Understanding Mercury Transport and Transformation by Computational Simulations

University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange

Doctoral Dissertations Graduate School

8-2017

Jing Zhou University of Tennessee, Knoxville, [email protected]

Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss

Recommended Citation Zhou, Jing, "Understanding Mercury Transport and Transformation by Computational Simulations. " PhD diss., University of Tennessee, 2017. https://trace.tennessee.edu/utk_graddiss/4675

This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council:

I am submitting herewith a dissertation written by Jing Zhou entitled "Understanding Mercury Transport and Transformation by Computational Simulations." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Life Sciences.

Jeremy Smith, Major Professor

We have read this dissertation and recommend its acceptance:

Jerry Parks, Xiaolin Cheng, Hong Guo, Francisco Barrera

Accepted for the Council:

Dixie L. Thompson

Vice Provost and Dean of the Graduate School

(Original signatures are on file with official studentecor r ds.) Understanding Mercury Transport and Transformation by Computational

Simulations

A Dissertation Presented for the

Doctor of Philosophy

Degree

The University of Tennessee, Knoxville

Jing Zhou

August 2017

ii DEDICATION

To my mom, dad, and Yiwen

iii ACKNOWLEDGEMENTS

I would like to thank my Ph.D. advisor Prof. Jeremy Smith for giving me the opportunity to come to the U.S. and carried out my research in the Center for Molecular Biophysics at the

University of Tennessee and Oak Ridge National Laboratory. He provided me guidance, resources and continuous support for my work throughout the years. Next, I would like to thank

Dr. Jerry Parks for teaching me every aspect to become an excellent scientist, from conducting scientific research to presenting research findings. He is always patient and willing to teach. My written and spoken English have been improved significantly because of him. Then, I would like to thank everyone in CMB who has helped me with my research, especially Dr. Xiaolin Cheng,

Dr. Demian Riccardi, Dr. Barmak Mostofian, and Dr. Micholas Smith for their generosity with their time and helpful discussion during the years of my Ph.D. Finally, I would like to thank my parents Jie Zhou and Qingying Liu for their unconditional love. They always have faith in me, which give me the courage and strength to go through all the difficulties I encountered during my

Ph.D. and in my life.

iv ABSTRACT

Mercury is a global pollutant that can be transported over long distance and bio-amplified within food chains. It has been shown that anaerobic microorganisms can produce neurotoxin methylmercury from inorganic mercury. However, the mechanisms for Hg substrates uptake and bio-transformed mercury product export are still not clear. Also, once Hg substrates are inside the cells, the enzymatic mechanisms of mercury methylation are still unknown. In this dissertation, we focused on using computational approaches to understand how microorganisms uptake and export mercury complexes and the biotransformation mechanisms of inorganic mercury to methylmercury at the molecular level. Here, we first explored the catalytic mechanism of mercury methylation enzyme HgcA using a simplified model of methylcobalamin

(the cofactor of HgcA). We found that the ligand substitution of the lower-axial side of methylcobalamin by the Cys residue from HgcA indeed facilitates methyl transfer. We then developed a consistent computational approach to investigate redox potential, pKas [pKitalic_as] and Co–ligand binding equilibrium constants for cobalamins. We used this approach to study the pH-dependent redox chemistry of aquacobalamin and yielded agreement with experimental values within 90 mV [millivolts] for reduction potentials and 1.0 log units both for pKas

[pKitalic_as] and log Kon/off [Kitalic_on/off]. This study built the foundation to explore the redox requirements for another mercury methylation enzyme HgcB. Finally, we tested the possibility of passive permeation of Hg complexes through a model cytoplasmic membrane using molecular dynamics simulations. We concluded that small neutral Hg complexes in this study, i.e. CH3Hg–

SCH3 and CH3S–Hg–SCH3, could permeate the model membrane without the facilitation of membrane proteins. We also investigated the kinetic aspect of the permeation processes and we

v predicted the permeability coefficients for the Hg-containing compounds are ~10-5 cm s-1

[centimeter per second].

Our studies here shed light on understanding the fundamental enzymatic mechanisms of mercury methylation, build the foundation for future study on the pH-dependent redox chemistry of metal-containing species, and established the future direction for studying the transport mechanisms of mercury complexes in microorganisms.

vi TABLE OF CONTENTS

CHAPTER 1 Introduction ...... 1

1.1 Physical Properties of Mercury ...... 1

1.2 Global Mercury Cycling ...... 1

1.3 Abiotic and Biotic Transformation of Mercury ...... 3

1.3.1 Elemental mercury oxidation ...... 3

1.3.2 Hg(II) reduction ...... 3

1.3.3 Hg(II) methylation ...... 4

1.3.4 MeHg demethylation ...... 4

1.4 Mercury Resistance Operon ...... 5

1.5 Enzymes for Mercury Methylation ...... 6

1.6 Uptake and Export of Mercury Complexes ...... 7

CHAPTER 2 Simulation Theory and Computation ...... 9

2.1 Theory of Quantum Mechanics ...... 9

2.1.1 Newton’s equation of motion ...... 9

2.1.2 Schrodinger equation ...... 10

2.1.3 Density functional theory ...... 11

2.1.4 Basis sets ...... 13

2.2 Theory of Molecular Dynamics ...... 15

2.2.1 Molecular mechanics force field ...... 16

2.2.2 Equation of motion ...... 18

2.2.3 Potential of mean force and umbrella sampling ...... 19

CHAPTER 3 Mercury Methylation by HgcA: Theory Supports Carbanion Transfer to Hg(II) .. 20

vii Abstract ...... 22

3.1 Introduction ...... 23

3.2 Computational Methods ...... 25

3.3 Results and Discussion ...... 28

3.3.1 Co-C bond homolysis ...... 28

3.3.2 Co-C bond heterolysis ...... 29

3.3.3 Reaction free energies ...... 30

3.3.4 Nonenzymatic Hg methylation ...... 31

3.3.5 Ligand exchange reactions ...... 32

3.4 Conclusions ...... 33

3.5 Appendix 1 ...... 35

CHAPTER 4 Toward Quantitatively Accurate Calculation of the Redox-associated Acid-base and Ligand Binding Equilibria of Aquacobalamin ...... 43

Abstract ...... 45

4.1 Introduction ...... 46

4.2 Computational Methods ...... 51

4.2.1 Standard states ...... 54

4.2.2 Thermochemistry ...... 55

4.3 Results and Discussion ...... 58

4.3.1 Co-ligand binding equilibria ...... 58

4.3.2 Acid dissociation constants ...... 59

4.3.3 Reduction potentials ...... 61

4.3.4 Pourbaix diagram ...... 63

viii 4.4 Conclusions ...... 64

4.5 Appendix 2 ...... 65

CHAPTER 5 Modeling of the Passive Diffusion of Mercury and Methylmercury Complexes

Through a Bacterial Cytoplasmic Membrane ...... 77

Abstract ...... 79

5.1 Introduction ...... 80

5.2 Computational Methods ...... 83

5.3 Results and Discussion ...... 87

5.3.1 Force field parameters ...... 87

5.3.2 Model membrane ...... 87

5.3.3 Free energy profiles ...... 88

5.3.4 Energy decomposition analysis ...... 91

5.3.5 Permeability coefficients ...... 94

5.3.6 Implications for Hg uptake in bacteria ...... 96

5.5 Appendix 3 ...... 98

CHAPTER 6 Conclusions and Future Outlook ...... 119

REFERENCES ...... 122

VITA ...... 157

ix LIST OF TABLES

Table 3.1 Computed Absolute and Relative Gas-Phase Bond Dissociation Energies and

Condensed Phase Reaction Free Energies for Co-C Bond Dissociation in CH3-Co(III)-

Corrin-Ligand Complexes...... 37

Table 3.2 Homolytic and Heterolytic Co-C Bond Dissociation Energies and Individual Energetic

Contributions...... 38

Table 3.3 Computed Gas-Phase and Condensed-Phase Free Energies and Individual Energetic

Contributions for Co-C Bond Dissociation in CH3-Co(III)-Corrin-Ligand Complexes...... 39

Table 3.4 Computed Gas-Phase and Aqueous Reaction Free Energies for Methyl Radical and

Carbanion Transfer from CH3-Co(III)-Corrin-Ligand Complexes to Hg(SCH3)2 and HgCl2.

...... 40

Table 3.5 Computed Gas-Phase and Aqueous Reaction Free Energies for Methyl Radical and

Carbanion Transfer from CH3-Co(III)-Corrin-Ligand Complexes to Hg(SCH3)2 and HgCl2

with Individual Energetic Contributions...... 41

Table 3.6 Computed Condensed-Phase Reaction Free Energies for Upper-Axial Ligand

Exchange in Co(III)-Corrin-Ligand Complexes...... 42

Table 3.7 Condensed-Phase Reaction Free Energies at 298K for CH3/SCH3 Upper-Axial Ligand

Exchange for Co(III)-Corrin Complexes with Individual Energetic Contributions...... 42

Table 4.1 Intrinsic Coulomb Radii used in SMD, Bondi van der Waals Radiiand the Computed

Solvation Free Energy of Water...... 66

Table 4.2 Free Energies at 298 K and Physical Constants...... 67

Table 4.3 Model Ligand Dissociation Reactions...... 67

Table 4.4 Experimental and Calculated Log Keq Values for Aquacobalamin Models...... 68

x Table 4.5 Model Acid Dissociation Reactions...... 68

Table 4.6. Experimental and Calculated pKas for Aquacobalamin Models...... 69

Table 4.7 Model One-Electron Reduction Reactions...... 70

Table 4.8. Experimental and Calculated Reduction Potentials for Aquacobalamin Models...... 71

Table 4.9 Aggregate Energetic Errors for the Three Computed Quantities...... 72

Table 5.1 Force Field Parameters for CH3SH in CHARMM Format...... 100

Table 5.2 Force Field Parameters for CH3CH2SCH3 in CHARMM Format...... 101

II Table 5.3 Force Field Parameters for CH3Hg –SCH3 in CHARMM Format...... 102

Table 5.4 Force Field Parameters for CH3S–SCH3 in CHARMM Format...... 103

Table 5.5 Force Field Parameters for CH3S–Hg–SCH3 in CHARMM Format...... 104

Table 5.6 Computed Average Dipole Moments for Five Solutes Over the Last 5 ns of NPT

Equilibration...... 104

Table 5.7 Calculated Passive Permeability Coefficients for the Five Solutes and Experimentally

Measured Pm for Hg-containing Compounds, Hydrogen Sulfide, Water and Selected Amino

Acids...... 105

xi LIST OF FIGURES

Figure 3.1 Proposed Hg methylation pathway...... 35

Figure 3.2 Displacements along the spurious imaginary mode...... 36

Figure 3.3 Aqueous reaction free energies relative to reactants for methyl radical and carbanion

transfer...... 36

Figure 4.1 Molecular structure of aquacob(III)alamin...... 73

Figure 4.2 Errors in the computed ligand dissociation constants (log Kon/off) for aquacobalamin

models...... 73

Figure 4.3 Errors in the computed pKas for aquacobalamin models...... 74

Figure 4.4 Errors in the computed reduction potentials for aquacobalamin models...... 75

Figure 4.5 Experimental and computed Pourbaix diagram for aquacobalamin...... 76

Figure 5.1 System pressure over the course of 20 ns NPT equilibration...... 106

Figure 5.2 Potential energy surfaces for torsional scans...... 107

Figure 5.3 Model cytoplasmic membrane system and partial density profiles...... 108

Figure 5.4 Computed free energy profiles for the passive transport of solutes across a model

cytoplasmic membrane...... 109

Figure 5.5 Computed free energy profiles...... 110

Figure 5.6 Electrostatic and nonpolar energy decomposition for the implicit membrane model.

...... 111

Figure 5.7 Computed free energy profiles for the passive diffusion...... 112

Figure 5.8 Energy decomposition of Esol-sys (blue) into Esol-water (green) and Esol-lip interaction

energies (orange)...... 113

Figure 5.9 Decomposition of non-bonded solute-lipid interaction energies (Esol-lip)...... 114

xii Figure 5.10 Non-bonded solute-tail interaction energies (Esol-tail) for CH3SH (red) and CH3Hg–

SCH3 (blue) normalized by the number of atoms in each molecule...... 115

Figure 5.11 Number of contacts with the lipid tail groups for CH3SH (green) and CH3Hg–SCH3

(red)...... 115

Figure 5.12 Interaction energies with PE/PG...... 116

Figure 5.13 Computed free energy profiles and non-bonded interaction energies...... 117

Figure 5.14 Energy decomposition of non-bonded solute-lipid interactions (Esol-lip)...... 118

xiii CHAPTER 1

Introduction

1.1 Physical Properties of Mercury

Mercury is a silver-white liquid metal. The atomic number for mercury is 80 and its molecular weigh is 200.59. The chemical formula for mercury is Hg. Mercury is the only metallic element that is liquid at normal temperature and pressure. The melting point for mercury is -38.83 °C.

The extreme low melting temperature for mercury lies in its electronic configuration — more specifically, the 6s orbital of mercury. Unlike other typical metals (e.g. gold), the 6s orbital is filled in mercury, which makes it difficult for mercury to form metal-metal bond with other mercury atoms. Another reason that mercury is liquid at normal temperature lies in relativistic effects. In heavy elements, such as gold or mercury, electrons have to move faster (close to the speed of light) to avoid falling into the nucleus. The 6s orbital in mercury contracts dramatically because of relativistic effects, which results in the 6s electrons are more close to the nucleus.

Thus, instead of forming bonds with other mercury atoms, the electrons stay closely to the nucleus. The weaker the metal bond is, less energy is required to break the metal bond — results in unusual low melting point for mercury. It is also worth mentioning that the predicted melting point for mercury is 82 °C without relative effects.1

1.2 Global Mercury Cycling

Mercury occurs naturally in the earth’s crust. It is a heavy metal with known toxicity to human.

Mercury can be released into the environment by both natural processes and anthropogenic activities. The main resources of natural mercury emission include volcano eruption and the weathering of cinnabar ore (HgS). The total estimated emission from natural resources is ~500

1 mega-grams (Mg) per year.2 However, the majority of annual mercury release is from anthropogenic emission, which contributes ~2000-4000 Mg/year. Combustion of fossil fuel, especially coal, is the major resource of anthropogenic emission. Other industries, such as cement production, gold production, waste disposal etc. also contribute to the release of mercury to the atmosphere.2

Mercury has three major forms in the environment, i.e. elemental mercury (Hg0), inorganic mercury (e.g. HgCl2) and organic form of mercury (e.g. methylmercury). The exposure pathways and the toxicity vary depending on the specific form of mercury. Inhalation of mercury vapor during industrial processes or dental amalgam is the major source of human exposure to elemental mercury. No significant toxicity of Hg0 is found through ingestion, due to the poor absorption in the gastrointestinal tract.3 However, the mercury vapor exposure through inhalation can lead to lung, kidney and brain damages.3

Inorganic mercury compounds exist in two oxidative states, i.e. mercurous (Hg+) and mercuric (Hg2+) mercury. Because inorganic mercury compounds are usually soluble, they are corrosive to the skin, eyes and gastrointestinal tract. Unlike elemental mercury, the bioavailability of inorganic mercury through ingestion is ~7% to 15%. The major target organ of inorganic mercury is kidney, but they cannot easily cross the blood-brain barrier.

The main exposure source of organic mercury is through the consumption of fish and shellfish contaminated by methylmercury (MeHg). MeHg has strong affinity to thiol groups.

When MeHg are ingested, they can combine with cysteine in the duodenum and the absorption rate for MeHg can reach almost 100%.4 Because of the strong affinity to thiols, they can also combine with glutathione and distribute to various tissues and organs through the blood vessels.5

MeHg interfere the functions of enzymes, cell membrane, and neuron delivery materials. MeHg

2 can pass easily through the blood brain barrier, accumulate in the central nervous system, and cause neuron disorders, such as oxidative stress, lipid peroxidation, and mitochondria dysfunction.5

1.3 Abiotic and Biotic Transformation of Mercury

1.3.1 Elemental mercury oxidation

Elemental mercury (Hg0) can be oxidized to Hg(II) in the environment biologically and abiotically. The abiotic oxidation process of Hg0 can happen in the atmosphere, natural waters or solids. In the presence of excess chloride, Hg0 can be photooxidized or dark-oxidized by various oxidants and free radicals.6 Biologically, Hg0 can be oxidized by aerobic soil bacteria, such as

Bacillus and Streptomyces.7 Bacterial hydroperoxidases, such as KatG and KatE in E. coli were suggested involved in the process of elemental mercury oxidation.7

1.3.2 Hg(II) reduction

Reduction of Hg(II) to Hg0 plays very important role in the partitioning of mercury into the atmosphere. Compared with Hg(II), Hg0 has lower aqueous solubility and higher volatility. Thus, the reduction of Hg(II) back to Hg0 facilitates the release of mercury into the atmosphere and contributes significantly to the global redistribution of mercury.8 Similarly, the reduction processes of Hg(II) can occur biologically or abiotically. In the abiotic reactions, Hg(II) can be reduced by organic free radicals through photochemical reactions9 or by flvic and humic acid- associated free radicals in the dark.10 Biologically, mercuric ion reductases, such as MerA, are involved in the reduction process of Hg(II).11

3 1.3.3 Hg(II) methylation

The methylation of Hg(II) transforms inorganic mercury compounds to organic mercury. Abiotic methylation of Hg(II) can occur in the present of some agents, such as humic and fulvic acids, carboxylic acids, and methylated tin compounds.12-14 Among the processes of biotic transformation of mercury, Hg(II) methylation raises the most concern, because of the extreme toxicity of MeHg and its high biovailability. Biologically, MeHg can be generated from inorganic Hg(II) in the environment by anaerobic microorganisms. It was suggested that Hg methylation is associated with reductive acetyl-coenzyme A (CoA) pathway.15 Recently, two genes, hgcA and hgcB, were discovered that are required for Hg methylation.16 It was found that the deletion of either one or both two genes abolishes the activity of mercury methylation. Also, both genes are present in the sequences of methylating bacteria and archaea genomes but absent in non-methylators. hgcA encodes a corrinoid protein that provides a methyl group to mercury substrates, whereas hgcB encodes a ferredoxin-like protein that provides electrons to reduce

HgcA after methyl transfer. 16

1.3.4 MeHg demethylation

It is also worth mentioning that methylmercury can also be demethylated reductively or oxidatively in the anaerobic environment. The reductive degradation pathway is mediated by mer operons, which leads to CH4 and elemental mercury. In contrast, the oxidative degradation

17 pathway of MeHg leads to the production of Hg(II), CO2 and small amount of CH4. The produced Hg(II) in the oxidative process of MeHg can be used as substrate for Hg methylation again.

4 1.4 Mercury Resistance Operon

Mercury is toxic and it has no known biological role in living organisms. Some bacteria and archaea have evolved mercury resistance mechanism, which is known as the mer operon.18, 19

Various genes are included in the mer operon and they play very different roles in the process of mercury detoxification. MerR is the regulatory protein of others proteins in the mer operon — it gets activated when bacteria are exposed to mercurial compounds. MerP is a periplasmic mercury binding protein, which scavenges HgII compounds and transfers them to membrane proteins, such as MerT and MerC. MerT is a key protein in the uptake of HgII in both gram- negative and gram-positive bacteria. MerT consists of three transmembrane helices and a cysteine pair in the first helix are involved in HgII uptake.18 MerC is predicted to have four transmemrane helices and site-directed mutagenesis studies of MerC showed a GMxCxxC metal binding motif is essential for HgII uptake.20, 21 Some other inner membrane spanning proteins, such as MerE, MerF and MerG, are also involved in the process of mercury transport. 18

Two enzymes, MerA and MerB, are essential for the enzymatic reactions of bacterial mercury resistance. MerA is a mercuric ion reductase protein, which catalyzes the reduction of inorganic HgII to elemental mercury Hg0. MerA is located in the cytoplasm and the source of electrons is from NADPH oxidase. HgII has strong affinity for thiols and it disrupts cell functions by binding to the thiol functional groups. The detoxification mechanism of MerA lies in the reduction of HgII to volatile Hg0 that lacks significant affinity for the function groups in living cells. MerB is another key enzyme in the process of bacterial mercury resistance. MerB is organomercurial lyase, which catalyzes the cleavage of carbon-mercury bond in organic mercury and releases less toxic inorganic HgII. The released HgII can be further reduced by MerA to produce Hg0, which can be easily exported. Two strictly conserved cysteine residues in the active

5 site of MerB are required for the Hg–C bond cleavage. A theoretical study of the catalytic mechanism of MerB showed that redistributing electron density into the leaving group lowers the activation free energy of Hg–C bond protonolysis.22 Various Mer proteins function together and make it possible for the mercury resistance in microorganisms.

1.5 Enzymes for Mercury Methylation

In this dissertation, we focused on investigating the process of biotransformation of inorganic mercury to methylmercury, especially the enzymes (i.e. HgcA and HgcB) that are involved in mercury methylation. Often corrinoid proteins, such as HgcA, employ methylcobalamin (MeCbl) as a cofactor to facilitate methyl transfer reactions. MeCbl consists of a macrocyclic corrin ring, a lower-axial dimethylbenzimidazole (DMB) ligand and an upper-axial methyl ligand.

Interestingly, when MeCbl binds to corrinoid proteins, the DMB tail of the cofactor can come off. In the case of methionine synthase, a histidine residue from the corrinoid protein coordinates to the lower side of the corrin ring instead, which is called “DMB-off/His-on”.23 A “DMB- off/His-off” form of MeCbl is observed in the crystal structure of the cobalt- and iron-containing corrinoid ion-sulfur protein (CoFeSP), which is a component of the acylCoA synthase complex.24 In the case of mercury methylation enzyme HgcA, a strictly conserved Cys residue was predicted to be a lower-axial ligand in the homology model of HgcA (i.e. DMB-off/Cys-on), which has never been observed in a corrinoid protein.25 In this study, we carried out density functional theory (DFT) calculations to compute reaction free energies of different lower-axial ligands and how they affect the transfer free energies of methyl groups in Chapter 3.

To understand the catalytic mechanisms of mercury methylation enzymes HgcB, the first step is to assess the requirement for its reduction capability. HgcB is a characterized by 2[4Fe-

4S] clusters, which presumably provides two electrons to reduce cob(III)alamin to cob(I)alamin

6 during the catalytic cycle of methylation. However, the experimentally determined redox potential for Cys-substituted cob(III)alamin is not available. Thus, it is useful to use computational approach to assess the redox potential for cobalamin systems with various lower- or upper-axial ligands. In Chapter 4, we used aquacobalamin as our model system and we developed a consistent computational approach to calculate its redox potential, pKas and ligand dissociation constants. We successfully reproduced the pH-dependent redox diagram of aquacobalamin and the errors for the redox potential are within 90 mV, whereas the errors for the pKas values are within 1.0 log unit.

1.6 Uptake and Export of Mercury Complexes

Another critical step in the process of mercury methylation by microorganism is to understand the transport mechanisms of mercury complexes. Both the processes of uptake Hg substrates and export of bio-transformed Hg products require cross the cell membranes of microorganisms. For gram-negative bacteria, Hg substrates need to cross the outer membrane first through passive diffusion or facilitated diffusion to enter the periplasmic area. Then, a few strategies may be used to cross the inner membrane.26 For the microorganisms that encode mer operon, a mer-based transport mechanism may be used, where MerP binds Hg(II) in the periplasm area and passes it to other mer proteins. For neutral, lipophilic mercury complexes, passive permeation mechanism may be used. For neutral or ionic mercury species, facilitated or active transport mechanism may be used through transmembrane channels or protein pumps.26 Although a few uptake mechanisms have been proposed, it is still not clear which mechanism is used for the transport of different Hg complexes. In Chapter 5, we examined the possibility for the passive permeation mechanism for neutral, small Hg compounds using molecular dynamics simulations. We also

7 predicted the permeability coefficients for the Hg-containing compounds, which provide insights on the kinetics of permeation processes.

8 CHAPTER 2

Simulation Theory and Computation

2.1 Theory of Quantum Mechanics

Quantum mechanics (QM) methods are widely applied to the problems in chemistry, biology and physics. Quantum mechanics calculations can be used to understand chemical reaction mechanisms —estimate the relative stability of molecules, identify reaction intermediates, and search for transition states. In combination with statistical mechanics, QM calculations can be used to obtain the thermodynamic properties of a system, such as enthalpy, entropy, and heat capacity. QM calculations can also be used to facilitate the interpretation of the frequencies and intensities of experimentally measured spectra in analytic chemistry. With the aid of thermodynamics cycle and continuum solvation model, we can apply QM methods to calculate the condense phase reaction free energies. We then can obtain the redox potential, pKa and dissociation constant of a system, subsequently.

2.1.1 Newton’s equation of motion

In classical mechanics, we can describe the motion of a particle using Newton’s second law. The position and velocity of a particle can be obtained from the equation of motion:

! � = �� = !" = � ! ! (2.1) !" !!!

where F is force, m is mass, a is the acceleration, v is velocity and x is coordinates. Based on the Newton’s equation, given the state of a system at anytime, the future state and motion, i.e. position, velocity and force applied on the system can be determined.

9 2.1.2 Schrodinger equation

However, Newton’s equation of motion can only be applied to macroscopic particles. For microscopic particles, based on the Heisenberg uncertainty principle, the exact position and velocity of a microscopic particle cannot be determined simultaneously. Alternatively, the state of a system can be described using the Schrodinger Equation in quantum mechanics (QM), which was derived by Austrian physicist Erwin Schrodinger in 1926. For a one-particle, one- dimensional system, the time-dependent Schrodinger equation is written as:

! ! − ℏ !! !,! = − ℏ ! ! !,! + � � ψ �, � (2.2) ! !" !! !!!

where � �, � is state function or wave function, � �, � is the potential energy of the system, m is the mass of the particle, � = −1, and ℏ is defined as h/2π.

For each measurable parameter in a physical system, a corresponding quantum mechanical operator is associated. The operator that is associated with system energy term is Hamiltonian operator Η, which is the sum of the potential energy operator � and the kinetic energy operator

�:

� = � + � (2.3)

The kinetic energy operator � is defined as:

! ! ! ! � = − ℏ ! + ! + ! (2.4) !! !!! !!! !!! and

! ! ! ∇!= ! + ! + ! (2.5) !!! !!! !!!

Therefore, the kinetic energy operator can also be written as

! � = − ℏ ∇! (2.6) !!

10 When apply the Hamiltonian operator on a wave function, we can simply get the total energy of a given system.

Hψ = Eψ (2.7)

For a M-nuclei and N-electron system, the Hamilton operator can be written as:

! ! ! ! ! ! ! ! ! !! ! ! ! ! ! !!!! H = − !!! ∇! − !!! ∇! − !!! !!! + !!! !!! + !!! !!! (2.8) ! ! !! !!" !!" !!"

The first and the second terms describe the kinetic energy of electrons and nuclei, respectively. The third term describes electron-nuclear attraction potential, whereas the fourth and the fifth terms in the Hamiltonian operator describe electron-electron repulsion potential and nuclear-nuclear repulsion potential, respectively. Among all the energetic terms in the equation of Hamilton operator, accurately computing the electron-electron interaction of a system is most challenging.

2.1.3 Density functional theory

As we have shown in section 2.1.2, wave function/state function contains all the possible information about a given system. The ultimate goal of quantum mechanics calculations is to solve the Schrodinger equation. However, for many-body system, it is impossible to solve the

Schrodinger equation by searching all acceptable N-electron wave functions. Thus, some approximations need to be introduced. One of the approximations is Born-Oppenheimer approximation. Because the mass of nuclei are more than 1800 times greater than an electron, the movement of nuclei can be treated as fixed and electrons can be seen as moving in the field of the fixed nuclei. In this approximation, the kinetic energy of nuclei is zero and nuclear-nuclear repulsion can be considered as a constant number.

Another effort to reduce the computational cost and to solve the many-body Schrodinger equation approximately is to replace the N-electron wave function by the electron density of the 11 system — this is the first concept of density functional theory (DFT). Density functional theory was born in 1964 when Hohenberg and Kohn published their groundbreaking paper in the

Physical Review.27 In this paper, they came up with two theorems, which are known as the first and the second Hohenberg-Kohn Theorems. Theorem I states that “the external potential

V!"#(r) is (to within a constant) a unique functional of ρ r ; since, in turn V!"#(r) fixes H, we see that full many particle ground state is a unique functional of ρ r .” In other words, the external potential is a unique functional of the electron density. Theorem II (Variational Principle) states that a universal functional for the energy E [n] can be defined in terms of the density. The exact ground state is the global minimum value of this functional.

Based on the Hohenberg-Kohn theorems, instead of dealing with wave functions directly, the electron density is used as the fundamental property instead. Thus, the total energy of a system can be obtained by determining the universal functional. The universal function F[ρ] contains the contributions of the kinetic energy T[ρ], the classic Coulomb interaction J[ρ] and non-classical contributions Encl[ρ], i.e. self-interaction correction, exchange and correlation effects.

F ρ r = T ρ r + J ρ r + E!"# ρ r (2.9)

However, the explicit forms of kinetic (T[ρ]) and non-classical contributions (Encl[ρ]) are unknown. It is not able to accurately determine the kinetic energy through an explicit functional.

Kohn and Sham tacked this problem by introducing the separation of the functional F[ρ] in the paper they published in 1965.28 Thus, the universal functional can be written as:

F ρ � = T! ρ � + J ρ � + E!" ρ � (2.10)

where Ts[ρ] is the non-interacting kinetic energy; EXC[ρ] is the exchange-correlation energy, which contains all the information that can not be determined exactly. By using the

12 Kohn-Sham approach, we can obtain as much information as possible accurately and only use an approximate functional to determine a small portion of the total energy. The one-electron K-S equation can be written as:

! ! ! !! !! ! !! − ∇ + ! dr! + V!" r! − ! φ! = ε!φ! (2.11) ! !!" !!"

The term in the parentheses is defined as Kohn-Sham one-electron operator f !". Thus, the equation above can be written as:

!" f φ! = ε!φ! (2.12)

Modern DFT methods aim to approximate the exact functional, especially the exchange- correlation energy term. DFT methods in general provide a good balance between accuracy and computational cost. One way to construct functional is to fit coefficients until the energies of the chosen systems are very close to the known targets, which is known as empirical approach. An alternative approach is to develop the functionals based on some known features of the exact funtionals.

2.1.4 Basis sets

In quantum chemistry, basis set is a set of one-particle orbitals that are used to construct molecular orbitals. Molecular orbital is the linear combination of atomic orbitals (LCAO), which is also know as LCAO approximation. The general expression for basis set function is given as:

� ∗ � !∗! (2.13)

where N is normalization constant, α is orbital exponent and r is radius.

In the early days of quantum chemistry, Slater-type orbitals (STOs) were used as basis functions because of their similarity to the eigenfunctions of the hydrogen atom. The general equation of STOs is given as:

13 !"# ! ! ! !!" ∅!"# �, �, � = �� (2.14)

where N is normalization constant; parameters a, b, c control angular momentum; parameter

ζ controls the width of the orbital.

Calculating many-center integrals in the STO equation is computationally expensive and the analytical techniques are not available. Later, Gaussian-type orbitals (GTOs) were proposed to mimic Slater-type orbitals. The linear combination of GTOs is used to approximate STO orbitals.

The general equation of GTOs is given as:

!"# ! ! ! !!!! ∅!"# �, �, � = �� (2.15)

Similarly, where N is normalization constant; parameters a, b, c control angular momentum; parameter ζ controls the width of the orbital. It is worth mentioning that, the difference in the equations of STOs and GTOs is if radius (r) is squared — this mathematical approach significantly reduced the computational cost. Today, GTOs are the most popular basis sets and a huge number of GTOs was generated in the past decades.

In general, basis sets can be divided into different types. Minimal basis sets uses the minimum number of basis sets to construct molecular orbitals, i.e. a single function for each atom in the molecule. Using a similar concept, double-zeta and triple-zeta basis sets use two and three functions, respectively, for each atomic orbital. Because valence electrons typically participate in forming chemical bonds, split-valence basis set addresses this problem by assigning more than one functions to valence orbitals. The typical notion of split-valence double- zeta basis set is written as n-ijG, where n indicates the number of functions for each core atomic orbital (inner shell orbitals), i and j indicate the number of functions that comprise the first and second STO of the double zeta, respectively. For example, 6-31G is a split-valence double-zeta basis set. Similarly, 6-311G is an example for split-valence triple-zeta basis set.

14 Simply by increasing the number of orbitals is not sufficient enough to describe molecular orbitals accurately. Some additional functions may be added, such as polarization functions and diffuse functions. Because atomic orbitals may be polarized to one side or the other side, additional functions are added to describe the polarization of electron density, which is called as polarization functions. Another common added function is diffuse function. From the general equation GTOs or STOs, we know that ζ controls the width of the orbitals. Diffuse functions have small ζ, which allows the electrons to be far away from the nucleus. Diffuse basis functions are very important for describing anions and the binding energies of van der Waals complexes.

2.2 Theory of Molecular Dynamics

In chapter 2.1, we discussed the basis of quantum mechanics and its potential applications in many different disciplines. Unlike quantum mechanics, molecular dynamics (MD) simulation treats molecules as a classical Newtonian system and the physical movements of atoms in the system can be described using Newton’s equation of motion. MD simulations have been widely used to study many biological problems, such as protein folding, drug discovery, protein-protein interaction, molecular recognition, or ion transport in membranes etc. MD simulations provide both static and dynamic information of a simulation system at the atomic level. It is a powerful tool itself to understand biological problems and it also can be a complement to experimental methods, such neutron scattering or X-ray crystallography. Because MD simulations do not describe the electronic structure of a system, they often cannot be used to study the properties that are involved in electrons, such as the breaking and forming of a chemical bond.

15 2.2.1 Molecular mechanics force field

Classical MD describes the potential energy of a molecular system using mathematical description. The Chemistry at HARvard Molecular Mechanics (CHARMM) force field29 is a typical force field for descripting the total potential energy of inter-atomic interactions. In general, potential energy (U(x)) contains two parts of energetic contribution — bonded interaction (Ubond(x)) and non-bonded interaction (Unon-bond(x)):

� � = �!"#$ � + �!"!!!"#$(�) (2.16)

The interaction between nearest groups (up to five atoms) that are connected through covalent bonds is described with bonded energy term (Ubond). The interaction beyond chemically bonded groups is represented with non-bonded energy term (Unon-bond). The bonded interaction in

CHARMM force field is given by:

! ! �!"#$ � = !"#$% �! � − �! + !"#$%& �! � − �! + !"!!"#$%& �! 1 + cos(�∅ − � +

! !"#$%#&$ �! � − �! (2.17)

The bonded interaction has four energy terms to describe bond stretching, angle bending, proper dihedral torsion and improper dihedral torsion, separately.

The non-bonded interaction in CHARMM force field is given by:

!"# !" !"# ! !!!! !!" !!" �!"!!!"#$ �!" = !"#$% !,! + !"#$% !,! ℇ!" − 2 (2.18) !!!" !!" !!"

!"# !"# !"# where �!" = �! + �! /2 and �!" = �!�!.

The non-bonded interaction has two energy terms, i.e. Coulomb interaction and Lennard-

Jones (LJ) interaction. The collection of the constants in equation 2.17 and 2.18 is called force field parameterization. For example, the force constant (kb) and equilibrium distance (b0) for a

16 particular bond need to be determined. Force field parameters can be usually derived from quantum mechanical calculations.

Force fields are usually specialized and they are not intended for all types of systems.

CHARMM force fields are widely used for both organic, inorganic and biologically related macromolecules, such DNA, RNA and lipids. Another popular force field is Assisted Model

Building and Energy Refinement (AMBER), which is widely used for proteins and DNAs.30

GROningen MOlecular Simulation (GROMOS), which is implemented in the MD simulation software GROMACS, is also a common force field for studying the molecular dynamics of biomolecule system.31

Today, most of the molecular mechanics force fields are classical force fields — the partial charge on each of the atoms is fixed and centered to the atomic nucleus. They are also called additive force fields, because the total electrostatic energy is the sum of the pairwise interaction between each atom. However, this approximation limits the ability of additive force fields to describe how molecules response to changing conditions. For example, a protein in the cell may interact with diverse range of environments, such as highly charged ions, polar or non-polar surfaces of other proteins, or amphipathic phospholipids bilayers. To solve this problem, polarizable force fields were developed to include electronic polarization in different electric environment. Unlike additive force fields, the partial charge on each atom in polarizable force fields is a variable and it changes as a function of external environment. One of the common polarizable force fields is CHARMM Drude polarizable force field, which was developed by

MacKerell and Roux.32 It is worth mentioning that because usually molecular mechanics force field cannot study bond forming or breaking, some reactive force fields were also developed to study chemical reactions, such as ReaxFF33 and Empirical valence bond (EVB).34

17 2.2.2 Equation of motion

In classical molecular mechanics, time-depended velocity and position of each atom in a simulation system can be determined by solving Newton’s equation of motion:

!� = � (2.19) !" !

!� = � (2.20) !"

The force F on each atom can be calculated from the first derivative of potential energy:

� = −∇�(�).

One of the commonly used algorithms to solve Newton’s equation of motion numerically is

Verlet algorithm.35 The Verlet algorithm assumes that the coordinates, velocities, and accelerations of particles in the system can be calculated by a Taylor series:

� � + �� = � � + � � �� + ! � � ��! + ⋯ (2.21) !

� � − �� = � � − � � �� + ! � � ��! − ⋯ (2.22) !

Addition of equation 2.21 and 2.22, the final form is:

� � + �� = 2� � − �(� − ��) + � � ��! (2.23)

Then, the velocities can be computed from coordinates using the following equation:

�(�) = � !!!" !�(!!!") (2.24) !!"

It is worth noting that time step δt has to be smaller than the fastest motions in the system, which is the vibration of hydrogen (δt ≤ 1 fs). Usually, a larger time step (δt = 2 fs)) can also be used by constraining the position of hydrogen atoms.

18 2.2.3 Potential of mean force and umbrella sampling

Potential of mean force (PMFs) is often used to characterize the free energy change as a function of a coordinate of the system.36 Many methods can be used to determine PMFs of a system, such as umbrella sampling, adaptive biasing force, and multiple-walker adaptive biasing force.

Umbrella sampling is the most common method used to compute PMFs along a given coordinate. Umbrella sampling is an enhanced sampling method, which overcomes the under sampling problem at energetically unfavorable configurations by applying restraint potentials.37

Along the reaction coordinate, an umbrella force (typically harmonic potential) is applied to restrain the system at a position z, which is often referred as “umbrella window”. At each window, the probability distribution biased by the umbrella potential is recorded in an umbrella histogram. To obtain PMFs from these umbrella histograms, i.e. unbiased probability distribution, Weighted Histogram Analysis Method (WHAM) is often used. 38

19 CHAPTER 3

Mercury Methylation by HgcA: Theory Supports Carbanion Transfer to

Hg(II)

20 HgcA is essential for the activity of mercury methylation in microorganisms — the deletion of

HgcA completely abolished the methylation activity. During the methylation process, HgcA acts as a methyl donor and transfers a methyl group from methylcobalamin to Hg substrates.

However, the detailed enzymatic mechanism for HgcA is still not clear. In this chapter, we investigated the enzymatic mechanism of HgcA by addressing two key questions involved in Hg methylation using quantum chemistry approach. One question is the potential role of Cys substitution. It is common for methylcobalamin to lose its lower axial ligand upon binding to enzymes. However, a Cys residue from HgcA coordinates to the cobalt in methylcobalamin has never been observed before. Also, this Cys residue is strictly conserved through genome sequences of Hg methylating microorganisms. Thus, it is important to investigate the potential role of this Cys substitution in the catalytic reactions of HgcA. The other question was the form of the transferred methyl group. In principle, methylcobalamin can transfer either methyl methyl

- II radical (CH3˙) or methyl carbanion (CH3 ) to Hg substrates. However, it is not clear which form of the methyl group is more favorable. In this chapter, we tested the hypothesis that the strictly conserved lower-axial Cys ligand could facilitate methyl carbanion transfer to Hg substrates using density theory functional calculations.

21 A version of this chapter was originally published by: Jing Zhou, Demian Riccardi, Ariana

Beste, Jeremy C. Smith, and Jerry M. Parks

Demian Riccardi, Ariana Beste, Jeremy C. Smith, and Jerry M. Parks. “Mercury Methylation by

HgcA: Theory Supports Carbanion Transfer to Hg(II)” Inorganic chemistry 53 (2014): 772–777

Contribution Statement: Jing Zhou conducted the calculations and wrote the draft of the manuscript. She also contributed significantly to data analysis and interpretation of the results. In this chapter, the article has been revised to provide more details.

Abstract

Many proteins use corrinoid cofactors to facilitate methyl transfer reactions. Recently, a corrinoid protein, HgcA, has been shown to be required for the production of the neurotoxin methylmercury by anaerobic bacteria. A strictly conserved Cys residue in HgcA was predicted to be a lower-axial ligand to Co(III), which has never been observed in a corrinoid protein. Here, we use density functional theory to study homolytic and heterolytic Co-C bond dissociation and methyl transfer to Hg(II) substrates with model methylcobalamin complexes containing a lower- axial Cys or His ligand to cobalt, the latter of which is commonly found in other corrinoid proteins. We find that Cys thiolate coordination to Co facilitates both methyl radical and methyl carbanion transfer to Hg(II) substrates, but carbanion transfer is more favorable overall in the condensed phase. Thus, our findings are consistent with HgcA representing a new class of corrinoid protein capable of transferring methyl groups to electrophilic substrates.

22 3.1 Introduction

+ Methylmercury ([CH3Hg(II)] ) is a potent neurotoxin that is produced in the environment from inorganic Hg.39 It has been known for more than four decades that anaerobic microorganisms produce methylmercury from inorganic Hg(II).40, 41 Two decades ago, a corrinoid, i.e. cobalamin-dependent, protein associated with the acetyl-CoA biochemical pathway was shown to be responsible for methylmercury production in the anaerobic bacterium Desulfovibrio desulfuricans LS,42 but the protein was not characterized further. In later work, on the basis of acetyl CoA pathway inhibition43 and cobalt limitation44 studies it was proposed that microorganisms lacking the complete acetyl-CoA pathway produce methylmercury through an alternate, cobalamin-independent pathway. Recently, it was shown that two genes, hgcA and hgcB, are required for methylmercury production by the model methylating sulfate-reducing bacterium Desulfovibrio desulfuricans ND13245 and the iron-reducing bacterium Geobacter sulfurreducens PCA.16 These genes encode a corrinoid protein, HgcA, and an auxiliary 2[4Fe-

4S] ferredoxin-like protein, HgcB, and the deletion of either gene abolished the ability of these organisms to produce methylmercury.16 The hgcAB gene pair has been found in a diverse set of microorganisms from bacterial and archaeal phyla, including the Proteobacteria, Firmicutes,

Chloroflexi and Euryarchaeota. Outside the Deltaproteobacteria, none of these microorganisms had been tested previously for their ability to methylate mercury, but the predicted mercury methylation phenotype for organisms possessing hgcAB has subsequently been confirmed for all organisms tested to date.46, 47

Corrinoid proteins use cobalamin or related cofactors to facilitate many types of reactions, including methyl transfer.48-50 In principle, methylcob(III)alamin can transfer a methyl group as a

+ - 49, 51, 52 carbocation (CH3 ), radical (CH3˙) or carbanion (CH3 ). The particular type of methyl

23 transfer that is carried out by a given corrinoid protein depends in part on the lower-axial ligand to the Co center of the cofactor. However, all cobalamin-dependent methyltransferases characterized so far have been found to transfer carbocations.23

Protein sequence analysis and homology modeling of HgcA from D. desulfuricans ND132 using an X-ray structure of the corrinoid iron-sulfur protein from Carboxydothermus hydrogenoformans Z-290124 as a template suggested that the 5,6-dimethylbenzimidazole (DMB) tail of the cofactor is not coordinated to Co (i.e., “DMB-off”), but a strictly conserved Cys residue in HgcA may be the lower-axial ligand to Co instead. UV-visible spectra were consistent with this mode of coordination, although they were not fully conclusive.16

Methylcobalamin is known to methylate inorganic Hg(II) to produce methylmercury non- enzymatically,53, 54 and coordination of Co by the DMB tail promotes this reaction51, 55 However, a thiolate ligand would be expected to coordinate strongly with CH3-cob(III)alamin if the DMB tail is absent or displaced. Thiolate-induced reductive cleavage of the Co-C bond in methylcobalamin and methylcobinamide to generate species with carbanionic character was proposed in the context of acetate and methane synthesis,56, 57 but, to our knowledge, not in the context of Hg methylation. Nevertheless, methylmercury formation by HgcA may involve the transfer of a carbanion to a Hg(II) substrate, with the Cys thiolate ligand playing a key role in stabilizing the Co(III) state during the reaction (Figure 3.1). Because methylation of the cofactor is presumed to involve initial transfer of a carbocation to a reduced Co(I) center followed by subsequent carbanion transfer to Hg(II), the cofactor in HgcA has been proposed to cycle between the Co(I), CH3-Co(III) and Co(III) states. Reduction of Co(III) back to the Co(I) state is then presumably carried out by HgcB.

24 Previous theoretical studies of methylcobalamins have focused on various aspects of Co-C homolysis,58-69 and spectral and electronic properties.70-79 To our knowledge, only one study has investigated carbanion dissociation in models of methylcobalamin,80 and none has considered the possible role of a lower-axial Cys thiolate ligand in promoting Co-C heterolysis. Here, we perform density functional theory calculations with empirical dispersion corrections to investigate whether a hypothetical lower-axial Cys thiolate ligand to Co could indeed facilitate methyl carbanion transfer to Hg(II) substrates. We represent cobalamin by corrin (C19H21N4Co).

That is, the side chains and DMB tail have been replaced by hydrogen, which is a common approach for studying cobalamins. The lower-axial ligand is represented by a Cys or His side chain in either its neutral or anionic protonation state (Scheme 3.1). We first compute both homolytic and heterolytic bond dissociation energies (BDEs) of the Co-C bond in models of methylcob(III)alamin with different lower-axial ligands, which allows direct comparison with previous studies. We then compute reaction free energies in the gaseous and condensed phases for methyl radical and carbanion transfer to two Hg(II) substrates. Finally, we compute ligand exchange free energies in which the methyl group bound to Co(III) is replaced with the leaving group from the Hg(II) substrate complex. Methyl carbocation dissociation and transfer reactions

+ are not considered here because Hg-C bond formation between Hg(II) and CH3 is not possible.

3.2 Computational Methods

All calculations were performed with NWChem81 or Gaussian 0982 using the BP8683-85 functional, which was shown to yield homolytic Co-C BDEs for cobalamins in good agreement with experimental measurements.63 The procedure used here to compute bond dissociation energies was similar to previous studies.60, 61, 63, 86 We also include empirical dispersion corrections, which have been shown to provide improved accuracy for density functional theory

25 calculations. BP86-D slightly overbinds the methyl group relative to experimental values in methylcobalamin,87 but these errors should largely cancel for the relative energetics of interest here. Cob(III)alamin and cob(II)alamin are low-spin d6 and d7 complexes, respectively, and it has been shown that the low-spin Co(III)-corrin-ligand and Co(II)-corrin-ligand models of the type considered here are the lowest in energy.66 Thus, all Co(III) and Co(II) complexes were assigned spin multiplicities of 1 and 2, respectively.

All geometries were fully optimized at the BP86 level of density functional theory in the gas phase using “tight” convergence criteria as defined in NWChem. The “grid=xfine” option in

NWChem was used for integral evaluation in all calculations. For geometry optimizations, the

Stuttgart-Dresden small-core effective core potential (ECP), also called SDD or ECP60MWB, which accounts for scalar relativistic effects, and its corresponding basis set,88 were used for Hg, and the 6-31G(d) basis set with spherical d functions was used for all other atoms. The SDD ECP has been used previously in conjunction with hybrid DFT to describe the Hg-C bond cleavage reaction catalyzed by the organomercurial lyase,89 Hg(II) solvation90 and Hg(II) ligand binding,91 and with the BP86 functional to describe Hg(II) complexation with a porphyrin.92

Vibrational frequency analysis was performed for the fully optimized geometries to confirm that they were energy minima and to compute zero-point energy (ZPE) and thermal corrections.

Vibrational frequencies were calculated analytically for closed-shell molecules and numerically for open-shell molecules. Although the convergence criteria for the geometry optimizations were set to “tight”, the Co(II)-corrin complex produced a spurious imaginary frequency (-25.38 cm-1) caused by inaccuracies in the numerical Hessian. Displacements along the spurious imaginary mode confirmed that the structure is indeed a minimum along this mode (Figure 3.2).

26 Single-point energies were computed at the optimized geometries with the SDD ECP and basis set for Hg and the 6-311++G(d,p) basis set for all other atoms. For simplicity, we refer to the 6-31G(d) and 6-311++G(d,p) basis sets as B1 and B2, respectively, with SDD being implied when Hg is present in the calculations. Empirical dispersion corrections93 with Becke-Johnson damping,94 (abbreviated as D3) were computed with the program DFT-D321 on geometries optimized with B1. Solvation effects were computed with B1 using the SMD continuum solvation model95 as implemented in Gaussian 09 with the default dielectric constant, ε = 78.4, and with ε = 4.0.

Gas-phase Co-C bond dissociation energies were computed as:

BDE = ∆EB2 + ∆EZPE, B1 + ∆Edisp + ∆EBSSE, B2 (3.1)

where ∆EB2 is the difference in DFT total energy (products minus reactant) computed with

B2, ∆EZPE, B1 is the zero-point energy correction obtained from vibrational frequency analysis computed with B1, ∆Edisp is the dispersion correction and ∆EBSSE is the standard counterpoise correction96 computed with B2.

Gas-phase reaction free energies at 298.15 K and 1 atm (∆G°r, gas) were computed for all processes as:

∆G°r, gas = ∆EB2 + ∆Edisp + ∆H°corr, B1 - T∆S°corr, B1 (3.2)

where the first two terms on the RHS are the same as for the BDEs, ∆H°corr, B1 and T∆S°corr, B1 are the thermal corrections to the enthalpy and entropy, respectively, computed with the standard ideal gas, rigid-rotor, harmonic approximation.

* Aqueous phase reaction free energies at 298.15 K and 1 M (∆G r, aq) were computed for all processes as:

* →* ∆G r, aq = ∆G°r, gas + ∆∆G° solv, B1 (3.3)

27 →* where ∆∆G° solv, B1 is the solvation free energy difference for the reaction computed with the SMD continuum solvent model. The individual solvation free energies for each solute include a contribution (∆G°→* = 1.89 kcal mol-1) arising from changing the standard state from 1 mol per 24.46 L in the gas phase to 1 M in the condensed phase.

3.3 Results and Discussion

3.3.1 Co-C bond homolysis

The computed gas-phase homolytic Co-C BDEs are all in the range of ~36-43 kcal mol-1 (Table

3.1), consistent with previous studies.58-61, 63, 66-68 The individual energetic contributions for both homolytic and heterolytic gas-phase Co-C BDEs are shown in Table 3.2. For heterolytic Co-C dissociation, the BDEs are of course much higher in the gas phase than for homolysis because of charge separation in the heterolytically dissociated fragments (Table 3.1). To enable direct comparisons of homolytic and heterolytic processes, we computed reaction free energies for Co-

C bond dissociation with a continuum representation of the solvent. The individual energetic contributions for condensed phase Co-C BDEs are listed in Table 3.3.

For methyl radical dissociation in the gas phase, the computed Co-C BDE with a neutral

Cys ligand (2) is 2.7 kcal mol-1 lower than for the neutral His ligand complex (3) (Table 3.1).

Similarly, the computed homolytic BDE for the Cys thiolate complex (4) is 3.6 kcal mol-1 lower than for the His imidazolate complex (5) (Table 3.1). These findings are consistent with a previous study that showed that lower-axial Co coordination by sulfides yielded the lowest homolytic BDEs among a series of small molecule and amino-acid side chain ligand models.66

Homolytic dissociation in the absence of a lower-axial ligand (1) was computed to be 6.6 kcal mol-1 less favorable than for the Cys-coordinated complex (2) (Table 3.1). We computed gas-

28 phase reaction free energies (∆G°r, gas) for each process and found that the sum of the enthalpic (-

3.3 to -4.5 kcal mol-1) and entropic contributions (7.2 to 12.9 kcal mol-1) provided net stabilization of the products relative to the corresponding BDE values. We also computed aqueous phase reaction free energies (∆G°r, aq) by including solvation contributions obtained with the Solvent Model based on Density95 (SMD) polarizable continuum model and the dielectric constant of water (SMD78.4). Solvation effects were generally slightly destabilizing for radical transfer (< 2 kcal mol-1) relative to the gas-phase reaction free energies (Table 3.1).

3.3.2 Co-C bond heterolysis

For methyl carbanion dissociation, the computed heterolytic BDE for the CH3-Co(III)-corrin complex with a neutral Cys ligand (2) is 4.2 kcal mol-1 less favorable than for the neutral His ligand complex (3) (Table 3.1) because the neutral Cys side chain interacts more weakly than neutral His with Co(III). In the absence of a lower-axial ligand, heterolytic dissociation (1) is much less favorable (by more than 36 kcal mol-1 in the gas phase and ~31 kcal mol-1 in water)

than for the Cys or His ligand complexes. Indeed, five-coordinate, “base-off” CH3- cob(III)alamin in corrinoid proteins is known to favor methyl carbocation transfer.48, 49, 80, 97

However, the heterolytic Co-C dissociation of the Cys thiolate complex (4) is 14.4 kcal mol-1 more favorable than for the His imidazolate complex (5). Similar to the homolytic processes, the sum of the enthalpic (-3.7 to -6.1 kcal mol-1) and entropic contributions (8.6 to 11.3 kcal mol-1) provided net stabilization of the products relative to the corresponding BDE values, with heterolytic dissociation of 4 remaining ~14 kcal mol-1 more favorable than for 5. Solvation stabilizes the charges of the dissociated species for heterolytic Co-C cleavage of 1-5 and greatly reduces their respective reaction free energies relative to the gas phase (Table 3.1). In the

aqueous phase (SMD78.4), dissociation of a carbanion for the Cys-on species (4) requires the least

29 energy (26.4 kcal mol-1) compared to all other homolytic and heterolytic dissociation processes.

However, homolysis becomes more favorable (by 14-24 kcal mol-1) when the dielectric constant

is lowered to approximate a protein environment (SMD4.0).

3.3.3 Reaction free energies

To compare methyl radical and carbanion transfer to Hg(II) in the condensed phase, we computed aqueous reaction free energies for both types of transfer from CH3-Co(III)-corrin- ligand complexes to two Hg(II) substrates (Scheme 3.2). Hg(II) bis thiolates, which were modeled as Hg(SCH3)2, were found to be the most prevalent form of Hg inside the cells of D.

98 desulfuricans ND132. We also consider HgCl2 as a substrate because it is readily methylated under aqueous, non-enzymatic conditions. In metalloproteins, endogenous protic acid ligands typically coordinate metal centers as anions,99 so we limit these analysis to complexes with a Cys or His ligand in the anionic protonation state (i.e., 4 and 5).

Similar to the trends observed for the gas-phase reaction free energies for Co-C bond

-1 dissociation, methyl radical transfer to Hg(SCH3)2 was computed to be 2.7 kcal mol more favorable for the complex with a Cys(-) ligand (Reaction A) than for His(-) (Reaction B, Table

3.4). Methyl radical transfer to HgCl2 is also favored for the Cys(-) complex (Reaction C) over the His(-) complex (Reaction D) by a similar amount. Including solvation (SMD78.4 and SMD4.0)

* - slightly increases the reaction free energies (∆G r, aq) for methyl radical transfer by ~2-4 kcal mol

1 relative to the gas phase. Comparing the gas-phase bond dissociation free energies (Table 3.1) to Reactions A through D (Table 3.4) reveals that the Hg-C interactions in the methylated Hg(II) complexes do not significantly enhance homolytic transfer. The individual contributions for both gas-phase and aqueous phase reaction free energies for methyl radical and methyl carbanion transfer are listed in Table 3.5.

30 - Methyl carbanion transfer to both Hg(SCH3)2 and HgCl2 were computed to be ~14 kcal mol

1 more favorable in the gas phase for the Cys(-) complex (Reactions E and G, respectively) compared with the corresponding His(-) complex (Reactions F and H, respectively) (Table 3.4).

-1 Methyl carbanion transfer to HgCl2 (Reactions G and H) is ~23 kcal mol more favorable in the gas phase than to Hg(SCH3)2 (Reactions E and F) for both Cys(-) and His(-) ligand complexes

91 (Table 3.4), consistent with the greater reactivity of Hg(II) in HgCl2. Solvation lowers the reaction free energies for methyl carbanion transfer drastically relative to the corresponding processes in the gas phase. The aqueous phase reaction free energy for carbanion transfer from

-1 -1 Cys(-) complex 4 to Hg(SCH3)2 (Reaction E) was computed to be 5.1 kcal mol , ~12 kcal mol more favorable than for His(-) complex 5 (Reaction F). Reactions G and H were both computed

-1 to be exergonic (Table 3.4), with carbanion transfer to HgCl2 being ~12 kcal mol more favorable for the Cys(-) complex (4) than for the His(-) complex (5). Compared to aqueous

-1 conditions (SMD78.4), these reactions (E-H) were computed to be 12-15 kcal mol less favorable in the approximated protein environment (SMD4.0). Nevertheless, when condensed phase effects are included, methyl carbanion transfer from Cys(-) complex 4 is still favored over His(-) complex 5 for both Hg(II) substrates. Perhaps more importantly, methyl carbanion transfer to

Hg(II) substrates is significantly more favorable overall than methyl radical transfer (Table 3.4 and Figure 3.3). In contrast to methyl radical transfer to Hg(II) substrates, the Hg-C interactions

- in the [CH3HgR2] complexes significantly enhance heterolytic transfer.

3.3.4 Nonenzymatic Hg methylation

The present findings are also relevant to the non-enzymatic methylation of Hg(II) by methylcobalamin,53, 54 which is known to be enhanced by coordination of the DMB tail to Co.51,

55 The DMB tail has only one nitrogen available for Co coordination because the second is

31 bonded to the ribofuranosyl moiety through an N-alkyl linkage. Thus, the neutral His (i.e., imidazole) complex (5) is the most relevant ligand for comparison. Indeed, substitution of DMB by imidazole in previous computational studies was shown to yield good accuracy for computing

58, 67, 100-102 Co-C strengths. Using the SMD78.4 bond dissociation free energies from Table 3.1,

-1 transfer of a carbanion from 3 to HgCl2 increases the reaction energy from -4.0 kcal mol

(Reaction H) to 5.3 kcal mol-1 relative to 5. Thus, the present calculations suggest that methyl carbanion transfer from methylcobalamin to HgCl2 is energetically feasible for methylcobalamin in the DMB-on configuration in the aqueous phase. In contrast, for SMD4.0 the corresponding substitution of the neutral imidazole for imidazolate increases the energetic cost from 9.4

(Reaction H) to 35.6 kcal mol-1. Apparently, swapping an anionic ligand for the DMB tail is necessary to achieve reasonable energetics in the protein environment for methyl transfer to an electrophilic substrate.

3.3.5 Ligand exchange reactions

n- - - In an aqueous environment, [CH3Hg(II)R2] (R = CH3S or Cl , n = 0 or 1) would likely lose one

R radical or anion to the solvent or another competitive acceptor to generate the neutral CH3HgR species. To approximate this process, we considered subsequent transfer of CH3S/Cl from the methylated Hg(II) complexes to the Co center in the Co-corrin-ligand models (Scheme 3.2) and computed gaseous and aqueous phase ligand exchange free energies.103 The neutral reactant and products states for the CH3/CH3S ligand exchange are independent of the nature of the methyl transfer (heterolytic versus homolytic). The gas-phase CH3/CH3S ligand exchange free energy for the Cys thiolate ligand complex was computed to be exergonic by 11.3 kcal mol-1 (Reaction

-1 I), and 3.5 kcal mol less favorable for the His complex (Reaction J). The corresponding CH3/Cl

-1 exchanges were even more exergonic by ~10 kcal mol , with ∆G°r, gas for Reaction K = -21.2

32 kcal mol-1 (Table 3.6 and Figure 3.3). The individual energetic contributions for upper-axial ligand exchange for Co(III)-Corrin Complexes are listed in Table 3.7. As expected on the basis of the overall charge neutrality in both the reactants and products for ligand exchange, solvation effects are minimal, decreasing the favorability of Reactions I-L by no more than 4.0 kcal mol-1 relative to the gas-phase free energy values. Thus, the current calculations predict that the corresponding differences in ligand affinity (i.e., Co-CH3 and Hg-R versus Co-R and Hg-CH3) favor the formation of methylmercury for both processes.

3.4 Conclusions

Our findings show that coordination of anionic lower-axial ligands to Co(III) and contributions from solvation favor transfer of a methyl carbanion over a methyl radical from CH3-Co(III)- corrin-ligand complexes to Hg(II) substrates. Under fully hydrated conditions in continuum solvent (SMD78.4), the energetics of carbanion dissociation are comparable to methyl radical dissociation, but the presence of an electrophilic Hg(II) substrate increases the favorability of carbanion transfer greatly compared to methyl radical transfer. Thus, our calculations support the proposal that the strictly conserved Cys in HgcA enhances the methylation of Hg(II). These findings may explain the apparent strong selective pressure to maintain the strictly conserved

Cys in HgcA orthologs, although a His variant of HgcA may also be capable of methyl transfer to a Hg(II) substrate if geometric perturbations are not too great.

The reaction free energies computed for carbanion transfer display a large dependence on the solvent dielectric constant due to charge separation in the product complexes. In the absence of structures for HgcA and any interacting protein partners that may be involved in substrate co- localization or charge stabilization, the electrostatic/dielectric environment for the methyl

33 transfer reaction cannot be determined. Nevertheless, our model calculations shed light on key mechanistic aspects of the mercury methylation reaction carried out by HgcA.

34 3.5 Appendix 1

Scheme 3.1 Methylcorrinoid model systems with various lower-axial ligands.

CH3 L = none 1 Cys 2 CoIII His 3 Cys- 4 L His- 5

Scheme 3.2 Methyl transfer to Hg(SCH3)2 and HgCl2 with subsequent ligand exchange.

II + [CH HgR] CH Co 3 3 R III + HgR L Co 2 III Co + CH3HgR L L L = Cys- R = CH3S- CoIII + [CH3HgR2] His- Cl- L

CH3-Cbl(III)-HgcA THF HgR2

CH3-THF

Cbl(I)-HgcA

CH3HgR + R- HgcB

- Cbl(III)-HgcA 2 e

Figure 3.1 Proposed Hg methylation pathway.

16 This figure was adapted from ref ; CH3-THF = 5-methyltetrahydrofolate;Cbl = cobalamin

35 -2338.47

-2338.47

Energy (au) -2338.47

-2338.47

-2338.47 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Displacement (Α)

Figure 3.2 Displacements along the spurious imaginary mode.

This was caused by inaccuracies in the numerical Hessian for Co(II)-corrin complex. The potential confirms that the structure is indeed a minimum along this mode.

Figure 3.3 Aqueous reaction free energies relative to reactants for methyl radical and carbanion transfer.

Reactions A-H indicate methyl transfer reactions and Rreactions I-L indicate ligand exchange free energies to Hg(SCH3)2 substrate (Left) and HgCl2 substrate (right).

36 Table 3.1 Computed Absolute and Relative Gas-Phase Bond Dissociation Energies and

Condensed Phase Reaction Free Energies for Co-C Bond Dissociation in CH3-Co(III)-Corrin-

Ligand Complexes.

a c Abs. Rel. Abs. Rel. Abs. Rel. Reaction * b * b BDE BDE ∆G°r, gas ∆G°r, gas ∆G r, aq ∆G r, aq Homolysis 1 42.6 6.6 37.4 7.7 36.8 (38.7) 5.9 (6.8) 2 36.0 0.0 29.7 0 30.9 (31.9) 0.0 (0.0) 3 38.7 2.7 29.2 -0.5 30.9 (31.6) 0.0 (-0.3)

4 36.2 0.0 26.7 0 28.5 (29.3) 0.0 (0.0) 5 39.8 3.6 29.3 2.6 30.2 (31.5) 1.7 (2.2) Heterolysis 1 275.1 36.3 269.1 34.6 80.9 (127.3) 31.2 (31.3) 2 238.8 0.0 234.5 0 49.7 (96.0) 0.0 (0.0) 3 234.6 -4.2 229.7 -4.8 47.8 (92.6) -1.9 (-3.4)

4 141.2 0.0 135.8 0 26.4 (53.2) 0.0 (0.0) 5 155.6 14.4 149.7 13.9 38.5 (66.4) 12.1(13.2) a Relative to the Cys ligand complex (2 or 4) within each charge/dissociation category. b ε = 78.4 (ε = 4.0). c all energies are in kcal mol-1

37 Table 3.2 Homolytic and Heterolytic Co-C Bond Dissociation Energies and Individual Energetic Contributions.

BP86/6-31G(d) BP86/6-311++G(d,p) Reaction h a b c d e a d f ∆EB1 ∆EZPE ∆Edisp ∆EBSSE BDE1 ∆EB2 ∆EBSSE BDE2

Chargeg 1 0 1

CH3-Cbl(III) → CH3· + Co(II) 46.8 -4.4 8.3 -6.2 44.5 42.0 -3.4 42.6

CH3-Cbl(III)-Cys → CH3· + Co(II)-Cys 41.3 -4.5 6.3 -6.4 36.8 35.2 -1.0 36.0

CH3-Cbl(III)-His → CH3· + Co(II)-His 40.7 -4.9 8.4 -5.3 39.0 36.1 -1.0 38.7

Chargeg 0 0 0

CH3-Cbl(III)-Cys(-) → CH3· + Co(II)-Cys(-) 38.1 -4.6 8.4 -6.3 35.5 33.4 -1.0 36.2

CH3-Cbl(III)-His(-) → CH3· + Co(II)-His(-) 41.5 -4.8 8.7 -5.0 40.4 37.0 -1.0 39.8

Chargeg 1 -1 2

CH3-Cbl(III) → CH3- + Co(III) 305.0 -7.1 8.2 -32.2 273.9 278.2 -4.2 275.1

CH3-Cbl(III)-Cys → CH3- + Co(III)-Cys 273.7 -5.1 4.3 -33.4 239.5 243.5 -3.8 238.8

CH3-Cbl(III)-His → CH3- + Co(III)-His 263.8 -5.2 6.9 -31.7 233.8 237.5 -4.7 234.6

Chargeg 0 -1 1

CH3-Cbl(III)-Cys(-) → CH3- + Co(III)-Cys(-) 171.7 -4.5 6.6 -32.8 141.0 143.7 -4.5 141.2

CH3-Cbl(III)-His(-) → CH3- + Co(III)-His(-) 182.9 -4.9 7.0 -31.1 153.9 158.0 -4.5 155.6 a Total DFT energy difference. bZero-point energy difference. c D3 dispersion correction. d Basis set superposition error correction. e

f g BDE1 = ∆EB1 + ∆EZPE, B1 + ∆Edisp + ∆EBSSE, B1. BDE2 = ∆EB2 + ∆EZPE, B1 + ∆Edisp + ∆EBSSE, B2. Total charges of the methylcorrinoid complex, methyl group, and corrinoid complex, respectively. h all energies are in kcal mol-1.

38 Table 3.3 Computed Gas-Phase and Condensed-Phase Free Energies and Individual Energetic

Contributions for Co-C Bond Dissociation in CH3-Co(III)-Corrin-Ligand Complexes.

e a b * c * d Reaction ∆Er, B2 ∆Er disp ∆G°corr, B1 ∆G°r, gas ∆∆G solv, B1 ∆G r, aq Homolysis

1 CH3-Co(III)-corrin 42.0 8.3 -12.9 37.4 -0.6 (1.3) 36.8 (38.7)

2 CH3-Co(III)-corrin-Cys 35.2 6.3 -11.7 29.7 1.2 (2.2) 30.9 (31.9)

3 CH3-Co(III)-corrin-His 36.1 8.4 -15.4 29.2 1.7 (2.4) 30.9 (31.6)

4 CH3-Co(III)-corrin-Cys(-) 33.4 8.4 -15.0 26.7 1.8 (2.6) 28.5 (29.3)

5 CH3-Co(III)-corrin-His(-) 37.0 8.7 -16.3 29.3 0.9 (2.2) 30.2 (31.5)

Heterolysis

1 CH3-Co(III)-corrin 278.2 8.2 -17.3 269.1 -188.2 (-141.8) 80.9 (127.3)

2 CH3-Co(III)-corrin-Cys 243.5 4.3 -13.3 234.5 -184.8 (-138.5) 49.7 (96.0)

3 CH3-Co(III)-corrin-His 237.5 6.9 -14.7 229.7 -181.9 (-137.1) 47.8 (92.6)

4 CH3-Co(III)-corrin-Cys(-) 143.7 6.6 -14.4 135.8 -109.4 (-82.6) 26.4 (53.2)

5 CH3-Co(III)-corrin-His(-) 158.0 7.0 -15.2 149.7 -111.2 (-83.3) 38.5 (66.4) a ∆G°corr, B1 = ∆H°corr, B1 - T∆S°corr, B1. b ∆G°r, gas = ∆Er, B2 + ∆Er, disp + ∆G°corr, B1. c * →* ∆∆G solv, B1 is the solvation free energy difference for the reaction computed with SMD. It also includes a ∆G° correction for each solute. Values were obtained with ε = 78.4 (ε = 4.0). d * * ∆G r, aq = ∆G°r, gas + ∆∆G solv, B1 e all energies are in kcal mol-1

39 Table 3.4 Computed Gas-Phase and Aqueous Reaction Free Energies for Methyl Radical and

Carbanion Transfer from CH3-Co(III)-Corrin-Ligand Complexes to Hg(SCH3)2 and HgCl2.

* a Reaction ∆G°r, gas ∆G r, aq

A CH3-Co(III)-corrin-Cys(-) + Hg(SCH3)2 → Co(II)-corrin- · 23.3 27.4 (26.6) Cys(-) + [CH3Hg(SCH3)2]

B CH3-Co(III)-corrin-His(-) + Hg(SCH3)2 → Co(II)-corrin- · 26.0 29.2 (28.8) His(-) + [CH3Hg(SCH3)2]

C CH3-Co(III)-corrin-Cys(-) + HgCl2 → Co(II)-corrin-Cys(-) + · 26.5 29.7 (29.1) [CH3HgCl2]

D CH3-Co(III)-corrin-His(-) + HgCl2 → Co(II)-corrin-His(-) + · 29.1 31.4 (31.3) [CH3HgCl2]

E CH3-Co(III)-corrin-Cys(-) + Hg(SCH3)2 → Co(III)-corrin- - 69.9 5.1 (19.1) Cys(-) + [CH3Hg(SCH3)2]

F CH3-Co(III)-corrin-His(-) + Hg(SCH3)2 → Co(III)-corrin- - 83.8 17.1 (32.3) His(-) + [CH3Hg(SCH3)2] G CH3-Co(III)-corrin-Cys(-) + HgCl2 → Co(III)-corrin-Cys(-) - 46.5 -16.0 (-3.8) + [CH3HgCl2] H CH3-Co(III)-corrin-His(-) + HgCl2 → Co(III)-corrin-His(-) + - 60.4 -4.0 (9.4) [CH3HgCl2] a ε = 78.4 (ε = 4.0)

40 Table 3.5 Computed Gas-Phase and Aqueous Reaction Free Energies for Methyl Radical and Carbanion Transfer from CH3-Co(III)-

Corrin-Ligand Complexes to Hg(SCH3)2 and HgCl2 with Individual Energetic Contributions.

a b * c * d Reaction ∆EB2 ∆Edisp ∆G°corr,B1 ∆G°r, gas ∆∆G solv, B1 ∆G r, aq (A) CH3-Co(III)-corrin-Cys(-) + Hg(SCH3)2 → · Co(II)-corrin-Cys(-) + [CH3Hg(SCH3)2] 25.1 3.5 -5.3 23.3 4.1 (3.3) 27.4 (26.6)

(B) CH3-Co(III)-corrin-His(-) + Hg(SCH3)2 → · Co(II)-corrin-His(-) + [CH3Hg(SCH3)2] 28.7 3.7 -6.5 26.0 3.2 (2.8) 29.2 (28.8)

(D) CH3-Co(III)-corrin-His(-) + HgCl2 → · Co(II)-corrin-His(-) + [CH3HgCl2] 30.7 5.5 -7.0 29.1 2.3 (2.2) 31.4 (31.3)

(E) CH3-Co(III)-corrin-Cys(-) + Hg(SCH3)2 → - Co(III)-corrin-Cys(-) + [CH3Hg(SCH3)2] 70.0 2.7 -2.8 69.9 -64.8 (-50.8) 5.1 (19.1)

(F) CH3-Co(III)-corrin-His(-) + Hg(SCH3)2 → - Co(III)-corrin-His(-) + [CH3Hg(SCH3)2] 84.3 3.1 -3.6 83.8 -66.7 (-51.5) 17.1 (32.3)

(G) CH3-Co(III)-corrin-Cys(-) + HgCl2 → - Co(III)-corrin-Cys(-) + [CH3HgCl2] 45.8 3.8 -3.1 46.5 -62.5 (-50.3) -16.0 (-3.8)

(H) CH3-Co(III)-corrin-His(-) + HgCl2 → - Co(III)-corrin-His(-) + [CH3HgCl2] 60.2 4.2 -4.0 60.4 -64.4 (-51.0) -4.0 (9.4) a ∆G°corr, B1 = ∆H°corr, B1 - T∆S°corr, B1. b ∆G°r, gas = ∆Er, B2 + ∆Er, disp + ∆G°corr, B1. c * →* ∆∆G solv, B1 is the solvation free energy difference for the reaction computed with SMD. It also includes a ∆G° correction for each solute. d * * ∆G r, aq = ∆G°r, gas + ∆∆G solv, B1

41 Table 3.6 Computed Condensed-Phase Reaction Free Energies for Upper-Axial Ligand

Exchange in Co(III)-Corrin-Ligand Complexes.

* a Reaction ∆G°r, gas ∆G r, aq I CH -Co(III)-corrin-Cys(-) + Hg(SCH ) → 3 3 2 -11.3 -9.3 (-10.7) CH3S-Co(III)-corrin-Cys(-) + CH3HgSCH3 J CH -Co(III)-corrin-His(-) + Hg(SCH ) → 3 3 2 -7.8 -6.0 (-7.1) CH3S-Co(III)-corrin-His(-) + CH3HgSCH3

K CH -Co(III)-corrin-Cys(-) + HgCl → 3 2 -21.2 -18.7 (-20.0) Cl-Co(III)-corrin-Cys(-) + CH3HgCl L CH -Co(III)-corrin-His(-) + HgCl → 3 2 -16.9 -13.0 (-14.7) Cl-Co(III)-corrin-His(-) + CH3HgCl a ε = 78.4 (ε = 4.0). See text.

Table 3.7 Condensed-Phase Reaction Free Energies at 298K for CH3/SCH3 Upper-Axial Ligand

Exchange for Co(III)-Corrin Complexes with Individual Energetic Contributions.

a b * c * d Reaction ∆EB2 ∆Edisp ∆G°corr,B1 ∆G°r, gas ∆∆G solv, B1 ∆G r, aq

(I) CH3-Co(III)-corrin-Cys(-) + Hg(SCH3)2 → CH3S-Co(III)-corrin-Cys(-) + CH3HgSCH3 -5.8 -4.8 -0.7 -11.3 2.0 (0.6) -9.3 (-10.7)

(J) CH -Co(III)-corrin-His(-) + Hg(SCH ) → 3 3 2 -2.8 -4.9 -0.1 -7.8 1.8 (0.7) -6.0 (-7.1) CH3S-Co(III)-corrin-His(-) + CH3HgSCH3

(K) CH -Co(III)-corrin-Cys(-) + HgCl → 3 2 -20.4 -0.8 0.1 -21.2 2.5 (1.2) -18.7 (-20.0) Cl-Co(III)-corrin-Cys(-) + CH3HgCl (L) CH -Co(III)-corrin-His(-) + HgCl → 3 2 -16.6 -0.7 0.3 -16.9 3.9 (2.2) -13.0 (-14.7) Cl-Co(III)-corrin-His(-) + CH3HgCl a ∆G°corr, B1 = ∆H°corr, B1 - T∆S°corr, B1. b ∆G°r, gas = ∆Er, B2 + ∆Er, disp + ∆G°corr, B1. c * →* ∆∆G solv, B1 is the solvation free energy difference for the reaction computed with SMD. It also includes a ∆G° correction for each solute. Values were obtained with ε = 78.4 (ε = 4.0). d * * ∆G r, aq = ∆G°r, gas + ∆∆G solv, B1

42 CHAPTER 4

Toward Quantitatively Accurate Calculation of the Redox-associated Acid-

base and Ligand Binding Equilibria of Aquacobalamin

43 HgcB is also essential for the activity of mercury methylation in microorganisms. HgcB is a ferredoxin-like protein, which was suggested to provide two electrons to reduce Cob(III)alamin-

HgcA to Cob(I)alamin-HgcA during the catalytic process. Thus, charactering the redox chemistry of cobalamin can provide the reduction requirement for HgcB, which is the first step toward understanding the catalytic mechanism of HgcB. However, it is very challenging to accurately compute the redox potentials for transition metal containing species, such as cobalamins. One challenge is to find a computational method that can describe the energies and structures of cobalamin accurately. Another challenge is the changes in ligand protonation states and metal coordination number upon reduction. In this chapter, we examined the two challenges by using density functional theory and continuum solvation model to calculate the equilibration constants, pKas and reduction potentials for models of aquacobalamin. We successfully developed a consistent computational approach for computing the pH-dependent redox of aquacobalamin.

44 A version of this chapter was originally published by: Ryne C. Johnston, Jing Zhou, Jeremy C.

Smith, and Jerry M. Parks.

Ryne C. Johnston, Jing Zhou, Jeremy C. Smith, and Jerry M. Parks. “Toward quantitatively accurate calculation of the redox-associated acid-base and ligand binding equilibria of aquacobalamin” The Journal of Physical Chemistry B 120 (2016): 7303-7318

Contribution statement: the student participated the original design of the work and wrote the first draft of the manuscript. In this chapter, the article has been revised to provide more details.

Abstract

Redox processes in complex transition metal-containing species are often intimately associated with changes in ligand protonation states and metal coordination number. A major challenge is therefore to develop consistent computational approaches for computing pH-dependent redox and ligand dissociation properties of organometallic species. Reduction of the Co center in the vitamin B12 derivative aquacobalamin can be accompanied by ligand dissociation, protonation, or both, making these properties difficult to compute accurately. We examine this challenge here by using density functional theory and continuum solvation to compute Co–ligand binding equilibrium constants (Kon/off), pKas and reduction potentials for models of aquacobalamin in aqueous solution. We consider two models for cobalamin ligand coordination: the first follows the hexa, penta, tetra coordination scheme for CoIII, CoII, and CoI species, respectively, and the second model features saturation of each vacant axial coordination site on CoII and CoI species with a single, explicit water molecule to maintain six directly interacting ligands or water

45 molecules in each oxidation state. Comparing these two coordination schemes in combination with five dispersion-corrected density functionals, we find that the accuracy of the computed properties is largely independent of the scheme used, but including only a continuum representation of the solvent yields marginally better results than saturating the first solvation shell around Co throughout. PBE performs best, displaying balanced accuracy and superior performance overall, with RMS errors of 80 mV for seven reduction potentials, 2.0 log units for five pKas and 2.3 log units for two log Kon/off values for the aquacobalamin system. Furthermore, we find that the BP86 functional commonly used in corrinoid studies suffers from erratic behavior and inaccurate descriptions of Co–axial ligand binding, leading to substantial errors in predicted pKas and Kon/off values. These findings demonstrate the effectiveness of the present approach for computing electrochemical and thermodynamic properties of a complex transition metal-containing cofactor.

4.1 Introduction

Many enzymes, such as the cobalamin-dependent isomerases, methyltransferases and reductive dehalogenases, use corrinoid cofactors to catalyze diverse reactions.25, 104-106 The redox properties of the cofactors are critical for carrying out their catalytic functions.107 Cobalamin consists of a macrocyclic corrin ring that coordinates a central Con+ cation with n = 1–3 (Figure

4.1). Whereas CoIII and CoII corrinoids are generally accessible under ambient redox conditions, the formation of CoI corrinoids typically requires strongly reducing conditions. The coordination number of Co is related to its oxidation state, usually varying from four in the CoI state to six in

CoIII.104, 108

The corrin ring of cobalamin is substituted by multiple methyl, acetamide and propionamide groups, with a nucleotide “tail” appended to the propionamide on ring D of the corrin through a

46 propanolamine linkage (Figure 4.1). The nucleotide tail terminates with 5,6- dimethylbenzimidazole (DMB), which can serve as an intramolecular ligand to Co in the α position. The β-axial ligand is variable, with water, methyl and deoxyadenosyl groups being present in aquacobalamin (also called B12a), methylcobalamin (MeCbl) and adenosylcobalamin

(AdoCbl), respectively.

The electrochemical properties of vitamin B12 derivatives have been characterized extensively by cyclic voltammetry.108-111 Corrinoids such as aquacobalamin display complex, interrelated redox, acid-base and Co–ligand binding equilibria, giving rise to both pH- independent and pH-dependent reduction potentials. At low pH, the intramolecular DMB ligand in aquacob(III)alamin is protonated and dissociates from Co, resulting in the “DMB-off” form of the cofactor. The most facile reductions for a given redox couple occur for DMB-off species. For example, the midpoint potentials for the CoIII/II and CoII/I couples in DMB-off aquacobalamin are

+0.27 V and –0.74 V, respectively, relative to the saturated calomel electrode (SCE).109, 110 For the analogous DMB-on species, Co coordination by DMB depresses the reduction potentials for these two couples to –0.04 and –0.85 V.109, 110 The large difference of 0.25 V in the CoIII/II couples between the DMB-on and DMB-off species is indicative of strong σ donation from

DMB to the CoIII center. Indeed, the affinity of CoIII for DMB is 107 times greater than for

108 II water. DMB binds much less strongly to Co , with Kon/off = 60, and the reduction potential for the DMB-on form is accordingly depressed by only 0.12 V relative to the DMB-off CoII species.

CoI is a so-called supernucleophile that does not bind DMB and is therefore always in a DMB- off configuration.

Computational approaches can provide detailed insight into the electrochemical and thermochemical properties of complex, redox-active systems. However, accurate calculation of

47 pKas and redox properties is challenging because these properties are particularly sensitive to errors in the underlying theoretical methods and models. For example, an error of 1.36 kcal mol-1 in the computed free energy of protonation leads to an error of 1.0 log unit in the pKa. Likewise, an error of 2.3 kcal mol-1 in the computed free energy of reduction corresponds to an error of 100 mV in the reduction potential. Achieving these levels of accuracy can be difficult for complex systems. Thus, care must be taken to account for various physicochemical factors that influence the accuracy of the calculations.

112, 113 Early calculations of pKas and reduction potentials in proteins used a simplified, implicit representation of solvent and protein electrostatics.114 These methods were subsequently extended to include local, explicit solvent molecules115 and configurational sampling with a free energy perturbation (FEP) approach. For example, classical free energy perturbation simulations reproduced the experimentally observed decrease in the reduction potential (ΔE° = -40 mV) of the R38L mutant of yeast cytochrome c relative to wild type.116

For many systems, in particular those that include transition metals, a quantum chemical description is required to obtain accurate results. Combining density functional theory (DFT) with a polarizable continuum solvent model is an established approach for computing reduction potentials of transition metal-containing systems.117 Typically, geometries of the reactants and products are optimized in the gas phase. Solvation free energies are then computed for each species with a polarizable continuum model, in some cases including explicit solvent molecules.118-121 A thermodynamic cycle is used to calculate the solution-phase free energy of reduction, from which the reduction potential is obtained via the Nernst equation.122, 123

Strategies involving the use of isodesmic reactions or reference potentials have been used to reduce systematic errors in computed reduction potentials.120, 124-126 Recently, reduction

48 potentials of 15 challenging transition metal complexes in aqueous solution were computed by first computing reduction potential of neutralized (protonated/deprotonated) cognates and then using multiple hydrogen atom addition/abstraction thermodynamic cycles to obtain the final potentials of the charged species.127 This method was found to provide substantial improvement over standard DFT+continuum approaches.

For redox processes that are coupled with protonation or deprotonation, acid dissociation constants (pKas) are typically computed with an appropriately constructed thermodynamic

128-130 cycle. An alternative approach for computing pKas and reduction potentials involves calculating solution-phase free energies directly in continuum solvent without the use of a thermodynamic cycle.131 Such an approach may be computationally more demanding, but has been suggested to be beneficial for systems in which solvent-induced geometric changes are significant.

Quantum mechanical/molecular mechanical (QM/MM) approaches132, 133 are also

117, 134, 135 commonly used to compute pKas and reduction potentials. The use of QM/MM-FEP with an accurate QM Hamiltonian, a correct description of long-range electrostatics and boundary effects, and adequate configurational sampling was shown to provide an accuracy of

~3 kcal mol-1 with respect to experiment.134 In a DFT-based study of phosphate diester hydrolysis reactions, solvation free energies were computed with continuum solvation

(COSMO), mixed cluster-continuum solvation with one to three explicit water molecules, or by

QM/MM-FEP simulations.136 Whereas the COSMO and QM/MM-FEP approaches both reproduced the experimental free energy barriers to within ~1 kcal mol-1, mixed cluster- continuum models provided slight overestimates of 1-2 kcal mol-1 when one or two explicit water molecules were included and the error increased to ~6 kcal mol-1 with three water

49 molecules. These deviations were attributed to errors in the configurational entropy arising from the inclusion of explicit water, and problems associated with their proper placement were also noted.

Whereas QM/MM calculations may be needed to compute accurate thermochemical and electrochemical properties, it is sometimes advantageous to use a QM cluster approach instead.137 Computed thermochemical and electrochemical properties have been used to probe redox-mediated mechanisms of transition metal catalysts. Accurate reduction potential-pH

(Pourbaix) diagrams have been computed for Ru-based water oxidation catalysts spanning a

2– 121, 138 range of oxidation states and ligand protonation states from to O to H2O. Computational studies of redox processes involving ligand association-dissociation equilibria have also been reported.118, 120, 139

Accurate calculation of the electronic properties of corrinoids with DFT requires a balanced description of closed-shell CoI and CoIII species and open-shell CoII species. The accuracy of computed energies is highly dependent on the density functional, with pure functionals generally outperforming hybrids.140-147 The importance of including empirical dispersion corrections in describing corrinoids with DFT, particularly in combination with polarizable continuum solvation, is an area of active investigation.145, 146, 148 Scalar relativistic effects for Co are only a minor source of error,142, 145 and may largely cancel with basis set superposition error.

CoIII/II reduction potentials have been computed with several density functionals in combination with a polarizable continuum solvent model for DMB-on MeCbl and AdoCbl.149

DFT models of corrinoids have been used to show that the stabilization of CoI provided by a hydrogen bond-donating water molecule raises CoII/I reduction potentials by ~100–225 mV.150

However, to our knowledge no computational studies of corrinoids have addressed cofactor

50 reduction accompanied by ligand dissociation, protonation, or both. Here, we use DFT and polarizable continuum solvation to compute reduction potentials, pKas and Co–ligand binding equilibrium constants for the aquacobalamin system. We show that PBE outperforms BP86, the most commonly applied density functional for computing structural and electronic properties of corrinoids. Furthermore, we show that including a small number of explicit water molecules that interact directly with Co at otherwise vacant coor dination sites does not provide an advantage over using only continuum solvation in the present case.

4.2 Computational Methods

Computational studies of cobalamins and related corrinoids commonly use simplified corrin- based models,140, 141, 143, 151-158 although there is a growing trend in favor of full cobalamin models in more recent work.142, 145, 146 Although using complete cobalamin models to compute reduction potentials is possible, it is undesirable in this case for the following reasons: (i)

Including flexible side chains and other groups would likely require conformational averaging and possibly the use of several explicit water molecules, (ii) Excluding the side chains and methyl groups on the corrin ring and the phosphoribosyl linker connecting the nucleotide to the corrin ring is not expected to affect the electronic structure of the Co–corrin to a large extent, and

(iii) Larger, complete cobalamin models are substantially more computationally demanding.

Thus, we sought to determine whether computationally efficient, corrin-based models of aquacobalamin and its derivatives are capable of achieving high accuracy in computing electrochemical and thermodynamic quantities.

159 The pKa of 5,6-dimethylbenzimidazole (DMB) is 5.6. In cobalamin, DMB is bound via the nucleotide loop to the corrin ring and can occupy the α-axial Co coordination site. In computational treatments of cobalamins, DMB is often replaced with imidazole. However, this

51 approach results in overbinding of the ligand to Co because of the comparatively stronger

159 electron donation by imidazole relative to DMB, (cf. imidazole pKa = 7.1 ). Thus, in our computational models we used benzimidazole, whose electronic structure is more similar to that of DMB (Bzm pKa = 5.6). Bzm was placed below the A-B ring methylidine bridge (Figure 4.1) in a conformation consistent with crystal structures of DMB-on cobalamin.160, 161 Alternative conformations are not expected to contribute much to overall energies due to the lack of chemically salient rotatable bonds. All side chains and methyl groups of the corrin ring were replaced by hydrogen, and the DMB tail was represented either by benzimidazole (Bzm) (Figure

4.1) or benzimidazolium (BzmH+). Although the DMB tail is covalently linked to the corrin ring in cobalamin, the cofactor was modeled here as two separate entities in models of base-off species, i.e., when the Bzm/BzmH+ ligand was dissociated from Co.

Computed solvation free energies for bare, ionic complexes or polar molecules within a polarizable continuum are often inaccurate due to an insufficient description of the strong interactions at the solute-solvent boundary. This deficiency may be overcome by including explicit solvent molecules to capture specific local ion-solvent interactions that are not adequately described by a continuum model.128, 129, 162-165 Therefore, to determine whether a mixed cluster-continuum approach is superior to continuum-only solvation, we considered two classes of models. Models in which the solvent is described exclusively by continuum solvation are referred to as canonical models; that is, CoIII species are hexacoordinated, CoII species are pentacoordinated, and CoI species are tetracoordinated. We also considered models in which a single, explicit water molecule was included at each vacant axial coordination site on Co, which we refer to as saturated models. Note that CoIII models are identical in the canonical and saturated schemes because the β-axial water is a coordinating ligand to CoIII rather than a solvent

52 molecule in that case. In all base-off models, an explicit water molecule was included as a hydrogen bond donor to N3 of the dissociated Bzm moiety, and as a hydrogen bond acceptor from N3–H of BzmH+.

We assessed the performance of five generalized-gradient approximation (GGA) functionals historically used in corrinoid DFT studies. The popular hybrid functional B3LYP166,

167 has been found to compute electronic spectra with reasonable accuracy,154, 155 but its tendency to favor open-shell species leads to substantial underestimation of Co–C homolytic bond dissociation energies (BDEs) in alkylcobalamins.143, 144, 168 B97-D is a pure functional that includes D2 dispersion in its construction.169 Benchmark studies have shown good performance in predicting BDEs143, 144 and reduction potentials of an enzyme-bound corrinoid.150 The same and other studies145, 148 also found that two other pure functionals, PBE170 and BP86,171-173 perform equally well for BDEs. PBE has also been shown to perform well for computing reduction potentials of octahedral complexes of group 8174 and first-row transition metals.168 The meta-GGA functional TPSS175 also performs well for computing BDEs of corrinoids.146 BP86 is the most commonly used functional in computational studies of corrinoids owing to its reliable geometries141 and balanced performance at accurately estimating Co–C BDEs,140, 142-144 UV- visible spectra,74, 176 reduction potentials149, 177 and reaction kinetics.178, 179 To our knowledge, all benchmark studies consistently rate it among the most accurate DFT methods for corrinoids and related systems.

Previous studies have found that using solution-phase optimized geometries provides better agreement with experimental geometries than those optimized in the gas phase.131, 180 However, the models considered here are conformationally quite rigid, exhibiting negligible geometric changes between gas-phase and continuum-phase optimized geometries (not shown). Thus, to

53 reduce computational cost all geometries were optimized in the gas phase with the 6-31G(d) 5D basis set. Vibrational frequencies were computed at the optimized geometries to confirm that each was a local minimum on the potential energy surface and to compute thermochemical quantities. All solvation free energies were computed with the 6-311+G(d,p) basis set at the gas- phase optimized geometries using the Solvation Model based on solute electron Density

(SMD)164 with water as the solvent. We considered both the default atomic radii and Bondi radii181 for the solutes (Table 4.1). Bondi radii were chosen because it has been shown previously that their use with SMD improves the accuracy of computed aqueous solvation163 and ligand binding free energies162 of group 12 metal cations and small inorganic ions. Furthermore, the use of Bondi radii resulted in lower errors overall compared with the default radii in our own exploratory redox calculations. The COSMO-RS solvation model182 has also been shown to provide good agreement with experimental ligand binding constants for several divalent metal cations183 and for reduction potentials of group 8 octahedral complexes,174 but was not tested here. Gas-phase single-point energies were calculated with the 6-311++G(d,p) basis set. Grimme

D3 dispersion corrections184 with Becke-Johnson damping185 (i.e., D3BJ) were computed with the program DFTD3186 for all functionals except B97-D, which includes dispersion in its construction. D3BJ corrections were added to the gas-phase single-point energies to obtain

! !"# ∆�(!) .

All electronic structure calculations were performed with Gaussian 09, revision D.01.187

CoIII, CoII and CoI species were modeled as low-spin d6, d7 and d8 complexes, respectively.188

4.2.1 Standard states

Standard reduction potentials, E°, correspond to a 1 M ideal solute concentration at 25 ºC, whereas the same 1 M standard state for free energies is commonly denoted by G*. G° instead

54 signifies free energies in the 1 atm ideal gas standard state. The superscript circle and star standard state notation can clearly lead to confusion. Therefore, in this work E° refers to standard reduction potentials, X1atm refers to 1 atm ideal gas standard state energies and X1M to energies in the 1 M ideal aqueous solution standard state for a given solute. To convert from the 1 atm to the

1 M standard states, we used the factor defined by Ben-Naim189 as the free energy of compressing a molar volume of an ideal gas (24.46 L mol–1) to a 1 M concentration, i.e., ∆G1 atm→1M = RT ln (24.46) = +1.89 kcal mol–1.

Including an explicit water molecule incurs a free energy cost of bringing the adventitious water from the concentration of bulk water (55.34 M at 298 K) to the 1M standard state of the solute, i.e., ∆G55M→1M = –RT ln(55.34) = 2.38 kcal mol-1. Multiple explicit water molecules can be added either as n individual water molecules (i.e., n∆G55M→1M) through a monomer thermodynamic cycle, or as a cluster of n waters, (H2O)n, (i.e., [H2O] = 55.34/n M) through a cluster cycle. The cluster cycle was shown to be superior to the monomer cycle for computing the hydration free energies of H+ and Cu2+.190 Of course, both cycles yield identical values when n = 1.

4.2.2 Thermochemistry

!!"# All gas-phase free energy differences, ∆�(!) , were computed as:

! !"# ! !"# ! !"# Δ�(!) = Δ�(!) + Δ�D3BJ + Δ�!"## ! (4.1)

! !"# !!"# where ∆�(!) , Δ�D3BJ and ∆�!"## (!) are the differences between products and reactants in the total electronic energy, dispersion correction (where applicable) and the thermal correction to the Gibbs free energy, respectively.

Equilibrium constants for the association/dissociation of the Bzm ligand were computed as

55 !∆!!" log � = !"/!"" !" (4.2) !"/!"" !"!" !"

!! where ∆�!"/!"" (!") is the aqueous free energy difference between the base-on (α-Bzm) and base-off (α-H2O) species. In the present case, axial ligand Y was displaced by a water ligand such that the Co coordination number remains constant. Scheme 4.1 illustrates the

!" thermodynamic cycle used to calculate Δ�!"/!"" (!").

The ∆∆G1atm→1M standard state correction and the ∆∆G55M→1M concentration correction were applied to account for extracting a water molecule from the bulk to replace Bzm. Thus,

!! ∆�!"/!"" (!") was computed as:

!" !"#$ !"#$→!" !" !" !!"→!" Δ�!"/!"" (!") = Δ�!"/!"" (!) + ΔΔ� + Δ�!"#$ on − Δ�!"#$ off + ΔΔ�

(4.3)

Acid dissociation constants were computed as:

!" ∆! ! p� = !! !" (4.4) ! !"!" !"

!! + The free energy of deprotonation, ∆�!!!(!"), for the reaction Y–H ⟶ Y + H was

!! computed with the blue thermodynamic cycle in Scheme 4.2. ∆�!!!(!") was computed in a

!" similar manner to Δ�!"/!"" (!") , but also includes the gas-phase free energy of a proton,

!"#$ ! !"#$ ! �(!) (H ), and its solvation free energy, Δ�!"#$ H (Table 4.2).

Liberated ligands may participate in secondary equilibria with the reaction media such as precipitation, rearrangement/reaction or protonation. Equilibria involving ligand protonation are of chief importance regarding corrinoids because protons compete with Co for DMB. The pKa is the proton concentration at which the fractions of proton-bound (base-off) and Co-bound (base-

56 on) DMB are equal. Thus, proton-coupled ligand dissociation (PCLD) is a conflation of base- on/-off equilibrium and competitive DMB binding to either Co or H+ (Scheme 4.2, all terms).

Standard reduction potentials (E°) were computed relative to the saturated calomel electrode

(SCE) as:

!!!!" ∘ !" ,!"# ∘ � = − �!"# (4.5) !!!

!" where Δ�!"# (!")is the aqueous free energy of reduction, ne is the number of electrons, F is

∘ the Faraday constant, and �!"# is the absolute potential of the SCE reference electrode. The

! !"# + proper choice of the absolute potential of the reference electrode and Δ�!"#$ (H ) has been

117 ∘ discussed in a recent review. In this work we used �!"# = 4.52 V, which corresponds to an absolute reduction potential of the standard hydrogen electrode (SHE = 4.28 V) plus 0.24 V, and

! !"# + Δ�!"#$ (H ).

The standard one-electron reduction potentials of many transition metal complexes

(LMM+1), in which MM+1 is reduced to the MM state and the coordination number of the metal center is conserved over a range of oxidation states, can be computed with the saturated cycle shown in the right panel of Scheme 4.3. Proton-coupled reductions require all terms in Scheme

4.3, but pH-independent reductions use only the terms in blue. In contrast, the coordination numbers of Co in corrinoids depend on the Co oxidation state, and decrease from six to four during sequential one-electron reduction from Co3+ to Co1+. Therefore, we constructed a canonical thermodynamic cycle to account for ligand release (Scheme 4.3).

! !"# The free energy of reduction, Δ�!"# (!), is the free energy difference between the reduced

!"#$ and oxidized species, which includes the gas-phase free energy of an electron, �(!) . No solvation free energy term for the electron is required. During redox processes involving ligand

57 dissociation, e.g., X–LCoM+1–Y ⟶ X + LCoM–Y, the bare solutes will become immediately

M M solvated (e.g., LCo –Y + H2O ⟶ H2O–LCo –Y). Although the bare solute cancels in the net reaction, its vestige remains in a non-cancelling ∆G55M→1M contribution.

4.3 Results and Discussion

4.3.1 Co-ligand binding equilibria

We first present base-on/-off equilibrium constants (log Kon/off) for aquacobalamin in both the

Co2+ and Co3+ oxidation states computed according to Scheme 4.1. In each case, the dissociated

α-Bzm ligand was replaced with a water molecule. Electron-rich CoI repels σ-donating ligands so

Keq is undefined in that case. The pH-independent base-on/-off equilibrium model reactions considered are shown in Table 4.3. The experimental and calculated log Keq values for aquacobalamin models are shown in Table 4.4, and the errors in the computed log Kon/off values are presented in Figure 4.2.

The experimental log Kon/off = 8.0 for aquacob(III)alamin reflects that α-coordination of the strongly σ-donating Bzm ligand provides greater stabilization to CoIII than a water molecule in the base-off complex (reaction a). Using the canonical models, all five functionals correctly capture the preference for Bzm, but they all overestimate the strength of the CoIII–Bzm interaction relative to that of CoIII–water. B3LYP and PBE produce the smallest errors (+2.7 and

+2.9 log units, respectively), whereas BP86 displays a more substantial error of +6.1 log units

(Figure 4.2).

The α and β ligands primarily interact with the redox-active Co 3dz2 orbital orthogonal to the corrin plane, and are therefore sensitive to trans-axial and Co electronic effects. An increase in electron density in the CoII state weakens the interactions with the β-ligand. Bzm coordination

58 is still favored, but to a much lesser degree (log Kon/off, exp = 1.9). All five functionals follow a similar trend of overestimating the base-on/off equilibrium in reaction b, though to a lesser extent than in CoIII. B3LYP and PBE again rank first and second, and BP86 still suffers from large error (> 4.6 log units).

We sought to determine if further improvements could be made in the accuracy of the models by including specific solvent-solute interactions in the form of microsolvation of the Co center with one or two explicit water molecules to maintain a first solvation shell around Co in all three oxidation states (i.e., saturated models). For base-on and base-off species, one and two water molecules were placed in the otherwise vacant axial positions, respectively. The use of saturated models had a small and mixed effect (± ~0.4 log units) on the computed equilibrium in reaction c. The errors increased slightly relative to the canonical models for B3LYP and BP86, and decreased by the same magnitude for B97-D, TPSS and PBE (Figure 4.2, saturated models).

The competition between Bzm and water, which favors N-coordination in both the Co2+ and

Co3+ oxidation states, was qualitatively reproduced by the five DFT methods and both solvation schemes. B3LYP performed the best and equally well for both the canonical and saturated models, with RMSE = 2.2 log units. PBE had similarly low RMS errors for the canonical (2.4) and saturated (2.2) models. The trend in RMSE continues, with B3LYP ≅ PBE > TPSS > B97-D

> BP86, although none of the functionals describes base-on/-off equilibria quantitatively with our models.

4.3.2 Acid dissociation constants

We computed pKa values for the aquacobalamin models listed in Table 4.5. In some cases, pKa is defined straightforwardly as acid dissociation, i.e., deprotonation of the axial water ligand in

59 B12a to form hydroxocobalamin, B12b (Table 4.5, entry 1). In other cases, however, ligand dissociation is concomitant with its protonation, i.e., PCLD, as in the protonation of DMB-on

+ B12r to form DMB-H -off B12r (Table 4.5, entries 3 and 5; DMB was modeled as Bzm). Upon dissociation from Co, we replaced BzmH+ with an explicit water molecule to maintain the same

Co coordination number between the acidic form and its conjugate base form.

Both coordination models share the same hexacoordinated CoIII pKa model reactions.

Inspection of Figure 4.3 shows that no overall trend arises between the methods for computing the β-water pKa for aquacob(III)alamin (Table 4.5, reaction 1), and that BP86 has the lowest error. The proton-coupled dissociation in reaction 2 stands in stark contrast, with all methods severely underestimating its pKa. All pure functionals perform very poorly, including BP86, whose enormous error is 6.5 log units too low. These limitations are echoed, to a lesser extent, in the PCLD for CoII. The canonical and saturated models give nearly identical results. B3LYP performs remarkably well and reproduces the pKa exactly in both models (reactions 3 and 4).

In the saturated models, CoI species were modeled with two trans-axial water molecules interacting through hydrogen bonds to the electron-rich CoI center, which would otherwise repel the electronegative water oxygens. However, because CoI is formally tetracoordinate, it has no protonable groups (except for the Co atom itself, vide infra). Although CoI was included in reactions 5 and 6 for illustrative purposes, it cancels and the two models are actually degenerate.

The calculation is therefore only a reflection of the pKa of Bzm and is approximately consistent with experiments. Reaction 7 is also degenerate with 5 and 6.

The experimental and calculated pKas for the aquacobalamin models are shown in Table

4.3. Most methods overestimate the pKa of the DMB tail in cob(I)alamin except for PBE, which predicts it almost exactly at 4.8 log units. Comparing them instead against the pKa of 5,6-DMB

60 (5.6, reaction 7) reveals that BP86 and B3LYP have the smallest errors. Overall, in the one reaction (4) in which microsolvation was used and was distinct from the canonical model, its effects are negligible. B3LYP and TPSS perform equally well as the best predictor of pKa, with

RMSE = 1.7 for both canonical and saturated models. TPSS is marginally more balanced than

B3LYP in both models, at –0.2 MSE versus 0.4 MSE for B3LYP. PBE is next best, with RMSE

= 2.0 for the canonical models and 2.1 for the saturated models, but returns a sizeable maximum error of –3.7 log units. In summary, the performance hierarchy for pKas is TPSS ≅ B3LYP >

PBE > B97-D ≫ BP86.

Because the computed pKa of Bzm is accurate to within 1.2 log units for all functionals

(Table 4.6), we conclude that the substantial inaccuracy in the computed pKas of PCLD reactions (2–4) is largely propagated from the equilibrium constants. Furthermore, the error in

Kon/off arises predominantly from either Co overbinding to Bzm, underbinding to water, or a combination of both. CoIII suffers the most from this behavior, although it also occurs to a lesser degree in CoII.

4.3.3 Reduction potentials

Next, we present the standard one-electron reduction potentials for seven CoIII/II and CoII/I couples of aquacobalamin computed with each of the dispersion-corrected density functionals. In two of the seven processes considered here for each coordination scheme, the reductions are proton-coupled (reactions A, D, I, and J).

The errors in the computed one-electron reduction potentials for the canonical aquacobalamin models (Table 4.7, entries A-G) are presented in the top panel of Figure 4.4. The experimental and calculated reduction potentials for aquacobalamin models are shown in Table

4.8. Visual inspection reveals that dispersion-corrected B3LYP has overall very poor

61 performance at modeling corrinoid redox processes. It overestimates CoIII/II potentials (A–D) by

> 0.37 V (RMSE) and severely underestimates CoII/I potentials (E–F) by < –0.66 V, resulting in an overall RMSE of 0.56 V. This over-/underestimation pattern is a consequence of the aforementioned favoring of open-shell species by hybrid functionals. The pure functional B97-D yields reduction potentials within 0.20 V RMSE of experimental values. PBE is by far the most accurate and balanced method for the canonical models, approaching the limit of DFT accuracy with RMSE = 0.08 V. BP86 is similarly balanced and next best at 0.14 V RMSE (Emax =

+0.24). TPSS tends to underestimate reduction potentials, especially for the CoII/I couple (MSE for CoII/I = -0.26), resulting in middling performance. For the canonical coordination system, the accuracies decrease as PBE > BP86 > TPSS > B97-D ≫ B3LYP.

The computed potentials for the saturated model reduction reactions (Table 4.7, entries H–

N) are shown in Figure 4.4. Including explicit waters moderately lowers the B3LYP errors by

~0.10 V to 0.45 V RMSE, but the CoII/I couples still suffer from gross underprediction. Unlike in the canonical series, non-hybrid functionals tend to predict CoII/I reduction potentials too high in the saturated models. The same magnitude of improvement was obtained with B97-D, bringing its RMSE down to 0.10 V, the lowest of all the saturated models. Conversely, PBE and BP86 display slightly larger errors (0.14 V and 0.18 V RMSE, respectively) and erratic performance compared to their canonical counterparts. BP86 is unbalanced in the CoII/I couples (Emax = 0.36

V). TPSS is slightly improved to 0.15 V RMSE, but generally underpredicts potentials especially upon Bzm complexation. TPSS predicts reduction potentials that are too low for the CoII/I couples, giving an RMSE of 0.15 V and Emax of 0.35 V. The saturated models follow a different accuracy pattern, B97-D > PBE > TPSS > BP86 ≫ B3LYP.

62 Although the presence of the additional water(s) in the saturated models benefits some methods (B3LYP, B97-D and TPSS), it erodes the accuracies of others (PBE and BP86). Thus, the saturated models do not provide a consistent advantage or confer any predictable effects over the canonical models for the reduction potentials considered here.

4.3.4 Pourbaix diagram

Having arrived at a balanced method with the PBE density functional and the canonical models, we used the resulting reduction potentials and pKas to construct a Pourbaix diagram, which maps out the reduction potentials for a given system as a function of pH. pKas are displayed as vertical lines and reduction potentials are shown as either horizontal or diagonal lines. pH-independent reduction potentials are horizontal and are bounded by the pKas of the reduced (above) and oxidized (below) species. At pH values outside these regions, reduction is proton-coupled, and the potential decreases linearly by –0.0591 V per pH log unit for one-electron, one-proton transfers.

Inspection of the Pourbaix diagram for aquacobalamin (Figure 4.5) reveals reasonably good agreement between the computed and experimentally determined reduction potentials, and

III moderate agreement for the pKas. Reduction from the Co species in the upper third of the diagram is depicted along the A-B-C-D line to the CoII species in the middle portion. The largest error in reduction potentials corresponds to the pH-independent reduction of base-off B12a to

II/I base-off B12r (error = +0.14 V, horizontal A). The computed potentials for the Co couples, line

E-F-G, closely match experimental values to within 0.08 V. The related computed pKa of the

CoIII PCLD (vertical 1) undershoots the experimentally determined value by –3.7 log units. CoII also suffers from an erroneously low PCLD (vertical 3), but only by –1.6 log units. With Bzm

63 I dissociated in the Co complex, vertical 4 is essentially only a computation of the Bzm pKa, which is itself an accurate prediction to within 0.8 log units.

The bottom left corner of the Pourbaix diagram, which is bounded by dashed lines, is the region in which hydridocob(III)alamin is suggested to exist, as evidenced by the evolution of H2 at low pH.191 Using models analogous to the others described in this work we obtained large errors of ~0.5 V and ~8 log units for the reduction potential and pKa, respectively, suggesting that more chemically complex models are likely required to describe these processes.179 See the

Supporting Information for additional discussion. However, because hydridocobalamin is not biologically relevant it was not pursued further here.

4.4 Conclusions

The accuracy of the present electrochemical and thermodynamic calculations is near the limit of what might be expected to be achievable with DFT and continuum solvation for a complex, transition metal-containing cofactor. Simplified, corrin-based models perform quite well in this context and their use is likely not a major source of error. Inclusion of a small number of explicit water molecules that directly interact with Co does not improve the accuracy of the calculations for computing reduction potentials relative to continuum-only solvation in this case. The use of the PBE density functional, as opposed to the commonly used BP86, is recommended for future computational studies of corrinoids. The methods described here should be useful for characterizing the electrochemical and thermodynamic properties of transition metal-containing species that exhibit redox-associated ligand binding and acid-base equilibria.

64 4.5 Appendix 2

Scheme 4.1 Thermodynamic Cycle Used to Compute Base-On/-Off Equilibrium Constants for

Aquacobalamin. L is the corrin ring, X is the β-axial H2O, Y is the α-axial Bzm or H2O ligand.

The X ligand is always present in the saturated models, but may vary in the canonical models.

1atm ∆GGon/off (g) M M X lLCo OH2 Y X LCo Y H2O ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G55M 1M 1M 1M 1M 1M ∆GGsolv ∆GGsolv ∆GGsolv ∆GGsolv 1M ∆GGon/off (aq) X lLCoM OH Y X LCoM Y H2O 2

Scheme 4.2 Thermodynamic Cycle Used to Compute pKas for Aquacobalamin. Acid dissociation includes only blue terms, but proton-coupled ligand dissociation includes all terms.

1atm ∆GG–HH+ (g) M + M X lLCo OH2 Y H H X LCo Y H2O

∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G55M 1M 1M 1M 1M 1M ∆GGsolv ∆GGsolv ∆GG ∆GGsolv 1M solv ∆GGsolv 1M ∆GG–HH+ (aq) + X lLCoM OH Y H H X LCoM Y H2O 2

65 Scheme 4.3 Thermodynamic Cycles Used to Compute Standard One-Electron Reduction

Potentials of Aquacobalamin with Saturated and Canonical Models. pH-independent reductions

use only blue terms, and proton-coupled reductions use all terms.

Canonical 1atm Saturated 1atm ∆Gred (g) ∆Gred (g) + H O M+1 – M + H O M+1 – M H 2 X LCo Y e lLCo Y/OH2 X Y H H 2 X LCo Y e X LCo Y/OH2 Y H

∆G1atm 1M∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G1atm 1M ∆G55M 1M ∆G1atm 1M ∆G55M 1M ∆G1atm 1M 1M 1M 1M 1M 1M 1M 1M 1M 1M ∆GG 1M ∆GGsolv ∆GGsolv ∆GGsolv ∆GGsolv ∆GG 1M ∆GGsolv ∆Gsolv ∆GGsolv solv ∆Gsolv solv ∆Gsolv 1M 1M ∆Gred (aq) ∆Gred (aq) + H O M+1 – M + H O M+1 – M H 2 X LCo Y e lLCo Y/OH2 X Y H H 2 X LCo Y e X LCo Y/OH2 Y H

Canonical 1atm Saturated 1atm ∆Gred (g) ∆Gred (g) + H O M+1 – M + H O M+1 – M H 2 X LCo Y e lLCo Y/OH2 X Y H H 2 X LCo Y e X LCo Y/OH2 Y H

Table 4.1 Intrinsic Coulomb Radii used in SMD, Bondi van der Waals Radiiand the Computed

Solvation Free Energy of Water.

Species SMD SMDBondi (Å) (Å) Atomic Radius (Å) H 1.20 1.20 C 1.85 1.70 N 1.89 1.55 O 1.52 1.52 Co 2.00 2.00 1M -1 ∆Gsolv (kcal mol ) Exp.

H2O -8.58 -6.25 -6.32

66 Table 4.2 Free Energies at 298 K and Physical Constants.

Energy Term Value (kcal mol–1) Ref ∆G1 atm→1M 1.89 189 ∆G55M→1M 2.38 128 !" + 192-194 Δ�!"#$(H ) –265.89 !" 195 Δ�!"#$(H2O) –6.32 ! !"# + 136 �(!) (H ) –6.28 ! !"# – 196 �(!) (e ) –0.868 Constant Value R 1.987 × 10–4 kcal mol–1 K–1 º E SCE 4.52 V F 23.061 kcal mol−1 V−1

Table 4.3 Model Ligand Dissociation Reactions.

III III a H2O–LCo –H2O + Bzm·H2O → H2O–LCo –Bzm + 2 H2O II II b LCo – H2O + Bzm·H2O → LCo –Bzm + 2 H2O II II c H2O –LCo – H2O + Bzm· H2O → H2O –LCo –Bzm + 2 H2O

67 Table 4.4 Experimental and Calculated Log Keq Values for Aquacobalamin Models.

Entry Reaction Exp B3LYP B97D PBE BP86 TPSS III a H2O–LCo –H2O + Bzm·H2O → 8.0 10.7 13.5 10.9 14.1 11.6 III H2O–LCo –Bzm + 2 H2O II b LCo –H2O + Bzm·H2O → 1.8 3.3 5.3 3.6 6.4 4.6 II LCo –Bzm + 2 H2O II c H2O–LCo –H2O + Bzm·H2O → 1.8 3.4 5.2 3.3 6.8 4.1 II H2O–LCo –Bzm + 2 H2O MSE 2.1 4.5 2.4 5.4 3.2 MUE 2.1 4.5 2.4 5.4 3.2 Canonical, Models a–b RMSE 2.2 4.6 2.4 5.4 3.3

Emax 2.7 5.5 2.9 6.1 3.6 MSE 2.1 4.5 2.2 5.6 3.0 MUE 2.1 4.5 2.2 5.6 3.0 Saturated, Models a, c RMSE 2.2 4.6 2.3 5.6 3.1

Emax 2.7 5.5 2.9 6.1 3.6

Table 4.5 Model Acid Dissociation Reactions.

III + 1 H2O–LCo –Bzm → HO–LCoIII–Bzm + H III + III + 2 H2O–LCo –H2O + BzmH ·H2O → H2O–LCo –Bzm + 2 H2O + H II + II + 3 LCo –H2O + BzmH ·H2O → LCo –Bzm + H2O + H II +· II + 4 H2O–LCo –H2O + BzmH H2O → H2O–LCo –Bzm + 2 H2O + H I + I + 5 LCo + BzmH ·H2O → LCo + Bzm·H2O + H I + I + 6 H2O–LCo –H2O + BzmH ·H2O → H2O–LCo –H2O + Bzm·H2O + H + + 7 BzmH ·H2O → Bzm·H2O + H

68 Table 4.6. Experimental and Calculated pKas for Aquacobalamin Models.

Entry Reaction Exp B3LYP B97D PBE BP86 TPSS III III + 1 H2O–LCo –Bzm → HO–LCo –Bzm + H 7.8 9.9 10.2 7.0 7.7 8.6 III + III + 2 H2O–LCo –H2O + BzmH ·H2O → H2O–LCo –Bzm + 2 H2O + H -2.4 -4.5 -6.6 -6.1 -8.9 -5.0 II + II + 3 LCo –H2O + BzmH ·H2O →LCo –Bzm + H2O + H 2.9 2.9 1.6 1.3 -1.2 2.0 I + I + 4 LCo + BzmH ·H2O → LCo + Bzm·H2O + H 4.7 6.2 6.9 4.7 5.2 6.6 II + II + 5 H2O–LCo –H2O + BzmH ·H2O → H2O–LCo –Bzm + 2 H2O + H 2.9 2.8 1.7 1.5 -1.6 2.5 I + I + 6 H2O–LCo –H2O + BzmH ·H2O → H2O–LCo –H2O + Bzm·H2O + H 4.7 6.2 6.9 4.7 5.2 6.6 + + 7 BzmH ·H2O → Bzm·H2O + H 5.6 6.2 6.9 4.7 5.2 6.6 MSE 0.4 -0.2 -1.4 -2.6 -0.2 MUE 1.4 2.5 1.5 2.8 1.6 Canonical, Models 1–4 RMSE 1.7 2.7 2.0 3.9 1.7

Emax 2.1 -4.2 -3.7 -6.5 -2.6 MSE 0.4 -0.2 -1.5 -2.7 -0.1 MUE 1.4 2.5 1.6 2.9 1.4 Saturated, Models 1–2, 5–6 RMSE 1.7 2.7 2.1 4.0 1.7

Emax 2.1 -4.2 -3.7 -6.5 -2.6

69 Table 4.7 Model One-Electron Reduction Reactions.

Canonical Co coordination III + – II + A H2O–LCo –H2O + BzmH ·H2O + e → LCo –H2O + BzmH ·H2O + H2O III + – II + B H2O–LCo –Bzm + H2O + H + e → LCo –H2O + BzmH ·H2O III – II C H2O–LCo –Bzm + e → LCo –Bzm + H2O III + – II D HO–LCo –Bzm + H + e → LCo –Bzm + H2O II + – I + E LCo –H2O + BzmH ·H2O + e → LCo + BzmH ·H2O + H2O II + – I + F LCo –Bzm + H2O + H + e → LCo + BzmH ·H2O II – I G LCo –Bzm + H2O + e → LCo + Bzm·H2O Saturated Co coordination III + – II + H H2O–LCo –H2O + BzmH ·H2O + e → H2O–LCo –H2O + BzmH ·H2O III – II + I H2O–LCo –Bzm + 2 H2O + H+ + e → H2O–LCo –H2O + BzmH ·H2O III – II J H2O–LCo –Bzm + e → H2O–LCo –Bzm III + – II K HO–LCo –Bzm + H + e → H2O–LCo –Bzm II + – I + L H2O–LCo –H2O + BzmH ·H2O + e → H2O–LCo –H2O + BzmH ·H2O II + – I + M H2O–LCo –Bzm + 2 H2O + H + e → H2O–LCo –H2O + BzmH ·H2O II – I N H2O–LCo –Bzm + 2 H2O + e → H2O–LCo –H2O + Bzm·H2O

70 Table 4.8. Experimental and Calculated Reduction Potentials for Aquacobalamin Models.

Entry Reactiona Exp B97D PBE BP86 TPSS Canonical Co coordination III + – II H2O–LCo –H2O + BzmH ·H2O + e → LCo – A + 0.27 0.59 0.43 0.51 0.30 H2O + BzmH ·H2O + H2O III + – II H2O–LCo –Bzm + H2O + H + e → LCo – B + 0.10 0.20 0.07 -0.02 0.00 H2O + BzmH ·H2O III – II C H2O–LCo –Bzm + e → LCo –Bzm + H2O -0.04 0.10 -0.01 0.05 -0.12 HO–LCoIII–Bzm + H+ + e– LCoII–Bzm + D → 0.41 0.71 0.41 0.51 0.39 H2O II + – I LCo –H2O + BzmH ·H2O + e → LCo + E + -0.74 -0.77 -0.72 -0.60 -0.93 BzmH ·H2O + H2O II + – I LCo –Bzm + H2O + H + e → LCo + F + -0.58 -0.67 -0.65 -0.67 -0.81 BzmH ·H2O II – I G LCo –Bzm + H2O + e → LCo + Bzm·H2O -0.85 -1.08 -0.93 -0.98 –1.20 MSE 0.07 0.00 0.03 -0.13 MUE 0.17 0.06 0.13 0.14 RMSE 0.20 0.08 0.14 0.18 Emax 0.32 0.16 0.24 -0.35 Saturated Co coordination III + – H2O–LCo –H2O + BzmH ·H2O + e → H II + 0.27 0.39 0.30 0.38 0.17 H2O–LCo –H2O + BzmH ·H2O III + – H2O–LCo –Bzm + 2 H2O + H + e → I II + 0.10 0.01 -0.06 -0.15 -0.13 H2O–LCo –H2O + BzmH ·H2O III – II J H2O–LCo –Bzm + e → H2O–LCo –Bzm -0.04 -0.10 -0.15 -0.05 -0.27 HO–LCoIII–Bzm + H+ + e– H O–LCoII– K → 2 0.41 0.51 0.26 0.40 0.23 Bzm II + – H2O–LCo –H2O + BzmH ·H2O + e → L I + -0.74 -0.57 -0.54 -0.38 -0.74 H2O–LCo –H2O + BzmH ·H2O II + – H2O–LCo –Bzm + 2 H2O + H + e → M I + -0.58 -0.47 -0.45 -0.48 -0.6 H2O–LCo –H2O + BzmH ·H2O II – H2O–LCo –Bzm + 2 H2O + e → N I -0.85 -0.88 -0.73 -0.78 -0.99 H2O–LCo –H2O + Bzm·H2O MSE 0.04 0.01 0.05 -0.13 MUE 0.10 0.13 0.13 0.13 RMSE 0.10 0.14 0.18 0.15 Emax 0.17 0.20 0.36 -0.23 a redox potentials are all in eV.

71 Table 4.9 Aggregate Energetic Errors for the Three Computed Quantities.

Canonical Saturated (kcal mol-1) (kcal mol-1)

DFT MSE MUE RMSE Emax MSE MUE RMSE Emax B3LYP 1.6 7.1 9.7 17.3 1.6 5.7 7.8 14.3 B97-D 1.1 3.2 4.7 7.5 1.4 2.2 3.7 7.5 PBE 1.1 1.8 2.4 5.0 1.0 2.7 3.1 5.0 BP86 2.4 3.7 4.7 8.9 2.3 3.8 5.1 8.9 TPSS 3.0 2.5 3.8 8.1 2.8 2.3 3.3 5.3

72 H2NOC H H B O C β CONH2 N N cobinamide CoIII α H2NOC N N H NOC 2 A CONH N D 2 H2NOC O N O HN HO DMB O P O computational model HO O OH

nucleotide loop aquacobalamin (B12a)

Figure 4.1 Molecular structure of aquacob(III)alamin.

Colored atoms in bold (left) were included in the computational model (right) used in this study.

Pendant groups on the corrin ring were replaced with hydrogens, and the 5,6- dimethylbenzimidazolyl (DMB) tail was represented by benzimidazole (Bzm).

Figure 4.2 Errors in the computed ligand dissociation constants (log Kon/off) for aquacobalamin models.

Figure 4.3 Errors in the computed pKas for aquacobalamin models.

108 pKas errors in Table 4.5 versus the corresponding experimental values from Ref . Both coordination schemes share hexacoordinate CoIII and degenerate CoI reactions. Figure constructed from data in Table 4.6.

Figure 4.4 Errors in the computed reduction potentials for aquacobalamin models. redox potential errors in Table 4.7 with respect to experimental values from Ref 108. Figure generated with data in Table 4.8 (in V vs SCE).

75 Eº III 1 2 III III 0.4 A

B C 0.0 D II

3 II -0.4

E III -0.8 F G I I 4 calculated -1.2 experimental pH -8 -6 -4 -2 0 2 4 6 8 10

(M) – – Co –corrin H2O HO H benzimidazole benzimidazolium

Figure 4.5 Experimental and computed Pourbaix diagram for aquacobalamin.

The calculated values were computed with the PBE functional and D3BJ dispersion corrections using the canonical models. Upper case letters refer to model reduction reactions (Tables 4.7 and

4.8) and numbers refer to pKas (Tables 4.5 and 4.6). Hydridocob(III)alamin was not included in the computed Pourbaix diagram.

76 CHAPTER 5

Modeling of the Passive Diffusion of Mercury and Methylmercury Complexes

Through a Bacterial Cytoplasmic Membrane

77 Mercury exits in the environment in different forms. One form of mercury can be transformed to another by microorganisms. The biotransformation of mercury often happens inside of microorganism cells. Both the processes of uptake mercury substrates and export of biotransformed mercury product involve crossing cell membranes. However, the exact uptake mechanism for Hg substrates is still not clear. Various mechanisms have been proposed for Hg uptake in microorganisms, such as mer-based transport, passive diffusion, facilitated diffusion and active transport. In this chapter, we examined the passive diffusion mechanism for small neutral Hg-containing compounds using molecular dynamics simulations. We also calculated the permeability coefficients for the neutral compounds and identified the components that contribute to the stabilization of those compounds inside the model membrane bilayer.

78 A version of this chapter was originally published by: Jing Zhou, Micholas Dean Smith, Sarah J.

Cooper, Xiaolin Cheng, Jeremy C. Smith, and Jerry M. Parks

Jing Zhou, Micholas Dean Smith, Sarah J. Cooper, Xiaolin Cheng, Jeremy C. Smith, and Jerry

M. Parks. Modeling of the Passive Diffusion of Mercury and Methylmercury Complexes

Through a Bacterial Cytoplasmic Membrane. Environ. Sci. Tech., 2017 (in revision)

Contribution statement: The student participated the design of this work. She conducted all the calculations, drafted the article, and performed the data analysis and results interpretation. In this chapter, the article has been revised to provide more details.

Abstract

Cellular uptake and export are important steps in the biotransformation of mercury (Hg) by microorganisms. However, the mechanisms of transport across biological membranes remain unclear. Membrane-bound transporters are known to be relevant, but passive diffusion may also

II II + be involved. Inorganic Hg and methylmercury ([CH3Hg ] ) are commonly complexed with thiolate ligands. Here, we have performed extensive molecular dynamics simulations of the

II + passive diffusion of Hg and [CH3Hg] complexes with thiolate ligands through a model bacterial cytoplasmic membrane. We find that the differences in free energy between the individual complexes in bulk water and at their most favorable position within the membrane are

~2 kcal mol-1. We provide a detailed description of the molecular interactions that drive the membrane crossing process. Favorable interactions with carbonyl and tail groups of phospholipids stabilize Hg-containing solutes in the tail-head interface region of the membrane.

79 II The calculated permeability coefficients for the neutral compounds CH3S–Hg –SCH3 and

-5 -1 CH3Hg–SCH3 are on the order of 10 cm s . We conclude that small, non-ionized Hg- containing species can diffuse readily through cytoplasmic membranes.

5.1 Introduction

Mercury is a global pollutant that exists naturally in the environment in various forms. All forms of Hg are toxic, but the degree of toxicity varies depending on the particular form.3, 5, 197, 198

Elemental mercury (Hg0) is the least toxic because it is poorly absorbed through ingestion (less than 0.01%) and is less reactive compared to other forms of Hg.199 Inorganic, divalent mercury

(HgII) is more toxic than Hg0 and it has an exceptionally strong affinity for thiols ⎯ the

II 200, 201 formation constant log β for Hg (SR)2 compounds is 35 – 40. This strong affinity for thiols leads to the binding of Hg to Cys residues, disrupting protein functions. The bioavailability of

HgII can also be affected by complexation with thiolates.202

Organic mercury is particularly toxic, and of particular relevance in this context is

+ methylmercury (MeHg). MeHg ([CH3Hg] ) has one free valence, and commonly binds a single thiolate to form CH3HgSR complexes. The stability constant for CH3HgSR complexes (log β) is

16.6, which suggests a strong affinity for thiols.203 MeHg can cross the blood-brain barrier and is a potent neurotoxin that primarily affects the central and peripheral nervous systems.204 MeHg bioaccumulates and biomagnifies in the food web; the concentration in fish can reach 107 times higher than in stream water.205, 206 Thus, MeHg affects human health primarily through the ingestion of fish and shellfish.205

Both the uptake and export of biotransformed Hg species involve crossing cell membranes.

Various mechanisms have been proposed for HgII uptake in microorganisms.18, 26 For those microorganisms encoding the mer operon, which detoxifies the cells from Hg, the uptake of HgII

80 into the cytoplasm may be mediated by mer transporters, such as MerC, MerT, and others.18, 26

For organisms lacking the mer system, Hg may be taken up through passive diffusion,207-209 facilitated diffusion or active transport.210-212

Experimental studies of passive diffusion mechanisms are very limited and have mainly

2-n focused on [HgCln] (n = 1–4) complexes, which are not among the most abundant biologically available forms for microorganisms.207-209 Recently, it has been suggested that heavy metal transporters may be involved in Hg uptake in Hg-methylating bacteria.211, 213, 214 Uptake of

CH3Hg–Cys by microorganisms and humans has been suggested to be the result of this complex being “mistaken” for the amino acid methionine, due to perceived structural215 and chemical component similarity.216 Using XANES spectroscopy, it was shown that intracellular HgII in D. desulfuricans ND132 cells is predominantly present in linear, bis thiolate complexes (i.e., RS–

HgII–SR).217

Few measurements of membrane permeabilities of Hg species have been reported, and these

II have been limited to inorganic Hg compounds such as HgCl2. Experimental approaches that have been used to measure the permeability of Hg2+ or Hg-containing compounds through model membranes have been summarized in a recent review.218 Widely varying values for Hg compounds have been found. For example, the diffusion of HgCl2 through an egg-PC and cholesterol (1:1) membrane was studied by measuring radioactive 203Hg isotope flux, leading to a value of the permeability coefficient of 1.3 × 10-2 cm s-1.219, 220 Using a similar method, the effect of lipid composition, pH and chloride concentration on the permeability of Hg(II) compounds across egg-PC and egg-PC/cholesterol membranes was studied, and, for example, at pH 5.0 the

-4 -1 221 measured permeability coefficient of HgCl2 was much lower, at 1.5 × 10 cm s . The permeability coefficient of free Hg2+ ions (i.e., without ligands) through a

81 diphytanoylphosphatidylcholine (DPhyPC) membrane was also measured with a 203Hg isotope method and was found to be very low, i.e. ~3.8 × 10-11 cm s-1.222

Experimental work on Hg permeability suffers from differences in measurements resulting from differing membrane compositions, the Hg compounds studied, and the experimental conditions.218 Hence, a consistent, systematic study is merited. In this regard, molecular dynamics (MD) simulation is a powerful technique to study the permeation of solutes through lipid membranes, as it can provide detailed insight into the effects and origins of solute properties and lipid composition on permeability.223-225 Several MD studies have been carried out on the passive diffusion and non-facilitated membrane permeation of amino acids.223, 226-229 In the aqueous phase, amino acids exist predominantly in their zwitterionic forms. However, inside the hydrophobic core of a lipid bilayer, protons may be transferred from the N-terminus to the C- terminus. Thus, in the above computational studies the N- and C- termini of the amino acids were omitted and only side chain analogues were used to avoid complications associated with possible changes in protonation state of the termini upon partitioning into hydrophobic membranes. Side chains may gain or lose protons during permeation processes as well. Although the effects of protonation state change of the termini on permeability are generally not considered, relative permeability differences between amino acids and related systems through membranes can still be ascertained as the effects of the termini are expected to cancel to a large extent for analogous systems.

Several MD simulation studies have been carried out for Hg0, Hg2+, and other charged and neutral Hg-containing molecules. 230-238 Although substantial effort has been made to understand the solution-phase dynamics of Hg species and the partitioning of amino acids into heterogeneous lipid membranes, to our knowledge the changes in membrane permeability of

82 thiols upon complexation by HgII or MeHgII have not been investigated. Thus, in this work we perform MD simulations to calculate the changes in free energy for transferring low molecular weight thiols with and without Hg or MeHg from aqueous solution into a membrane bilayer.

II + Specifically, we investigate how the complexation of Hg or [CH3Hg] alters the permeability characteristics of CH3SH and CH3S–SCH3, which are side chain analogues of the amino acids

Cys and Met, respectively. First, we develop CHARMM molecular mechanics force field parameters for the selected solutes. We then compute free energy profiles for the passive diffusion of the solutes across a lipid bilayer that mimics the composition of gram-negative bacterial inner membranes (i.e., 75% POPE (1-hexadecanoyl-2-(9Z-octadecenoyl)-sn-glycero-3- phosphoethanolamine) and 25% POPG (1-hexadecanoyl-2-(9Z-octadecenoyl)-sn-glycero-3- phospho-(1'-rac-glycerol)). Next, we identify the energetic factors that contribute to the observed differences between the thiols and their Hg-containing counterparts and compute the permeability coefficients for those solutes. We also examine whether a simplified implicit membrane model reproduces the energetic trends determined in the all-atom free energy simulations.

5.2 Computational Methods

Most Hg-methylating bacteria are gram-negative.26, 239 Gram-negative bacteria are composed of two cell envelopes, the outer and inner membranes, and a thin peptidoglycan cell wall between the two membranes. The outer membrane is asymmetric and the main components of the outer leaflet are lipopolysaccharides (LPS), whereas the inner leaflet comprises phospholipids. In contrast, the inner membrane is symmetric and is mainly composed of phospholipids in both leaflets. 240

83 To our knowledge, the inner membrane compositions of Hg-methylating bacteria have not been thoroughly characterized. However, the inner membrane composition of Desulfovibrio gigas, which does not methylate Hg, was found to be 30% phosphatidylethanolamine (PE) and

70% phosphatidylglycerol (PG).241 For comparison, the inner membrane of E. coli consists of

~70-80% PE, 15-20% PG and 5% or less of cardiolipin (CL).242, 243 Gram-positive bacteria lack an outer membrane, but have thicker peptidoglycan cell walls. For Gram-positive bacteria such as Bacillus subtilis the inner membrane composition is approximately 70% PG, 12% PE and 4%

CL.244 Although the compositions of bacterial inner membranes vary among different species and strains, studying a model bacterial membrane can be expected to provide general insight into bacterial inner membrane permeability.

We constructed models of five environmentally relevant neutral thiol compounds, i.e.

CH3SH (a low molecular weight thiol and Cys side-chain analogue), CH3CH2SCH3 (thioether and Met side chain analogue), CH3S–SCH3 (disulfide analogue), and the Hg-containing

II complexes CH3Hg–SCH3 and CH3S–Hg –SCH3 (Scheme 5.1). The CHARMM 36 all-atom additive force field245 was used to describe the POPE and POPG phospholipids together with

TIP3P water246 and Na+ and Cl- counterions.247 Force field parameters for the Hg-containing

II compounds CH3Hg–SCH3 and CH3S–Hg –SCH3 were optimized with the Force Field Toolkit

(ffTK)248, which is a plugin implemented in VMD.249 For consistency, the parameters for

CH3SH, CH3CH2SCH3 and CH3S–SCH3 were also optimized with the same approach.

The initial coordinates for the membrane used in our simulations were taken from a previously published, thoroughly equilibrated (2.1 µs NPT) system with a POPE:POPG ratio of

3:1 and 0.15 M NaCl.250 This membrane system consists of 128 POPE lipids, 42 POPG lipids, and 6040 water molecules. We performed an additional 1 ns equilibration in the NVT ensemble

84 followed by 20 ns NPT equilibration. The system pressure is shown in Figure 5.1 To prepare the membrane systems containing the desired solutes, the final snapshot of the 20 ns of NPT equilibration was selected. Each solute was placed in the water layer and overlapping water molecules were removed. Energy minimization followed by 1 ns of NVT equilibration was performed to bring each system to 303.15 K. Another 20 ns NPT equilibration was performed after the NVT equilibration.

All MD simulations were carried out with GROMACS program (version 5.1.1)251 at a pressure of 1 bar using the Berendsen barostat252 with a relaxation time of 2 ps, and temperature of 303.15 K using the v-rescale thermostat253 with a relaxation time of 1 ps with periodic boundary conditions. Semi-isotropic coupling was applied such that changes of the box size in the Z-direction (normal to the membrane bilayer) were uncoupled from the X- and Y-directions.

Electrostatic interactions were treated with the particle-mesh Ewald (PME) full-range electrostatics method.254 A switching function was used to treat van der Waals interactions by gradually reducing the force to zero between 0.8 and 1.2 nm. All bonds involving hydrogen atoms were constrained with the LINCS algorithm.255

To generate initial configurations for umbrella sampling, solutes were pulled through the membrane system along the Z-axis using steered molecular dynamics (SMD) simulations. The solutes were initially positioned in the water layer of the upper leaflet and were pulled through the membrane bilayer with a constant harmonic force of 239 kcal mol-1 nm-2 over 10 ns at a pulling rate of 1 nm ns-1. The starting configurations for umbrella sampling simulations were then obtained by extracting snapshots from the SMD simulations from 0 to 3.5 nm from the center of the bilayer with 0.1 nm spacing. Because the bilayer system is symmetric, we simulated diffusion through half of the membrane and then symmetrized the results. To avoid edge effects

85 near the center of membrane (z = 0), we also included three extra windows at z = -0.1, -0.2 and -

0.3 nm, for a total of 39 umbrella sampling windows for each solute. For each window, 5 ns

NVT equilibration was performed and followed by 20 ns umbrella sampling simulations with a biasing harmonic restraint force of 239 kcal mol-1 nm-2. A total of 780 ns of umbrella sampling was performed for each solute. The weighted histogram analysis method (WHAM)38 implemented in the WHAM module of GROMACS was used to reweight the probability distributions and generate potential of mean force profiles. Statistical errors were estimated by bootstrap analysis with the number of bootstraps set to 200. The free energy for each solute in bulk water was normalized to zero to facilitate comparison.

Following the Marrink-Berendsen solubility-diffusivity model,256 permeability coefficients

(Pm) were calculated using the generalized Langevin equation as described in ref 257.

∆! ! !! !"# ( ) ! = !" �� (5.1) ! !! !(!)

where D(z) is the local diffusion coefficient, which is estimated using the Hummer positional autocorrelation function,258, 259 ΔG(z) is the potential of mean force, R is the gas constant (8.314 J mol-1 K-1); T is the temperature and z is the position of the solute along the membrane normal.

In additional calculations, an implicit membrane model was considered. For these calculations, a dielectric slab model of the cytoplasmic membrane was constructed using

APBSmem version 2.02260, 261 The membrane model was 5.0 nm thick (excluding bulk solvent) with dielectric constants ε = 80 for bulk solvent, ε = 10 for the 0.7 nm-thick head group region, and ε = 2 for the 3.6 nm-thick hydrophobic lipid tail region.262 Polar and nonpolar solvation free energies were computed with the Adaptive Poisson-Boltzmann Solver (APBS) version 1.4263 with each solute located at the following six positions: bulk water (z = 3.5 nm), the bulk-head

86 group interface (z = 2.5 nm), the center of the head group region (z = 2.2 nm), the head-tail interface (z = 1.8 nm), the center of one “leaflet” of the lipid tail region (z = 0.9 nm) and the center of the membrane (z = 0.0 nm). APBS calculates the electrostatic solvation energy of solutes by solving the Poisson-Boltzmann equation. For these calculations, atomic partial charges were taken from the ffTK parameters developed in this study, with radii from the

PARSE force field for H, C and S atoms.264, 265 The PARSE force field does not include a radius for Hg, so the Bondi radius of 1.7 Å was used.266 Solvation free energies were computed as the sum of electrostatic (ΔGelec) and nonpolar solvation free energies (ΔGnp):

ΔGsolv = ΔGelec + ΔGnp (5.2)

Electrostatic contributions were calculated with APBS, and nonpolar contributions were calculated as described previously267 with MSMS version 2.6.1,268 which is called by

APBSmem.

5.3 Results and Discussion

5.3.1 Force field parameters

The optimized geometries and partial atomic charges for the five solutes are shown in Scheme

II II 5.2. The partial charges of Hg are 0.53 and 0.55 for CH3Hg–SCH3 and CH3S–Hg –SCH3, respectively, values of about one quarter of the formal charge of Hg2+. Optimized force constants and equilibrium values for bonds, angles and dihedrals are provided in Tables 5.1-5.5 The fits to the quantum mechanical potential energy surfaces from torsional scans are shown in Figure 5.2.

5.3.2 Model membrane

To assist in the discussion of free energy profiles of the five solutes, we adopted the four-region membrane notation proposed by Marrink and Berendsen256 and computed partial density profiles

87 of the simulation system (Figure 5.3). The center of the membrane system is defined as the reference point (i.e., z = 0). Region I (z = 0–1.0 nm) contains primarily the lipid tail groups, as is apparent from the partial density maximum in this region. Region II (z = 1.0–2.0 nm) is the interfacial area between the hydrophobic core and hydrophilic groups. The density of the tail groups drops dramatically in this region, whereas the densities of water, phosphate and the polar head groups increase. Carbonyl groups are a major component in this region; the density increases to a maximum at z = 1.6 nm and then drops off. Correspondingly, the density of the whole system also reaches a maximum of ~1,300 kg cm-3 at the interface of regions II and III.

Region III (z = 2.0–2.5 nm) is the interface between bulk water and phospholipid head groups.

Water molecules, charged phosphate groups and head groups are the main components of this region, although some carbonyl and lipid tail densities are present. Region IV (z > 2.5 nm) consists mainly of bulk water. However, small fractions of the phosphate and head group densities are also present in this region.

5.3.3 Free energy profiles

II + To investigate how complexation with Hg and [CH3Hg] affects the partitioning of low molecular weight thiols into the model bacterial inner membrane and how CH3Hg–SCH3 compares with CH3CH2SCH3, we divided the five solutes into two groups on the basis of their structural characteristics. We first discuss and compare the free energy profile for CH3Hg–SCH3 with those of CH3SH and CH3CH2SCH3 (Figure 5.4, A-C) and then compare CH3S–SCH3 to

II CH3S–Hg –SCH3 (Figure 5.4, D-E).

Because the membrane bilayer in this study is symmetric, we confine our discussion to only half the system. For CH3SH, the calculated free energy difference between the solute in bulk water and at the center of membrane (z = 0) is ~1.5 kcal mol-1. Two isoenergetic free energy

88 minima for CH3SH are present: one at the center of the membrane (region I), and the other at the interface of the tail and head groups (region II, Figure 5.4, A). Two small local energy maxima are present in region I (z = ~0.7 nm) and region III (z = ~2.2 nm), respectively. Overall, CH3SH prefers the hydrophobic environment and partitions favorably in a relatively broad region (z =

~0–1.5 nm).

CH3CH2SCH3 shows a similar distribution pattern to the Cys analogue (CH3SH) (Figure

5.4, B). The free energy difference between CH3CH2SCH3 in bulk water and the global

-1 minimum in the center of the membrane is ~2.8 kcal mol , somewhat larger than that of CH3SH.

CH3CH2SCH3 is slightly more hydrophobic and therefore partitions more readily into the tail region. A similar solvation free energy difference was also observed in a previous study of Cys and Met side chains in a DOPC membrane bilayer.227 The global energy minimum for

CH3CH2SCH3 is also located at the center of the membrane (i.e., z = 0). However, the local minimum in region II is less favorable than the global minimum, which is at z = 0, by ~0.5 kcal mol-1.

CH3Hg–SCH3 shows a different distribution pattern ⎯ it is relatively energetically unfavorable for this molecule to reside in either bulk water or the hydrophobic tail region and these two regions are roughly isoenergetic (Figure 5.4, C). Instead, the global free energy minimum is located at the interface of the head and tail groups (region II). The free energy difference between the global minimum (region II) and bulk water (region IV) is ~2 kcal mol-1 for CH3Hg–SCH3. A local minimum is present in the hydrophobic tail area (region I) where the global minima for CH3SH and CH3Hg–SCH3 are located.

II The free energy profile for CH3S–Hg –SCH3 is very similar to that of CH3S–SCH3, which does not contain Hg (Figure 5.4, D and E). The free energy difference between the solute in bulk

89 -1 water and at the global minimum is ~2 kcal mol for both compounds. Unlike CH3Hg–SCH3,

II partitioning of CH3S–SCH3 and CH3S–Hg –SCH3 in the hydrophobic core is more favorable

II than in the bulk water. The global free energy minima for CH3S–SCH3 and CH3S–Hg –SCH3 are both located at the interface between the hydrophobic acyl chains and the polar carbonyl and phosphate groups (region II).

Overall, our free energy calculations show that the energy difference in bulk water and at the most favorable position inside the membrane for each solute in this study is ~2 kcal mol-1.

Thus, these small, neutral, Hg-containing complexes are likely to diffuse rapidly through the cytoplasmic membrane passively.

Implicit membrane models based on Poisson-Boltzmann theory can offer insight into membrane permeation at a fraction of the computational cost of all-atom MD simulations. We constructed a simple five-slab continuum model260, 262 and compared the free energy profiles to the all-atom results. This five-slab partitioning should not be confused with the four-region description in section 3.2. The dielectric constant, or relative permittivity, ε, describes how a molecule interacts with an electric field. The use of three dielectric constants to represent the solvent, hydrophilic head groups, and hydrophobic tails of a symmetric lipid bilayer provides an intuitive physical description of the membrane environment both within each region and at the interfaces of adjacent regions.

The implicit membrane model qualitatively reproduces the trends observed in the all-atom

MD simulations (Figure 5.5), including the effects of incorporating Hg into the solutes.

However, the dielectric continuum model generally overestimates the favorability of the solute in the membrane relative to bulk water by ~1–3 kcal mol-1. Solvation free energies computed with an implicit membrane model are the sum of an electrostatic (ΔGelec) and a nonpolar term (ΔGnp).

90 Inspection of these two quantities shows that at all membrane depths the magnitude of ΔGnp for all five neutral solutes is larger than ΔGelec and the two terms have opposite signs (Figure 5.6).

Therefore, the difference with the all-atom MD arises from the difference between the positive

(unfavorable) electrostatic interactions and the negative (favorable) nonpolar interactions being larger. Nevertheless, the dielectric slab model offers a useful and rapid approach to estimate the free energy profiles and predict favorable positions of Hg-containing solutes within membrane systems.

5.3.4 Energy decomposition analysis

We observed distinct differences in the all-atom free energy profiles for CH3SH and CH3Hg–

+ SCH3, indicating that complexation of CH3SH by [CH3Hg] indeed alters its partitioning (Figure

5.4). To examine the thermodynamic driving forces that govern the partitioning behavior of the solutes, we computed the total non-bonded interaction energies between the solutes and the rest of the system (Esol-sys) over the 20 ns umbrella sampling trajectories for CH3SH and CH3Hg–

SCH3 (Figure 5.7).

In both cases, we found that Esol-sys favors partitioning from bulk water into the interface between region II and region III. The two energy minima of Esol-sys for CH3SH and CH3Hg–

SCH3 are both located at around z = 2 nm, at which point the membrane has the most diverse chemical composition (Figure 5.3), providing a suitable environment for amphiphilic compounds. As the solutes move toward the tail region, Esol-sys becomes unfavorable for both

CH3SH and CH3Hg–SCH3. However, for CH3SH, the increase in Esol-sys (from z = 2 to z = 0 nm)

-1 is ~4 kcal mol , whereas Esol-sys for CH3Hg–SCH3 increases much more dramatically, by ~10 kcal mol-1.

91 To characterize the individual contributions to Esol-sys (Figure 5.7), we decomposed ΔEsol-sys into solute-water (Esol-water) and solute-lipid (Esol-lip) interaction energies (Figure 5.8).

Unsurprisingly, Esol-water and Esol-lip showed opposite trends — when moving solutes toward the hydrophobic core, the interactions with lipids becoming more favorable and the interactions with water less favorable. As a result, the energy minima in ΔEsol-sys for the solutes are all located at z

= ~2 nm (Figure 5.8).

To identify which specific lipid components stabilize the solutes inside the membrane and understand sources of the difference in the free energy profiles between CH3SH and CH3Hg–

SCH3, we further decomposed Esol-lip into solute-lipid head (Esol-head), solute-phosphate (Esol- phosphate), solute-carbonyl (Esol-carbonyl) and solute-tail (Esol-tail) interaction energies (Scheme 5.3).

For CH3SH and CH3Hg–SCH3, the total non-bonded interaction energies between the individual solutes and lipid head groups (Esol-head) are favorable, and no statistically significant difference in

Esol-head was found (Figure 5.9 A). As expected, both solutes interact favorably with the charged phosphate groups (Figure 5.9 B), and again, no significant difference in Esol-phosphate was observed. However, we found that CH3Hg–SCH3 interacts more strongly with the carbonyl groups than does CH3SH (Figure 5.9 C). This effect arises because Hg, which has a positive partial charge (+0.53) in CH3Hg–SCH3, has a strong affinity for the negatively charged carbonyl oxygens. It is also interesting that CH3SH and CH3Hg–SCH3 show significant differences in their

-1 interactions with the lipid tail groups, with CH3Hg–SCH3 interacting ~7.5 kcal mol more favorably than CH3SH (Figure 5.9 D). However, we then normalized Esol-tail by the number of atoms in each molecule and found that Esol-tail for CH3Hg–SCH3 and Cys nearly overlap (Figure

5.10). Therefore, the more favorable Esol-tail interactions for CH3Hg–SCH3 come mainly from an additional number of contacts with the tail groups (Figure 5.11).

92 Both POPE and POPG contain two acyl chains comprising one saturated (chain A) and one unsaturated (chain B) tail (Scheme 5.1). CH3SH interacts with each of the two chains of both lipids in a very similar manner (Figure 5.12). However, CH3Hg–SCH3 interacts more strongly with chain B than with chain A (Figure 5.12).

II – Unlike the CH3SH and CH3Hg–SCH3 pair, complexation of Hg by two CH3S ligands to

II form CH3S–Hg –SCH3 does not result in a different free-energy minimum in the membrane relative to CH3S–SCH3 (Figure 5.4, D and E). For both solutes the global minima are located in region II. Again, to understand the thermodynamic contributions to the observed free energy profiles, we calculated the non-bonded interaction energies between each solute and the rest of the system. Similar to the findings for the CH3SH and CH3Hg–SCH3 pair, the minima in Esol-sys

II for CH3S–SCH3 and CH3S–Hg –SCH3 are located around z = 2 nm (Figure 5.13). As the two solutes are moved from their respective minima (z = ~2 nm) to the center of the membrane (z = 0 nm), Esol-sys for both solutes becomes unfavorable, but the increase in Esol-sys is different. For

II -1 CH3S–Hg –SCH3, Esol-sys increases by ~13 kcal mol , whereas the non-Hg containing compound

-1 CH3S–SCH3 increases by only ~5 kcal mol . Thus, more energy is required to partition CH3S–

II Hg –SCH3 from region II to the center of the membrane.

Again, we divided the POPE and POPG phospholipids into four groups: lipid head, phosphate, carbonyl and tail groups (Scheme 5.3), and compared the interaction energies

II between the solutes (CH3S–SCH3 and CH3S–Hg –SCH3) and individual groups (Figure 5.14).

II Similar to the CH3SH and CH3Hg–SCH3 pair, CH3S–SCH3 and CH3S–Hg –SCH3 show similar interaction energies with the lipid head groups and phosphate groups. The Hg-containing

II compound CH3S–Hg –SCH3 again exhibits more favorable interactions with the carbonyl group

II -1 than CH3S–SCH3, and CH3S–Hg –SCH3 also shows ~5 kcal mol stronger interactions with the

93 tail groups than does CH3S–SCH3. Therefore, compared with CH3S–SCH3, the major source of

II the more favorable Esol-lip interaction for CH3S–Hg –SCH3 comes from the stronger interaction with the lipid tail and carbonyl groups.

5.3.5 Permeability coefficients

Using the Marrink-Berendsen solubility-diffusion model,256 we computed the permeability coefficients for all five solutes using the data from the all-atom umbrella sampling simulations

(Table 5.7). We found that, although CH3SH and CH3Hg–SCH3 showed distinct distribution patterns inside the membrane, their permeability coefficients are quite similar, with Pm = 6.08

-5 -1 -5 -1 ×10 cm s for CH3SH and 8.06 × 10 cm s for CH3Hg–SCH3. In contrast, comparing CH3S–

II II m -5 -1 SCH3 with the CH3S–Hg –SCH3, we found that CH3S–Hg –SCH3 (P = 1.63 × 10 cm s )

-6 -1 permeates significantly faster than CH3S–SCH3 (6.32 × 10 cm s ) (Table 5.7). The above

II + results indicate that complexation with either Hg or [CH3Hg] increases the permeability relative to the corresponding non-Hg-containing compounds. We also found that CH3Hg–SCH3 diffuses the most rapidly among the five solutes in this study.

Experimentally measured Pm values for the solutes presented in this study have not been reported. However, we can compare the predicted Pm with values obtained for other Hg- containing compounds, HgCl2 and CH3HgCl, and also with water (Table 5.7). An

m experimentally measured P value for HgCl2 through an egg lecithin-cholesterol membrane is

-2 -1 220 m 1.3 × 10 cm s . In contrast, a P value estimated for HgCl2 crossing egg-PC and egg-

PC/cholesterol membranes was measured to be significantly lower: 1.5 × 10-4 cm s-1 at pH

221 5.0. In another study, the permeability coefficient of HgCl2 through the cytoplasmic membrane of a marine diatom was measured to be 7.4 × 10-4 cm s-1.207 Hence, there is

94 considerable variation in the measured HgCl2 rates. Nevertheless, all are orders of magnitude faster than the rates estimated here for the solutes studied.

m -3 For CH3HgCl, a measured P value through an egg-PC/cholesterol membrane is 2.6 × 10 cm s-1,221 whereas the value obtained through a marine diatom membrane is 7.2 × 10-4 cm s-1.207

CH3HgCl would thus appear to permeate through membranes even more rapidly than HgCl2.

This observation seems to be consistent with our findings — the addition of a methyl group increases permeability through cell membranes.

m The experimentally measured P value for H2O diffusing through a dipalmitoylphosphocholine (DPPC) membrane (95% DPPC) is 2.6 × 10-5 cm s-1, which is

269 similar to the present value estimated for CH3Hg–SCH3. However, in another experiment, the

m -3 -1 219 P for H2O through an egg PC-decane membrane was much faster, at 3.4 × 10 cm s .

Thiolate-bound Hg species are among the most abundant forms of HgII in intracellular environments and are likely to be involved in HgII uptake. In the present study, we have shown that neutral side chain analogues of Hg(Cys)2 and CH3Hg–Cys can cross a model membrane passively. However, free amino acids, such as cysteine, generally are present in zwitterionic forms in the condensed phase. Thus, it is important to consider the permeability of the zwitterionic forms of Hg(Cys)2 and CH3Hg–Cys and to examine the feasibility of passive diffusion of those complexes.

Passive diffusion coefficients have been measured experimentally for various amino acids, including polar, non-polar and charged species (Table 5.7).270 Their Pm values are in the range of

~10-10 to 10-12 cm s-1, which is on the same order as divalent Hg2+ (10-11 cm s-1).222 However, neutralizing the termini of the amino acid lysine through methylation increases the permeability by a factor of ~1010 (Table 5.7).271 Therefore, changing neutral side chain analogues to the 95 corresponding zwitterion complexes reduces the permeation rates considerably. Although

II + complexation with Hg or [CH3Hg] increases the permeability of the Cys side chain analogue somewhat—in the present calculations at most by approximately threefold—this enhancement would not be enough to compensate for the increased unfavorability resulting from the presence of the N- and C- termini. Thus, for zwitterionic Hg-coordinated amino acids, membrane-bound transporters may be required for uptake, export, or both. Nevertheless, for small, neutral Hg-

II containing compounds (e.g. CH3S–Hg –SCH3, CH3Hg–SCH3, and similar molecules) the present calculations suggest that passive diffusion cannot be excluded. Our results are consistent with MD work on the preferred locations for partitioning Cys and Met side-chain analogues into a dioleoylphosphatidylcholine (DOPC) bilayer, in which it was found that both molecules favorably transfer from bulk water to the center of the membrane. In another study, a similar distribution pattern was observed for Cys and Met side-chain analogues in a dimyristoylphosphatidylcholine (DMPC) model membrane.229 Lastly, we note that Hg-amino acid complexes can have coordination numbers higher than 2 for Hg.272 In addition to thiolate ligands, amine and carboxylate groups can also coordinate Hg,273 and this may facilitate the permeation of Hg complexes as well.

5.3.6 Implications for Hg uptake in bacteria

Previous experimental studies have attributed the uptake of Hg in bacteria to the result of accidental uptake by metal transporters and facilitation by complexation with cysteine.211, 213

Here we have examined the feasibility of passive diffusion of neutral, low molecular weight thiolate-Hg complexes through a model gram-negative bacterial cytoplasmic membrane. We find that, without facilitation by membrane-bounded transporters, it is energetically feasible for thiolate-Hg complexes to diffuse through the membrane. The calculated permeability

96 coefficients for these compounds are ~10-5 to 10-6 cm s-1, which is on the same order of the

269 passive diffusion rate of H2O through a DPPC membrane. As reported previously, it takes less than 1 ns for a water molecule to permeate a POPE/POPC membrane,250 and one might thus expect a comparable time scale for the present Hg complexes in a POPE/POPG membrane. Thus, appreciable amounts of Hg in this form would diffuse passively across the membrane. The passive diffusion coefficients for full amino acids, as opposed to side chain analogues, have been measured to be ~10-10 to 10-12 cm s-1, suggesting that amino acid complexes diffuse too slowly to permit substantial passive uptake. In these cases, as suggested by Schaefer et al.,213 metal transporters are likely required for efficient Hg(Cys)2 uptake.

97 5.5 Appendix 3

Scheme 5.1 POPE, POPG and five solutes.

POPE$ O O OH P O OH Chain$A$ O O O O H Chain$B$ O O O POPG$ P O Chain$A$ O O O NH3 O H Chain$B$ O

CH3SH$ CH3CH2SCH3$ CH3Hg–SCH3$

CH3S–SCH3$ CH3S–Hg–SCH3$

98 Scheme 5.2 Optimized Geometries and Partial Charges for the Selected Five Solutes

CH3SH CH3S–SCH3

II CH3CH2SCH3 CH3S–Hg –SCH3

CH3Hg–SCH3

99 Scheme 5.3 Structures of POPE/POPG and Regions of Head Groups (A), Phosphates (B),

Carbonyls (C) and Tail Groups (D).

C! B! D! O O A! P O O O O NH3 POPE$ O H O O OH O P O OH O O O POPG$ O H

Table 5.1 Force Field Parameters for CH3SH in CHARMM Format.

Bond Force constanta Equilibrium distancea (kcal mol-1 Å-2) (Å) CT3 HA3 360.436 (322.0) 1.089 (1.111) CT3 S 232.268 (240.0) 1.811 (1.816) S HS 287.773 (275.0) 1.337 (1.325) Angle Force constanta Equilibrium anglea (kcal mol-1 rad-2) (degree) CT3 S HS 64.350 (43.0) 94.844 (95.0)

HA3 CT3 HA3 37.196 (35.5) 109.890 (108.4) HA3 CT3 S 47.956 110.050 Dihedral Force constanta Periodicity Phase (kcal mol-1) (degree) HA3 CT3 S HS 0.259 (0.2) 3 0.0 a Values in parentheses are from ref 29.

100 Table 5.2 Force Field Parameters for CH3CH2SCH3 in CHARMM Format.

Bond Force constanta Equilibrium distancea (kcal mol-1 Å-2) (Å) CT3 CT2 301.890 (222.500) 1.521 (1.5280)

CT3 HA3 358.366 (322.000) 1.092 (1.1110)

CT2 HA2 342.589 (309.000) 1.093 (1.1110)

CT2 S 220.376 (198.000) 1.810 (1.8180)

CT3 S 224.321 (240.000) 1.800 (1.8160)

Angle Force constanta Equilibrium anglea (kcal mol-1 rad-2) (degree) CT3 CT2 S 61.579 113.695 CT3 CT2 HA2 52.491 (34.600) 109.754 (110.10) CT2 S CT3 85.254 (34.000) 98.077 (95.0000) CT2 CT3 HA3 49.222 (34.600) 110.717 (110.10) HA3 CT3 HA3 43.915 (35.500) 109.260 (108.40) HA2 CT2 S 56.398 106.585 HA2 CT2 HA2 29.969 (35.500) 107.362 (109.00) S CT3 HA3 44.649 (34.600) 110.238 (110.10) Dihedral Force constanta Periodicitya Phase (kcal mol-1) (degree) HA3 CT3 CT2 (0.1600) (3) (0.00) HA2 CT3 CT2 S CT3 0.5260 1 0.00

CT3 CT2 S CT3 0.2920 2 0.00

CT3 CT2 S CT3 1.9990 3 0.00

HA2 CT2 S CT3 0.4610 3 180.00

HA3 CT3 CT2 S 0.4990 3 0.00 CT2 S CT3 HA3 0.2610 (0.2800) 3 0.00 a Values in parentheses are from ref 29.

101 II Table 5.3 Force Field Parameters for CH3Hg –SCH3 in CHARMM Format.

Bond Force constant Equilibrium (kcal mol-1 Å-2) distance (Å) CT3 HA3 370.849 1.090 CT3 MER 263.133 2.701 MER S 131.215 2.331 S CT3 242.952 1.787 Angle Force constant Equilibrium angle (kcal mol-1 rad-2) (degree) CT3 MER S 41.725 176.917 HA3 CT3 MER 168.724 110.558 HA3 CT3 HA3 94.656 108.885 MER S CT3 242.526 97.238 S CT3 HA3 37.129 108.059 Dihedral Force constant Periodicity Phase (kcal mol-1) (degree) HA3 CT3 MER S 0.000 1 0.0 CT3 MER S CT3 0.000 1 0.0 MER S CT3 HA3 0.151 3 0.0

102 Table 5.4 Force Field Parameters for CH3S–SCH3 in CHARMM Format.

Bond Force constanta Equilibrium distancea (kcal mol-1 Å-2) (Å) CT3 HA3 359.224 (322.000) 1.093 (1.1110) CT3 SM 221.897 (214.000) 1.818 (1.8160) SM SM 188.079 (173.000) 2.070 (2.0290)

Angle Force Constanta Equilibrium anglea (kcal mol-1 rad-2) (degree) CT3 SM SM 79.464 (72.500) 103.749 (103.3000) HA3 CT3 SM 45.356 (38.000) 110.150 (111.0000)

HA3 CT3 HA3 42.169 (35.500) 109.549 (108.40) Dihedral Force constanta Periodicity Phase (kcal mol-1) (degree) CT3 SM SM CT3 0.3880 (1.0000) 1 0.00 CT3 SM SM CT3 3.7400 (4.1000) 2 0.00

CT3 SM SM CT3 0.7850 (0.9000) 3 0.00 HA3 CT3 SM SM 0.2760 (0.1580) 3 0.00 a Values in parentheses are from ref 29.

103 Table 5.5 Force Field Parameters for CH3S–Hg–SCH3 in CHARMM Format.

Equilibrium Force constanta Bond distancea (kcal mol-1 Å-2) (Å) CT3 HA3 357.926 1.089 CT3 S 206.529 1.818 S MER 180.583 (97) 2.329 (2.319) Equilibrium Force constanta Angle anglea (kcal mol-1 rad-2) (degree) CT3 S MER 232.848 (47.1) 100.906 (102.9) HA3 CT3 S 47.377 108.690 HA3 CT3 HA3 38.723 108.522 S MER S 33.027 (26) 179.915 (178.5)

Force constanta Phasea Dihedral Periodicitya (kcal mol-1) (degree)

CT3 S MER S 0.0 1 HA3 CT3 S 0.1820 (0.2) 3 (3) 0.0(0.0) MER a Values in parentheses are from ref 237.

Table 5.6 Computed Average Dipole Moments for Five Solutes Over the Last 5 ns of NPT

Equilibration.

Dipole moment Standard

(D) deviation (D)

CH3SH 2.07 0.08

CH3CH2SCH3 2.44 0.24

CH3Hg–SCH3 2.11 0.07

CH3S–SCH3 2.76 0.27 II CH3S–Hg –SCH3 1.76 0.91

104 Table 5.7 Calculated Passive Permeability Coefficients for the Five Solutes and Experimentally

Measured Pm for Hg-containing Compounds, Hydrogen Sulfide, Water and Selected Amino

Acids.

Permeability Compound Type of membrane Ref. Coefficient (cm s-1) -5 CH3SH 6.08 × 10 -6 model cytoplasmic CH3CH2SCH3 3.41 × 10 -5 membrane This CH3Hg–SCH3 8.06 × 10 -6 (75% POPE/25% study CH3S–SCH3 6.32 × 10 -5 POPC) CH3S–Hg–SCH3 1.63 × 10 egg lecithin- 1.3 × 10-2 220 cholesterol HgCl egg-PC/cholesterol 2 1.5 × 10-4 221 (pH = 5.0) 7.4 × 10-4 marine diatom 207 egg-PC/cholesterol 2.6 × 10-3 221 CH3HgCl (pH = 5.0) 7.2 × 10-4 marine diatom 207 Hg2+ 3.8 × 10-11 DPhyPC 222 reconstituted E. coli H S 0.5 274 2 inner membrane 2.6 × 10-5 DPPC (95%) 269 H O 2 3.4 × 10-3 egg PC-decane 219 5.7 × 10-12 Egg-PC 270 glycine 2.0 × 10-11 DMPC 270 5.5 × 10-12 Egg-PC 270 serine 1.6 × 10-11 DMPC 270 5.1 × 10-12 Egg-PC 270 lysine 1.9 × 10-11 DMPC 270 lysine (neutral) 2.1 × 10-2 Egg-PC 275 tryptophan 4.1 × 10-10 Egg-PC 270 phenylalanine 2.5 × 10-10 Egg-PC 270

105

Figure 5.1 System pressure over the course of 20 ns NPT equilibration.

A 100-point moving average is indicated by the red line.

106 CH3SH A" C" CH3S–SCH3

CH3CH2SCH3 B" D" II CH3S–Hg –SCH3

CH Hg–SCH C" 3 3

Figure 5.2 Potential energy surfaces for torsional scans.

Black: QM energies calculated at the MP2/6-31G(d) level of theory; Blue: MM energy obtained with the final optimized parameters.

107 I" II" III" IV"

Distance"from"membrane"center"(Z)"

Figure 5.3 Model cytoplasmic membrane system and partial density profiles.

The vertical lines divide half of the membrane system into four regions. Region I: lipid tail groups (z = 0–1 nm); Region II: hydrophobic-hydrophilic interface (z = 1–2 nm); Region III: head group-water interface (z = 2–2.5 nm); Region IV: bulk water (z > 2.5 nm). Water molecules are shown in the CPK representation in red and white. The lipid tails are shown as cyan lines. O,

N, and P are shown as red, blue and gold spheres, respectively.

108 I II III IV I II III IV A 1 D 1 CH3SH CH3S-SCH3 ) ) 1 1 - 0 - 0

-1 -1 G (kcal mol G (kcal mol -2

D -2 D

-3 -3 1 0 0.5 1 1.5 2 2.5 3 3.5 1 0 0.5 1 1.5 2 2.5 3 3.5 B CH3CH2SCH3 E CH3S-Hg-SCH3 ) ) 0 1 1 - 0 -

-1 -1 G (kcal mol

G (kcal mol -2 -2 D D

-3 -3 0 0.5 1 1.5 2 2.5 3 3.5 1 0 0.5 1 1.5 2 2.5 3 3.5 C CH3HgSCH3 Distance from membrane center (Z) )

1 0 -

-1

G (kcal mol -2 D

-3 0 0.5 1 1.5 2 2.5 3 3.5 Distance from membrane center (Z)

Figure 5.4 Computed free energy profiles for the passive transport of solutes across a model cytoplasmic membrane.

109 CH3SH% CH3S'SCH3%

CH3CH2SCH3% CH3S'Hg'SCH3%

1.8 nm 0.7 nm

ε=2 ε=10 ε!=80

CH3HgSCH3% 0.0 0.9 1.8 2.2 2.5 3.5

(nm)

Figure 5.5 Computed free energy profiles.

All-atom umbrella sampling MD (A-E, purple) and dielectric continuum membrane models (A-

E, blue); Schematic representation of the continuum model (F); Only half the membrane is shown.

110

Figure 5.6 Electrostatic and nonpolar energy decomposition for the implicit membrane model.

111 I" II" III" IV" I" II" III" IV"

A C

CH3SH" CH3Hg–SCH3"

B D

CH3SH" CH3Hg–SCH3"

Figure 5.7 Computed free energy profiles for the passive diffusion.

(A) CH3SH and (C) CH3Hg–SCH3 through a PE/PG bilayer and non-bonded interaction energies between the solutes and the rest of the system (B and D).

112 A B

CH3SH& CH3S–SCH3& C D

II CH3Hg–SCH3& CH3S–Hg –SCH3&

Figure 5.8 Energy decomposition of Esol-sys (blue) into Esol-water (green) and Esol-lip interaction energies (orange).

113 I" II" III" IV" I" II" III" IV"

A B

C D

Figure 5.9 Decomposition of non-bonded solute-lipid interaction energies (Esol-lip).

(Red: CH3SH; Blue: CH3Hg–SCH3). (A) Solute-lipid head interaction energies. (B) Solute- phosphate interaction energies. (C) Solute-carbonyl interaction energies. (D) Solute-tail interaction energies.

114

Figure 5.10 Non-bonded solute-tail interaction energies (Esol-tail) for CH3SH (red) and CH3Hg–

SCH3 (blue) normalized by the number of atoms in each molecule.

Figure 5.11 Number of contacts with the lipid tail groups for CH3SH (green) and CH3Hg–SCH3

(red).

115 A" B"

Figure

5.12 Interaction energies with PE/PG.

(Left) Interaction energies of CH3SH with PE/PG lipid tail chains A (red) and B (blue). (Right)

Interaction energies of CH3Hg–SCH3 with PE/PG lipid tail chains A (red) and B (blue).

116 I" II" III" IV" I" II" III" IV" A C

CH3S(SCH3" CH3S(Hg(SCH3"

B D

CH3S(SCH3" CH3S(Hg(SCH3"

Figure 5.13 Computed free energy profiles and non-bonded interaction energies.

II Computed free energy profiles for the passive diffusion of CH3S–SCH3 and CH3S–Hg –SCH3 through a PE/PG membrane (A and C), and non-bonded interaction energies between the solute and the rest of the system Esol-sys (B and D).

117 A B

C D

Figure 5.14 Energy decomposition of non-bonded solute-lipid interactions (Esol-lip).

II (Orange: CH3S–SCH3; Green: CH3S–Hg –SCH3). Interaction energies for (A) solute-lipid head groups, (B) solute-phosphates, (C) solute-carbonyls, and (D) solute-tail groups.

118 CHAPTER 6

Conclusions and Future Outlook

In this study, we used computational approaches, i.e. quantum chemistry calculations and molecular dynamics simulations to understand two very important aspects of mercury methylation —1) the biotransformation mechanism of mercury from inorganic form to methylmercury; and 2) the transport of mercury substrates through cell membranes.

To understand the enzymatic mechanisms of mercury methylation enzyme HgcA, we first focused on methylcobalamin, which is the cofactor of HgcA. To understand the potential role of this Cys substitution of the lower-axial side of methylcobalmin in HgcA, we conducted quantum chemistry calculations and investigated the effects of Cys ligand on the strength of methyl-cobalt bond and methyl transfer free energies. We constructed the simplified models of methylcobalamin with both deprotonated and protonated cysteine side chains, together with imidazole and imidazolate (which represents the original ligand of methylcobalamin). We found that cysteine ligand facilitated both methyl radical and methylcarbanion transfer to the two mercury substrates in this study. However, methyl carbanion transfer is more favorable in both cases. This research shed light on understanding the role of Cys substitution in methylcobalamin in the catalytic process of mercury methylation.

During the process of mercury methylation, mercury methylation enzyme HgcB serves as an electron donor and reduce cob(III)alamin after the transfer of a methyl group. In this study, we used density functional theory and continuum solvation to compute reduction potentials, pKas and Co–ligand binding equilibrium constants (Kon/off) for aquacobalamin in aqueous solution. We identify an approach that yields agreement with experiments to within 90 mV for reduction potentials and 1.0 log units both for pKas and log Kon/off. These findings demonstrate the

119 effectiveness computational approach for charactering electrochemical and thermodynamic properties of a complex transition metal-containing cofactor and set the foundation for exploring the redox requirements for HgcB.

For the transport mechanism of mercury substrates and bio-transformed products, we found that small, neutral mercury complexes are energetically feasible to cross a cytoplasmic model membrane passively. The energy difference between in bulk water and the global energy minimum for each Hg-containing complex in this study is only ~2 kcal mol-1. We also identified the energetic factors that stabilize Hg complexes in phospholipids, i.e. the strong favorable non- bonded interaction with the tail and carbonyl groups of lipid bilayer. The calculated permeability coefficients for these neutral Hg complexes are on the order of 10-5 cm s-1, which could be expected as a similar rate as passive permeation of water molecules through a membrane bilayer.

We also found that an implicit model membrane can be used to qualitatively reproduce the free energy profiles of the partition of Hg compounds into membrane bilayers, which might be useful for high throughput screening of Hg-containing compounds.

In the future, for the effort of understanding the mechanisms of mercury methylation, a few further computational studies could be conducted: 1) Transition state search: in the current study, we only investigated the reactants, intermediates and products of abiotic mercury methylation reactions. However, searching the transition states would help us understand the kinetic aspect for the abiotic methylation reactions, such as reaction rate constants. 2) Full structure of the cofactor: in this study, only simplified model of methylcobalamin was used. In the future, with the improvement of computational power, a full structure of methylcobalamin could be used and the results could be compared with current truncated models. 3) Structure of HgcA: when the structure of HgcA is solved, a QM/MM study on HgcA could be conducted to investigate its

120 enzymatic mechanism. In the current study, only the cofactor was considered and the effects of the rest of the enzyme on methyl transfer were not fully investigated. 4) Redox chemistry of cobalamins with Cys ligand: in the current study, only the pH-dependent redox chemistry of aquacobalamin was studied. The consistent computational approach we discovered in this study could be applied to investigate the redox chemistry of cobalamin/methylcobalamin with Cys as the lower-axial ligand, which would provide direct insights on the enzymatic mechanisms of

HgcA and HgcB.

For the investigation of the transport mechanism, again, a few further studies could be carried out: 1) Outer membrane: instead of only focusing on the inner membrane of gram- negative bacteria, a model of outer membrane could be constructed and the permeation of mercury complexes though both outer and inner membrane could be investigated; 2) Full Hg- amino acid complexes: in the current study, only side chain analogues of amino acids were considered in the simulations. In the future study, the full amino acids bound Hg complexes could be used and constant-pH MD simulations should be performed to account for the protonation/deprotonation processes during the permeation. 3) Force field parameterization: the current study provides a rapid way to develop molecular mechanics force field parameters for various Hg-containing compounds. In the future, the approach could be used for parameterizing more small Hg complexes, which would facilitate future MD simulations on sorts of mercury systems.

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156 VITA

Jing Zhou was born in Xinjiang, China. She studied Environmental Science at Dalian University of Technology in Dalian, China. Then, she went to graduate school with the postgraduate qualification examination waived and continued studying Environmental Science at Dalian

University of Technology. In 2011, she came to the U.S. to pursue her Ph.D. degree in computational biophysics. She was the first person who was waived from GRE test in the department history. During her Ph.D., she performed her research at the Center of Molecular biophysics at the University of Tennessee and Oak Ridge National Laboratory. She published three first/co-first author papers during this time.

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