new conformational equilibrium in response to altered interactions in the excited state. Among the conformational changes, are adjustment of distances from the peptide cations to the excited state chromophore, and the populations of side chain conformations drifting to new equilibrium values in the excited state. This process is driven by an overall stabilization of the excited tripeptide that is accompanied by a dramatic shift in the relative contributions of indole-protein and indole-water to the relaxation energy and the Stokes shift. The interactions between indole and the rest of the peptide take on increasing importance during the intermediate period, while the water contribution diminishes, particularly for the KN and N isomers.

There has also been discussion as to whether slow protein relaxation dynamics is a feature intrinsic to the layer of water bound to protein,6, 16, 17, 41, 42, 100–102 or whether it reﬂects protein dynamics.18, 47, 103 In chapter 3 we examine this problem in greater detail by examining an ensemble of non-equilibrium trajectories where the coordinates of the protein are ﬁxed during the relaxation process. In the case of the KWK tripeptide, especially the KN and N isomers, the remainder of the peptide clearly has a role in the relaxation dynamics, both in terms of direct stabilization of the chromophore, as seen by the indole-protein contribution in Fig. 2.9, and through correlated, cooperative dynamics involving solvent, as detailed in section 2.4.2 and

Fig. 2.6.

40 CHAPTER 3

Protein hydration dynamics in myoglobin

3.1 Introduction

In chapter 2, we discussed both the equilibrium and non-equilibrium relaxation

processes for the tripeptide KWK, following photoexcitation in solution. We showed

that the dynamics of the nearby side chains play a crucial role in the relaxation pro-

cess. The role of protein dynamics in establishing the slow relaxation components

observed in ﬂuorescence Stokes shift experiments is examined in more detail here for

the protein myoglobin. As described in chapter 2, time-dependent ﬂuorescence Stokes

shift experiments reveal the dynamics with which the environment of a chromophore

relaxes following photoexcitation of the tryptophan. In these experiments, the re-

laxation dynamics of small molecules in water is complete on a time scale of several

picoseconds, while near proteins the dynamics can take tens of picoseconds or even

longer.16, 41, 42, 92, 96, 104

There have been two explanations for the molecular origin of the long time scale

dynamics near proteins that have been advanced in the last decade. Nandi and Bagchi

developed a model for water near biological molecules which involved a dynamic equi-

librium between “bound” water molecules incapable of independent reorientation, and

41 “free” waters capable of rapid reorientation.17 Based on this model, Bagchi, Zewail and coworkers propose that the observed slow dynamics near proteins as monitored in time-dependent ﬂuorescence experiments is an inherent feature of water in the potential ﬁeld of a protein.16, 17, 41, 43, 45, 100, 101, 105 In their analysis, the strong electrostatic potential from the protein, rotationally immobilizes the nearby water molecules. In their model, the observed long time scale for relaxation dynamics is set by the time for exchange of waters between a bound state near the protein and a “quasi-free” state, what is commonly referred to as the residence time mechanism.

In contrast, Halle and Nilsson18, 47 assume that the strength of water-protein interactions is comparable to water-water interactions. Hence the local dynamics of water close to a protein, while not identical to bulk water, should also not be on a vastly diﬀerent time scale. Instead, Halle and Nilsson propose that the interactions between the protein and chromophore play an active role in solvation, and that it is the slow dynamics of the protein in aqueous solvent that leads to the observed long time scale in time-dependent Stokes shift experiments. Nilsson and Halle simulated the ﬂuorescence Stokes shift of monellin,18 using linear response theory and found that when the theoretical Stokes shift was separated into chromophore-protein and chromophore-water contributions, only the former exhibited slow dynamics. In the previous chapter we showed that for the tri-peptide KWK, it is the motions of the nearby lysine side chain that sets the timescale of the slow component observed in the TDFSS experiments. We will show however that the visual presence of a slow component in the protein or water component as Halle et al. proposed originally, cannot be used as a reliable indicator for the molecular origin of the Stokes shift.

42 In this chapter we theoretically examine the relaxation dynamics of myoglobin following photoexcitation in aqueous solvent. In order to test the role of protein

ﬂuctuations in establishing the slow component of the Stokes shift, we track the evolution of an ensemble in which the protein degrees of freedom are constrained after photoexcitation and only the water molecules evolve in time, as well as an ensemble in which all degrees of freedom are active. By freezing the protein, we isolate and quantify the inherent dynamics of the aqueous solvent. Molecular dynamics with frozen degrees of freedom or with degrees of freedom separately thermostatted into hot and cold groups have been previously used to determine the types of motion that enable the protein glass transition.106–108

By comparison with studies where both protein and water are allowed to move, we can test the assumptions of the Nandi-Bagchi-Zewail and Halle-Nilsson models.

If slow dynamics is an inherent feature of water trapped in the strong potential

ﬁeld of a protein, one should still observe slow dynamics when the protein is frozen.

Alternatively, if protein motion is essential for observation of slow evolution of the

Stokes shift, then the slow components should be absent in the frozen protein studies.

For the case study of tryptophan 7 (W7) in myoglobin presented here, we ﬁnd that the evidence conﬁrms Nilsson and Halle’s emphasis on the importance of protein motion.

However, we ﬁnd that Nilsson and Halle18 come to their conclusion for the wrong reason. They base their conclusion on the fact that the water contribution to the

ﬂuorescence Stokes shift exhibited no slow (∼ 50-100ps) component, while the protein contribution was characterized by a long-time component. Because protein and water dynamics are intimately coupled, we ﬁnd that slow dynamics of the total Stokes shift may visually originate in either the water or protein component, or both. One of those

43 components may appear flat at long time because of competing effects, even though underlying dynamics involving that component are taking place. However, Halle and Nilsson’s emphasis that protein flexibility is essential for the slow component of the Stokes shift seems to hold for the case of W7 in myoglobin we study here. We have investigated the effect of protein flexibility on the dynamics of nearby water.

Freezing the protein does not make a qualitative diﬀerence in the dynamics of water in the hydration layer, although slowing of some features is noted. Even when water dynamics is slowed by freezing the protein, we have documented that slow water dynamics near a frozen protein, if present, would be well within the detection limits of our simulations.

We do not take this as proof that a single explanation holds for chromophore relaxation dynamics in all proteins, although it is replicated in several other systems that have been studied in our group. Even though protein flexibility is essential, two other points deserve emphasis: first, it is coupled protein-water motion that sets the time scale for the relaxation process. Freezing water, like freezing the protein, eliminates the slow component of the Stokes shift in a rather obvious way: a protein molecule cannot fluctuate if it is constrained within an ice-cube!20 Second, inherent slow dynamics of the hydration layer cannot produce a slow component in the Stokes shift for W7 in myoglobin without protein flexibility. It should be stressed though that the protein fluctuations play a critical role in energetically stabilizing the excited state dipole. Recently, Zhong and co-workers15, 109 have suggested that the slow component of the Stokes shift is the result of “water network restructuring” that, in view of our calculations,20, 21 must be “facilitated” by protein motion. This picture ignores the large contribution of protein-chromophore interactions to the overall Stokes shift, and

44 artiﬁcially and unequally partitions the coupled protein-water dynamics by giving the

water network a dominant role in setting the time scale and relegating the protein

to a catalyst. Our calculations on several protein systems furnish evidence that the

nearby side chains and even the protein backbone are active participants in the slow

relaxation process. Eventually, as more cases are examined in detail, a comprehensive

picture of protein solvation dynamics will emerge. Here, we take the term “solvation”

in a broad sense that encompasses solvation via interactions with water and with

protein.

In section 3.2 we brieﬂy describe the molecular dynamics methods employed in this study. Then in section 3.3 we describe a long 30ns molecular dynamics trajectory for myoglobin in its ground state. There we ﬁnd that dynamical events in myoglobin occur on time scales extending out to at least 10ns. In section 3.4 the dynamics of myoglobin following photo-excitation is examined. Freezing the protein coordinates following photo-excitation allows us to unambiguously tease out the contribution of protein motion, in the relaxation process. In section 3.5 we analyze the residence times of water in the hydration shell and the nature of protein-water coupling in the hydration shell. Finally, in section 3.6 we draw conclusions from our results.

3.2 Simulation methods

The 154-residue protein myoglobin was simulated using a double precision version of the GROMACS package1, 2, 64 and GROMOS96 force ﬁeld.65 The initial conﬁgu- ration of myoglobin is taken from the crystal structure with Protein Data Bank110

ID code 1MBD. The SPC/E water model is used for the same reasons described in chapter 2. The non-bonded pair list was produced using a cut-oﬀ of 9A.˚ Long

45 range electrostatic interactions were handled using the smoothed particle mesh Ewald

(SPME) algorithm67, 68 with a real space cutoﬀ length of 9A.˚ The cutoﬀ length for the

Lennard-Jones potential was set at 14A.˚ All bond lengths were constrained using the

LINCS algorithm,69 allowing a 2fs time step in the simulation. Periodic boundary conditions were implemented using a truncated triclinic box of side length 60A˚ and solvated with 4537 water molecules. In order to make the whole system neutral, two sodium ions were introduced into the system. The Nos´e-Hoover thermostat70, 71, 111 was used to maintain the system at 295K. The photoexcitation process from the S0 to La state is modeled in the same way as we did for the tripeptide in chapter 2.

3.3 Analysis of a structural transition

Molecular dynamics simulations of myoglobin have been reported in the literature on several occasions.112–136 However, most of these studies involve trajectories much shorter than 1ns, although a few stand out as signiﬁcantly longer with trajectories of 1ns,132 1.1ns,122 1-2ns,123 80ns,133 and 90ns.134 The system was equilibrated for

800ps, and thereafter we sampled a trajectory of ground state myoglobin extending over 30ns and found structural ﬂuctuations occurring on a time scale of several nanoseconds. Therefore, signiﬁcantly shorter trajectories will miss dynamics on this time scale.

Over the course of the long ground state simulation, we observe a structural transition occurring after 10ns which is manifested in the S0-La energy gap shown in

Fig. 3.1. The signature of the transition appears in S0-La energy diﬀerences (Figs. 3.1a and b), and in structural parameters (Figs. 3.1c and d). Although the transition occurs on the ground state potential energy surface, it is clearly exhibited when tracking

46 Figure 3.1: Various energetic and structural features related to the indole group of tryptophan residue 7 during a 30ns trajectory in which the indole charges were that of the S0 ground state. Properties were calculated every 200fs. a) Indole-protein and indole-water interaction energy differences, upper and lower curves, respectively, between the excited La and ground state S0 potential energy surfaces. The indole- protein and indole-water energies were close to each other during the first 10ns, but are shifted and referred to different axis (note left- and right-hand scales) in the plot for clarity. b) Most of the jump of the indole-protein La-S0 interaction energy difference is accounted for by the interaction between the indole and the protein backbone between residues 77 and 86. c) Dot product of a unit vector along the dipole moment of the peptide bond between residues 78 and 79 with that of the indole group. d) Similar to previous plot for the peptide bond between residues 80 and 81.

47 energy diﬀerences between La and S0 states, as one would calculate for the Stokes shift

(section 3.4.1). The transition is signaled by a clear jump of roughly 20kJmol−1 in

the indole-protein and indole-water La-S0 interaction energies diﬀerences (Fig. 3.1a).

The structural transition at 10ns is associated with the loop region between α-helices

E and F, residues 77-86, as shown in Fig. 3.2. The loop is closer to the indole during

the ﬁrst 10ns of the molecular dynamics run. After the transition, the loop residues

ﬂuctuate more, and α-helix E is more disordered near the loop. We refer to the

structure of the ﬁrst 10ns of our trajectory as isomer 1, and the remainder of the trajectory as isomer 2. Fig. 3.1b demonstrates that the jump in indole-protein energy is accounted for by the change in interaction between the indole and the protein backbone. Backbone interactions have been previously implicated in the determination of peptide conformational stability.137–140 We searched for a clear signal of the transition in the interaction between the indole and several nearby charged residues and found none. The implications of this observation are discussed in the concluding section.

In isomer 1, the backbone dipoles tend to be anti-parallel to the indole dipole.

Figs. 3.1c and 3.1d show the dot product of a unit vector along the dipole of a particular peptide bond with the unit vector along the indole group dipole. The peptide bonds joining residues 78 and 79, and 80 and 81 are considered in Figs. 3.1c and 3.1d, respectively. In both cases, the dot product is negative during the ﬁrst 10ns,

reﬂecting the anti-parallel orientation of isomer 1. After the transition to isomer 2, the

dot product is either near zero or positive. The change in orientation of the backbone

dipoles relative to W7 is evident in the snapshots of isomer 1 and 2 presented in

Fig. 3.2. Our 30ns sampling does not establish whether isomer 1 is a metastable

state visited before the system ﬁnally reached equilibrium after 10ns, or whether the

48 Figure 3.2: Representative snapshots of tryptophan W7 and the loop region consisting of residues 77-86 that portray the structural transition quantified in Fig. 3.1. On the left, the E and F helices, the tryptophan W7, and some waters of hydration are shown. The proximity of the loop joining helices E and F is evident. On the right, snapshots from the isomer 1 and 2 sub-states are shown. The atoms of the peptide bonds connecting residues 78 and 79, and 80 and 81 are explicitly shown, reflecting the shift in angles relative to W7 which is quantified in Figs. 3.1c and d.

system will ﬂuctuate between isomers 1 and 2 indeﬁnitely. There is a slight indication

that the system is returning to isomer 1 after 30ns. Simulations an order of magnitude longer than the ones we performed might be needed to ﬁrmly establish the true status of these structures. Simulations of this length are not feasible, so instead we present relaxation dynamics calculated separately for isomer 1 and isomer 2.

If isomer 1 and isomer 2 are truly locally stable states between which myoglobin

ﬂuctuates in equilibrium, this behavior certainly has precedence in the literature. In trajectories of 1ns duration, Tournier and Smith found evidence of modes in myoglobin that were governed by bistable potential energy surfaces, and which would lead to infrequent transitions between two conﬁgurations.132 We believe that the set of bistable modes they discovered was limited by the time scale of their simulations, and that longer simulations would have revealed more modes with dynamics on longer

49 time scales. The motion leading to infrequent transitions between isomer 1 and isomer 2 is probably one example of many such bi- or multiply-stable conformations which myoglobin accesses in equilibrium. Local sub-states of myoglobin revealed by vibrational spectroscopy of a bound CO molecule have been discussed by Frauenfelder et al.141

Fig. 3.1a provides evidence of a negative correlation between the protein and water interactions as observed in the energetic changes in the indole-protein and indole- water energetics over time which follow opposite trends in their evolution. This is seen in the time evolution of the indole-protein and indole-water energetics. There is actually a competition between water and protein to stabilize the indole chromophore.

Evidence for a negative correlation between protein and water interactions has also been reported by Bandyopadhyay et al. in their simulations of the HP-36 fragment.45

Nilsson and Halle18 have explained this behavior in terms of a simple dielectric model.

These results for myoglobin are consistent with those documented in chapter 2 where we detailed competitive stabilization in simulation studies of the indole chromophore in the lys-trp-lys tripeptide.19 Similar eﬀects are seen below when W7 is in an excited electronic state. Competition between protein and water energetics to stabilize the indole appears to be a common phenomenon that occurs in all the proteins that we have examined in our group.

3.4 Dynamics of ﬂexible and frozen myoglobin following photoexcitation

In this section we report calculations of dynamical quantities, the ﬂuorescence

Stokes shift and ﬂuorescence anisotropy, following photo-excitation. Non-equilibrium trajectories of an ensemble sampled from an equilibrium simulation of the ground S0

50 0 0 a) linear response b) non-equilibrium ) -1 -5 protein -5 protein

-10 -10 water water energy (kJ mol -15 -15 total total 0 50 100 150 0 50 100 150

0 0 total loop c) non-equilibrium )

-1 backbone -5 -5 d) non-equilibrium water = total (frozen protein) -10 -10 water

energy (kJ mol water (dynamic protein) -15 total (dynamic protein) -15

0 50 100 150 0 50 100 150 time (ps) time (ps)

Figure 3.3: Fluorescence Stokes shift for isomer 1. a) Linear response theory estimate for the total Stokes shift, and the contributions from indole-water and indole-protein interactions. The time interval used to calculate the linear response correlation functions, Eqs. (3.1) and (3.2), and sampled for initial conditions of the non-equilibrium trajectories is indicated in Fig. 3.1a. b) Total Stokes shift, and the contributions from indole-water and indole-protein interactions calculated from 360 non-equilibrium molecular dynamics trajectories. Error bars represent one standard deviation as estimated from block averages obtained by breaking the total data set into three parts.5 c) Comparison of the Stokes shift calculated with full protein dynamics, as in (b), or from 120 trajectories propagated with the protein coordinates frozen following photoexcitation. When the protein is frozen, the water response is the total response. d) Contribution of the loop region (residues 77-86) to the Stokes shift, and the contribution that arises from the backbone atoms of the loop.

state are propagated on the excited La state surface. These results are also compared

with a linear response theory approximation to the dynamics. The dynamics are

calculated with all the atoms in the system unconstrained and also with the protein

51 frozen at the moment of photo-excitation so that the protein motions cannot contribute to the slow component of the Stokes shift. The purpose of the frozen protein

(FP) studies is to establish how protein motion contributes to the relaxation following photo-excitation. In the FP studies, the initial ensemble of water and protein conﬁgurations is sampled from the ground state, and hence there is static disorder

(ground state heterogeneity) of the protein conﬁgurations among the non-equilibrium

FP trajectories. However, there is no protein motion within each FP trajectory. Since the protein is incapable of absorbing energy during the FP trajectories, the solvent is not cooled by the frozen protein despite the name.

3.4.1 Fluorescence Stokes shift

As shown in chapter 2, an important point of comparison between experiment and theory is the time-dependent fluorescence Stokes shift (FSS), which is the energy difference between the photon absorbed upon photo-excitation and the fluorescence photon later emitted from the excited state. The non-equilibrium (NEQ) Stokes shift

∆EStokes(t) is calculated in the same way as it was done for the tri-peptide detailed in the previous chapter.

92, 93 ∆EStokes(t) can also be estimated from linear response theory.

−1 2 ∆EStokes(t) ≈ (kBT ) h∆Eindole(t)∆Eindole(0)i − ∆Eindole(0) (3.1) The average in Eq. (3.1) is taken over equilibrium trajectories. In the linear response approximation, the average may be taken in either the ground or excited state.93 Nils- son and Halle have emphasized recently18 that the correct formula for decomposing

52 the linear response estimate into protein and water contributions is

x −1 x x ∆EStokes(t) ≈ (kBT ) [h∆Eindole(t)∆Eindole(0)i−h∆Eindole(0)∆Eindole(0)i] , x = p,w.

(3.2)

0 0 a) linear response b) non-equilibrium )

-1 -5 water -5 water -10 -10 protein protein -15 -15

energy (kJ mol -20 total -20 total -25 -25 0 50 100 150 0 50 100 150 0 0 c) non-equilibrium

) d) non-equilibrium

-1 -5 -5 water = total (frozen protein) backbone -10 -10 water (dynamic protein) -15 -15 total protein

energy (kJ mol -20 -20 total (dynamic protein) -25 -25 0 50 100 150 0 50 100 150 time (ps) time (ps)

Figure 3.4: Same as Fig. 3.3 but for isomer 2. The time interval used to calculate the the linear response correlation functions for isomer 2 and sampled for initial conditions of the non-equilibrium trajectories is indicated in Fig. 3.1a. 100 trajectories were used to calculate non-equilibrium response with full protein dynamics, and 200 trajectories with the protein frozen. In panel (d), the protein backbone response is compared with the total protein response, indicating that backbone dynamics dominates the protein response.

53 The Stokes shift obtained from simulations was analyzed by ﬁtting to the following functional form.

2 −(t/τg) −t/τ1 −t/τ1′ −t/τ2 ∆EStokes(t) = cge + c1e + c1′ e + c2e + S∞ (NEQ) (3.3)

2 −(t/τg) −t/τ1 −t/τ2 ∆EStokes(t) = cge + c1e + c2e + S∞ (linear response) (3.4)

The first term describes the fast inertial response which is Gaussian within classical statistical mechanics.92, 93, 96, 142 This is followed by two phenomenological exponential decay terms. The first, associated with time scale τ1, is on the order of picoseconds and describes rapid orientational response to the excited state dipole. (Actually, the non-equilibrium data was sufficiently detailed and needed two terms of this order for an adequate fit. They are labeled τ1 and τ1′ in Table 3.1.) The second exponential component is on the order of tens of picoseconds. The molecular origin of the relaxation with time scale τ2 is the main focus of this chapter. Finally, S∞ = − ci is Xi the infinite-time Stokes shift.

−1 Table 3.1: Stokes shift data. All energies (S∞’s and c’s) are in units of kJmol and all times (τ’s) in unit of ps.

isomer 1 isomer 2 linear response non-equilibrium linear response non-equilibrium cg,τg 9.9 0.12 4.0 .018 12.5 0.13 2.9 .015 c1,τ1 3.6 1.4 6.1 .080 2.7 2.2 8.2 .075 c1′ ,τ1′ 4.9 1.6 4.7 1.4 c2,τ2 2.0 23 2.7 56.3 7.9 67 6.7 58.1 S∞ -15.5 -17.7 -23.3 -22.5 p S∞ -4.1 -5.3 -14.6 -14.3 w S∞ -11.4 -12.2 -8.7 -8.2

54 The Stokes shift calculated for isomer 1 (Fig. 3.3) and isomer 2 (Fig. 3.4) exhibit

diﬀerent dynamics when examined visually, although we will see that the underlying

processes are actually quite similar. For isomer 1, the protein response shows little

time-dependence beyond ∼ 20ps while the water response is responsible for the slowest

τ2 = 56ps component present in the overall response. These features are seen in the linear response approximation (Fig. 3.3a) and in the response calculated from non- equilibrium molecular dynamics trajectories (Fig. 3.3b). In contrast, for isomer 2 the water shows no apparent long time component, and the longest time component in the full response (τ2 = 58ps) arises from the protein contribution. Again, these features are seen in the linear response approximation (Fig. 3.4a) and the full non-equilibrium molecular dynamics results (Fig. 3.4b). The contributions from water and protein to the ultrafast inertial drop have roughly equal magnitude in isomers 1 and 2. Then the water contribution steadily increases for isomer 1, making it the majority contributor to the total Stokes shift. In contrast, it is the protein contribution that increases beyond the inertial drop in the data for isomer 2, and the protein contribution is the major contribution to the inﬁnite-time Stokes shift for the second isomer. Despite the seeming divergence in the dynamics of isomer 1 and 2, we will show that the underlying processes in the two cases are very similar.

As can be seen from Figs. 3.3 and 3.4, the linear response approximation (panel a), evaluated using the ground state trajectory that gave rise to the data in Fig. 3.1, provides a favorable picture of the relaxation dynamics following photo-excitation for both isomers when compared with the non-equilibrium simulations, although there are statistical errors. The linear response approximation appears particularly good for isomer 2 because the slope of the Stokes shift curve and weight of the slow component

55 are relatively large. Hence statistical errors in the linear response Stokes shift are

masked. These statistical errors arise because there are limited regions of time, 9 and

15ns for isomer 1 and 2, respectively, indicated at the top of Fig. 3.1a, which we can designate the system as clearly being in either isomer 1 or isomer 2. Hence there is a limited time over which we can accumulate accurate linear response correlation functions, Eqs. (3.1) and (3.2) and we thus place more emphasis on the analysis and interpretation of our non-equilibrium simulations.

-7

-8 ) -1 -9

energy (kJ mol -10

-11 c = 2 kJ mol-1 c c = 3 kJ mol 2 2 = 6 kJ mol 2 -1 -12 -1 0 20 40 60 80 100 time (ps)

Figure 3.5: The actual Stokes shift calculated from non-equilibrium trajectories for isomer 1 with the protein frozen at the moment of photo-excitation is compared with −t/τ2 curves that contain a slow component c2e where τ2 = 120ps. Several diﬀerent −1 values of c2 are explored: c2 = 2, 3 and 6kJmol .

Although the dynamics with respect to their protein and water contributions to the Stokes shift are visually diﬀerent, freezing both isomers 1 and isomer 2 at the instant of photo-excitation removes all long time dynamics (panel (c) of Figs. 3.3 and

3.4). The fact that the protein response in isomer 1 and water response in isomer

2 appear ﬂat at long times is the result of fortuitous cancellations. (We believe

56 that the long time protein response for isomer 1 and water response for isomer 2

are close to ﬂat, and there is no theoretical reason why they would be exactly ﬂat.)

A careful inspection of the protein component of isomer 1 and water component of

isomer 2 shows that in fact, similar coupled water-protein dynamics is occurring on

the time scale of τ2. Completely eliminating the contribution of protein in the FP simulations, eliminates this coupled motion and removes the slow relaxation time component from the dynamics. Hence, the slow dynamics arises from coupled water- protein dynamics, and is not an intrinsic feature of water in the potential ﬁeld of the protein. Of course, when protein motion is said to be required, it is always understood that the protein is solvated and moves in a bath of water molecules.

It has been well established that cooperative water motion, especially translational motion, accompanies protein motion beyond harmonic ﬂuctuations.44, 106–108, 143, 144

Even though long time correlations are present in the hydration layer, inherently slow water motion, in the absence of protein motion does not lead to the long-time component in the Stokes shift for W7 of myoglobin. It should be pointed out that for isomer 1 shown in Fig. 3.3 the weight of the slow component observed in the indole-water energetics is quite small although what is important is the comparison between the total Stokes shift of the dynamic protein and that of the frozen protein ensemble. It is quite clear that freezing the protein completely eliminates the slow component of the total Stokes shift observed in the dynamic protein ensemble.

It is important to check whether freezing the protein makes the water slower, and as a result may not allow for the slow component to be seen when the non-equilibrium trajectories are carried out to only 100ps for the FP ensemble. In section 3.5 we ﬁnd that water residence times increase by a factor of 1.8-1.9 when the protein is frozen.

57 7.4o o 9 o o 7.7 9 7.2 8.9 7.6 8.8 7 7.5 8.6 indole-glu4 distance (A)

indole-glu4 distance (A) 8.8 indole-lys79 distance (A) indole-lys79 distance (A) 6.8 7.4 8.4 0 50 100 150 0 50 100 150 -11.5 -13.5 ) ) ) ) -1 -1 -1 -1 -14 -15 -14 -12 -15 -14.5

-12.5 -16 -16 -15 indole-glu4 energy (kJ mol indole-glu4 energy (kJ mol indole-lys79 energy (kJ mol indole-lys79 energy (kJ mol

0 50 100 150 0 50 100 150 time (ps) time (ps)

Figure 3.6: Top panels: Time evolution of the distance of two nearby charged residues, Lys79 and Glu4, the indole chromophore in isomer 1 (left) and isomer 2 (right) following photo-excitation. Distances are measured from the center of mass of the indole chromophore to the center of masses of the side chain amino and carboxylic acid groups of the lysine and glutamic acid, respectively. In isomer 1 the distance both become smaller, while in isomer 2 they become larger. Bottom panels: The energetic response of the positively and negatively charged residues shows opposite trends for both isomer 1 and 2, and they roughly cancel. For comparison with data in Figs. 3.3 and 3.4 the interaction energy diﬀerence between La and S0 states are plotted in the bottom panels.

The Nandi-Bagchi-Zewail explanation for the slow component of the Stokes shift as

described in 3.1, is set by a residence time mechanism involving the exchange of

waters between the hydration shell and bulk water. If their mechanism was operative

we might expect a slow component of τ2 ≈ 120ps instead of 56 or 58ps, as found

for isomers 1 and 2 respectively in Table 3.1. In Fig. 3.5 we explore the eﬀects of

−t/τ2 having a very slow component c2e present in the Stokes shift for the frozen protein

simulations. We examined the analytic ﬁt to the Stokes shift of isomer 1 and doubled

the value of τ2 to 120ps. The contribution of the slow component for isomer 1 in the

−1 ﬂexible protein case was c2 = 2.4kJmol . We considered the possibility that this

58 component was present in the frozen protein simulations but with a time constant

−1 increased by a factor close to 2. We examined values of c2 equal to 2 and 3kJmol , which bracket this value, in Fig. 3.5. From Fig. 3.5, we see that the presence of a slow component with τ2 = 120ps would be clearly visible. In the ﬂexible protein simulations for isomer 2 the weight of the slow component is 6.5kJmol−1. Therefore,

−1 we also considered c2 = 6kJmol in Fig. 3.5. If a slow component with this weight was present in the frozen protein simulations, it would be quite obvious.

For the FP dynamics of both isomer 1 and 2, the total response, which is the response of the water, only has a Gaussian inertial feature and a 2-4ps time component. It is signiﬁcant that this qualitative feature of the dynamics occurs whether the protein response has no apparent slow component, as for isomer 1, or whether it exhibits a slow component, as for isomer 2. We also note that the magnitude of the water contribution to the total Stokes shift depends very little on whether the protein is frozen or not. Therefore, water in the hydration shell surrounding the protein is equally able to respond by librational motions to the charge redistribution of the chromophore with and without protein ﬂexibility.

Many locations on the protein respond to the charge redistribution following photo-excitation. Beyond the inertial component, many of these responses cancel each other, as discussed below. In isomer 2, the interaction of the chromophore with the protein backbone of the loop joining helices E and F does not cancel with any other interactions, and characterizes the overall protein response. The carbonyl and amide groups of the backbone carry substantial dipole moments, about 3.5 Debye in the force ﬁeld we are using. The loop joining helices E and F containing residues

77-86 is more ﬂexible in isomer 2 than in isomer 1. In Fig. 3.4d, it is shown that

59 0

water with 5 A of indole

-5 ) -1

protein backbone dipoles

-10 energy (kJ mol protein

-15

0 50 100 150 time (ps)

Figure 3.7: Interaction energy of the indole chromophore with water within 5A˚ of the indole, backbone dipoles of the loop connecting helices E and F, and the interaction with the total protein. The average was accumulated for non-equilibrium trajectories sampled for isomer 2.

the overall protein response past the inertial component largely arises from the interaction of backbone dipoles of this loop with the chromophore. In isomer 1, there is indeed some response from the backbone (Fig. 3.3d). However, the loop is less

ﬂexible in isomer 1 and the response is smaller. Figs. 3.3d and 3.4d show that even though the loop contains charged residues, their contribution to the long time Stokes shift is minor, and the overall response after a few picoseconds is that of the backbone dipoles.

An example of canceling interactions for both isomer 1 and 2 is shown in Fig. 3.6.

Lys79 and Glu4 are nearby charged residues. Following photo-excitation, they both move closer to the indole chromophore in isomer 1, and farther from the chromophore in isomer 2. While their spatial response is similar, these positively and negatively charged group contribute oppositely to the stabilization of the chromophore. As seen

60 0

-5 experiment ) -1 -10

-15 isomer 1 energy (kJ mol

-20 isomer 2

-25 0 50 100 150 times (ps)

Figure 3.8: Comparison of calculated and experimental Stokes shift.

in Fig. 3.6, when one interaction becomes more favorable, the other becomes less favorable. Hence their contributions roughly cancel. Besides showing how cancellations arise, this example is important because it demonstrates that protein dynamics on the ∼ 60ps time scale occurs for both isomer 1 and 2, despite the fact that the total protein response on this time scale (panel b of Figs. 3.3 and 3.4) is ﬂat at long times for isomer 1, but the major contributor to the overall long time dynamics for isomer

2. Fig. 3.7 furnishes another example of coupled water-protein dynamics occurring on a ∼ 60ps time scale for isomer 2, even though the overall water response appears

ﬂat in this time range in Fig. 3.4b. Solvation by the hydration layer surrounding the indole chromophore is seen in Fig. 3.7 to overshoot its eventual asymptotic value.

Water and protein tend to compete to stabilize the chromophore.18, 19, 45 Hence, it is

61 expected that water solvation in the hydration layer surrounding the indole moves

opposite to protein stabilization in Fig. 3.7.

The calculated and experimental20 Stokes shifts, compared in Fig. 3.8, are in

qualitative agreement at long times, especially for isomer 2. However, there exists a

sharp disagreement concerning the sub-picosecond, ultrafast behavior. In our work

on the tri-peptide we also ﬁnd a disagreement between theory and experiment for

this component. Evidently, for the system studied here, either the calculations insert

an inertial drop of ∼ −20kJmol−1 that should not be present, or the experiments

miss it. It very likely that some ultrafast solvation is missed either because of limited

experimental time resolution or the estimation of the zero-time Stokes shift. The

focus of this work is the long time behavior of the Stokes shift, which seems to be

qualitatively reproduced by our simple model.

3.4.2 Fluorescence anisotropy

The ﬂuorescence anisotropy provides information on the rotational dynamics of

the chromophore following photo-excitation. The ensemble averaging over initial

conditions after excitation, was described by 360 non-equilibrium trajectories. The

ﬂuorescence anisotropy r(t) was deﬁned in chapter 2. The anisotropy r(t) can be

ﬁtted by one Gaussian and two exponentials,

2 −(t/τg) −t/τ1 −t/τ2 r(t)= cge + c1e + c2e , (3.5)

where cg + c1 + c2 = 0.4. The parameters cg,τg,c1,τ1 and c2 are determined from the non-equilibrium trajectories for isomer 1 and 2. In Fig. 3.9 the ﬁts are compared with simulation data. The length of those trajectories does not permit an accurate

62 0.4 isomer 2 (shifted up by .05)

isomer 1

0.3 0.2

r(t) experiment 0.1

0 0.2 0 1000 2000

experiment

0.1 0 10 20 30 40 50 60 t (ps)

Figure 3.9: Anisotropy calculated from non-equilibrium molecular dynamics simulations and from experiment.7 Least-squared ﬁts are shown in addition to the simulation and experimental data. The parameters extracted from the ﬁt to simulation data are given in Table 3.2. The long-time behavior of the experimental data, characterized by a time constant of 6.6ns, is shown in the inset.

determination of the longest time component. Our calculated value of τ2 = 5.8-

5.9ns is in reasonable agreement with previously reported values of 6.43-6.56ns,145

5ns146 7-9ns,129 and 6.6ns recently measured7 for native apomyoglobin from a variety

of species. Since the anisotropy decay at this scale is controlled by the shape of

the protein globule and the viscosity of water, agreement of the long time constant

between simulation and experiment is a good indicator that GROMACS96 force ﬁeld

and SPC/E water model gives us reasonable description of the protein shape and

solvent viscosity as it did in the previous chapter for KWK.

The simulation results are dominated by the overall rotation component, and to

a lesser extent the inertial regime. The 15ps (isomer 1) and 25ps (isomer 2) compo-

nents that reﬂect the local wobbling of the indole within the protein have very small

weights. The fact that the second component has such small weight indicates that

63 isomer 1 isomer 2 (τg,cg) (.12, .042) (.16, .05) (τ1,c1) ( 15, .008) (26, .01) (τ2,c2) (5863, .35) (5863, .34)

Table 3.2: Parameters obtained by fitting the calculated fluorescence anisotropy, using the functional form specified in Eq. (3.5). The weights (c’s) are dimensionless and the time constants are in units of ps.

the amplitude of indole wobbling is small. The long component of the experimental results7 has a time scale of 6.6ns, in good agreement with the simulations and in rough agreement with previous measurements.129, 146

3.5 Water residence time and protein-water coupling in the hydration shell

isomer 1

(t)> 4 hyd

frozen protein 2 frozen protein full dynamics full dynamics isomer 2

0 0 10 20 30 40 50 60 70 times (ps)

Figure 3.10: Residence time correlation function for waters within 5A˚ of Trp7 in the excited La electronic state for isomer 1 (solid curves) and isomer 2 (dashed curves). The correlation functions for frozen protein simulations lie above those with full dynamics.

64 We calculated residence time correlation functions for water molecules within 5A˚ of Trp7 in a manner proposed by Brunne et al.,147 and applied by Makarov et al.128 to myoglobin. The residence time correlation function hnhyd(t)i is the average number

of waters at time t0 + t that were continuously present in the hydration shell since

147 time t0. As pointed out by Brunne et al., the words “continuously present” must

be quantiﬁed by the frequency with which the waters were monitored to determine

whether they were still in the hydration later. It is always conceivable that some

water molecules might have strayed outside the hydration layer between times at

which distances from the proteins were calculated. We used a time interval of 1ps for

assessing distances of waters from Trp7. The data was sampled from the last 110ps

of 140ps trajectories in the excited La state following photoexcitation. In the frozen

protein trajectories, all relaxation has concluded by this point, and the residence time

correlation functions of Fig. 3.10 represent equilibrium in the excited La state. During

this same time period, a residual portion of the slow protein dynamics is still occurring

during the 110ps over which the data of Fig. 3.10 is accumulated. In the non-frozen

case, the residence times represent an average over this phase of the motion in which

the protein, and water coupled to it, are slowly relaxing. We do not anticipate that

this slow relaxation has a signiﬁcant eﬀect on residence time dynamics.

From the initial value of hnhyd(t)i at time t=0 shown in Fig. 3.10, there are, on

average, almost 7 waters in the hydration shell of Trp7 in isomer 1, and about 3

waters for isomer 2. This diﬀerence in the number of waters around Trp7 in isomer

1 and isomer 2 is probably due to the structural readjustment of the loop region

documented in section 3.3. This is also manifested in the Stokes shift contributions

of the water in the two isomers. Our non-equilibrium Stokes shift calculations reveal

65 that the contribution from the water is 4kJmol−1 larger for isomer 1 than it is for isomer 2. As found by Makarov et al.,128 a sum of several exponentials are needed to

fit hnhyd(t)i. We found that a double exponential fit was accurate, and the residence times we report are the time constant for the slower component. Isomer 1 exhibits a faster turnover of water molecules, with a residence time of 45ps compared to the residence time 67ps of isomer 2. In part, this reflects the larger number of waters for isomer 1 within the 5A˚ envelope we use to define the hydration shell. These extra waters are more labile. The numbers of waters still in residence after 100ps is similar, much closer than the initial values, for isomers 1 and 2.

While isomer 1 can “shake off” the extra labile waters when it is not frozen, it is significant that the frozen and full dynamics plots of hnhyd(t)i in Fig. 3.10 run approximately parallel to each other for both isomer 1 and 2. Fixing the protein coordinates at the moment of photo-excitation makes some difference in the exchange of labile waters on a time scale of . 10ps, but makes less difference in the longer time scale dynamics that sets the residence time. For both isomer 1 and 2, the residence time of water in the hydration layer of the unconstrained protein is roughly

1.8 times shorter than that of the frozen protein. In the Nandi-Bagchi-Zewail model the residence time mechanism sets the time scale for the slow component of the Stokes shift. Therefore, it is important to verify, as we have done here, that the dynamics of water exchange between the protein hydration layer and bulk water is not so strongly aﬀected by freezing the protein that it would eliminate this mechanism. In section

3.4.1, we already explored the possible eﬀect of a longer residence time on the Stokes shift if the residence time did indeed coincide with the slow component of the Stokes shift.

66 As would be expected we find that longer residence time of waters of hydration correlates with close proximity to the protein. Furthermore, the lateral diffusion of water in the hydration layer is enhanced by protein flexibility.21 This sheds important insight into the nature of the coupling between protein and water motion. The coupling of the lateral diffusion of the water molecules near the indole and the motion of the indole is illustrated in Fig. 3.11 where the displacement cross-correlation of indole and its waters of solvation are plotted. The cross-correlation is positive for both the tightly bound waters with residence time tres > 50ps and the more labile waters with

20ps < tres < 30ps, indicating that the locking of water and side group translations

extends to at least 5A˚ into the solvent. The data suggests that as the indole ring

ﬂuctuates in water, it drags the solvent with it.

tres > 50ps 0.3 | (0) (0) i i r r − − ) ) t t ( ( 0.2 i i r r | · | (0) (0) N N 20ps < tres < 30ps r r 0.1 − − ) ) t t ( ( N N r r | 0 0 10 20 30 40 50 times (ps)

Figure 3.11: Cross-correlation of the normalized displacements of the indole nitrogen atom with those of the waters hydrating the indole group. The correlation is accumulated separately for waters with residence times 20ps 50.

67 3.6 Conclusions

Our studies reveal that slow (∼ 60ps) time scale component of the Stokes shift of photoexcited W7 in myoglobin arises from coupled protein-water motion. When the total Stokes shift is broken into contributions from water and protein, the slow dynamics may apparently arise from either contribution. However, protein ﬂexibil- ity is required to observe the slow Stokes shift dynamics, regardless of whether the water or the protein contribution to the Stokes shift carries most of the slow component. The surrounding protein environment of the tryptophan is explicitly involved in energetically stabilizing the excited state chromophore.

Our calculations of the Stokes shift via both linear response theory and non-

equilibrium molecular dynamics, predict a slow ∼ 60ps component to the Stokes shift,

in agreement with experiment.20 The origin of such a slow component in the Stokes

shift has been a matter of discussion and debate recently. Here we summarize previous

arguments and our conclusions regarding these issues. Bagchi, Zewail and co-workers

proposed that the slow dynamics is a manifestation of very tightly bound waters in the

hydration layer surrounding the protein.16, 17, 41, 43, 45, 100, 101, 105 In their model, the time

for waters to exchange between the hydration layer, where they are rotationally frozen,

and the surrounding bulk solvent dictates the slow time scale observed in the Stokes

shift. Alternatively, Halle and Nilsson18, 47 propose that interactions between protein

and chromophore play an active role in solvation, and that it is the slow dynamics

of the protein that leads to the observed long time scale in time-dependent Stokes

shift experiments. By repeating simulations of the same process with all protein

motions frozen at the instant of photo-excitation, we establish that protein motion

is essential for observation of the slow Stokes shift component for W7 in myoglobin.

68 We took care to verify that freezing the protein does not shut down the exchange

of water between hydration layer and the bulk. Hence, freezing the protein should

not eliminate the slow dynamics according the the Nandi-Bagchi-Zewail mechanism,

although quantitative, not qualitative, modiﬁcations as a consequence of freezing the

protein will occur because waters near a rigid protein have a longer residence time

than near a ﬂexible protein. We observe that the slow dynamics disappear when the

protein is frozen.

Shaw et al. concluded that slow components in the ﬂuorescence Stokes shift from dansyl chloride labels of α-chymotrypsin were exclusively due to slow dynamics of hydration water.148 Their interpretation of the Stokes shift was based on their previous

observation of long components of a residence time correlation function in molecular

dynamics studies.149 Our ﬁndings provide reasons to reevaluate the conclusions of

Shaw et al.: while hydration water may exhibit slow dynamical features in orientational or residence time correlation functions or diﬀusion, this does not imply that the Stokes shift dynamics will have a slow component or that the slow components, even if they have similar time scales, have the same physical origin. The crucial role of protein dynamics, as revealed by our frozen protein studies, should be considered.

Even though we have emphasized protein motion in our analysis of the slow

ﬂuorescence Stokes shift dynamics of W7 in myoglobin, the role of solvent in this process should not be deprecated. Protein motion must be taken to mean solvated

protein motion. It is ﬁrmly established that protein motion, beyond local vibra-

tional ﬂuctuations, is facilitated by solvent motion, especially by translation of water

molecules.44, 106–108, 143, 144 The coupling between protein and solvent ﬂuctuations have

69 also been demonstrated experimentally in a study of lysozyme in trehalose and glyc-

erol.150 In that work the temperature dependence of low-frequency protein vibrational

dynamics was shown to track the corresponding low-frequency dynamics of the sol-

vent.

Nilsson and Halle’s emphasis on protein motion is based on their observation that the protein contribution to the Stokes shift they calculated for monellin has a slow component, but the water component did not.18 One can only conclude that if they would have obtained Fig. 3.3b for isomer 1, Nilsson and Halle might have given up on their hypothesis since the protein contribution in that case has no slow component, or at most a very weak one. In this case, the total Stokes shift for isomer

1 contains a slow component that depends on protein ﬂexibility, even though the protein contribution to the Stokes shift has no apparent slow component. The actual slow protein dynamics is masked by canceling contributions. One should examine all components – protein, water, total, and, in fact, other dynamical variables as well – for a complete understanding of the relaxation process. The various components can cancel, and contribution from diﬀerent parts of the protein to each component can also cancel.

There is something to be learned from the apparent insensitivity of the Stokes shift

to the interaction between the indole chromophore and neighboring charge groups. In

Fig. 3.6 we see that the charged groups each contribute ∼ 1kJmol−1 to the “solvation” of the excited chromophore in isomer 2, which is small compared to the 11.2kJmol−1

[Fig. 3.4] contributed by the protein backbone. Our calculations indicate that site-

speciﬁc mutation experiments must be interpreted with caution.109 Insensitivity of

the Stokes shift to site-speciﬁc mutation cannot be taken as evidence that the protein

70 is not involved in the relaxation process following photo-excitation of a chromophore.

The protein contributes 30% of the total Stokes shift for isomer 1, and 64% for isomer

2. Yet, Figs. 3.3-3.7 indicate that replacement of any of the neighboring charged residues with an uncharged, non-polar residue would likely have minor eﬀect on the

Stokes shift. In this regard, we also note that the transition between isomer 1 and isomer 2 is signaled by the interaction between the chromophore and the protein backbone, and not by the interaction between the chromophore and nearby charged sidechain groups.

71 CHAPTER 4

A model for the water amorphous silica interface: the undissociated surface

4.1 Introduction

The interface between amorphous silica and water is one of the most ubiquitous

and important in chemical, biochemical, and environmental systems.151, 152 Besides

various forms of what is commonly known as “glass”, amorphous silica is also present

as an oxidized external layer in silicon-based devices.153, 154 The strong aﬃnity of

biomolecules for hydroxylated silica surfaces, and the variety of chemical modiﬁcations

possible, make silica a key material for chromatographic applications.155 The strong

interactions of aqueous solvent and adsorbates with the surface of silica makes this

system interesting and challenging. Speciﬁcally, the surface hydroxyl groups on silica

can form strong hydrogen-bond complexes with water, and with biological molecules,

for example via phosphate groups.156 The interaction with certain silicas can have

pathological eﬀects on the cellular system of the human body.151, 157 Silica and silicon

with an oxidized surface layer of amorphous silica153 are materials commonly used

for fabrication of micro- and nanoﬂuidic devices. Electrochemical and electrokinetic

72 function of these devices depends on the microscopic properties of the silica-water

interface.

Modeling crystalline and amorphous silica has been approached with empirical potentials,158–167 and also by ab initio simulation methods.168–176 Since the structure of silica is determined by making and breaking covalent bonds, ab initio methods are

preferred, but not always feasible. In particular, generating starting conﬁgurations

for simulations of amorphous silica involves a lengthy annealing process177 which is

not feasible using purely ab initio methods. As a result, all ab initio simulations of

amorphous silica to date are based on starting conﬁgurations generated by an anneal-

ing process involving an empirical potential. The most popular choice of empirical

potential for silica is the van Beest-Kramer-van Santen164 (BKS) model. This model

correctly reproduces the structural features of many crystalline phases of silica and

amorphous silica. While it might have shortcomings, especially for surfaces,167, 178 the

BKS model has been employed and evaluated in a large number of studies.

Our objective is the development of a potential model that is tractable for large

scale simulations, that can take advantage of well-tested models for bulk silica and

water, and that provides a pathway for integration with common force ﬁelds for

biological simulation. To accomplish these goals, we have constructed our model

as an extension of the BKS model164 for amorphous silica and the SPC/E model3

for liquid water. The BKS is a 2-body potential and the SPC/E model is a rigid,

non-polarizable water model. Both are computationally eﬃcient and have been used

extensively. Speciﬁcally the SPC/E water model has been used in the protein-water

simulations that were described in detail in the previous chapters.

73 Feuston and Garofalini have previously constructed a remarkable model for the water-amorphous silica interface.163, 179–182 In their model, silicon, oxygen, and hydrogen atoms are not pre-assigned to molecular units such as water molecules. The hydrogen and oxygen atoms may evolve to be part of either a silanol group or water molecule, depending on the course of the simulation. For example, Feuston and Garo- falini formed a hydroxylated silica surface in their simulations by placing water near a freshly cleaved surface, allowed surface chemistry to happen at 1000K, and then annealing to ambient conditions. If the model contains all the right “chemistry” that governs silica-water reactions, this is an attractive route to modeling the silica-water interface. However, it is not clear that the right chemistry is built into the Feuston-

Garofalini model. For example, when used to model pure water, 1.4% of the water molecules engage in symmetric hydrogen bonds in which a hydrogen atom is roughly equidistant to two oxygen atoms.181 Rustad and Hay183, 184 developed an improved model in this vein which was capable of yielding reasonable acid dissociation energies for orthosilicic acid in gas and solution phase. The adsorption sites of single water molecules on the dehydroxylated amorphous silica surface has been considered by

Bakaev and Steele,185 and on the hydroxylated surface by Leed and Pantano.186

Since we are ultimately interested in properties like diﬀusion and non-equilibrium

ﬂow near silica surfaces, we require that the bulk water region be described by a model for which properties like the density, diﬀusion constant and viscosity have been systematically tuned and benchmarked. Another goal of ours is to incorporate biomolecules near the silica-water interface. Therefore, instead of the Feuston-

Garofalini or Rustad-Hay models, more standard water models are desired because force-ﬁelds for biological simulations have already been developed. Unfortunately,

74 not enough atomic-scale experimental information is known about the silica-water

interface to provide a rigorous benchmark of this aspect for any model at this point.

In this chapter, we devise a model for the hydrated, hydroxylated silica surface as an appropriate extension of the BKS model for amorphous silica164 and the SPC/E model for water.3 To that end, we have attempted to cast the interaction model as much as possible in a form compatible with the BKS and SPC/E models. However, surface behavior is distinct from bulk behavior, and we have found it expedient to include some 3-body interaction terms that are not found in the BKS potential. Since it is not possible to predict ahead of the surface annealing process which silicon and oxygen atoms will be part of surface silanols and siloxane bridges, and because we aimed for a simple potential model with ﬁxed partial charges, we constrained the charges of all silicon and oxygen atoms to be those found in the BKS model. The parameters of our model were determined using ab initio quantum chemical studies on small fragments. In this respect, the procedure used to develop our model is opposite to the one employed by Cruz-Chu et al.,27 who optimized interactions parameters by matching a bulk property, the contact angle of a water drop. This procedure could only be carried out when the surface was suﬃciently hydrophobic to have a non- zero contact angle which, in practice, did not allow optimization when the surface contained silanol groups.

We anticipate that our model will be useful in empirical potential studies, and as a starting point for ab initio calculations. The model presented here should be regarded as an initial version to be re-calibrated and reﬁned by comparison with ab initio simulations and experiment. The dissociation of silanol groups is an important

75 chemical feature of the hydroxylated silica surface, leading to its characteristic neg-

ative charge. The development of the model for the dissociated surface is presented

in the next chapter along with the validation of our potential with ab initio MD

simulations.

In section 4.2 the procedure for developing our model is described in detail. The functional form of the potential and ultimate parameter values are given. This functional form should be regarded as a minimal form required to obtain reasonable physical behavior. In section 4.3 results of the simulation of the silica-water interface are presented. The protocol for generation of the slab is described. The heat of immersion is an important benchmark. Our model is shown to fall within the range of available experimental values. We also report structural features of the silica-water interface that result from our interaction model and describe a protocol for hydrox- ylating and annealing the silica surface. Finally in section 4.4, we conclude with a short discussion of the potential applications of this model.

4.2 Development of a model for hydrated amorphous silica

4.2.1 Formulation of the potential

So we could rely on a well-tested model of the bulk, we designed our model of the hydrated silica surface as an extension of the BKS164 and SPC/E3 potential. The BKS

potential is a sum of pair-wise Coulomb and Buckingham (exponential repulsion +

r−6 attraction) interactions. In the BKS model, silicon and oxygen atoms are assigned

charges of +2.4 and −1.2 respectively. To maintain a model with ﬁxed charges, we

kept the same charges for surface atoms, even though in reality the BKS charges

are artiﬁcially large and, in any case, the eﬀective partial charges at the surface are

76 expected to be diﬀerent from the bulk. In order to avoid overbinding of water to the

silica surface we found it necessary to distinguish between silanol type and siloxane

type oxygens, for the short range potentials, while using the same charge of −1.2.

As shown below, an acceptable ﬁt to ab initio data could be achieved with these

ﬁxed charges for the silanol oxygens. Charge neutrality of the undissociated surface requires that the charge on hydrogen atoms be +0.6.

It is remarkable that the BKS potential describes many crystalline forms, as well

164 as amorphous SiO2 using no more than pair interactions. We were not successful devising a potential for the surface based on pair interactions, and found it necessary to include 3-body terms. The most important is a SiOH angle bending term, which we found to be described well by the truncated Vessal form,187, 188

a 2 2 a a−1 2 3 uTV (θ, rSiO, rOH) = k θ (θ − θ0) (θ + θ0 − 2π) − π (θ − θ0) (π − θ0) − DTV h 2 i −8 8 8 exp −ρ (rSiO + rOH) , (4.1) where θ is the Si-O-H angle, rSiO and rOH are the two bond lengths, and there are

three adjustable parameters k,a and θ0. The usual truncated Vessal potential is zero

at θ0 and positive elsewhere. The exponential factor, which cuts the interaction at any θ =6 θ0 from a positive value to zero when either rSiO or rOH becomes large, thereby provides a large energetic incentive for the the SiO bond and especially the

OH bond to break. While the OH bonds are in principle dissociable, the current form of our model does not encompass dissociative behavior, least of all through a cut-oﬀ in an angle potential. Therefore, a negative energy contribution of −DTV is added

to balance the reward for dissociation that arises as an artifact because the otherwise

positive truncated Vessal potential is cut-oﬀ at large separations.

77 While a combination of Coulomb, Buckingham and Si-O-H bending potentials gave an acceptable ﬁt to ab initio data (see below), we found that thermal simulations of a model with just these interactions led to unphysical associations, hydrogen atoms that were simultaneously strongly bound to two oxygen atoms, or silanol oxygen atoms that accepted a second hydrogen, i.e. -SiOH2 groups. We blocked out unphysical O-H-O and H-O-H association using two more 3-body terms given in

Eqs. (4.2-4.3). Also included is a Si-O-Si blocking potential that is aimed at preventing silanol oxygens from forming three coordinated species on the surface shown in

Eq. (4.4) assuming that this is a defect that will not form on a realistic amorphous silica surface.

−4 4 4 ′ ′ uOSHOS (rOSH, rOSH) = k exp −ρ (rOSH + rO H) (4.2) h S i −4 4 4 ′ ′ uHOSH(rOSH, rOSH ) = k exp −ρ (rOSH + rOSH ) (4.3) ′ −4 4 4 uSiOSi(rSiO, rOSi ) = k exp −ρ (rOSi + rOSi′ ) (4.4) In the formulation of our potential, the symbol O with a subscript “X” refers to a siloxane-bulk type oxygen, the symbol O without a subscript refers exclusively to silanol oxygens, and O with a subscript “S” refers to a general silica oxygen, either silanol or siloxane. Hence Eqs. (4.2-4.3) apply to all silica oxygens while Eq. (4.4) applies only to silanol oxygens.

The total hydroxylated silica interaction potential is of the following form.

Usilica = UBKS + Usurface (4.5) N − NO − Si i 1 q2 S i 1 q2 U = Si + OS + u (r ) (4.6) BKS r r B(OSOS) ij Xi=2 Xj=1 ij Xi=2 Xj=1 ij N NO Si S q q + Si OS + u (r ) r B(SiOS) ij Xi=1 Xj=1 ij 78 NO N NO N S H q q S H U = OS H + u (r ) (4.7) surface r B(OSH) ij Xi=1 Xj=1 ij Xi=1 Xj=1

NSi NO NH NOS i−1 NH

+ uTV (θijk, rij, rjk)+ uOSHOS (rik, rjk) Xi=2 Xj=1 Xk=1 Xi=2 Xj=1 Xk=1

NH i−1 NOS NSi i−1 NO

+ uHOSH(rik, rjk)++ uSiOSi(rik, rjk) Xi=2 Xj=1 Xk=1 Xi=2 Xj=1 Xk=1

In Eqs. (4.6) and (4.7), uB(r) is the Buckingham potential, a combination of exponential repulsion and r−6 attraction. Since the r−6 term diverges as r → 0,

an unmodiﬁed Buckingham potential has an unphysical maximum at small r, and then plunges to −∞ at even smaller r. Therefore, it is standard185, 189 to modify the

Buckingham potential at short range to eliminate the unphysical maximum and make

it smoothly repulsive at small r. For interactions in Table 4.1 where C6 is not zero,

we implemented a small r patch of the form,

−r/ρ C6 Ae − r6 , r ≥ r0 uB(r)= C12 , (4.8) B + r12 , r

modiﬁed Buckingham, and the parameters B and C12 are chosen to the value and

derivative of the potential continuous at r0.

The water-silica interactions in our model are also sums of Buckingham interac-

tions. In practice, we found that we could dispense with the London dispersion term

between the silanol hydrogens and water molecules, and eliminate the Buckingham

potential altogether for interactions of water hydrogen atoms with either silicon or

silanol hydrogen atoms because a large Coulomb repulsion already precludes close

79 contacts.

N NO NO NH Si W q q S W q q U = Si OW + u (r ) + OS HW + u (r ) silica-water r B(SiOW) ij r B(OSHW) ij Xi=1 Xj=1 ij Xi=1 Xj=1 ij N NO N NO H W q q O W q q + H OW + u (r ) + O OW + u (r ) r B(HOW) ij r B(OOW) ij Xi=1 Xj=1 ij Xi=1 Xj=1 ij N NH N NH NO NO Si W q q H W q q X W q q + Si HW + H HW + OX OW (4.9) r r r Xi=1 Xj=1 ij Xi=1 Xj=1 ij Xi=1 Xj=1 ij In the above equations, the subscript “W” indicates atoms that are part of water molecules. We took the interaction between water molecules as the SPC/E model.3 and used the SPC/E charges in the interaction potential. In principle, other water- water potentials could be used in place of SPC/E. However, using diﬀerent charges on the water molecules would presumably degrade the quality of the ﬁt to ab initio

water-silica interactions. Alternatively, one could introduce an inconsistency between

water-water and water-silica Coulomb interactions.

The procedure used to ﬁt the potentials and the quality of ﬁts are described below.

Here, for the convenience of those wishing to use the potentials, the ﬁnal parameters

are collected in Tables 4.1 and 4.2. As before, O with a subscript “X” refers to

oxygen types that are not connected to hydrogens, O without a subscript refers to

silanol oxygens, and O with a subscript “S” includes all silanol and siloxane oxygens.

Besides the Coulomb potential, there are no other interactions between pairs not

listed in Table 4.1, or triples not listed in Table 4.2.

4.2.2 Adjustment to match ab initio data

The free parameters in Eqs. (4.5-4.9) were adjusted to best match ab initio quan-

tum mechanical calculations for the single-silanol and geminal fragments shown in

Fig. 4.1, with or without a neighboring water molecule. These clusters were excised

80 6 atom pair A(eV ) ρ(A˚) C6(eV A˚ ) Si-OS 18003.75 0.2052048 133.5381 OS-OS 1388.773 0.3623188 175.0000 OS-H 10907.00 0.1253934 4.088270 OS-HW 70.79500 0.3062000 0.000000 O-OW 2840.780 0.318112 230.9240 H-OW 70.79500 0.2662000 0.000000 Si-OW 1049.880 0.4000000 0.000000

Table 4.1: Pairwise potential Buckingham parameters

Atom Triplet k(eV ) θ0(deg) a ρ(A˚) D(eV ) Si-OS-H 0.164816 64.2835 −0.423721 1.85 1.24 − 1.5 H-OS-H 13.00000 0.00 0.00 1.4 0 OS-H-OS 13.00000 0.00 0.00 1.4 0 Si-O-Si 30.00000 0.00 0.00 1.6 0

Table 4.2: Three-body potential parameters. The Si-O-H parameters control the truncated Vessal angle potential of Eq. (4.1), and the H-O-H, O-H-O and Si-O-Si parameters are for the blocking potentials of Eqs. (4.2-4.4).

from a silica slab taken from molecular dynamics calculations. The dangling oxygen atoms that would be connected to the silicon atoms in the slab were capped with hydrogen atoms. This section is devoted to describing the quality of that match.

The Born-Oppenheimer energy surface was obtained using MP2 perturbation the- ory83–87 to account for electron correlation. The 6-311G** basis set was adequate to describe the energetics of silica surface fragments, and energy diﬀerences negligibly changed when the basis was improved to the 6-311++G** level. However, potentials involving interactions between water molecules and silica fragments required the

81 OH Stretch

silanol site

< Si−O−H

Capping Hydrogens

Figure 4.1: Ab initio calculations were performed for the single-silanol (left) and geminal (right) clusters shown here to determine parameters for our empirical potential. A subset of the capping hydrogens are indicated.

larger 6-311++G** basis set. All electronic structure calculations were performed using Gaussian03.190

One of the challenges of developing robust empirical potentials is ensuring an adequate sampling of the configurational space used in deriving the potentials, that will eventually be explored in statistical simulations. Our initial attempts to use configurations from molecular dynamics (MD) simulations in a force matching scheme191 were not successful for two reasons. First, our initial parameter guesses generated configurations that were too far from the ones that eventually proved to be most probable, and the desired configurations were not sampled adequately in MD simulations. We then sampled a series of configurations on coordinate grids to generate better initial parameter guesses. Even with those better initial parameters, iterating the parameters to match the energies of configurations sampled from MD simulations did not lead to physically reasonable potential functions. We eventually concluded that coordinate grids were most effective for fitting the type of potential functions proposed in section 4.2.1. Tabacchi and co-workers192 report similar difficulties in their efforts to fit potentials for NaCl by force matching. They also conclude that

82 an extensive force database is required to develop physically meaningful parameters

for their empirical potentials. Like Tabacchi and co-workers, we also attempted to

expand the conﬁgurational search space by raising the temperature of the system but

this did not aid in getting physical potentials. While Izvekov and co-workers193 have been successful in using the force matching technique, their work involved potentials that depend linearly on parameters which is not true for most of our model potentials.

Thus all the configurations that were used to fit our potentials were generated from grids that sampled a broad region of configuration space.

4.2.3 Silanol groups

The short range potential functions for silanol -SiOH groups consists of SiO and

OH stretching potentials, and an SiOH angle bending term. The SiO stretch is constrained to be that of the BKS model, facilitating use of our potential as an extension of BKS. The configurations used to generate fitting points for the silanol potentials were based on the geminal-silanol fragment shown in Fig. 4.1. These clusters were obtained from a larger slab. All the clusters were capped with hydrogen atoms where they would join the rest of the slab. The OH stretch and SiOH angle parameters were fit using a geminal cluster as shown in Fig. 4.1. The OH distance for each -SiOH group on the geminal was varied between 0.7A˚ to 1.3A˚ forming a two dimensional grid. The angle grid was formed by fixing the OH distance to approximately 0.95A˚ which is the equilibrium bond length for the OH stretch and the angle was varied between 1.1 and π radians.

Typical results comparing ab initio and ﬁtted energies are shown in Fig. 4.2. In

Fig. 4.2a, the stretching potential is tested for a geminal fragment. The complicated

83 3.5

4 3

2.5 3

2 1.5

1 1

Fitted Empirical Energies, eV 0.5 Ab Initio and Fitted Energies, eV

0 0 0 0.5 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5 3 a) Ab Initio Energies, eV b) Si-O-H Angle (rad)

Figure 4.2: Fitted vs. ab initio energies for a) OH stretches of a geminal fragment, and b) SiOH angle. In the left-hand plot, points that agree perfectly would lie on the line with unit slope.

coupling between the two OH groups are captured in an approximate way by the various Coulomb and short range terms. Fig. 4.2b shows how the truncated Vessal form [Eq. (4.1)] captures the angle bending behavior.

Figure 4.3: A conﬁguration in which a hydrogen atom is simultaneously within covalent bonding distance of two oxygens. Such divalent hydrogen conﬁgurations, as well as spurious -SiOH2 groups, are eliminated by the HOH and OHO blocking potentials, Eqs. (4.2-4.3).

84 Although the Coulomb, bond stretching and angle bending potentials described the most stable regions of the silanol fragment Fig. 4.2, this empirical potential gave rise to other, spurious minima that did not correspond to actual physically stable configurations. MD simulations performed with only the terms in the potential mentioned above gave rise to configurations in which surface hydrogens divalently bonded to two oxygens, particularly in geminal silanols because of proximity effects. This is shown in Fig. 4.3. However the divalent bonding also occurred between two silanol groups that were not members of the same geminal pair. This effect is not surprising given that the OH binding energy is significant. We also discovered that certain oxygens could acquire a second hydrogen, resulting in a -SiOH2 group. In order to eliminate these unphysical minima on the potential surface, we introduced “blocking” potentials: HOH and OHO 3-body terms which raise the energy of forming divalent hydrogen or -SiOH2 configurations. These terms [Eqs. (4.2-4.3)] have no angle dependence. They become highly repulsive when a hydrogen atom is simultaneously within covalent bonding distance of two oxygens, or when an oxygen is within covalent bonding distance of two hydrogens. The exponential range parameter ρ is set to a value that decreases these blocking potentials to nearly zero when at least one of the oxygen-hydrogen distances is typical of non-covalent hydrogen bonds. The blocking potentials were not part of a fit to ab initio data. Instead, the blocking potential parameters were adjusted by trial and error until unphysical configurations were no longer observed and physical configurations were weakly affected. There is a considerable room for adjustment of the blocking potential parameters without significantly affecting the properties of the model. Moreover, in simulations the blocking potentials are most important during equilibration or annealing at high temperature.

85 The additive constant DTV in Eq. (4.1), and the strength of the three-body blocking

potentials in Eqs. (4.2) and (4.3) are less important for simulations near 300K and might be reduced after equilibration and annealing depending on the nature of the surface. In our simulations we also found the formation of a hydrogenated siloxane species where the silanol group is shared between two silicons. Ma and co-workers have reported the formation of this species in their ab initio simulations but also found that on addition of water the hydrogenated species went away resulting in the formation of a silanol group.194 It is still unclear whether this species will exist on a

realistic surface but, given the scarcity of evidence for this species in the literature, we

discourage formation of this species in our model with the Si-O-Si 3-body potential.

Only 5% of silanol oxygens are in close proximity to a second silicon atom.

4.2.4 Water-hydroxylated silica interactions

The water-silica potentials were ﬁt using various possible paths of water approach

to the isolated silanol group shown in Fig. 4.1. By choosing likely paths of approach,

we ﬁx important regions of the potential surface. Initial testing reported below sug-

gests that the potential provides a reasonable interpolation between the conﬁgurations

where it was matched to ab initio data. In choosing paths of approach, we followed

Saengswang et al.195 and used 1) silanol donor-water acceptor, 2) water donor-silanol

acceptor, and 3) simultaneous donor-acceptor paths. These three paths are shown

in Fig. 4.4. The water-silanol separation was varied from 0.5A˚ to approximately 6A˚

to get a comprehensive sweep of the potential energy surface. The water model ge-

ometry was the SPC/E water model3 which was also used in our MD simulations.

86 Further simulations and the resulting thermodynamics of wetting indicated that ap-

plying interactions determined from water-silanol group interactions (as in Fig. 4.4)

to all oxygens on the surface leads to overbinding of water to siloxane oxygens on the

surface. We thus distinguished between silanol oxygens and siloxane oxygens. Shown

in Fig. 4.5 are three paths of approach to a siloxane cluster which we used in ab initio

calculations in an attempt to calibrate water-siloxane interactions. Notice that in

these clusters the silicons are capped with hydrogens.

Path 1 Path 2 Path 3

Figure 4.4: Paths of approach for water near silanols

Path 1 Path 2 Path3

Figure 4.5: Paths of approach for water near siloxanes

In the entire set of water-hydroxylated silica pair interactions, only the water oxygen-silanol oxygen (O-OW in Table 4.1) interaction carries a London dispersion

87 force. As in the construction of most water potentials, the dispersion forces centered on the hydrogen atoms are neglected. Furthermore, in typical configurations, water oxygens are not close to silicon atoms. Therefore, we also neglected a dispersion interaction between silicon atoms and water. It was still necessary to retain the exponential repulsion between water oxygens and all atoms of hydroxylated silica, and between silica oxygen and water hydrogens. Without the exponential repulsion present in H-OW, Si-OW, and O-HW interactions, the attractive Coulomb infinity is discovered within a few picoseconds of MD simulation, leading to unphysical dissolution of hydrogen, silicon and oxygen atoms from the slab. Even with the exponential repulsion, the Coulomb singularity still exists. However, the exponential repulsion causes the system to avoid the region of the attractive Coulomb singularities. We did not find it necessary to block out this singularity with a short-range patch as in Eq. (4.8), although this certainly could be done if needed, say, for simulations at high temperatures. Although not designed for a realistic description of aqueous dissociation chemistry, the potential form given in section 4.2.1 is in principle dissociable. Part of the freedom to dissociate Si-O bonds is accessed during annealing of the initially hydroxylated surface and leads to physically reasonable configurations.

However, our potential is not designed to model the energetics of dissociation.

The Buckingham + Coulomb form of our potential, together with the many constraints on partial charges (BKS charges for silica Si and O, SPC/E charges for HW and OW) we imposed to mesh our interface model with established bulk potentials, does not have enough ﬂexibility to simultaneously give a good ﬁt to all three paths in Fig. 4.4. Path 1 leads to the water-hydroxylated silica complex with the highest binding energy, and is therefore a probable approach that a water molecule would

88 1

0.8 Path1

0.6

0.4 Path2 0.2

-0.2 Path3 energy (eV)

-0.4 Geminal -0.6

-0.8

-1 2 3 4 5 6 distance (Å)

Figure 4.6: Fitted (open symbols) vs. ab initio (ﬁlled symbols) energies for the paths of approach shown in Fig. 4.4, and for approach of a water to a geminal fragment along the path shown in Fig. 4.7. The four paths are vertically oﬀset from each other on the graph for clarity.

make to the silica surface. Therefore, we weighted it more heavily than the other paths. Fig. 4.6 shows all the ab initio energies for all three paths of approach, and the predictions of our empirical potential for each of those paths. As can be seen from the fits, path 1 and path 3 give decent agreement with ab initio. Our model is not sufficiently flexible to simultaneously yield high quality fits to all 4 paths of approach.

We tested the transferability of our potential model, parametrized for approach of water to a single silanol, by comparing the empirical potential and ab initio results for the approach of a water molecule to a geminal fragment. Ferrari et al. have done a more extensive study on the energetics of water near geminal type silanols.196 Our path of approach shown in Fig. 4.7 was adopted from their ES-2-W scheme. As can be

89 seen in Fig. 4.6, the interaction of water with the geminal fragment is similar to that in

the single silanol, and hence our potential gives a qualitatively correct representation

of this interaction. In principle, there are many situations that should be checked

for transferability. Testing of all these situations is beyond the scope of this work,

although to some degree the veriﬁcation of macroscopic properties like the heat of

immersion (section 4.3.2) and in the next chapter, the radial distribution functions

with ab initio simulations, suggests that none of the interactions are seriously in error.

Figure 4.7: Path of approach of water to a geminal silanol fragment.

The limited ﬂexibility of our empirical potential and the constraints of matching the BKS and SPC/E model charges precludes a physically meaningful ﬁt to water interactions with capped silicate clusters in all possible situations. An example is the poor job reproducing the interaction potential between a water molecule and the siloxane-containing fragment shown in Fig. 4.5. Approach of a water to the siloxane group in Fig. 4.5 is dominated by the large positive BKS model charges on the two silicon atoms. The combination of the large charges from the BKS model and

SPC/E water model make it impossible to avoid overly attractive interactions when the water oxygen is turned toward the siloxane group (path 1) and overly repulsive

90 interactions when the water hydrogen faces the siloxane (path 2). Further testing of our model in condensed phase simulations indicated that this eﬀect is mitigated when water approaches a larger fragment with a silicon-oxygen ratio closer to 0.5 than 2. In the next chapter using ab initio simulations, we will show that despite the poor performance of the empirical potential in reproducing the paths of approach of water to a siloxane oxygen, we are still successful in reproducing the hydrophobic- hydrophilic nature of the silica surface shown in Fig. 4.12.

1.8

1.6

1.4

1.2 Path2 1

0.8 energy (eV)

0.6

0.4 Path3

0.2 Path1 0 2 3 4 5 6 7 8 distance (Å)

Figure 4.8: Fitted empirical (open symbols) and ab initio energies (filled symbols) for water approaches to siloxane fragments. Our model was designed to match the more important interactions with silanol groups (see Fig. 4.6) and, as shown here, is not sufficiently flexible to also match ab initio data for approach of waters to this siloxane fragment.

4.2.5 Orthosilicic acid

While our potential is optimized with emphasis on silanol groups on the bulk surface and their interactions with water, for completeness we document how well the

91 Table 4.3: Structural properties of gas phase orthosilicic acid. Angles are in degrees and distances in A.˚ parameter this work Sauer197 r(SiO) 1.615 1.63 r(OH) 0.95 0.95 ∠SiOH 114.69 117.15 ∠OSiO 106.76 115.79 ∠HOSiO −10.88 −33.34

potential describes isolated orthosilicic acid because this species has been considered

on several occasions in past studies (See reference 198 and references therein). The

lowest energy structure predicted by our potential is the S4 structure also found

in ab initio calculations.197 Geometrical parameters for the minimum energy gas phase structure of orthosilicic acid are given in Table 4.3. The bond lengths and angle compare well to previously published ab initio data,197 the largest deviations occurring for the HOSiO dihedral angle.

4.3 Slab Studies

4.3.1 Slab Generation

In order to test various structural and energetic properties predicted by our empir-

ical potentials we conducted a series of molecular dynamics simulations of a hydrated

silica slab with a hydroxylated surface. In this section we present the methodology

used to generate the amorphous silica slab, and afterwords present an analysis of the

structural and thermodynamic properties of the slab interacting with water. All sim-

ulations were conducted using the DLPOLY package which is particularly suited for

materials simulations.199 A time step of 1fs was used. The SHAKE algorithm was

92 used when rigid waters are present. Electrostatics were calculated using the SPME method.67, 68 A cutoﬀ of 9.0A˚ was used for the Buckingham interactions, and 3.0A˚ for the 3-body potentials.

The starting structure was bulk crystalline tridymite with no free surfaces. Its starting dimensions were 33.5A˚ by 34A˚ by 39A,˚ consisting of 896 silicon atoms and

1792 oxygen atoms. The protocol that was used to generate amorphous silica from the starting material was adopted from cycle I-IV of Huﬀ and co-workers.177 It began with heating to 8000K followed by annealing at 4000K and 2000K. We cleaved the surface by opening a gap in the z dimension and followed with annealing for a limited time at

300K. Shown in the table below are the population of non-bonded oxygens (NBO’s),

2-membered (2M) rings and 3-coordinated silicons on the surface as a function of annealing time following cleavage. Also shown is the silanol density that resulted from diﬀerent annealing times after hydroxylation with the procedure described below.

Variable annealing time subsequent to cleavage provides a mechanism for controlling the surface population of geminal, vicinal and isolated silanols.

Table 4.4: Population of NBO’s, 2M-rings, and 3-coordinated silicons on silica surface as a function of annealing time of a freshly cleaved surface at 300K. annealing time (ps) NBO’s 2M-rings 3-coord.silicons silanol density (nm−2) 0.10 48 24 18 6.60 0.25 28 32 13 5.56 1.65 17 31 4 4.45 2.00 16 26 4 3.89

Unfortunately, the detailed structure of the aqueous silica surface, its mechanism of hydroxylation, and the distribution silanol groups between isolated, vicinal and

93 geminal silanols has not been conclusively established. Because we are not performing ab initio simulations, and realistic ab initio simulations to anneal a silica surface and react it with water are not currently feasible, we generated a hydroxylated starting conﬁguration via two transformations of the cleaved and partially annealed surface:

2M rings were reacted to form vicinal silanols and NBO’s reacted to form geminal silanol pairs. Ceresoli et al.178 have studied 2M rings on the silica surface. Bakos and co-workers,200 Masini and Bernasconi,201 Du et al.,202 and Mischler et al.203 have performed ab initio and mixed quantum-classical simulations to study how water interacts with amorphous silica in bulk and have found that water interacts with 2M rings on the silica surface to generate two close by silanol groups, known as vicinal silanols. Following the mechanism elucidated in these works, we converted each 2M ring into vicinal silanols according to the reaction,

O−H O−H O Si Si + H 2 O Si Si O O . (4.10)

For lack of more detailed information on mechanisms of hydroxylation, we use the NBO’s to only generate geminal silanols. Reviewing the situation in 1979, Iler151 stated that geminal silanols probably do not exist on a dried silica surface. How- ever, subsequent NMR experiments indicated that geminal silanols are present on the surface of both dried silica, and silica in contact with water vapor.204–206 The NMR experiments by Maciel and coworkers were performed either on silica in contact with water vapor, or on samples evacuated at room temperature or 200◦C.204–206 They determined that geminal silanols comprise only ∼ 6% of the total silanol population.

In contrast, second harmonic generation (SHG)207 and evanescent wave spectroscopic experiments208 on silica in contact with liquid water indicate that ∼ 80% of the

94 silanols are geminals. Also, X-ray photo-electron spectroscopy (XPS) studies of poly-

crystalline quartz in contact with solutions of varying pH found a nearly constant

1.8:1 ratio of surface oxygen to surface silicon atoms, indicating that most surface

silanol sites were geminals.209 There is considerable justiﬁcation for transforming non-bridging oxygens (NBO’s) on the partially annealed cleaved surface to a geminal silanol by the reaction,

O H−O O−H

Si + H 2 O Si . (4.11)

This procedure was also followed by Rignanese et al.210 However, it is likely an over- simpliﬁcation and will require validation with ab initio MD simulations. Walsh et

al. have investigated the reaction of NBO’s with water, ﬁnding that the reaction can

lead to either geminal or vicinal silanols, depending on the surface structure adja-

cent to the NBO.211 Our hydroxylation and annealing procedure, as described below,

brings several properties of our surface in line with experimental measurements, but

it must be regarded as preliminary pending further theoretical and experimental ef-

forts to characterize the hydroxylated amorphous silica surface. The actual chemistry,

as indicated above, is almost certainly more complex. Signiﬁcant reconstruction of

the surface took place during annealing of the initial hydroxylated conﬁguration de-

scribed above. The initial hydroxylated surface was quenched to a local potential

energy minimum before further annealing. The quenching process removed some

particularly high energy and presumably unrealistic features. For example, in rare

instances a single silicon atom has an NBO attached to it and is also part of a 2M-

Ring. Under our hydroxylation protocol, this leads to a presumably bad starting

conﬁguration with three hydroxyl groups attached to one silicon. We have found

95 that quenching of these high energy conﬁgurations can induce reconstruction of these

over-hydroxylated silicons to more reasonable conﬁgurations. Alternatively, excess

silanol groups can be transferred to 3-coordinated silicons. Ab initio simulations by

Ma et al.194 provide some evidence that such reconstruction is realistic. Similarly

geminal silanols can also form on silicons that are 5-coordinated and some care may

have to be taken in the initial few ps of the simulations to ensure that the surface

remains physically stable. Adjusting the magnitude of DTV to a more negative value

is useful at this stage to ensure that the energy made available by relaxation of the

surface does not induce dissociation of fragments from the surface.

Once hydroxylated, the surface was resistant to further “chemical” change. We analyzed hydroxylated surfaces for unusual bonding conﬁgurations and found they were quite rare. For example, the surface with silanol density of 6.4nm−2 exhibited three

NBO’s [Fig. 4.9a] that reformed after all the NBO’s following cleavage were reacted according to Eq. (4.11). Also, we found three 3-coordinated oxygens [Fig. 4.9b] and a single silicon that was triply hydroxylated [Fig. 4.9c]. The vast majority of the bonding maintained its original pattern. Due to the scarcity of resources in the literature, the actual concentration of these surface defects remains an open question. For our heat of immersion calculations we generated two surfaces with diﬀerent silanol densities using the protocol described earlier. The surface with a higher silanol density of

6.4nm−2 is in good agreement with those quoted in some previous studies.151, 212 This surface yields ∼70% geminals and ∼30% vicinal silanol groups. Surface relaxation can lead to isolated silanols as well. Because the silicons prefer to be 4-coordinated, surface relaxation due to an overcoordinated silicon can result in the transfer of a hydroxyl group to an undercoordinated silicon but only occurs to our knowledge at

a) b) c)

Figure 4.9: Rare defects taken from the amorphous silica surface with a silanol density of 6.4nm−2. a) NBO, b) 3-coordinated oxygen, and c) silicon with three hydroxyl groups. Defects are indicated with arrows.

the beginning of the simulations when the surface is at a high potential energy. This

is in good agreement with second harmonic generation (SHG)207 and evanescent wave

spectroscopic experiments,208 but a much higher fraction of geminals than found by

NMR spectroscopy.204–206 Rarivomanantsoa et al. have found a signiﬁcant number of

NBO’s at a surface governed by the BKS potential.213 They report that 15% of the surface oxygens are NBO’s. The surface with the lower silanol density of 4.0nm−2 also falls in the range of silanol densities quoted by other reports in the literature. This surface yields 26 2M-Rings on the surface and 17 NBO’s. The relative populations of geminal and vicinals are now ∼40% and ∼60% respectively, in better agreement with NMR studies as mentioned earlier on.

Clearly, more theoretical and experimental work is needed to better characterize the silica surface. Besides resolving inconsistencies in experimental data, better theoretical annealing of the silica surface, both with respect to better annealing protocols and extending treatment to ab initio methods, is needed. For example, Ceresoli and co-workers178 ﬁnd that performing the annealing using the BKS potential generates

97 good bulk silica but generates a surface that has too many over and under coordinated silicons and oxygens. However, these surface properties depend upon the annealing protocol and sampling temperature.213, 214 The annealing procedure for the cleaved silica surface aﬀects the starting point for our hydroxylation procedure, and ultimately the characteristics of the hydroxylated surface.

4.3.2 Heat of Immersion

Since the properties of amorphous silica depend on preparation, it is not surprising that the heat of immersion varies between different experiments and different samples.151 Measurements of the heat of immersion date back to the work of Boyd and Harkins, who reported a value of 0.6Jm−2. Taylor and co-workers215, 216 report the heat of immersion as 0.16Jm−2 and claim that it is independent of the sample specific surface area. However, Makrides and Hackerman217 demonstrate a specific surface area dependence of the heat of immersion and quote ranges between 0.16 and

0.88Jm−2 depending on the type of dehydration pre-treatment to rid the system off extraneous water. In fact, Makrides and co-workers quote a value as high as 1.45Jm−2 for one of their surfaces. Chikazawa and co-workers218, 219 report heat of immersion values for various silicas in the range of 0.157 − 0.23Jm−2 and suggest that this value is quite sensitive to the degree of crystallinity of the surface as well as the density of surface silanols. Clearly the experimental values cover a range of values, due to differences in porosity and specific surface area, different degassing temperatures, and the type and extent of defects on the surface. Despite the variability in experimental values, the heat of immersion provides an important benchmark for our model.

98 The theoretical calculation for the heat of immersion requires three separate simulations: a dry silica slab, pure water, and hydrated slab. The dry slab simulation was done with NVT dynamics, and a separation of 60A˚ between the top of one slab and the bottom of its periodic replica in the next cell. The pure water and hydrated slab simulations were conducted using NPT dynamics. They contained 3320 waters. For the slab-water simulation, we generated a starting condition by inserting waters into the system no closer than 3.5A˚ from the slab. During the subsequent NPT dynamics

the water approached the slab and penetrated it to some extent, as described in the

following section. Water did not penetrate to the voids deep in the bulk that the BKS

model silica is known to contain. These voids were not ﬁlled by other means in the

hydrated slab simulation. This is justiﬁed because such deeply buried water would

not be removed during the drying process and would not contribute to the heat of

immersion.

The pressure-volume contribution to the enthalpy of immersion was calculated and found to be negligible compared to the average potential energy. The data used in the calculation of the heat of immersion is given in Table 4.5. In the table we show the heat of immersion for two surfaces with diﬀerent silanol densities. The surface with the lower silanol density yields a heat of immersion that is in better agreement with most of the reported experimental values. However, the heat of immersion for the higher silanol density system also falls at the higher range of quoted heats of immersion. Long range corrections for the r−6 dispersion energy, which are only approximately implemented for inhomogeneous systems, were a minor correction to the total energy, and were not included in the numbers reported in Table 4.5.

99 Table 4.5: Average potential energy for systems consisting of 3220 water molecules used to calculate the heat of immersion. Error bars for each run are estimated by the blocking method5 by partitioning each run into 4 blocks. The combined surface area of the two sides of the silica slab is 2.16 × 10−17m2. The two sets of data are for surfaces containing silanol densities of 4.0nm−2 and 6.4nm−2. System henergyi (4.0nm−2) henergyi (6.4nm−2) dry silica slab (eV ) −52397.38(0.084) −52962.60(0.073) water (eV ) −1596.80(0.12) −1596.80(0.12) hydrated slab (eV ) −54031.81(0.62) −54671.62(0.42) enthalpy change (eV ) −37.63(0.82) −112.22(0.62) heat of immersion (Jm−2) 0.279(0.0061) 0.832(0.0046)

H−Bonded Chain

Silica Surface

Figure 4.10: Hydrogen bonded silanol chain on our silica surface.

4.3.3 Structural features of the hydroxylated silica-water interface

The radial distribution functions (rdf’s) for silanol O-H and Si-O separations in-

dicate that the equilibrium O-H and Si-O distances are, as expected, approximately

0.96A˚ and 1.63A˚ respectively. The Si-O rdf essentially reﬂects the contributions of

100 bulk Si-O pairs. However these distances do not signiﬁcantly change on the silica sur-

face. The Si-O-H angles vary depend on the surface morphology and type of silanol.

Our surface yields a fairly broad range of angles between 105 and 130◦. Previous simulations and electronic structure calculations yield an Si-O-H angle of about 121◦.

The smaller angles sampled on our surface are indicative of pockets of silanol clusters on the surface that form linear hydrogen bonds as shown in Fig. 4.10 which eﬀectively reduces the Si-O-H angle.

0.06 0.015 ρ (siloxane oxygen) OX ρ (water oxygen) OW 0.05 ρ O (silanol oxygen)

0.04 0.01 ) ) -3 -3

0.03 density (Å density (Å 0.02 0.005

0.01

0 0 -40 -30 -20 -10 0 10 20 30 40 z (Å)

Figure 4.11: Number densities for water and siloxane oxygens (solid curve and long dash curves, referred to left axis) and silanol oxygens (short dash curve, referred to right axis) along a direction perpendicular to a silica slab with surface silanol density of 6.4nm−2.

Shown in Fig. 4.11 are the number density distributions for silanol, siloxane and

silanol oxygens along a direction perpendicular to the surface of a slab with silanol

density of 6.4nm−2. Our z-density for water relative to the surface are somewhat

sharper than those calculated by Warne et al.220 Regions on the silica surface with

101 high silanol densities and hence closely knit hydrogen-bonded networks Fig. 4.10 serve

as regions of higher water density and potentially higher heats of immersion. This is

consistent with results from Takei and Chikazawa218 and Fubini et al.221 who propose that hydrogen bonded clusters of silanols can lead to higher heats of immersion due to stronger water-silica interactions. This will be conﬁrmed in our discussion of Figs. 4.12 and 4.13.

Figure 4.12: Figure showing aﬃnity of water for hydrophilic regions on the silica surface. See discussion in text.

Further evidence for the aﬃnity of water to regions of higher silanol density is seen

in Fig. 4.12 which illustrates existence of hydrophilic regions and hydrophobic patches

on our silica surface. It should be noted that Fubini and co-workers222 distinguish

hydrophobicity and hydrophilicity of the silica surface according to the presence of

diﬀerent silanol groups (vicinal vs isolated) on the surface. While this may have an

eﬀect on the aﬃnity of water to the silanols, we distinguish the hydrophobic and

hydrophilic regions based on the relative silanol and siloxane density. Fig. 4.12 is a

snapshot looking down into the slab in the z-direction. The patches outlined in the

102 left panel of Fig. 4.12 contain only surface siloxane bonds with no silanols, and are

apparently hydrophobic as seen in the distribution of surface waters shown in the

right hand panel. This effect is quantified in Fig. 4.13 which depicts the difference in

the radial density of water oxygens surrounding silanol oxygens and surface siloxane

oxygens. Furthermore in Fig. 4.12 one can also see that the presence of voids that can

lead to water clustering and possible channels for water trickling and diﬀusing into

the surface. Bakos and co-workers200 have elucidated mechanisms for water diﬀusion

through amorphous silica.

0.02 −3 o 0.015 (A ) OW ρ 0.01

0.005

2 4 6 o 8 10 12 r (A)

Figure 4.13: Radial density of water molecules surrounding silanol oxygens (solid curve) and surface siloxane oxygens (dashed curve). Siloxane oxygens were identiﬁed as surface siloxanes if they were at least 12.5A˚ from the center of the slab. (See Fig. 4.11.) Asymptotically, the density of water oxygens is approaching one half the 1 ˚−3 bulk water density ( 2 0.0335A ) because there are no water molecules in the half space below the surface.

4.4 Conclusions

Further understanding of the surface properties of amorphous silica is central to

the theory of electrochemistry and electrokinetic phenomena, and important for a

103 variety of applications. The silica surface ﬁgures prominently in the literature on

the electric double layer, and induced electrokinetic eﬀects.223, 224 The availability of

reactive silanol groups furnishes a strategy for tailoring the silica surface by chemi-

cal modiﬁcation for selective metal ion extraction.225 The surface potential of silica

leads to electroosmotic flow,224 which is a useful way to induce fluid flow in micro- and nanochannels.226 The surface potential can be controlled by pH and chemical

modiﬁcation.

Covalent attachment or physical adsorption of biomolecules to silica is a com-

mon strategy for analytical and biomedical applications.227–234 In the case of human

carbonic anhydrase, the regions of the protein that bind to silica nanoparticles has

been examined.235 The eﬀect of succinylation on the adsorption of lysozyme to the

amorphous silica surface of an oxidized silica wafer has also been reported.236 Time-

resolved ﬂuorescence has been used to monitor the adsorption on silica particles of

small peptides,28 including the lys-trp-lys peptide, a target of our recent theoretical

study19 which was described in detail in the second chapter.

The toxicity of silica, which is highly dependent on the surface properties, has

been discussed in detail by Iler151 and Fubini.157 Biomolecule-silica interactions in-

volve electrostatic, hydrogen bonding and hydrophobic forces. The complexity and

nature of these forces and their eﬀect on equilibrium and non-equilibrium properties

of biomolecules is poorly understood at the atomistic scale. A deeper understanding

of the interactions between water, biomolecules and amorphous silica using molecular

simulations may provide further insight into physical, chemical and toxic eﬀects of

amorphous silica.

104 The empirical model for the water-amorphous silica surface that we have described in this chapter, does not allow for dissociated silanol groups on the surface. This is essential for the description of the surface charge of the silica surface at most relevant pH conditions, and the modeling of electrokinetic phenomena in this system. The details of the development of the dissociated surface is described in the next chapter where we also describe the validation of our empirical potential using ab initio MD simulations on a smaller hydrated slab system.

105 CHAPTER 5

The dissociated amorphous silica surface: Model development and evaluation

5.1 Introduction

In chapter 4 we described the development of our empirical potential for the undissociated water-amorphous silica interface. Our silanol densities and heat of immersion were in good agreement with available experimental data. In this chapter we describe the extension of that model to include dissociated silanol groups on the surface. At pH 7 the amorphous silica surface is negatively charged. This arises due to the deprotonation of silanol groups on the surface. An accurate and detailed treatment of the dissociated surface, is critical for modeling of electrokinetic phenomena as well as the interaction of biomolecules with the silica surface.

Feuston and Garofalini163, 180 have developed an impressive model for the water- amorphous silica interface. In their model, which has been applied and extended,182, 237–239 the silicon, oxygen and hydrogen atoms are not ﬁxed to any molecular unit such as a silanol or water group, but instead can spatially evolve over the course of the simulation based on the interaction potential. Garofalini and co-workers have recently

106 developed an improved dissociative water potential for molecular dynamics simula-

tions,240 and have applied it to study the chemisorption of water on silica surfaces

yielding important insights into the surface chemistry of water near silica.238, 239, 241, 242

To our knowledge, the applicability of this model to dissociated silica surfaces has not been assessed. Rustad and Hay183 have also developed a dissociated model that

yields reasonable acid dissociation energies for orthosilicic acid in the gas and aque-

ous phase. The applicability of this model for very large scale simulations needed for

device applications is however limited.

Schulten and co-workers27 have quite recently developed an empirical potential for

the water-amorphous silica interface. Their model is exclusively for water interact-

ing with a rigid silica prepared using other models. Their intended ﬁtting procedure

was to choose interaction parameters to match the water contact angle reported for

quartz surface as a function of the degree of hydroxylation.243 The parameters for

their surface without silanol groups were adjusted to reproduce the water contact

angle for the corresponding quartz surface. However, Schulten and co-workers re-

port that their model could not reproduce the experimental contacts angles of Lamb

and Furlong243 for any ﬁnite degree of hydroxylation. However, contact angle mea-

surements at low degrees of hydroxylation are diﬃcult because the dehydroxylated

surface rapidly reacts with water, and other measurements reports very diﬀerent

contact angles for dehydroxylated silica.244 Jenkins and co-workers245–247 simulated

amorphous silica nanoparticles in water starting with initial conﬁgurations obtained

from DMOL3248 calculations. Then the simulation was continued using empirical potentials from the OPLS-AA force ﬁeld249 and borrowed from a simulation of the

quartz surface.250 Puibasset and Pelenq have modeled the adsorption of water in

107 mesoporous silica from sub-monolayer coverage to saturation pressures using grand

canonical Monte Carlo simulations.251–255 Treatment of quartz surfaces involves similar atom types, but compared to silica is considerably simpliﬁed by the regularity

of the quartz surface. MacKerell and co-workers156 have developed a model for the

quartz-water interface which is not designed to characterize dissociated silanol groups.

Freund,256 and Qiao and Aluru257, 258 have studied electrokinetic transport in elec-

trokinetic channels where the negative charge is distributed on Lennard-Jones wall

particles. In these simple models, the heterogeneity and surface roughness are not

captured. Aluru and co-workers have also performed similar studies for the interface

between water and a more realistic, electrically neutral quartz surface.259 Lorenz et al.260, 261 have employed a modiﬁed version of the silica-water potential developed

by Schulten and co-workers27 to study charge inversion in the presence of divalent

cations and electrokinetic phenomena associated with mono- and divalent cations.

In addition to developing an empirical potential, we have used ab initio molecular dynamics (AIMD) simulations in this work, to test several features of our empirical model, including the strong variability in relative hydrophobicity/hydrophilicity with surface silanol density reported in our earlier work.24, 25 The physisorption and

chemisorption of small numbers of water molecules near silica has also been exam-

ined previously by ab initio methods. Physisorption has been studied using quantum

chemical fragment calculations by Saengsawang et al.195 Cheng et al. studied the re-

262 action of an SiO2 molecule in a cluster with up to six water molecules. Sutton and

co-workers have studied the hydroxylation mechanisms of diﬀerent silica clusters with

ab initio optimization methods using DFT.211 These calculations shed important in-

sight into the activation barriers for chemical reactions between water molecules and

108 silica clusters, although thermal eﬀects are not included in these calculations.211 Sim- ilar types of calculations have recently been performed by Kone˘cn´yand Doren263 and

Ugliengo and co-workers.264 With an eye toward dissolution of silica, Criscenti et al studied the reaction of a silanol-containing cluster with a hydronium ion in the presence of four water molecules.265 Ma et al.194 have conducted ab initio MD simulations of water near diﬀerent defects found in silica clusters and ﬁnd that several waters are needed for the hydroxylation mechanisms they observe. More recently Hamad, and

Bromley266 have conducted longer thermal ab initio simulations to study the hydroxylation mechanisms of non-bridging oxygens (NBO’s) in small silica clusters. These results suggest that the NBO’s are a negatively charged, closed-shell species, whose hydroxylation is quite sensitive to the surface morphology. Du et al. have investigated the reaction of one or two water molecules with an amorphous silica surface using

QM/MM techniques,202 yielding information about the initial steps of silica surface hydroxylation. Ab initio molecular dynamics have been used to study the reactions of water with the amorphous silica surface by Miasini and Bernasconi201 and Mis- chler et al.,203 and the pKa of silanol groups on crystalline silica surfaces by Leung et al.267 Tielens et al.268 initiated an AIMD simulation of a hydroxylated silica slab using a starting point from Garofalini’s empirical potential models, and studied the surface structure, making detailed comparisons with experiment. They calculated the deprotonation energy of silanol groups and the binding energy of individual water molecules. Trilocca and Cormack have reported AIMD studies of liquid water near the related water-bioglass interface269 and Leung et al. have reconstructed the bonding arrangement on crystalline silicate surfaces to mimic the amorphous surface.267 To

109 our knowledge, ab initio molecular dynamics of the amorphous silica-water interface, along the lines of what we provide in section 5.3, have not been reported.

We have performed AIMD simulations on a small hydrated silica slab in which in which one surface does not contain silanols and the other surface contains several silanols, one of which is dissociated. The relative wetting properties of silanol-rich and silanol-poor regions is conﬁrmed, although the AIMD system was too small to quantitatively compare radial density distributions. We also compared AIMD and empirical results for a single orthosilicic acid molecule in water. Our potential was not designed to ﬁt the properties of orthosilicic acid, but at least the comparison is much more direct because the size of the silicate system is not an issue. We

find that the number of waters in the first and second solvent shells compares well for orthosilicic acid, although the radial densities of waters surrounding the silanol groups of orthosilicic acid are more structured in the AIMD simulations. A direct comparison between AIMD and empirical potential results is clouded by several factors. The empirical potential simulations of a silica surface encompass much more surface variability than the smaller, AIMD system. A further limit on our ability to benchmark our empirical potential with AIMD is the limitation on the accuracy of currently available density functionals and the numerical methods available for their implementation. The BLYP270, 271 and PBE272 functionals, as normally implemented, tend to over-structure liquid water and under-estimate the diffusion constant.273–275

The degree of over-structuring is sensitive to the details of the implementation, and system size.275 Lee and Tuckerman have shown that very accurate basis sets are needed to converge liquid state properties,276, 277 including the diﬀusion constant.278

110 Exceptionally large charge-density cut-oﬀs are needed to obtain a converged water density.279

In section 5.2 we describe the potential form that is used to model our interface between the dissociated silica surface, water and salt. Within this section we provide all the parameters of the model for the use of interested readers. We also compare the quality of our empirical potentials to the ab initio quantum chemistry cluster calculations that are used to generate our potentials. A comparison of some properties from the ab initio MD simulations on the smaller system to those predicted from our empirical model are reported in section 5.3. We also describe speciﬁc chemical events that occur during the ﬁrst few picoseconds of our AIMD simulations. Finally we end with a conclusion in section 5.4.

5.2 Development of a model for dissociated amorphous silica

5.2.1 Formulation of the potential

Our goal is to model the amorphous silica/water interface using a computationally inexpensive model with sufficient realism to capture essential features of the electrical double layer, electrokinetic phenomena and adsorbate binding. These phenomena require simulations that extend to large spatial and temporal scales. Models that can describe surface chemistry, either so-called dissociating potentials163, 179–184 or AIMD methods, are extremely valuable, but they are not sufficiently tractable for the large- scale calculations we envision. The chemical bond structure will be fixed in the model we propose, although the surface is not constrained to be rigid. For example, the equilibrium between undissociated and dissociated silanols will not be dynamic.

For many purposes, the eﬀects of the chemically diverse features of the silica surface

111 can be captured by a distribution of various species on a surface of suﬃcient size, or

a collection of diﬀerent surface realizations.176

Like our empirical potential for the undissociated amorphous silica surface,24, 25 our model for the hydrated dissociated amorphous silica surface extends the BKS model for bulk silica164 and SPC/E model for water3 to describe the water-silica interface.

Hence the bulk silica and water regions are described by models that have been

tested in a variety of physical situations. The BKS and SPC/E potentials succeed

in describing physical properties of silicates, both crystalline and amorphous, and

water, respectively, but they also have limitations. Among the limitations, especially

for the BKS model, is unrealistically large partial charges, which are in place to

mimic other physical eﬀects. Concern about the large partial charges was a major

motivation for us to compare with AIMD results. The simplicity of these models is

both a virtue and limitation: a virtue in the sense that large-scale simulations are

possible, but a limitation in that, even with the extensions put in place for surface

species, the functional form cannot ﬁt all the available data obtained in fragment ab

initio calculations.

In keeping with the BKS model,164 all silicon and oxygen atoms of the silica are

assigned charges of +2.4 and −1.2. The BKS potential is a sum of pair-wise Coulomb

and Buckingham (exponential repulsion + r−6 attraction) interactions. In order to

avoid over-binding of water to our undissociated silica surface, we found it necessary

to distinguish between silanol type and siloxane type oxygens, for the short range

potentials.24, 25 As shown before, an acceptable ﬁt to ab initio data could be achieved with these ﬁxed charges25 for the water-silanol clusters. Charge neutrality of the

undissociated surface requires that the charge on hydrogen atoms be +0.6. We have

112 added a dissociated oxygen type, O− to include dissociated groups on the surface.

The charge of the O− group was required to have a value of −1.6 to maintain a charge of −1 for each dissociated silanol generated in our simulations,

As mentioned above, our potential is designed to maintain a given bonded con-

ﬁguration, and not to predict making or breaking of chemical bonds. In some cases, the model has to be extended to prevent unintentional, and sometimes unphysical, bond formation driven by strong Coulomb interactions. Our potential for the undissociated surface included 3-body components that prevented the hydrogen atoms of silanols from binding to more than one oxygen atom.25 We refer to these components as “blocking potentials”. After the introduction of O− groups, thermal simulations without the additional blocking potentials yielded species where the dissociated oxygen group (O−) formed new bonds, either bonding to more than one silicon, mim- icking a newly formed siloxane bond, or forming another (unphysical) species where the dissociated oxygen is divalently bonded to a silanol hydrogen and a silicon atom.

We introduced two blocking potentials in addition to those used for the undissociated surface, given below in Eqs. (5.1) and (5.2), which stabilized the chemical bond structure.

−4 4 4 ′ ′ uSiODSi(rSiOD , rODSi ) = k exp −ρ (rSiOD + rODSi ) (5.1) −4 4 4 ′ ′ uSiODH(rSiOD , rODH ) = k exp −ρ (rSiOD + rODH ) (5.2) − Eq. (5.1) is a 3-body interaction between the O of a dissociated silanol group (OD) and two Si atoms (Si, Si′). Eq. (5.2) is a similar potential involving a Si atom, O−, and the hydrogen of a nearby silanol group.

Since the BKS potential164 consists of Buckingham potentials between the oxygen atoms, we also included three other Buckingham interaction potentials between each

113 pair of O− groups, a silanol oxygen and O− group, and ﬁnally an O− and siloxane

oxygen. The total silica interaction potential including dissociated groups on the

surface is now of the following form,

U = Upair + U3−body (5.3) − N N 1 q q U = i j + u (r ) (5.4) pair r ij ij Xi=2 Xj=1 ij While Buckingham potentials are often used to describe inorganic solids like silica,

Lennard-Jones potentials are commonly used for water, as for SPC/E, ions in water, and biomolecules. Since we need to interface with common force ﬁelds, we employed

Lennard-Jones potentials, denoted by the symbol “LJ”, for the salt, water and silica interactions described below. The procedure used to ﬁt the potentials and the quality of ﬁts are described in the following section.

For the convenience of those wishing to use the potentials, the ﬁnal parameters forming the interaction potentials Upair and U3−body for the extension of our undissociated surface, are collected in Tables 5.1, 5.2 and 5.3. Readers are referred to our previous work for the other interaction parameters that were unchanged in modeling the dissociated surface.25 In the tables, the subscript “X” refers to oxygen types that are not connected to hydrogens but diﬀerent from dissociated types (i.e. O−), the subscript “D” refers to oxygen types that are dissociated, and the subscript “H” refers to oxygens that are part of silanol OH groups.

5.2.2 Parameter adjustment to match ab initio data

Using fragments excised from a silica surface, ab initio quantum mechanical calculations were performed from which we ﬁt our empirical potentials. As in our previous work,25 the parameters of empirical potentials are adjusted to match ab initio data

114 6 atom pair A(eV ) ρ(A˚) C6(eV A˚ ) Si-OD 13536.40 0.219247 128.344 OD-OD 1388.773 0.3623188 175.0000 OD-H 5907.000 0.1254160 0.000000 OD-OW 6533.490 0.284692 336.7540 OD-HW 70.79500 0.306200 0.000000 + Na -OH 5151.600 0.2725004 60.44529 + Na -OX 5151.600 0.2763590 60.00000 + Na -OD 40286.40 0.2133588 70.40000

Table 5.1: Pairwise potential Buckingham parameters

Atom Triplet k(eV ) θ0(deg) a ρ(A˚) D(eV ) Si-OD-Si 1000.000 0.00 0.00 1.6 0 Si-OD-H 100.0000 0.00 0.00 1.6 0

Table 5.2: 3-body interactions parameters

ion/atom pair ǫ(eV ) σ(A˚) + Na -OW 0.005406 2.8760000 Cl−-Si 0.010823 3.8805759 − Cl -OW 0.005406 3.7840000 Cl−-Na+ 0.004336 3.4920000 Cl−-H 0.006378 3.6253307

Table 5.3: Pairwise potential Leonard Jones parameters

generated for coordinate grids. This section is devoted to describing the quality of the match between our empirical potentials and ab initio data. The Born-Oppenheimer energy surface was obtained using MP2 perturbation theory83–87 to account for electron correlation. We use the 6-311++G** basis set and all electronic structure calculations were performed using Gaussian03.190

115 Dissociated groups

a) b)

12 O 10

Energy (eV) 4

0 1 1.5 2 2.5 3 3.5 4 - Si-O Distance (Å)

Figure 5.1: Fitted (solid line) vs. ab initio energies (solid black circles) for b) Si-O− stretch for fragment shown in a).

The potential for the dissociated groups Si-O− consists of a single Si-O− Buck-

ingham plus Coulomb interactions. The Si-O− distance in the fragment shown in

Fig. 5.1a is varied between 0.7A˚ and 4.0A,˚ and the resulting energies used to ﬁt the

Buckingham potential form. The quality of the ﬁt for the Si-O− stretch is shown in

Fig. 5.1b.

As indicated earlier, we found that thermal simulations without blocking poten-

tials yielded conﬁgurations as seen in the left panel Fig. 5.2 where an O− is divalently

bonded to two silicons. We also found that the hydrogens of silanol oxygens can

transfer to dissociated oxygens during the simulations as seen in the right panel of

Fig. 5.2. In this defect, the hydrogen on the dissociated oxygen group originated via

the deprotonation of the silanol oxygen shown in translucent red. Our model is not

116 Figure 5.2: Left panel shows the formation of a 2-membered ring involving a dissociated oxygen that is divalently bonded to two silicons. The dotted white arrow points in both cases to the dissociated oxygen involved in the interaction. In the right panel, the dotted yellow arrow shows the hydrogen that originates from a one of the hydroxyl groups of a geminal silanol.

intended to capture realistic deprotonation and protonation of oxygen species on the surface. In order to prevent new chemical structures from forming on the surface, we inserted three-body blocking potentials as described in Eqs. (5.1) and (5.2). These were not ﬁt to ab initio data. Instead, the parameters were adjusted by trial and error until these defects no longer occurred. Our potential form also includes the BKS

Buckingham potential between the dissociated oxygen type and all other oxygens and silicons of the silica to ensure that the surface bond structure remains intact.

Water-dissociated silica interactions

The water-dissociated silica potentials were ﬁt using a path of approach for a water molecule near a dissociated group shown in the left panel of Fig. 5.3. The water-dissociated oxygen separation was varied from 1.8A˚ to approximately 13A˚ to obtain a comprehensive sweep of the potential energy surface. The water geometry

117 Path 1 Path 2

Figure 5.3: Paths of approach for water near a dissociated silanol

was ﬁxed to that of thee SPC/E model,3 and not allowed to relax as it approached the

dissociated silanol. This scheme is similar to our design of a potential between water

and undissociated silanols, for which the reader is referred to our previous work.24, 25

In most common water-water and water-ion potentials, only the water oxygen carries a non-Coulombic interaction, like a Lennard-Jones potential. The potential surface for these common water potentials contains basins where the potential diverges to −∞ when a hydrogen is superimposed on an oxygen. These unphysical regions are never discovered in simulations. However, the dissociated silanol oxygen carries a large negative charge and the attractive Coulomb inﬁnity was discovered in preliminary simulations. We found it necessary to include an exponential repulsive Buckingham between the dissociated oxygen and water hydrogen (OD-HW potential).

In order to test the transferability of our water-dissociated silica potential to another path of approach, a water molecule was brought toward a dissociated oxygen shown in the right panel of Fig. 5.3. Ab initio calculations indicate that path 1

118 2 2

Path 1 Path 2

1 1 Energy (eV)

0 0 2 4 6 8 10 2 4 6 - - O - OW Distance (Å) O - OW Distance (Å)

Figure 5.4: Fitted (solid line) vs. ab initio (ﬁlled symbols) energies for the paths of approach shown in Fig. 5.3. On the left are path 1 energies and on the right path 2 energies.

(Fig. 5.3) is the more favorable path for approach of a water to a dissociated silanol.

We were not successful in reproducing this feature in our empirical potential using the available ﬂexibility in the Buckingham + Coulomb form of our potential, together with the many constraints on partial charges (BKS charges for silica Si and O, SPC/E charges for HW and OW). Fig. 5.4 shows all the ab initio energies for the two paths of approach, and the predictions of our empirical potential for each of these paths.

Rather than “split the diﬀerence”, we chose to ﬁt the ab initio results along path 1

because preliminary simulations indicated that the binding geometry of path 1 was

the preferred, even when the most stable orientation of an isolated water was the

bifurcated structure of path 2. This tendency is conﬁrmed for the ﬁnal form of the

119 potential. Fig. 5.5 shows the distribution of the angle between the vectors OW-OD and

− OW-HW for waters within 3.5A˚ of each O group on the dissociated surface. These

results show that in the thermalized simulations the cosine of the angle of one of the

two water hydrogens is close to 1, and hence path 1 is the most likely orientation

on the surface despite the fact that our empirical potential predicts a higher binding

energy for a single water molecule along path 2. In Fig. 5.5 there is a second peak near

1 cos θ = − 3 for the hydrogen not hydrogen bonding to the dissociated oxygen. The inset in Fig. 5.5 reveals a very small peak corresponding to the bifurcated structure.

0.4

0.2

probability 5 0 0.2 0.4 0.6 0.8

0 -1 -0.5 0 0.5 1 cos(θ)

Figure 5.5: Distribution of the dot product between unit vectors linking water oxygens to a dissociated surface oxygen (OW −OD) within a distance of 3.5A˚, and vectors along each of the two hydrogen bonds. The data conﬁrms that in the thermal simulations, path 1 (Fig. 5.3) is favored over path 2. Inset shows a small peak near the cosine of half the tetrahedral angle, the angle of the bifurcated structure of path 2.

120 Na+ and Cl− silica and water interactions

Initial simulations indicated that the Na+ ions can strongly interact not only

with dissociated silanols, but also silanol and siloxane oxygens. For this reason we

selected fragments from our simulations with and without a dissociated silanol, where

a Na+ ion interacts with all species in order to generate empirical potentials for these

interactions.

a) Na +b) Na + c) − OH O − OO OH Na + OH

Figure 5.6: The three fragments used for silica-sodium interactions labeled a) with a single OD, b) with a single OD and silanol OH and c) with three silanol OH’s. Unlabeled red-spheres correspond to siloxane oxygens in our empirical potential. The blue sphere is the sodium ion.

Shown in Fig. 5.6 are the three fragments that were used for the ab initio calculations. The ﬁrst fragment consists of a sodium ion interacting with a single dissociated oxygen and siloxane oxygens. The second fragment consists of a sodium ion interacting with the silanol and siloxane oxygens while the third fragment consists of a sodium ion interacting with all three species of oxygens. The free parameters of the sodium-oxygen Buckingham potential given in Table 4.1 were adjusted to match the ab initio binding energies.

121 For the fragments with a dissociated oxygen, it was not possible to generate a full potential energy surface representing the approach of a Na+ ion to a surface fragment using ground state ab initio methods. Without solvent, the ground state of this system at large separations is a neutral sodium atom and neutral fragment. The ground state becomes ionic in character as the sodium approaches the fragment. Hence we relied on the binding energy to ﬁx the non-Coulombic interaction parameters between the

Na+ ion and silica, the partial charges being constrained to the BKS values. The binding energy was calculated by separately calculating the energy of the ion-fragment complex, and then the energies of the isolated ion and fragment.

+ + ∆Ebind = E(fragment/Na ) − E(fragment) − E(Na ) (5.5)

The comparison of the empirical and ab initio binding energies of a Na+ ion to the

three fragments shown in Fig. 5.6 are reported in Table 5.4. The Si-O bond length

and the position of the sodium ion was initially optimized with an ab initio calculation

for the ﬁrst fragment shown in Fig. 5.6a. The Si-O bond length used in the other two

fragments was very close to the optimized bond length obtained for the ﬁrst fragment.

Fragment ab initio (eV) empirical (eV) Frag 1 -6.44 -5.59 Frag 2 -6.85 -7.35 Frag 3 -3.05 -2.98

Table 5.4: Fitted and ab initio binding energies for silica-Na+ fragments.

Chloride ions are repelled from a negatively charged silica surface and, compared to sodium, chloride ions will have considerably weaker interactions with the silica

122 surface. Hence, the interactions between the chloride ions and the silica surface were

calibrated without further quantum chemical calculations using available potentials

in the GROMOS96 force ﬁeld.280 Our preliminary simulations also indicated that the

Cl− ions quickly explore the Coulomb inﬁnity between the Cl− ions and positively charged silicon and silanol hydrogen atoms. For this reason short range LJ potentials were inserted between these species. These potentials were derived using combining rules with potentials from the GROMOS96 force ﬁeld. The interaction parameters between the sodium and chloride ions and water were obtained from previous work by Dang.281 The parameters used in our simulations are shown in Table 5.3.

5.3 Comparison of ab initio and empirical results

5.3.1 Simulation methods

In this section we describe the evaluation of our empirical potential using ab

initio MD simulations on a smaller hydrated slab system. Owing to computational

feasibility, AIMD simulations were limited to rather small systems. The starting

conﬁguration for the AIMD simulations was generated by annealing a bulk crystalline

silica tridymite structure with no free surfaces measuring 10.13A˚ by 17.55A˚ by 8.275A,˚

and consisting of 32 silicon atoms and 64 oxygen atoms using the BKS potential164

with dispersion interactions truncated to half of the shortest side of the box. The

protocol that was used to generate amorphous silica from the starting material was

adopted from cycle I-IV of Huﬀ and co-workers,177 as in our previous work. We

cleaved the surface by opening a gap in the z-dimension, followed by annealing for

5ps at 300K. This small surface yielded one 2-membered ring on one surface and

no structural features on the other surface that would lead to silanol groups. The

123 2-membered ring was converted into a vicinal silanol group, initially yielding a total of 2 silanols on one of the surfaces and no silanols on the other. After hydroxylation a total of 71 waters were added to the system. This hydrated silica slab was then used as input for the ab initio MD simulations. Further reaction of water with the surface during the ab initio MD simulations led to the appearance of more silanol groups on the side that already contained silanols, and none on the other side of the slab. This is appealing because it furnished a means to test our findings25 that silanol groups make the silica surface hydrophilic, while surfaces depleted in silanols are relatively hydrophobic. Unfortunately, we were unsuccessful in conducting a classical simulation of systems of the hydroxylated surface using our empirical potential due to technical limitations implementing 3-body interactions in the DLPOLY package for a small system size. For this reason we could not use a starting configuration for the ab initio MD simulations obtained by first equilibrating with our empirical potential, or compare data for AIMD and empirical simulations of exactly the same system.

The AIMD simulations were conducted using Quickstep which is part of the CP2K package.282, 283 In these calculations, ab initio Born-Oppenheimer molecular dynamics is used for propagation of the classical nuclei. The electronic orbitals are converged to the Born-Oppenheimer surface at every step in the molecular dynamics simulation. The wave function was optimized using an orbital transformation method284 in conjunction with the DIIS scheme,285, 286 as described in Ref.283. The convergence criterion for optimization of the wave function was set to 10−6. Using the Gaussian and plane waves (GPW) method, the wave function was expanded in the Gaussian

DZVP basis set. While a triple-zeta basis set was not feasible for the silica slab, simulations using the larger TZV2P basis set were used to check convergence of our radial

124 distribution functions with respect to basis set size for orthosilicic acid in water, as

reported below. An auxiliary basis set of plane waves was used to expand the electron

density up to a plane wave cutoﬀ of 300 Ry. We used the Becke-Lee-Yang-Parr gradi-

ent correction270, 271 to the local density approximation and Goddecker-Tetter-Hutter

(GTH) pseudopotentials.287 A time step of 0.5fs was used in all ab initio simulations.

During the ﬁrst 3ps of the simulation, we observe several chemical processes that oc-

cur on the surface. These chemical processes will be documented in detail later. At

this stage, reaction with water addes 3 silanols to the surface that already contained

2 silanols. Exchange of hydrogen and oxygen atoms between the water molecules and

atoms on the silica surface results in the formation of an extra proton that, during

the length of our simulations, ﬂuctuates between two Eigen structures and samples

a Zundel complex during the ﬂuctuations. The presence of the excess proton in the

solvent near the surface during the course of the simulation suggests that the silica

slab is negatively charged, which is conﬁrmed below. The simulation with the proton

in the bulk was then run for a total of approximately 22ps. For data analysis, the

ﬁrst 6ps of this simulation was treated as equilibration. An additional simulation was

begun from a conﬁguration chosen from the ﬁrst 3ps of this simulation, where the

proton was replaced by a Na+ ion. This simulation was run for a total of approxi-

mately 15ps. For the data analysis, the ﬁrst 4.5ps of the run with Na+ was treated as

equilibration. All the AIMD simulations described were conducted within the NVE

ensemble.

We also conducted AIMD simulations of orthosilicic acid using the DZVP and

TZV2P basis sets. These simulations consist of a single orthosilicic acid molecule

(Si(OH)4) surrounded by 66 water molecules in a box of side length 12.75A.˚ Using the

125 same methodology described above, AIMD simulations of length 20ps were conducted

using the DZVP basis set and 15ps using the TZV2P basis set. Simulations of this

system were also performed using our empirical model.

Our empirical simulations for the dissociated surface consists of a box measuring

33.24A˚ by 33.24A˚ by 144.22A.˚ Along the box height of 144.22A,˚ the silica slab occupies approximately 108A˚ and water ﬁlls the remainder. The charge density of the surface was 0.795e nm−2. The dissociated groups in our empirical model, are formed by explicitly choosing silanol groups for deprotonation to form O− groups. Due to

the lack of any experimental or theoretical insight, the silanols are deprotonated in

a random fashion except that we never deprotonate both hydroxyl groups of geminal

silanols because we expect that charge repulsion will make doubly-dissociated gem-

inals a high energy species. For the simulations reported here using our empirical

model, dissociated sites are chosen so that they are separated by at least 6A.˚

5.3.2 Radial densities near silanol groups of silica and orthosilicic acid

Shown in Fig. 5.7 is a comparison of the radial distribution functions for water

near the silanol oxygens and siloxanes from our empirical model, and for the ab initio

simulations for the two systems described above. We note that the striking diﬀerence

in water density near silanol and siloxane oxygens, originally noted in our study of

the undissociated surface,25 is conﬁrmed by AIMD. Previously we had reported25 that

our empirical model did not perform favorably in reproducing the paths of approach

of a single water molecule to a siloxane group compared to ab initio results. This

discrepancy does not appear to directly aﬀect the hydrophobic/hydrophilic property

of the surface. Water is depleted near siloxanes regardless of the proximity of silanol

126 0.04 empirical AIMD AIMD 0.03 ) -3 0.02 (r) (Å ρ 0.01

0 8

4 n(r)

0 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 r (Å) r (Å) r (Å)

Figure 5.7: Radial density of water (top row), and cumulative number of neighboring waters (bottom row) near silanol (solid line) and siloxanes (thick dashed lines) for empirical model shown in left panel, AIMD simulation with proton in middle panel and AIMD simulation with Na+ shown in right panel. The green and red thick lines are radial densities near siloxanes in only hydrophilic and only hydrophobic regions respectively.

groups. It occurs on both sides of the AIMD slab, the side with no silanols and the side with 5 silanol groups (red and green curves in Fig. 5.7).

The comparison between empirical and AIMD in Fig. 5.7 shows a slight under- binding, and an apparent lack of structuring of water by our empirical potential compared to AIMD. The radial distribution function (RDF) for the water oxygen-silanol oxygen peaks at about 3.0A˚ in our empirical model, but is peaked at about 2.7A˚ in

127 0.04

0.03 ) -3

(Å 0.02 ρ

0.01

0 10 8 6

n(r) 4 2 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 r (Å) r (Å) r (Å) r (Å)

Figure 5.8: Radial density of water (top row), and cumulative number of neighboring waters (bottom row) near four individual silanol groups from empirical potential simulations.

the ab initio simulations. Studies of orthosilicic acid reported below confirm that part of this trend can be attributed to the empirical potential parameters, which tend to under-structure water near silanol groups. However, very limited sampling of silanol group environments in the AIMD runs also contribute significantly to the difference between AIMD and empirical results in Fig. 5.7. As noted earlier, it was not possible to carry out empirical and AIMD simulations on exactly the same system. The empirical potential simulations were performed on a much larger sample. The surface area of the slab used in the empirical potential simulations is approximately 8 times that used in our AIMD simulations. Thus the empirical potential simulations encompass

128 a much larger range of silanol environments. The variety of local environments is illustrated by radial density plots for water near four individual silanol groups in our empirical potential simulations shown in Fig. 5.8. A buried silanol group is found in the left-most plot, and the cumulative population plot beneath it shows that relatively few waters are surrounding it. All four examples exhibit a sharper first peak than the overall average for the empirical potential surface in Fig. 5.7, where such features are washed out. The right-most plot in Fig. 5.8 shows a silanol group with abundant exposure to water and a pronounced minimum between first and second peaks. In contrast to the diversity encompassed by the empirical simulation, the environments for the five silanol groups in the ab initio simulations were relatively similar and individual radial water densities near individual silanol groups for the AIMD runs did not show strong variation. In order to obtain a quantitative comparison of the radial distribution functions, larger AIMD system sizes over multiple realizations that have similar surface morphology to those used in our larger empirical model would be required.

In the left and right panels of Fig. 5.9 we compare the radial densities of sodium ions and water about dissociated groups and the radial density of water about sodium ions from our empirical model and AIMD simulations respectively. As mentioned before, the AIMD simulations consist of only a single sodium ion while the empirical model simulations are averaged over many sodium ions and dissociated O− groups. As for silanol groups (see discussion of Fig. 5.7), we cannot make a direct comparison of

O− groups averaged over the entire empirical potential surfaces with a single O− group in the AIMD simulation. With these caveats, a comparison of the positions of the maxima of the various densities suggests that our empirical model for the dissociated

129 surface at least does not contradict the AIMD results. The O−-Na+ density (over

10 dissociated oxygens) peaks at about 2.3A˚ in the AIMD simulations and 2.45A˚ for

− the single dissociated oxygen in our empirical model. The OW-O density peaks at

about 2.65A˚ in the AIMD simulations and 2.6A˚ in the empirical model and ﬁnally

+ the Na -OW density peaks at about 2.4A˚ in the AIMD and at 2.45A˚ in our empirical

model. The empirical model qualitatively reproduces the trend observed in the AIMD

− simulations of a larger ﬁrst peak position in the O -OW radial density compared to

− + + the ﬁrst peak positions in the O -Na and Na -OW densities.

0.2

Empirical 0.1 AIMD 0.15

0.1 0.05

0.05

0 1 1.5 2 2.5 3 3.5 4 1 1.5 2 2.5 3 3.5 4 r (Å) r (Å)

+ − Figure 5.9: Radial density of Na ions near O groups (solid thick line), OW near − + O groups (solid dashed lines) and Na near OW (solid dotted line) for our empirical model in the left panel and AIMD simulations in the right panel.

The radial densities of the water oxygens and atoms on orthosilicic acid are shown in the ﬁgure Fig. 5.10. The radial densities show good agreement between the DZVP

130 Si - OW O - OW H - OW 0.08

0.06 ) -3 0.04 (r) (Å ρ 0.02

0 30

20 n(r) 10

0 2 3 4 5 6 2 3 4 5 6 1 2 3 4 5 6 r(Å) r(Å) r(Å)

Figure 5.10: Radial density of water (top row) and cumulative number of neighboring waters (bottom row) near silicon, oxygen and hydrogen atoms of orthosilicic acid shown for DZVP (solid black), TZVP (solid dashed) and empirical model (solid dotted).

and TZV2P basis sets suggesting that the radial densities in Fig. 5.7 confirming the hydrophilic (hydrophobic) property of silanols (siloxanes), is at the very least qualitatively converged with respect to basis set. Convergence with respect to the charge density cut-off was not explored.279 We find that our empirical model, which was not designed to model orthosilicic acid, under-structures the water near the orthosilicic acid. However, the cumulative neighbor populations shown in the bottom row of

Fig. 5.10 demonstrate that the number of waters near orthosilicic acid matches well between AIMD and our empirical model.

131 5.3.3 Description of surface chemistry in AIMD simulations

We observed interesting chemical processes occurring on the surface within the ﬁrst

3ps after a freshly cleaved silica surface was exposed to water in ab initio simulations.

This resulted in the formation of three more silanol groups on one surface. Some of these important events will be reviewed in this section. These results should be viewed as preliminary information on processes that deserve much further study. It should be noted that the starting configuration for the AIMD simulations was not pre- equilibrated using our classical potential and hence represents a high energy starting configuration that is subject to significant surface relaxation. Further work is needed to show how sensitive the occurrence of these chemical events are to larger system sizes, and different initial surface morphologies that may arise from annealing and equilibration protocols using our classical model.

In the schematic shown in Fig. 5.11, three separate process that occur on our surface are illustrated. The ﬁrst process shows the conversion of an isolated silanol to a geminal silanol and another isolated silanol, resulting in the addition of two more silanols to the surface. The intermediate steps are seen more clearly in Fig. 5.12.

As a water molecule binds strongly to the silicon atom of the isolated silanol, one of the Si-O bonds associated with the silicon atom lengthens resulting in a non-bridging oxygen (Fig. 5.12i). At the same time, the water molecule splits donating an OH

+ group to the silicon, transiently forming a hydronium ion H3O (Fig. 5.12ii). The proton that forms the transient hydronium is then recaptured by the newly formed silanol. Simultaneously, the hydrogen that was originally added as part of the OH group to the silicon, is transferred to the non-bridging oxygen (Fig. 5.12iii). The resulting product is a geminal silanol and an isolated silanol (Fig. 5.12iv). The role of

132 1) H H H H O O + O O + H2O Si O Si Si Si

2) H O + + 2 H2O Si + H O Si 3

3) H H O H O + 2 Si Si

Figure 5.11: Three different chemical processes that occur within the first 3ps of our AIMD simulations labeled 1-3. The first shows the conversion of an isolated silanol to a geminal silanol an another isolated silanol. The second shows the formation of an isolated silanol and a hydronium ion and the third shows a single water molecule sticking to an exposed silicon atom on our hydrophobic surface.

the formation of transient hydronium ions during the chemisorption of small numbers of waters onto the silica surface has previously been observed by Du et al. in QM/MM simulations, by Mahadevan and Garofalini using a dissociating potential model,238, 240 and, for large silica clusters, by Ma et al. with ab initio MD simulations.194

Snapshots from the second hydroxylation scheme of Fig. 5.11 are shown in Fig. 5.13.

A two-coordinate silicon is transformed into an isolated silanol along with the transfer of a proton to the water. Ma and co-workers194 who have also conducted ab initio

MD simulations of water near silica clusters, found that the two-coordinate silicons in their simulations were highly unreactive with water. In our simulations we observe that as the water molecule strongly binds to the under-coordinated silicon, the OH

133 i) ii) iii) iv)

Figure 5.12: Steps in the formation of a geminal and isolated silanol from an initial single silanol, process (1) in Fig. 5.11. The atoms of the water molecule that reacts with the surface are shown in blue in all four frames. i) Arrows point to water that attacks silicon atom and Si-O bond that begins to break. ii) Arrows point to the non bridging oxygen formed after the Si-O bond breaks and the hydronium ion transiently formed. iii) Arrow points to the proton transferred from the newly formed silanol to the NBO. iv) Final products are a geminal and a single silanol.

group of the water is transferred to the silicon, and the proton is transferred to the

+ surrounding water forming a hydronium ion H3O . During the transfer of the OH group from the water to the silicon, one of the Si-O bond lengths associated with the silicon increases by approximately 0.2A.˚ This process involves charge separation

between the slab and the solvent, as illustrated by the charges in Table 5.5 obtained

using the DDAP10 charge partitioning method from 192 conﬁgurations after an ex-

cess proton is transferred to the solvent. The silica slab carries close to a full electron

charge (−0.923), and the solvent a corresponding positive charge. All the oxygens

of the silica slab have a charge close to −0.8, including NBOs. After a proton was

transferred to the solvent and the surface was stabilized, we could identify a buried

NBO within a cleft on the surface which was solvated by a single water molecule.

This could be considered as the location of the excess charge on the silica slab.

134 Species Slab + excess proton Slab + Na+ Slab −0.923 −0.807 O (Silanols) −0.659 −0.690 O (Siloxanes, hydrophilic side) −0.830 −0.792 O (Siloxanes, hydrophobic side) −0.782 −0.794 NBO −0.832 −0.904

Table 5.5: Average charges of species in AIMD simulations. Charges were obtained according to the DDAP10 charge partitioning scheme, which is based on the electron density.

i) ii) iii)

Figure 5.13: The left and middle frames illustrate steps in the formation of an isolated silanol from an under-coordinated silicon, scheme 2 of Fig. 5.11. The atoms of the water molecule that reacts with the surface are shown in blue in these frames. i) Water attacks an undercoordinated silicon atom. ii) An OH group is added to silicon and hydronium ion formed. iii) The frame on the right shows a water molecule on the hydrophobic surface that binds to an exposed silicon atom without further reaction during the length of the AIMD simulation.

The initial conﬁguration for the AIMD simulation with the Na+ was constructed

+ + by replacing a proton from the newly formed H3O (Fig. 5.13ii) with a Na . The

newly formed silanol (Fig. 5.13ii) was deprotonated to form a non-bridging oxygen

(NBO), and the proton transferred to a nearby siloxane oxygen which was converted

135 thereafter into a silanol. The charge partitioning analysis was conducted for 192

conﬁgurations sampled from our simulations with the Na+. The magnitude of the

charges are shown in Table 5.5. The average charge of the Na+ in our simulations is

+0.726 indicating that a signiﬁcant amount of the positive charge has leaked to its

surroundings. Furthermore the data also suggests that a signiﬁcant proportion of the

formal −1 charge of a singly-dissociated silica surface leaks out on to its environment.

Charge transfer between solvated ions and solvent has already been reported in several

systems. Klein and co-workers288 conducted ab initio simulations of a zwitterionic peptide, halide anions and alkali cations in water. They observed a substantial amount of charge transfer between the carboxylate terminus and the solvent (0.1e). Similar values were also found for K+ and Na+ ions. Chloride and bromine anions were found to transfer more electronic charge (0.26e) onto the surrounding solvent.

It is interesting that the charges of the oxygens of hydrophilic silanol groups are less than the oxygen from hydrophobic siloxane bonds in Table 5.5, once again conﬁrming that hydrogen bonding interactions are not purely electrostatic. The magnitude of the density derived charges from the AIMD simulations, especially for silica atoms which follow the BKS model, are less than the charges used in our model. However, these diﬀerences do not preclude qualitative agreement between the empirical and AIMD predictions of the hydrophobic/hydrophilic property of the silica surface. Future work in the development and improvement of empirical models for amorphous silica may require adjustment of the charges in the empirical potential, guided by data shown in Table 5.5.

Finally, we ﬁnd that the oxygen of a single water molecule interacts intimately with a 4 coordinated silicon atom throughout the length of our simulation on the

136 hydrophobic side of the silica surface (third scheme of Fig. 5.11 and right panel of

Fig. 5.13). The Si−OW distance for this water molecule ﬂuctuates between 1.8−2.0A.˚

Although the silicon atom is quite exposed to solvent, we do not observe any chemistry occurring at this site within the timescales of the simulations conducted. Perhaps longer simulations would lead to a hydroxylation event.

5.4 Conclusions

In this chapter we described the extension of the empirical model for the water-

amorphous silica interface to include dissociated silanols which is essential for an

accurate modeling of electrokinetic phenomena and the interactions of biomolecules

with the surface. The extended model now includes deprotonated silanol groups,

where water, sodium and chloride ions can interact with the surface. We deployed

the same strategy that was used in the previous chapter, ﬁtting the parameters of

our empirical potential to accurate ab initio cluster calculations.

In chapter 4 we showed that our empirical model did a reasonable job in reproducing the experimental hydration enthalpy of silica. We also showed that our silica surface is characterized by hydrophilic and hydrophobic patches which aﬀects the wetting behavior of water. In this chapter we described the validation of our empirical model using ab initio MD simulations of a smaller hydrated slab system. Both the ab initio MD simulations and our empirical model reproduce the hydrophilic- hydrophobic property giving us more conﬁdence in the validity of the model. During our ab initio MD simulations, we also observe several chemical processes that result

137 in the formation of silanol groups on the surface. More detailed calculations are required, to verify that these mechanisms are realistic and not an artifact of starting our simulations from an unrelaxed surface.

Having constructed and evaluated our model for the dissociated amorphous silica- water interface, we can now move on to some important applications. The silica surface has important applications in both fundamental aspects of electrokinetic phe- nomena223, 224 as well as its use in biomedical applications.289 In the next chapter two important applications of the model are highlighted. The ﬁrst involves the use of our model to study the molecular details of the Stern layer which is an important problem in physical chemistry. The second involves the modeling of small peptides near the silica surface. In order to simulate biomolecules near the surface, we require interaction parameters between the atoms of the biomolecules and the silica surface.

In the next chapter we describe how these interaction parameters were obtained and illustrate some preliminary predictions of the binding modes of the peptide near the surface using our model that is interfaced with the GROMOS96 forceﬁeld.65

138 CHAPTER 6

Applications of the model: Stern Layer Physics and Biomolecules near Silica

6.1 Introduction

In the previous two chapters we described the development of a tractable model

for the water/amorphous silica interface,25 and extended it to treat dissociation of

the silanol groups,26 ··· Si-O-H → · · · Si-O− + H+, which gives the surface a negative

charge. The bulk water and amorphous silica regions are described by the SPC/E3

and BKS164 potentials, respectively. The complex hydroxylated amorphous silica

surface depends on preparation history, and has not been precisely characterized,

either experimentally or theoretically.152 However, we believe that our model captures

enough features correctly to qualitatively describe electrokinetic phenomena near this

important interface.

The calculated heat of immersion agrees with experiment.25 Benchmarks against

more accurate ab initio simulations are only feasible for smaller system sizes and

run times, and would have to be repeated over many realizations of the disordered

surface before quantitative comparison with larger analytical model simulations can

be performed. However, the benchmarks that we have performed indicate that our

139 interaction model captures at least one important feature of the water/amorphous

silica interface, the relative hydrophobicity of siloxane (··· Si-O-Si··· ) compared to silanol (··· Si-O-H) groups. The silica surface is a patchwork of domains of varying hydrophilicity and hydrophobicity, according to the local surface density of silanol groups (Fig.12 of Ref.25). The distinction between hydrophilic and hydrophobic regions is captured well by the empirical potential model. In this chapter we will show that the presence of hydrophobic and hydrophilic patches on the surface, appears to be one of the factors that also aﬀects the movement of ions in the Stern layer.

In this chapter we brieﬂy describe two applications of our model. In section

6.2, the application of our model in unraveling the molecular details of the Stern layer is presented. In section 6.3 we brieﬂy illustrate our procedure for simulating biomolecules near the silica surface. The application of the model to study the binding modes of certain peptides near the silica surface is then discussed within that section.

Finally we end with a conclusion of our main results in section 6.4.

6.2 Stern layer physics

It is well known that for a charged surface near an electrolyte, an imbalance in the cation and anion distribution occurs near the surface to compensate the surface charge. This is known as the electric double layer.223, 290 When an electric field is applied to the electrolyte solution, the cations and anions respond the external force. The cations will move in the direction of the electric field while the anions will move in the opposite direction. This motion is also known as electrophoretic motion. If the field is applied parallel to a charged surface, the net charge in the

ﬂuid, or charge segregation near a surface, will induce a net body force on the ﬂuid

140 causing ﬂuid motion known as electroosmotic ﬂow. The static and dynamic properties

of the electrical double layer is a classic problem in physical chemistry, biology and

colloid science. There are also many important applications of this phenomenon. For

example, electroosmotic ﬂow provides a method to generate controlled ﬂuid transport

in nanoscale devices,291 and a microscopic understanding of electrokinetic transport is essential for predicting device characteristics.

It is well established that the observed electroosmotic flow is less than the amount expected based on the measured surface charge density σ0. Hence the electrokinetic charge density σelkin(the observed charge) is not equal to σ0. This led Stern in 1924 to propose that an immobile layer of fluid and counter-ions lies next to the surface23 as this would imply that only the hydrodynamically mobile part of the double layer is “seen”.292 Separation of the ion atmosphere into the immobile Stern layer and a mobile diffuse outer layer, the Gouy-Chapman-Stern model, has become a canonical part of the double layer literature, although certainly more elaborate models have been proposed.293 Charmas and co-workers for example, have advanced the possibility of a four layer model which is an extension to the triple layer model,294 to describe the layering of counterions and co-ions near the charged surface. However, in all these models and in the bulk of the scientific literature that invoke these models, the existence of a stagnant layer of fluid extending 3 to 10A˚ from the surface is a concept that is taken very literally.292, 293, 295 Fig. 6.1 shows the classical picture of the Stern layer from a recent review article and a popular text book on electrochemistry. In this section we will describe the application of our model to understanding the foundation of the Stern model for the surface of amorphous silica and dispel the myth that a stagnant layer of liquid exists within the Stern layer.

141 Figure 6.1: Current concepts of the Stern layer: a) A recent review article by Yuan 8 et al., showing the electroosmotic velocity veo(x) vanishing at a plane outside the Stern layer, and b) a popular text book on electrochemistry by Bockris, Reddy, and Galdoa-Aldeco9 (page 883) depicting ions of the Stern layer as “stuck”.

When the Stern model is used within the framework of electrokinetic phenomena, the surface where hydrodynamic stick (no-slip) boundary conditions are enforced, resides near the boundary between the Stern layer and the diﬀuse layer. While the

Stern model successfully rationalizes a vast body of experimental data, certain conceptual problems have arisen. If the water and ions in the Stern layer is considered completely static, then the process of surface conduction, the contribution to ionic current arising from the altered charge density near the surface,296, 297 cannot be accounted for. Surface conduction becomes increasingly important with smaller channel size and also with lower salt concentration, as the bulk region contributes less to the total current relative to the counter-ion atmosphere of the charged surface. Under these conditions, the Stern layer contains a signiﬁcant fraction of the total counter-ion population, and the remaining counter-ion population cannot account for observed surface conduction. Most of the experimental evidence for oxides is based on the fact

142 that conductance measurements indicate a substantially higher surface charge than electrophoretic mobilities.298, 299 If the Stern layer is considered as a region where both ions and water are immobile, then one is forced to conclude that ions within the immobile layer have mobilities near bulk values, a model known as the dynamic

Stern layer,296, 297, 300–303 to describe the measured surface conduction.

Using the empirical model that was presented in the previous two chapters, we now have the machinery to address the validity of these ideas. We find that a more complex picture of the surface region can account for surface conduction without invoking the passage of ions through immobile solvent. It should be noted that there have been some attempts using molecular simulations to challenge the validity of the existence of stagnant layers of water near charged surfaces.259, 304 However these studies have involved the application of unrealistic and unvalidated models for the charged surface without a deeper analysis of the molecular details of the Stern layer as we have done using our model. To explore the static and dynamic properties of a partially dissociated silica surface, an electric field was applied along the x-axis seen in Fig. 6.3 and temperature in the non-equilibrium molecular dynamics simulation maintained at 300K using the Nosé-Hoover thermostat.70, 71 The field is much larger than typical experimental fields, and is used to enhance signal-to-noise from simulations.

Fig. 6.3 shows the density of water, Na+ ions and the O− atoms of dissociated silanol groups near a silica slab. The conditions of this study correspond to low salt concentrations, perhaps in the millimolar range, where Cl− co-ions would be scarce.

As can be seen in Fig. 6.3, the Na+ counter-ions accumulate near the surface and exhibit signiﬁcant mobility. One measure of their mobility is their residence time, the average time that a Na+ ion will linger near one of the O− atoms on the silica

143 1000 1000

800 800

600 600

400 400 Residence time Residence time 200 200

0 0 1 2 3 4 5 6 5 10 15 # of waters around O- # of siloxanes around O- 15 1000

800

600 10 400 # of siloxanes Residence time 200 5 0 1 2 3 4 5 6 0 1 2 3 4 # of waters around O- # of silanol OH

Figure 6.2: Scatter plots showing the eﬀect of the number of siloxanes surrounding each O− group and its correlations with number of waters around dissociated oxygens and the associated residence time of the Na+ counter-ions.

surface.147 Residence time correlation functions were ﬁt to a sum of two exponentials as done in chapter 3. The reported residence time is the time constant for the slower, and major exponential contribution. The residence time ranges from an upper limit of ∼1000ps to a lower limit of ∼10ps. This suggests that many of the counter-ions actively hop from site to site on the surface, and are not “stuck”.

One of the origins of the large variation observed in the residence times of Na+ ions near the O− atoms is the solvent accessibility of the dissociated oxygens. The top left panel of Fig. 6.2 shows that for many cases, O− groups surrounded by a fewer number of waters, tend to be sites where the Na+ ions have longer residence times. We have shown in the previous chapters that our silica surface is made up of hydrophobic and hydrophilic patches. It thus seemed natural to examine the number

144 a)

+ 30 b) Na

20 H2O (m/s) x v 10

0 -40 -20 0 20 40 0.05 c) − 0.04 O x 10

) 0.03 -3 H2O (Å

ρ 0.02

0.01 + Na x 10 0 -40 -20 0 20 40 z (Å)

Figure 6.3: (a) Configuration taken from a typical non-equilibrium molecular dynamics simulation used to generate data in Figs. 6.3. The O− atoms of dissociated silanol groups are the large red spheres of the (centered) silica slab. Na+ and Cl− ions are visible in solution. (b) Average velocities of Na+ ions and water with a surface charge density of 12.7µC cm−2 = 0.795e nm−2, no ions except the Na+ ions needed to neutralize the silica, and an applied electric field of 7 × 108V m−1. Meaningless velocity spikes appear inside the silica slab where fluid rarely penetrates, and sampling is in- m sufficient to average normal thermal motion (∼ 400 s ) to zero. (c) Densities of water, Na+ions and O− groups of dissociated silanols. The vertical dashed lines are guides for the eye to facilitate comparison of the velocity and density profiles.

145 of siloxane oxygens around each O− group as this would be one of the factors that would aﬀect its degree of water accessibility. The bottom left panel of Fig. 6.2 shows that the number of waters around the dissociated oxygens is negatively correlated with the number of siloxanes surrounding the O− group. As a consequence of this, the top right panel of Fig. 6.2 shows that the residence times of the Na+ ions are

positively correlated with the number of siloxanes around the dissociated O− groups.

Thus the data suggests that for a good proportion of the O− groups on the surface, longer residence time sites for the Na+ ions are associated with regions of low solvent accessibility due to a more hydrophobic environment while shorter residence time sites are associated with regions with fewer neighbouring siloxanes. The ion and water mobility can also be measured with the velocity distribution as a function of distance from the surface, shown in Fig. 6.3. Comparing Figs. 6.3b and 6.3c, the velocity proﬁle is seen to approach zero at roughly 20A˚ from the center of the silica slab, right at the silica surface, and not 3-10A˚ from the surface as the Stern layer model would imply. Similar results are seen for larger salt concentrations conducted in our group.

Apart from the mobility of ions and water in the Stern layer, our simulations also shed important insight into the configurational characteristics of the ions in close proximity to the surface. In the Gouy-Chapman-Stern model the ions are thought to lie on the Stern plane which is depicted as a uniformly parallel plane to the surface as seen in Fig. 6.1. However the data in Fig. 6.3 showing the density of Na+ ions, indicate that the distribution of ions near the surface is different from what one would expect from the Gouy-Chapman-Stern model. Our simulations suggest that there are no “sharp” boundaries between the diffuse and Stern layer. Since the silica surface

146 0.4

0.3 (m/s) x

v 0.2

0.1

-40 -20 0 20 40 z (Å)

Figure 6.4: Comparison of velocity profiles from simulations with solutions to the Navier-Stokes equation (solid smooth curves). Stick boundary conditions are enforced at points that generated the best agreement with the molecular dynamics velocity µC profile across the channel. The velocity profiles are for a surface charge of 12.7 cm2 = e 0.795 nm2 , and for zero salt concentration. The two extra continuum hydrodynamics curves were calculated by enforcing stick boundary conditions at successive points 1A˚ closer to the point where the actual molecular dynamics velocity profile approached zero.

is heterogeneous and rough, the layering of Na+ ions near the charged surface is also not uniform.

The data presented in Fig. 6.3 and Fig. 6.2 seems to suggest that the Stern layer concept has limited validity. The immobile layer was originally proposed to explain the experimental fact that the driving force for electroosmotic ﬂow was typically less than what one would expect based on the measured wall charge. Charge within an immobile Stern layer behind the surface where stick boundary conditions are enforced

147 cannot drive ﬂuid ﬂow, and hence was thought to explain observed phenomena. The

data in Fig. 6.3 shows that it is the gradually attenuating velocity of the ions and

water upon approaching the surface and not a stagnant layer of ﬂuid and ions that

explains why the EOF ﬂow is less than the one predicted from the surface charge. The

velocity proﬁle for the water shown in Fig. 6.3 can be compared with the predictions

made by the Navier-Stokes equation of continuum hydrodynamics using the charge

density from the MD simulations as input. This has been performed in our group for

systems with various salt concentrations. The comparison of the velocity proﬁle from

the MD simulations and Navier-Stokes equation is illustrated in Fig. 6.4 for the system

shown in Fig. 6.3. The results indicate that there is very little room for adjusting the

eﬀective stick boundary condition for solving the Navier-Stokes equation. However,

when the stick boundary condition is placed ∼3A˚ into the fluid from where the MD velocity profile goes to zero, the agreement between the MD velocity profile and the

Navier-Stokes prediction is actually quite good.

The gradual decrease in mobility near the surface that is observed in Fig. 6.3 may be attributed to increased viscosity near the walls, to surface roughness, or a combination of these two effects. Since increased viscosity and surface roughness have many similar signatures, we may be able to eliminate or confirm certain mechanisms, but ultimately it may prove meaningless to distinguish between increased viscosity and roughness, e.g. roughness may be understood as an increased effective viscosity. We note that even with the appearance of an immobile fluid layer at extremely large surface charge, there is no evidence that ions are mobile within immobile solvent. In Fig. 6.5, the difference in Na+ and water flow velocities, i.e. the total ion current minus its convective component, for the highly charged surface is

148 0.06 − O x 5 )

-3 0.04 H2O

(Å + ρ 0.02 Na x 3 0

+ vNa + vNa - vH O 40 2 (m/s) x 20 v v H2O

0 -40 -20 0z (Å) 20 40

Figure 6.5: Densities (top) and flow velocities (bottom) near an almost completely µC e dissociated silica surface with a large surface charge of 58.7 cm2 = 3.67 nm2 in the limit of low salt concentration. Because of the extremely large surface charge, the fluid is less mobile near the surface, which is apparent comparing the location of the dotted lines in this figure and Fig. 6.3. The local ion mobility of sodium ions is proportional

+ to (vNa − vH2O).

149 proportional to the local ion mobility. The ion mobility does not maintain its bulk

value or even level oﬀ at a reduced value, but instead vanishes where the solvent

is not mobile. Simulations for more typical surfaces charges (Figs. 6.3) also do not

show evidence of anomalous ion mobility near the surface. Nevertheless, the surface

conductivity calculated from the data is in qualitative agreement with experiment.

The clearest comparison can be made with no added salt, as in Fig. 6.3, where the

entire ion current is the result of surface conduction and the surface conductivity can

e σ + + be calculated from 2K = E dz ρNa (z)vNa (z), where the factor of 2 is included R because there are two surfaces driving ion transport in the simulations. The surface conductivity of Na+ near silica in the limit of vanishing salt concentration calculated in this manner is Kσ = 2.5nS(nanoSiemens). Establishing a precise experimental value for comparison is diﬃcult, although the existence of the eﬀect is clear under conditions where bulk conduction is suppressed. One of the earliest measurements by Rutgers placed Kσ in the limit of vanishing KCl concentration in the range of

10nS.305 Jednacak-Biscan et al.’s measurements of Kσ ranged from 1.78 to 4.63nS

for water, and 6.46nS for 10−5M NaCl in contact with fused silica.306 Most recently,

Erickson, Li and Werner reported Kσ to be 1.31nS for vanishing KCl concentration

near silica.307 The dynamic Stern layer model was originally constructed to ratio-

nalize the reduced electrical conductivity contribution that came from the diﬀuse ion

layer. However, our results indicate that the surface conductivity in the calculations

is consistent with experimental estimates.

150 a) b) c)

Figure 6.6: Paths of approach showing methane molecule near a) silanol, b) siloxane and c) dissociated oxygen. For visual clarity the rest of the silica cluster is not shown.

6.3 Biomolecules near silica

As indicated in section 6.1 and in the previous two chapters, one of the original motivations for the development of a realistic model for the water amorphous silica interface was to study the structure and dynamics of biomolecules near the silica surface. Current interest in this area is particularly intense. Applications in the area of biomedical engineering include devices for lab-on-a-chip biomedical308 and transdermal iontophoretic drug delivery309 applications. The ﬂow of DNA through silica nanopores, now being explored for rapid sequencing schemes, is governed by the electrokinetic properties of the electrolyte.310

6.3.1 Parameters for protein-silica interactions

In order to extend our empirical potential to simulate biomolecules, we make use use of forcefields that have already been used to simulate peptides, proteins, DNA and lipids. Specifically the GROMOS96 forcefield65 which has been successfuly used in our group for other systems, is interfaced with our empirical model for the silica surface, although the use of other biomolecular forcefields is certainly plausible if needed. The ingredients for simulating any biomolecule near the silica surface are the interaction

151 parameters between the atoms of the biomolecules and those on the silica surface.

Each atom of any biomolecule in the GROMOS96 forceﬁeld65 is characterized by a

b b b charge qi which controls the Coulomb interactions and an eﬀective ǫii and σii, which controls the short range Leonard-Jones binding energy and position of repulsive wall.

In chapter 4 and chapter 5 we described our model for the amorphous silica-water interface. The pairwise potentials were implemented using a patched Buckingham potential (exponential repulsion + r−6 attraction). In order to interface the silica surface potential with the GROMOS96 forceﬁeld, the Buckingham potentials were

ﬁt to Leonard-Jones (r−12 repulsion and r−6 attraction) potentials to extract the s s ǫjj and σjj parameters. The superscript b refers to a biomolecular atom type while the superscript s refers to a silica surface atom type. We then apply the canonical

Lorentz-Berelot combining rules to determine the short range interaction parameters between atom types b and s. An arithmetic average is used for the sigma’s, while a geometric average is used for the epsilon’s,

1 σps = (σp + σs ) ij 2 ii jj 1 ps p s 2 ǫij = (ǫiiǫjj) (6.1)

ps ps Our strategy for calibrating the parameters σij and ǫij , involves the optimization

s s of the silica surface Leonard-Jones interaction parameters σjj and ǫjj, with input from ab initio quantum chemistry calculations on a small training set of silica clusters with model compounds that represent important chemical groups on aminoacids. It would be ideal to conduct fragment calculations for each of the 20 aminoacids like we did for the water molecule in the previous two chapters. However, this is not computationally feasible.

152 a) b)

+ Figure 6.7: Paths of approach showing an ammonium cation (NH4 ) molecule near a) silanol and b) dissociated oxygen. For visual clarity the rest of the silica cluster is not shown.

The training data set used in our parameterization procedure, consists of a single

methane molecule approaching a silanol, siloxane and dissociated oxygen seperately,

+ shown in Fig. 6.6. We include in the database, a protonated NH3 group and a

single methanol molecule approaching a silanol and dissociated oxygen (Fig. 6.7 and

Fig. 6.8) and also an acetate anion approaching a silanol group shown in the left

panel of Fig. 6.9. Finally, we also include a single benzene molecule approaching a

s s cluster that consists of a hydrophobic patch. The parameters σjj and ǫjj are then ﬁt

to the ab initio energies which were performed with the Gaussian package190 and the

6-311++G** basis set. Details of the ﬁtting procedure and the parameters deployed for the simulations described below, will be documented in the thesis of one of the members of our group.

6.3.2 Tri-peptides near amorphous silica surface

There is a lack of detailed experiments in the literature that will allow us to make

quantitative comparisons and predictions with our empirical model. In order to shed

some light on the nature of binding modes between amino acid side chains and the

153 a) b)

Figure 6.8: Paths of approach showing a single methanol molecule near a) silanol and b) dissociated oxygen. For visual clarity the rest of the silica cluster is not shown.

a) b)

Figure 6.9: Path of approach showing an acetate anion on the left panel and a benzene molecule on the right panel near a silica cluster.

154 silica surface, we have examined the properties of two tripeptides Lys-Trp-Lys(KWK)

and Glu-Trp-Glu(EWE) at the silica interface. Brennan and co-workers28 have experimentally examined the ﬂuorescence anisotropy of tryptophan near silica nanoparticles for both KWK and EWE. They ﬁnd that the limiting anisotropy of KWK is larger than that of EWE. For KWK or EWE in bulk water, the limiting anisotropy should be exactly zero. Thus, a non-zero limiting anistropy is an indication of rotational immobilization of the tryptophan on the surface. Brennan et al. speculate that it is

+ the binding of the protonated NH3 groups of KWK to the dissociated silica surface that immobilizes the tripeptide. In EWE, the negatively charged side groups of glutamic acid are repelled from the deprotonated silica surface and hence the tripeptide is not severely immobilized. A quantitative comparison of the limiting anisotropies of

KWK and EWE using our model is computationally prohibitive as this would require averaging over numerous trajectories in the excited state.

The adsorption of lysine side chains to silica has also been examined in several other recent experiments. Stievano and co-workers examined the adsorption of glycine and lysine onto amorphous silica at various pH conditions.311 At pH=7 they ﬁnd that there is an increased selectivity for lysine in an equimolar mixture of glycine and lysine in solution, to bind to the surface. This result indicates that the strong electrostatic

+ interactions between the NH3 group(s) of the lysine and the negatively charged silica surface, play an important role in the adsorption process. Kitadai and co-workers312 have used ATR-IR vibrational spectroscopy to study the adsorption of lysine in different dissociation states on amorphous silica. They ﬁnd that between the pH range of 7.1-9.8, majority of the lysine adsorbed on silica is in its cationic state while a smaller percentage is in the zwitterionic state. In their analysis, the zwitterionic

155 1) 2) 3) 3) 4) 1) 2)

Figure 6.10: Left and right panels show snapshots of a single KWK tripeptide bound to the silica surface. Diﬀerent regions of the tripeptide can bind to the surface. Numbers on the ﬁgures are described in the text. For visual clarity the solvent is not shown.

state is deﬁned as a protonated lysine side chain with a neutral N-terminus. These

results corroborate those observed by Stievano et al. However, Zimmerman and co-

workers have found that at pH 5.7 there is no measurable adsorption of lysine to silica

phases.313 Furthermore, hydrophobic moieties such as tryptophan and ditryptophan

were characterized by signiﬁcant adsorption leading to the conclusion that the non-

polar siloxane groups are important sites for hydrophobic binding of amino acids on

the silica surface. In all these studies however, a molecular picture of the binding

modes on the surface is lacking. We have recently begun to use our model to describe

the molecular details of the binding modes of the tripeptides KWK and EWE to the

surface.

In chapter 2 the structure and dynamics of KWK for the tryptophan in its ground and excited electronic state was examined to provide molecular insight into TDFSS experiments. We were thus able to provide an equilibriated initial conformation of

KWK for the computational adsorption study. The binding modes for the ground

156 state KWK and EWE molecules with different initial starting configurations is briefly illustrated in this chapter. More details of other binding modes and details of the dynamics of the tripeptides will be examined in the thesis of one of the members of our group. The KWK and EWE tripeptides were placed ∼ 10A˚ from a partially dissociated silica surface with a surface charge of 0.46e nm−2. Molecular dynamics simulations were then conducted using the Nosé-Hoover thermostat70, 71 maintaining a sytem temperature of 300K. The simulations were run for several nanoseconds to ensure that the tripeptide had sufficient time to either bind to the surface or remain in the bulk. The examples illustrated in this chapter are for cases where strong binding of the tripeptide was observed.

The left and right panels of Fig. 6.10 show KWK bound to the silica surface using our model. On the left panel, KWK is bound to the surface with 3 binding modes whereas on the right panel, there are 4 binding modes to the surface. In the left panel

+ the labels 1) and 2) correspond to the NH3 group(s) of the lysine interacting strongly with the dissociated silanol groups of the surface whereas the label 3) indicates the negatively charged C-terminus interacting with a silicon atom on the surface. In the

+ right panel, the labels 2) and 3) correspond to the NH3 group(s) binding strongly to the O− groups. The label 1) indicates a region where the hydrogen atoms on the benzene part of the tryptophan are in close proximity to the surface and ﬁnally the

+ label 4) is where the NH3 is intimate with silanol groups on the surface. The left and right panels of Fig. 6.11 show EWE bound to the silica surface. In the left panel the label 1) shows the tryptophan stacking on to a partially hydrophobic region of

+ our surface, whereas the label 2) corresponds to the NH3 group interacting with a silanol. On the right panel the label 1) shows the negatively charged C-terminus

157 2) 1)

1) 2)

Figure 6.11: Left and right panels show snapshots of a single EWE tripeptide bound to the silica surface. Diﬀerent regions of the tripeptide can bind to the surface. Numbers on the ﬁgures are described in the text. For visual clarity the solvent is not shown.

+ interacting with the silanols while label 2) shows the NH3 group strongly bound to a dissociated oxygen. The binding modes illustrated in Fig. 6.10 and Fig. 6.11 are not an exhaustive representation of what can occur on the surface, but suggest that the binding modes are quite rich and involve the hydrophobic tryptophan and the

+ negatively charged C-terminus in addition to the NH3 group.

6.4 Conclusions

In this chapter we brieﬂy summarized two applications of the empirical model that

was developed for the water-amorphous silica interface described in detail in chap-

ters 4 and 5. With a realistic description of the silica surface, we were able to shed

important insights into the validity of the ideas behind the Gouy-Chapman-Stern

model. The results of this chapter show that the water in the electrical double layer

is not immobile. Except for extremely large surface charge density, it is a region of

gradually reduced mobility. The classical Stern model is successful as an “eﬀective”

158 model that reproduces some experimental features. However, conceptual problems

arise when it is taken literally. Molecular simulations show no evidence that ions have

enhanced mobility relative to solvent near a charged surface. Nevertheless, the sim-

ulations exhibit a surface conductivity similar to experiment, indicating that eﬀects

previously attributed to anomalously large surface conductivity can be explained by

a uniﬁed model without anomalous transport near the surface. We note recent ef-

forts to reconcile measurements of the ζ-potential by different methods without the assumptions of the dynamic Stern layer model.314 Our analysis should provide guidance for the formulation of a unified model. It will also assist in the evaluation of recent reports of either ice-like or liquid-like water films315, 316 at the water-silica interface. With regard to device design, our results show that continuum hydrodynamics performs remarkably well away from channel walls, but must be combined with a molecular perspective within a few Angstroms of the surface.

We also highlighted the extension of our empirical model to interface with the

GROMOS96 biomolecular forceﬁeld. The interaction parameters between the silica surface and biomolecule atom types are obtained by comparison with ab initio cluster calculations using molecules that capture essential groups in several aminoacids. At this point it is not computationally feasible to parametrize our interaction parameters using quantum chemistry calculations with entire aminoacids. We have used our model to examine the binding properties of two tripeptides namely KWK and

EWE to the surface. The results show that the binding modes of both KWK and

EWE to the surface are quite rich and perhaps unexpected based on experimental interpretations.

159 CHAPTER 7

A theoretical study of CPD dimer repair I

7.1 Introduction

Exposure to far UV radiation induces DNA damage in the form of cyclobutane

pyrimidine dimers (CPDs)317–319 shown in Fig. 7.1. This is the most prevalent mech-

anism for UV-induced mutations,320 and has been implicated as a ﬁrst step in the

generation of tumors.321, 322 Cyclobutane dimer lesions can be repaired by the enzyme

photolyase, in which absorption of a blue light photon initiates a sequence of photo-

chemical events leading to the injection of an electron at the site of a CPD lesion in

DNA. The electron catalyzes the repair of the cyclobutane dimer, splitting the CPD

into the original pyrimidine units, and is subsequently recaptured by the photolyase

protein. DNA photolyase is not found universally in all organisms: it is not present

in placental mammals, but it is found in other organisms such as archea and bacteria,

including some vertebrates.

Interest in the mechanism of CPD lesion repair is intense because of the health beneﬁts of preventing or reversing events leading to mutations. Mice that have been genetically modiﬁed to express photolyase exhibit greatly increased resistance to skin cancer.322 There have been many studies of the action of DNA photolyase, and the

160 electron injection mechanism has recently been directly observed using ultrafast laser

spectroscopy.29 There have also been many studies of model compounds, usually

a CPD moiety linked to an electron donor in which dimer splitting is initiated by

photo-induced electron transfer to the cyclobutane dimer.323–325 There have been

several theoretical studies of photolyase and the dimer splitting reaction.326–328 While

signiﬁcant progress has been made on both the experimental and theoretical fronts,

our understanding of the repair mechanism is still far from complete. Ultimately, what

is desired is an understanding of the remarkable eﬃciency of lesion repair catalyzed

by DNA photolyase.

Ab initio simulations of the cis,syn-thymine cyclobutane dimer splitting in aqueous

solvent are reported in this chapter. The motion of both the CPD unit and the solvent

are governed by a potential surface calculated using electronic density functional

theory. Umbrella sampling has been used to elucidate the free energy surface for

dimer splitting. The important role of water has previously been identiﬁed in quantum

chemical cluster calculations.328 These calculations only included up to three waters

near the CPD unit, too few to build a realistic picture of dimer splitting in solvent

but enough to identify the importance of solvent. Dimer splitting within a DNA

oligomer has previously been theoretically investigated using QM/MM techniques.327

No water molecules were treated quantum mechanically in that study, so issues like

charge transfer between dimer and solvent were not addressed. Recently Masson et al. 329 have reported QM/MM simulations of the thymine dimer in the active site of

DNA photolyase. In this study, a glutamic acid and the thymine dimer were treated quantum mechanically and proton transfer was found to occur between the carboxylic acid of the glutamic acid and one of the carbonyl oxygens of the dimer. Our results

161 conﬁrm the crucial role of water, including a signiﬁcant degree of charge transfer

between the CPD and neighboring water molecules, not reported in any previous

theoretical treatments because the models used in these studies could not describe

charge delocalization on to the solvent.326–329 Furthermore, water motions also emerge as a critical part of the reaction coordinate, facilitating the splitting process.

Splitting of CPD radical ions has been studied using a series of model compounds, or within photolyase. The results of our work are most relevant to the model compound literature, which has been reviewed on several occasions.318, 330–332 Model studies involve a CPD which is either tethered to a chromophore that donates an electron upon photoexcitation, or in solution with a sufficient concentration of chromophores, or simple CPDs exposed to a source of electrons such as ionizing radiation. Model compounds offer an opportunity to investigate the basic reactions without the complexity of the enzymatic environment. Some of the earliest work on model compounds found that CPD anions did not split at liquid nitrogen temperature.323 Later studies found that dimer splitting was facile at 77K.333, 334 Model compound experiments in which an indole-based chromophore was tethered to the CPD have tended to exhibit increased dimer splitting efficiency in non-polar solvents,335, 336 leading to the conclusion that the back electron transfer which competes with splitting was in the inverted

Marcus regime. Three recent works by Song et al. observed the opposite trend with respect to solvent polarity using indole-based chromophores,324, 325, 337 and suggested that the length of the tether may account for the opposite trend. Flavin-based chromophores have tended to induce more eﬃcient dimer splitting with increasing solvent polarity.318, 332 In this chapter we use our ground state calculations to provide a framework for understanding the molecular mechanisms by which back electron transfer

162 Figure 7.1: Thymine cyclobutane dimer.

and bond splitting compete and hence aﬀect the quantum yields of repair in diﬀer-

ent solvent environments. Yeh and Falvey found that splitting of the thymine dimer,

triggered by electron transfer from N,N-dimethylanaline in aqueous solution following

a nanosecond laser pulse, was slow enough to follow spectroscopically on the millisec-

ond time scale. Other studies have observed much faster rates of dimer splitting.334

A recent study in which dimer splitting was induced using electrons from ionizing

radiation found that solvated electrons were consumed at essentially the same rate

as dimers were split, and gave an upper limit of 35ns for the splitting time scale.338

Hopefully, progress of the theoretical description of dimer anion splitting will provide

clues that will help reconcile these various reports.

As early as 1987, Hartman et al. used H¨uckel molecular orbital theory to predict

that the cis,syn-CPD anion ring opening proceeds via splitting of the C5-C5′ bond

followed by rupture of the C6-C6′ bond.339 Synchronous concerted cycloreversion of the cyclobutane ring is not symmetry-allowed by Woodward-Hofmann rules. Heelis calculated the enthalpy of splitting for the neutral and anionic dimer using the PM3 semiempirical method.340 Cis,syn-CPD anion ring opening was studied by R¨osch

and coworkers using AM1 semiempirical theory,326 and subsequently Hartree-Fock

163 and MP2 methods.341 The enthalpy for splitting the pyrimidine dimer radical anion determined in these studies was not strongly diﬀerent from that of the neutral dimer.

Splitting could be either exo- or endothermic, depending on the pyrimidine type and level of theory. However, the reaction barrier was dramatically lowered in the radical anion. The splitting reaction was predicted to occur via stepwise splitting of the

C5-C5′ bond, followed by rupture of the C6-C6′ bond to complete the repair of the dimer. In the anion, the localization of excess charge on the C4=O4 and C4′=O4′ carbonyl groups and C5,C5′ carbons varied during the course of the reaction, as did the tendency of the charge to localize on one member of the dimer or be equally shared across both pyrimidines. Since charge was more localized at minima of the reaction surface than at transition states, incorporation of solvation effects using a continuum model in the AM1 calculations predicted that dimer splitting would be slower in more polar solvent. In many ways, these first papers framed many of the issues that were re-visited in subsequent studies using progressively more refined levels of ab initio theory and treatment of solvent.

Saettel and Wiest found that inclusion of up to three water molecules had a profound inﬂuence on splitting the uracil dimer radical ion.328 The water molecules increased the adiabatic electron aﬃnity of the dimer by over 20kcal mol−1. The

splitting reaction was much more exothermic, and essentially barrierless although

they found a larger barrier for the breakage of the C5-C5′ bond than the C6-C6′ bond.

Masson and co-workers,327, 329 ﬁnd a small barrier of 2.5kcal mol−1 for the breakage

of the C6-C6′ bond in their QM/MM simulations in both the DNA oligomer and the

active site of DNA photolyase. Recently, Kawabata and co-workers have performed

gas phase ab initio MD simulations of the thymine dimer with both Hartree Fock

164 and B3LYP levels of theory. They ﬁnd that the C5-C5′ bond breaks spontaneously within the ﬁrst 100fs but do not run their simulations long enough to determine the timescales over which the C6-C6′ bond breaks.342

We report in this chapter, our results on the molecular mechanisms involved in the repair of the cyclobutane thymine dimer in water, treating the electronic degrees of freedom for all the thymine dimer atoms and the surrounding water molecules.

In this chapter, we begin by reviewing in section 7.2, the computational methods used in our calculations. In section 7.3 we illustrate the 1D proﬁles for splitting of the C5-C5′ and C6-C6′ bonds, in addition to the 2D free energy surface, showing the remarkable acceleration in splitting achieved compared to the large activation barrier for splitting the neutral dimer. We also estimate the splitting rate of the

C6-C6′ bond from our umbrella sampling simulations using classical transition state theory. The fate of the dimer after back electron transfer once it has returned to the neutral surface is explored in section 7.4. Conﬁgurational changes along the splitting process is documented in section 7.5. In section 7.6 we advance a simple model using our ground state calculations that illustrates the mechanism by which environmental factors such as solvent polarity aﬀect the extent of competition between the splitting process and back electron transfer. Finally we end with conclusions of our work in section 7.7.

7.2 Computational methods

7.2.1 Electronic structure methods for ab initio simulation

Ab initio molecular dynamics simulations of the thymine CPD were conducted using Quickstep which is part of the CP2K package.282, 283 In these calculations, ab

165 initio Born-Oppenheimer molecular dynamics is used for propagation of the classical nuclei. The electronic orbitals are converged to the Born-Oppenheimer surface at every step in the molecular dynamics simulation. The wave function was optimized using an orbital transformation method284 in conjunction with the DIIS scheme,285, 286 as described in Ref.283. The convergence criterion for optimization of the wave function was set to 10−6. Using the Gaussian and plane waves (GPW) method, the wave function was expanded in the Gaussian DZVP basis set. An auxiliary basis set of plane waves was used to expand the electron density up to a plane wave cutoﬀ of 300 Ry. We used the Becke-Lee-Yang-Parr gradient correction270, 271 to the local density approximation and Goddecker-Tetter-Hutter (GTH) pseudopotentials.287

In all anion simulations the local spin density approximation (LSD) is used for the exchange-correlation energy.

-717.99 -717.96

-718 -717.98

-718.02 -717.99 TZV2P (a.u)

-718.03 -718 DZVP-MOLOPT (a.u)

-718.05 -718.02 -717.59 -717.57 -717.56 -717.54 -717.59 -717.57 -717.56 -717.54 DZVP (a.u) DZVP (a.u)

Figure 7.2: Comparison of DZVP, TZV2P and DZVP-MOLOPT energies in a box of length 9.8A˚ with 32 waters. The solid line in both panels indicates a linear ﬁt with slope 1.0006

166 Shown in the left panel of Fig. 7.2, is a comparison of DZVP and TZV2P basis

set energies in a box size of 9.8A˚ including all the 32 waters which is the system we use in our simulations below. The TZV2P basis set is too costly for use in the umbrella sampling calculations reported below, but we were able to compare double and triple zeta basis sets at isolated conﬁgurations picked at various points across the splitting of the C5-C5′ bond. In the right panel of Fig. 7.2 we show a comparison of

DZVP and DZVP-MOLOPT basis (molecularly optimized) set energies for the same set of conﬁgurations. The molecularly optimized basis sets include diﬀuse functions with small exponents for all primitive functions and have been shown to outperform basis sets of similar or slightly larger size343 but are also too costly for the type of simulations we are interested in. The slope of the line in both the left and right panels is close to 1, but the scatter from the line in Fig. 7.2 indicates the DZVP calculations are not fully converged with respect to basis set. The RMSD of the

DZVP and TZV2P energy data sets is 3.76 × 10−3a.u while that of the DZVP and

DZVP-MOLOPT energy data sets is 2.77 × 10−3a.u. These are typical errors that one would expect from DFT calculations with even much larger basis sets.344, 345

7.2.2 Molecular dynamics, umbrella sampling, and WHAM

A timestep of 0.5 fs was used in all simulations. The system consists of the thymine dimer solvated by 32 waters in a cubic periodic box of side length 9.8A.˚ The umbrella sampling simulations were performed within the NVT ensemble using the Nos´e thermostat70, 71 with a time constant of 0.2ps. The system temperature was maintained at 300K in the simulations. Several powerful methods have been developed for determining free energies from simulations. Some of the most popular techniques

167 are umbrella sampling,346 Jarzynski’s identity based on non-equilibrium sampling,347

adaptive force bias,348, 349 and more recently metadynamics.350 The weighted his-

togram analysis method351, 352 (WHAM) greatly improves the accuracy and eﬃciency

of combining distributions from umbrella sampling,353, 354 and this combination was

our choice for determining the reaction free energy surface for dimer splitting.

Umbrella sampling allows the system to sample regions that are otherwise explored infrequently in the microcanonical or canonical ensemble by constraining the system along a speciﬁc reaction coordinate η(rN ), where rN denotes the Cartesian coordinates

N N 2 of all particles in the system. A biasing harmonic potential Wi(η(r )) = k(η(r )−ηi) conﬁnes the system in a speciﬁc window i. The unbiased probability distribution for

u the ith window ρi (η) for the reaction coordinate η is expressed in terms of the biased

b probability ρi (η) which is accumulated under the inﬂuence of the window potential

Wi(η) obtained from our simulations as,

u b ρi (η) = exp (β[Wi(η) − Ci]) ρi (η) (7.1)

b The constants Ci could be determined by matching ρi (η) at the boundary between

adjacent windows as in the original formulation of umbrella sampling by Torrie

and Valleau,346 but are more eﬃciently and accurately determined in the WHAM

method351, 353, 354 by writing the total probability distribution ρ(η) as a weighted sum of contributions from each of the windows,

Nw u ρ(η) = C wi(η)ρi (η) , (7.2) Xi=1 where C with no subscripts is an overall normalization constant and Nw is the number of windows used. The weights wi(η), are normalized such that

wi(η) = 1, (7.3) Xi=1 168 and the weights wi are chosen in such a manner that the total error in ρ(η) is minimized at each value of η.351, 353, 354 In our analysis, a convergence criterion of 10−12 was used for determining the constants Ci.

Previous work326–328, 341, 355 and our own preliminary studies suggest that the C5-

C5′ and C6-C6′ bond lengths are essential reaction coordinates. We have found that a detailed and complete mechanism of splitting must explicitly involve additional dimensions to understand the crucial role of the surrounding solvent. Including an additional solvent reaction coordinate significantly corrects the splitting rate, especially the C5-C5′ bond. However, it does not affect the qualitative conclusions presented in this chapter, and the two-dimensional free energy surface with respect to the C5-C5′ and C6-C6′ bond lengths presented in this chapter is a useful starting point. Details of the role of solvent in the splitting process are discussed in the next chapter. As will be shown later, the initial reaction path is mainly along the C5-C5′ coordinate, while the later stages of the splitting reaction involve more motion along the C6-C6′ distance. The reaction coordinate η(rN ) was first chosen to be the C5-C5′ distance to explore the initial cleavage of the C5-C5′ bond on the anion surface. 20 windows were placed to constrain the C5-C5′ distance between the range of 1.6 − 2.7A.˚ 356 For the cleavage of the second bond on the anion surface, the C6-C6′ bond length was subsequently chosen as the reaction coordinate. 33 windows were placed to constrain the C6-C6′ distance between the range of 1.6 − 3.0A.˚ 357 We also conducted umbrella sampling simulations for the neutral surface along the C5-C5′ coordinate to estimate the extent of kinetic trapping in this state. For the cleavage of the C5-C5′ bond on the neutral surface, 19 windows were placed to constrain the C5-C5′ distance within the range of 1.6 − 2.6A˚358 The force constant k for the harmonic potentials in all the

169 windows for the anion system was 448.175 kcal mol−1A˚−2 while that of the neutral

system was 559.788 kcal mol−1A˚−2. This force constant ensured that in each of the

windows, the system sampled a region in which the reaction free energy surface varied

by an amount comparable to kBT . The combination of k and window placement gave

good overlap between the distributions. Even though just one reaction coordinate

was constrained during any of the umbrella sampling runs, we could still extract a

two- (or, in principle, n-) dimensional free energy surface by accumulating probability

distributions along several degrees of freedom within each umbrella sampling window.

Thus, we are able to construct a two-dimensional free energy surface in the reaction

variables C5-C5′ and C6-C6′ .

Each window was equilibrated for 1ps. In order to gauge the sensitivity of the free

energy curves to the simulation length, the curves were ﬁrst constructed from ∼ 4-

5ps umbrella sampling trajectories and then compared with an aggregate trajectory

consisting of an additional trajectory of similar length for each window. Our results

suggest that the free energy curves constructed from the ∼ 4-5ps and ∼ 9-10ps long umbrella sampling trajectories, give good agreement indicating convergence with respect to simulation length. Longer sampling times are computationally prohibitive.

However, a comparison of the splitting dynamics predicted from the equilibrium free energy curves obtained from the umbrella sampling simulations with non-equilibrium trajectories, indicate that our umbrella sampling simulations adequately predict the timescales and mechanisms associated with splitting of both the C5-C5′ and C6-C6′ bonds. An analysis of our non-equilibrium trajectories of the splitting of the C5-C5′

and C6-C6′ bonds, is the subject of the next chapter.

170 8

2 free energy (kcal/mol)

0 1.6 1.8 2 2.2 2.4 C5-C5 Distance Å

Figure 7.3: Free energy surface for lengthening the C5-C5′ bond in thymine CPD anion. The solid curve was obtained from 4-5ps trajectories in each umbrella sampling window, the dashed curve from 9-10ps trajectories.

7.3 Free energy surfaces

In this section we present results from the umbrella sampling free energy calculations. In order to demonstrate the remarkable acceleration of the dimer splitting kinetics which is caused by the injection of an electron, we conducted umbrella sampling simulations on both the anion and neutral thymine dimer systems. For the neutral surface, we limited umbrella sampling runs to the part of the C5-C5′ coordi-

nate which was suﬃcient to demonstrate the enormous activation energy needed for

bond breaking on the neutral surface. We ﬁrst lay out the overall topography of our

171 15 2 1

free energy (kcal/mol) 3

4 0 1.6 1.8 2 2.2 2.4 2.6 2.8 3 C6-C6 Distance (Å)

Figure 7.4: Free energy surface for lengthening the C6-C6′ bond in thymine CPD anion. The solid curve was obtained from 4-5ps trajectories in each umbrella sampling window, the dashed curve from 9-10ps trajectories.

free energy surfaces along the C5-C5′ and C6-C6′ coordinates for the anion surface and then use TST to estimate the splitting time of the C6-C6′ bond.

7.3.1 Anion: C5-C5′ and C6-C6′

Both experimental29 and theoretical327–329 studies have established that adding an electron to the thymine dimer results in the cleavage of both bonds. The present work provides information about the free energy surface for the process of bond breaking in aqueous solution. This surface determines the reaction path and whether the process is concerted or not. Shown in Fig. 7.3 is the free energy curve associated with the breakage of the C5-C5′ bond. There is in fact a small barrier of 0.6 kcal mol−1 for

172 the cleavage of this bond. However, this barrier is so small, roughly kBT at room temperature, that the time scale for escape over the barrier would be comparable to relaxation in the reactant well (left hand corner of Fig. 7.3) and transition state theory is not meaningful in this situation. Durbeej and Eriksson359 conducted gas phase optimizations of the thymine dimer using DFT and found the breakage of the

C5-C5′ bond to be barrierless. However Voityuk et.al326 who conducted gas phase optimizations of the thymine dimer in continuum solvents at the AM1 level of theory found signiﬁcant barriers for the breakage of the C5-C5′ bond. Our equilibrium

umbrella sampling simulations suggest that upon uptake of the electron, the system

will rapidly move to the local free energy minimum where the first bond is partially cleaved, the right-hand well in Fig. 7.3. The small barrier shown in Fig. 7.3 for the splitting of the C5-C5′ bond and the 2D Surface in Fig. 7.5, suggest that the system will rapidly move to the local free energy minimum where the first bond is partially cleaved on addition of an electron. In the next chapter, we will demonstrate that multidimensional or non-equilibrium effects can change the underlying mechanism and timescale associated with splitting of the C5-C5′ bond although the overall timescale for splitting of both bonds occurs within several picoseconds.

We now turn our attention to the rate-limiting part of the bond splitting process that involves the cleavage of the C6-C6′ bond. The free energy curve along the

C6-C6′ coordinate (Fig. 7.4) shows a small barrier of 1.5 kcal mol−1, followed by

a release of 14.6 kcal mol−1 after passage over the barrier. In Fig. 7.4 we have

labeled four points for future reference: Point 1 is the partially cleaved free energy

minimum where the C5-C5′ bond is broken while the C6-C6′ bond is intact. Point

2 is the transition state for C6-C6′ bond splitting. Point 3 is intermediate between

173 triga h atal lae oa iiu fo on 1 point 13 (from is minimum local cleaved partially the at overall starting The environments. protein photolyase and DNA in repair egto 1 sol of in height other clea each from the away which diﬀuse minimum eventually they energy when free surmount shallow a is there b 4 4 point point At at Finally, products. cleaved and state transition the labeled. is contours several on value energy The energy. iue75 vrl ecinfe nrysraefrthymine for surface energy free reaction Overall ( 7.5: Figure no sbte ecie yatodmninlfe nryi t in energy free two-dimensional a by described better is anion pe on siaeo h are f2 of barrier the of estimate bound upper itne Fg .) hssraewsotie yaccumulati by obtained was surface This 7.5). (Fig. distances C6-C6 clmol kcal . 1 ′ clmol kcal odi nat( intact is bond − . 1 5 .Tefe nrywl nwihteC5-C5 the which in well energy free The ). clmol kcal − 1 h ofrainlcagsdrn pitn ftethymine the of splitting during changes conformational The .

− r 1

r C6−C6’ C5 si xeln gemn ihHte n co-worker’s and Hutter with agreement excellent in is − C5 7 ′ 2 = . 57 ,r A, ˚ 174 . r 5 C6 C5−C5’ 0 clmol kcal − C6 ′ 2 1 = −4 −12 − . 61 1 htwsfudfrbt self- both for found was that A ˚ sasge stezr of zero the as assigned is ) ′ odi rknadthe and broken is bond t od r cleaved. are bonds oth eC5-C5 he opit4i i.7.4) Fig. in 4 point to ghsorm nthe in histograms ng ecinfe energy free reaction P no repair anion CPD e rget will fragments ved to.Orbarrier Our ution. ′ n C6-C6 and 2,329 327, CPD ′ C6-C6′ distance while the C5-C5′ distance was constrained by umbrella sampling,

and then accumulating histograms in the C5-C5′ distance while the C6-C6′ distance was constrained by umbrella sampling (Fig. 7.4). The two data sets were aligned by setting the bottom of the free energy well in which the C5-C5′ bond is broken and

′ the C6-C6 bond is intact (rC5−C5′ = 2.57A,˚ rC6−C6′ = 1.61A˚), which is shared by the two data sets, to the same arbitrary value, zero. Fig. 7.5 reveals that during the splitting of the C5-C5′ bond the C6-C6′ bond is intact, although there is a minor opening of the C6-C6′ bond. During this stage of the repair the C5-C5′ bond length widens from 1.60A˚ to 2.57A.˚ After cleavage of the C5-C5′ bond, further lengthening of the C5-C5′ bond by 0.35A˚ and somewhat smaller, but still signiﬁcant lengthening of the C6-C6′ bond by 0.14A˚ is required to reach the transition state for cleavage of

the C6-C6′ bond. After passage through this transition state, the reaction proceeds

mostly by major lengthening of the C6-C6′ bond by 1.2A˚ and minor lengthening of

the C5-C5′ bond by about 0.2A˚ which completely cleaves both bonds. The diﬀerence

in average potential energy between points 1 and 4 of Fig. 7.4 is 12.6±2.0 kcal mol−1.

Since the overall splitting free energy is 13.1 kcal mol−1, this indicates that entropic

contributions are small.

Our free energy curves indicate that the total free energy of splitting starting from

the equilibrium conﬁguration of the unsplit neutral dimer is −19.8 kcal mol−1. This

is in fairly good agreement with the splitting energy of −21 kcal mol−1 reported by

Wiest and co-workers328 on a uracil anion cluster with 3 waters, although the splitting

mechanism is different and specific for their fragment system. They find a barrier for

the cleavage of the C5-C5′ bond while the splitting of the C6-C6′ bond is found to

be barrierless. The calculations of Wiest et al. do not incorporate thermal eﬀects

175 as they perform geometry optimizations of their uracil dimer with 3 waters. The

only available experimental data to our knowledge on the free energy of splitting of

pyrimidine dimers is by Falvey and co-workers360 who report a free energy of splitting of −20 kcal mol−1, with which our value of −19.8 kcal mol−1 is in good agreement.

7.3.2 Estimates of ksplit

From our free energy surfaces, we can estimate ksplit for the bond breaking process.

The rate-determining step is the cleavage of the C6-C6′ bond. The probability that

reactants thermalized in the partially cleaved state will sample the transition state

can be calculated using the data in Fig. 7.4. The transition state theory rate for

cleavage of the C6-C6′ bond is evaluated from the following expression,

h|v|i 12 −1 1 ksplit = P (|rC6 − rC6′ |TST ) = 2.0 × 10 s , = 0.5ps (7.4) 2 ksplit

The eﬀective mass used for determining the velocity h|v|i was 6a.u. Our TST es-

timate of 0.5ps is rigorously a lower bound to the splitting time. These results are

consistent with recent theoretical studies that demonstrate the ultrafast nature of

CPD splitting within a DNA duplex and in photolyase.327, 329 They are also consis-

tent with a recent pulse radiolysis study in which the products of CPD anion splitting

in water appeared at the same rate at which hydrated electrons were consumed.338

This rate is rigorously the fastest time scale on which both bonds would split and

simply provides an upper bound to the rate of splitting. The time scale for reaction

− of eaq with thymine CPD was 35ns, so the splitting time had to be negligible com-

pared to this time scale. In this same work, using DFT gas phase calculations of

the thymine dimer with the phosphate backbone, Chatgilialoglu et al.338 estimated a

176 barrier of 3.2kcalmol−1 for splitting the C6-C6′ bond. Assuming a negligible temperature dependence of the back electron transfer, Song and co-workers325 determined

the temperature dependent splitting eﬃciency of model compounds where the CPD is

tethered to an indole and predicted an activation barrier for splitting of 1.9kJ mol−1

in equal glycerol/water mixtures as the solvent. Kim and Rose estimate an upper

bound of 2.6kcalmol−1 in similar model compounds.361 All these experimental results

corroborate our theoretical predictions.

Kao et al. tracked the dynamics of thymine dimer repair in photolyase using

femtosecond spectroscopy.29 They observed electron donation from the FADH−∗ to

the dimer on a time scale of 170ps when the data is ﬁt to a stretched exponential, or

60 and 335ps time scales when the data is ﬁt to a double exponential. The FADH.

intermediate was directly monitored, and its decay following return of the electron af-

ter dimer splitting occurred on a stretched exponential time scale of 560ps. Since the

dimer splitting eﬃciency was close to 100%, 560ps is an upper bound to the inverse

dimer splitting rate. If dimer splitting was the rate-determining step for the 560ps

process, this would either indicate that we underestimated the activation energy for

dimer splitting by 4.2kcalmol−1, or that the activation free energy for dimer splitting

is somewhat higher when the enzyme is in the active site of photolyase. Alternatively

the actual dimer splitting may not be the rate-determining step for electron return to

the excited FADH. co-factor. This is possible in a scenario where the splitting of the

C5-C5′ and C6-C6′ bonds occurs on a fast timescale, after which the electron resides

on the dimer with both C5-C5′ and C6-C6′ bonds split awaiting back ET. It is worth

noting that several gas-phase studies have shown that an error of 2-3kcalmol−1 would

not be surprising in the energetics obtained from DFT calculations.344, 345 When one

177 factors in errors due to ﬁnite box size and improper treatment of electron correlation

with the BLYP functional, it would not be surprising if we underestimated our acti-

vation energy for dimer splitting by 2-3kcal mol−1. It should also be noted that the enzymatic system is neutral (D∗ + A 99K D+ + A−) while most theoretical studies of

this system including ours, are anionic systems. At this point we cannot rule out the

possibility that these diﬀerences could change the underlying physics of the splitting

process.

7.3.3 Neutral

free energy (kcal/mol) 10

0 1.6 1.8 2 2.2 2.4 2.6 C5-C5 Distance Å

Figure 7.6: Free energy surface for lengthening the C5-C5′ bond in neutral thymine dimer.

178 Shown in Fig. 7.6 is the free energy curve along the C5-C5′ coordinate for the neutral thymine dimer. As can be seen from this figure, a lower limit for the barrier is approximately 39 kcal mol−1. While we were unable to determine the full free energy profile for splitting on the neutral surface, we have determined that the difference in average potential energy between the split neutral products (both C5-C5′ and

C6-C6′ split) and unsplit neutral reactants (both C5-C5′ and C6-C6′ uncleaved) is approximately −23.3±3.0 kcal mol−1 showing that the splitting reaction is exothermic on the neutral surface, and by roughly the same amount as splitting on the anion surface. At room temperature, the minimum barrier of 39 kcal mol−1 will not be overcome by thermal ﬂuctuations and the system would be kinetically trapped in this state, as observed experimentally. Without repair, the cyclobutane dimer remains within the DNA and would ultimately prevent DNA replication and lead to mutations and possibly cell death.29

Recently there has been an interest in understanding the mechanisms by which

UV radiation leads to the thymine dimer photoproducts. Experiments have shown that thymine dimers are formed within 1ps after photoexcitation.362 Dimer formation is the inverse of the reaction we study. Therefore, we can exploit experimental and theoretical results pertaining to dimer formation to test some of our ﬁndings. On the neutral ground state surface, the thymine bases must surmount a large activation barrier to form the CPD dimers. Unfortunately, there have been no theoretical studies to our knowledge reported on the splitting or dimerization of neutral thymines in solvent. However, we can compare our relative energetics to recent work by Robb and coworkers363 who have performed high level gas phase CASSCF and CASPT2 calculations to determine the dimerization barrier of thymine bases on the ground

179 state and ﬁrst singlet excited state. Robb et.al report a barrier of approximately

41kcal mol−1 to reach the TST in the direction of splitting starting from the closed dimer. This compares well with our lower limit of 39kcal mol−1. They also report that the split thymine neutral products (in their case the reactants for a dimerization process) is 19kcal mol−1 more stable than the unsplit reactants (in their case the products for dimerization) which is in good agreement with our predicted value of the potential energy diﬀerence of approximately 23kcal mol−1. Later in section 7.4

we show that a one-dimensional downhill curve beyond the transition state on the

neutral surface, suﬃciently describes the dynamics of splitting after back electron

transfer . Our results are also consistent with experimental estimates of −19kcalmol−1

for the enthalpy of splitting of neutral di-methyl thymine dimers (DMTD) using

photothermal techniques.360

7.4 Back electron transfer (BET) from Anion Dimer

An important aspect of the repair mechanism that has been examined experimen-

tally to date29 is the back electron transfer (BET) process from the anion dimer to

the electron donor. While detailed modeling and understanding of the BET process

is beyond the scope of this work, we address aspects of BET that we believe play a

crucial role in the repair process. BET is essential for the completion of biological

repair insofar as the split anion is not yet a healed DNA segment. Where and when

the BET occurs during the splitting process can either result in ring reclosure (no

repair) or completion of splitting on the neutral surface. The fate of the complex

following BET, failed or successful repair, will depend on the spatial arrangement of

the complex at the instant of BET. The split anion system has a distribution of bond

180 4

C5-C5 Anion C5-C5 Neutral

C6-C6 Anion

2 C6-C6 Neutral

0 2.6 2.8 3 3.2 3.4 3.6 Distance Å

Figure 7.7: Distribution of C5-C5′ (solid) and C6-C6′ (dashed curves) distances before and after back ET on anion and neutral surfaces. In each case, the distribution on the neutral surface lies at larger distances compared to the neutral.

lengths distinct from the neutral base pair, even when splitting is initially achieved

and before the fragments have a chance to separate in solution. In Fig. 7.7 we show

the equilibrium distances of the broken C5-C5′ and C6-C6′ bonds on the anion and neutral surface. The results indicate that the equilibrium broken C5-C5′ and C6-C6′

distances are longer on the neutral surface than on the anion surface. Substantial con-

ﬁgurational adjustment, especially in the C6-C6′ distance, will take place after back

ET while the base pairs are still adjacent in solution. The geometry re-arrangement

that we observe once the electron is vertically detached from the anion surface to the

neutral surface is consistent with observations made by Adamowicz and co-workers364

who have conducted geometry optimizations of uracil monomers with several waters

181 on both anion and neutral surfaces. Adomowicz et al. show that there does not exist

a stable neutral geometry at the minimum energy point on the anion surface. Hence

when the system is optimized on the neutral surface, starting from the minimum on

the anion surface, signiﬁcant reorganization occurs in the structure.

In the absence of an explicit cation donor to re-accept the electron, we model the back ET process simply as a vertical detachment of the electron from the anion placing the system on the neutral surface. The vertical detachment treatment would be valid within the Marcus picture of electron transfer if the system has already overcome any barriers in the collective solvent polarization coordinate or if the back

ET is occurring in a virtually barrierless region along the collective solvent coordinate.

These assumptions, do not allow us to determine the rate of back ET but allow us to address some important issues regarding the role of back ET in DNA repair.

Assuming that the back ET can occur on the same timescale as splitting or faster, we can determine how far along the dimer splitting reaction coordinate the system must be before back ET leads to successful ring opening, and not reclosure of the

CPD dimer. Conceivably, this point may be quite diﬀerent from the dimer splitting transition state. However the results presented below indicate that the point where back ET generally leads to successful ring opening is rather close to the dimer anion transition state, lying slightly before the transition state is reached from the reactant side on the anion surface.

We selected 653 statistically independent conﬁgurations from our umbrella sampling windows at various points before and after the transition state. All 653 con-

ﬁgurations obtained from sampling the dimer anion were propagated with energy conserving dynamics on the neutral surface for 120fs which was suﬃcient time to

182 a) b)

Figure 7.8: Dynamics of a) C5-C5′ or b) C6-C6′ bond length afer back ET leading to either ring closure (gray curves) or ring splitting (black curves)

distinguish eventual ring closing from successful repair. Fig. 7.8 shows that once back

ET takes place, ring closure or splitting of the C5-C5′ and C6-C6′ bonds is complete

within 80fs. The population that undergoes ring closure after back ET quickly equi- librates into the deep well of the neutral free energy proﬁle in the left hand corner of

Fig. 7.6. Similarly, for the population that undergoes splitting after back ET, both the C5-C5′ and C6-C6′ bonds instantaneously move toward the split products indicating that a one-dimensional downhill free energy proﬁle beyond the TST on the neutral surface is suﬃcient for describing the evolution of the system after back ET has occurred.

The location of the circles in Fig. 7.9 indicates the sampling of initial C5-C5′ and

C6-C6′ bond distances among the 653 trajectories that were propagated on the neutral

surface to model back electron transfer (BET). The initial conditions are shown in

Fig. 7.9 relative to the same free energy surface shown in Fig. 7.5 for trajectories

183 3.0

2.5 ¢ C6 - C6 r

2.0

1.5 2.0 2.5 3.0 3.5 ¢ rC5-C5

Figure 7.9: Overall free energy surface with open white circles for trajectories that split after back ET and solid black circles for trajectories that close after back ET.

that were propagated on the neutral surface. The open white circles represent initial points that lead to ring splitting while the solid circles represent points that led to ring closure. Although there is some overlap in the distribution of white and black circles along the C5-C5′ and C6-C6′ coordinates, there is a critical region, roughly

0.2A˚ before the dimer anion splitting transition state, where the quantum yield for successful repair shifts from near zero to almost unity. The bifurcation between trajectories leading to ring re-formation and splitting in Fig. 7.9 implies a free energy maximum of the neutral surface in this region, but not necessarily a transition state.

The initial conditions in Fig. 7.9 are sampled near the minimum free energy path of the anion surface, not the neutral. Therefore the free energy maximum implied by

184 the circles in Fig. 7.9 is not necessarily a saddle point on the neutral surface, and is

not a transition state for the splitting reaction on the neutral surface.

Fig. 7.10 furnishes further evidence that a free energy maximum on the neutral

surface along the C6-C6′ bond is quite close to that on the anion surface. Fig. 7.10 is a

scatter plot of the potential energies (the potential energies have been shifted relative

to some minimum) on the neutral surface at time t = 0 after back ET has occurred as a function of C6-C6′ bond distances shown for both ring splitting and ring closure trajectories. Fig. 7.10 shows that average potential energy on the neutral surface has a maximum before the anion surface TST, the latter indicated with a vertical solid line in Fig. 7.9. The maximum of the neutral surface potential energies lies close to where trajectories shift from mostly reclosing to mostly splitting, suggesting that the energy maximum is also a free energy maximum, entropic eﬀects are minor, and that

Fig. 7.10 is an approximate cut through the neutral free energy surface in the vicinity of the anion splitting reaction path.

7.5 Conﬁgurational properties

In this section we detail the change in nuclear coordinates that occur during the bond splitting process. Speciﬁcally we monitor the changes in the C5-C6 (C5′-

C6′), C6-N1 (C6′-N1′) and C=O (carbonyl oxygen) distances which are illustrated in Fig. 7.11. Because the distributions are very similar for both bases we only show the distributions for the bonds on one thymine base. Also shown in the ﬁgure is the

C5-C6-C6′-C5′ dihedral angle which exhibits some unique features near the transition state.

185 energy (kcal/mol)

o r (A) C6−C6

Figure 7.10: Potential energies on the neutral surface at time t=0 after back ET for splitting trajectories (solid grey circles) and trajectories undergoing ring closure (solid black circles). The vertical solid line is the position of the TST on the anion surface. The solid red line is a 4th order polynomial ﬁt through the simulation data of the shifted potential energies.

The C5-C6 and C5′-C6′ distances show a decreasing trend from 1.53 to 1.40A˚ over the course of the splitting process. This is consistent with the fact that as the C5-C5′ and C6-C6′ bonds split, the C5-C6 and C5′-C6′ bonds develop double bond character. At the AM1 level of theory, Voityuk and co-workers326 suggested a

qualitative scheme for the underlying mechanism of CPD dimer splitting in which

the double bond is formed only in one base, say C5′-C6′, as the C6-C6′ bond splits.

The excess electron would then be localized on the C6 carbon atom once both the

C5-C5′ and C6-C6′ bonds are split. We can test the mechanism proposed by Voityuk

186 20 20

4 3 2 2 15 1 15 4 3 1

10 10

5 5

0 0 1.3 1.4 1.5 1.6 1.3 1.4 1.5 1.6 C5-C6 Distance (Å) C6-N1 Distance (Å) 20 1,3 and 4 0.1 15 O2

2 10 0.05 O4 5

0 0 0 20 40 60 80 1.2 1.25 1.3 1.35 C5-C6-C6 -C5 dihedral angle (degrees) C4-O4, C2-O2 Distances (Å)

Figure 7.11: Conﬁgurational changes during the splitting of the dimer.

et al. by tracking bond length changes that are indicative of double bond formation.

Shown in Fig. 7.12 is the evolution of the C5-C6 and C5′-C6′ bonds for 4 diﬀerent non-equilibrium trajectories that were begun in the minima where the the C5-C5′ bond was already split and whose C6-C6′ bond split within 4.5ps. The data shows that as the C6-C6′ bond splits, the double bond character in the C5(C5′)-C6(C6′) bond develops simultaneously without any noticeable lag between them.

The data shown in Fig. 7.12 challenges the interpretations of experiments performed by MacFarlane and Stanley365 on the repair of the CPD unit in the active site of photolyase. Stanley and co-workers use the absorption of light at 265nm to monitor the formation of the C5-C6 and C5′-C6′ double bonds. They propose that the cleavage of the ﬁrst bond is limited by the electron transfer lifetime and occurs

187 within 60ps which indicates the formation of only one double bond between the carbon atoms. Furthermore, they also ﬁnd an increase in the transient absorption signal on a timescale of 1500ps which they suggest indicates the splitting of the second bond and the formation of the second double bond between the carbon atoms. However our results shown in Fig. 7.12 are at odds with their interpretations. Fig. 7.12 shows that as the C6-C6′ bond splits, the double bond forms simultaneously in both bases. Thus, if the formation of a double bond is used as a signature for splitting of the C5-C5′ and C6-C6′ bonds, its formation implies that both bonds have broken. Hutter and co-workers329 have recently provided an illuminating critique to these experiments.

However, they suggest that because the spin density of the electron is localized on the

C6 or C6′ atoms, the formation of the second double bond after splitting of the bonds would be unfavorable. Fig. 7.12 shows that for our system, regardless of the diﬀer- ences in spin density between the C6 or C6′ atoms, the C5-C6 and C5′-C6′ double bonds form at the same time.

The C6-N1 and C6′-N1′ distances show a similar decreasing trend, very similar to C5-C6 bond distance, as the bond splits. The carbonyl oxygen distances do not show any signiﬁcant distance changes as the bond splits. However we do ﬁnd that the C4-O4(C4′-O4′) carbonyl distances are longer than those of the C2-O2(C2′-O2′) across points 1 through 4.366 Finally the C5-C6-C6′-C5′ dihedral angle exhibits dramatic changes as it approaches the transition state. The dihedral angle can change from 2-3 degrees before the transition state to about 50 degrees near the transition state and thereafter relaxes back to 6 degrees after crossing this region. This kind of distortion at the transition state has been observed in previous work although they were done with gas-phase and small cluster calculations.326, 328, 359 Four representative

188 1.6 1.6 1.5 1.5 1.4 1.4 1.3

C5-C6 (C5-C6 ) Distance (Å) 1.2 1.3 0 1000 2000 3000 4000 C5-C6 (C5-C6) Distance (Å) 0 1000 2000 3000 4000 time (fs) time (fs)

1.6 1.6

1.5 1.5

1.4 1.4 C5-C6 (C5-C6) Distance (Å) 1.3 C5-C6 (C5-C6) Distance (Å) 1.3 0 1000 2000 3000 4000 0 1000 2000 3000 4000 time (fs) time (fs)

Figure 7.12: C5-C6 (solid curve) and C5′-C6′ (dashed curve) bond lengths over time for four splitting trajectories. The sharp decrease in bond length reﬂects formation of double bond character, which is seen to be simultaneous in both bases, as splitting of the C6-C6′ bond occurs. The circled regions indicate where the C6-C6′ bond splits.

snapshots along points 1-4 are illustrated in Fig. 7.13 to demonstrate the conﬁgura-

tional changes that occur during splitting and the open conﬁguration that can occur

near the transition state region.

7.6 A framework for understanding the competition between bond splitting and charge recombination

As indicated earlier, there have been a number of experiments on model com-

pounds containing a photoinduced electron donor tethered to a CPD unit, that have

shed light on the role of the solvent environment in the repair process. The splitting

eﬃciency (quantum yield) in model compounds is generally far below that achieved

by the enzyme photolyase. For model compounds in which electron transfer to the

189 1) 2)

3) 4)

Figure 7.13: Snapshots of typical conﬁgurations analyzed along umbrella sampling C6-C6′ coordinate.

CPD results in a zwitterionic charge transfer (CT) state and the tether is short, there is a clear experimental trend in which greater splitting eﬃciency is associated with decreased solvent polarity.336, 337 This trend has been explained324, 325, 335–337 by at- tributing splitting ineﬃciency to short-circuiting of the process by premature back electron transfer (BET) in the Marcus inverted regime. Polar solvents stabilize the zwitterionic CT state, the reactant for BET, more than the product. Hence increased solvent polarity means smaller driving force and, in the inverted regime, more rapid

BET that could short-circuit the repair. However, this is not a complete explanation.

While early BET can short-circuit repair, BET at the proper stage of the reaction is

190 required to complete a successful repair. A mechanism that explains why BET could occur at the proper moment for repair in some situations, most notably in the enzyme photolyase,29 and not in others has not been addressed previously in the literature.

Our computational studies suggest a qualitative framework which can rationalize the strong dependence of splitting eﬃciency on solvent properties, and why repair is so eﬃcient in photolyase.

Energy CT [T−T] TST slow BET [T T] Fast BET slow BET

Neutral [T−T] [T T]

Splitting Coordinate

Figure 7.14: Schematic showing placement of a neutral ground state and CT state with respect to the dimer splitting coordinate.

Our studies indicate that the splitting of the C5-C5′ and C6-C6′ bonds of the

CPD anion is complete within several picoseconds in water. We consider the general properties of the anion and neutral free energy surfaces. Our studies, and previous theoretical and experimental works,328, 355, 360 have found that the overall splitting free energy is similar in the anion and neutral dimer. The main diﬀerence is the markedly reduced free energy barrier for splitting of the anion. Our studies shown in section

191 7.3, indicate that, in water, the activation free energy for splitting of the neutral is at least 39kcal mol−1, much larger than the splitting barrier of the anion, and close to the value obtained in gas phase calculations.363 We showed that by approximating the

BET as a vertical detachment of the electron, the transition state for dimer splitting on the anion free energy surface lines up with a free energy maximum along the splitting coordinate on the neutral surface. This maximum divides trajectories that lead to dimer reformation following BET, from trajectories that lead to successful repair. These properties along the splitting coordinate are depicted in the schematic shown in Fig. 7.14 which illustrates the energetic changes along a combined splitting coordinate of the C5-C5′ and C6-C6′ bonds. In the subsequent discussion, we will develop a qualitative framework that explains observed trends when the donor and acceptor, before electron transfer, are neutral, such as in many model compound studies. Then after forward electron transfer, the donor is a cation and together with the dimer anion, forms a zwitterionic charge transfer (CT) state. We believe the model provides a useful framework for understanding other situations, such as when the electron-donating group is anionic and therefore the CT state also contains a single negative charge.

The CT state, reached by photoexcitation, lies above the neutral state and BET is generally thought to occur in the inverted Marcus regime, as shown in Fig. 7.15 where BET near the transition state for splitting is depicted as nearly barrierless. In

Fig. 7.15, the splitting of the C5-C5′ and C6-C6′ bond is encapsulated into a combined splitting coordinate q which tracks progress from reactants to products in the two- dimensional surface of Fig. 7.5, or a higher dimensional surface if a solvent reaction coordinate is included. The role of solvent ﬂuctuations is captured by a collective

192 decreasing solvent polarity G

(solvent polarization) X CPD anion

q (dimer splitting reaction coordinate)

CPD neutral

Figure 7.15: Schematic showing placement of a neutral ground state and CT state with respect to the dimer splitting and solvent polarization coordinates. The white curve is the minimum free energy path from dimer to split products on the CT surface. The red curve above the white curve is the intersection between the anion and neutral surfaces. Decreasing solvent polarity will raise a zwitterionic CT state surface, as shown in the ﬁgure, and increase the activation energy for BET.

solvent polarization coordinate X which is assumed to be harmonic. The neutral state is located at X = 0, while the equilibrium solvent polarization in a zwitterionic

CT state is non-zero. Motion along X may represent relaxation after forward ET, or a ﬂuctuation leading to the transition state for BET. In constructing this model we tacitly assume that the presence of a donor cation or donor radical species will not qualitatively change the splitting energetics. As the CPD splits (motion along the white line in Fig. 7.15), BET is driven by a solvent polarization ﬂuctuation along the

193 X coordinate in Fig. 7.15 that brings the CT reactants to a point where they are in

resonance with the neutral products (solid red line).

polarization)

X (solvent

q (dimer splitting reaction coordinate)

Figure 7.16: Schematic showing placement of neutral ground state (white) and CT state (blue) with respect to the dimer splitting and solvent polarization coordinates in a non-polar solvent. The activation barrier for BET is very large throughout the splitting process and a short-circuiting channel would have signiﬁcant eﬀect only if the activation barrier for splitting was large.

If, as shown in Fig. 7.14 and Fig. 7.15 similar overall reaction free energy but larger splitting barrier on the neutral dimer surface compared to the anion are generic features, then it also must be a generic feature that the free energy diﬀerence between

CT and neutral surface grows as one moves along the reaction coordinate in either direction away from the transition state. Consequently, moving away from the dimer splitting transition state, the reaction free energy for BET becomes more negative and the activation energy for BET increases. The BET rate is a maximum in the

194 dimer splitting transition state region. In order to achieve higher splitting eﬃciency, the system must rapidly move through the transition state region and/or ensure that the magnitude of BET in this region is slow enough so that it doesn’t compete with splitting. The fact that the main diﬀerence between CT and neutral free energy surfaces is the larger splitting barrier in the neutral state, implies that the region of fastest BET occurs near the transition state where the white and red curves in

Fig. 7.15 are close to each other. As mentioned earlier, the conﬁguration of the dimer at the neutral and CT transition state is similar, suggesting that once the system passes the splitting barrier on the CT surface without short-circuiting BET in this region, subsequent BET from the product region of the anion surface will take the system to the product region of the neutral surface.

The scheme of Fig. 7.15 implies that potential short-circuiting of the dimer repair principally occurs via BET near the transition state, and the rate of BET at this point is strongly modulated by the solvent (see Fig. 7.16 and Fig. 7.17). Polar solvents will lower the anion surface, decrease the driving force for BET, and in the inverted region increase the degree of short-circuiting of dimer repair. Rapid splitting of the

C5-C5′ and C6-C6′ bonds on the picosecond timescale and a suﬃciently non-polar environment will suppress short-circuiting through BET until the system reaches the split product well on the CT state. At this point, BET from the charge transfer state to states of similar energy within the dense vibrational manifold of the ground state will likely occur on a somewhat slower, perhaps nanosecond time scale typical of radiationless processes in molecules of this size.367–369 We showed in the previous section that BET beyond the transition state region on the anion surface, leads to repair and further lengthening of the C5-C5′ and C6-C6′ bonds. This model provides

195 G

polarization)

X (solvent

q (dimer splitting reaction coordinate)

Figure 7.17: Schematic showing placement of neutral ground state (white) and CT state (blue) with respect to the dimer splitting and solvent polarization coordinates for a situation in a highly polar solvent. In this scenario the CT surface is lowered to a point where there are two regions along the splitting coordinate where activation barrier for BET is zero. The BET in this situation can occur in the normal region near the TST although the barrier is still small.

a potential mechanism to explain how high quantum yields of repair are achieved in the active site of photolyase. To our knowledge, Savéant was the first to consider how the rate of electron transfer could be modulated during a bond-breaking process, and his study served as the inspiration for our model.370 We have discussed the effect of solvent polarity in terms of the effect on the relative position of the reactant and produce free energy surfaces, which is the dominant effect because the BET rate depends exponentially on activation energy. When influenced by dynamic solvent effects,371 the increased polarity is associated with smaller longitudinal relaxation

196 time and faster BET rates, further increasing the likelihood of short-circuiting of the repair in polar solvent.

In this section, we have discussed the role of solvent polarity on the BET rate.

However, both thermodynamic and dynamical effects of solvent will play a critical role in modulating the splitting rate of the bonds. In the next chapter, we show that the solvent plays an important role in the splitting of the C5-C5′ and C6-C6′ bonds. Thus, while non-polar solvents slow down the charge-recombination process throughout the splitting process, a larger activation barrier for splitting could induce short circuiting from the partially cleaved minima. An important aspect that should be considered in greater detail, are the non-equilibrium initial conditions of the solvent polarization coordinate X following forward ET. In our discussion above, we have tacitly assumed that the non-equilibrium relaxation of X to the minima on the CT state occurs on a faster timescale than the splitting process. However, this may not be true in general. If we assume that the variable X is undergoing Brownian motion in a harmonic potential, the timescale of relaxation decays exponentially and is proportional to the viscosity of the environment. If the initial distribution begins to the left of the solid white line in Fig. 7.15 as one might expect for a zwitterionic CT state, then a slower non-equilibrium relaxation of X could effectively bypass the region of maximum BET. The framework we propose does not explain the trends observed in longer spacer model compounds where an increase in quantum yields are observed for solvents with higher polarity.337 Furthermore, the quantum yields of repair with different longer spacer model compounds can also differ.337 The longer spacer model compounds might be characterized by different conformational flexibility337 compared to the short spacer compounds, which will in turn affect the driving force for BET.

197 Clearly more detailed calculations like the ones we have done in this work, in diﬀerent solvents need to be performed before the controversies are settled.

7.7 Conclusions

Our ab initio MD simulations of the cyclobutane thymine dimer surrounded by

32 waters show that the splitting of the C5-C5′ and C6-C6′ bond is complete within several ps. The 2D-free energy surface in Fig. 7.5 suggests that the splitting process is asynchronous concerted, although we will demonstrate in the next chapter, that multidimensional and non-equilibrium eﬀects can give the splitting process some stepwise character although this does not change the overall splitting times of the C5-C5′ and C6-C6′ bonds signiﬁcantly.

Numerous experiments have been performed on the repair dynamics of the thymine dimer using model compounds where the CPD unit is tethered to an electron donor that can be photoexcited.324, 325, 335–337 Additionally, the repair of the anion thymine dimer has also been monitored spectroscopically in the active site of photolyase.29

There are no experiments to our knowledge that directly spectroscopically probe the evolution of the thymine anion dimer. A recent work by Stanley and co-workers365 uses electronic absorption spectroscopy to monitor the formation of the repair photoproducts. However, this method is very sensitive to the environmental changes in the active site of the protein and does not provide a direct measurement of the splitting timescales.

The theoretical method and choice of basis set is always a concern in any type of ab initio calculation. While our results are consistent with other theoretical works in the literature on similar systems,327 inadequate basis sets, ﬁnite box size eﬀects and

198 errors in energetics could aﬀect the splitting timescales. Furthermore, as indicated

earlier, all theoretical calculations of this system are anionic systems, while most of the

experiments that involve the donation of an electron to the dimer, are neutral systems

overall. If the donor and acceptor are in close proximity, the splitting dynamics might

be aﬀected. The only experiments to our knowledge that our theoretical calculations

can compare directly with are those by Carrell and co-workers338 where dimer splitting was induced by ionizing radiation. Their results provide an upper bound to the splitting time of 35ns for the splitting of the C5-C5′ and C6-C6′ bonds. In these experiments, the splitting of the thymine dimer occurs on an overall anion potential surface, like our calculations.

The umbrella sampling simulations generates a free energy surface in two impor-

tant reaction coordinates, the C5-C5′ and C6-C6′ bonds lengths, which provides the

broad outlines for the reaction mechanism. This surface quantiﬁes how the reaction

coordinate evolves from principally along the C5-C5′ distance early in the reaction to

along the C6-C6′ distance as the second bond is cleaved. There is a local minimum

where the C5-C5′ bond is partially cleaved and the C6-C6′ bond is intact followed

by a rather small 1.5kcal mol−1 transition state. Using TST theory we predict that

the splitting time of the C6-C6′ bond to be ∼ 0.5ps. The return of the electron from

the anion dimer to the donor cation should be considered as a critical part in the

biological repair of the dimer both in the active site of the protein as well as in model systems. Our simulations ﬁnd a substantial amount of reorganization of the C5-C5′ and C6-C6′ bonds once back ET occurs. Our work shows that back ET can result in either ring closure, where the C5-C5′ and C6-C6′ bonds reform hence reversing repair, or ring splitting, where the C5-C5′ and C6-C6′ bonds undergo further lengthening.

199 There exists a free energy maximum on the neutral surface quite close to the TST

position on the anion surface. Hence if back ET occurs after the transition state on

the anion surface, then the quantum yield of splitting will be close to unity.

Using a simple model that takes advantage of generic thermodynamic properties

along the splitting coordinate on both the anion and neutral surfaces, we have shown

that the back ET rate in the Marcus inverted region will ﬁrst increase, pass through a

maximum, and then later decrease during the splitting process. The precise placement

of the CT and neutral surfaces with respect to each other, as shown in Fig. 7.15 and the

activation barrier of splitting on the CT state, will either enhance or suppress short-

circuiting via BET and hence control the splitting eﬃciency. Our generic model helps

provide a framework for understanding why the quantum yields of repair of short-

spaced tethers increase with non-polar environments. However, more work is needed

in this area to understand why the trends in quantum yields of repair are reversed

for longer-spaced tethers. This will require detailed calculations using ab initio MD methods of the dimer splitting in diﬀerent solvents and an explicit treatment of both the forward and backward electron transfer processes, which is beyond the scope of the current study.

200 CHAPTER 8

A theoretical picture of CPD dimer repair: II

8.1 Introduction

Cyclobutane pyrimidine dimers are a form of damage that occur in DNA via UV radiation.317–319 The enzyme photolyase can repair these damaged bases by injecting an electron at the site of damage.29, 319 There have been several experimental29, 319, 365 and theoretical eﬀorts327–329 made to understand the mechanism by which the enzyme and model systems repair the dimers. The splitting of cyclobutane pyrimidine dimer anions has also been studied in numerous experiments on model compounds in a variety of solvents.323–325 The reader is referred to the previous chapter for a detailed review. In this chapter we continue our study of the splitting of the cyclobutane pyrimidine dimer in water, which has direct bearing on model compound studies and implications for DNA repair in photolyase.

We will begin by summarizing some of the main results of the ﬁrst chapter on the mechanisms in the repair of the cyclobutane thymine dimer. Ab initio simulations of the cis,syn-thymine cyclobutane pyrimidine dimer (CPD) splitting in aqueous solvent were conducted. The motion of both the CPD unit and the solvent is governed by a potential surface calculated using electronic density functional theory. Umbrella

201 sampling was used to elucidate a two-dimensional free energy surface for dimer anion

splitting with respect to the C5-C5′ and C6-C6′ bond lengths. Our 2D free energy

surface predicts that the splitting of the C5-C5′ and C6-C6′ bonds is asynchronous

concerted and complete within several picoseconds, consistent with recent theoreti-

cal work by Masson et al.327, 329 In contrast, the activation barrier for splitting the

thymine dimer on the neutral surface is exceedingly large and would not be accom-

plished by thermal ﬂuctuations.

Without modeling the electron donor, we were unable to determine the rate of back ET from our previous calculations. However assuming a vertical detachment of the electron from the anion to the neutral surface we ﬁnd some interesting features on the role of back ET in DNA repair. Firstly, the CPD unit undergoes signiﬁcant reorganization in the C5-C5′ and C6-C6′ bond lengths once back ET takes place.

Furthermore, we also find that the configurational position of the TST on the neutral surface is quite close to that on the anion surface. This implies that if back ET occurs after the TST on the anion surface, the quantum yield of repair would be close to unity. However back ET significantly before the TST on the anion surface, will lead to a very low repair quantum yield. Thus the back ET process should be considered as an intrinsic part of biological repair.

In this chapter, we discuss the role of multidimensional effects involving the role of solvent, on the splitting of the C5-C5′ bond. Our calculations show that the solvent plays a critical role in the splitting of both the C5-C5′ and C6-C6′ bonds although its effects are more drastic on the splitting of the C5-C5′ bond. Because the splitting of the C5-C5′ bond is the first step in the splitting process after forward electron transfer, we suspected that non-equilibrium effects might play an important role.

202 Our results suggest that the non-equilibrium initial conditions involving the solvent, are likely to play a role during the splitting process of the C5-C5′ bond and perhaps the C6-C6′ bond as well. In previous studies,327, 329 the surrounding solvent was not treated quantum mechanically and so issues such as charge transfer (CT) from the

CPD unit to the solvent could not be examined. In this chapter we present evidence that the CT delocalization onto the solvent observed in the previous chapter, is not artifact of DFT by performing quantum chemistry fragment calculations.

We begin in section 8.2 by discussing the multidimensional nature of the free energy landscape involved in the splitting of the C5-C5′ bond. Within this section we also discuss the role of solvent and dynamic changes in the electron density on the dimer, during the splitting process. As mentioned earlier, we ﬁnd a signiﬁcant amount of charge delocalization onto the solvent. In section 8.3 we verify this result with benchmarks that validate that the charge delocalization onto the solvent is not an artifact of the electronic structure calculation. In section 8.4, we discuss the partitioning of electron density between the dimer and solvent during the splitting the C6-C6′ bond. Changes in the solvent density around the C6 and C6′ carbon atoms during the splitting process are also detailed in this section. In section 8.5 we document the role of charge transfer to the C6(C6′) carbon atoms and increase in water density near the C6(C6′) carbon atoms, in the splitting of the C6-C6′ bond.

Finally we end with conclusions of our work in section 8.6.

203 3

< 50 fs 2.5

> 200 fs 2 Splitting Population

Unsplitting Population C5-C5 Distance (Å) 1.5

1 0 100 200 300 400 500 Time (fs)

Figure 8.1: Non-equilibrium dynamics of C5-C5′ bond after electron injection leading to splitting and unsplitting populations. Also shown are trajectories from the splitting population that split within 50 fs and between 200-500 fs.

8.2 Multidimensional and possible non-equilibrium eﬀects during C5-C5′ bond splitting

The free energy surfaces presented in the previous chapter, were calculated using

an equilibrium distribution, or as close as one can be approximated with ﬁnite sam-

pling, for all degrees of freedom except those constrained in the umbrella sampling.

Technical details concerning the umbrella sampling are given in the previous chap-

ter. These surfaces indicate that opening the C5-C5′ bond involves only a very small free energy barrier and a larger barrier of 1.5kcal mol−1 for cleavage of the C6-C6′

bond. Hence the newly formed anion is expected to quickly reach equilibrium at the

local free energy minimum associated with the partially cleaved C5-C5′ bond and

intact C6-C6′ bond. However, this picture assumes that all coordinates orthogonal to

204 Figure 8.2: Snapshot showing location of single water molecule near the O4 carbonyl oxygen

the C5-C5′ partial cleavage reaction coordinate reach local equilibrium on a shorter timescale than the fast splitting time predicted by the small barrier shown in previous chapter. The nascent anion with the C5-C5′ and C6-C6′ bonds intact, is formed by the transfer of an electron to the neutral system, where the solvent is equilibrated near a neutral CPD unit. This opens the possibility that non-equilibrium eﬀects could affect this stage of the dimer splitting reaction. Regardless of whether non-equilibrium eﬀects occur, it is always possible that involvement of additional degrees of freedom in the reaction process should be considered to better understand the reaction path and more accurately estimate the true free energy barrier for the reaction.

In this work we do not model the electron transfer process from a potential donor to the thymine dimer. Hence, we cannot specify the typical dimer and solvent con-

ﬁgurations where electron transfer occurs, which would form the nascent distribution on the anion surface for dimer splitting. To obtain some information on the likelihood of multidimensional and non-equilibrium eﬀects, we adopted the equilibrium

205 distribution of the neutral thymine dimer surrounded with 32 waters, as the initial nuclear conﬁgurational distribution following electron transfer. Masson et al.,329 who have recently conducted QM/MM simulations of the thymine dimer in the active site of the photolyase protein, made a similar choice for their initial conﬁgurations. With this caveat concerning the initial distribution, we have studied the non-equilibrium dynamics of the anion dimer starting from the equilibrium distribution of the neutral.

The results presented below indicate that the one and two-dimensional free energy profiles presented in the previous chapter, might not capture the full complexity of the reaction dynamics. In particular we show that solvent motion comes into play, requiring an additional reaction coordinate describing the configuration of nearby water molecules. Of course, to definitively determine whether non-equilibrium effects will play a role, we would need a better estimate of the initial distribution following electron transfer. This will depend on the chemical identity of the electron donor and is beyond the scope of this study.

To study the non-equilibrium relaxation of the dimer anion during the ﬁrst 0.5ps following electron transfer, 343 conﬁgurations were sampled from an equilibrium simulation of the neutral system consisting of the thymine dimer surrounded by 32 waters with both C5-C5′ and C6-C6′ bonds intact. The neutral system was equilibrated for

7ps, after which initial conﬁgurations for non-equilibrium trajectories were taken from an ensuing 20ps of simulation. The initial velocities for the non-equilibrium simulations were chosen from a Maxwell-Boltzmann distribution at 300K. We monitored the C5-C5′ and C6-C6′ distances as well as the evolution of other charge and con-

ﬁgurational properties. Fig. 8.1 shows that for 52% of the trajectories, the C5-C5′ bond rapidly elongated from 1.6A˚ to 2.5A˚ within the 500fs run time while the other

206 0.9 0.4 0.2

0 C5−HW Distance (A)

r C5−C5

Figure 8.3: 2D Surface for potential of mean force between C5 and HW of all waters with distances in Angstroms and free energy in kcal mol−1

48% remained uncleaved at 1.6A˚ and appear to be opening on a longer time scale

than that which would be inferred by our equilibrium free energy curve along the

C5-C5’ coordinate documented in the previous chapter (barrier of 0.6kcal mol−1).

Fig. 8.1 also shows the non-equilibrium average of trajectories that split within 50fs

and those that split between 200 − 500fs. These populations are later analyzed separately. Masson et al.329 also found that the C5-C5′ bond in one of their seven

trajectories remained intact for an unusually longer time of 400fs. In our simulations

the C6-C6′ bond remained intact, near 1.6A˚ in all but 14 of our 343 non-equilibrium trajectories. In those 14 cases, splitting of the C6-C6′ bond was preceded by splitting

of the C5-C5′ bond. The delocalization of the excess charge onto the solvent, detailed in the following section, is evident in both the splitting and unsplitting populations.

207 3

2.5

Anion 2

1.5 Neutral

0.5

0 2.5 3 3.5 4 Closest C5-HW Distance Å

Figure 8.4: Distribution of the distance of the closest water hydrogen to the C5 atom on the neutral surface and the ﬁrst two umbrella windows on the anion surface.

The involvement of aqueous solvent in the reaction dynamics, is revealed by tracking several solute-solvent coordinates. During our umbrella sampling simulations we

find that a single water molecule as shown in Fig. 8.2, stays close to the O4 carbonyl oxygen throughout most of the simulation time. After much longer simulations and larger system sizes we would expect to sample configurations where water molecules would exchange with the bulk and interact with the other carbonyl oxygen. The configurational position of the water molecules close to the C5 carbon atom are important in determining the evolution of the two populations (splitting and un-splitting trajectories) following electron addition. Fig. 8.3 shows a 2D surface of the potential of mean force (PMF) of the distance between the C5 carbon atom and hydrogens on the waters obtained from all our umbrella sampling windows along the C5-C5′ coordinate. For visual clarity, only the region between the C5-C5′ bond length of 1.6-1.9A˚

208 and C5-HW distance between 2.5-3.8A˚ is shown which eﬀectively corresponds to the

close waters near the C5 carbon atom. The plot shows some interesting features.

There exists a shallow minimum at a C5-C5′ distance of 1.6A˚ and a C5-HW distance of 3.0A˚ corresponding to the location of the closest waters near the C5 carbon atom.

In Fig. 8.3, the free energy is assigned to have a value zero at this local minimum. In

Fig. 8.4 we show the distribution of the closest C5-HW distance amongst waters near the C5 carbon atom on the neutral surface as well as the ﬁrst two umbrella windows on the anion surface where the C5-C5′ distance was constrained to 1.59A˚ and 1.64A˚ respectively. The ﬁgure shows that on the neutral surface the closest water hydrogen is located further out at approximately 3.3A˚ on a softer potential while on the anion

surface the closest hydrogen of the waters is located at a distance of approximately

3.0A˚ on a tighter potential. This implies that transfer of an electron to an equilibrium

distribution of neutral dimers will place most of the initial conﬁgurations near a free

energy maximum at approximately 0.9kcal mol−1 in Fig. 8.3, from which trajectories

may evolve toward direct splitting of the C5-C5′ bond, or become trapped in the local

free energy minimum shown in Fig. 8.3. This subtle diﬀerence between the location

of the nearest neighbor water molecule to the C5 carbon atom on the neutral and

anion surface, determines the fate of the splitting and unsplitting populations, and

makes water an important participant in the reaction coordinate for the repair of the

CPD unit.

In Fig. 8.5 we show the evolution of the C5-C5′ bond and the closest C5-HW

distance for the non-equilibrium swarm of trajectories. The yellow arrows on both

ﬁgures serve as a guide to illustrate that the equilibrium free energy analysis incor-

porating solvent in the reaction coordinate shown in Fig. 8.3, is consistent with the

209 split < 50 fs split 200−500 fs a) b) Closest C5−HW (A)

r r C5−C5 C5−C5

Figure 8.5: Non-equilibrium swarm of trajectories in left panel a) that split within 50fs and right panel b) that split between 200 − 500fs.

non-equilibrium trajectories. The left panel of Fig. 8.5 shows the non-equilibrium swarm of trajectories that split within 50fs while the right panel of Fig. 8.5 shows the non-equilibrium swarm of trajectories that splits between 200-500fs. The swarm that splits on the faster timescale doesn’t exhibit a strong density of trajectories in the region indicated in the ﬁgures with a rectangular box corresponding to the free energy minimum at rC5−C5′ = 1.6A˚, rC5−HW = 3.0A˚ in Fig. 8.3. The trajectories that split within 50fs bypass or brieﬂy linger in the rectangular region of the left panel in

Fig. 8.5. They do not become deactivated in the free energy minimum corresponding to this region. For these trajectories we observe that as the C5-C5′ bond splits, the distance between the closest water hydrogen and the C5 carbon atom also decreases by 0.3A.˚ The trajectories that split between 200 − 500fs are seen to populate the free energy well near rC5−C5′ = 1.6A˚, rC5−HW = 3.0A˚ (Fig. 8.3 and right panel of

210 Fig. 8.5). When comparing the left and right panels of Fig. 8.5, note that roughly

the same number of trajectories is plotted in each ﬁgure. After equilibration into the

shallow minimum, where the C5-C5′ bond is still intact, the trajectories on the right panel of Fig. 8.5 can then undergo splitting of the C5-C5′ bond through some minor increase in the closest water hydrogen distance to the C5 atom.

split < 50 fs unsplitting and 200−500 fs a) b) charge on C5 atom

r r C5−C5 C5−C5

Figure 8.6: Non-equilibrium swarm of trajectories showing evolution of charge on C5 carbon atom for splitting and unsplitting populations

Several features of the charge and electronic orbital distributions observed in our

non-equilibrium trajectories and umbrella sampling studies agree with previous the-

oretical work. Rosch and co-workers326 studied the evolution of the spin densities at

the C5 and C5′ carbon atoms for the gas phase thymine dimer and proposed that as

the C5-C5′ bond splits, the unpaired electron localizes at the C5′ carbon atom. In

the left panel of Fig. 8.6 we show the evolution of the charge on the C5 carbon atom

for the trajectories that split within the ﬁrst 50fs and on the right panel we show the

211 unsplitting population and trajectories that split between 200 − 500fs. Charges were calculated using the density derived DDAP10 charges. The data shows that as the

C5-C5′ bond splits, there is partial localization of electron density on the C5 carbon atom in the splitting populations. The data in the left panels of Fig. 8.5 and Fig. 8.6 show that the splitting of the C5-C5′ bond, is accompanied by a simultaneous charge transfer to the C5 carbon atom and a decrease in the closest water hydrogen distance to the C5 carbon atom by roughly 0.3A.˚ For the unsplitting populations and the swarm that split over a longer timescale, the average charge on the C5 carbon atom is close to zero when the C5-C5′ bond is intact, after which bond splitting leads to localization of charge on the C5 carbon atom. We observe the same eﬀect at the C5′ carbon atom and hence report only the behavior at the C5 carbon atom.

Figure 8.7: Isosurfaces showing location of diﬀerence in electron density between anion and neutral systems. The isosurface on the left represents a positive isovalue while that on the left represents a negative isovalue. Solid yellow arrow on the left points to the C4-O4σ orbital while the dashed yellow arrow on the left points to the C5-C5′σ∗ orbital. The solid yellow arrows on the right point to the C4-O4π∗ and C2-O2π∗ orbitals.

212 In order to provide some qualitative insight into the mechanism of bond breaking

(C5-C5′ first followed by C6-C6′ second), we have calculated maps of the electron density difference between anion and neutral states for configurations with both bonds intact. A map for one such configuration is displayed in Fig. 8.7 where the ball-and- stick representations of the waters have been removed for visual clarity. A positive isovalue for the electron density is plotted on the left in Fig. 8.7, revealing where electron density is enhanced following electron transfer. A negative isovalue is plotted on the right in Fig. 8.7, indicating regions of depleted electron density resulting from electron transfer. Pockets of density outside of the dimer correspond to regions where the electron density is delocalized on the water. The left panel of Fig. 8.7 shows quite clearly that when the electron is added to the neutral system, there is an increase in electron density in the C4-O4σ and in the C5-C5′σ∗ orbitals. The increase in electron density seems to be more significant at the C4-O4(C4′-O4′) carbonyls but occurs at the C2-O2(C2′-O2′) carbonyls as well. In the right panel in Fig. 8.7 we observe regions of decrease in electron density at the C4-O4π∗ orbital. As before, this seems to be most significant at the C4-O4(C4′-O4′) carbonyls but also occurs at the

C2-O2(C2′-O2′) carbonyls. We also ﬁnd a decrease in electron density in the C5-C5′σ orbital in another fragment but the data is not shown for brevity. Delocalization of electron density from the C4-O4π∗ orbital was recently suggested by Masson et al.329 as the mechanism for the rapid splitting of the C5-C5′ bond upon electron addition.

The foregoing observations concerning the electron density in Fig. 8.7 are consistent with the mechanisms suggested in previous theoretical works.328, 329, 339

As mentioned earlier, Masson et al.329 observe a longer C5-C5′ bond splitting time in one of their trajectories, consistent with the non-equilibrium eﬀects we have

213 O4−C4−C5−C5 Dihedral Angle (radians) r r C5−C5 C5−C5

Figure 8.8: On the left is the 2D free energy surface for the C4-O4-C5-C5′ dihedral angle and C5-C5′ bond. On the right the path of a swarm of non-equilibrium trajectories over these two coordinates is shown. The trajectories that split are black (top right), while those that do not split within the observation window of 0.5 − 1ps are shown in red (bottom right).

documented. They attribute the delayed C5-C5′ bond splitting to a diﬀerent extent of C4-O4π∗ and C5-C5′σ∗ orbital coupling in one of their trajectories, associated with a smaller and more widely ﬂuctuating O4-C4-C5-C5′ dihedral angle. So far, we have

not found evidence to associate smaller dihedral angle with delayed C5-C5′ bond

splitting, although it may not be entirely appropriate to compare dimer splitting

in DNA photolyase with splitting of the free dimer anion in solution treated here.

214 The right panel of Fig. 8.8 shows that at the instant of electron injection there is no discernible diﬀerence between the splitting and unsplitting populations along the

O4-C4-C5-C5′ dihedral angle coordinate. Both splitting and unsplitting populations at the instant of electron injection have an average O4-C4-C5-C5′ dihedral angle of approximately −76o. On the right panel of Fig. 8.8, the unsplitting population is colored in red. Furthermore, the ﬂuctuations also appear to be very similar. The non-equilibrium trajectories that split along the C5-C5′ bond show some widening of the dihedral angle to more negative values, consistent with the shift of the minimum free energy toward more negative values of the dihedral angle with increasing C5-C5′ bond length observed in the free energy surface in the left and right panels of Fig. 8.8 as indicated by the yellow arrows.

Having accumulated many trajectories that involve the splitting of the C5-C5′ bond, we can examine the distribution of splitting times. Fig. 8.9 shows the distribution of splitting times for the C5-C5′ bond among 179 non-equilibrium trajectories with initial conditions randomly sampled from an equilibrium distribution of the neutral dimer and run for a total of 1ps. There is a big peak between 0-50fs indicating that majority of the splitting population cleaves within a very short time. However, we do observe a long tail of splitting times beyond 50 fs all the way up to 1 ps. The long tail corresponds to trajectories that ﬁrst equilibrate into the region shown in

Fig. 8.3 with the C5-C5′ intact and at a C5-HW bond distance of 3.0A˚ which corresponds to the closest water hydrogen approach to the C5 atom. The C5-C5′ and

C6-C6′ bonds for 49 of the trajectories, a substantial fraction of the initial sample, remain unsplit after 1ps of running time. In the previous chapter, we stated that the two-dimensional free energy surface in the C5-C5′ and C6-C6′ bond lengths, suggests

215 an asynchronous concerted process for the bond splitting. Even though the C5-C5′ and C6-C6′ bonds are broken sequentially, between the initial state following electron transfer and split products, there is only one signiﬁcant transition state, the one separating the partially cleaved conﬁguration (C5-C5′ bond cleaved, C6-C6′ intact) and the split products. This applies for the swarm of trajectories that split within

50fs shown in the left panel of Fig. 8.5. However the swarm of trajectories that split between 200-500fs and the 49 trajectories that remain unsplit and trapped in the shallow minimum shown in Fig. 8.3, indicate that enlarging the reaction coordinate to include solvent can reveal a stepwise character to the reaction. The probability of proceeding directly to the partially cleaved locally stable state or being trapped in the shallow minimum found in Fig. 8.3 depends on the nascent configurational distribution following electron transfer. The first reaction mechanism is concerted, while the second is stepwise because the system surmounts two free energy barriers on the way to split products. Consequently, a stringent assignment of stepwise versus concerted mechanism is complicated by the non-equilibrium effects involving the role of solvent.

The results of this section should be taken as a possible example of the type of non-equilibrium or multi-dimensional effects that can result from the initial distribution following electron transfer, and how these may require additional reaction coordinates, in this case involving solvent, for their description. Non-equilibrium effects that could occur in the model compounds323–325 or in the active site of the protein29 might be more complex and should be explored in greater detail. Our non- equilibrium trajectories were initially sampled from a relatively short 20ps simulation of the neutral solvated CPD unit. Macromolecular fluctuations on longer timescales

216 # of trajectories

Time (fs)

Figure 8.9: Distribution of splitting times for C5-C5′ bond

that are likely prevalent in the active site of the protein and in model compounds with a long tether to the photoreceptor, might also provide conditions for other multidimensional and non-equilibrium eﬀects that are beyond the scope of this study.

Other non-equilibrium eﬀects might arise from coupled motion involving the solvent.

Within a Marcus picture of electron transfer, there is a certain timescale associated with the non-equilibrium relaxation of the surrounding solvent to stabilize the CT state formed after forward ET. The magnitude of this timescale and how it is coupled to splitting of the bonds will play a critical role in the mechanisms of the splitting process.369, 371

It is worth noting that the X-ray crystal structure of the protein photolyase, PDB code 1TEZ,372 shows that the adenine di-nucleotide of the cofactor FADH-, occupies a similar topographical position in the active site, as the closest water described in our simulations above. This might suggest a role for the adeninine di-nucleotide to

217 participate in the splitting of the C5-C5′ bond as suggested by experiments by Zhong and co-workers.29 However, more detailed simulations of this system in the active site of the protein will be required to conﬁrm this mechanism and the role of the adenine di-nucleotide in DNA repair.

8.3 Methodological issues regarding charge delocalization

A central issue in a substantial portion of the previous work on CPD splitting is the location of the excess electron density during the course of the splitting process.326–328, 341, 355 During the entire splitting process we find a significant degree of charge delocalization onto the water. Before presenting results it is necessary to discuss several methodological difficulties associated with calculating the disposal of excess charge. Charge delocalization can sometimes arise as an artifact in density functional theory calculations. The SIE (self interaction error) is well known to plague DFT type calculations, especially for excited states but also in ground state systems.373 Furthermore, assignment of charge to different locations is susceptible to some arbitrariness based on the partitioning scheme, with density-based methods more reliable than schemes based on atomic orbital coefficients, such as Mulliken charges.374 We classify schemes based on fitting to the electrostatic potential among the density-based schemes, since Poisson’s equation directly relates the density and electrostatic potential.

In light of the well-known diﬃculties involved in calculating and partitioning the charge density, we tested the validity of the charge delocalization observed in our simulations by examining calculations using several Gaussian basis sets and levels of theory, and for the dimer clustered with diﬀerent numbers of water molecules.

218 We chose a conﬁguration at the shallow free energy minimum where both C5-C5′

and C6-C6′ bonds are intact (top left hand corner of Fig.8.4 in the previous chap-

ter) and included a variable number of waters from the full simulation conﬁguration

in the test calculations. Inclusion of all 32 waters was not possible for the more

expensive methods. In order to make sure that the delocalization eﬀect was not spe-

ciﬁc to the conﬁguration where the C5-C5′ and C6-C6′ were intact, we repeated the

CP2K/Gaussian comparison for the Hartree Fock calculations, with one conﬁguration

chosen from the partially cleaved minima (top left hand corner of Fig.4 in previous

chapter) and for another conﬁguration chosen from the split products well (bottom

right hand corner of Fig.4 in previous chapter). Gaussian calculations were performed

using the Gaussian 03/09 package.190

Table 8.1 shows the total amount of excess charge on the water for conﬁgura- tions of the thymine dimer anion surrounded by either 6 or 10 waters. The charges from CP2K are the density derived DDAP charges10 while those from Gaussian are obtained by using the CHELPG11, 12 utility. The results show that moving to more

ﬂexible basis sets still results in a substantial amount of charge delocalization. Fur- thermore, using Hartree-Fock methods, which are not plagued by SIE, the charge delocalization is also quite substantial. Hence, signiﬁcant charge delocalization onto water molecules appears not be be an artifact of using density functional theory for this anionic system. We have also computed the extent of charge delocalization onto the water using the long range corrected density functional LC-BLYP developed by Hirao and co-workers375 that is available in Gaussian 09. In the LC-BLYP density functional, the long range part of the exchange interaction is treated with full Hartree-Fock exchange and has been shown to improve the description of charge

219 Table 8.1: Total T<>T anion charge delocalized on water molecules according to DDAP10 (CP2K) or CHELP11, 12 (Gaus- sian) density-based charge partitioning. The number of water molecules from the original simulation configuration is indicated. The CP2K calculations were performed in a cubic periodic cell of side length 9.8A˚ except for two values, indicated with a dagger (†), in which a cell dimension of 14.8A˚ was used and double dagger (‡) in which a cell dimension of 20.8 was used. The last 6 rows are CP2K and Gaussian (ROHF and LC-BLYP) calculations performed with different configurations as described in the text. method software basis 6 water 10 water BLYP CP2K DZVP −0.288, −0.154†, −0.159‡ −0.706, −0.499†, −0.501‡ † ‡ † ‡ 220 BLYP CP2K TZV2P −0.337, −0.184 , −0.194 −0.813, −0.577 , −0.580 ROHF Gaussian 6-311++G** −0.412 −0.351 LC-BLYP Gaussian 6-311++G** −0.122 −0.395 BLYP Gaussian 6-311++G** −0.311 −0.499 B3LYP Gaussian 6-311++G** −0.193 −0.441 BLYP Gaussian aug-cc-PVDZ −0.345 −0.572 BLYP CP2K DZVP −0.310, −0.333†, −0.332‡ −0.317, −0.338†, −0.342‡ ROHF Gaussian 6-311++G** −0.219 −0.384 LC-BLYP Gaussian 6-311++G** −0.242 −0.411 BLYP CP2K DZVP −0.304, −0.398†, −0.398‡, −0.423, −0.593†, −0.598‡ ROHF Gaussian 6-311++G** −0.291 −0.589 LC-BLYP Gaussian 6-311++G** −0.345 −0.646 transfer states. The results shown in the Table 8.1 show that the LC-BLYP func-

tional still exhibits signiﬁcant charge delocalization onto the solvent for all fragments.

The comparison of the Hartree-Fock methods to the CP2K results for two diﬀerent

fragment conﬁgurations along the splitting process shown in the last 6 rows of Ta-

ble 8.1, demonstrate the the charge delocalization occurs throughout the splitting

process of the the C5-C5′ and C6-C6′ bonds. It is worth noting that charge transfer between solute and solvent has already been reported in several systems. Klein and co-workers288 conducted ab initio simulations of a zwitterionic peptide, halide anions and alkali cations in water. They observed a substantial amount of charge transfer between the carboxylate terminus and the solvent (0.1e). Chloride and bromine anions were found to transfer more electronic charge (0.26e) onto the surrounding solvent.

CT eﬀects in halide-water clusters have also been reported by Hynes et al.376 Truhlar and co-workers have recently observed substantial CT (0.18 − 0.32e) to surrounding

water in diﬀerent anionic solutes.377 Perhaps more pertinent to larger protein-water systems, Merz and co-workers378 determined that for a cold shock protein A(CspA), a substantial amount of charge was transferred from the protein surface to the surrounding solvent using PM3 and AM1 semi-empirical methods. Interestingly, the negatively charged residues Glu and Asp were found to transfer the most charge to the water (approximately 0.2e on average). Merz et al.379 have also veriﬁed through extensive benchmarking on various systems that the qualitative nature of the charge transfer between the solute and solvent is captured by both semi-empirical and ab initio methods.

221 The scheme that is used to partition the total charge among atomic and molecular species is not unique. Design of an optimal, universal charge scheme is still an un- resolved issue in the literature, and the best choice of method will vary from system to system. In order to test the sensitivity of our results to the type of charge scheme applied we have also calculated MK (Merz-Kollman),380, 381 NPA (natural population analysis)382, 383 and Mulliken charges384 for the 6 and 10 water thymine fragment of the nascent anion. We have also compared different charge schemes for the two other fragments that were chosen at different points along the splitting process. Those results are provided in Table 8.2. There is a qualitative difference in the charge scheme assignments between electrostatic potential derived (CHELPG and MK), NPA and

Mulliken charges. The extent of charge delocalization is much less with NPA charges, although still signiﬁcant. As expected, the Mulliken charges are very sensitive to the level of theory and basis set. Szefczyk and co-workers374 have shown that at least for

Lewis acid/base systems, CHELPG charges work much better than NPA charges in predicting the extent of charge transfer in these systems. Furthermore, NPA charges are not ﬁt to any underlying electronic density. We therefore place the most conﬁdence in our charge distributions from density-based charge schemes, although qualitatively

NPA also indicates signiﬁcant charge delocalization. The density-based charges are reported in the discussions that follow.

The gas phase CPD anion has been described as a dipole bound state (DP) while the addition of water to the CPD anion is thought to stabilize the valence bound state(VB).328 The solvated CPD anion that we study has properties intermediate be-

tween a dipole bound and valence bound (VB) anion (where the electron is exclusively

localized within the framework of the molecule). While not delocalized to the same

222 Table 8.2: Total T<>T anion charge delocalized on water molecules according to several charge partitioning schemes. waters method basis CHELPG MK NPA Mulliken 6 BLYP 6-311++G** −0.311 −0.313 −0.233 −0.138 10 BLYP 6-311++G** −0.499 −0.550 −0.186 0.043 10 UHF 6-311++G** −0.351 −0.390 −0.107 0.228 6 ROHF 6-311++G** −0.412 −0.418 −0.377 0.207 10 ROHF 6-311++G** −0.351 −0.389 −0.108 0.227 10 ROHF 6-311++G** −0.384 −0.537 −0.128 0.381 10 ROHF 6-311++G** −0.589 −0.698 −0.154 0.260

extent as a DP anion, the solvated CPD anion in our work, exhibits a large degree of

electron delocalization onto the neighboring solvent. However, splitting of the dimer

after accepting an electron triggered by population of an anti-bonding molecular or-

bital a characteristic consistent with a VB anion, occurs in the CPD anion that we

study. Furthermore, there is also a substantial change in the bond lengths of the

dimer after back donation of an electron from the split dimer. Thus, signiﬁcant rear-

rangement of the molecular framework can occur for this anionic system even though

a signiﬁcant amount of electron density is delocalized onto the solvent.

8.4 Evolution of molecular properties during splitting

In this section we document the evolution of molecular properties during the

splitting process. Speciﬁcally, we look at the distribution of the electron density

on both the dimer and solvent as well as the solvent density around the regions

undergoing splitting. We focus on the rate determining step, namely the splitting of

the C6-C6′ bond. Four points along the reaction coordinate, identiﬁed in Fig.4 of the

preceding paper, are examined in detail: (1) the minima of the partially split dimer

223 where the C5-C5′ bond is broken and the C6-C6′ bond is intact, (2) near the transition

state, (3) a point beyond the transition state on the way to the split products, and

(4) the completely split dimer. Umbrella sampling trajectories at these four points

were run for at least 5-6ps longer than the other umbrella sampling windows, to

converge as best as possible, molecular properties reported below. We will detail

the evolution of several molecular properties that occur during the splitting of the

dimer: the partition of the total excess charge between the two pyrimidine units and

the solvent, the evolution of the charge on the C5-C5′ and C6-C6′ bonds where the

splitting occurs, and ﬁnally the evolution of the total number of water hydrogens

around each of the 4 carbon atoms associated with the C5-C5′ and C6-C6′ bonds.

The partition of excess charge between the two bases and on the aqueous solvent is displayed using a ternary plot. A point at the bottom left and right hand corners of the triangle in Fig. 8.10 represents the full electron charge on each base respectively, while the top corner of the triangle represents full electron transfer onto the solvent.

The assignment of charge to the C5,C5′,C6 and C6′ atoms as reported in Fig. 8.10 was accomplished using the DDAP scheme, as discussed at the beginning of section

8.3. The number of water neighbors of a particular C5(C5′) or C6(C6′) carbon atom was counted by determining the number of water hydrogens that were within 3A˚ of the carbon atom.

At all points along the splitting process, the majority of the excess electron charge is localized on the dimer although there is a substantial leakage of the electron density onto the water. For points 1, 2 and 3 the average charge on the dimer is −0.6 and

hence the water supports −0.4 of an elementary charge. The variation of the fraction of density-based charge on the solvent is quite wide, ranging from no transfer to

224 1 2

3 4

Figure 8.10: Electron charge partitioning between water and two thymine bases during splitting of the C6-C6′ bond at 4 points along the splitting of the C6-C6′ bond as described in the text.

complete transfer of the excess charge, as shown by the ternary plots in Figs. 8.10. In fact at the transition state there appears to be stronger ﬂuctuations of the electron density onto the solvent. The variance of the distributions of the total charge on the water at points 1, 2, 3 and 4 are: 0.021, 0.028, 0.02 and 0.02 respectively. This is also seen in the ternary plot of the transition state which exhibits a signiﬁcantly greater spread onto the region near the top corner. As the system reaches the products at

225 point 4, we observe further localization of the electron charge onto the dimer as it

supports −0.72 of the total electron density.

We also monitored the total charge on each base at four stages of the splitting process. In gas phase calculations using AM1 semi-empirical theory, Voityuk et al.326 found that the charge is localized on one base throughout the splitting process except at the transition state. Our density functional results in the presence of solvent indicate that the electron density is delocalized on both bases throughout all stages of the splitting process. This is consistent with recent work by Kawabata and co- workers342 who perform ab initio simulations of a gas phase thymine anion dimer with

Hartree Fock and B3LYP electronic structure theory. They observe that the electron is approximately equally shared between both bases throughout the splitting of the

C5-C5′ bond. During the 13-15ps sampling time we are limited to by the cost of ab initio simulations, the excess charged is trapped or solvation occurs asymmetrically

between the two bases. For example, we showed earlier in Fig. 8.2 that a single

water molecule interacts with a carbonyl oxygen throughout the simulation time. For

similar reasons during our simulations, the number of waters near the C6 and C6′

carbon atoms for example, are not equal. After much longer simulations, we would

expect to sample conﬁgurations where the charge is localized on the other base or

the pattern of solvation is reversed. We are unable to simulate these systems for

the hundreds of picoseconds needed for the system to jump to conﬁgurations where

the other carbonyl receives a hydrogen bond, rendering the sampling non-ergodic.

Error bars shown in Table 8.3 and Table 8.4 are calculated using a standard blocking

method.5 They indicate variability during the short runs feasible with the AIMD

226 method but of course do not capture the error which arises from inability to sample processes whose time scale is longer than the simulation length.

Rosch and co-workers326 were the ﬁrst to point out the critical processes that occur at the C5,C6,C5′ and C6′ carbon atoms during the splitting process. Table 8.3 provides the average charges of the C5,C6,C5′ and C6′ carbon atoms and the combined

C5,C5′ and C6,C6′ charge at the four points described earlier along the splitting of the C6-C6′ bond. On the anion surface the C5,C5′ carbon atoms, which incur initial cleavage, carry a substantial amount of excess charge. The C6,C6′ carbon atoms remain electron deficient at both points 1 and 2 by about 0.3-0.4 electron charges. The data shows that the electron deficiency of carbons C6 and C6′ reduces significantly after passage through the transition state.

Table 8.4 gives the average number of water neighbors around each carbon atom.

We observe that our equilibrium umbrella sampling simulations predict that as the

C6-C6′ bond splits there is an increase in water density near the C6 and C6′ carbon atoms. During the splitting of the C6-C6′ bond there is also an increase in electron density at the atoms undergoing splitting.

As indicated earlier, the electron density shows marked delocalization onto the solvent. In order to understand the mechanism of coupling better, the coupling of charge fluctuations of water and carbonyl oxygens are tracked in Fig. 8.11. Panel (a) in Fig. 8.11 exhibits the correlation between the O2 and O4 charges at the transition state and the total charge on the water. The O2 and O4 points lie roughly in ellipsoidal regions whose major axis have slopes −0.66 and −0.58, respectively, as estimated by the linear fits to the data points indicated in Fig. 8.11. In other words, as the charge on the O2 and O4 carbonyl oxygens fluctuates, on average 66% and 58%, respectively,

227 Table 8.3: Charge on carbon atoms: C5,C5′,C6,C6′ ′ ′ ′ ′

228 Point C5 C5 C5+C5 C6 C6 C6+C6 1 −0.08(0.013) −0.23(0.004) −0.31 0.14(0.005) 0.31(0.003) 0.45 2 −0.13(0.014) −0.18(0.011) −0.31 0.09(0.016) 0.23(0.027) 0.32 3 −0.07(0.009) −0.12(0.009) −0.19 −0.09(0.016) 0.01(0.007) −0.08 4 −0.04(0.009) −0.17(0.012) −0.21 −0.13(0.024) 0.08(0.014) −0.05 Table 8.4: Average number of water hydrogens near C5,C5′,C6 and C6′ carbons. Error bars for each data set are estimated by the blocking method5 by partitioning each run into 4 blocks. C5 C5′ C6 C6′ Point µ µ µ µ 1 0.32(0.06) 0.07(0.01) 0.21(0.05) 0.24(0.02) 2 0.38(0.07) 0.44(0.18) 0.49(0.10) 0.52(0.08) 3 0.85(0.04) 0.77(0.04) 0.83(0.02) 1.04(0.05) 4 0.20(0.03) 0.63(0.12) 1.12(0.07) 1.25(0.10)

of the change in oxygen charge is reﬂected in an opposite change in the total charge on

water. Panel (b) indicates that a signiﬁcant proportion of the charge exchange with

the O4 atom involves the closest water hydrogen atom: On average 35% of change

in the O4 oxygen charge is reﬂected in a compensating change in the charge of the

proximal water hydrogen alone. Panels (c) and (d) in Fig. 8.11 depict the charge

exchange between the O2/O2′ carbonyl oxygens and O4/O4′ oxygens at points 1 and

3. For the O2/O2′ oxygens 70% and 67% of a charge deviation on the O2/O2′ oxygens at points 1 and 3, respectively, were reﬂected in an opposite deviation of the total water charge. In contrast, 47% and 56% of a deviation of the O4/O4′ charge was reﬂected in an opposite deviation of the water. These results suggest a role for the carbonyl oxygens in the process of electron transfer to or from the CPD dimer. They are also consistent with observations made by Truhlar and co-workers377 showing

substantial CT in systems stabilized by hydrogen bonding.

8.5 Molecular mechanisms of C6-C6′ Splitting

In section 8.4 we demonstrated that during the splitting of the C6-C6′ bond, the

electron density on the C6 and C6′ carbon atoms increases. We also showed that

229 Figure 8.11: Charge coupling between carbonyl oxygens and solvent. The individual plots are discussed in the text. The degree of coupling of charge ﬂuctuations is assessed using a linear ﬁt to the data, which is indicated with a dashed line for O2/O2’ and a solid line for O4/O4’.

the number of waters near the C6 and C6′ carbon atoms increases as the C6-C6′ bond splits. In this section we provide further evidence that the reaction involves a dynamical role for solvent in addition to the charge transfer to the C6 and C6′ carbon

230 h itiuino pitn ieie o h trajectories the for lifetimes splitting pane right of the distribution In the well. quite performs prediction TST our and ugssta h pitn ieo h C6-C6 the of time splitting the that suggests C6-C6 the where rjcoiswudsltwti 0 within split would trajectories eso h itiuino pitn ie fteC6-C6 the of times splitting of th distribution the On show we timescale. this within cleaved trajectories these of 50% fteTTetmt f0 of estimate TST the If h pitn ieo h C6-C6 the of time splitting the rjcoista pi ihn4 within split that trajectories tm.Ulk h C5-C5 the Unlike atoms. trajectories equilibrium iue81:Dsrbto fsltigtmsfrC6-C6 for times splitting of Distribution 8.12: Figure o pert hneteeetv reeeg are o spli for barrier energy free eﬀective the change to appear not 4nneulbimtaetre eepoaae rmtep the from propagated were trajectories non-equilibrium 44

# of trajectories ′ odwsitc n eernfr4 for run were and intact was bond Time (fs) . ′ p a orgrul od prxmtl 0 fte44 the of 60% approximately hold, rigorously to was 5ps odsltig ovn atcpto nterato does reaction the in participation solvent splitting, bond . p.Terslssgetta u S rdcinof prediction TST our that suggest results The 5ps. ′ . p.Hwvr h itiuinsoni i.8.12 Fig. in shown distribution the However, 5ps. odoeetmtstert yasalamount. small a by rate the overestimates bond 231 ′ odi ihnafwpicoseconds(2-3ps) few a within is bond . 5 ps ′ odfrtenon-equilibrium the for bond h C6-C6 The . ′ rmornon-equilibrium our from odfrgop fnon- of groups for bond tn fteC6-C6 the of tting Time (fs) etpnlo i.8.12 Fig. of panel left e rilycevdminima cleaved artially fFg .2w show we 8.12 Fig. of l ′ odfrabout for bond ′ bond. simulations that were begun at the nascent anion with both bonds intact as illustrated

in the previous chapter, where both the C5-C5′ and C6-C6′ bond split within 0.5-1ps.

At this point, we cannot rule out the possibility that these trajectories are also subject

to non-equilibrium eﬀects, however the distribution of splitting lifetimes suggest TST

also performs adequately for this population of trajectories. closest C6−HW Distance (A)

r (A) C6−C6

Figure 8.13: Left panel shows the evolution of the C6-C6′ distance with the closest water distance to the C6 atom for splitting trajectories while right panel shows the same for trajectories that do not split within the timescale of our simulation runs.

The left panel of Fig. 8.13 shows the relationship between the C6-C6′ bond distance

and closest C6-HW distance for the trajectories whose C6-C6′ bond split within the

timescale of our simulation. The ﬁgure shows that the splitting of the C6-C6′ bond is

characterized by an increase in water density near the C6 carbon atom. These results

are consistent with our equilibrium umbrella sampling results above in Table. 8.4.

232 The behavior is similar near the C6′ carbon atom so we only show the data for the

C6 atom. On the right panel of Fig. 8.13 we show the closest C6-HW distance and

C6-C6′ bond distance for those trajectories whose C6-C6′ bond did not split within

4.5ps. The vertical blue line shows the predicted TST C6-C6′ distance at 1.77A.˚

The ﬁgure also shows that there are a few trajectories that undergo recrossings at

the TST without leading to cleaved photoproducts. The eﬀect of recrossings can

be considered as either a correction factor to the TST estimate, often expressed as

the pre-exponential transmission factor, or an underestimation of the free energy

barrier that results from a less than optimal choice of reaction coordinate.385 More sophisticated methods385 can be used to determine the transmission factor κ, but is

beyond the scope of this study. Since the number of recrossings is small, they do not

change the timescales of splitting by a signiﬁcant amount for this CPD anion system.

In our equilibrium umbrella sampling simulations shown in section 8.4, we showed

that as the C6-C6′ bond splits, there was localization of electron density onto the

C6 and C6′ carbon atoms. Fig. 8.14 furnishes further evidence that the localization of charge onto the C6 (and C6′) atoms is an important part of the splitting of the

C6-C6′ bond. The left panel of Fig. 8.14 shows the distribution of the charge on the C6 carbon atom and the closest C6-HW water distance for the non-equilibrium trajectories propagated from the partially cleaved minima. The localization of charge onto the C6 atom is coupled to a solvation coordinate that involves the movement of a water hydrogen toward the C6 carbon atom. The data in the left panel of Fig. 8.14 is color coded in red for regions of the trajectories where the C6-C6′ bond distance is greater than 1.85A,˚ and in black when the distance is less than 1.85A.˚ The right panel of Fig. 8.14 shows the distribution of charge on the C6 carbon atom and the

233 hwsmlrbhvo.I grgt hyla otedt hw i shown data the to lead they aggregate In behavior. similar show rvdsfrhrisgtit h opigo h yaisof dynamics the of coupling the into insight further provides pitn n h hretase oteC6(C6 the to transfer charge the and splitting oadmr eaievle.Tedsrbtoso hreadC and charge of distributions The values. negative more toward C6-C6 t the splitting of splitting the the for that panel shows left the on detailed distribution same iia rnsadaelf u o brevity. for out left are and trends similar ohsltigadusltigtaetre.O h et h r the left, the On water closest where trajectories. and unsplitting trajectory atom C6 and on splitting charge both of Distribution 8.14: Figure h 4 the uigte4 the during trajectorie non-reactive those for distance water C6-HW closest 1 . 85

naayi notednmc ftesltigpoesi h indi the in process splitting the of dynamics the into analysis An closest C6−HW Distance (A) A ˚ . 5 h aai lc ntergti o rjcoista remai that trajectories for is right the on black in data The . ps u ie h aai e stesm nbt panels. both in same the is red in data The time. run . 5 ps iuainrnigtm.I h akrudpotdi e st is red in plotted background the In time. running simulation r C6-C6 products C6 Charge reactants ′ > 1 . 85 A ˚ hl h lc aesprin where portions labels black the while , ′ odivle hf nteaeaeC charge C6 average the in shift a involves bond 234 ′ abnao.Teohrtrajectories other The atom. carbon ) products non−reactive trajectories ae,teC6-C6 the water, dlbl at fthe of parts labels ed aetre.Tedata The rajectories. C6 Charge htrmi unsplit remain that s 6 ′ H itneshow distance -HW itnet 6for C6 to distance iultrajectories vidual is 8.13-8.14. Figs. n npi during unsplit n r C6-C6 ′ bond ′ he < 4 4 3.5 3.5 3 2.5 3 2 2.5

C6-C6 Distance (Å) 1.5

1 Closest C6-HW Distance (Å) 2 0 1000 2000 3000 4000 0 1000 2000 3000 4000 time (fs) time (fs) 0.6 3.5 0.4

0.2 3

0 2.5

charge on C6/C6 -0.2

-0.4 2 0 1000 2000 3000 4000 Closest C6 -HW Distance (Å) 0 1000 2000 3000 4000 time (fs) time (fs)

Figure 8.15: Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′.

The four panels in Fig. 8.16 show the evolution of the C6-C6′ bond, closest water to C6 and C6′ carbon and the charge on the C6(C6′) carbon atoms. The splitting

of the C6-C6′ bond in this particular trajectory occurs at about 2ps. On that same

timescale we observe the water near the C6 and C6′ move closer to it by about 0.5A.˚

Three other trajectories showing similar behavior are examined in Figs. 8.15-8.18).

Generally, we ﬁnd that the C6 and C6′ charges become less positive as the C6-C6′

235 bond splits, although the timing of the C6 and possibly the C6′ as well, is not as closely tied to bond splitting as is the closer approach of a nearby water.

3.5 3.5

3 3

2.5 2.5 2 C6-C6 Distance (Å) 1.5

Closest C6-HW Distance (Å) 2 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 time (fs) time (fs) 4 0.6 C6’ 0.4 3.5

0.2 3 0 2.5 charge on C6/C6 -0.2 C6

-0.4 Closest C6 -HW Distance (Å) 2 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 time (fs) time (fs)

Figure 8.16: Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. As the C6-C6′ bond splits at about 2ps a water molecule moves closer toward the C6(C6′) carbon atom. For this trajectory we ﬁnd that the charge on both the C6 and C6′ carbon atoms transitions from less negative to more negative at the same time, when the C6-C6′ bond splits.

236 After analyzing several other trajectories similar to the ones shown in Figs. 8.15-

8.18, we ﬁnd that the dynamics of the increase in electron density on the C6 and

C6′ carbon atom can can range from either occurring simultaneously with the C6-C6′ bond splitting, to beginning almost a picosecond before the C6-C6′ bond splits. The results of Figs.8.13-8.14 show that the splitting of the C6-C6′ bond is strongly coupled to the increase in local water density near the C6 and C6′ carbon atoms. Furthermore these processes occur on the wide range of C6-C6′ bond splitting times observed in

Figs. 8.16-8.18. Our results are consistent with Masson et al.’s observation that the amino acids Arg350 and Arg232 in the active site of DNA photolyase may play an important role in triggering ring splitting either through direct hydrogen bonding with the thymine base or indirectly through hydrogen bonding with water molecules.329

However, our analysis focuses on the increase in local water density near the C6 and

C6′ carbon atoms.

8.6 Conclusions

Ab initio MD simulations of the cyclobutane pyrimidine dimer (CPD) surrounded

by 32 waters reported in our previous386 work and this paper, show that the splitting of the C5-C5′ and C6-C6′ bond in water is complete within several picoseconds.

These results are consistent with recent simulations by Masson et al.327, 329 on dimer

splitting for self-repair in DNA and in DNA photolyase. For both the splitting of

the C5-C5′ and C6-C6′ bonds we ﬁnd that surrounding solvent plays an essential role

in facilitating the splitting process. This has important implications for the role of

the surrounding amino acids in the active site of the protein and is consistent with

femtosecond experiments that report dynamic active site solvation in photolyase.29

237 4 3.5 3.5 3 3 2.5 2 2.5

C6-C6 Distance (Å) 1.5

1 Closest C6-HW Distance (Å) 0 1000 2000 0 1000 2000 time (fs) time (fs) 0.6 3.5

0.4

0.2 3

-0.2 2.5 charge on C6/C6 atom -0.4 0 1000 2000 Closest C6 -HW Distance (Å) 0 1000 2000 time (fs) time (fs)

Figure 8.17: Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. The splitting of the C6-C6′ bond for this trajectory occurs at about 900fs. However for this trajectory we ﬁnd that the charge on the C6 carbon atom gradually decreases between 400−1000fs (the decrease begins before the split of the C6-C6′ bond) while the charge on the C6′ carbon atom decreases over a shorter time interval at about 900fs.

Future experiments that involve site mutagenesis of amino acids near the C6 and C6′ carbon atoms will help verify these results.

The reaction in water is asynchronous because the C5-C5′ bond opens before the

C6-C6′ bond. The two dimensional free energy surface with respect to the C5-C5′

238 4 3.5 3.5 3 3 2.5 2 2.5

C6-C6 Distance (Å) 1.5

1 Closest C6-HW Distance (Å) 2 0 500 1000 0 500 1000 time (fs) time (fs) 0.4 3.5

0.2 3 0 2.5

charge on C6/C6 -0.2

-0.4 2 0 500 1000 Closest C6 -HW Distance (Å) 0 500 1000 time (fs) time (fs)

Figure 8.18: Top left panel shows C6-C6′ bond splitting over time, top right panel shows closest water distance to C6, bottom left shows charge on C6 and C6′ and bottom right shows closest water distance to C6′. For this trajectory, the splitting of the C6-C6′ bond occurs at 250fs. The charge on the C6 and C6′ carbon atoms and the movement of a water molecule closer to these atoms for this trajectory, transitions on a similar timescale as the splitting of the C6-C6′ bond.

and C6-C6′ bond lengths developed in our previous paper indicate that the reaction is concerted because the only signiﬁcant reaction barrier is the one separating the partially cleaved (broken C5-C5′ bond) structure from the split products. There is a

very small barrier along the way to the partially cleaved structure, but it is so small we

would hesitate to claim that it deﬁnes a reaction intermediate. However, in this work

239 we demonstrate that coupling to solvent can impart a stepwise character to CPD

anion splitting. A signiﬁcant number of non-equilibrium trajectories taken on the

order of a picosecond for cleavage of the C5-C5′ bond, which is not accounted for by

the two-dimensional free energy surface in the C5-C5′ and C6-C6′ bond lengths. We

have traced this to coupling of C5-C5′ bond cleavage to motion of neighboring water

molecules, which can trap the system near free energy traps. Since the relevance

of the solvent associated free energy barrier to C5-C5′ bond splitting depends on

the conﬁgurational distribution created by forward electron transfer, and because the

reaction is still quite fast and intermediates diﬃcult to identify experimentally, it may

be premature to call for a classiﬁcation of the splitting reaction from concerted to

stepwise. This will depend on factors outside the scope of this work, including the

chemical identity of the electron donor. Since the dimer anion splitting time scale is

so short, we speculate that, after forward electron transfer but before splitting, the

system may not have enough time to relax in a local free energy maximum before

splitting. Hence a quantitative description of the reaction may require treatment of

non-equilibrium eﬀects.

Because we treat both the CPD unit and the surrounding pocket of 32 waters quantum mechanically, we are able to address issues like charge transfer (CT) between the dimer and surrounding solvent. Our ab initio MD simulations show that there is a substantial amount of the CT from the dimer to the solvent throughout the splitting of both the C5-C5′ and C6-C6′ bonds. In this work, we have veriﬁed through quantum chemical cluster calculations, that the CT we observe in this anionic system, is not an artifact of DFT. Hartree-Fock theory, which does not suﬀer from the self- interaction error, still predicts a substantial amount of charge transfer to the solvent.

240 Furthermore, benchmarks using the long range corrected density functional (LC-

BLYP) that has been designed to overcome the problem of charge transfer artifacts

which occur using standard density functionals, also show substantial CT from the

dimer to the solvent. Focusing on several points along the splitting of the C6-C6′ bond, we ﬁnd that before the reactants equilibrate into the split product well, the water supports 40% of the electron density. Upon reaching the split products, the electron density on the water reduces to 30%. Throughout the splitting process, the electron density is delocalized over both bases. This is consistent with recent ab initio

gas phase simulations of the CPD with Hartree Fock and B3LYP levels of theory.342

Our simulations show that there is a considerable amount of reorganization of

both the CPD unit and the surrounding solvent during the splitting of the C6-C6′

bond. During the splitting of the C6-C6′ bond we ﬁnd that there is an increase in

the electron density of the C6 and C6′ carbon atoms. We also ﬁnd an increase in

the water density near these atoms. This is veriﬁed in both our equilibrium umbrella

sampling simulations as well as non-equilibrium trajectories. These results suggest

that the fast dynamical motions of the amino acids in the active site of the protein

on the ps timescale, will play an essential role in biological repair of the anion CPD

dimer. Using TST theory we predict that the splitting time of the C6-C6′ bond to be

∼ 0.5ps. This is strictly a lower bound to the splitting time but our non-equilibrium

trajectories suggest that the TST estimate adequately predicts the splitting time for

the C6-C6′ bond.

In conclusion, the results of the previous386 and current work shed important new

insights into the mechanistic details of the DNA repair. The non-equilibrium trajec-

tories propagated from the nascent anion where both the C5-C5′ and C6-C6′ bonds

241 are intact, reveal that the initial conditions prior to electron transfer can change the

splitting time of the C5-C5′ bond from the femtosecond to the picosecond timescale,

although it is still a fast process. This eﬀect can be thought of as a multidimen-

sional eﬀect that includes the explicit role for solvent in the repair process, thereby

going beyond the 2D picture of the reaction coordinate involving only the C5-C5′ and

C6-C6′ bonds as reaction coordinates. It is likely that corrections to transition state theory from non-equilibrium eﬀects will be required. Experimental validation of this mechanism will require sophisticated experiments that can probe the existence of the unsplit nascent anion population. Our calculations identify several crucial interactions between the dimer and aqueous solvent as essential for cleavage of the C5-C5′

bond. Reasoning that interactions near the same dimer sites in photolyase would

play a similar role, we speculate that the adenine dinucleotide of the FADH cofactor

in the active site of the protein might play an analagous role in the repair enzyme.29

242 CHAPTER 9

Summary

Almost ten years ago, Gerstein and Levitt14 observed that the role of water in biological systems had been undermined and to some extent interpreted in a very naive manner, by many in the scientiﬁc community. The role of water as a matrix, that plays an active participant in fundamental phenomena at both organic and inorganic water- interfaces, is a central theme in the three projects that have formed my dissertation.

These projects have examined the dynamics of water near the surface of amorphous silica (glass), the water dynamics near the surface of proteins (known as hydration dynamics) and finally the role of water in DNA repair. In all these topics, involving widely different fields, similar issues arise. How mobile or immobile is the water near the surface? Is the water an active participant or a passive background in biomolecular function and in important cellular reactions like DNA repair? Our detailed theoretical studies on all these systems unequivocally show that water near these interfaces, plays an essential and active role in understanding phenomena such as DNA repair or protein dynamics. Understanding the molecular details of the water- biomolecule-silica interface will have significant impact in several areas encompassing both science and engineering applications.

243 It is well known that water is essential for life both at the cellular and molecular level.13 Cellular functions are halted in the absence of water because most proteins

are not able to perform their biological functions at low hydration levels. For example,

a minimal amount of hydration level is required to begin biological functionality in

proteins. An-harmonic vibrational and diﬀusive motions on the picosecond timescale

are suppressed in dry proteins.107 The understanding of protein dynamics in aqueous solution is critical in many biological processes such as protein folding.30, 31 Dur- ing the process of molecular recognition between two species, protein-peptide and protein-protein interfaces do not interact directly, but are instead, mediated by water molecules at the interface.387 Water also plays a critical role in maintaining the structural integrity of biomolecules as well as participating in enzymatic catalysis.15 An understanding of the structure and dynamics of water at biomolecular interfaces is paramount for a more nuanced perspective on the role of water in biological function.

In a recent review detailing the role of water as an active constituent of cell biology,13 Philip Ball states that “...the ground rules for interpreting the hydration

of larger biomolecules have not really been established”. In chapters 2, and 3 we

illustrated some of the “ground rules”, that we believe will play an important role

in understanding the role water as an active participant of cellular function. Protein

and water motions are intimately coupled and occur on a broad range of timescales.

Furthermore, our calculations have helped resolve some important controversies in the

literature regarding the origin of the slow component in time dependent ﬂuorescence

Stokes shift experiments.

In this dissertation, we have illustrated the role of water in DNA repair. In chap-

ters 7 and 8 we examined the role of water in a speciﬁc biological function, namely

244 DNA repair. Our model system consists of two DNA thymine bases surrounded by

a pocket of hydration water. Damaged DNA bases are formed by UV radiation and

if left unrepaired can lead to mutations and ultimately death.29 The mechanism na-

ture has employed to repair these lesions, is via photoreduction using an enzymatic

protein called DNA Photolyase.29 A molecular picture of the mechanisms involved in

the repair process should help provide critical insight for future therapeutic applica-

tions. Our theoretical calculations demonstrate that the polarity of the surrounding

solvent in which DNA repair is occurring, plays an important role in achieving a high

quantum repair yield. There have been some attempts to use some DNA repair pro-

teins including photolyase as topical sunscreen treatments.388, 389 The results of our

calculations and the theoretical framework for achieving eﬃcient DNA repair detailed

in chapter 7, should provide some guidance for the design and improvement of more

eﬀective sunscreen treatments.

The surface of silica has been intensively studied for many years. Our interest in the silica surface stems from its wide use in biomedical engineering devices for the transport of biomolecules. Silica-DNA interactions are the basis of a standard purification scheme for nucleic acids,390, 391 and novel microfabricated device applications.392, 393 There is recent interest in using silica nanochannels to stretch and sequence DNA.310, 394 Silicates and silica exhibit widely varying health effects, with considerable effort devoted to elucidating mechanisms of toxicity.157, 395

The importance of the interactions of silica with biomolecules has prompted a number of fundamental investigations of the interactions of silica with nucleic acids396–402 and proteins.28, 234–236 In addition to devices fabricated from silica, the amorphous silica-water interface is important in silicon-based devices where silicon

245 Figure 9.1: Nanonozzle made of silica walls with our empirical model

acquires an oxide coating in contact with aqueous solution.291, 403 Recently, silica has also become of interest in understanding the chemical reactions that resulted in the appearance of life (prebiotic chemistry). Minerals such as silica could have played an important role in organizing and concentrating organic molecules to convert them into essential large molecules for life22 such as proteins and DNA, which are essential for all biological function. In all these applications it is quite clear that a molecular picture of the water-protein/DNA-silica interface will provide crucial information for understanding various phenomena of signiﬁcant importance.

In this dissertation we have taken important steps in understanding the water-

protein/DNA-silica interface through computational and theoretical methods. We

examined the water-protein interface in chapters 2, and 3. In chapters 4 and 5

we described the development of a model for the water-amorphous silica interface.

Our empirical model is designed to perform device-type simulations that are used in

bio-medical engineering applications. For example shown in Fig. 9.1 is a nanonozzle

device that is currently being modeled by a member of our group. The walls of the

nanonozzle are made of amorphous silica using our empirical model. Several features

246 of our water-silica interface from our empirical model are qualitatively reproduced

by more accurate ab initio MD simulations. In chapter 6 we brieﬂy summarized two important applications of our model: debunking the myth of a hydrodynamically stagnant Stern layer and preliminary results in the binding of biomolecules to the silica surface. More experiments on a wide variety of biomolecules near the silica interface are needed for us to make closer comparisons with experiment and also to allow us to validate and improve our models.

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