SINGLE-MOLECULE SPECTROSCOPY AND IMAGING STUDIES OF PROTEIN FOLDING-UNFOLDING CONFORMATIONAL DYNAMICS: THE MULTIPLE-STATE AND MULTIPLE-CHANNEL ENERGY LANDSCAPE
Zijian Wang
A Dissertation
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
May 2016
Committee:
H. Peter Lu, Advisor
Gabriela Bidart-Bouzat Graduate Faculty Representative
Ksenija D. Glusac
George Bullerjahn
© 2016
Zijian Wang
All Rights Reserved iii ABSTRACT
H. Peter Lu, Advisor
Protein conformational dynamics often plays a critical role in protein functions. We have characterized the spontaneous folding-unfolding conformational fluctuation dynamics of calmodulin (CaM) at thermodynamic equilibrium conditions by using single-molecule fluorescence resonance energy transfer (FRET) spectroscopy. We studied protein folding
dynamics under simulated biological conditions to gain a deep, mechanistic understanding of
this important biological process. We have identified multiple folding transition pathways and
characterized the underlying energy landscape of the single-molecule protein conformational
fluctuation trajectories. Our results suggest that the folding dynamics of CaM molecules
involves a complex multiple-pathway multiple-state energy landscape, rather than an energy
landscape of two-state dynamical process. Our probing single-molecule FRET fluctuation
experiments demonstrate a new approach of studying spontaneous protein folding-unfolding
conformational dynamics at the equilibrium that features recording long time single-molecule
conformational fluctuation trajectories. This technique yields rich statistical and dynamical
information far beyond traditional ensemble-averaged measurements.
We characterize the conformational dynamics of single CaM interacting with C28W. The single CaM molecules are partially unfolded by GdmCl, and the folded and unfolded CaM molecules are approximately equally populated. Under this condition, the majority of the single protein CaM undergoes spontaneous folding-unfolding conformational fluctuations. Using single molecule FRET spectroscopy, we study each of the single protein’s conformational dynamics in iv the presence of C28W-CaM interactions. The results show an interesting folding-upon-binding
dynamic process, and a conformational selection mechanism is further confirmed.
The effect of molecular crowding on protein folding process is a key issue in the understanding of protein folding dynamics in living cells. Due to the complexity and interplay between various interactions existing in an equally favored environment of protein folding and unfolding conformational dynamics, such simple reduced entropic enhancement model do not suffice in describing protein folding conformational dynamics. We observe, at higher concentration of crowding reagent Ficoll 70, single protein molecules spontaneously denature into unfolded proteins which involves a combined process of polymer-polymer interaction, entropic effects and solvation thermodynamics and dynamics. Such heterogeneous unfolding process can serve as a first step to a mechanistic understanding of living cell disease as a result of molecular crowding effect, protein aggregates and fibril formation.
v
To My Mom
Whose Insights Influence Me the Most vi ACKNOWLEDGMENTS
First and foremost I want to thank my advisor H. Peter Lu. It has been an honor to be one of
his graduate students. He has taught me, both consciously and unconsciously, how good
experiments are done. I appreciate all his contributions of time, ideas and funding to make my
Ph. D. experience productive. I am also grateful for the excellent example he has provided as a
successful chemist and professor.
I am thankful to all my dissertation committee members: Dr. Ksenija D. Glusac, Dr. George
Bullerjahn and Dr. Gabriela Bidart-Bouzat for their precious time. I also want to acknowledge all
the group members, both current members and past members from Dr. H. Peter Lu’s group, for
setting a competitive, productive and hard-working environment. I also want to thank Dr.
Desheng Zheng, Dr. Yufan He, Dr. Yuanmin Wang, Dr. Jin Cao and Dr. Qing Guo for their
friendship and help. Especially, I’d like to thank Dr. Takashige Fujiwara for training me on tuning Lasers and technical support.
I gratefully acknowledge Delta Electronics Inc. for generously providing me the Delta
Electronics Research fellowship. The Delta Electronics Research fellowship supported me for the 2012-2013 academic year.
I would also like to thank many faculty and staff members at the Center for Photochemical
Sciences and the Department of Chemistry: Nora Cassidy, Alita Frater, Charles Codding, Doug
Martin, and Hilda Miranda, for their help.
Lastly, I would like to thank my family for all their love and encouragement, for my parents who raised me with a love of science and supported me in all my pursuits. Without their understanding and love, I would never be able to finish this journey.
vii
TABLE OF CONTENTS
Page
CHAPTER I. INTRODUCTION……………………… ...... 1
1.1 Introduction to Single-Molecule Fluorescence Spectroscopy...... 1
1.2 Single-Molecule Studies of Protein Conformational Dynamics ...... 3
1.3 An Overview of Single-Molecule Studies of Protein Folding ...... 4
1.4 Our Sample Protein Calmodulin (CaM) ...... 7
1.5 Research Objective, Specific Aims and Dissertation Overview ...... 9
1.6 Reference ...... 11
CHAPTER II. EXPERIMENTAL SECTION ...... 18
2.1 Principles of Experimental Techniques ...... 18
2.1.1 Principles of Confocal Microscopy ...... 18
2.1.2 Principles of Fluorescence Resonance Energy Transfer ...... 20
2.1.3 Signal Detection Techniques: Introduction to APD ...... 25
2.2 Experimental Details ...... 26
2.2.1 Experimental Setup of Single-Molecule FRET combined with Confocal
Microscope...... 26
2.2.2 Materials and Sample Preparation……………………………… ...... 29
2.2.3 Statistical Analyses of Single-Molecule Intensity Trajectories ...... 32
2.3 Protein Folding Dynamics in Condensed Phases...... 35
2.4 Theory of Polymer Solutions ...... 37
2.5 References ...... 38 viii
CHAPTER III. PROBING SINGLE- MOLECULE PROTEIN FOLDING
CONFORMATIONAL DYNAMICS USING SINGLE-MOLECULE FRET
SPECTROSCOPY………………………...... 41
3.1 Introduction ...... 41
3.2 Materials and Methods ...... 43
3.2.1 Sample Preparation and Characterization…………………………… . 43
3.2.2 Single-Molecule Imaging and FRET Measurements………………… 45
3.3 Results and Discussion ...... 47
3.3.1 Single-Molecule FRET Trajectories Monitored Unfolding of Single CaM
molecules…………………………… ...... 47
3.3.2 Autocorrelation Analyses of CaM Folding-Unfolding Conformational
Fluctuation Dynamics …………………………… ...... 50
3.3.3 Non-Exponential Distribution of Folding Waiting Time Indicates Multiple
Folding Intermediates …………………………… ...... 58
3.3.4 Model Analyses of Conformational Dynamics and Energy Landscape of
Single-Molecule CaM Folding …………………………… ...... 61
3.4 Conclusions ...... 69
3.5 References ...... 70
CHAPTER IV. PROBING SINGLE-MOLECULE PROTEIN FOLDING-UNPON-BINDING
CONFORMATIONAL DYNAMICS USING SINGLE-MOLECULE FRET SPECTROSCOPY.
...... ………………………...... 80
4.1 Introduction ...... 80
4.2 Materials and Methods ...... 83 ix
4.2.1 Sample Preparation and Characterization…………………………… . 83
4.2.2 Single-Molecule Imaging and FRET Measurement ...... 84
4.3 Results and Discussion ...... 85
4.4 Conclusions ...... 92
4.5 References ...... 93
CHAPTER V. PROBING SINGLE-MOLECULE PROTEIN FOLDING CONFORMATIONAL
DYNAMICS IN CROWDED EVIRONMENT USING SINGLE-MOLECULE FRET
SPECTROSCOPY ………………………… ...... ………………………………… 98
5.1 Introduction ...... 98
5.2 Materials and Methods ...... 99
5.3 Results and Discussion ...... 102
5.4 Conclusions ...... 114
5.5 Reference ...... 115
x
LIST OF FIGURES
Figure Page
1.1 Conceptual Figure of FRET ...... 3
1.2 Flexible Conformations of a Protein ...... 4
1.3 Protein Folding Energy Landscape ...... 7
1.4 3D Crystal Structure of CaM ...... 9
2.1 Conceptual Figure of Confocal Microscope ...... 20
2.2 FRET Efficiency vs Inter-Dye Distance Curve ...... 21
2.3 Conceptual Figure of Protein Folding FRET ...... 24
2.4 Conceptual Figure of FRET ...... 25
2.5 A Schematic Representation of APD ...... 26
2.6 Our Single-Molecule Setup...... 28
2.7 A Cartoon of Our Sample ...... 32
2.8 TCAD Map in a Typical Single-Molecule Experiment ...... 34
2.9 A Schematic Representation of Molecular Crowding ...... 38
3.1 Our Single-Molecule Imaging System...... 46
3.2 Typical Trajectories and Data ...... 48
3.3 Correlation Analyses of Single-Molecule Data ...... 52
3.4 Single-Molecule Conformational Fluctuation Dynamics ...... 54
3.5 Waiting-Time Distribution of Single-Molecule Data ...... 60
3.6 Protein Folding Pathway Distribution ...... 66
4.1 Protein Folding Binding Process ...... 82
4.2 Single-Molecule Imaging and Correlation Analysis...... 86 xi
4.3 Protein Folding Binding and EFRET ...... 87
4.4 Waiting Time Distribution Analysis of Protein Folding ...... 89
4.5 Folding Pathway Distribution in Protein Folding Binding ...... 91
5.1 Single-Molecule Imaging and Analysis ...... 103
5.2 EFRET Distributions ...... 104
5.3 Correlation Analyses ...... 106
5.4 Folding Pathway Distribution in Protein Folding ...... 112
5.5 A Cartoon Showing Folding Process ...... 113
xii
LIST OF TABLES
Table Page
2.1 List of concentrations used in our experiments ...... 30
2.2 List of concentrations used in our folding-binding experiments ...... 31
4.1 List of concentrations used in our folding-binding experiments ...... 84
1
CHAPTER I. INTRODUCTION
This chapter is dedicated to the introduction of single-molecule studies of protein
conformational dynamics and a brief introduction of single-molecule protein folding.
1.1 Introduction to Single-Molecule Fluorescence Spectroscopy
Single-molecule spectroscopy developed in the 1990s is by far the most important technique
to study one molecule at a time.1-13 The dynamics and heterogeneity revealed by single-molecule
experiments proved to be invaluable, when researchers try to understand biological processes at
the molecular level. Single-molecule fluorescence spectroscopy is powerful for studying
complex biological processes, such as enzymatic reactions14, 15, protein folding dynamics,16-18
and other dynamic processes.19 Single-molecule fluorescence imaging is a powerful tool to
probe details in living cells and nanostructures.20-22 Single-molecule fluorescence resonance
energy transfer (smFRET) spectroscopy probes conformational changes of dye labeled individual biomolecules with a sensitivity down to about 1 nm to 8 nm spatial range and sub-millisecond temporal resolution,23, 24 being an ideal approach to analyze protein conformational dynamics.
Single-molecule FRET spectroscopy can monitor conformational changes of macromolecules
containing fluorophores. Depending on the photophysics properties of the fluorophores,
single-molecule FRET spectroscopy typically can reveal detailed molecular scale dynamics and the conformational fluctuation information of biomolecules.25 New developments in
single-molecule spectroscopy revolutionized the study of traditional biophysics. Recently, new
developments in this technique also made it possible to probe various interaction pathways in
which real biological processes occur.26 The experimental output of a single-molecule FRET 2
experiment is typically a photon trajectory containing rich fluctuation dynamic information which cannot be straightforwardly obtained by ensemble-averaged experiments. By removal of
ensemble average, one can analyze detailed molecular scale dynamics from such experiments. Of particular relevance to my research is the observation of single-molecule trajectories which record dynamic events of individual systems in condensed phases. Motivated by the experimental developments, theorists have analyzed intermittency, interconversion between two conformational states, and photon statistics.
Single-molecule fluorescence resonance energy transfer (smFRET), which applies FRET at the single-molecule level, is a measurable technique for studying real-time structural dynamics of individual biomolecules. It measures distance typically in 10-80 Å range. Generally speaking, a pair of donor and acceptor is attached to two specific sites of one or two target molecules, and energy transfer from donor to acceptor occurs through non-radiative induced dipole-dipole interaction energy transfer mechanism. The energy transfer efficiency (EFRET) between the two fluorophores depends on the inter-distance between the donor fluorophore and acceptor fluorophore attached to the same molecule:
1 EFRET 6 1+rR / 0
where r is the separate distance between two fluorophores, the FRET donor and acceptor,
respectively. R0, the Förster radius, is a function of dipole orientations of two fluorophores,
refractive index of the medium, spectral overlap integral between donor emission and acceptor
absorbance, and quantum yield of the donor. 3
Figure 1.1. Conceptual Figure of FRET. Förster resonance energy transfer or fluorescence resonance energy transfer (FRET) Jablonski diagram.
1.2 Single-Molecule Studies of Protein Conformational Dynamics
Proteins participate in various processes inside living cells such as metabolism, gene
expression, cell signaling, and protein-protein interactions. A mechanistic understanding of protein conformation, structure and function is critical in biophysics studies. The structure and function relationship of proteins confused generations of scientists. Such structure and function relationship is critical to understand biochemical reactions and biological processes involved in living cells. Ensemble-averaged techniques such as X-ray diffraction and nuclear magnetic resonance studies only reveal averaged blurred physical pictures of the true protein motions.
Only single-molecule techniques can reveal the temporal and spatial heterogeneity of protein conformational motion and dynamics by removal of ensemble average.
One type of protein which is of critical importance is the flexible protein involved in various signaling processes inside living cells.24, 26 These proteins play the role of messengers delivering messages from side to side inside living cells by engaging themselves in extensive 4
protein-protein interactions. The nature of such protein-protein interactions is still a mystery and under extensive studies. Based on limited experimental data, various models have been proposed to understand the nature of such interaction processes such as induced fit and conformational
selection models. One of the best ways to resolve this puzzle is by removal of ensemble average
using single-molecule techniques. The rich information obtainable in detailed fluctuation
dynamic trajectories of single-molecule techniques can provide detailed mechanistic
understanding of critical questions of this kind.
Figure 1.2. Flexible Conformations of a Protein. A cartoon showing the flexible confirmations a
protein can take in real living cell environments where extensive protein-protein interactions
exist. The conformational fluctuation dynamic model is adapted to account for folding reaction
and binding flexibility.
1.3 An Overview of Single-Molecule Studies of Protein Folding
Over the last 50 years, there have been intensive studies on protein folding mechanisms and dynamics.27-30 A widely accepted perspective suggests that a protein folding process is essentially 5
a navigation on a funnel-shaped energy landscape towards a global energy minimum.31-33 This multi-dimensional energy landscape is typically rugged and complex involving multiple folding routes and metastable states. Single-molecule FRET is a powerful approach to reveal selectively the folded and unfolded protein conformational subpopulations from otherwise hidden in ensemble-averaged overall population distribution.34-36 Using smFRET, there are significant advances in analyzing the protein unfolded state dynamics,34, 35 and protein folding
dynamics.36 Generally, a two-state model with two distinct folded and unfolded conformations is sufficient to describe the protein folding dynamic processes. However, for large proteins with
more than 100 amino acids, this simple two-state folding dynamic scheme is often insufficient or
inapplicable.37-40
Since the question about the spontaneity of proteins folding into their native state via sampling of an enormous number of possible conformations first appeared 50 years ago, the
protein folding problem, although with significant progress, still remains to be a fascinating topic.
Theoretically, the protein folding process is navigation on a funnel-shaped energy landscape towards a global energy minimum. This multi-dimensional energy landscape can be rugged and extremely complex involving multiple folding routes and metastable states. Using smFRET, there are advances in characterization of protein unfolded state dynamics, protein collapse (from unfolded state to a compact yet folded state) dynamics, protein folding dynamics19 and ‘one-state’
downhill folding process.41-44 Usually, a two-state model with two distinct folded and unfolded conformations is sufficient to describe the dynamic processes. However, for large proteins with
more than 100 amino acids, this simple two-state folding dynamic scheme is not applicable. A 6
recent example is a demonstration of existence of six distinct folding intermediates of a 214
amino acid protein adenylate kinase.45
After gene expression, single proteins start to fold into a unique functional structure without
external help. However, inside the living cells, this process normally happens in a crowded
environment which involves various kinds of protein-protein interactions. Little is known about
the folding dynamics of single CaM molecules in the presence of extensive interaction with other peptide molecules. The motivation of our study is to probe the folding-unfolding conformational
dynamics, which is the most important conformational dynamics of single proteins in this
“crowded” environment in the presence of polymer molecules. The outcome of this study helps us to understand the critical role played by protein-protein interactions in the single protein folding process, which can provide insight into the future study of protein misfolding and protein aggregates related to human diseases (e.g., amyloid diseases) inside living cells.
Single-molecule techniques are powerful tools to probe molecular scale dynamic processes without ensemble averaging. The molecular details of single protein folding are readily
observed one molecule at a time in single-molecule experiments. As a key advantage,
single-molecule FRET allows a clear separation of folded and unfolded subpopulations, and thus
enables a further quantitative analysis of the properties of protein conformational fluctuation
dynamics without interference from undesired ensemble averaged signals. Since
single-molecule FRET can provide distance and protein conformational fluctuation dynamic
information without ensemble-averaging, it is promising to observe intramolecular
conformational dynamics at equilibrium. 7
Figure 1.3. Protein Folding Energy Landscape. A cartoon showing the existence of possible multiple pathways involved in the single-molecule protein folding process. It is consistent with the multidimensional funnel-shaped folding energy landscape physical picture which was theoretically proposed.
1.4 Our Sample Protein Calmodulin (CaM)
CaM, a 148-residue protein responsible for intracellular calcium-sensing, plays a crucial role
in a number of biological processes including cell signaling, muscle contraction, and energy
metabolism. CaM has two globular domains, and the conformational dynamics of the domains
has been under extensive studies.46-48 Traditional methods, such as nuclear magnetic resonance
and X-ray crystallography,49, 50 have provided detailed insights into the mechanisms and 8
dynamics of CaM conformational changes. However, the complexity of the protein dynamics, especially, the conformational fluctuations involved in CaM biological functions are still not fully characterized by using ensemble-averaged dynamic measurements or by static structural
analyses alone. CaM is capable of regulating activities of many proteins via interacting with Ca2+
ions. When the intracellular calcium level is high, four Ca2+ ions bind to the CaM in order to
reduce Ca2+ level. Calmodulin has four EF-hand motifs that change its conformation upon
binding Ca2+ ions. Each EF-hand motif contains two α-helices connected by a 12-residue peptide loop. The calcium ion changes the conformation of CaM by binding to the loop region and changes the relative positions of the α-helices. Upon binding Ca2+, CaM undergoes large
conformational changes which can be directly measured by single-molecule fluorescence
techniques in real-time. The crystal structure of Ca2+-loaded CaM exhibits a dumbbell shape
structure which forms an excellent prototype for single-molecule studies.
Single-molecule spectroscopy is capable of dissecting protein conformational fluctuations
under physiological conditions in real time. As a result of the flexibility and the dumbbell shape
of the protein CaM, it is possible to monitor the conformational dynamics of CaM with
single-molecule FRET spectroscopy. The typical time-resolution of single-molecule FRET spectroscopy is milliseconds, which are the characteristic time scales of protein motion. Our
work on probing the folding-unfolding conformational dynamics of CaM under denature
conditions of guanidinium chloride (GdmCl) by using single-molecule FRET spectroscopy is a significant step towards a mechanistic molecular scale understanding of CaM folding process. 9
Figure 1.4. 3D Crystal Structure of CaM. Three dimensional crystal structure of calmodulin
from protein data bank. The blue balls indicate the calcium ion. As we can see from the picture, calmodulin has two globular domains each consisting of two calcium ion binding sites.
C28W is a short peptide chain consisting of 28 amino acid residues. C28W is an oligomer
acting as the effective binding domain of the plasma membrane Ca-ATPase. The binding of
C28W to CaM can have significant effect on CaM protein conformations. A mechanistic
understanding of the binding induced conformational dynamic process is under extensive study.
In general, a two-state dynamic model involving loosely binding and tightly binding terminals is sufficient to describe such dynamic process. A main focus of our study is to further probe the role played by C28W-CaM protein-protein interactions in the CaM protein folding process.
1.5. Research Objective and Specific Aims, and Dissertation Overview
Our work is to probe the folding-unfolding conformational fluctuation dynamics of
CaM under denature conditions by using smFRET spectroscopy. The protein folding-unfolding
conformational dynamics is the essential part of this thesis study. We have identified the critical 10
concentration of GdmCl, at which single-molecule CaM undergoes spontaneous folding-unfolding conformational fluctuation with about equal probability of dwelling on the
folded and unfolded conformational states. Thermodynamically, such a condition is ideal for
studying equilibrium spontaneous fluctuations without external driving force. Recording
single-molecule conformational fluctuation trajectories and analyzing equilibrium fluctuation
dynamics, we are able to identify the nature of the CaM folding dynamics which involves
multiple pathways and multiple states. Using a dynamic model analysis, we have further
identified the distribution of the folding transition pathways and the energetic features of the
folding energy landscape of CaM.
We use single-molecule FRET spectroscopy to probe the folding-unfolding conformational
dynamics of CaM interacting with C28W under the mild unfolding concentration of denaturant
solvent guanidinium chloride (GdmCl). The critical concentration of denaturant GdmCl, at which
single protein undergoes folding-unfolding conformational fluctuation, has been characterized by
our previous study. Since the interaction characterized by previous studies revealed an induced
binding picture in the native state of CaM, we see a more complicated dynamic picture of CaM interacting with C28W under a partially denatured condition at which single CaM molecules
have larger conformational space to explore.51
In chapter five of this thesis, we observe, at higher concentration of crowding reagent Ficoll
70, single protein molecules spontaneously denature into unfolded proteins which are a combined process of polymer-polymer interactions, entropic effects and solvation thermodynamics. Such a heterogeneous unfolding process can serve as a first step to a 11
mechanistic understanding of living cell disease as a result of molecular crowding effects, protein aggregates and fibril formations.
1.6 Reference:
1 Nie, S.; Zare R. N. Optical Detection of Single Molecules. Annu. Rev. Biophys. Biomol.
Struct. 1997, 26, 567-596.
2 Moerner, W. E.; Orrit, M. Illuminating Single Molecules in Condensed Matter. Science 1999,
283 (5480), 1670-1676.
3 Betzig, E.; Chichester, R.J. Single Molecules Observed by Near-Field Scanning Optical
Microscopy. Science 1993, 262, 1422-1425.
4 Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Imaging and Time-Resolved
Spectroscopy of Single Molecules at an Interface. Science 1996, 272, 255-258.
5 Xie, X. S.; Trautman, J. K. Optical Studies of Single Molecules at Room Temperature. Annu.
Rev. Phys. Chem. 1998, 49, 441-480.
6 Ishijima, A.; Yanagida, T. Single Molecule Nanobioscience. Trends Biochem. Sci. 2001, 26
(7), 438-444.
7 Weiss, S. Fluorescence Spectroscopy of Single Biomolecules. Science 1999, 283 (5408),
1676-1683.
8 Moerner, W. E. New Directions in Single-Molecule Imaging and Analysis. Proc. Natl. Acad.
Sci. U.S.A. 2007, 104 (31), 12596-12602.
9 Orrit, M. The Motions of an Enzyme Soloist. Science 2003, 302 (5643), 239-240. 12
10 Betzig, E.; Patterson, G.H.; Sougrat, R.; Lindwasser, O.W.; Olenych, S.; Bonifacino, J.S.;
Davidson, M.W.; Lippincott-Schwartz, J.; Hess, H.F. Imaging Intracellular Fluorescent
Proteins at Nanometer Resolution. Science, 2006, 313 ( 5793) 1642-1645.
11 Hell, S.W.; Wichmann, J. Breaking the diffraction resolution limit by stimulated emission:
stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 1994, 19(11) 780-782.
12 Rust, M.J.; Bates, M.; Zhuang, X. Stochastic optical reconstruction microscopy (STORM)
provides sub-diffraction-limit image resolution. Nat. Methods. 2006, 3(10): 793–795.
13 Lu, H. P. Probing Single-Molecule Protein Conformational Dynamics. Acc. Chem. Res. 2005,
38 (7), 557-565.
14 Lu, H. P.; Xun, L. Y.; Xie, X. S. Single-Molecule Enzymatic Dynamics. Science 1998, 282
(5395), 1877-1882.
15 English, B. P.; Min, W.; van Oijen, A. M.; Lee, K. T.; Luo, G. B.; Sun, H. Y.; Cherayil, B. J.;
Kou, S. C.; Xie, X. S. Ever-Fluctuating Single Enzyme Molecules: Michaelis-Menten
Equation Revisited. Nat. Chem. Biol. 2006, 2 (2), 87-94.
16 Schuler, B.; Lipman, E. A.; Eaton, W. A. Probing The Free-Energy Surface for Protein
Folding with Single-Molecule Fluorescence Spectroscopy. Nature 2002, 419(6908), 743-747.
17 Rief, M.; Gautel, M.; Oesterhelt, F.; Fernandez, J.M.; Gaub, H.E. Reversible unfolding of
individual titin immunoglobulin domains by AFM. Science. 1997 276(5315):1109-12.
18 Rief, M.; Oesterhelt, F.; Heymann, B.; Gaub, H.E. Single Molecule Force Spectroscopy on
Polysaccharides by Atomic Force Microscopy. Science. 1997 275(5304): 1295-1297. 13
19 Lu, H. P.; Iakoucheva, L. M.; Ackerman, E. J. Single-Molecule Conformational Dynamics of
Fluctuating Noncovalent DNA-Protein Interactions in DNA Damage Recognition. J. Am.
Chem. Soc. 2001, 123 (37), 9184-9185.
20 Tan, X.; Nalbant, P.; Toutchkine, A.; Hu, D. H.; Vorpagel, E. R.; Hahn, K. M.; Lu, H. P.
Single-Molecule Study of Protein-Protein Interaction Dynamics in a Cell Signaling System. J.
Phys. Chem. B. 2004, 108 (2), 737-744.
21 Liu, S.; Bokinsky, G.; Walter, N. G.; Zhuang, X. Dissecting the Multistep Reaction Pathway
of an RNA Enzyme by Single-Molecule Kinetic "Fingerprinting". Proc. Natl. Acad. Sci.
U.S.A. 2007, 104 (31), 12634-12639.
22 Visscher, K.; Schnitzer, M. J.; Block, S. M. Single Kinesin Molecules Studied with a
Molecular Force Clamp. Nature 1999, 400 (6740), 184-189.
23 Roy, R.; Hohng, S.; Ha, T. A Practical Guide to Single-Molecule FRET. Nat. Methods 2008,
5 (6), 507-516.
24 Selvin, P. R.; Ha, T. Single-Molecule Techniques: A Laboratory Manual; Cold Spring Harbor
Laboratory Press: Cold Spring Harbor, NY, 2008.
25 Ha, T. J.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.;
Weiss, S. Single-Molecule Fluorescence Spectroscopy of Enzyme Conformational Dynamics
and Cleavage Mechanism. Proc. Natl. Acad. Sci. U.S.A. 1999, 96 (3), 893-898.
26 Chen, Y.; Hu, D. H.; Vorpagel, E. R.; Lu, H. P. Probing Single-Molecule T4 Lysozyme
Conformational Dynamics by Intramolecular Fluorescence Energy Transfer. J. Phys. Chem.
B 2003, 107 (31), 7947-7956. 14
27 Anfinsen, C. B.; Haber, E.; Sela, M.; White, F. H., Jr. The Kinetics of Formation of Native
Ribonuclease During Oxidation of the Reduced Polypeptide Chain. Proc. Natl. Acad. Sci.
USA 1961, 47, 1309-1314.
28 Schuler, B.; Eaton, W. A. Protein Folding Studied by Single-Molecule FRET. Curr. Opin.
Struc. Biol. 2008, 18 (1), 16-26.
29 Schuler, B.; Hofmann, H. Single-Molecule Spectroscopy of Protein Folding
Dynamics-Expanding Scope and Timescales. Curr. Opin. Struc. Biol. 2013, 23 (1), 36-47.
30 Zoldak, G.; Rief, M. Force as a Single Molecule Probe of Multidimensional Protein Energy
Landscapes. Curr. Opin. Struc. Biol. 2013, 23 (1), 48-57.
31 Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Theory of Protein Folding: the Energy
Landscape Perspective. Annu. Rev. Phys. Chem. 1997, 48, 545-600.
32 Dill, K. A.; Chan, H. S. From Levinthal to Pathways to Funnels. Nat. Struct. Biol. 1997, 4 (1),
10-19.
33 Thirumalai, D.; Klimov, D. K. Deciphering the Timescales and Mechanisms of Protein
Folding Using Minimal Off-Lattice Models. Curr. Opin. Struc. Biol. 1999, 9 (2), 197-207.
34 Deniz, A. A.; Laurence, T. A.; Beligere, G. S.; Dahan, M.; Martin, A. B.; Chemla, D. S.;
Dawson, P. E.; Schultz, P. G.; Weiss, S. Single-Molecule Protein Folding: Diffusion
Fluorescence Resonance Energy Transfer Studies of the Denaturation of Chymotrypsin
Inhibitor 2. Proc. Natl. Acad. Sci. USA 2000, 97 (10), 5179-5184.
35 Nettels, D.; Gopich, I. V.; Hoffmann, A.; Schuler, B. Ultrafast Dynamics of Protein Collapse
from Single-Molecule Photon Statistics. Proc. Natl. Acad. Sci. USA 2007, 104 (8), 15
2655-2660.
36 Nettels, D.; Hoffmann, A.; Schuler, B. Unfolded Protein and Peptide Dynamics Investigated
with Single-Molecule FRET and Correlation Spectroscopy from Picoseconds to Seconds. J.
Phys. Chem. B 2008, 112 (19), 6137-6146.
37 Haran G. How, When and Why Proteins Collapse: the Relation to Folding. Curr. Opin. Struc.
Biol. 2012, 22 (1), 14-20.
38 Sherman, E.; Haran, G. Coil-Globule Transition in the Denatured State of a Small Protein.
Proc. Natl. Acad. Sci. USA 2006, 103 (31), 11539-11543.
39 Aznauryan, M.; Nettels, D.; Holla, A.; Hofmann, H.; Schuler, B. Single-Molecule
Spectroscopy of Cold Denaturation and the Temperature-Induced Collapse of Unfolded
Proteins. J. Am. Chem. Soc., 2013, 135 (38), 14040-14043.
40 Hoffmann, A.; Kane, A.; Nettels, D.; Hertzog, D. E.; Baumgartel, P.; Lengefeld, J.; Reichardt,
G.; Horsley, D. A.; Seckler, R.; Bakajin, O.; et al. Mapping Protein Collapse with
Single-Molecule Fluorescence and Kinetic Synchrotron Radiation Circular Dichroism
Spectroscopy. Proc. Natl. Acad. Sci. USA 2007, 104 (1), 105-110.
41 Chung, H. S.; Louis, J. M.; Eaton, W. A. Experimental Determination of Upper Bound for
Transition Path Times in Protein Folding from Single-Molecule Photon-by-Photon
Trajectories. Proc. Natl. Acad. Sci. USA 2009, 106 (29), 11837-11844.
42 Chung, H. S.; McHale, K.; Louis, J. M.; Eaton, W. A. Single-Molecule Fluorescence
Experiments Determine Protein Folding Transition Path Times. Science 2012, 335 (6071),
981-984. 16
43 Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Eastwood, M. P.;
Bank, J. A.; Jumper, J. M.; Salmon, J. K.; Shan, Y.; et al. Atomic-Level Characterization of
the Structural Dynamics of Proteins. Science 2010, 330 (6002), 341-346.
44 Garcia-Mira, M. M.; Sadqi, M.; Fischer, N.; Sanchez-Ruiz, J. M.; Munoz, V. Experimental
Identification of Downhill Protein Folding. Science 2002, 298 (5601), 2191-2195.
45 Pirchi, M.; Ziv, G.; Riven, I.; Cohen, S. S.; Zohar, N.; Barak, Y.; Haran, G. Single-Molecule
Fluorescence Spectroscopy Maps the Folding Landscape of a Large Protein. Nat. Commun.
2011, 2, 493.
46 Chin, D.; Means, A. R. Calmodulin: A Prototypical Calcium Sensor. Trends Cell Biol. 2000,
10 (8), 322-328.
47 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-Binding Domains - Just 2-Faced or
Multifaceted. Trends Biochem. Sci. 1995, 20 (1), 38-42.
48 Liu, R.; Hu, D.; Tan, X.; Lu, H. P. Revealing Two-State Protein-Protein Interactions of
Calmodulin by Single-Molecule Spectroscopy. J. Am. Chem. Soc. 2006, 128 (31),
10034-10042.
49 Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J.
Three-Dimensional Structure of Calmodulin. Nature 1985, 315 (6014), 37-40.
50 Chattopadhyaya, R.; Meador, W. E.; Means, A. R.; Quiocho, F. A., Calmodulin Structure
Refined at 1.7 Angstrom Resolution. J. Mol. Biol. 1992, 228 (4), 1177-1192.
51 Slaughter, B. D.; Unruh, J. R.; Price, E. S.; Huynh, J. L.; Bieber Urbauer, R. J.; Johnson, C.
K. Sampling Unfolding Intermediates in Calmodulin by Single-Molecule Spectroscopy. J. 17
Am. Chem. Soc. 2005, 127 (34), 12107-12114.
18
CHAPTER II. EXPERIMENTAL SECTION
This chapter is dedicated to the description of experimental techniques in our single-molecule protein folding studies and the sample preparation procedures used in our experiments.
2.1 Principles of Experimental Techniques
2.1.1 Principles of Confocal Microscopy
Developed in 1940, confocal microscopy is one of the most commonly used microscope techniques in biological and biophysical research. It is first developed by Marvin Minsky, then at
Harvard. It has the advantage in resolution over traditional microscopes in that it has the ability
to control depth of field, elimination or reduction of background signals away from the focal
plane which are out-of-focused lights. The key element to the confocal microscope approach is
the use of spatial filtering techniques to eliminate and reduce out-of-focus light signals. The
confocal microscopy is specifically designed for biological research in living organisms to
improve spatial resolution which is powerful and revolutionary. By 1971, lasers were introduced
as the light sources for confocal microscopy. In the mid-1980s, confocal microscopes have been evolved into their modern form similar to the ones in modern biological research labs used on a daily basis. A conceptual figure of confocal microscopy is shown in figure 2.1. The central idea of confocal microscopes is to use two pinhole apertures at both ends of the optical path: one aperture is put in front of the laser light source, and another aperture is set in front of the photon detector. Once these two pinhole apertures form optical conjugate planes, fluorescence signals from unwanted parts of the specimen which are from out of focus plane are blocked.1-6 19
The principle in laser scanning microscopy is presented in figure 2.1. Coherent light emitted
by the laser light source system passes through a pinhole aperture in a conjugate plane (confocal)
with a scanning point on the specimen and a second pinhole aperture positioned in front of the
detector (APD). As the laser is reflected by a dichromatic mirror, we scanned across the sample in a defined focal plane, secondary fluorescence signals emitted from points on the sample (in the same focal plane) reflect back through the dichromatic mirror and are focused as a confocal point at the detector pinhole aperture with undesired signals rejected. The unwanted
fluorescence signal is blocked by the pinhole and a diffraction limited image with typically a resolution of the excitation laser wavelength is obtained with significantly higher resolution.
We further combine this technique with a piezo controlled scanner. By carefully controlling the
step size of approximately 200 nanometers, we can easily achieve diffraction limited images of
single-molecules. By focusing the laser spot onto single molecules, we continue to record
single-molecule trajectories which contain dynamic information recording single-molecule
dynamic properties. Such combined techniques help us to remove ensemble-averaged signals
to reveal heterogeneity. By studying detailed fluctuation dynamics, we obtain valuable
information about biological systems at the single-molecule level.
In traditional wide field microscopy, the entire specimen is subjected to light illumination from an incoherent mercury lamp, and the resulting image of secondary fluorescence emission
(blurring the image) can be viewed directly in the eyepieces or projected onto the surface of a photo-detector (APD or CCD). In contrast to this simple concept, the mechanism of image formation in a confocal microscope is fundamentally different. It helps us to achieve higher 20
spatial resolution using pinhole systems. As discussed above, the confocal fluorescence
microscope consists of a laser excitation source, a scanning component with optical and
electronic components, electronic detectors, and a computer for acquisition of molecular images.
The scanning component is at the heart of the confocal system and is the part we used for raster
scanning the sample, as well as collecting the photon signals from the sample. A typical scanning
component contains inputs from the external laser sources, fluorescence filter sets and
dichromatic mirrors and a piezo raster scanning system.
Figure 2.1. Conceptual Figure of Confocal Microscope. A scheme showing a conceptual basis of
a modern confocal microscope which consists of laser light sources, detectors, sample stage
filters, and pinholes.
2.1.2 Principles of Fluorescence Resonance Energy Transfer
Fluorescence resonance energy transfer between two dyes, donor and acceptor, has proven to be a powerful spectroscopic technique for measuring distances within molecular systems.
Excitation energy of the donors is transferred to the acceptor via an induced dipole-dipole 21
non-radiative interaction.7-13 FRET efficiency measures the relative populations in an induced
dipole interaction via energy transfer. The efficiency of energy transfer can be determined by
spectroscopic approach. The transfer efficiency, E, is given by energy transfer results in a decrease in fluorescence measurable parameters. However, to study kinetics in ensemble
measurements using fluorescence intensity and excited-state lifetime measurements of the donor
and FRET, the reactions have to be synchronized to be at the initial step. To probe dynamic
information of a system, we subsequently measure the decay of the synchronized signal as a
function of time. To quantify the ensemble measurements FRET signal, the molecules have to be
prepared in one state before transferring energy to the acceptor molecules.
1.0
0.8
R =5.4nm 0.6 0 FRET E 0.4
0.2
0 2 4 6 8 10 Distance (nm) Figure 2.2. FRET Efficiency vs Inter-Dye Distance Curve. A calculated sinusoidal shaped
function curve of FRET Efficiency versus distance between two dye molecules in question is
shown. The R0 which corresponds to a 50% of FRET efficiency of Cy3-Cy5 dye pair is 5.4nm. 22
Fluorescence resonance energy transfer is a form of electronic energy transfer between
fluorescent, typically organic, molecules. The energy transfer process between the donor and
the acceptor molecules is via the non-radiative energy transfer mechanism involving a virtue photon. The excited-state lifetime of the donor molecule is reduced in such energy transfer dynamics which is different from an emission reabsorption mechanism. The nature of such energy transfer processes between the donor and the acceptor molecules is not via transmission of photons. Historically, FRET is referred to as an energy transfer by inducing electronic resonance between the donor and acceptor molecules. Effective energetic coupling of FRET between the donor and acceptor molecules also requires a emission and absorption spectral overlap between the donor and acceptor molecules. Theoretically, such a spectral overlap bundles a lot of complicated information into a simple functional form which is firstly derived by
Forster. The spectral overlap includes nuclear overlap factors, which are separated from the
electronic coupling term by the Born-Oppenheimer approximation, since the photon absorption is considered instantaneous, which turns the spectral overlap into the form of quantum mechanical coupling factors. Energy conservation and nuclear overlap factors, separated from the electronic coupling by the Franck-Condon principle, are shown to relate emission and absorption events of the donor and acceptor molecules.7-13 The energy transfer rate can be written
as:
23
if the electronic coupling is independent of energy, then we can write,
which describes the rate of the energy transfer process.
The electronic coupling between the donor and the acceptor molecules can be described by a coulombic contribution part and a short range contribution part. It is assumed that the coulombic part plays a major role in the energetic coupling between the donor and acceptor molecules.
In addition to the dipole-dipole interaction, an orientation factor is also taken into account. This orientation factor describes the rotation of the dipoles of our dye molecules used in our FRET measurements.
However, in our single-molecule experiments the orientation factor is fixed to be 2/3. Such fact is due to the experimental condition of our single-molecule experiments. The typical
time-resolution of single-molecule experiments is at the millisecond time scale, yet single dye orientation dynamics is at the picosecond time scale. To our first approximation we only need to use the averaged orientational factor.
Single-molecule fluorescence resonance energy transfer (single molecule FRET), which applies FRET at single molecule level, is a measurable technique for studying real-time 24
structural dynamics of individual biomolecules, with measuring distance typically in 30-80 Å
range. Generally, a donor-acceptor pair is attached to two specific sites of one or two target molecules, and the energy transfer from donor to acceptor occurs through non-radiative induced
dipole-dipole interactions. Practically, we use the distance dependent formula for distance
conversion in our single-molecule FRET experiments. The energy transfer efficiency (EFRET)
depends on the inter-distance between the donor fluorophore and acceptor fluorophore:
1 EFRET 6 1+rR / 0
where r is the separate distance between two fluorophores, the FRET donor and acceptor, respectively. R0, as the Förster radius, is a function of dipole orientations of two fluorophores, refractive index of the medium, spectral overlap integral between donor emission and acceptor absorbance, and quantum yield of the donor as discussed in details above.
Figure 2.3. Conceptual Figure of Protein Folding FRET. A cartoon representing using smFRET to monitor single-molecule protein, DNA and various biomolecule conformational motions. By monitoring emission intensities from donor and acceptor organic dye molecules, conformational 25
information can be obtained from experimental data.
Figure 2.4. Conceptual Figure of FRET. Energy levels involved in typical FRET experiments.
The laser light source is used to first excite the donor molecule and then the donor molecule
transfers its excitation energy to the acceptor molecule via non-radiative dipole-dipole interaction.
The energy transfer efficiency depends on the distance between the donor and acceptor
molecules making FRET highly sensitive to a distance change.
2.1.3 Signal Detection techniques: Introduction to APD
Avalanche photodiode (APD) is used in our single-molecule experiments due to its low dark count and high photon to electron transition efficiency. It is a highly sensitive tool to probe molecular scale dynamics by recording molecular scale signal photon by photon. The time-resolution in our experiment is typically in milliseconds, roughly the same scale as protein conformational dynamics. An avalanche photodiode is a semiconductor-based photodetector (photodiode) which is operated with a relatively high reverse 26
voltage. The carrier generation process amplifies the low signal; subsequently we reach single
photon counting sensitivity in our single-molecule experiments. The avalanche process effectively
amplifies the photocurrent which effectively turns low signals to measurable signals in our
experiments. Therefore, avalanche photodiodes can be used for sensitive detections.
Figure 2.5. A Schematic Representation of APD. A schematic representation of the working
mechanism of the typical avalanche photodiode.
2.2 Experimental Details
2.2.1 Experimental Setup of Single-Molecule FRET Combined with Confocal
Microscope
We use single-molecule photon-stamping spectroscopic approach to record FRET
trajectories of CaM at different concentrations of denaturant solvents. Using this approach, we
are able to record the emission photon time trajectories from both the donor and acceptor with
specific detection time for each detected photon. The experimental setup is an inverted confocal microscope (Axiovert 200, Zeiss) that uses a crystal laser (532nm CW) as the light source for excitation. The laser beam focuses through a 100× oil immersion objective lens (1.3 27
NA, 100×, Zeiss) onto the upper surface of cover slip after the excitation light is reflected up by a dichroic beam splitter (z532rdc, Chroma Technology). To obtain confocal microscopy image,
we use an x-y closed-loop piezo position scanning stage for raster-scan of the sample sandwich
(Figure 2.6A). The fluorescence is collected through the same objective, and the FRET photon signal is split by a dichroic beam splitter (640dcxr, Chroma Technology) into two different
wavelengths. We use two Si avalanche photodiode single photon counting modules
(SPCM-AQR-16, Perkin Elmer Optoelectronics): 570nm for the donor channel and 670nm for the acceptor channel.14, 15
We use the same single-molecule photon stamping approach to record FRET trajectories at
different concentration of C28W. This approach records photon emissions from donor and acceptor channels one by one with arrival times, and the intensity trajectory can be constructed
as a function of time. Förster resonance energy transfer or fluorescence resonance energy transfer
(FRET) is a certain type of energy transfer realized by non-radiative dipole-dipole
interaction. The experimental setup is an inverted confocal microscope (Axiovert 200, Zeiss)
which uses a crystal laser (532nm CW) as the light source for excitation (Figure 2.6). The laser
beam focuses through a 100× oil immersion objective lens (1.3 NA, 100×, Zeiss) onto the upper
surface of the cover slip after reflected up by a dichroic beam splitter (z532rdc, Chroma
Technology). To obtain confocal microscopy images, we use an x-y closed-loop piezo position
scanning stage for raster-scan of the sample sandwich. The fluorescence is collected through the
same objective and the signal is split by a dichroic beam splitter (640dcxr) into two different
wavelengths: 570nm and 670nm which are the emission wavelengths of Cy3 and Cy5 28
respectively. To detect the signal from the two channels, two Si avalanche photodiode single photon counting modules (SPCM-AQR-16, Perkin Elmer Optoelectronics) are used for recording
the photons from the donor and acceptor.
Figure 2.6. Our Single-Molecule Setup. (A) Single-molecule fluorescent experimental setup. It
is an inverted confocal microscope (Axiovert 200, Zeiss) which uses a laser (532nm CW) as the
excitation light source.35, 40 Fluorescence photons from donor and acceptor are both directed onto
avalanche photodiodes to acquire emission images and FRET intensity trajectories. (B) Image
obtained from confocal microscope of single CaM molecules. The left-hand side is the image
obtained from the Cy3 donor channel and the right-hand side is the image obtained from the Cy5
acceptor channel. The bright spots are single molecules with diffraction limited (~300nm in 29
diameter) image. Each image is obtained by laser focus raster-scanning and collecting fluorescence of Cy3-Cy5 D-A labeled single-molecule CaM.
2.2.2 Materials and sample preparation
Sample Preparation and Characterization. The CaM is mutated with cysteine residues on
N-terminal domain at residue 34 and C-terminal domain at residue 110, and a FRET dye pair
Cy3/Cy5 as donor/acceptor is covalently tethered onto the protein via thiolation reactions. In
our experiment, the change of FRET efficiency (EFRET) ranges from 0.6 to 0.2 corresponding to
the donor-acceptor (D-A) distance change of about 5.0 to 6.7 nm, and the Forster radius R0 of
Cy3-Cy5 pair is ~5.4 nm. The samples for single-molecule conformational folding-unfolding
dynamics measurements are prepared inside a 1% agarose gel with 99% of buffer solution (Type
VII, Sigma). We make samples of CaM into different concentrations of denaturant GdmCl in
the mixture of 1 nM CaM, 1.25μL and oxygen scavenger with Trolox solution to obtain a 10μL mixture of enzyme and denaturant solvent. The Trolox solution is prepared previously by
dissolving about 1 mM 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1
mg/mL glucose oxidase, 0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent
dyes from photobleaching or blinking as a result of triplet state oxygen quenching as well as
other photophysical processes. We then heat the 10μL 1% agarose gel just above its
gel-transition temperature (26°C) and quickly mix the above enzyme solution with denaturant
solution and the gel between two clean cover glasses to form a sandwiched sample. All
solutions are prepared with 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES buffer) 30
at pH 7.4. To probe conformational dynamics of single-molecule enzymes at different
concentration of denaturant solvents, we carry out concentration dependent experiments with
different ratio of mixture in the sample.
Trolox+Oxygen CaM GdmCl Agarose Gel Scavenger ～1 nM CaM+0M 0.2μL 200nM 0μL 8M 9.8μL 10μL Gdmcl ～1 nM CaM+1M 0.2μL 200nM 2.5μL 8M 7.3μL 10μL Gdmcl ～1 nM CaM+2M 0.2μL 200nM 5μL 8M 4.8μL 10μL Gdmcl
Table 2.1. List of concentrations used in our experiments.
In our protein-protein interaction experiments, the single CaM molecule has mutation on
N-terminal domain at residue 34 and C-terminal domain at residue 110, and fluorescent dye pair
Cy3/Cy5 was tethered onto the protein via thiolation. These two dyes serve as a spectroscopic ruler for the measurement of conformational fluctuation of the protein molecule interacting with
C28W. In our experiment, the change of FRET efficiency corresponds to the distance change of about 2 nm. On the other hand, the Forster radius R0 of Cy3-Cy5 pair is ~5.4 nm, so the distance
change of the two dyes monitoring the conformational change falls into measureable range. In
our experiment, the samples for single-molecule conformational folding-unfolding dynamics measurements are prepared inside the agarose gel (1% by weight, Type VII, Sigma). For example, we make a sample of CaM into 2 M of denaturant solvent GdmCl by first mixing 0.2μL 200 nM
CaM, 2.5μL 8 M GdmCl, 0.1mM CaCl2 and 8.55μL oxygen scavenger with Trolox solution to obtain a 10μL mixture of protein and denaturant solvent with 100nM C28W. The Trolox solution 31
is made previously by dissolving about 1 mM
6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1 mg/mL glucose oxidase,
0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent dye from
photobleaching or blinking as a result of triplet state formation or other irreversible
photophysical processes. We then heat the 10μL 1% agarose gel just above its gel-transition
temperature (26°C) and quickly mix the above protein with denaturant solvent solution with the
gel between two clean cover glasses to form a sandwich. All solutions are prepared with
Phosphate buffered saline (PBS buffer) at pH 7.4. Since we want to probe conformational
dynamics of single protein molecule at different concentration of C28W peptide, we carry out concentration dependent experiments with different ratio of mixture in the sandwich as listed
below.
Trolox+Oxygen Agarose CaM GdmCl Scavenger Gel ～1 nM CaM+2M 0.2μL 200nM 2.5μL 8M 9.8μL 10μL Gdmcl+100 nM C28W ～1 nM CaM+2M 0.2μL 200nM 2.5μL 8M 8.55μL 10μL Gdmcl+500 nM C28W ～1 nM CaM+2M Gdmcl+1000 nM 0.2μL 200nM 2.5μL 8M 7.3μL 10μL C28W
Table 2.2. List of concentrations used in our folding-binding experiments.
In our single-molecule crowding experiment, all solutions are prepared with HEPES buffer at pH
7.4. Since we want to probe conformational dynamics of single enzyme molecule at different
concentration of Ficoll 70, we carry out concentration dependent experiments with different ratio
of mixture in the sandwich. 32
Figure 2.7. A Cartoon of Our Sample. We prepare our samples in agarose gel 1% by weight.
The agarose gel formed pores with diameter about 200 nm. The single protein molecules have
the size of approximately 6 nm. The protein molecules which are much smaller in dimensions
compared to the pore size can freely rotate inside the pore.
2.2.3 Statistical Analyses of Single-Molecule Intensity Trajectories.
To analyze the FRET signal fluctuation trajectories in order to obtain the CaM conformational folding-unfolding conformational dynamics, we have applied a newly developed
2D regional correlation mapping analysis to analyze our single-molecule photon-stamping trajectories. The 2D regional correlation mapping analysis calculates a two-dimensional
cross-correlation amplitude distribution and acts as a guide to find the anti-correlated portion of a selected trajectory. In such analysis, each of the single-molecule FRET trajectories are scanned
with different starting and ending time, and the cross-correlation amplitude of each time segment
with distinct starting and ending time are calculated. Color bar is used to indicate the amplitude
of cross-correlation in order to locate the anti-correlated portion with negative value of
cross-correlation amplitudes. 33
stop tstop t Ccross(,:)()()()() tt start stop ItItdtAD ItItAD tstart tstart
Where IA and ID are the photon count intensities of donor and acceptor, and tstart and tstop give the
scanning window width. The cross-correlation functions are calculated with different tstart and tstop along a pair of single-molecule FRET trajectories {IA(t)} and {ID(t)}. The detailed description of the analysis algorithm can be found elsewhere. Applying this method, we are able to identify the time segments along a specific trajectory with a strong anti-correlated cross-correlation indicated by a negative value of cross-correlation amplitudes (cold color).
Typically, single-molecule FRET trajectories are dominated by shot noises or averaged intensity drifts as a result of local environment fluctuations. Our two-dimensional cross-correlation
amplitude distribution analysis enables us to locate true anti-correlated segments from single-molecule FRET trajectories for further dynamics analyses.
We apply auto-correlation and cross-correlation calculations to analyze our single-molecule
photon-stamping trajectories after the identification of each anti-correlated single-molecule time segments. The cross-correlation and auto-correlation function are defined as:
IAD0 I t IA 0 IADD I t I Ctcross IIAD00 IIIIA 00 AD D
IAA0 I t IA 0 IAAA I t I auto Ct 22 IA 0 IIAA0
where IA(t) and ID(t) representing acceptor and donor intensitie, and
means of the intensity trajectories respectively. 34
Figure 2.8. TCAD Map in a Typical Single-Molecule Experiment. (Upper panel) The TCAD
map and cross correlation functions calculated from a simulated two-band fluctuation trajectory
that consists of three sections: cross-correlated (I: 1–500 data points), non-correlated (II: 501–
1000 data points) and anti-correlated (III: 1001–1500 data points). (A) 2D regional correlation
analysis by TCAD mapping. The hot color represents the positive amplitude and the cold color
represents the negative amplitude. (B) Correlation functions calculated from the three sections of
correlated, non-correlated, and anti-correlated fluctuation data corresponding to sections I, II, III, and the whole data trajectory (I + II + III). It is evident that a conventional correlation calculation from the whole data trajectory gives no correlation amplitude, whereas the 2D regional 35
correlation analysis gives definitive analysis of the correlation behavior for each specific
fluctuation in the long trajectory. (Lower panel) An example of 2D regional correlation analysis
of single-molecule FRET fluctuation data. The experimental FRET two-band (D – A) fluorescence intensity fluctuation trajectory is measured from a D–A labeled kinase enzyme
protein molecule showing a conformational change fluctuation in a buffer solution. (C) A TCAD
map calculated from a two-band (D–A) FRET fluorescence fluctuation trajectory. The red and
black trajectories are the donor and acceptor signals, respectively. (D) Cross correlation functions
calculated from different sections of the trajectory. It is clear that the dynamics can be averaged
out if only a whole-trajectory calculation is carried out. The anti-correlated FRET fluctuations can only dominate the fluorescence intensity trajectories in fraction of time periods but not all the time due to non-correlated and correlated thermal fluctuation background noises.
2.3 Protein Folding Dynamics in Condensed Phases
The new single-molecule techniques have allowed the investigation of the mechanism of
formation of basic structural elements of proteins. Since the basic structure elements of
proteins fold at a faster time scale than typical measurement time scales of single-molecule
FRET spectroscopy, which is at the millisecond time scale, it cannot be directly probed. However,
the folding dynamics speed limit can be calculated and simulated. The measured protein folding
dynamics time scale is often much longer than the theoretical limit. Such elongation of time
scales typically implies the existence of a folding barrier and multiple intermediate states of
protein folding. In other words, by directly measuring protein folding dynamics using
single-molecule techniques, we can directly measure the height and energetic features of the 36
protein folding dynamics. We employ condensed phase dynamic models to model protein
folding dynamic processes in condensed phases. The simplest model describing chemical
dynamics in the condensed phase is Kramer’s theory. Another fact, which is not so obvious, is
that sometimes for a simple protein involving fewer than 100 amino acids the activation barrier
of the protein folding process may disappear. The measured folding time of these proteins serves
as a benchmark to further understand larger and more complex proteins involving more amino acids. Such is the hypothesis we use, when we try to understand the energetic features of
protein folding dynamics in condensed phases.
Direct applications of Kramer’s theory of unimolecular reaction rates in condensed phases
will give us an upper bond estimation of the height of the activation barrier. Such theory assumes
that the activation barrier crossing dynamics can be described by a one-dimensional diffusion
along a reaction coordinate. The time of the folding dynamic process can be expressed by
τfolding = 2πτlimit exp(ΔG/kT) where τfolding is the folding time of single-molecule CaM measured in our experiment, τlimit is the theoretical upper bound of single-molecule CaM folding time, and ΔG is the free energy
barrier and k is the Boltzmann’s constant T is the temperature.
The vast majority of measurements yield the formation time of a loop is less than 0.1 μs, and
α-helices formation is approximately 0.5 μs. The formation time of β hairpins is greater than
0.5 μs. From these data we understand the theoretical folding time limit should be at the
microsecond scale. By using single-molecule FRET spectroscopy we further measure the
distance changes in protein folding dynamic processes. We also can measure the characteristic 37
timescale of protein folding dynamic processes. From these two, we further can characterize
the dynamic behavior of protein folding in condensed phases. The conformational diffusion
coefficients calculated from the distance changes and folding time can give us a quantitative understanding of the energetic features of condensed phase protein folding dynamic processes.
2.4 Theory of Polymer Solutions
Proteins are heteropolymer made of 20 different monomer types (amino acids). They self-assemble into well-defined three dimensional structures to perform biological functions. In principle, protein solutions can be understood as polymer solutions. Protein dynamics is also a form of polymer dynamics. The denatured state of proteins has been described for many years as
being similar to a random coil-like polymer. By tuning the chemical property of the polymer solution, we performed our single-molecule folding-unfolding experiments by changing the
solvent properties. The protein molecules subsequently undergo conformational changes in
different solvent environments. Protein molecules change from the unfolded state to the folded
state. This phase transition is known in polymer science as the coil-globule transition. In good
0.55 solvents, the radius of gyration is Rg = 0.345N nm. This formula is confirmed by small-angle
X-ray scattering. The hydrodynamic radius is 1.5 times smaller than the radius of gyration.
Since linear scaling theory holds for small degrees of polymerization, using the linear length scaling suggested by the homopolymer collapse theory, theoretical upper bound of single-molecule CaM folding time can be estimated by a simple diffusion model.
Synthetic polymers such as PEG, Ficoll are commonly used as a means to simulate
molecular crowding in living cells. Polymers of different sizes were used in the past to study 38
protein-protein associations under crowded environments. Such studies have a significant
contribution to the understanding of diseases resulting from over-expression of proteins inside
living cells. However, the whole polymer solution and matrix is highly dynamic instead of
static. So our single-molecule study proves to be a powerful tool to study such complex dynamic properties.
Figure 2.9. A Schematic Representation of Molecular Crowding. Schematic representation of
proteins in crowded polymer solutions. As we change the concentration of the matrix polymer solution, the protein-protein interaction pattern changes.
2.5 References
1 Nie, S.; Zare R. N. Optical Detection of Single Molecules. Annu. Rev. Biophys. Biomol.
Struct. 1997, 26, 567-596.
2 Minsky, M. Microscopy Apparatus: US 3,013,467.
3 Davidovits, P.; Egger, M. D. Scanning Laser Microscope. Nature 1969, 223 (5208): 831. 39
4 Egger, M. D. (1971). Scanning Laser Microscope for Biological Investigations. Applied
optics. 1971, 10 (7): 1615–1619
5 Amos, W.B.; White, J.G.: How the Confocal Laser Scanning Microscope Entered Biological
Research. In: Biology of the Cell / under the Auspices of the European Cell Biology
Organization. Band 95, Nummer 6, September 2003, S. 335–342
6 Prasad, V.; Semwogerere, D.; Weeks, E.R. Confocal Microscopy of Colloids. J. Phys.: Cond.
Mat. 2007 19, 113102.
7 Förster, T. Zwischenmolekulare Energiewanderung und Fluoreszenz. Annalen der Physik
1948, 437, 55-75.
8 Förster T. Fluorescence of Organic Compounds Gettingen: Vandenhoeck & Ruprecht:
1951:312.
9 Stryer, L.; Haugland, R. P. Energy Transfer: A Spectroscopic Ruler. Proc. Natl. Acad. Sci.
USA 1967, 58, 719-730.
10 Clegg, R.M. Fluorescence Resonance Energy Transfer. Curr. Opin. in Biotech. 1995, 6:103-l
10.
11 Ha, T.; Enderle, T.H.; Ogletree, D.F.; Chemla, D.S.; Selvein, P.R.; Weiss, S. Probing the
Interaction Between Two Single Molecules: Fluorescence Resonance Energy Transfer
Between a Single Donor and a Single Acceptor. Proc. Natl. Acad. Sci. USA 1996, 93,
6264-6268.
12 Deniz, A.A.; Dahan, M.; Grunwell, J.R.; Ha, T.; Faulhaber, A.E.; Chemla, D.S.; Weiss, S.;
Schultz, P.G. Single-Pair Fluorescence Resonance Energy Transfer on Freely Diffusing 40
Molecules: Observation of Förster Distance Dependence and Subpopulations Proc. Natl.
Acad. Sci. USA 1999, 96, 3670–3675.
13 Ambrose, E.J. A Surface Contact Microscope for the Study of Cell Movements. Nature 1956,
178 (4543): 1194.
14 Yanagida, T.; Sako, Y.; Minoghchi, S. Single-Molecule Imaging of EGFR Signalling on the
Surface of Living Cells. Nature Cell Biology 2000, 2 (3): 168–172.
15 He, Y.; Lu, M.; Lu, H.P. Single-Molecule Photon Stamping FRET Spectroscopy Study of
Enzymatic Conformational Dynamics. Phys. Chem. Chem. Phys., 2013, 15, 770-775.
41
CHAPTER III. PROBING SINGLE-MOLECULE PROTEIN FOLDING
CONFORMATIONAL DYNAMICS USING SINGLE-MOLECULE FRET
SPECTROSCOPY
This chapter is dedicated to the study of single-molecule protein folding using single-molecule FRET.
3.1 Introduction
Single-molecule fluorescence spectroscopy is powerful to study complex biological processes one molecule at a time.1 Sub populations involved in enzymatic reactions2,3, protein folding dynamics4 and other dynamic processes5,6 can be well characterized without ensemble
averaging. Single-molecule fluorescence resonance energy transfer (smFRET) spectroscopy monitors conformational changes of dye labeled single biomolecules with sensitivity down to a 2
nm to 10 nm.7 Such distance sensitivity and millisecond temporal resolution makes smFRET an
ideal tool to probe protein conformational dynamics.
Since Anfinsen first posed the question about the spontaneity of proteins folding into their native state through an enormous number of possible conformations 50 years ago, the protein
folding problem, although with significant progress, still remains to be a fascinating topic.8
Theoretically, the protein folding process can be understood as a navigation on a funnel-shaped
energy landscape towards a global energy minimum, the folded state.9-11 This multi-dimensional
energy landscape can be rugged and extremely complex involving multiple folding routes and
metastable states. Experimentally, mainly two types are involved: force-probe techniques using 42
atomic force microscopy (AFM) or optical tweezers,12 and fluorescent spectroscopy especially smFRET. Single-molecule FRET is previously applied to reveal folded and unfolded protein subpopulations from otherwise ensemble average population distribution.4, 13 Subsequently, using smFRET, there are advances in characterization of protein unfolded state dynamics,13-15 protein collapse (from unfolded state to a compact yet folded state) dynamics16-18 and protein folding dynamics.19 Most recently, based on previous work,20 a remarkable application of smFRET to determine the transition path times of protein folding is achieved.21 The average transition path times are reproduced well in an all-atom explicit solvent simulation on a special-purpose super computer ANTON, which recently become available.22 On the other hand, distinct from two-state folders, protein with ‘one-state’ downhill folding process is also investigated via smFRET, and its dynamics well specified.23 For the studies mentioned above, two-state folders with two distinct folded and unfolded conformations serve the purpose well. However, when it comes to large protein with more than 100 amino acids, this simple two-state folding dynamic scheme does not apply. A recent example is a study of a 214 amino acid protein adenylate kinase, six distinct folding intermediates may exist.24
Calmodulin (CaM) is a 148-residue protein responsible for intracellular calcium-sensing.
It is crucial in many biological processes including muscle contraction and energy metabolism.25,
26 CaM has two globular domains, and the conformational dynamics of the two domains is under
extensive studies.27 Traditional methods involving nuclear magnetic resonance and X-ray
crystallography have provided detailed insights into the mechanisms and dynamics of CaM
conformational motions.28-30 As a result of the flexibility and the dumbbell shape of the protein, 43
with dye labeling at the two domains, it is possible to monitor the conformational dynamics of
CaM with single-molecule spectroscopy, such as smFRET.27 The typical time-resolution can be milliseconds which is the characteristic time scale of protein motions. Similarly, free diffused types of experiments have been carried out on single CaM in different concentrations of denaturant urea. However, dynamic information is limited in such experiments due to the limitation of the length of single-molecule trajectories (typically microsecond scale).31-39
In this chapter, we use single-molecule FRET spectroscopy to probe the folding-unfolding conformational dynamics of CaM under the mild denatured condition of denaturant guanidinium
chloride (GdmCl). The critical concentration of GdmCl, at which single proteins undergo folding-unfolding conformational fluctuation, has been achieved. Subpopulation of proteins with folded and unfolded states equally populated is obtained. These results allow us to address the following intriguing questions about single-molecule protein folding-unfolding dynamics. What exactly are the sequences of microscopic events that ultimately take single CaM molecules from the unfolded conformation to the folded native states? Is it a simple two-state folding dynamic scheme or more complex process involved multiple states? Is there a distribution of such sequences or folding transition paths, and what will be the underlying energy landscape nature of such a folding channel distribution? Is it static disorder or dynamic disorder associated with such an energy landscape or is it a highly dynamic energy landscape with certain distinct “ruggedness” present along each folding routes?
3.2 Materials and Methods
3.2.1. Sample Preparation and Characterization. 44
The CaM is mutated with cysteine residues on N-terminal domain at residue 34 and
C-terminal domain at residue 110, and a FRET dye pair Cy3/Cy5 as donor-acceptor (D-A) is
covalently tethered onto the protein on mutated cysteine residue 34 at N-terminal domain and on mutated cysteine residue 110 at C-terminal domain via thiolation reactions.40 In our experiment,
the change of FRET efficiency (EFRET) ranges from 0.6 to 0.2 corresponding to the D-A distance
change of about 5.0 nm to 6.7 nm in single-molecule protein conformation, and the Forster radius R0 of Cy3-Cy5 pair is ~5.4 nm at which EFRET of Cy3-Cy5 is 0.5. The samples for
single-molecule conformational folding-unfolding dynamics measurements are prepared with a 1%
agarose gel containing 99% of buffer solution (Type VII, Sigma). Single CaM molecules can rotate freely to perform biological functions and chemicals such as electrolytes and denaturant
GdmCl can diffuse uninterruptedly.6, 40, 41 We make samples of CaM into different concentrations of denaturant GdmCl in the mixture of 1 nM CaM, 1.25μL and oxygen scavenger with Trolox solution to obtain a 10μL mixture of protein and denaturant solvent GdmCl solution. The
Trolox solution is prepared by dissolving about 1 mM
6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1 mg/mL glucose oxidase,
0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent dye from
photobleaching or blinking due to the triplet state oxygen quenching as well as other
photophysical processes.40 We then heat the 10μL 1% agarose gel just above its gel-transition
temperature (26°C) and quickly mix the above protein solution with denaturant solution GdmCl
and the gel between two clean cover glasses to form a sandwiched sample. All solutions are
prepared with 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES buffer) at pH 7.4 45
with 1mM EGTA.38 To probe conformational dynamics of single-molecule protein at different
concentration of denaturant solvent, we carry out concentration dependent experiments with different ratio of mixture in the sample.40
3.2.2. Single-Molecule Imaging and FRET Measurements.
We use single-molecule photon-stamping spectroscopic approach to record smFRET D-A trajectories of CaM at different concentrations of denaturant solvent GdmCl. Using this approach, we are able to record the emission photon time trajectories from both donor and acceptor with specific detection time for each detected photons. The experimental setup is an inverted confocal microscope (Axiovert 200, Zeiss) that uses a laser (532nm, CW) as the light source for excitation.40 The Laser beam focuses through a 100× oil immersion objective lens (1.3
NA, 100×, Zeiss) onto the upper surface of cover slip after the excitation light is reflected up by a dichroic beam splitter (z532rdc, Chroma Technology). To obtain confocal microscopy image,
we use an x-y closed-loop piezo position scanning stage for raster-scan of the sample sandwich
(Figure 3.1A). The fluorescence is collected through the same objective, and the FRET photon signal is split by a dichroic beam splitter (640dcxr, Chroma Technology) into two different
wavelength 570nm for the donor channel and 670nm for the acceptor channel with two Si
avalanche photodiode single photon counting modules (SPCM-AQR-16, Perkin Elmer
Optoelectronics). A detailed description of the experimental setup is reported previously. 35, 40 46
Figure 3.1. Our Single-Molecule Imaging System. (A) Single-molecule fluorescent experimental setup. It is an inverted confocal microscope (Axiovert 200, Zeiss) which uses a laser (532nm CW) as the excitation light source.35, 40 Fluorescence photons from donor and acceptor are both
directed onto avalanche photodiodes to acquire emission images and FRET intensity trajectories.
(B) Image obtained from Confocal Microscope of single CaM molecule. The left-hand side is
image obtained from the Cy3 donor channel and the right-hand side is image obtained from the
Cy5 acceptor channel. The bright spots are single molecules with diffraction limited (~300nm
in diameter) image. Each image is obtained by laser focus raster-scanning and collecting
fluorescence of Cy3-Cy5 D-A labeled single-molecule CaM.
47
3.3 Results and Discussion
3.3.1 Single-Molecule FRET Trajectories Monitored Unfolding of Single CaM
Molecules.
Figure 3.1B shows typical images from our smFRET imaging microscopy using an inverted
confocal microscope. By raster-scanning the sample, a 20μm×20μm sample image yields
bright spots with 300nm resolution of single molecules. We attribute that the imaging spot features are due to single CaM molecules confined in agarose gel. Single CaM molecules embedded in agarose gel can rotate freely to perform its biological functioning and chemicals such as electrolytes and denaturant GdmCl can diffuse uninterruptedly.40, 42 From each specific single-molecule CaM imaging spot, we are able to obtain continuous D-A fluorescence intensity trajectories (Figure 3.2A). Typically, we gather a number of single-molecule fluorescence intensity trajectories at different concentrations of denaturant GdmCl, and we calculate the EFRET of each of the single-molecule fluorescence intensity trajectories measured using this equation.
ItA() EtFRET () AA IAD()() t I t DD
Where A and D are the emission quantum yields of acceptor and donor dyes, respectively, and A and D are the acceptor and donor detection efficiencies, respectively. Here the
AA correction factor is ~1 in our experiment conditions. DD 48
Figure 3.2. Typical Trajectories and Data. (A) Typical D-A signals and EFRET trajectories. Green and red lines indicate the donor and acceptor channel respectively. (B) Single-molecule EFRET trajectory calculated following formula. (C) The histogram distribution from EFRET trajectory gives the average EFRET of a certain single-molecule. (D-F) Distribution of EFRET of different samples at different concentration of GdmCl, we carry out concentration dependent experiment of GdmCl of 0M 1M and 2M. The decrease in EFRET mean values characterizes the unfolding of CaM molecule at higher concentration of denaturant solvent.
To identify the specific condition that facilitates the CaM to have a measurable probability of staying either folded or unfolded states, we have characterized the folding and unfolding state 49
distributions by single-molecule fluorescence intensity trajectories measurements of EFRET under
different denaturant conditions (Figure 3.2D-2F). The decrease in EFRET mean values of the single-molecule CaM EFRET distributions are due to the increased unfolding probability of the single CaM molecules under the increased denaturant GdmCl concentrations from zero to 2 M.
The EFRET distribution consists of both the folded subpopulation with EFRET 0.6 and unfolded
subpopulation with EFRET 0.2. Single-molecule FRET spectroscopy allows folded and unfolded
molecules to be distinguished on the basis of the significant distance dependence of energy
transfer between smFRET donor and acceptor dyes. More importantly, single-molecule
sub-populations of partially folded with equal amount of time dwelling on folded and unfolded
conformational states can be thoroughly examined by studying detailed fluctuation dynamics of
each single-molecule fluorescence intensity trajectory. We locate and record singe-molecule trajectories from individual molecules undergoing spontaneous folding-unfolding conformational fluctuation under the condition providing a roughly 50%-50% folding-unfolding conformational state probability, i.e. the transition midpoint. At the titration midpoint, approximately half of
the population of CaM is in folded conformational state whereas another half of the population is
in unfolded conformational state. Our ensemble-averaged titration experiment of Cy3-Cy5 D-A labeled CaM molecules in solution with different concentration of GdmCl yields 2M concentration of denaturant GdmCl to be the titration midpoint where the folded and unfolded conformational states of CaM molecules are equally populated (Supporting Information). In term of single-molecule experiments, such titration midpoint condition is ideal for studying spontaneous folding-unfolding conformational fluctuation dynamics, since individual molecule 50
undergoes spontaneous conformational fluctuations without external driving force. The EFRET
distribution measured under no GdmCl condition, at which CaM molecules are in folded native
states, has a mean of 0.55 ± 0.07 that corresponds to 5.2 ± 0.2 nm D-A distance, a folded
conformation state; whereas the distribution of EFRET measured under 2M GdmCl has a mean of
0.36 ± 0.17 that corresponds to 6.1 ± 0.8 nm D-A distance, an unfolded conformation state. On
average, a decrease in EFRET corresponds to distance change between the D-A Cy3-Cy5 dye pair
which further indicates a conformational distance change along the FRET coordinate.
Therefore, under the unfolding effect of denaturant GdmCl, we measured that the D-A Cy3-Cy5
dye pair distance change of 0.9 ± 1.0 nm for the folded and unfolded states of CaM. In our
experiments, single-molecule CaM is embedded in 1% agarose gel in which a single CaM
molecule can rotate freely to perform its biological functions, and chemicals, such as electrolyte and denaturant GdmCl, can diffuse uninterruptedly.40, 42
3.3.2. Autocorrelation Analyses of CaM Folding-Unfolding Conformational Fluctuation
Dynamics.
We analyze the fluctuation dynamics of our single-molecule FRET trajectories by
calculating the autocorrelation functions of selected segments using our 2D regional correlation
mapping analysis.39, 40 By applying the 2D regional correlation mapping analysis, we identify
specific anti-correlated segments along a trajectory and zoom into that segment to study detailed
dynamic fluctuation information by calculating autocorrelation and cross-correlation functions.
Fitting the autocorrelation functions with single exponential functions, we are able to
characterize the rate of protein conformational fluctuation (Figure 3.3).39, 40 The correlation rate 51
of protein conformational fluctuation measured by single-molecule D-A fluorescence intensity fluctuation trajectories gives a broad distribution due to the local environment heterogeneity,
thermal fluctuations, dynamic disorder and static disorder.2-4 At low concentration of GdmCl, autocorrelation function analysis of single-molecule trajectories of CaM molecules shows a typical autocorrelation rate that corresponds to millisecond time scale, the characteristic
timescale of native state protein motions.2-4, 39, 40 Nevertheless, Figure 3.4B shows a significant
distinction of distributions of autocorrelation rates between different individual CaM molecules
under different concentration of denaturant GdmCl. The CaM molecules, in native states, show
more significant autocorrelation rates at millisecond time scale. However, the significant
correlation rates diminishes for unfolded CaM single-molecules, which is due to the unfolding of
CaM molecules turning to random coils under the denaturant GdmCl condition; and the correlation fluctuation rates of single-molecule protein regulated conformational motion becomes slower. The two-dimensional regional cross-correlation analyses help us to identify time segments along each single-molecule intensity trajectory with significant anti-correlations
(Figure 3.3F). We zoom in to study each of the anti-correlated time segments by calculating the
cross-correlation and autocorrelation respectively.
52
Figure 3.3. Correlation Analyses of Single-Molecule Data (A) A part of single-molecule intensity-time trajectories of the donor and acceptor from the long trajectories shown in Figure
2A. (B) Autocorrelation functions of the donor (green) and the acceptor (red) calculated from
single-molecule fluorescence intensity trajectory shown in (A). The time interval, we calculate
the autocorrelation functions and cross-correlation function is indicated by the blue frame. The
-1 fitted single exponentials (green and red) yield fluctuation rate kdonor = 2.2 ± 0.7 s and kacceptor=
-1 3.1 ± 0.6 s . (C) A part of calculated EFRET trajectory by using formula. (D) Cross-correlation
function from the single-molecule intensity-time trajectories of the donor and acceptor shown in 53
-1 (A). The fitted single exponentials (black) yield fluctuation rate kcross =2.0 ± 0.2 s which is
similar to the fluctuation rates captured by autocorrelation functions of the donor and the
acceptor. (E) Distribution of EFRET measured in (C) yields a mean of EFRET 0.42 ± 0.04. (F)
The result of analysis on the single-molecule donor-acceptor fluorescence trajectories shown in
(A). The cold color represents that the D-A intensity fluctuation is anti-correlated, whereas the warm color represents that the D-A is correlated.
The fluctuation dynamics of correlation function analyses yields fluctuation rates of conformational dynamics of single protein molecules.3, 4 Since the fitted exponential function of autocorrelation function has a similar fluctuation rate of donor and acceptor channel which indicates the autocorrelation come from the same source, the single-molecule protein
conformational fluctuations (Figure 3.3B and 3.3D). Fitted exponential function of
cross-correlation function yielding similar fluctuation rate further confirms the anti-correlated
cross-correlation function between the donor and acceptor fluctuation intensity trajectories with
the essentially same correlation rate within the error bar (Figure 3.3D), a typical anti-correlation
FRET D-A trajectory fluctuation dynamics showing a protein conformational motion measured by anti-correlated smFRET D-A intensity trajectories. Such protein conformational motion
captured by smFRET gives anti-correlated two-band D-A fluorescence intensity trajectories.
Both autocorrelation functions from the donor and acceptor signal trajectories and the anti-correlated cross correlation function between the donor and acceptor signal fluctuation trajectories have essentially the same fluctuation rate, which strongly indicates that the 54
fluctuations are dominated by the protein folding-unfolding conformational fluctuation probed
by the smFRET D-A signal fluctuation trajectory measurement (Figure 3). We focus on the autocorrelations from the donor channel only, and we plot the fitted exponential autocorrelation function rates at various concentrations of denaturants GdmCl in which single-molecule protein
CaM undergoes different conformational fluctuation dynamics as a result of different local environment. The time interval at which the autocorrelation functions are calculated, we also compute the EFRET (Figure 3.3A, 3.3C and 3.3E), and these two parameters, autocorrelation function fluctuation rate and EFRET, serve as a characteristic value to represent a local fluctuation dynamics. The two-dimensional contour plot of EFRET vs fitted autocorrelation function correlation rate is shown in Figure 4A. As the single CaM molecules get unfolded, not only the
EFRET decreases, but also the fluctuation rate of the autocorrelation function decreases.
Figure 3.4. Single-Molecule Conformational Fluctuation Dynamics. (A) Contour plot of EFRET
vs fitted autocorrelation function correlation rate. We see as the proteins become gradually
unfolded, the autocorrelation fluctuation rate of the protein dynamics become slower by a factor
of 100. We construct this contour plot by calculating autocorrelation function at a specific time
interval along a trajectory and compute the EFRET at this time interval (Figure 3.3A, 3.3C and 55
3.3E). These two parameters, autocorrelation function fluctuation rate and EFRET, correspond to one point on the contour plot, serving as a characteristic value to represent a local fluctuation dynamic behavior. (B) Distribution of fluctuation rate of correlation functions at various concentration of denaturant solvent. The autocorrelation fluctuation rates are 18 ± 10 s-1, 9 ±
11 s-1 , and 3 ± 3 s-1 at 0M GdmCl (blue), 1M GdmCl (green), and 2M GdmCl (red), respectively.
Quantitatively, the fitted exponential functions obtained from fitting the single-molecule
FRET intensity trajectory donor autocorrelation functions give the fluctuation rates from different single-molecule trajectories and distinct individual molecules at different concentrations of denaturant GdmCl. Single molecules experience different local environments and undergo distinct conformational fluctuation dynamics probed by autocorrelation function analyses.
Figure 4B, the distribution of these various autocorrelation fluctuation rates, shows a significant shift of the distribution as the concentration of GdmCl increases resulting in denaturing of single-molecule CaM which turns single-molecule CaM into random coils. From
autocorrelation fluctuation conformational dynamic analyses, the mean autocorrelation
fluctuation rates are 18 ± 10 s-1 , 9 ± 11 s-1 , and 3 ± 3 s-1 at 0M GdmCl, 1M GdmCl and 2M
GdmCl, respectively. We attribute the significantly different fluctuation dynamics to the CaM folding-unfolding conformational states and fluctuation dynamics under the different denature
GdmCl conditions, which create heterogeneous local environments. In 2M concentration of
GdmCl, CaM molecules denature into random coils without ordered secondary and tertiary structures, and the conformational dynamics probed by autocorrelation function reveals slow fluctuation dynamics at rate of 3 ± 3 s-1 which is a result of loss of regulated protein motion at the 56
timescale of millisecond as is expected for native state protein. The distribution of fluctuation
rates also become narrower as the single-molecule CaM unfolds in 2M denaturant GdmCl. The narrower distribution of conformational fluctuation rates is related to protein conformational space sampling speed which is an essential part of various recognition processes involved in biological function.2-4, 13, 35
To further understanding the folding-unfolding conformational fluctuation dynamics probed
by autocorrelation function analyses of single-molecule D-A fluorescence intensity trajectories
measured at the folding-unfolding titration equilibrium conditions, we use a kinetic model to account for the single-molecule protein CaM folding-unfolding conformational fluctuation
dynamics.3, 43, 44 Conventional kinetics experiments measure the relaxation of concentration of a
large ensemble of molecules after a perturbation (such as fast mixing or a temperature jump).
In contrast, single-molecule experiments measure the probability at specific states of an individual molecule conformational fluctuation, and the dynamic information can be extracted by measuring single-molecule spontaneous fluctuation dynamics at equilibrium; specified by the
Onsager’s regression hypothesis and the fluctuation dissipation theorem.44-46 The fluctuation dissipation theorem dictates that the relaxation of macroscopic non-equilibrium disturbances is governed by the same laws as the regression of spontaneous microscopic fluctuations in an equilibrium system.44-46 For a two-state spontaneous fluctuation dynamic model, the autocorrelation function directly probes the fluctuation dynamic process under detailed balance by reflecting the summation of forward and backward reaction rate kf + kb as the fluctuation rate of fitted exponential function of autocorrelation. We generalize this argument by expressing a 57
multiple-step fluctuation dynamic process by separately model the forward and backward reaction rate kf and kb by dividing the whole dynamic process into forward and backward half
reactions.43-46 For a three-state kinetic scheme, the mean first passage time of the rate process, or
reaction, is calculated by the flux method under detailed balance rate processes.43 We express
the observed forward and backward reaction rate by a polynomial of all reaction rates involved.
Where k1 and k-1 are the forward and backward reaction rates of step-one reaction, and k2 and k-2 are the forward and backward reaction rates of step-two reaction. In such a case, by assuming k-2 to be small, we derive the expression of the mean first passage time of the forward reaction:
kk 12 1 t . By further assuming k-1 equals zero, we get the mean first passage time of k1 k 2 k 2 11 the forward half reaction t . The reciprocal of t gives us the observed forward kk12 kk12 reaction rate kf . By the same argument, the observed backward reaction rate is kk12 kk12 kb . For a two-state dynamic scheme, the autocorrelation function is kk12
kfb k t C t e .3 For a generalized three-state (or easily generalized n-state) dynamic scheme, the
43-46 observed kf and kb is a polynomial of rate constant of each steps. It is clear that the
autocorrelation function analysis is a capable approach to probe the conformational fluctuations
of single proteins under spontaneous detailed balanced folding-unfolding conformational
fluctuations. By probing autocorrelation function fluctuation rates from single-molecule D-A
intensity fluctuation dynamic trajectories, we are able to directly probe and monitor protein
conformational fluctuation dynamics rates.47-52 58
3.3.3. Non-Exponential Distribution of Folding Waiting Time Indicates Multiple
Folding Intermediates.
Subtle conformational dynamic signatures are straightforwardly analyzed by the distribution
of on-times and off-times of mFRET D-A intensity fluctuation trajectories. 2, 3, 13, 53 The on-time
and off-time are the “waiting time” for the CaM folding and unfolding conformational dynamics, respectively. Such on-time and off-time or “waiting time” correspond to the dwelling time of
protein folding-unfolding conformational states. The nature of single-molecule CaM folding dynamic processes lies in the unique feature of such “waiting time” distributions. To characterize such detailed dynamic behavior, we further bin our data in the smFRET intensity trajectories to one millisecond bin (Figure 3.5A). The histogram of donor intensity trajectory
yields a distinct two-peaked occurrence distribution. The peak corresponding to the high
photon counts is unfolded state of single-molecule CaM, while the low photon count peak represents folded state of single-molecule CaM. To obtain a folding waiting time distribution,
we set up a threshold, at which the waiting times of the folding and unfolding states are
separately identified and read out. For the trajectory shown in Figure 3.5, we choose the value
10 as the threshold value, and subsequent folding waiting time distribution is shown in Figure
3.5C.3 Those short unfolding events that last less than three binning times of 3 ms total cannot be reliably differentiated from the measurement photon counting shot noise and are not counted as unfolding events.13, 53
Noticeably, the folding waiting time distribution is non-exponential resulting from a non-two-state folding-unfolding dynamic model.2, 3, 13 The distribution is also distinct from a 59
Gaussian distribution and has a broad coverage of time scales.3 The broad folding waiting time
distribution, reflecting the heterogeneity, is typically associated with complex protein
conformational dynamics involving multiple states and multiple pathways. This distinction clearly rules out the possibility of two-state folding-unfolding dynamics for single-molecule
CaM. The gamma distribution shaped folding waiting time distribution indicates a more complex dynamic mechanism involving a convolution of multiple Poisson processes of the folding-unfolding conformational fluctuations associated with multiple intermediates and multiple steps, which suggests multiple-state and multiple-pathway funnel-shaped folding energy landscape involving transition states, metastable states, and misfolded states.53, 63 Detailed spontaneous conformational fluctuation dynamics measurements yield such distinct statistics of folding waiting time distribution which, from dynamic perspective, is likely associated with a multiple-step Markovian dynamic process.53 Our detailed analysis of the folding waiting time distribution confirms a multiple folding pathways with multiple intermediates. Compared to a random search for the folded native state, our single-molecule spectroscopic analysis reveals that the CaM folding process is much more complex with multiple folding pathways running parallel with one another. Opposite to one-dimension reaction coordinate, single-molecule CaM folding process involving a folding network without rate-limiting step as considered in most two-state chemical reaction modeling of protein folding.53 60
Figure 3.5. Waiting-Time Distribution of Single-Molecule Data. (A) Donor intensity trajectory obtained from our single-molecule confocal microscopy with 1 ms binning time. The black dotted line indicates the threshold criterion separating the on- and off-time. (B) A histogram of such trajectory yields two peaks separating the “on” and “off” time which in our experiment correspond to folding and unfolding waiting time. Subsequently, a distribution of such “on” and “off” can be constructed. (C) The on-time distribution is a gamma shaped distribution representing a multiple step dynamic scheme. It is different in shape from both exponential distribution resulting from two-state dynamic scheme and Gaussian distribution. Simulated data (red line) from a multiple step Markovian dynamic process which facilitates a one dimensional random walk type of conformation diffusional process.
61
3.3.4. Model Analyses of Conformational Dynamics and Energy Landscape of
Single-Molecule CaM Folding.
We attribute the non-exponential folding waiting time distribution to the existence of multiple folding intermediates. 3, 13, 53, 54 To further characterize this multiple intermediate state dynamics, we exploit a one dimensional random walk model, which has been used successfully in the modeling of multiple step single-molecule enzymatic reaction.13, 53 The basic approach is
as the following: without prior knowledge of the shape of the energy landscape, we assume a
uniform rate k to each step of the overall rate process involved in single-molecule CaM
folding-unfolding conformational dynamics. Each step of one dimensional random walk model
is considered to be a Poisson process modeling single-molecule protein folding intermediate conversion process. The convolution of several Poisson process with uniform rate k gives
gamma function shaped distribution (Eqn. 2-4) to model non-exponential non-Gaussian shaped
folding waiting time distribution of single-molecule CaM folding-unfolding conformational
dynamics. This distribution reproduces the mean and standard deviation of the original folding
waiting time distribution of single-molecule CaM folding-unfolding conformational dynamics.
The number of Poisson process steps modeling single-molecule protein folding intermediate
conversion process involved in this convolution calculation gives an estimation of how many
Poisson rate processes are present in the overall rate process of single-molecule CaM folding-unfolding conformational dynamics. This number is the lower bound estimation of the number of intermediate involved in the dynamics process of protein folding. Quantitatively, the mean value of the original non-exponential folding waiting time distribution is 13.2 ± 9.0 ms. 62
The simulation data yields mean value 13.0 ± 7.2 ms which reproduces the original distribution well. The simulated distribution involves two Poisson rate processes which indicates a 2-step three-state dynamic process (Figure 3.5D).
P t Aexp t / where P(t) is the probability distribution of the Poisson rate process step times, τ is the averaged Poisson rate process step time, and A is the distribution weight constant.
The Poisson rate process step time is the duration between two adjacent states, and it is different from the formation time of the intermediate states or folded state of single-molecule CaM folding-unfolding conformational dynamics. In our model the folding waiting time distritution is the convolution distribution of Poisson rate process step times. To calculate the convolution of function f(t) and g(t), the integration equation is
t f g t f v g t v dv 0 Based on equation 6, a consecutive intermediate steps involved in a two-state dynamic model of
folding-unfolding conformational fluctuation is expressed as a convolution of two consecutive
exponential waiting-time distribution. The general probability function involving arbitrary
number of folding intermediates is deduced to be
n1 n ttexp / PATn n 1!
Where n (1, 2, 3,…, N) is the index of the intermediate steps; is the mean formation time of a
folding intermediate through a single-step process and A is the normalizing factor of this
probability distribution.
To further specify the shape of the energy landscape, we carry out a more detailed dynamic 63
analysis by calculating the conformational diffusion coefficients of single-molecule CaM
folding-unfolding conformational dynamics. Via a dynamic modeling, the folding waiting time
distribution gives the conformational diffusion coefficients.3 Briefly, we model the
folding-unfolding conformational dynamics of single-molecule CaM as a classical particle one-dimensional multiple-step random walk in the presence of a force field, and the position
distribution density function can be calculated by the Master equation.13 Following derivation of our previous work, the conformational diffusion coefficient of single-molecule CaM folding-unfolding dynamic process is
2 t2 X t unfold N D 3 2 tunfold
t where D is the conformational diffusion coefficient. The mean unfolding time, unfold , and the t 2 standard deviation of the unfolding time distribtuion, unfold ， are directly measured in our
experiment. The total drifting distance of the folding-unfolding conformational motion,
XtN , is associated to the folding-unfolding conformational distance change. From EFRET
distribution data, we already obtain the mean conformational drift distance XtN to be 0.9 ±
1.0 nm. Using equation 8,13 we calculate the diffusion coefficient D of this two-step dynamic
process to be 1.4×10-13 cm2/s. The diffusion coefficient is directly related to the shape of the
underlying energy landscape, since it reflects the roughness of the potential energy surface of
single-molecule CaM folding-unfolding conformational dynamic process.
Theoretically, we estimate the size of single-molecule CaM in the presence of denaturant
GdmCl. Although there are different models involving complex intra-chain molecular 64
interactions, we choose Gaussian chain model because it is the most simplified model and
55-58 catches the essential properties of an unfolded protein. The unfolded radius of gyration Rg of
0.55 the single-molecule CaM protein in GdmCl, Rg = 0.345N nm is 5.4 nm, which is consistent
with experimental value of 6.1 ± 0.8 nm. N is the number of monomers in the polypeptide
56 chain. Such scaling relation of Rg is strongly supported by small-angle X-ray scattering. The
folding speed limits of single domain proteins are provided experimentally59, and the
single-molecule single domain protein folding time is well characterized under Gaussian chain
assumption.56, 59 The vast majority of measurements yield the formation time of loop is less than
0.1 μs, and α–helix formation is approximately 0.5 μs. The formation time of β hairpin is greater than 0.5 μs.59 Since linear scaling theory holds for small degree of polymerization, using the linear length scaling suggested by the homopolymer collapse theory,60 theoretical upper
bound of single-molecule CaM folding time τlimit of 148 amino acid CaM is 3.0μs. Since CaM
polypeptide chain is more like of a heteropolymer than a homopolymer there are additional
factors to be taken into account while describing protein collapse. The estimation of theoretical
upper bound of single-molecule CaM folding time τlimit based on homopolymer collapse theory is
essentially accurate.61 We note that the folding time τ =
2 2 1.1 2 59 coefficient and
-7 2 We estimated Dlimit to be 1.9 × 10 cm /s as the theoretical upper bound of single-molecule CaM
conformational diffusion.59 The roughness of the free energy barrier involved in the
2 2 folding-unfolding dynamic process is determined by D = Dlimit exp(-β ε ), ε is a measurement of the roughness of the single-molecule CaM protein folding free energy barrier.62-64 For CaM 65
folding-unfolding conformational diffusion, the diffusion coefficient D is 1.4×10-13 cm2/s from our experimental measurement discussed above, which gives the roughness of the single-molecule CaM protein folding free energy barrier ε of 3.8±0.8kT; k is the Boltzmann
constant and T is the temperature. Compared with the hydrogen bonding (~2-12 kT),74, 75 this value of free energy barrier roughness is at the scale of hydrogen bonding interaction energy in a protein folding process associating with breaking and forming of a number of hydrogen bonds.
On the other hand, the height of the free energy barrier is estimated by using Kramer’s
barrier-crossing theory.59 We first estimate the actual folding time of CaM by using τ =
2 0.5 to be 0.89s in which (
process. In our experiment the single-molecule CaM folding-unfolding conformational
diffusion coefficient D is 1.4×10-13 cm2/s. We use Kramer’s theory to estimate the empirical free energy barrier of single-molecule protein folding process. Kramer’s theory assumes that the dynamic process of protein folding can be described as a one-dimensional diffusion along a reaction coordinate, and the minimum and maximum of the free energy surface are parabolic.59
From Kramer’s theory,
τfolding = 2πτlimit exp(ΔG/kT) where τfolding is the folding time of single-molecule CaM measured in our experiment, τlimit is the theoretical upper bound of single-molecule CaM folding time, and ΔG Is the free energy
barrier and k is the Boltzmann’s constant T is the temperature. The height of the free energy
barrier ΔG is estimated to be 11kT, which is consistent with previous optical tweezers 66
measurement for CaM.63 Our measurement yields an free energy barrier slightly lower than
optical tweezers measurements, this difference is likely due to the distinct structure involved in the measurement assays using different denature methods resulting in slightly different energetic feature of energy landscape.65 Nevertheless, our analysis reveals that instead of a two-state dynamic scheme our study shows a more complex and higher dimensional dynamic process on a multiple-pathway multiple-state energy landscape. By recording detailed fluctuation dynamics at the thermodynamic equilibrium under the condition of 2M GdmCl, we characterize such unique dynamic feature via a conformational diffusional modeling of single-molecule CaM folding-unfolding conformational dynamic process.
Figure 3.6. Protein Folding Pathway Distribution. (A) We postulate a schematic representation
of protein folding process along one specific pathway based on our single-molecule spectroscopy
measurements. The nuclear coordinate Q is a projected one dimensional coordinate of a three 67
dimensional funnel shaped energy landscape. We estimate the roughness of the potential
energy surface and the free energy barrier height based on dynamic modeling. The roughness
of the potential surface 3.8±0.8kT is likely to be entropic traps which are the thermodynamic features of multiple folding intermediates observed in the folding-unfolding dynamic process of
CaM. The 11kT obtained from Kramer’s theory of barrier crossing is likely to be the empirical
overall free energy barrier height. (B) The distribution we constructed with number of steps involved in each of the dynamic process vs. conformational diffusion coefficient. The vertical axis is occurrence. (C) We extract the distribution of folding pathways of single CaM molecule by measurements of spontaneous conformational fluctuations at folding-unfolding
thermodynamic titration equilibrium. Different single-molecule CaM protein folding pathways
are labeled with different color with distinct probability. Two-step folding dynamic process
involving one intermediate labeled with red has a probability of 23% among all single-molecule
protein folding-unfolding conformational fluctuation dynamic analyses. Different folding
dynamic process involving multiple intermediate labeled with black, purple and blue which have
a probability of 17%, 33% and 21%. (D) A conceptual representation of single-molecule CaM
protein folding-unfolding conformational dynamic process measured by our single-molecule
FRET. In general a multiple-state folding dynamic process involving more than one
intermediate is observed.
To study the heterogeneity of the CaM folding process, we have analyzed 52 single-molecule protein folding-unfolding conformational fluctuation trajectories to acquire a distribution of conformational diffusion coefficient versus number of steps involving Poisson 68
rate processes (Figure 3.6B). For each of the single-molecule FRET folding-unfolding signal fluctuation trajectories, we simulate the number of steps involved in the single-molecule CaM folding-unfolding conformational dynamic process, and we also calculate the single-molecule
CaM folding-unfolding conformational diffusion coefficient. A two dimensional distribution is
constructed with conformational diffusion coefficient vs. number of steps (Figure 3.6B). This
distribution is clearly a manifestation of a multiple-pathway multiple-state energy landscape with distinct folding pathways on which single-molecule CaM navigate. Moreover, these various folding pathways have a distribution with distinct probabilities. We count the total number of
occurrence of each single-molecule CaM folding-unfolding fluctuations dynamics with same number of steps involving Poisson rate processes, and calculate the ratio of each protein folding pathway among all the single-molecule folding-unfolding fluctuation dynamics trajectories we measure. Our results suggest that there are at least four different folding pathways of CaM molecule folding process (Figure 3.6B and 3.6C) involving multiple intermediate states have different probabilities ranged from 17% to 33%, based on all single-molecule protein folding-unfolding conformational fluctuation trajectories analyzed (Figure 3.6C and 3.6D).
Furthermore, we have identified that the different protein folding pathways involve different
protein folding conformational diffusion coefficients, a significant indication of
multiple-pathway and multiple-states protein folding energy.18, 19 The comparable energy scale of
the roughness 3.8±0.8kT and hydrogen bonding is a further manifestation of a protein folding energy landscape with many local minima corresponds to multiple folding intermediates (Figure
3.6D). Presumably, the folding intermediates is likely to have partially folded domains of 69
single-molecule CaM.65
3.4 Conclusions
Using more sensitive single-molecule spectroscopic measurements, we have achieved the
specification of the underlying protein folding pathways by monitoring the protein
folding-unfolding dynamics at equilibrium. We have characterized the multiple-pathway
multiple-state folding dynamics and energy landscape of single CaM molecules under conditions
of various denaturant GdmCl by using single-molecule FRET spectroscopy measurements and
correlated model analysis.66-70 We utilized the protein folding-unfolding at the denaturant
titration midpoint condition in our single-molecule CaM folding-unfolding experiments to probe
single-molecule CaM undergo spontaneous folding-unfolding conformational fluctuations, identifying the correlated conformational fluctuation rates and single-molecule EFRET distributions. Folded state of single-molecule CaM corresponds to a high EFRET and a fast fluctuation rate at millisecond time scale, whereas unfolded state of single-molecule CaM
71-78 corresponds to a low EFRET and a slow fluctuation rate at second time scale. We characterized detailed single-molecule CaM folding-unfolding fluctuation dynamics by analyzing folding waiting time distribution that indicates the existence of multiple intermediate states.
Furthermore, we have identified the specific folding routes with distinct probability distributions.
The free energy barriers and roughness of free energy barrier calculated from the dynamic model based on our experimental results provide the primary energetic features of CaM folding-unfolding conformational dynamics. The comparable energy scales of roughness and free energy barrier suggest that the multiple intermediate states serve as entropic traps on the 70
folding energy landscape. More interestingly, our dynamic model gives an estimation of the
number of folding intermediates along each of the folding pathways. Overall, the approach of
our dynamics measurements under equilibrium dynamic is demonstrated to be effective and
powerful to explore the folding funnel energy landscape and to verify the theoretical model of
multiple-pathway and multiple-states folding energy landscape based on fluctuation dissipation
theorem. Presumably, a fluctuating folding energy landscape with multiple-state
multiple-pathway is likely to be more energetically efficient and kinetically effective for a
consecutive protein folding dynamical process in living cells. 3.5 Reference:
1 For a review, see Nie, S.; Zare R. N. Optical detection of single molecules. Annu. Rev.
Biophys. Biomol. Struct. 1997, 26, 567-596.
2 Lu, H. P. Probing Single-molecule protein conformational dynamics. Acc. Chem. Res. 2005,
38 (7), 557–565.
3 Lu, H. P.; Xun, L. Y.; Xie, X. S. Single-molecule enzymatic dynamics. Science 1998, 282
(5395), 1877–1882.
4 English, B. P.; Min, W.; van Oijen, A. M.; Lee, K. T.; Luo, G. B.; Sun, H. Y.; Cherayil, B. J.;
Kou, S. C.; Xie, X. S. Ever-fluctuating single enzyme molecules: Michaelis-Menten equation
revisited. Nat. Chem. Biol. 2006, 2 (2), 87–94
5 Schuler, B.; Lipman, E. A.; Eaton, W. A. Probing the free-energy surface for protein folding
with single-molecule fluorescence spectroscopy. Nature 2002, 419, 743-747.
6 Lu, H. P.; Iakoucheva, L. M.; Ackerman, E. J. Single-molecule conformational dynamics of 71
fluctuating noncovalent DNA-Protein interactions in DNA damage recognition. J. Am. Chem.
Soc. 2001, 123 (37), 9184-9185.
7 Tan, X.; Nalbant, P.; Toutchkine, A.; Hu, D.; Vorpagel, E. R.; Hahn, K.M.; Lu, H. P.
Single-molecule study of protein−protein interaction dynamics in a cell signaling system. J.
Phys. Chem. B. 2004, 108 (2), 737-744.
8 Liu, S. X.; Bokinsky, G.; Walter, N. G.; Zhuang, X. W. Dissecting the multistep reaction
pathway of an RNA enzyme by single-molecule kinetic “fingerprinting”. Proc. Natl. Acad.
Sci. U.S.A. 2007, 104 (31), 12634–12639.
9 Visscher, K.; Schnitzer, M. J.; Block, S. M. Single kinesin molecules studied with a
molecular force clamp. Nature 1999, 400, 184–189.
10 Roy, R.; Hohng, S.; Ha, T. A practical guide to single-molecule FRET. Nat. Methods 2008, 5,
507–516.
11 Selvin, P. R.; Ha, T. Single-Molecule Techniques: A Laboratory Manual; Cold Spring Harbor
Laboratory Press: Cold Spring Harbor, NY, 2008.
12 Ha, T. J.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.;
Weiss, S. Single-molecule fluorescence spectroscopy of enzyme conformational dynamics
and cleavage mechanism. Proc. Natl. Acad. Sci. U.S.A. 1999, 96 (3), 893–898.
13 Chen, Y.; Hu, D. H.; Vorpagel, E. R.; Lu, H. P. Probing single-molecule T4 lysozyme
conformational dynamics by intramolecular fluorescence energy transfer. J. Phys. Chem. B
2003, 107 (31), 7947–7956.
14 Anfinsen, C.; Haber, E.; Sela, M.; White, F. H. The kinetics of formation of native 72
ribonuclease during oxidation of the reduced polypeptide chain. Proc. Natl. Acad. Sci. USA
1961, 47 (9), 1309–1314.
15 For a review, see Eaton, W. A.; Schuler, B. Protein folding studied by single molecule FRET.
Curr. Opin. Struct. Biol. 2008, 18 (1), 16-26.
16 For a review, see Schuler, B.; Hofmann, H. Single-molecule spectroscopy of protein folding
dynamics—expanding scope and timescales. Curr. Opin. Struct. Biol. 2013, 23 (1), 36-47.
17 For a review, see Rief, M. Force as a single molecule probe of multidimensional protein
energy landscapes. Curr. Opin. Struct. Biol. 2013, 23 (1), 48-57.
18 Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Theory of protein folding: the energy
landscape perspective. Annu. Rev. Phys. Chem. 1997, 48, 545–600.
19 Dill, K. A.; Chan, H. S. From Levinthal to pathways to funnels. Nat. Struct. Biol. 1997, 4,
10–19.
20 Thirumalai, D.; Klimov, D. K. Deciphering the timescales and mechanisms of protein folding
using minimal off-lattice models. Curr. Opin. Struct. Biol. 1999, 9 (2), 197–207.
21 Deniz A. A.; Laurence T. A.; Beligere G. S.; Dahan M.; Martin A. B.; Chemla D. S.; Dawson
P. E.; Schultz P. G.; Weiss S. Single-molecule protein folding: Diffusion fluorescence
resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2. Proc. Natl.
Acad. Sci. USA 2000, 97 (10), 5179-5184.
22 Nettels D.; Gopich I. V.; Hoffmann A.; Schuler B. Ultrafast dynamics of protein collapse
from single-molecule photon statistics. Proc. Natl. Acad. Sci. USA 2007, 104 (8), 2655-2660.
23 Nettels D.; Hoffmann A.; Schuler B. Unfolded Protein and Peptide Dynamics Investigated 73
with Single-Molecule FRET and Correlation Spectroscopy from Picoseconds to Seconds. J.
Phys. Chem. B 2008, 112 (19), 6137-6146.
24 Haran G. How, when and why proteins collapse: the relation to folding. Curr. Opin. Struct.
Biol. 2012, 22 (1), 14-20.
25 Sherman E.; Haran G. Coil–globule transition in the denatured state of a small protein. Proc.
Natl. Acad. Sci. USA 2006, 103 (31), 11539-11543.
26 Ziv G.; Thirumalai D.; Haran G. Collapse transition in proteins. Phys. Chem. Chem. Phys.
2009, 11, 83-93.
27 Hoffmann A.; Kane A.; Nettels D.; Hertzog D. E.; Baumgärtel P.; Lengefeld J.; Reichardt G.;
Horsley D. A.; Seckler R.; Bakajin O.; Schuler B. Mapping protein collapse with
single-molecule fluorescence and kinetic synchrotron radiation circular dichroism
spectroscopy. Proc. Natl. Acad. Sci. USA 2007, 104 (1), 105-110.
28 Chung H. S.; Louis J. M.; Eaton W. A. Experimental determination of upper bound for
transition path times in protein folding from single-molecule photon-by-photon trajectories.
Proc. Natl. Acad. Sci. USA 2009, 106 (29), 11837-11844.
29 Chung H. S.; McHale K.; Louis J. M.; Eaton W. A. Single-molecule fluorescence
experiments determine protein folding transition path times. Science 2012, 335 (6071),
981-984.
30 Shaw D. E.; Maragakis P.; Lindorff-Larsen K.; Piana S.; Dror R. O. Atomic-level
characterization of the structural dynamics of proteins. Science 2010, 330 (6002), 341-346.
31 Garcia-Mira M. M.; Sadqi M.; Fischer N.; Sanchez-Ruiz J. M.; Munoz V. Experimental 74
identification of downhill protein folding. Science 2002, 298 (5601), 2191-2195.
32 Pirchi M.; Ziv G.; Riven I.; Cohen S. S.; Zohar N.; Barak Y.; Haran G. Single-molecule
fluorescence maps the folding landscape of a large protein. Nat. Commun. 2011, 2, 493.
33 Chin, D.; Means, A. R. Calmodulin: a prototypical calcium sensor. Trends in Cell Biology
2000, 10 (8), 322-328.
34 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-binding domains: just two faced or
multi-faceted? Trends Biochem. Sci. 1995, 20 (1), 38-42.
35 Liu, R. C.; Hu, D. H.; Tan, X.; Lu, H. P. Revealing two-state protein-protein interactions of
calmodulin by single-molecule spectroscopy. J. Am. Chem. Soc. 2006, 128 (31), 10034–
10042.
36 Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J.
Three-dimensional structure of calmodulin. Nature 1985, 315, 37-40.
37 Chattopadhyaya, R.; Meadorl, W. E.; Means, A. R.; Quiocho, F. A. Calmodulin structure
refined at 1.7 A resolution. J. Mol. Biol. 1992, 228 (4), 1177-1192.
38 Slaughter B. D.; Unruh J. R.; Price E. S.; Huynh J. L.; Bieber Urbauer R. J.; Johnson C. K.
Sampling unfolding intermediates in calmodulin by single-molecule spectroscopy. J. Am.
Chem. Soc. 2005, 127 (34), 12107-12114.
39 Wang, X.; Lu, H. P. 2D Regional correlation analysis of single-molecule time trajectories. J.
Phys. Chem. B. 2008, 112 (47), 14920-14926.
40 He, Y.; Li, Y.; Mukherjee, S.; Wu, Y.; Yan, H.; Lu, H. P. Probing single-molecule enzyme
active-site conformational state intermittent coherence. J. Am. Chem. Soc. 2011, 133 (36), 75
14389-14395.
41 Nie, S.; Chiu, D. T.; Zare R. N. Probing individual molecules with confocal fluorescence
microscopy. Science 1994, 266 (5187), 1018–1021.
42 We have obtained the SEM imaging of agarose gel by super-critical point sample preparation
at different concentration of agarose gel from 0.2% to 2%. The imaged pore size formed by
the network of agarose gel averagely rage from 300 nm to 50 nm. Single-molecule CaM
freely rotate and perform biological function in agarose gel matrix and the translational
motion of individual CaM does not extend beyond the laser diffraction limited focus spot.
43 Cao, J. S. Michaelis−Menten equation and detailed balance in enzymatic networks. J. Phys.
Chem. B 2011, 115 (18), 5493-5498.
44 Chandler, D. Introduction to Modern Statistical Mechanics; Oxford University Press: New
York, 1987.
45 Oppenheim, I.; Shuler, K. E.; Weiss, G. H. Stochastic Processes in Physics and Chemistry;
MIT Press: Cambridge, MA, 1977.
46 Huang, K. Lectures on Statistical Physics and Protein Folding; World Scientific Publishing:
Singapore, 2005.
47 Barkai, E.; Jung, Y.; Silbey, R. Time-dependent fluctuations in single molecule spectroscopy:
a generalized Wiener-Khintchine approach.Phys. Rev. Lett. 2001, 87 (20), 207403
48 Barkai, E.; Silbey, R.; Zumofen, G. Transition from simple to complex behavior of single
molecule line shapes in disordered condensed phase. J. Chem. Phys. 2000, 113, 5853–5867.
49 Flomenbom, O.; Klafter, J.; Szabo, A. What Can One Learn from Two-State Single-Molecule 76
Trajectories? Biophys. J. 2005, 88 (6), 3780–3783.
50 Flomenbom, O.; Velonia, K.; Loos, D.; Masuo, S.; Cotlet, M.; Engelborghs, Y.; Hofkens, J.;
Rowan, A. E.; Nolte, R. J. M.; Van der Auweraer, M.; de Schryver, F. C.; Klafter, J. Stretched
exponential decay and correlations in the catalytic activity of fluctuating single lipase
molecules. Proc. Natl. Acad. Sci. U.S.A. 2005, 102 (31), 2368–2372.
51 He, Y.; Barkai, E. Super- and sub-Poissonian photon statistics for single molecule
spectroscopy. J. Chem. Phys. 2005, 122 (18), 184703.
52 Zwanzig, R. Nonequilibrium Statistical Mechanics; Oxford University Press: New York,
2001.
53 Wang, Y.; Lu, H. P. Bunching effect in single-molecule T4 lysozyme nonequilibrium
conformational dynamics under enzymatic reactions. J. Phys. Chem. B 2010, 114 (19),
6669-6674.
54 Xie, X. S. Single-molecule approach to enzymology. Single Mol. 2001, 4, 229-236.
55 Uversky, V. N. Natively unfolded proteins: A point where biology waits for physics. Protein
Sci. 2002, 11 (4), 739–756.
56 Ziv, G.; Thirumalai, D.; Haran, G. Collapse transition in proteins. Phy. Chem. Chem. Phys.
2009, 11, 83-93.
57 de Gennes, P.-G. Scaling concepts in polymer physics; Cornell University Press: Ithaca,
1979.
58 Des Cloizeaux, J.; Jannink, G. Polymers in solution: their modeling and structure; Clarendon
Press: Oxford, 1990. 77
59 Kubelka, J. J.; Hofrichter, J. J.; Eaton, W. A. The protein folding 'speed limit'. Curr. Opin.
Struct. Biol. 2004, 14, 76-88.
60 Pitard E. Influence of hydrodynamics on the dynamics of a homopolymer. Eur. Phys. J. B
1999, 7, 665-673.
61 The more sophisticated heteropolymer model considering the complexity of specific amino
acids interactions in the polypeptide chain may be more accurate. Such discussion requires
detailed simulation study which is beyond the scope of our current paper.
62 Socci N. D.; Onuchic J. N.; Wolynes P. Diffusive dynamics of the reaction coordinate for
protein folding funnels. J. Chem. Phys 1996, 104 (15), 5860-5868.
63 Stigler, J.; Ziegler, F.; Gieseke, A.; Gebhardt, J. C.; Rief, M. The complex Folding network of
single calmodulin molecules. Science 2011, 334 (6055), 512-516.
64 Zwanzig, R. Diffusion in a rough potential. Proc. Natl. Acad. Sci. U.S.A. 1988, 85,
2029-2030.
65 Stirnemann, G.; Kang, S.; Zhou, R.; Berne, B. J. How force unfolding differs from chemical
denaturation. Proc. Natl. Acad. Sci. U.S.A .2014, 111 (9), 3413-3418
66 Wang, J.; Oliveira, R. J.; Chu, X.K.; Whitford, P. C.; Chahine, J.; Wei, H.; Wang, E.K.;
Onuchic, J. N.; Leite, V. B. P. Topography of funneled landscapes determines the
thermodynamics and kinetics of protein folding. Proc. Natl. Acad. Sci. USA, 2012, 109 (39),
15763–8.
67 Dutta, P.; Sen, P.; Halder, A.; Mukherjee, S.; Sen, S.; Bhattacharyya, K. Solvation dynamics
in a protein–surfactant complex. Chemical Physics Letters 2003, 377 (1), 229-235. Pal, N.; 78
Verma, S. D.; Sen, S. Probe position dependence of DNA dynamics: comparison of the
time-resolved stokes shift of groove-bound to base-stacked probes. J. Am. Chem. Soc. 2010,
132 (27), 9277-9279.
68 Sen, S.; Paraggio, N. A.; Gearheart, L. A.; Connor, E. E.; Issa, A.; Coleman, R. S.; Wyatt, M.
D.; Berg M. A. Effect of protein binding on ultrafast DNA dynamics: characterization of a
DNA: APE1 complex. Biophysical Journal 2005, 89 (6), 4129-4138
69 Biju, V.; Anas, A.; Akita, H.; Shibu, E. S.; Itoh, T.; Harashima, H.; Ishikawa M. FRET from
quantum dots to photodecompose undesired acceptors and report the condensation and
decondensation of plasmid DNA. ACS nano 2012, 6 (5), 3776-3788
70 Zheng, D.; Kaldaras, L.; Lu, H. P. Total internal reflection fluorescence microscopy
imaging-guided confocal single-molecule fluorescence spectroscopy. Rev. Sci. Instrum. 2012,
83 (1), 013110−013110−5.
71 Zheng, D.; Lu, H. P. Single-molecule enzymatic conformational dynamics: spilling out the
product molecules. J. Phys. Chem. B. 2014, 118 (31), 9128-9140.
72 Lu, M.; Lu, H. P. Probing protein multidimensional conformational fluctuations by
single-molecule multiparameter photon stamping spectroscopy. J. Phys. Chem. B. 2014, 118
(41), 11943-11955.
73 Bartko, A. P.; Dickson R. M. Imaging three-dimensional single molecule orientations. J. Phys.
Chem. B. 1999, 103 (51), 11237–11241
74 Sticke, D. F.; Presta, L. G.; Dill, K. A.; Rose, G. D. Hydrogen bonding in globular proteins. J.
Mol. Biol. 1992, 226, 1143-1159. 79
75 Rose, G. D.; Wolfenden, R. Hydrogen-bonding, hydrophobicity, packing, and protein-folding.
Annu. Rev. Bioph. Biom. 1993, 22, 381−415.
76 Bates, M.; Huang, B.; Dempsey, G. T.; Zhuang, X. W. Multicolor super-resolution imaging
with photo-switchable fluorescent probes. Science 2007, 317, 1749-1753.
77 Hohng, S.; Joo, C.; Ha, T. Single-molecule three-color FRET. Biophys. J. 2004, 87,
1328-1337.
78 Lee, N. K.; Kapanidis, A. N.; Koh, H. R.; Korlann, Y.; Ho, S. O.; Kim, Y.; Gassman, N.; Kim,
S. K.; Weiss, S. Three-color alternating-laser excitation of single molecules: Monitoring
multiple interactions and distances. Biophys. J. 2007, 92, 303-312.
80
CHAPTER IV. PROBING SINGLE-MOLECULE PROTEIN
FOLDING-UNPON-BINDING CONFORMATIONAL DYNAMICS USING
SINGLE-MOLECULE FRET SPECTROSCOPY
This chapter is dedicated to the study of single molecule protein folding study in the presence of protein-protein interaction.
4.1 Introduction
Single-molecule spectroscopy developed in the 1990s is by far the most important technique to study one molecule at a time. The dynamics and heterogeneity revealed by single-molecule experiments prove to be invaluable when researchers try to understand biological processes at
the molecular level, such as cell signaling.1-6 Recently, new developments in this technique also
make it possible to probe various interaction pathways in which real biological processes
occur.7-10 For example, one study involving investigation of protein-protein interactions of
calmodulin (CaM) with peptide shows these interactions can significantly alter the normal
conformational dynamics of the target protein.11
After gene expressions, single proteins start to fold into a unique functional structure without external help. However, inside the living cells, this process normally happens in a crowded
environment which involves various kinds of protein-protein interaction. Little is known about
the folding dynamics of single CaM molecules in the presence of extensive interactions with
other peptide molecules. The motivation of this study is to probe the folding-unfolding
conformational dynamics, which is the most important conformational dynamics of single 81
proteins, in this “crowded” environment. The outcome of this study will help us to understand the critical role played by protein-protein interactions in the single protein folding process, which
can provide insight into the future study of protein misfolding and protein aggregates related to
human diseases (e.g., amyloid diseases).12
Calmodulin (CaM) is a 148-residue protein responsible for intracellular calcium-sensing. It
is crucial in many biological processes including muscle contraction and energy metabolism.6,7
CaM has two globular domains and the binding mechanism between calcium ions and the two domains of CaM are under extensive studies.8,9 Traditional methods involving nuclear magnetic resonance and X-ray crystallography have provided detailed insights into the mechanisms and dynamics of this reaction.7-9 As a result of the flexibility and the dumbbell shape of the protein,
with dye labeling at the two domains, it is possible to monitor the dynamics of CaM with
single-molecule spectroscopy, such as fluorescence resonance energy transfer (FRET).12 The
typical time-resolution can be milliseconds which is the characteristic time scale of protein
motions.
Cyanine is a commonly used dye molecule, which can be attached onto the protein with
thiolation. The CaM has mutations at residue 34 and residue 110 on the N- and C-terminal
respectively, and fluorescent dye pair Cy3/Cy5 was tethered onto the protein. These two dyes
served as a spectroscopic ruler for the measurement of conformational fluctuations of the protein
molecules, since the measurement efficiency of energy transfer between the two dye molecules
will reveal distance information of the protein conformation: 82
Where R0 is the distance at which energy transfer is 50% efficient. For our specific dye pair
Cy3-Cy5, the R0 value is measured to be 5.4 nm.
Figure 4.1. Protein Folding Binding Process. A cartoon of protein folding-binding process.
C28W is an oligomer of 28 amino acid residues which can interact with CaM through
binding to one of the two terminals of the two domains. Previous research proved a two-state
interaction picture for the CaM/C28W and figured out the general induced bending motion of the
CaM through interaction with C28W.11
In this chapter, we use single-molecule FRET spectroscopy to probe the folding-unfolding
conformational dynamics of CaM interacting with C28W under the mild unfolding concentration
of denaturant solvent guanidinium chloride (GdmCl) (Figure 2). The critical concentration of
denaturant of GdmCl, at which single proteins undergo folding-unfolding conformational
fluctuations, has been characterized by our previous study. Since the interaction characterized by
previous studies revealed an induced binding picture in native states of CaM, we observe a more
complicated dynamic picture of CaM interacting with C28W under partially denatured
conditions at which single CaM molecules have large conformational space to explore.
83
4.2 Materials and Methods
4.2.1 Sample Preparation and Characterization
The single CaM molecule has mutation on N-terminal domain at residue 34 and C-terminal
domain at residue 110, and fluorescent dye pair Cy3/Cy5 was tethered onto the protein via
thiolation. These two dyes served as a spectroscopic ruler for the measurement of conformational
fluctuation of the protein molecule interacting with C28W. In our experiment, the change of
FRET efficiency corresponds to the distance change of about 2 nm. On the other hand, the
Forster radius R0 of Cy3-Cy5 pair is ~5 nm, so the distance change of the two dyes monitoring the conformational change falls into measureable range. In our experiment, the samples for single-molecule conformational folding-unfolding dynamics measurements are prepared inside the agarose gel (1% by weight, Type VII, Sigma). For example, we make a sample of CaM into 2
M of denaturant solvent GdmCl by first mixing 0.2μL 200 nM CaM, 2.5μL 8 M GdmCl, 0.1mM
CaCl2 and 8.55μL oxygen scavenger with Trolox solution to obtain a 10μL mixture of protein and denaturant solvent with 100nM C28W. The Trolox solution is made previously by dissolving about 1 mM 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1 mg/mL
glucose oxidase, 0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent dye from photobleaching or blinking as a result of triplet state formation or other irreversible
photophysical processes. We then heat the 10μL 1% agarose gel just above its gel-transition
temperature (26°C) and quickly mix the above protein with denaturant solvent solution with the
gel between two clean cover glasses to form a sandwich. All solutions are prepared with
Phosphate buffered saline (PBS buffer) at pH 7.4. Since we want to probe conformational 84
dynamics of single protein molecule at different concentration of C28W peptide, we carry out concentration dependent experiments with different ratio of mixture in the sandwich as listed below.10
Trolox+Oxygen CaM GdmCl Agarose Gel Scavenger ～1 nM CaM+2M 0.2μL 200nM 2.5μL 8M 9.8μL 10μL Gdmcl+100 nM C28W ～1 nM CaM+2M 0.2μL 200nM 2.5μL 8M 8.55μL 10μL Gdmcl+500 nM C28W ～1 nM CaM+2M 0.2μL 200nM 2.5μL 8M 7.3μL 10μL Gdmcl+1000 nM C28W
Table 4.1. List of concentrations used in our folding-binding experiments.
4.2.2 Single-Molecule Imaging and FRET Measurement
Single-Molecule photon stamping approach is used to record FRET trajectories at different concentration of C28W. This approach records emission of photons from donor and acceptor
channel one by one with arrival time, and the intensity trajectory can be constructed as a function of time. Förster resonance energy transfer or fluorescence resonance energy transfer (FRET) is a certain type of energy transfer realized by nonradiative dipole-dipole interaction (Figure
4.4). The experimental setup is an inverted confocal microscope (Axiovert 200, Zeiss) which uses a crystal laser (532nm CW) as the light source for excitation (Figure 5). The Laser beam focused through a 100× oil immersion objective lens (1.3 NA, 100×, Zeiss) onto the upper surface of cover slip after reflected up by a dichroic beam splitter (z532rdc, Chroma Technology).
To obtain confocal microscopy image, we use an x-y closed-loop piezo position scanning stage for raster-scan of the sample sandwich. The fluorescence is collected through the same objective 85
and the signal is split by a dichroic beam splitter (640dcxr) into two different wavelength 570nm
and 670nm which are the emission wavelength of Cy3 and Cy5 respectively. To detect the signal
from the two channels, two Si avalanche photodiode single photon counting modules
(SPCM-AQR-16, Perkin Elmer Optoelectronics) were used for recording the photons from donor
and acceptor. A more detailed description of the experimental setup is in the literature.10,11
4.3 Results and Discussion
Figure 4.2 shows typical image obtained by our inverted confocal microscopy. By raster-scan the sample, a 20μm × 20μm sample image gives bright spots of single CaM molecules confined in the network formed by agarose gel (~200nm in diameter). The spots indicating single protein molecules are diffraction limited (～300nm). We then focus our laser
beam on each specific sample spot to gain continuous donor-acceptor (D-A) fluorescence
intensity trajectories shown in figure 2. Typically, we gather approximately seventy data points at
different concentration of C28W peptide, and the FRET efficiency of each of the sample
measured is calculated.
12-15 Here the correction factor (φA×ηA)/(φD×ηD) is ~1 in our experiment conditions. 86
Figure 4.2. Single-Molecule Imaging and Correlation Analysis. Typical Donor/Acceptor signals
and FRET efficiency trajectories. Green and red lines indicate the donor and acceptor channel respectively. The histogram distribution from FRET Efficiency trajectory gives the FRET efficiency of a certain single-molecule.
We observe shifts in the peak values of the distribution of all efficiencies at different concentration of C28W interacting with folding-unfolding fluctuating CaM resulting in either decrease or increase of FRET efficiency (Figure 3). These changes in FRET efficiency clearly evidence the conformational change of single CaM molecules interacting with different concentration of C28W. The samples with FRET efficiency at around 0.6 are assigned to be in the native state and those with FRET efficiency at 0.3 are assigned to be the unfolded ones. In this study, we only focus on those fluctuating CaM molecules which interact with different concentrations of C28W, so to obtain different distribution at various concentration of denaturant 87
solvent is unnecessary. When the folded and unfolded single CaM molecules are approximately
equally populated, those molecules with FRET efficiency at 0.4 are those fluctuating proteins
interacting with C28W peptide.
Figure 4.3. Protein Folding Binding and EFRET. Distribution of FRET efficiency of different
samples at different concentration of GdmCl. The shift in peak values characterizes the unfolding
of CaM molecule at higher concentration of denaturant solvent.
We analyze the dynamical behaviors of our data sets by calculating the autocorrelation functions. By fitting the autocorrelation functions with exponential decays, we are able to 88
characterize the time scale of protein motion (Figure 1). Each fitted autocorrelation function gives us correlation lifetime of FRET efficiency, and the lifetimes have a broad distribution as a result of environmental heterogeneity. We also observe that at high concentration of C28W, CaM has a typical autocorrelation function which has a sharp decay as a result of our induced folding hypothetical picture.15-21 The shift of FRET efficiency distribution reveals the interesting induced folding or induced unfolding phenomenon.
The exponential decays obtained from fitting the autocorrelation functions give decay
lifetime from different sample points at different concentration of GdmCl. We plot distribution of
these various fluctuation lifetimes and an interesting shift of the distribution as the concentration
of GdmCl increased emerged (Figure 1). In our previous work, at 2M of denaturant solvent, there
are more big taus compared to the lower concentration and blank samples. We attribute this change to denature of the CaM molecule. At high concentration of GdmCl, most of the CaM molecules are denatured into random coil, and the conformational dynamics reveal weak correlation (slow protein motion at time scale of ~10s).22-28 89
Figure 4.4. Waiting Time Distribution Analysis of Protein Folding. Single-molecule
folding-unfolding fluctuation trajectory is shown on the upper channel. The distinct high-low
fluctuation pattern indicates a protein folding-unfolding conformational dynamics. We analyzed such folding-unfolding process by the bunching effect and simulated the number of possible intermediate states.
The conformational diffusion coefficients can also be calculated from the folding waiting time distribution. From FRET efficiency distribution data, we already obtained the mean
29-35 conformational drift distance XtN to be 1.22nm. Using this formula, we calculate the
diffusion coefficient of this 2-step dynamic process to be D~2.92×10-13 cm2/s. The diffusion coefficient is directly related to the underlying energy landscape, since it represents the local 90
mean square fluctuation of the activation barrier of the folding-unfolding dynamic process.
2 t2 X t unfold N D 3 2 tunfold
Theoretically, using polymer theory,36-39 the unfolded radius of gyration of the protein in
0.55 GdmCl can be calculated Rg = 0.345N nm which is 5.39 nm (experiment value 6.70 nm). The folding speed limits of single domain proteins are provided experimentally40 and the folding time well characterized with a Gaussian chain assumption.40 Using the linear length scaling suggested
41 by the homopolymer collapse theory, theoretical upper bound folding timeτlimit of 148 amino acid CaM is 3 μs. Notice folding time τ =
2 2 1.1 2 -8 2
2 2 -13 can be determined by D = Dlimitexp(-β ΔE ). In our case, diffusion coefficient D~2.92×10
cm2/s which givesΔE is about 3.7 kT. Compared with hydrogen bonding (2 – 12kT), this value of activation barrier fluctuation is at reasonable scale. The net increase of such “energy landscape
roughness” is about 20%, a significant change which could be due to a recognition process
between the ligand and the target protein. On the other hand, the height of the activation barrier
can be estimated using Kramer’s dynamics.40 The actual folding time of CaM can be calculated to be 0.26s. From Kramer’s dynamics, τfolding = 2πτlimit exp(ΔG/kT). So the height of the
activation barrierΔG = 10.2 kT, consistent with previous optical tweezers measurement.42 91
Figure 4.5. Folding Pathway Distribution in Protein Folding Binding. The single-molecule protein folding pathway distribution features a multiple-channel and multiple-state
conformational dynamics. The convergence of such a distribution clearly revealed a
conformational-selection mechanism of folding-upon-binding dynamical process.
We analyze 35 trajectories to acquire a distribution of such dynamic processes. We characterized each single protein folding-unfolding conformational dynamics by calculating the
diffusion coefficients and the number of intermediate states. Folding-unfolding trajectories with
same number of steps and similar conformational gathered into different domains which is a
manifestation of the underlying multi-dimensional energy landscape. This cluster is a clear proof
of the existence of folding pathway distribution. Moreover, these various folding pathways have
a distribution with different probabilities assigned to each of them. To better see this, we
constructed a two dimensional color plot, with the color bar indicating occurrence. Four different
folding pathways started to emerge, and the probability of each of these pathways are calculated 92
(Figure 4.5).
4.4 Conclusion
In this study, we characterize the conformational dynamics of single CaM under interaction
with C28W. We denature single CaM molecules by adding in 2M denaturant GdmCl, and the
ratio between folded and unfolded CaM molecules is approximately one to one. Under this
condition, the majority of the single protein undergoes folding-unfolding fluctuation which has
been studied by our previous research. Our hypothesis is that the addition of C28W peptide,
which can bind to the two heads of single CaM molecules, will significantly change the
conformation of the single protein and further enhance the folding process of single proteins. We
probe this folding process by measuring single-molecule FRET which can reveal conformational
dynamic information.43
The limitation of our present study will lie in the complexity of the effect on proteins of
denaturant, the chemical GdmCl. It is well studied that the effect of the chemical denaturant
GdmCl on protein will be the destruction of the secondary and tertiary structure. The unfolding
process is a result of loss of hydrophobic interaction between amino acids. However, the binding
process of C28W to CaM is also a result of hydrophobic amino acid interactions between these
two. Whether the denaturant will also have any effect on the C28W-CaM interaction remains
unknown. This effect could intrinsically make our experiment more complex. However, if we
can observe a substantial change in the measured distribution of FRET efficiency, we know the
C28W-CaM interaction is active and we can carry out our following dynamic analyses. 93
4.5 Reference:
1 Moerner, W. E.; Orrit, M. Illuminating Single Molecules in Condensed Matter Science 1999,
283 (5408), 1670-1676.
2 Nie, S.; Zare, R. N. Optical Detection of Single Molecules. Annual Review of Biophysics and
Biomolecular Structure 1997, 26, 567-596.
3 Weiss, S. Fluorescence Spectroscopy of Single Biomolecules. Science 1999, 283 (5408),
1676-1683.
4 For reviews, see: Acc. Chem. Res. (special issue on single molecule spectroscopy) 2005, 38
(7).
5 For a review, see: Protein-Ligand Interactions;Nienhaus, G. U., Ed.; Humana Press: New
Jersey, 2005.
6 Chin, D.; Means, A. R. Trends in Cell Biology 2000, 10 (8), 322-328.
7 James, P.; Vorherr, T.; Carafoli, E. Calmodulin: a prototypical calcium sensor. Trends
Biochem. Sci. 1995, 20 (1), 38-42.
8 Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J.
Three-dimensional structure of calmodulin. Nature 1985, 315, 37-40.
9 Chattopadhyaya, R.; Meadorl, W. E.; Means, A. R.; Quiocho, F. A. Calmodulin structure
refined at 1.7 Å resolution. J. Mol. Biol. 1992, 228 (4), 1177-1192.
10 Chen, Y.; Hu, D. H.; Vorpagel, E. R.; Lu, H. P. Probing Single-Molecule T4 Lysozyme
Conformational Dynamics by Intramolecular Fluorescence Energy Transfer. J. Phys. Chem.
B. 2003, 107, 7947–7956. 94
11 Liu, R. C.; Hu, D. H.; Tan, X.; Lu, H. P. Revealing Two-State Protein−Protein Interactions of
Calmodulin by Single-Molecule Spectroscopy. J. Am. Chem. Soc. 2006, 128, 10034–10042.
12 Dobson, C. M. Protein chemistry. In the footsteps of alchemists. Science 2004, 304,
1259-1262
13 Deniz AA, Laurence TA, Beligere GS, Dahan M, Martin AB, Chemla DS, Dawson PE,
Schultz PG, Weiss S: Protein folding from a highly disordered denatured state: The folding
pathway of chymotrypsin inhibitor 2 at atomic resolution. Proc Natl Acad Sci USA 2000, 97,
5179-5184.
14 Nettels D, Gopich IV, Hoffmann A, Schuler B. Ultrafast dynamics of protein collapse from
single-molecule photon statistics. Proc Natl Acad Sci USA 2007, 104, 2655-2660.
15 Nettels D, Hoffmann A, Schuler B. Unfolded Protein and Peptide Dynamics Investigated
with Single-Molecule FRET and Correlation Spectroscopy from Picoseconds to Seconds. J
Phys Chem B 2008, 112, 6137-6146.
16 Haran G. How, when and why proteins collapse: the relation to folding. Curr Opin Struct
Biol 2012, 22, 14-20.
17 Sherman E, Haran G. Coil–globule transition in the denatured state of a small protein. Proc
Natl Acad Sci USA 2006, 103:11539-11543.
18 Ziv G, Thirumalai D, Haran G. Collapse transition in proteins. Phys Chem Chem Phys 2009,
11:83-93.
19 Hoffmann A, Kane A, Nettels D, Hertzog DE, Baumga¨ rtel P, Lengefeld J, Reichardt G, 95
Horsley DA, Seckler R, Bakajin O et al.. Mapping protein collapse with single-molecule
fluorescence and kinetic synchrotron radiation circular dichroism spectroscopy. Proc Natl
Acad Sci USA 2007, 104:105-110.
20 Chung HS, Louis JM, Eaton WA. Experimental determination of upper bound for transition
path times in protein folding from single-molecule photon-by-photon trajectories. Proc Natl
Acad Sci USA 2009, 106:11837-11844.
21 Chung HS, McHale K, Louis JM, Eaton WA. Single-Molecule Fluorescence Experiments
Determine Protein Folding Transition Path Times. Science 2012, 335:981-984.
22 Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO. Atomic-level characterization
of the structural dynamics of proteins. Science 2010, 330:341-346.
23 Garcia-Mira MM, Sadqi M, Fischer N, Sanchez-Ruiz JM, Munoz V. Experimental
Identification of Downhill Protein Folding. Science 2002, 298:2191-2195.
24 Pirchi M, Ziv G, Riven I, Cohen SS, Zohar N, Barak Y, Haran G. Single-molecule
fluorescence spectroscopy maps the folding landscape of a large protein. Nat Commun 2011,
2, 493.
25 Chin, D.; Means, A. R. Calmodulin: a prototypical calcium sensor. Trends in Cell Biology
2000, 10 (8), 322-328.
26 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-binding domains: just two faced or
multi-faceted? Trends Biochem. Sci. 1995, 20 (1), 38-42.
27 Liu, R. C.; Hu, D. H.; Tan, X.; Lu, H. P. Revealing Two-State Protein−Protein Interactions of
Calmodulin by Single-Molecule Spectroscopy. J. Am. Chem. Soc. 2006, 128, 10034–10042. 96
28 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-binding domains: just two faced or
multi-faceted? Trends Biochem. Sci. 1995, 20 (1), 38-42.
29 Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J.
Three-dimensional structure of calmodulin. Nature 1985, 315, 37-40.
30 Chattopadhyaya, R.; Meadorl, W. E.; Means, A. R.; Quiocho, F. A. Calmodulin structure
refined at 1.7 Å resolution. J. Mol. Biol. 1992, 228 (4), 1177-1192.
31 Slaughter B. D., Unruh J. R., Price E. S., Huynh J. L., Bieber Urbauer R. J., Johnson C. K.
Sampling Unfolding Intermediates in Calmodulin by Single-Molecule Spectroscopy. J Am
Chem Soc 2005, 127, 12107-12114.
32 Wang, X.; Lu, H. P. 2D Regional Correlation Analysis of Single-Molecule Time
Trajectories. J. Phys. Chem. B. 2008, 112, 14920-14926.
33 He, Y.; Li, Y.; Mukherjee, S.; Wu, Y.; Yan, H.; Lu, H. P. Probing Single-Molecule Enzyme
Active-Site Conformational State Intermittent Coherence. J. Am. Chem. Soc. 2011, 133,
14389-14395.
34 Wang, Y.; Lu, H. P. Bunching Effect in Single-Molecule T4 Lysozyme Nonequilibrium
Conformational Dynamics under Enzymatic Reactions. J. Phys. Chem. B 2010, 114,
6669-6674.
35 Xie, X. S. Single-Molecule Approach to Enzymology. Single Mol. 2001, 4, 229-236.
36 Uversky, V. N. Natively unfolded proteins: a point where biology waits for physics. Protein
Sci. 2002, 11, 739–756.
37 Ziv, G.; Thirumalai, D.; Haran, G. Collapse transition in proteins. Phy. Chem. Chem. Phys. 97
2009, 11(1), 83-93.
38 de Gennes, P.-G. Scaling concepts in polymer physics; Cornell University Press: Ithaca,
1979.
39 Des Cloizeaux, J.; Jannink, G. Polymers in solution: their modeling and structure; Clarendon
Press: Oxford, 1990.
40 Kubelka, J. J.; Hofrichter, J. J.; Eaton, W. A. The protein folding 'speed limit'. Curr. Opin.
Struct. Biol. 2004, 14(1), 76-78.
41 Pitard E. Influence of hydrodynamics on the dynamics of a homopolymer. Eur. Phys. J. B
1999, 7, 665-673.
42 Socci N. D.; Onuchic J. N.; Wolynes P. Diffusive dynamics of the reaction coordinate for
protein folding funnels. J. Chem. Phys 1996, 104, 5860-5868.
43 Stigler, J.; Ziegler, F.; Gieseke, A.; Gebhardt, J. C.; Rief, M. The complex folding network of
single calmodulin molecules. Science 2011, 334, 512-516.
98
CHAPTER V. PROBING SINGLE-MOLECULE PROTEIN FOLDING
CONFORMATIONAL DYNAMICS IN CROWDED EVIRONMENT USING
SINGLE-MOLECULE FRET SPECTROSCOPY
This chapter is dedicated to the study of single-molecule protein folding dynamics in the presence of molecular crowding effects.
5.1. Introduction
The interior of living cells contains large numbers of macromolecules such as proteins, DNA and RNA molecules1-5. Volume fraction of occupied macromolecular agents is as large as 40%6,
7. Existence of such macromolecular networks has significant effects on the behavior of protein
conformational dynamics inside such networks6-8. For example, enzymatic reactions and
amyloid formations are profoundly affected in real crowded biological environments7. Protein
folding processes in the presence of molecular crowding is crucial to understand protein folding processes inside living cells. Various molecular scale microenvironments are readily emulated by molecular crowding effects such as extensive protein-macromolecule interactions and molecular confinement effects.7
Single-molecule techniques are powerful tools to probe molecular scale dynamic processes without ensemble averaging9-15. Molecular details of single protein folding are readily observed one molecule at a time12. As a key advantage, single-molecule FRET allows a clear separation of the folded and unfolded subpopulations, and thus enables a further quantitative
analysis of the properties of single-molecule protein conformational fluctuation dynamics 99
without interference from undesired ensemble averaged signals10, 12. Since single-molecule
FRET can provide distance and protein conformational fluctuation dynamic information without ensemble-averaging, it is promising to show intramolecular conformational dynamics to be observed at the thermal equilibrium10.
5.2 Materials and Methods
The single CaM molecule is mutated on N-terminal domain at residue 34 and C-terminal
domain at residue 110, and fluorescent dye pair Cy3/Cy5 are tethered onto the protein via
thiolation. These two dyes serve as a spectroscopic ruler for the measurement of
conformational fluctuation of the protein molecules in different concentration of crowding
reagent Ficoll 70. On the other hand, the Forster radius R0 of Cy3-Cy5 pair is ~5.4 nm, so the distance change of the two dyes monitoring the conformational change falls into measureable
range. In our experiment, we prepare the samples for single-molecule conformational
folding-unfolding dynamics measurements in the presence of crowding reagent Ficoll 70 inside the agarose gel (1% by weight, Type VII, Sigma). We make samples of CaM into different concentrations of denaturant solvent GdmCl in the mixture of 200 nM CaM, 1.25μL and oxygen scavenger with Trolox solution to obtain a 10μL mixture of enzyme and denaturant solvent.
The Trolox solution is made previously by dissolving about 1 mM
6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1 mg/mL glucose oxidase,
0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent dye from
photobleaching or blinking as a result of triplet state formation and other photophysical
processes. We then heat the 10μL 1% agarose gel just above its gel-transition temperature 100
(26°C) and quickly mix the above enzyme solution with denaturant solvent solution and the gel between two clean cover glasses to form a sandwich. All solutions are prepared with HEPES buffer at pH 7.4. Since we want to probe conformational dynamics of single enzyme molecule at different concentration of Ficoll 70, we carry out concentration dependent experiments with different ratio of mixture in the sandwich (Supporting Information).
Single-molecule photon stamping approach is used to record FRET trajectories at different
concentration of crowding reagent. This approach records emission of photons from donor and
acceptor channel one by one with arrival time. We construct the intensity trajectory as a function
of time with desired time resolution from recorded raw data. The experimental setup is an
inverted confocal microscope (Axiovert 200, Zeiss) which used a crystal laser (532nm CW)
delivering excitation. The Laser beam focus through a 100× oil immersion objective lens (1.3
NA, 100×, Zeiss) onto the upper surface of cover slip after reflected up by a dichroic beam
splitter (z532rdc, Chroma Technology). To obtain confocal microscopy image, we use an x-y
closed-loop piezo position scanning stage for raster-scanning of the sample sandwich.
Fluorescence from single molecules is collected through the same objective and the signal was
split by a dichroic beam splitter (640dcxr) into two different wavelengths 570nm for the donor
channel and 670nm for the acceptor channel. To detect the signal from two channels, two Si avalanche photodiode single photon counting modules (SPCM-AQR-16, Perkin Elmer
Optoelectronics) are used to record photons from donor and acceptor. A more detailed description of the experimental setup is in the literature.16-20
We first apply a 2D regional correlation mapping analysis to our single-molecule photon 101
stamping data. This 2D regional correlation mapping analysis calculates a two-dimensional
cross-correlation amplitude distribution (TCAD). In this analysis, each of the trajectories is
scanned with different starting and ending time. The cross-correlation amplitude of each time
segment with distinct starting and ending time are calculated. We use color bar to indicate the
stop tstop t amplitude of cross-correlation. Ccross(,:)()()()() tt start stop ItItdtAD ItItAD . tstart tstart
Where IA and ID are the two-band photon count intensities signal of donor and acceptor, and tstart and tstop give the scanning window width. The cross-correlation functions are calculated with different tstart and tstop along a pair of smFRET trajectories {IA(t)} and {ID(t)}. The cross-correlation functions are calculated with different starting and ending time. Via this method, we identify time segments along a specific trajectory with strong cross-correlation indicated by cold color blue. Since typically, single-molecule FRET trajectories are dominated by shot noises or average intensity drifts as a result of undesired protein motion. This method enabled us to locate true anti-correlated segments from single molecule trajectories for our further dynamics analyses.
We apply auto-correlation and cross-correlation analyses to our single-molecule
photo-stamping data after the identification of each anti-correlated single-molecule time
segments. The cross-correlation and auto-correlation function are defined to be
IAD0 I t IA 0 IADD I t I Ctcross IIAD00 IIIIA 00 AD D 102
IAA0 I t IA 0 IAAA I t I auto Ct 22 IA 0 IIAA0
where IA(t) and ID(t) representing acceptor and donor intensitie, and
means of the intensity trajectories respectively. Ccross(t) and Cauto(t) are cross-correlation and
autocorrelation functions.21-23
5.3 Results and Discussion
Figure 5.1 shows typical image from our inverted confocal microscopy. By raster-scan the
sample, a 20μm × 20μm sample image yields bright spots of single CaM molecules confined
in the network formed by agarose gel (~200nm in diameter). The spots indicating single
protein molecule are diffraction limited with approximately 300nm in diameter. We pin-point
each specific sample spot to gain continuous donor-acceptor (D-A) fluorescence intensity
trajectories shown in Figure 5.1. Typically, we gather more than seventy data points which consists of single-molecule trajectories of 40 seconds long at different concentration of
denaturant GdmCl, and we calculate the EFRET of each of the sample measured using the formula.
ItA() EtFRET () AA IAD()() t I t DD
Where A and D are the emission quantum yields of acceptor and donor dye molecules,
respectively, and A and D are the acceptor and donor detection efficiencies, respectively.
AA Here the correction factor is ~1 in our experiment conditions. DD 103
Figure 5.1. Single-Molecule Imaging and Analysis. Image obtained from Confocal Microscope of single CaM molecule. The bright spots are single molecules with diffraction limited (~300nm
in diameter) image. Typical Donor/Acceptor signals and EFRET trajectories. Green and red lines indicate the donor and acceptor channel respectively. The histogram distribution from EFRET trajectory gives the EFRET of a certain single-molecule. 104
Figure 5.2. EFRET Distributions. Distribution of FRET efficiency of different samples at different concentration of Ficoll 70. The shift in peak values characterizes the unfolding of CaM molecule
at higher concentration of crowding reagent.
The shifts in peak values of the distribution of all FRET efficiencies at different 105
concentration of Ficoll 70 mixed with CaM are the results of change of FRET efficiency (Figure
5.2) which are due to the unfolding and refolding of the single protein molecules. These changes in EFRET clearly evidence the conformational change of single CaM molecules under different concentrations of Ficoll 70. The EFRET distribution is consisting of both the folded
subpopulation with EFRET 0.6 and unfoled subpopulation with EFRET 0.3. In this study, we only
focus on the folding-unfolding fluctuating CaM molecules with EFRET 0.45. An ensemble average measurements and single-molecule measurements yield similar results that the 2M denature condition is the critical point of such titration. The FRET efficiency distribution at
50g/L Ficoll 70 is 0.36 and at 100g/L Ficoll 70 is 0.41, at which CaM molecules start to refold.
This conformational change measured by FRET is strong evidence of single CaM molecules enhanced stability by crowding reagent Ficoll 70. 24-30 As we increase Ficoll 70 concentration close to living cell macromolecule concentration ~300g/L, a remarkable decrease and broadening of EFRET distribution is observed. Such heterogeneous unfolding process as a result of crowding
effect cannot be resolved by conventional ensemble average measurements.31-39 We resolve
subpopulations of unfold and fold protein conformations and study detailed dynamic fluctuations
at the equilibrium. Mechanistic understanding of the single molecule protein folding energy
landscape can be extracted from this analysis.
106
Figure 5.3. Correlation Analyses. Autocorrelation function calculated from FRET efficiency
trajectory. In different concentrations of crowding reagent, the CaM molecule in its native state
show a correlation decay. Auto-correlations from intensity trajectory. Donor intensity trajectory
obtained from our single-molecule confocal microscopy (1 ms). The black line indicates the
threshold criterion separating the on- and off-time. Brown lines are the identified successive on- and off-time. The on-time distribution is a gamma shaped distribution representing a multiple step dynamic scheme. The simulated data is also shown.
We analyze the dynamical behaviors of our data sets by calculating the autocorrelation functions. By fitting the autocorrelation functions with exponential decays, we are capable of 107
characterizing the time scale of protein conformational fluctuation (Figure 5.3). Qualitatively,
each exponential function gives correlation lifetime of donor channel, and the broad distribution
of the lifetimes is a result of local environment heterogeneity. At low concentration of Ficoll 70,
CaM has a typical autocorrelation function with a sharp decay as a result of native protein
motion with typical time scale of millisecond. A strong contrast is shown in Figure 5.3. In
higher concentration of Ficoll 70, the CaM molecules, in its denatured states, show weak auto-correlation decay yielding second scale dynamics. Second scale dynamics is considerably slower than millisecond scale dynamics. This slow conformational fluctuation dynamics is due to the unfolding of CaM molecule in crowdedness which turns the proteins into random coils; the
correlation of protein’s regular motion becomes weaker. The two-dimensional regional
cross-correlation analyses help us to identify the time segments with strong anti-correlation of each single-molecule intensity trajectory. We zoom in to study each of the anti-correlated time segments by calculating the cross-correlation and auto-correlation respectively.
Subtle conformational dynamic signatures can be straightforwardly analyzed by the distribution of on- and off-times. The on-time and off-time are the “waiting time” for the CaM
folding and unfolding. To characterize such detailed dynamic behavior, we further bin our
trajectories to be one millisecond as shown (Figure 5.3). To obtain a folding waiting time distribution, we set up a threshold, at which the folding and unfolding states are separated. For the trajectory shown in Figure 5.3, we choose the value 7 as the threshold value, and subsequent folding waiting time distribution is shown.
Noticeably, the folding waiting time distribution is non-exponential resulting from a 108
multiple-state folding-unfolding dynamic scheme. Such distribution is also distinct from a
Gaussian distribution. This distinction clearly rules out the possibility of two-state
folding-unfolding dynamics for single CaM molecules. The gamma shaped folding waiting
time distribution indicates a more complex dynamic scheme involving multiple intermediates
and multiple steps. We attribute the non-exponential folding waiting time distribution to the
existence of multiple folding intermediates. To further characterize this multiple-intermediate
state dynamics, we exploit a one dimensional random walk model, which has been applied successfully in the modeling of multiple step single-molecule enzymatic reaction. We assume a
uniform rate constant k to each step, since we don’t have prior knowledge of the shape of the underling energy surface. The convolution of several Poisson process with uniform k gives gamma function shaped distribution to reproduce the mean and standard deviation of the original folding waiting time distribution with certain accuracy. The error of this recipe will be reflected in the difference between the simulated and measured mean. The number of Poisson steps involved in this convolution calculation gives an estimation of the lower bound of how many
Poisson rate processes are present. Since we assigned each Poisson step to a folding intermediate,
the simulated step number will be our best estimation of folding intermediate state number.
P t Aexp t / where P(t) is the probability distribution of the Poisson rate process step times, τ is the averaged
Poisson rate process step time, and A is the distribution weight constant. To calculate the
convolution of function f(t) and g(t), the integration equation is 109
t f g t f v g t v dv 0 n1 n ttexp / PATn n 1!
Where n (1, 2, 3,…, N) is the index of the intermediate steps; is the mean formation time of a folding intermediate through a single-step process and A is the normalizing factor of this probability distribution. The simulated distribution shown in the figure involves two Poisson rate processes which indicated a 2-step three state dynamics.40-42
Presumably, macromolecular crowding effect plays an enhancing role in protein folding process. However from our single-molecule experiment, we deduce polymer crowding might have enhancing and diminishing the protein folding stability in that over-crowdedness could potentially reduce the stability of protein molecules in the matrix. Such is a consequence of a balance of hydrophobic, hydrophilic and solvation thermodynamics and dynamics. Using polymer solution theory, we straightforwardly understand such counterintuitive phenomenon by calculating Helmholtz free energy and force exerted by the polymer matrix. In concentrated polymer solution of Ficoll 70, the very existence of another polymer will automatically exert a force on the target polymer. Size of the polymer R=N0.5φ-0.35b, where b is the monomer size,
φ the volume fraction and N degrees of polymerization. Blob size g=(Nb2)/(φ2R2). In our current analyses, our target polymer is the single-molecule CaM protein molecules. Since we increase rather than decrease the artificial crowder molecule Ficoll 70, the Ficoll 70 molecule applies a force on the CaM protein molecules. The exerted force is at molecular scale force typically at pico-newton scale used to unfolding or manipulates protein molecules. Since 110
polymer force is in principle entropic force originates from thermal fluctuation, it only makes sense to consider such subtle force and time scale in condensed phase protein folding dynamics.
To further quantitatively understand the force feature of our current experiment, we calculate
thermodynamic quantities from equilibrium polymer solution theory. The entropic nature of the
forces applied in single-molecule protein folding experiment can be straightforwardly calculated
from statistical mechanics. Since statistical mechanics results are textbook standards, we don’t
have to start from classical partition function, rather we directly use equipartition theorem. From
equipartition theorem, to every degree of freedom, there is thermal energy kT associated to that degree of freedom solely as a result of entropy and thermal fluctuation energy. The Helmholtz free energy F = (kTN)/g = (kTφ2R2)/b2 is essentially the amount of kT thermal energy stored in
an extended polymer. The physical picture of polymer solution chemistry directly implies an
extended fibril like equilibrium solution dynamics of single protein molecules. Basically, it means when we increase the concentration of polymer solution, due to monomer-monomer
interactions, the polymers automatically reorganize themselves to form the concentrated polymer solution. To estimate the forces in this macroscopic dynamic polymer solution, we differentiate the Helmholtz free energy with respect to R to get the force exerted on target polymer f =
(2kTN0.5φ1.65)/b. For Ficoll 70, the specific volumeφ is 0.67ml/g. In our experiment, the
crowded region has a polymer concentration of 300g/L, the volume fraction of Ficoll 70 is 20%.
In this crowded region, we observe protein unfolding resolved from single-molecule data. The
monomer size of polymer Ficoll 70 is 3.9 Å. So the calculated force is 18.8 pN. From AFM and optical tweezer experiments, such force is strong enough to denature protein into unfolded 111
states. More recently, an experiment demonstrates that such force can also crush single proteins
into unfolded states.
We also estimate the conformational diffusion coefficient from the folding waiting time
distribution. From our previous experiments, we already have the mean conformational drift
distance XtN to be 1.22nm. Using formula , we calculate the diffusion coefficient D of this
2-step dynamic process to be 13.2×10-13 cm2/s. The diffusion coefficient is directly related to
the shape of the underlying energy landscape, since it reflects the local mean square fluctuation
of the activation barrier of the folding-unfolding dynamic process.
2 t2 X t unfold N D 3 2 tunfold
t where D is the conformational diffusion coefficient. The mean unfolding time, unfold , and the
t 2 standard deviation of the unfolding time distribtuion, unfold ， are directly measured in our
experiment. The total drifting distance of the folding-unfolding conformational motion,
Xt N , is associated to the folding-unfolding conformational distance change. The activation barrier is as high as 12 kT, a 10% increase from simple protein folding experiments. However the increase in the local mean square fluctuation is approximately 20%. This extraordinary fact lies in the molecular scale interaction between the polymer Ficoll 70 and our target protein CaM. We compare this number to standard Hydrogen bonding, which is typically 2-10kT. The existence of
crowding reagent increases the fluctuation dynamics of hydrogen bonding within CaM protein
molecule by making the folding energy landscape “rougher”. Such subtle molecular scale
conformational interaction energy might play a key role in sub-cellular protein-protein 112 interactions.
Figure 5.4. Folding Pathway Distribution in Protein Folding. The scatter plot we constructed with number of steps involved in each of the dynamic process vs. conformational diffusion coefficient. The folding-unfolding dynamics pattern naturally clustered into separated domains.
Subsequently, a CaM folding energy landscape can be extracted, and a distribution of the folding paths with distinct probability assigned to each of them can be achieved.
We have analyzed approximately 30 trajectories under different crowding conditions to acquire a distribution of such dynamic pattern. For each of them, we simulate the number of steps involved in the dynamic process, and we also calculate the folding-unfolding 113 conformational diffusion coefficient. A two dimensional scatter plot is constructed with conformational diffusion coefficient vs. number of steps (Figure 5.4). Clearly, a pattern emerged. Folding-unfolding trajectories with same number of steps and similar conformational diffusion coefficient cluster together. This cluster behavior is clearly a manifestation of an energy landscape with distinct folding pathways. Moreover, these various folding pathways have a distribution with distinct probabilities. To better see this, we convert the two-dimensional scatter plot to be a two dimensional energy landscape plot with color arrow indicating different folding pathways. Our results suggest four different folding pathways of
CaM molecule folding process both in the crowding enhancing and diminishing regions.
Figure 5.5. A Cartoon Showing Folding Process. A cartoon showing a combination of molecular scale effects lead to protein unfolding under buffer condition. Such molecular crowding effects leading to a protein unfolding can be seen as a concerted effect of solvation and macromolecular crowding.
114
5.4 Conclusions
We demonstrate single-molecule protein folding-unfolding conformational dynamics in the
presence of molecular crowding effect provided by Ficoll 70. In our single-molecule FRET experiment, we observe large heterogeneity of EFRET which is clear evidence of single-molecule protein refolding and unfolding processes. Such remarkable detailed information of
conformational dynamics eludes ensemble-averaged experiments due to averaging. The enhanced folding process is entropic driven process which stabilizes single protein molecules and refolds proteins into their native states. However, at higher concentrations of crowding reagent Ficoll 70, we observe the unfolding of single protein molecules which are a combined process of polymer-polymer interactions, entropic and solvation mechanism. Utilizing the polymer solution theory, we show such unfolding processes can be understood as an isotropic force exerted on single-molecule protein solely due to the existence of host polymers.
Subtle conformational fluctuation dynamics can be readily observed and studied by single-molecule techniques. The longer folding conformational fluctuation time indicates an enthalpic trap provided by the presence of molecular crowding reagents. In other words, extensive polymer-polymer interactions slow down folding conformational fluctuations by favoring the unfolded states of single-molecule proteins. By our dynamic model, we observe a converged folding pathway due to normal crowding reagents as a result of entropic effects.
Simply, the existence of polymer provides excluded volume which decreases the sampling conformations available for protein molecules. However, in concentrated regime of polymer solutions, such entropic effects are out-favored by polymer-polymer interactions and solvation 115
effects which destabilize single-protein molecules. The unfolding process due to molecular
crowding is highly heterogeneous, which is a manifestation of complex, cooperative biological
mechanisms.
5.5 Reference:
1 Lu, H. P.; Xun, L. Y.; Xie, X. S. Single-Molecule Enzymatic Dynamics. Science 1998, 282,
1877–1882.
2 Chen, Y.; Hu, D. H.; Vorpagel, E. R.; Lu, H. P. Probing Single-Molecule T4 Lysozyme
Conformational Dynamics by Intramolecular Fluorescence Energy Transfer. J. Phys. Chem.
B 2003, 107, 7947–7956.
3 Schuler, B.; Lipman, E. A.; Eaton, W. A. Probing The Free-Energy Surface for Protein
Folding with Single-Molecule Fluorescence Spectroscopy. Nature 2002, 419, 743-747.
4 Lu, H. P.; Iakoucheva, L. M.; Ackerman, E. J. Single-Molecule Conformational Dynamics of
Fluctuating Noncovalent DNA-Protein Interactions in DNA Damage Recognition. J. Am.
Chem. Soc. 2001, 123, 9184-9185.
5 Tan, X.; Nalbant, P.; Toutchkine, A.; Hu, D.; Vorpagel, E. R.; Hahn, K.M.; Lu, H. P.
Single-Molecule Study of Protein-Protein Interaction Dynamics in a Cell Signaling System. J.
Phys. Chem. B. 2004 108, 737-744.
6 Ha, T. J.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.;
Weiss, S. Single-Molecule Fluorescence Spectroscopy of Enzyme Conformational Dynamics
and Cleavage Mechanism. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 893–898.
7 Anfinsen, C. B.; Haber, E.; Sela, M.; White, F. H., Jr. The Kinetics of Formation of Native 116
Ribonuclease During Oxidation of the Reduced Polypeptide Chain. Proc. Natl. Acad. Sci.
USA 1961, 47, 1309-1314.
8 Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Theory of Protein Folding: the Energy
Landscape Perspective. Annu. Rev. Phys. Chem. 1997, 48, 545-600.
9 Dill, K. A.; Chan, H. S. From Levinthal to Pathways to Funnels. Nat. Struct. Biol. 1997, 4 (1),
10-19.
10 Thirumalai, D.; Klimov, D. K. Deciphering the Timescales and Mechanisms of Protein
Folding Using Minimal Off-Lattice Models. Curr. Opin. Struc. Biol. 1999, 9 (2), 197-207.
11 Zoldak, G.; Rief, M. Force as a Single Molecule Probe of Multidimensional Protein Energy
Landscapes. Curr. Opin. Struc. Biol. 2013, 23 (1), 48-57.
12 Deniz, A. A.; Laurence, T. A.; Beligere, G. S.; Dahan, M.; Martin, A. B.; Chemla, D. S.;
Dawson, P. E.; Schultz, P. G.; Weiss, S. Single-Molecule Protein Folding: Diffusion
Fluorescence Resonance Energy Transfer Studies of the Denaturation of Chymotrypsin
Inhibitor 2. Proc. Natl. Acad. Sci. USA 2000, 97 (10), 5179-5184.
13 Nettels, D.; Gopich, I. V.; Hoffmann, A.; Schuler, B. Ultrafast Dynamics of Protein Collapse
from Single-Molecule Photon Statistics. Proc. Natl. Acad. Sci. USA 2007, 104 (8),
2655-2660.
14 Nettels, D.; Hoffmann, A.; Schuler, B. Unfolded Protein and Peptide Dynamics Investigated
with Single-Molecule FRET and Correlation Spectroscopy from Picoseconds to Seconds. J.
Phys. Chem. B 2008, 112 (19), 6137-6146.
15 Haran G. How, When and Why Proteins Collapse: the Relation to Folding. Curr. Opin. Struc. 117
Biol. 2012, 22 (1), 14-20.
16 Sherman, E.; Haran, G. Coil-Globule Transition in the Denatured State of a Small Protein.
Proc. Natl. Acad. Sci. USA 2006, 103 (31), 11539-11543.
17 Ziv, G.; Thirumalai, D.; Haran, G. Collapse Transition in Proteins. Phy. Chem. Chem. Phys.
2009, 11 (1), 83-93.
18 Hoffmann, A.; Kane, A.; Nettels, D.; Hertzog, D. E.; Baumgartel, P.; Lengefeld, J.; Reichardt,
G.; Horsley, D. A.; Seckler, R.; Bakajin, O.; et al. Mapping Protein Collapse with
Single-Molecule Fluorescence and Kinetic Synchrotron Radiation Circular Dichroism
Spectroscopy. Proc. Natl. Acad. Sci. USA 2007, 104 (1), 105-110.
19 Chung, H. S.; Louis, J. M.; Eaton, W. A. Experimental Determination of Upper Bound for
Transition Path Times in Protein Folding from Single-Molecule Photon-by-Photon
Trajectories. Proc. Natl. Acad. Sci. USA 2009, 106 (29), 11837-11844.
20 Chung, H. S.; McHale, K.; Louis, J. M.; Eaton, W. A. Single-Molecule Fluorescence
Experiments Determine Protein Folding Transition Path Times. Science 2012, 335 (6071),
981-984.
21 Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Eastwood, M. P.;
Bank, J. A.; Jumper, J. M.; Salmon, J. K.; Shan, Y.; et al. Atomic-Level Characterization of
the Structural Dynamics of Proteins. Science 2010, 330 (6002), 341-346.
22 Garcia-Mira, M. M.; Sadqi, M.; Fischer, N.; Sanchez-Ruiz, J. M.; Munoz, V. Experimental
Identification of Downhill Protein Folding. Science 2002, 298 (5601), 2191-2195Pirchi M.;
Ziv G.; Riven I.; Cohen S. S.; Zohar N.; Barak Y.; Haran G. Nat. Commun. 2011, 2, 493-450. 118
23 Chin, D.; Means, A. R. Calmodulin: A Prototypical Calcium Sensor. Trends Cell Biol. 2000,
10 (8), 322-328.
24 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-Binding Domains - Just 2-Faced or
Multifaceted. Trends Biochem. Sci. 1995, 20 (1), 38-42.
25 Liu, R.; Hu, D.; Tan, X.; Lu, H. P. Revealing Two-State Protein-Protein Interactions of
Calmodulin by Single-Molecule Spectroscopy. J. Am. Chem. Soc. 2006, 128 (31),
10034-10042.
26 James, P.; Vorherr, T.; Carafoli, E. Calmodulin-Binding Domains - Just 2-Faced or
Multifaceted. Trends Biochem. Sci. 1995, 20 (1), 38-42.
27 Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J.
Three-Dimensional Structure of Calmodulin. Nature 1985, 315 (6014), 37-40.
28 Chattopadhyaya, R.; Meador, W. E.; Means, A. R.; Quiocho, F. A., Calmodulin Structure
Refined at 1.7 Angstrom Resolution. J. Mol. Biol. 1992, 228 (4), 1177-1192.
29 Slaughter, B. D.; Unruh, J. R.; Price, E. S.; Huynh, J. L.; Bieber Urbauer, R. J.; Johnson, C.
K. Sampling Unfolding Intermediates in Calmodulin by Single-Molecule Spectroscopy. J.
Am. Chem. Soc. 2005, 127 (34), 12107-12114.
30 Wang, X.; Lu, H. P. 2D Regional Correlation Analysis of Single-Molecule Time Trajectories.
J. Phys. Chem. B. 2008, 112 (47), 14920-14926.
31 He, Y.; Li, Y.; Mukherjee, S.; Wu, Y.; Yan, H.; Lu, H. P. Probing Single-Molecule Enzyme
Active-Site Conformational State Intermittent Coherence. J. Am. Chem. Soc. 2011, 133 (36),
14389-14395. 119
32 Wang, Y.; Lu, H. P. Bunching Effect in Single-Molecule T4 Lysozyme Nonequilibrium
Conformational Dynamics Under Enzymatic Reactions. J. Phys. Chem. B 2010, 114 (19),
6669-6674.
33 Xie, X. S. Single-Molecule Approach to Enzymology. Single Mol. 2001, 2 (4), 229-236.
34 Uversky, V. N. Natively Unfolded Proteins: A Point Where Biology Waits for Physics.
Protein Sci. 2002, 11 (4), 739-756.
35 Ziv, G.; Thirumalai, D.; Haran, G. Collapse Transition in Proteins. Phy. Chem. Chem. Phys.
2009, 11 (1), 83-93.
36 de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca,
1979.
37 Des Cloizeaux, J.; Jannink, G. Polymers in Solution: Their Modeling and Structure;
Clarendon Press: Oxford, 1990.
38 Kubelka, J.; Hofrichter, J.; Eaton, W. A. The Protein Folding 'Speed Limit'. Curr. Opin. Struc.
Biol. 2004, 14 (1), 76-88.
39 Pitard E. Influence of Hydrodynamics on the Dynamics of a Homopolymer. Eur. Phys. J. B
1999, 7 (4), 665-673.
40 Socci, N. D.; Onuchic, J. N.; Wolynes, P. G. Diffusive Dynamics of the Reaction Coordinate
for Protein Folding Funnels. J. Chem. Phys 1996, 104 (15), 5860-5868.
41 Stigler, J.; Ziegler, F.; Gieseke, A.; Gebhardt, J. C. M.; Rief, M. The Complex Folding
Network of Single Calmodulin Molecules. Science 2011, 334 (6055), 512-516.
42 Zwanzig, R. Diffusion in a Rough Potential. Proc. Natl. Acad. Sci. U.S.A. 1988, 85 (7), 120
2029-2030.