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FOLDING

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EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION OF EARLY
EVENTS IN PROTEIN FOLDING

By
Vijay R. Singh

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Physics and Astronomy
Biochemistry and Molecular Biology

2009

ABSTRACT

EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION OF
EARLY EVENTS IN PROTEIN FOLDING

By
Vijay R. Singh

Knowledge of the early events in protein folding and its characterization is essen-
tial for complete comprehension of the protein folding problem: structure, pathways,
and mechanisms. The chemical heterogeneity, topological entanglements, and dy-
namic nature of the unfolded state conformation pose a huge challenge to a accurate
description. Recent years have witnessed a boost in the efforts to develop experimen-
tal techniques to characterize the unfolded state of protein under folding conditions.
This will have immense implications not only in diagnostic and therapeutic strate-
gies for tackling protein misfolding and aggregation based diseases but also in paving
way for development of evolutionarily superior biological structures and design of
effective drugs against resist ant pathogens.

Using an experimental technique that involves monitoring the tryptophan triplet-
triplet optical absorption to measure its lifetime against intramolecular TYp/Cys
contact quenching, we investigated the unfolded state of two structurally similar but
sequentially nonhomologous still well behaved Bl domains of proteins - L and G.
Employing the Szabo, Schulten, and Schulten (SSS) theory with a wormlike chain
polymer model, we observe that the loss of denaturant yields an unfolded state that
is less diffusive and more compact than the fully denatured state. This reflects the

complex internal dynamics of the proteins mediated by transient interactions through

the chain.

Polyglutamine amino acid motif is implicated in several neurodegenerative dis-
eases, all of which exhibit aggregation in vivo. To understand the mechanism and
correlation between the long glutamine stretches and consequent destabilizion of
the proteins leading to amyloid fibrilation, we probed the structural properties of
polyglutamine polypeptides using Trp/Cys contact quenching. Modeling the length
dependence of contact formation rates with a wormlike chain with excluded volume,
we find the polyglutamine peptides to be a unusually “stiff” polymer with a persis-
tence length of ~ 13.0 A. This propensity for extended conformation can explain
both the decrease in stability of the host protein and the propensity to form amyloids
once unfolded.

A detailed atomic level characterization and the intricate interplay between ki-
netic and» thermodynamic controls at various phases of protein folding can be ob-
tained using accurate molecular modeling and simulations. This complements the
experimental techniques by providing insights at higher temporal and structural res-
olutions, generally inaccessible to experiments. We consolidated this technique with
'Irp/Cys contact quenching to characterize the unfolded states of protein L. Making
quantitative comparisons between experimentally obtained denaturant-induced un-
folded ensemble and computationally simulated temperature-induced unfolded en-
semble, we observe a low intrachain diflusion rate that decreases with denaturant
concentration. This low diffusion can limit the folding speed and its origin can be

quantified by close inspection of the simulated trajectories.

ACKNOWLEDGMENT

It has been a five year long journey and as I bring my graduate life to a close, I
realize how various people have helped and guided me to be the person I am today.

First and foremost I would like to thank my advisor Dr. Lisa Lapidus ..... You
have given me the freedom to explore and gently nudged me in the right direction
when I was stranded. You have also helped me put my thoughts in newer and better
perspective and listened to me patiently while I made my naive arguments and
proposals ..... I surely could not have asked for a better advisor, mentor and friend.
I will always take pride in acknowledging you as my mentor through my graduate
experience. Apart from science, I have also learned valuable time management and
leadership skills from you that are helping me develop a more harmonious personality.

I also welcome the rewarding experience and guidance that I received from Dr.
Wedemeyer ...... You walked me through the areas of computational biophysics. Your
thoughts and ideas infuse a lot a positive aggression in me to tackle the problems in
science from multiple perspectives.

During the course of this endeavor I have had the opportunity to meet and grow
with many people, colleagues and otherwise. Michaela executed many of the initial
experiments in addition to performing protein expression and purification ..... I picked
up my first lessons in cell culture from you. A very special thanks to Terry ...... But
for your hard work, skill, and dedication, many of us in the lab would not be able to
confront our research problems with such ease and planning.

Beyond friends and colleagues is family. My family has been a source of inspira-

tion and perspiration for me....I would like to express my gratitude to you. My Uncle-

iv

Aunt and their extended family (Sandhya and family, Vandana and family)....You
stand behind me all through my life and teach me the value of education and re-
sponsibility. I am the man I am because of you. To Kavitha and Sanjay ..... These
words would not have been written but for you. My parents ..... You had the foresight
to send me to better schools, away from home, when I was yet to comprehend the
magnitude of your decision.

And finally to my wife Kasturi Chatterjee, who is on the way to her own grad-
uation, for always being there for me. For always having the faith and trust in my

endeavors. And for understanding me even when I do not make any sense.

TABLE OF CONTENTS

List of Tables ................................. viii
List of Figures ................................ ix
Introduction to Proteins and The Protein Folding Problem . . 1
1.1 The Protein Folding Problem ...................... 1
1.2 Amino Acids and Proteins ........................ 3
1.3 Forces and Interactions .......................... 7
1.4 Time Scales and Energy ......................... 9
1.5 Foundation for Protein Folding Studies ................. 11
1.6 Mechanism and Hypothesis for Protein Folding ............ 13
1.7 Unfolded States and Protein Folding .................. 15
Transient Absorption Spectroscopy Applied to Polymer Dynamics 20
2.1 Introduction ................................ 20
2.2 Application of Pump-Probe Spectroscopy ................ 22
2.3 The Instrumentation ........................... 27
2.4 The Sample Preparation ......................... 30
2.5 Data Acquisition and Analysis ...................... 31
2.6 Reaction and Diffusion Limited Rates .................. 34
2.7 SSS Theory and Polymer Chain Model ................. 35
Unfolded States of Proteins and Peptides: Experimental Investiga-

tion .............................. 40
3.1 Introduction ................................ 40
3.2 Results for Polyglutamine ........................ 42
3.3 Wormlike Chain Modeling of Polyglutamine .............. 47
3.4 Proteins L and G ............................. 55
3.5 Structure and Stability of Proteins L and G .............. 56
3.6 Contact Formation Kinetics ....................... 61
3.7 Dynamics of Proteins L and G ...................... 66

vi

4 Protein L Simulations and Experiment ............ 76

4.1 Introduction ................................ 76
4.2 Methods: Simulations and Experiment ................. 78
4.3 Results and Discussion .......................... 80
4.4 Comparison: Simulation and Experiment ................ 93
5 Summary ........................... 101
Appendix 107
A Polymer Models for Describing Unfolded State Conformations . 107
A1 Keely-Jointed Chain ........................... 108
A2 Gaussian Chain .............................. 110
A.3 Worm-Like Chain Model ......................... 112
B Calibrating Simulated Unfolded Ensembles with Experiment: Poly-
mer Theory Approach ..................... 115
B.1 Dill Polymer-Model ............................ 116
R2 Ziv Polymer-Model ............................ 117
R3 Fitting Polymer Theory Models to Simulated Data .......... 118
BA Comparing Simulated and Experimental Unfolded Ensembles ..... 119
Bibliography ......................... 124

vii

1.1

1.2

3.1

3.2

3.3

3.4

3.5

B.1

LIST OF TABLES

Time scales in Protein Folding ...................... 11
Energy Scales in Protein Folding .................... 11
Polyglutamine Fit Parameters ...................... 45
Polyglutamine Peptide Diflusion Coeflicients .............. 51
Thermodynamic Parameters for protein L ............... 62
Proteins L and G: Parameters for Wormlike Chain Simulations . . . . 71
Proteins L and G: Diffusion Coeflicients. ................ 73
Average Radius of Gyration from Simulations ............. 119

viii

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

3.1

3.2

3.3

LIST OF FIGURES

Amino Acids and Protein Polymerization ................ 4
Structural Hierarchy in Protein Structure ................ 6
Energy Landscape for Protein Folding ................. 16
Time Span of Folding Events and Pump-Probe Spectroscopy ..... 21
Electronic Energy Levels of Tryptophan ................ 23
Schematic of Loop Formation and Quenching ............. 25
Transient Absorption Instrumentation ................. 28
Representative Tryptophan 'IIiplet Kinetics .............. 32

Observed Rates and Fits: Reaction-Limited and Diffusion-Limited Rates 33

Illustration of Reaction Limited Rate .................. 35
Illustration of Difl‘usion Limited Rate .................. 36
Polyglutamine: Viscosity and Observed Rates .............. 44
Polyglutamine: Reaction-Limited and Diffusion-Limited Rates . . . . 46
Polyglutamine Rates Compare to AGQ Rates ............. 48

ix

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Polyglutamine Sum of Squares. ..................... 49

Polyglutamine Observed Kinetics ..................... 50
Native Structure of Protein G ...................... 57
Native Structure of Protein L ...................... 58
Model for Contact Formation ...................... 59
Tryptophan Absorbance Profile ..................... 60
Unfolded Fraction of Proteins L and G ................. 61
Observed Rates for Proteins L and G .................. 63
Energy Landscape Representation: Final Folding Conditions ..... 65
Proteins L and G: Viscosity and Observed Rates ............ 67
Protein L and G: Reaction and Difl‘usion Limited Rate ........ .68
Protein L: F22A, K23C, W47 Observed Triplet Kinetics. ....... 81
Protein L F22A, K23C, W47: Viscosity and Observed Rate ...... 82
Protein L MD 400K Time Evolution of RMSD with respect to Various

Conformations ............................... 83
Protein L T57C Probability Distribution from 400K to 800K ..... 84
Protein L Autocorrelation Function ................... 85
Protein L T57C Relaxation Time Constant with Temperature . . . . 86
Protein L T57C MD 300K Probability Distribuiton of Distances . . . 87
Autocorrelation Function Protein L T57C 300K ............ 88

4.9 Convergence of simulated intermolecular distance distributions . . . . 90
4.10 Relative entropy: A measure of convergence .............. 91

4.11 Reaction-Limited and Diffusion-Limited Rates for Protein L F22A,
K23C .................................... 93

4.12 Reaction-Limited Rate for Protein L (K23C): Experimental and Sim—
ulated ................................... 95

4.13 Reaction-Limited Rate for Protein L (T57C): Experimental and Sim-
ulated ................................... 96

4.14 Compare Experimental and Computational Diffusion Coefficient: T57C 98

4.15 Compare Experimental and Computational DiEusion Coefficient: K23C 99

A1 Freely-Jointed Chain Model ....................... 108
A2 Gaussian Chain Model .......................... 111
A.3 Worm-Like Chain Model ......................... 114
B.1 Polymer Model Fit for Radius of Gyration - 1 ............. 120
8.2 Polymer Model Fit for Radius of Gyration - 2 ............. 121
3.3 Coil-Globule Transition in Denatured Proteins ............. 123

Chapter 1

Introduction to Proteins and The

Protein Folding Problem

1.1 The Protein Folding Problem

Proteins are biological heteropolymers understood to be constituted from twenty
different species of monomers called amino acids. They form some of the most
versatile molecules in living beings, playing significant role in almost all the biological
ftmctions. About half the dry mass of the human body is proteins. Protein functions
include operating as antibodies to defend against pathogens, transport and storage of
ions and molecules (like oxygen by hemoglobin, iron by transferrin), form the building
blocks of other biological structures (for instance, bones and hairs are constituted
mainly by collagen), and enzymatic catalysis of most chemical reactions. For proteins

to successfully perform their biological function, they are known to adopt a well

1

defined unique three-dimensional structure.

The architecture of the biologically active protein depends on its amino acid se-
quence and the biological function of the protein itself is strongly correlated to its
structure. Therefore, any deviation from the native state conformation can lead to
the so called “protein-misfolding diseases”. A common feature among many such
diseases, such as the Alzheimer’s, Parkinson’s, and Prion diseases such as bovine
spongiform encephalopathy (BS E) and its human equivalent Creutzfeld-Jakob dis-
ease (CJ D), is formation of toxic aggregation or amyloid fibrils in viva [1—3]. Devel-
opment of any therapeutic treatment against such diseases requires a knowledge of
the dynamics, kinetics, mechanisms, and thermodynamics of the folding pathways
and concomitant conformations [4, 5]. This constitutes THE PROTEIN FOLD-
ING PROBLEM - accurately predicting the three-dimensional (most often) ther-
modynamically stable native state of a protein from the knowledge of its amino acid
sequence under normal physiological conditions [6]. This involves not only predicting
of the native state but also delineating the mechanism as to how the protein folds. A
complete solution to the protein folding problem is possible only through a compre-
hensive understanding of the unfolded state ensemble under folding conditions [7,8].
The characteristics of normative states has yet to be fully comprehended and its role
in protein folding is now being actively investigated. Large amounts of research has
been invested on studying the native states of proteins and hence we currently have
plenty of information on the folded configurations. It is essential to understand the
properties of the unfolded states of a protein under native conditions to predict the

overall and complete behavior of the protein. This will have deep impacts in pro-

2

tein engineering and drug design to not only combat the current pathogens through
immune resistant therapeutic strategies but also to design evolutionarily superior

biological machinery.

1.2 Amino Acids and Proteins

In the cells, proteins and polypeptide chains are synthesized linearly in the ribosomes
through a polycondensation reaction of amino acids. An a-amino acid is constituted
of a carboxyl group, an amino group, a hydrogen atom and a distinctive side chain
(R group) chemically bonded to the a-carbon atom. The structure of this R-group
distinguishes the amino acids from one another by according them different physical
characteristics - polar and non polar, aromatic, hydrophobic or hydrophilic, basic or
acidic, etc. The a-carbon atom is asymmetric and all Ca atoms except for glycine
have the same chirality of left-handedness. The 20 most common naturally occurring

amino acids are:

0 N on-Polar Hydrophobic Sidechain Residues: Alanine, Isoleucine, Leucine, Me—
thionine, Phenylalanine, Proline, Tryptophan, Valine.

0 Polar Neutral Residues: Asparagine, Cysteine, Glutamine, Glycine, Serine,
Threonine, Tyrosine.

o Positively Charged (Basic) Residues: Arginine, Histidine, Lysine.

o Negatively Charged (Acidic) Residues: Aspartic acid, Glutamic acid.

A peptide bond between the carboxyl and amino groups of adjacent amino acid

residues causes the polymerization of the resultant protein as shown in figure 1.1.

3

1 $2
-coo- +NH3-c-coo-
H

+NH3-

I-n -FU

$1 '32
+NH3" (IZ'CO'NH' C'COO-
M

H Peptide H
bond

Figure 1.1: Amino Acids and Protein Polymerization.

 

Protein sequence is determined by gene sequence, the protein sequence governs
the protein structure; and the protein function is determined by its structure. There
are various physical interactions - electrostatics of charge and partial charges, geome-
try of hydrophobic collapse and stereochemistry of amino acid residues, and strength
of various chemical bonds, etc., - at work right from its genesis in the ribosomes that
define a protein’s native structure [9]. Proteins with similar structure appear to
have a similar physiological ftmction. Therefore, the key to understanding protein
ftmction is in its geometrical architecture. Existence of regular local ordering in the
structure of proteins was theoretically predicted by Pauling and Corey in the year
1951 [10, 11]. They predicted the existences of a-helices and fl—sheets that are en-

4

ergetically more stable and have a well defined network of hydrogen bonds. This
represents a loss in the degree of freedom when the protein adopts its native state.
Following that, innumerable protein structures have been solved and a few repetitive
folding motifs seem to be a common theme in all the protein architectures. They
in fact seem to form the building block for the comprehensive structure. Based on
the current database of solved protein structures, the strata in protein architecture

is segregated into four levels of structural hierarchy (Figure 1.2):

1. Primary Structure: This is just the chemical composition of amino acid se-
quence linearly along the main chain backbone. The primary structure of every
protein is unique. By convention, the protein primary structure is numbered
from the amino terminal to the carboxyl terminal.

2. Secondary Structure: Local ordering in the linear sequences of the chemically
bonded amino acids form the secondary structure. Governed and driven by
the energy considerations, they are defined by backbone hydrogen bonding and
bond rotations. Depending on the network of the hydrogen-bonds between the
amide group and the carboxyl group, the secondary structure motif could either
be a a-helix, a fl-sheet or a turn. In a-helices the H-bonds are aligned parallel
to the helical axis, while in the B-sheets the H-bonds lies perpendicular to axis
of the strand.

3. Tertiary Structure: The thermodynamically and kinetically stable three dimen-
sional structure formed by packing together of the secondary structure elements
is referred to as the tertiary structure. This, in most cases, is the biologically

active and functional protein self-assembled by the considerations of energy,

5

(a)

   

(C)

Figure 1.2: Structural Hierarchy in Protein Structure: (8.) Primary structure be-
ing the linear chemical sequence, (b) Secondary structures a-helix and ,B-sheet, (c)
Tertiary structure made up by synthesis of secondary structure elements, and (d)
Quaternary structure. Figure (b) is adopted from Petsko and Ringe [12].

entropy, and hydrophobicity.

4. Quarternary Structure: An ensemble of smaller units of tertiary structures,
usually stabilized by weak inter-residue interactions, to form an integrated
structure of multiple domains where each domain is constituted by a single

distinct polypeptide chain.

1.3 Forces and Interactions

The secondary structures in proteins and polypeptides are usually not stable in
isolation and the tertiary and quaternary protein structures are only marginally more
stable compared to the unfolded conformation ensemble. A delicate balance between
the forces that drive the protein towards folding and those that oppose it lends the
native state a stability that generally corresponds to a thermodynamically global
energy minimum. Typically the free energy difference due to protein folding is in the
range of -5 to -15 kcal/mol [13, 14]. The current consensus for the dominating effects
in protein folding are hydr0phobic forces, network of hydrogen bonding, and entropic
considerations [9]. Other factors involved in folding and stability are: disulfide salt-
bridges, Van der Waals forces, electrostatic Coulomb interactions, solvent pH, and
temperature.

The Hydrophobic Effect: Hydrophobic effect is defined as the free energy as-
sociated with transfer of hydrophobic surface from protein interior to water. Seven
of the twenty amino acids are considered to have strongly hydrophobic side chains.

Residues valine, isoleucine, leucine, methionine, phenylalanine, alanine, and proline

7

“’1

I054-

each have a non polar side chain and so cannot form any hydrogen-bond with wa-
ter molecules. They in fact disrupt the hydrogen-bond network favorable to water
molecules and force them in forming an ordered (decreased entropy) cage-like or ice-
like structure around the non-polar group [15]. This entropic loss can be minimized
by minimizing the surface area of the non-polar group accessible to the polar solvent.
This results in the molecules with hydrophobic side chains coalescing together to ex-
clude the water molecules and thus collapsing into a compact globular state. The
degree of compaction and relative strength of the stability of native conformation
depends on distribution of hydrophobic residues along the primary sequence of the
protein chain. However, the hydrophobic effect alone cannot account for the observed
regular geometric structures in a protein core and therefore other molecular forces

and interactions must be taken into consideration to describe the unique native state.

Hydrogen-Bonding: This is a partial sharing of a hydrogen between two atoms
where the hydrogen is covalently bonded to one of the electronegative atoms. The
link is provided by electrostatics and strength dictated by the electronegativity and
orientation of the bonding atoms. Thermodynamically each hydrogen-bond is hy-
pothesized to contribute -1 to -5 kcal / mole, depending on its chemical environment,
towards the protein native state stability. If the hydrogen-bonding between protein-
solvent becomes dominant it will lead to unfolding of the protein chain fractions.
Therefore, if the protein chain segments need to maintain the identities of their 10-
cal secondary structure, it is necessary for them to be hydrophobic enough so that
protein intramolecular hydrogen-bonding dominates. Those segments of the protein

chain that have protein-solvent hydrogen-bond dominating will primarily have a dis-

8

 

ordered or coil structure [9]. Since the network of hydrogen bond is well defined in
the secondary structure motifs of a protein, it seems plausible that the hydrophobic
interactions first collapse the relevant protein chains segments; following this collapse
and consequent geometric rearrangement of the hydrophobic side chains into an min—
imal “frustrating” configuration, the spatially short range hydrogen-bonds begin to

take effect and cause the formation of secondary structures.

Configurational Entropy: As far as the protein alone is considered, entropic
effects would be an opposing force to protein folding since the native state configu-
rations are extremely compact and the efi'ective volume occupied by a folded protein
is much smaller than an unfolded protein conformation. The entropy considerations
cannot, in general, be isolated from the hydrophobic effects. The nonpolar protein
segments trigger the hydrophobic effect in the solvent resulting in high entropic bar-
rier of the collapsed state to minimize the accessible surface area of nonpolar residues

to the polar solvent.

A delicate balance between these two opposing factors - forces that drive pro-
tein towards folding and forces that inhibit protein folding - provides the marginal

stability of the native state conformation.

1.4 Time Scales and Energy

Protein folding kinetics and dynamics is largely mapped onto two time scales: the
events occurring from femtoseconds to milliseconds are referred to as the microscopic

regime and the timescales beyond a millisecond are referred to as the macroscopic

9

 

regime. Events in protein folding reactions span about 15 orders of magnitude in
time. This is a rather large temporal range considering the dimensions of the protein.
The slowest folding proteins take a few minutes or sometimes even hours to fold
while some smaller proteins (less than ~ 100 amino acid residues) fold within 100
microseconds. For a comprehensive understanding of protein folding - pathways,
kinetics, thermodynamics and mechanisms - it is essential to decipher the relation
between the motions at various time scales. Understanding the interlink between
the faster and slower processes will help better predict protein folding and native
structure from sequence and consequently the functions. A typical distribution of
protein folding events and associated time scales is shown in table 1.1. The transition
from an apparently random configuration to the native structure involves events such
as bond stretching, bond angle bending, formations of loops, secondary structure
elements and their self-assembly, formation of disulfide bonds, folding of the protein
itself, and breathing motion of the native state. To capture all the cardinal processes
in the relaxation kinetics of the protein, it is essential to accurately capture and

understand the time scales of the motions involved.

The evolving experimental techniques are pushing towards improved temporal
resolution for quantifying and studying the protein folding events on a wide range of
timescales. The bonded interactions generally make the highest contributions to the
net energy of any molecule at the atomic level. An example of energy scales involved
for various interaction in the aqueous environment of protein is shown in table 1.2.
The electrostatic interaction is governed by the Coulomb’s law (U = kql q2/er) and

is dependent on the charge of the atoms under consideration. Plindamentally, both

10

 

Time Scale (3) Event Description
10—15 - 10—12 Bond stretching and angle bending.

10—12 - 10—9 Surface side chain motion and loop motion; Local
breathing and collective motion.

10—9 - 10'”6 Formation of secondary structure and loops; Helix-
coil transition and global hydrophobic collapse.
10"6 - 10—3 Formation of “intermediates”; Folding of smaller
proteins.

>10"3 Cis-trans prolyl-peptidyl isomerization; Protein
folding.

 

 

 

 

 

Table 1.1: Typical time scales in protein folding events. Note the wide temporal
range.

Van der Waals and hydrogen bond interactions are electrostatic in their origin. The
Van der Waals interaction arises from transient asymmetrical charge distribution in
atoms resulting in a dipole formation. This causes a mutual attraction between the
atoms until they approach the minimum mutual distance (Van der Waals contact)

where repulsive forces between the outer electron clouds begin to dominate.

 

 

Energy Scale(kcal / mole) Description
20-150 Covalent bonds
1-5 Hydrogen bonds; Electrostatic interaction
1-2 Aromatic-Aromatic interaction
<1 Van der Waals attraction

 

Table 1.2: Typical energy scales measured in protein folding reactions.

1.5 Foundation for Protein Folding Studies

The central dogma of genetics enunciates the process of biosynthesis of proteins. It

explains the transcription of DNA to RNA and translation of RNA into proteins.

11

Therefore, knowledge of the genes can reveal the sequence information of the pro-
tein. The primary sequence of proteins can also be determined by mass spectrometry.
The very first protein structures to be solved experiment ally (X—ray crystallography)
were for myoglobin and hemoglobin in around 1958 [16, 17]. By 1962 Anfinsen demon-
strated that the amino acid sequence contains all the information necessary for the
formation of the native state. Under right conditions, folding and unfolding of a
protein can be reversibly achieved in vitro [18,19]. These results had far reaching
consequences in that it opened up the possibility of studying the protein in isolation

- experimentally and computationally.

The Anfinsen Experiment: One of the fundamental observations [18] that
promises success in the study of protein folding is provided by the Anfinsens exper-
iment. It provided the very first evidence of the possibility that all the information
needed for correct folding of the protein from any arbitrary unfolded state is latent
in the amino acid sequence. The experiment demonstrated that Ribonuclease A can
be fully denatured by reducing the disulfide bonds and dissolving it in 8M urea.
Subsequently it can be reversibly renatured by diluting away the urea and oxidizing
it to allow the disulfide formation. More than 90% of the native state activity was

restored.

He therefore proposed the thermodynamic hypothesis of protein folding according
to which the native conformation of a protein is thermodynamically the most stable
state (corresponding to lowest free energy) and the protein adopts this structure spon-
taneously. This mean that all the information needed to form the three-dimensional

structure of the protein was inherent in the sequence itself. This hypothesis was

12

 

eventually challenged as further research into the protein folding and mechanisms
revealed the role of the other molecules in viva that assist protein folding.
Levinthal’s Paradox: Consider a polypeptide chain with one hundred amino
acid residues. Assuming each amino acid to have only 3 possible conformations, the
whole polypeptide chain will have 3100 possible conformations. If the transition time
between each conformational state is 1 picosecond, it would take the protein 16 x
1027 years to find its native state. The Age of the universe is believed to be 15x
109 years. If the protein is to attain its correctly folded configuration by sequentially
sampling all the possible conformations, it would require a time longer than the age
of the universe to arrive at its correct native conformation. But most proteins have
been observed to fold on a submillisecond timescale. Therefore, the folding pathway
towards the native state cannot really be an unbiased random search but rather has
to be some specific pathway that is biased towards the native structure which is

kinetically the most accessible state [20].

1.6 Mechanism and Hypothesis for Protein Fold-
ing

Traditionally two main mechanisms for protein folding has been proposed - the Ther-
modynamic hypothesis and the Kinetic hypothesis [21]. The thermodynamic hypoth-
esis proposes that the native state adopted by a protein is thermodynamically the
most most stable conformation and corresponds to the global free energy minimum.

The native state is completely determined by the interatomic interactions which are

13

in turn determined by the amino acid sequence of the protein chain and the en-
vironment it is in. The Kinetic hypothesis, on the other hand, suggests that the
native state is that which is kinetically the most accessible conformation, and the
biologically active protein need not necessarily correspond to the state of minimal

free energy.

The thermodynamic hypothesis of protein folding gained support primarily from
Anfinsen’s experiment on protein denaturation and renaturation which established
that the native state of the protein correspond to the global free energy minimum un-
der the given constraints of the physiological conditions. The native state established
is the same in vivo and in vitro. The support for the kinetic pathway mechanism
sprouts mainly from the Levinthal’s paradox. He argued that if the protein were to
sample all of the conformation space, it would take astronomical time for the protein
to reach its native state. Since the proteins are known to adopt their native structure
in a fraction of that time, it must be that only a small fraction of this pathway is
kinetically sampled. This kinetic sampling leads to a native state that is lower in
energy to most other states, but is not necessarily the lowest energy state (the global
energy minima) [22]. For example, the biologically active state of plasminogen acti-
vator inhibitor(PAI-1) is not the stable conformation state with minimal free energy
but is a metastable state [23]. The large volume of the configuration space makes it
impossible for the protein to always achieve the lowest energy state. However, given

long enough sampling time, the protein will eventually find this state.

Although the debate about the validity of one over the other is not absolutely

settled, a synergy between the two seems to be fast emerging that makes the kinetic

14

 

hypothesis a larger view that subsumes the thermodynamic hypothesis [21,22,24,25].
It has been proposed that an initial collapse of the protein is governed by kinetics, this
is followed by the rate-limiting step of slower relaxations of the protein into the native
state and is dictated by thermodynamics [26]. Further advances in experimental
techniques have probed the early events in protein folding to a greater atomic and
temporal resolution to reveal finer details of the protein folding process. It has led to
the “New View” of protein folding wherein the pathway to native state is not single,
unique, well defined, and constrained but there is a muliplicity of pathways to choose
from that can lead to the native state conformation. The folding pathways can be
represented by a flea energy landscape as shown in figure 1.3 or equivalently by a
entropic landscape in which the protein diffuses through sampling the kinetically
accessible conformations and eventually adopt the appropriate native state. The
energy landscape is often like a funnel in which the minimum energy conformation
connotes the native state. In the context of the kinetic hypothesis, the misfolded

states of any protein are essentially kinetically trapped conformations.

1.7 Unfolded States and Protein Folding

Quite often the protein folding problem is viewed as three different, but closely
related, issues [6]. The first issue is that of the folding code through which in-
teratomic forces acting on and by the amino acid residues of the polypeptide chain
determine the three-dimensional native state by thermodynamic considerations. The

second issue is the computational problem of predicting the native state using both

15

"‘I

II‘

 

N

Figure 1.3: Depiction of a typical energy landscape for protein folding. This figure
is adopted from Dill and Chan [27]

knowledge-based (homology modeling) and physics-based methods. The third issue
is that of kinetics — the speed at which protein folds and factors that govern this rate.
To obtain solutions to any of these problems it is essential to not only characterize

the native state conformation but also investigate the details and characteristics of

16

the unfolded conformation ensembles. It is the distribution of the unfolded chain
conformation that provides information on interatomic distances and their relative
orientations which govern the magnitude of various interatomic forces and interac-

tions that trigger the protein folding reaction. Therefore, the progenitors of protein

folding should be embedded in the unfolded state conformation.

Characterizing the unfolded states of a protein under folding conditions continue
to remain puzzling and challenging on account of their conformational heterogeneity
and rapid dynamics. Traditionally the unfolded conformational ensemble of proteins
were considered to be random polymers that are non-interacting and lacking any
defined structure. However, development of experimental techniques and advances
in NMR spectroscopy suggest the presence of residual structure in the unfolded
states of many proteins [28—30]. Another structural element that is yet to be fully
understood is the loops that connect other secondary structures. The stability of the
native state conformations have been observed to be dependent on the loop lengths
too. Loop formation is one of the most ftmdamental process occurring in protein
folding and dynamics. It is only when nonlocal chain segments come in close spatial
contact that the long range and short range interatomic interactions begin to guide
the protein folding towards the energy minimum of the folding funnel. The rate of
intramolecular contact formation in the protein chains also characterizes the kinetics
of sampling the free energy landscape. It also sets the timescales for the loop closure
and consequently for speed of protein folding. The characteristics of this intrachain
loop diffusion forms a significant aspect of the unfolded state attributes.

A quantitative description of the unfolded state topology and the intramolecular

17

contact formation in the early stage of protein folding can be obtained through a
statistical treatment of the conformations by investigating them through well de-
scribed physics based polymer models. This will enable us to develop a picture of
the unfolded state conformation distribution which is sequence dependent and will
have all the information needed to achieve the native state conformation. It would
be impossible to describe discrete conformations of the unfolded states owing to its
dynamic heterogeneity and the degeneracy of free energy associated with multiple
conformations. For an analytical treatment of the experimental data and to obtain
a macroscopic description of probability distributions, often the freely-jointed chain
does well to capture the characteristics of long chains. But for shorter chains and
for chains in mild denaturing conditions, a wormlike chain with excluded volume
interaction is employed that incorporates an intrinsic stiffness. The details of some

of the polymer models are discussed in appendix A.

This probability distribution obtained from the polymer models can be used to
model the experimental data and describe the conformational distribution of the
unfolded protein. Time evolution of the structural reconfiguration and other folding
events can be characterized through the diffusion coefficient and the intramolecular
end-to-end distance probability. In this work I have used a wormlike chain model
to incorporate the property of “stiffness” and excluded volume, but this model did
not consider the hydrophobic effects and the residual structure in the unfolded frac-
tions of the protein under folding conditions. The growing experimental evidence of
nascent structures in early stages of protein folding suggests that we definitely need

to invoke these effects in the polymer models for a more accurate description of the

18

characteristics of unfolded states. Many of these shortcomings can be transcended
by using all-atom molecular dynamics simulations that incorporate all the chemical
and structural details of amino acid.

It is now being acknowledged that protein misfolding and aggregation may have
its seed in unfolded fractions or the partly structured folding intermediates. Hence,
the earliest steps in the protein folding process, such as loop formation mentioned
above, may hold the key to understanding the pathogenesis related to aggregation,
misfolding and amyloid formation. Adding another step towards understanding of
protein and peptide structures and their early stages in particular, I present in this
thesis, a few experimental results for molecules with and without known propensities
for aggregation and model them with a wormlike chain polymer model and all-atom

molecular dynamics simulations.

19

Chapter 2

Transient Absorption Spectroscopy

Applied to Polymer Dynamics

2.1 Introduction

To study and characterize the unfolded states of a protein, it is essential to un-
derstand one of the most fundamental processes - intrachain loop formation [31].
Since the slower processes are, in principle, a consequence of the faster processes, the
driving mechanism for various phenomena can be better understood by estimating
the underlying time scales involved. Such fast processes as loop formation can be
measured using pump-probe laser spectroscopy to cover a large orders of magnitude
in time (until at least a millisecond as depicted in figure 2.1) limited only by the

relative lifetime of the metastable states.

Function of the pump is to induce a time evolving perturbation in the sample.

20

Pump-Probe Spectroscopy

‘:.i 7. L r: ~9n__

Ia

 

 

 

‘0 I ’ "0 Time
I I I I I I I r
I I I I I I I ’
fs ps ns ns ms 5 105
H |—-| H F :
Bond L00? Hairpin Protein folding
stretching formation folding

Figure 2.1: Time Span of Folding Events and Pump-Probe Spectroscopy.

This perturbation is studied in the presence of a quencher which systematically
represses the perturbation by processes such as collision or an electron transfer among
other possible pathways. The probe beam monitors the donor electronic states for
any changes. It is therefore essential to ensure a choice of the probe wavelength such
that it has an intraband resonance with the electronic excitations of the donor. To
minimize possible disruptions of the sample, and also to ensure that the detector is
not saturated, the probe is generally chosen to have energy lower than the pump
beam. For more true and accurate measurements it is desirable to have a pulse
repetition rate in the pump to be less than the ground state repopulation time of

the donor.

Operating in the linear regime of the detector and within the damage threshold
of the sample, one of most straightforward and direct measurements is that of the

optical density (also called absorbance). Its relation to the probe intensity is given

21

by the Beer-Lambert law as

00:... (.170) (2..)

where IO is the intensity of the reference beam and I is the intensity of the beam
after it passes through the sample. The probe signal decay thus recorded can largely

be fit to a sum of first order decaying exponentials.

2.2 Application of Pump-Probe Spectroscopy

For the study of loop formation dynamics (intramolecular contact formation) in
proteins and peptides, using pump-probe laser spectroscopy in the UV-Vis - spectral

domain it is essential to have:

1. Two lasers: A probe beam and a short pulsed laser for pump.
2. A long lived target (donor) for perturbation/ excitation.

3. A quencher (acceptor) to monitor the donor perturbation against.

The roles of donor and acceptor are very well adopted by two naturally occur-
ring amino acids tryptophan and cysteine respectively [32]. Upon absorption of UV
light at about 289 nm, the triplet energy states of tryptophan is populated via a
non radiative intersystem crossing from the higher singlet energy states as shown in
figure 2.2.

Quantum mechanically this transition between states of different spin multiplici-

ties is forbidden. But the spin-orbit interaction is known to partially eliminate such

22

 

 

 

 

Energy

 

 

Figure 2.2: Electronic energy levels of tryptophan. The spin of an excited electron
can be reversed achieving intersystem cross over.

forbiddeness and the transition probability is increased with overlapping of the cor-
responding vibrational states [33]. In the absence of any quencher this triplet state
lives for more than ~ 40 microseconds [34—36]. The lifetime of this triplet state is
reduced in presence of cysteine, an efficient quencher. At physiological pH, cysteine
is the most efficient quencher, with a rate of at least 400-fold faster than all other
amino acids with the exception of tryptophan. The rate of quenching with cysteine
is about 2.0 x 108M ’13-1 [32], where M stands for mole.

The experiment yields an observed rate for varying temperatures and viscosities
in a range of denaturant concentrations. To minimize the decay rate uncertainties,
the signals are averaged for 128 pulsed laser shots. The general form for the observed

triplet decay rate can be expressed as [31],

kobs = “0 + 2 him“ ‘I' Z kink] (2.2)
i i

23

where 160 is the decay rate in absence of any quencher i. kgmz' and kg”; are
the unimolecular and bimolecular quenching rates respectively. [2] is the quencher
concentration. In almost every experiment performed, we typically employ a single
quencher. The bimolecular rates do not make any significant contributions to the
observed rate on account of the low sample concentrations (~ 30nM) used in the
experiments. Also, the tryptophan and cysteine are engineered to be close enough in
sequence separation to make kgmz' ~ 10x faster than k0. Consequently equation (2.2)

simplifies to kobs , with effectively only one quencher z' in the protein chain.

= kgmz

To study the rate of intramolecular contact formation in a loop formed by trypto-
phan at one end and cysteine at the other (figure 2.3), we engineer these residues into
the protein or peptide if they do not already exist. The rate of end-to-end contact
formation is then studied using optical (triplet to triplet [34, 36, 37]) absorption by
measuring the lifetime of the excited triplet state of tryptophan. In presence of cys-

teine the quenching rates follow an exponential decaying distance dependence [38,39]:

9(7‘) = 40 exp I-fl(7‘ - a0)] (2-3)

where r is the intramolecular distance, a0 is the distance of closest approach
(defined to be 4A), 90 = 4.2 ns-l, and fl = 40nm—1. The quenching is a very short
range process.

In the process of diffusing towards and away from each other, the metastable
triplet state of the donor is quenched by the close van der Waal contact with the

acceptor. Using the kinetic model of figure 2.3, the observed lifetime of the donor

24

C .
hv kD+ q
—" —"__ ———>
kD_ *

Figure 2.3: Schematic of loop formation and quenching. Tl'yptophan triplet states
are selectively populated by UV pulse. The loop ends diffuse towards and away from
each other at rates k D + and kD— respectively. Upon a van der Waals contact,
cysteine quenches the tryptophan triplet states at a rate q.

 

can be approximated by treating it as a two step process -

1. The two ends diffuse towards each other at a rate k D + to form the encounter
complex (C*).
2. Cysteine either quenches the excited triplet state with rate q or they diffuse

away from each other at a rate 1‘0—

Representing it in the form of a chemical reaction to determine the rate equation,

* q
C ——>P (2.4)

 

 

25

Where R represents the ensemble of protein molecules with various end-to-end dis-
tances. C * is the ensemble of molecules forming the encounter complex and P depicts
the conformational ensemble after quenching. Using a steady state approximation

for the encounter complex formation,

 

d[C*]
-—dt— — O (2.5)
that is, the encounter complex does not accumulate over time.
d[C*] ..
dt =0=kD+[R]—(kp_+q)[0 ] (2.6)
(ill) I _ _ an: _ I‘:D+
dt _ kobSIRI - QIC I - q (I‘D— + q [RI (2-7)
Hence, the observed rate is given as
kb=kD —9——skD ¢ (2.8)
0 3 + kD— + q 'I'

where k D + is rate of diffusion of the loop ends towards each other, kD— is the
rate of diffusion away from each other, q is the quenching rate and d) is probability of
quenching. For q >> kD— , the observed rate reduces to the diffusion limited rate:

kobs = k D +. And for q << kD— , it gives the reaction limited rate:

kD+
“abs = q (’91:) = quq 2 Mg, (2.9)

26

where k R is the reaction limited rate, and K eq is the equilibrium constant for forming
the encounter complex. In our experiments usually q ~ (“0— , and hence we need to
isolate both the reaction-limited and diffusion-limited rates. The observed rate can

be rearranged to be written as,

— +
kob 1904.07, T) 16120")

 

1 1 1 (2.10)
s

where we posit that the difiusion limited rate, k D +, depends on both tempera;-
ture (T) and viscosity(n) of the solvent and the reaction-limited rate, kR, depends
on temperature alone [38]. This makes it possible to extract these individual rate
coefficients by performing the experiments at varying temperatures and viscosities.
The technique was developed and first built at the Laboratory of Chemical Physics,
National Institutes of Health.

2.3 The Instrumentation

For the measurement of transient absorption in a transmission mode, the instrument
is designed to have a collinear geometry as shown in figure 2.4.

For the tryptophan excitation a l-mJ, 8-ns UV pulse at 289 nm is employed. A
266nm fourth harmonic of N szAG laser is Raman shifted using 1m long methane
cell with a pressure of about 250 psi. It has been observed and documented that
photodestruction of tryptophan increases at lower excitation wavelengths [40]. To

minimize the photodamage, we shift the wavelength of the excitation pulse to 289

27

 

I» CH4 Raman Cell / Prism

  

 

He — Cd Laser
I"

  
 

Beam Splitter Mirror

    
 

 

  
 
 

   

 

   

 

   

a; I

8

._1

E3 Photodetectors

: \ UV Filter Dichroic Mirror

Z / .

L 1
Temperature Controlled ND Filter

Cuvette Holder

 

 

 

Figure 2.4: Transient Absorption Instrumentation

nm.

After the nanosecond UV excitation, the tryptophan triplet states are monitored
using a continuous wave 441 nm (He-Cd laser). The output beam from the CW
laser is split into two parts: a reference beam and a sample probe beam. Changes
in the transmitted probe beam intensity is measured using a silicon photodiode
(New-Focus), recorded with a digital oscilloscope (Tektronix TDS), and stored on a
computer using GPIB interface. Any possible pump leakage and high frequency ca-
ble noise is subtracted from both parts of the probe beam by recording a background
with the pump in absence of the probe beam. Since the triplet lifetime can range

from nanosecond to few milliseconds, the absorption is recorded to cover a wide dy-

28

namic temporal range of 10 ns to 10 ms. This is accomplished by using two different
oscilloscopes. The UV pulses have a tendency also to produce radicals which can
have a lifetime of about a millisecond and absorb light near 450nm, and this gets
convolved with the triplet lifetime measurement [32,36]. It is therefore necessary to
record and observe for a long enough time that encompasses the essential and critical
experimental events to be able to sift all possible contributions to the decay. The
protein / peptide sample solution cuvette is placed in a Peltier temperature controlled
sample holder(Quantum Northwest). The data is collected at five different tempera—
tures of 0, 10, 20, 30 and 40 degree Celsius and varying viscosities. The viscosity is an
important parameter in equation (2.10) and is varied by using measured quantities
of sucrose in the solvent. More recently, we have also incorporated a digital signal
amplifier (LeCroy DA1886A differential amplifier). The output fiom this amplifier
of 100MHz bandwidth used in comparator mode with gain of 1x is coupled to a 350
MHz four channel preamplifier (SR445A, SRS Inc.) that can be used in a cascaded
configuration with a gain of 5x at each stage. I predominantly used a total gain of
5x for most experiments. This allows to lower the sample concentration and also
decrease the pump pulse power thereby reducing the production of free radicals and
hydrated electrons.

The optical alignment of the instrument can be optimized using benzophenone,
an organic compound, in acetonitrile. At a concentration of about 50pM , it has a
decay time of almost 20011.3. N-acetyl—L—tryptophanamide (NATA) is also regularly
used for optical alignment of this instrument. NATA dissolved in deionized water

and degassed with nitrous oxide (discussed below), has a measured lifetime of about

29

40ps.

2.4 The Sample Preparation

The crux of measuring the transient absorption using this pump-probe spectroscopy
lies in the excited triplet state of tryptophan. It is hence necessary to eliminate other
detrimental competing quenchers which can be an encumbrance to the success of the
experiment in terms of its accuracy. Molecular oxygen, with its unique triplet ground
state, is an efi‘icient quencher of the tryptophan triplet state [41]. The succession of
UV pulse excitations in the sample generates other detrimental photoproducts like
radicals and hydrated electrons that interfere with triplet lifetime measurements.
A proposed mechanism for tryptophan triplet decay is via an electron transfer to
the sulfur in cysteine side chain [36, 42]. Presence of free radicals can also pose as
efficient competers for the triplet quenching through electron transfer. The radicals
also have an absorption band which is in resonance with triplet-triplet absorption.
A spectral amplitude at 3ps is attributed to combination of radicals and hydrated
electrons [32].

The buffer is therefore treated with nitrous oxide (N20) by bubbling it to remove
any oxygen in the solvent. This also helps scavenge solvated electrons created by the
UV pulse. A 10mm sealable cuvette serves well to hold the buffer for it. Protein and
peptide samples are then diluted to about 20-30 [1M in this buffer. The formation
of weak covalent disulfide bonds between the sidechains (the Thiol groups -SH) of

two cysteine residues by oxidation also hampers the quenching process. To keep

30

the cysteines reduced and avoid dimerization, measurements are made in presence of
lmM Tris(2-carboxyethyl)phosphine hydrochloride (TCEP). Typically dithiothreitol
(DTT) is employed as a reducing agent during protein purification. But since DTT is
a competing quencher for cysteine, it is preferable to use TCEP in place of DTT. The
experiments are then performed with varying the solvent viscosity. Viscosity of the
solution containing sucrose, denaturant(usually guanidinium hydochloride) and the
buffer is measured in a temperature controlled cone-cup viscometer(LVDV-II+CP,

Brookfield Engineering). The temperature is varied from 0 through 40 degree Celsius.

2.5 Data Acquisition and Analysis

Using the ftmdamental idea of the experiment shown in figure 2.3, the absorbance
profile of the tryptophan triplet at 441nm is monitored and recorded after its excita
tion using the pulsed laser. A representative trace of this triplet kinetics in shown in
figure 2.5. The absorption profile exhibits an exponential decay and the triplet life-
time undergoes a rapid decay with close Van der Waals contact between tryptophan

and cysteine.

Using the relationship between the observed triplet lifetime and the microscopic
rate coeficients (equation (2.10)), a plot of 1 / kobs against the solution viscosity (17)
at each temperature, the intercept gives the reaction-limited rate, l/kR, and the
slope is proportional to the diffusion-limited rate k D + as shown in figure 2.6. For

fitting we assume the data can be well modeled by

31

Absorbance

Figure 2.5: Representative Tryptophan Triplet Kinetics for Protein G (T510). The
red points correspond to the kinetics in 2M guanidinium hydrochloride (GdnHCl)
and can be fit to a sum of two single exponentials. The faster rate is a contribution
from the unfolded fractions of the protein and slower rate from the folded fraction.
The black points correspond to the kinetics in 5M GdnHCl and is fit to a single
exponential.

and,

 

   
 
  

0.8 l-
0.6 [-
0.4 -
0.2 -

0.0
le-6

I

 

[CR 2 kROexp(

L
l

le-S

 

 

le-4

1e-3

le-2

Time (s)

32

Eo(T - T0))

RTTO

(2.11)

k _ I9D+0T
D+ " "T0

 

exr>('r(T - T0)) (2-12)

where, T is the temperature, 77 is the solution viscosity, and “7120’ E0, k D +0,
and 'y are fitting parameters. It: R0 and k D +0 are the values of k R and k D + at the

reference temperature T0 of 293K.

 

l(kobs (sec)

 

 

 

 

i
q-
'r
q-

l l l
V r r

0 2 4 6 8 10 12 l4 16 18
viscosity (cP)

Figure 2.6: Observed Rate fit to equations (2.12) and (2.11). This representative
plot is for protein G (E19C) at 0 C (red), 10 C (green), 20 C (blue), 30 C (pink),
and 40 C (cyan).

33

2.6 Reaction and Diffusion Limited Rates

The reaction limited rate is the observed rate measured when diffusion is sufficiently
fast and predominates over the quenching rate, kD— >> q. The encounter com-
plex is formed and broken multiple times before quenching of the donor occurs.
Consequently an equilibrium end-to—end distance distribution is maintained at every
instant and hence I: R provides direct information about the distance distribution.
The population of molecules forming the encounter complex is in equilibrium with
the ensemble of all chain conformations. The reaction limited rate depends only
on the quenching rate and the equilibrium end-to-end distance distribution. The
quenching rate being well described implies a relationship of direct proportionality

between I: R and Peq(r).

k 1c
hobs = #‘tq = Keqq 5 hr; = A Peq(r)q(r)dr (2.13)

For a constant K eq and a well defined q, k R will be determined solely by Peg (r).
This implies, on the quenching timescale, since the encounter complex and the end-
to—end distance of rest of the protein ensemble will be in a dynamic equilibrium, the
essential shape of Peq(r) will not change with time as illustrated in the figure 2.7.
Only the peak of the distribution diminishes with time.

The diffusion limited rate, k D +, is the rate of bringing the ends of the loop
together. This is the measured rate for the case when kD- << q. The result is
formation of short range contact between the donor and acceptor resulting in the

encounter complex. The diffusion limited rate depends in a complex way on both

34

 

 

 

 

 

Figure 2.7: Illustration of Reaction Limited Rate: The abscissa shows the end-to-end
loop distance. Ordinate gives the probability of unquenched molecules.

on the diffusional dynamics of chain ends and the end-to-end distance distribution.
When the diffusion rate-limit predominates, more and more of the encounter complex
is formed and the donor immediately quenched since the loop ends cannot diffuse
away fast enough. With time, one would notice a asymmetrical rightwards shift in

Peq(r) for smaller end-to-end distance regime as shown in figure 2.8 below.

2.7 SSS Theory and Polymer Chain Model

The theory of Szabo, Schulten, and Schulten (SSS) constitutes a description of the

dynamics of end-to—end distance of a polymer. It treats polymer dynamics as motion

35

 

Figure 2.8: Illustration of Diffusion Limited Rate: The abscissa shows the end-to-end
loop distance. Ordinate gives the probability of unquenched molecules.

on a one-dimensional potential of mean force corresponding to the equilibrium end-
to-end distance distribution Peq(r) [43]. The rate of bringing two reactive ends of
a polymer chain in close contact by diffusion under the influence of potential gives
an estimate of the first passage time. The observed rate is calculated by solving a
Smoluchowski-like diffusion equation for a difl‘usion process in a field defined by -

36

where k B is the Boltzmann constant and Peq(r) is the equilibrium end-to-end dis-
tance distribution of the loop ends. For a distance dependent quenching rate, the

observed rate derived through SSS theory is found to be [38,43],

 

I I I 00
= — + —2 / (5q(t)6q(0))dt, (2.15)
kobs “R k R 0

where 6q = q(r) — k R and k R = (q) = [if Peq(:r)q(a:)d:c is the reaction-limited rate.
The time integral of the sink-sink correlation function is analytically evaluated to
be,

1 tmam-t
<6q<t>6q<0>> = W [0 6g<to>6q<t+to>dta (2.16)

where tmag; is length of the trajectory. For difiusion on a 1D potential, the expression

for the observed rate becomes (using equation (2.16)),

1 1 1 IC _ lo 2
Eg=fi+gja (D(a:)Peq(:v)) 1M: 5q(y)Peq(y)dv] da: (217)

where the reaction-limited rate is given by,

lc
kR= fa Peq(x)q(:r)d:r (2.18)

37

and the second term in equation (2.17) gives the diffusion limited-rate,

2
k—1_D+ =k_2 l/lc (D( @136qu ))1[‘/$lc 54(U)P6q(y)dy[ dz (2.19)

In order to be able to take advantage of the above analytical expression (equa-
tion (2.17)) for numerical evaluation, we will need to generate a distribution of the
’Irp-Cys distances to form Peq(r). Some of the common ways of generating the

end-to—end distance distribution are -

a) Gaussian (random-walk) Chain approximations: The connected monomer sub-

units, having no orientational correlation, are approximated as a random walk with

 

 

a Gaussian probability.
2 -3/2 2
2 21r(r ) —3r
P = 4 —— e — 2.20
“m 7" I 3 ) xp (2%) ( )
The reaction-limited and diffusion-limited rate for small a is given by,
2
41rqa 3a

—— (2.21)

=12vr<r2>>3/2expm( 203)

47rDa
k = (2.22)
1” cars/3):”?

b) WormLike Chain: This is the simplest model of a polymer chain that takes

38

into consideration the stiffness of the chain characterized by Kuhn length (n) and/ or
the persistence length (lp). The chains are made more realistic by invoking the
excluded volume effects. Assume a sphere of diameter da at each end of the peptide
bond. The volume excluded by the backbone and side chain is treated as a hard-
sphere interaction. There is no one specific expression that gives the probability
distribution. Typically the wormlike chains can be generated using a Monte Carlo
algorithm using parameters of a persistence length lp, and excluded volume diameter
da [44]. A normalized histogram of Trp-Cys distances is used as P(r).

c) Molecular Dynamics (MD): Using MD simulations to obtain the probability dis-
tribution of end-to-end distances tenders the most realistic chain statistics owing to
the all atom details and realistic bond chemistry employed in these simulations. The
conformational distributions are generated using the high performance computing
cluster (HPCC) using AMBER molecular dynamics simulation package. Performing
simulations with explicit-solvent is computationally more expensive. Since our goal
here is mainly to generate the equilibrium distribution P (r) and not be concerned
with the precise kinetics we can perform the simulation using implicit-solvent mod-
els. Following the simulation of trajectories, a normalized histogram (0.1 Abinning)
of Tfp—Cys distances was used as P(r).

39

Chapter 3

Unfolded States of Proteins and
Peptides: Experimental

Investigation

3.1 Introduction

It is now being acknowledged that protein misfolding and aggregation may have its
seed in unfolded fractions or the partly structured folding intermediate. Hence, the
earliest steps in the protein folding process, such as loop formation, may hold the
key to understanding the pathogenesis related to aggregation, misfolding and amy-
loid formation. Adding another step towards understanding of protein and peptide
structure, I present in this chapter some experimental results for molecules with and

without known propensities for aggregation.

40

Protein L and Protein G are two bacterial immunoglobulin-binding a/B proteins
that have been widely studied and are known to be relatively aggregation free under
physiological conditions. The thermodynamic and kinetic properties of their fold-
ing have been addressed and recorded in great detail [45,46]. This makes them a
good target for our experimentation. Both proteins L and G share the same native
topology with a central a - helix resting on a four-stranded ,6 — sheet composed of
N- and C—terminal fl — hairpins. The Tm/Cys triplet quenching method has been
used to investigate the unfolded states of two domains of proteins L and G under
various concentrations of denaturant guanidinium hydrochloride (GdnHCl) [44]. Our
experimental results suggest that under conditions that favor folding, the unfolded

fractions of proteins L and G are compact and viscous [44, 47].

The polyglutamine amino acid stretches .in numerous proteins are implicated in
least nine neurodegenerative diseases like the Huntington and Spinobulbar muscular
atrophy, all of which seem to exhibit aggregation in vivo [48]. Not much is known
about the structure of monomeric polyglutamine peptide sequence. Even the mech-
anism of its aggregation is poorly understood. The length of glutamine repeat is
strongly related to the onset of the disease. The greater the number of glutamines
in the sequence, the earlier will be the disease onset. These proteins appear to have
a pathological threshold of glutamine repeats and become cytotoxic with aggrega-
tion. It has been suggested that the polyglutamine expansion induces a significant
conformational distortion in the host protein that initiates the formation of aggrega-
tion [49]. Generally any abnormal, misfolded or other extraneous protein in cells is

subjected to degradation by proteasomes. The fact that many proteins with polyglu-

41

tamine sequences beyond the pathological threshold seem to evade this fate suggests
that the misfolded structure may inhibit binding to the proteasome. This could be
a consequence of very large structural change. To understand the mechanism and
correlation between the long glutamine stretches and consequent destabilization of
the proteins leading to amyloid fibrillation, it is essential to obtain information on
structural properties of polyglutamine. This would provide insights into pathogenesis

of polyglutamine related diseases and possible therapeutic development.

In first part of this chapter, I present results of experimental measurements that
seek to describe the accessible conformational ensemble of monomeric unstructured
polyglutamine. The technique of intramolecular Trp/Cys contact quenching was used
to measure intramolecular diffusion and rate of end-to-end contact formation. Mod-
eling the length dependence of contact formation rates with a wormlike chain, we find
the persistence length of polyglutamine peptides to be ~ 13.0 A [50]. This is a rather
stiff polymer in comparison to that reported for other peptide sequences and dena—
tured proteins. This polymer “stiffness” possibly renders the polyglutamine sequence
an extended (a—helical) conformation that hinders the host protein in adopting its
intrinsic native state. Consequently the destable misfolded state forms a nucleus for

aggregation and amyloid formation.

3.2 Results for Polyglutamine

Five different lengths of polypeptides of polyglutamine sequences were experimen-

tally studied. They were synthesized using solid-phase synthesis with the sequence,

42

K KCQnWK K , with n = 4, 7, 10, 13 and 16. Lengths 4-13 were made by Syn-
BioSci (Livermore, CA) and n = 16 was a kind gift from Regina Murphy of the
University of Wisconsin. The polyglutamine peptide sequences by themselves are
insoluble in most solvents. However, to make them soluble they are often synthe-
sized by introducing lysines at the N- and C- terminus. Following the solubilization
and disaggregation method of Chen and Wetzel [51], the synthesized polyglutamine
samples were treated with volatile solvents of Trifluoroacetic acid (TFA) and Hex-
afluoroisopropanol (HFIP). As predicted, the solubility of polyglutamine increased
in aqueous buffer and rate of aggregation drastically reduced. In spite of this, the
peptide sequence is known to eventually aggregate and form amyloid fibrils at physi-
ological pH. The sample is therefore stored at, and experiments performed in aqueous

buffer at pH 3.0.

Experiments were then performed following the protocol discussed earlier (chapter
2). Since these peptides are easily prone to aggregation, all samples were used within
30 minutes after thawing so aggregation is unlikely. However, if aggregation did
occur, the kinetics of the tryptophan triplet would exhibit two decays: a fast decay
corresponding to the monomeric species that can undergo contact quenching (~ Spa),
and a slower one for the aggregated species that cannot undergo intramolecular
contact quenching (~ 40ps). This longer decay was not observed in the experiment,

confirming absence of any aggregation.

Figure 3.1 shows the plot of 1 / kobs versus viscosity (1]) for the various polyglu-
tamine length sequences. Each subplot displays the data set of “obs at five temper-

atures and four concentrations of sucrose. The results of the fits of observated rates

43

 

 

   

 

 

 

 

 

 

 

 

 

 

 

9e-6 l- 2e-5 --
Tn“ 8c—6 0 23-5 "
v le-5 --
m
7c-6 -
§ le-S ‘-
\ 6&6 le-5 - °
T 5“ " 8e-6- -
4c-6 : : : : 63.6 ..
0 2 4 6 8 10 4e-6 ; ; , .
Viscosity (CF) 0 2 4 6 8 10
(a) (b)
1e-5
913-6"
8&6"
’17? 7c-6 0
Us 6e-6"
.D
g 5e-6‘
.— 4c-6-
3c-6-
2e-6 : c ‘r

0 2 4 6 8 10
Wscosity(cP)
(c)

Figure 3.1: Viscosity versus observed tryptophan triplet lifetimes at various temper-
atures for K K CQnWK K where (a) n = 4, (b) n = 10, and (c) n = 7. The lines are
the fits to equations (2.11) and (2.12) with the fit parameters given in Table 3.1.

to Equation (2.11) and (2.12) for different length peptides are shown in Table 3.1.
However, for fitting purposes the diffusion-limited rate, Equation (2.12), was modi-
fied to discard the temperature dependence since empirically, in this work, we do not
observe a temperature dependence on the slopes. Consequently, the k D + equation
takes the form: kD+(n) = kD+0/77- The fitted [CR and kD+ at T = 293 K and n
= 1 cP are plotted in Figure 3.2. An interesting feature emerging from this plot is
the trend of reaction-limited rate, k R (the blue points in figure 3.2). It is seen to
be increasing with the polyglutamine sequence length, and there is an apparent turn
over in this rate at 12 ~ 13. Is this a general property of all peptide sequences ap-
proaching this length scale? Or, do the chemical and physical properties of glutamine
and possibly other closely associated amino acid residues have some implication in

this trend? We will seek to answer such questions with further analysis.

 

n (“ROG—1) kD+O(3_1) 30
4 1.79 x 105 4.11 x 106 1.38
7 2.61 x 105 2.45 x 106 2.19
10 2.42 x 105 8.04 x 105 4.81
13 2.77 x 105 1.36 x 106 1.23
16 3.13 x 105 2.31 x 105 0

 

 

 

 

 

 

 

Table 3.1: Polyglutamine Fit Parameters from equations (2.11) and (2.12). Q16 was
constrained to have E0 = 0 for good convergence of the fit.

Figure 3.3 shows a comparison with previous measurements on polypeptide se-
quence cys—(ala-gly-gln)n-trp with n = 1 to 9. We notice that the polyglutamine
rates are much lower than that for unstructured AGQ peptides. Moreover, the
reaction-limited rates in both sequences have an opposing trend. The k R in AGQ

sequences are monotonically decreasing with the sequence length [52]. This opposing

45

 

1e+7

le+6 ‘

Rate (s‘l)

le+5 '

 

 

 

2 4 6 81012141618
Polyglutamine Length (11)

Figure 3.2: Polyglutamine: Reaction—Limited (Blue) and Diffusion—Limited Rates
(Red).

trend between the two different polypeptides rates is limited to the reaction—limited
rate alone. The nature of diffusion-limited rate is very similar in both, although
the absolute values of k: D + are lower for the polyglutamine peptides. Since AGQ
polypeptides have only 33% of the glutamine content compared to polyglutamine,
the former would be expected to have higher a flexibility. This suggests that the turn

over of k R observed in polyglutamine sequence is a special property associated with

46

this sequence and possibly with closely related (physical and chemical) sequences.
Huang and Nau have shown that glutamine is more rigid than most amino acid

residues except for His, Arg, Lys, Val, Ile and Pro [53].

3.3 Wormlike Chain Modeling of Polyglutamine

For a more quantitative analysis of the observed rate we use the Szabo, Schulten, and
Schulten (SSS) theory which gives the reaction-limited and diffusion-limited rates as
equations (2.18) and (2.19) respectively [38,43]. As is evident from figure 3.3 the
length dependence of observed rates cannot be explained with a simple freely jointed
chain model. The peptides are therefore modeled as wormlike chains with excluded
volume. The one-dimensional end-to-end distance distribution Peq (r), needed for

analytical evaluation of k R and k D + is obtained fi'om the wormlike chains [50].

Figure 3.4 shows the sum of squares of difference between measured and predicted
k R for all five lengths for various values of 1;; and da. The curve of least-squares
is not uniform in all directions and the axis of shallow descent is not along either
parameter axis. Therefore, it is difficult to assign an uncorrelated error to either of
these parameters. Nevertheless, changing either of these parameters by 10% results
in increase of sum of squares of at least a factor of 5 so we chose 0.4 A as the error

for da and 1.3 A as the error for lp.

The AGQ peptides show a reaction-limited rate monotonically decreasing with
sequence length, hallmark of a flexible polymer. Contrastingly, for the shortest

lengths of polyglutamine peptides, the reaction-limited rate (as also the observed

47

 

108

I 'Ullll
D

107

k(s")

10‘5

 

 

 

 

105
3 4 5 6 7 8 910 20 30

number of peptide bonds

Figure 3.3: Number of peptide bonds between the Tim and Cys (11 + 1) versus
reaction—limited (blue points) and diffusion-limited (red points) rates for polyglu-
tamine peptides (circles). The triangles are rates for AlarGly-Gln peptides in water
at pH 7 reported in [52]. The red line is power law fit to k~ ~(n + 1)"3/2. The blue
line plots the rates predicted by equation (2. 18) using the wormlike chain parameters
lp= 13Aandda =4A (solid); lp= 12Aandda =4A (longdash); and 113— 14A
and da = 4 A (short dash).

48

 

 

 

 

 

 

 

 

 

Figure 3.4: Sum of squared difference between the measured 11: R and the k R calcu-
lated from Equation (2.18) for all 5 peptides. P(r) was calculated from ensembles of
wormlike chains for various values of lp and da.

rate shown in figure 3.5) increases with length rather than decrease. This indicates
that the polyglutamine peptides behave more like the flexible peptides (in so far
as the trend in the rates), after a threshold length of about 13 residues. Modeling
these peptides as wormlike chains with excluded volume suggest that an apparent
persistence length for this sequence is ~ 13.0 A whereas for AGQ, the persistence
length was found to be ~ 5.5 A [52].

For the polyglutamine sequences, although k R increases with length and begins

to turn over at the longest length, k D + decreases monotonically with length and can

49

 

le+6

le+5 1

kobs (3'1)

 

 

 

I V

1e+4 .... .
2 4 6 81012141618

Polyglutamine Length (11)

Figure 3.5: Polyglutamine observed kinetics at 20 degree C.

be reasonably fit with a power law dependence k D + ~ 71—3/2, as would be expected
for a flexible peptide [52]. Looking at the mathematical relation between I: R and
k D + (equations (2.21) and (2.22)), one would expect, for a fixed (loop independent)
diffusion coefficient, a similar length dependence of k R and 1913+. Given that the only
free parameters in diffusion-limited rate are D and P(r), it must be that the difl‘usion
coefficient cannot be regarded as loop length independent and must be allowed to
change to reflect the trend in k D +. This appears to be a property peculiar to
polyglutamine sequences and not observed in AGQ polypeptides. To evaluate the

50

difl‘usion coefficient D, we use the experimentally determined value of kD+ and the
P(r) calculated for each peptide with IP = 13.0 A and da = 4.0 A, in the diffusion-
limited rate equation (2.19). For each peptide length, the diffusion coefficients are
shown in Table 3.2. Evidently, there is a substantial decrease in the dynamics of

increasing loop lengths as manifested through D.

 

n D x 10‘7(cm28_1)

 

4 16.6
7 10.5
10 4.3
13 6.6
16 1.5

 

Table 3.2: Diflusion Coeficients from Equation (2.19) using wormlike chain models
with 1,, = 13.0 21, da = 4.0 )4.

There have been a number of computational and structural studies on polyglu-
tamine peptides of multiple stretches. The crystal structure of a Q10 inserted in C12
shows domain swapping within a dimer with the glutamine stretch extended between
the two domains, but the structure of the stretch itself could not be determined, in-
dicating it had much conformational flexibility [54,55]. Various plausible structures
have been proposed for monomeric polyglutamine peptides. Initial studies by Chen
et.al., [56], suggest peptides with stretches containing 5 to 44 consecutive glutamines
to be unstructured. According Perutz et al., [57] shorter polyglutamine repeats
have a random coil conformation, whereas longer repeats tend to form fl-strand
structures. Other simulation studies have suggested a highly compact random coil
structure. Using a coarse grain model, Khare et. al., [58] and Marchut et. al., [59]

have independently hinted that all polyglutamine chains have a tendency to fold

51

into a beta-helical structure. Crick and Pappu [60,61], using molecular dynamics at
room temperature, show that polyglutamine peptides exhibit existence of partially
collapsed states. Armen et. al., [62] have used explicit solvent all-atom molecular
dynamics to conclude that polyglutamines of various lengths fold predominately into
an alpha—extended chain conformation. Other simulation of this system suggests
an extended random coil, rather than a-helix, fl-sheet, or PPII structure, best fits
the measured thermodynamics with a Flory characteristic ratio of ~3.2 [63]. Thus
there has been disparate views on the structure of polyglutamine. Apart from the
possibility that a high conformational flexibility and large scale fluctuations makes
it hard to experimentally get a handle on the structural and dynamics information,
the disparities could arise for other reasons - not incorporating any water interaction
with the polypeptide; the force-fields employed in the simulations may not be ac-
curate enough; the water model used may not accurately produce solvent-mediated

hydrogen bonded interactions.

Presence of positively charged lysine residues flanking the glutamines may be a
reason the contact formation rates are 10-100 times lower for this sequence compared
to the same length of AGQ peptides. The lysines are incorporated to achieve better
solvent solubility of the polypeptide. A mutual electrostatic repulsion between these
charged residues could prevent the formation of close intramolecular contact in polyg-
lutamine. But control experiments on the peptides with up to 170 mM NaCl showed
a similar contact formation rate with almost no repression. Therefore, long-range
Coulomb interactions do not appear to affect the peptide dynamics. A short-range

interactions due to lysine being next to both cysteine and tryptophan could play a

52

role in slowing of the contact formation rates. But this should affect all lengths of
polyglutamine in a homogeneous way. However, the observed length dependence of
kR, which largely determined the ~ 13.0 A persistence length, cannot be explained

by this short-range interaction.

For the polyglutamine peptides, a single set of wormlike chain parameters (IP
and da) were found to simultaneously fit the reaction-limited rates at all lengths.
However, the diffusion coefficient varied by a factor of 10 over the length range.
In contrast, the diflusion coeflicients for the AGQ peptides, found to be typically
about 1.5 x 10—6cm23-1, varied by only 15%. This suggests that the homogeneous
(chemically insensitive) wormlike chain is not a perfect model for the dynamics of
polyglutamine. Also, all but the shortest lengths of polyglutamine has a significantly
lower D than the AGQ peptides, perhaps because fluctuating residual structure
influences the conformational population. One alternative model is to add random
fl-strand structure to a wormlike chain. To simulate fluctuating 6 structure within
the wormlike chain, individual amino acids (10 links) were randomly assigned a polar
angle of 0°. While the inclusion of fl-strand orientation on randomly selected residues
does decrease k R in proportion to the relative population of )6 structure, it cannot
produce the observed turnover in length dependence if the underlying wormlike chain
has a short (4 A) persistence length. Another alternative would be to add a 6-
helical structure. Although not attempted, it could reproduce the turn around in the
observed rates, depending on the helical pitch and relative positions of tryptophan
and cysteine in the structure. Nonetheless any description of polyglutamine peptides

must have a high intrinsic stiffness.

53

Polyglutamine appears to be much more stifler than most random peptides or
unfolded proteins and is therefore likely significantly stifler than the rest of the host
protein in vivo. Small stretches of glutamine may not significantly alter the native
conformation, but long stretches could put significant mechanical stress on the folded
protein, making it more prone to aggregation from an unfolded state. Wetzel and
others have suggested that the aggregation of polyglutamine follows a nucleation-
propagation model in which the monomeric nucleus is in rapid and reversible pre-

equilibrium with normal monomeric protein [64].

However, recent results by Klein et. al., show that monomeric polyglutamine
peptides both above and below the pathogenic threshold show no diflerence in struc-
ture [65]. This suggests that there is no structural transition in different lengths
of polyglutamine sequence part of the host protein. The aggregation nucleus may
simply be a highly extended conformation which is usually very improbable in a
very flexible chain. Thus a pathogenic protein may be one that is destabilized by an
intrinsically stiff sequence and then prone to aggregation through bimolecular con-
tact of extended conformations. Huang and Nau have showed that most amino acids
were more flexible than glutamine. using a similar contact quenching technique, they
measured k D + ~ 7 x 1063"1 for a Q6 peptide [53]. This is in agreement with our
results if one accounts for the fact that the previous peptide had no tails beyond the

probe and quencher which decreases the contact rate by about a factor of 3 [52].

In summary, we find the polyglutamine peptide to be much more “rigid” than
most peptides. Characterized by the persistence length, the polyglutamine sequences

I ~ 13 A are about 2-3 peptide bonds more stiffer. In the context of amyloid
P

54

formation and pathogenesis, this stiffness could lead to an extended conformation
between domain ends. Shorter lengths may not alter the native state conformation,
but longer glutamine stretches can prevent certain intramolecular interactions and
bond formations and leaving the protein deprived of necessary native contacts. This
leads to a misfolded and destable protein conformation with propensities for aggre-
gation and consequent cytotoxicity. Could this be the general algorithm of protein
aggregation based diseases: higher intrinsic stiffness of at least a part of the pro—
tein, formation of extended conformation depriving the native contacts, resulting in
misfolded, unstable conformation and aggregation, reduction in proteosome binding,
ending up cytotoxic and neurodegenarative? Even if this were to be true, a detailed
knowledge of the mechanisms involved would necessitate probing the various phe-
nomena at the atomic scale. Knowing the underlying principles, will then provide

insights for development of effective therapeutic agents.

3.4 Proteins L and G

We investigated the nature of the unfolded states of structurally similar but sequen-
tially nonhomologous Bl domains of proteins L and G using end-to-end contact
formation measurements. The Bl domain of Protein L is 8 kDa, 63 residues long.
To express this protein, the plasmids were transformed into BL21(DE3) Escherichia
coli cells. On account of its N-terminal hexa-His tag, the protein L was purified by
Ni-aflinity chromatography. The purified proteins were verified by N-terminal se-
quencing and MALDI—TOF mass spectrometry. Protein G BI domain is 6.8 kDa, 56

55

residues long. After expression of the protein in BL21(DE3) Escherichia coli cells,
it was purified by anion exchange chromatography [44].

Scalley et.al., used a variety of experimental techniques to conclude that folding
kinetics of protein L can be characterized by a single exponential. Thus, a simple two-
state model adequately describes the thermodynamics and kinetics. However they
also suggest the possibility of a partially collapsed unfolded chain at lower dentaurant
concentrations [66]. Measurement of fluorescence quenching by iodide suggests a
submillisecond conformational change: a partial chain collapse. Unlike protein L,
Park et.al., demonstrated, using continuous-flow fluorescence measurements, that
protein G exhibits presence of an intermediate and is not a simple two-state folder
[67,68]. In the backdrop of these observations, we find the unfolded fractions of

proteins L and G to be compact and viscous.

3.5 Structure and Stability of Proteins L and G

Both domains (B1) of proteins L and G have a single tryptophan residue near the
beginning of the C—terminal hairpin, 'I‘l‘p43 of the wild-type protein G and 'Iip47
of the well-studied Y47W mutant of the protein L [69]. Both domains have been

mutated to have a cysteine in one of two positions (figures 3.6 and 3.7):

1. Near the end of the N-terminal hairpin (K23C and E19C in proteins L and G,
respectively), forming a 24—residue loop with the tryptophan; or
2. In the final strand of the C—terminal hairpin (T570 and T51C in protein L and

G, respectively), forming a 10- and 8-residue loop.

56

 

Figure 3.6: Structure and locations of mutations for the Protein G Bl Domain.

The model for contact formation measurement between tryptophan and cysteine
is depicted in figure 3.8. The two pertinent amino acid residues are always placed far
apart relative to each other in the native state. However, in terms of their sequence
separation, they are less than 50 residues apart. Following the optical excitation
of the tryptophan triplet states, the decay to ground state is either by a natural
process or through contact quenching by cysteine. A Trp/Cys contact formation will
be observed only in the denatured or unfolded fractions of the protein. The observed

triplet decay is rapid enough that the protein conformations cannot interconvert

57

 

Figure 3.7: Structure and locations of mutations for the Protein L Bl Domain.

between any disordered state and the native folded conformation in the time span of

the experiment.

For proteins L and G in intermediate concentrations of denaturant (GdnHCl),
two kinetic phases are observed for the tryptophan triplet decay (figure 3.9).

The fast rate is attributed to intramolecular contact with cysteine in the unfolded
state and the slow rate to natural decay of tryptophan triplet in the folded or partially
folded state. The observed contact formation rates provides stability information

from fast phase amplitudes, and structural and kinetics information from life-time

58

 

 

\ f

1,.
.8
gaff

kfast

\ -
,1 8
(eff 3-

-5

Figure 3.8: Model for contact formation in proteins and peptides. A Trp/Cyc contact
quenching is possible only in the denatured ensemble of the protein chain. Under
the influence of chemical denaturants the protein is forced to reconfigure and adopt
a “disordered” state.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

measurements. The two phases observed at intermediate denaturant concentrations
are extracted by fitting the observed rate to a sum of two first order decays. The fast
phase amplitude provides estimate on the relative population of unfolded fraction
as shown in figure 3.10. This plot indicates that the equilibrium stability of both
proteins, regardless of mutant, is essentially the same.

These equilibrium unfolding curves are generally in agreement with that reported
by Park et al. for protein G [67,68] but are significantly different from those reported

59

 

1.0
0.8
0.6
0.4
0.2

0.0 = =
1e-6 1e-5 le-4 1e-3 1e-2

Time (s)

Figure 3.9: Normalized absorbance of the tryptophan triplet state of the T51C mu-
tant as a function of time for various concentrations of GdnHCl. The absorbance
decay in solution with 2 M (red), 2.5 M (blue), 3 M (green), and 4 M (dark) GdnHCl.

Absorbance

 

 

 

 

by Scalley et al. for protein L [66], both of which measured equilibrium fluorescence.
The kinetic and equilibrium data for protein L was found by Scalley et a1. and Yi
et al. to be well described by a two-state folding model [66, 70]. However, folding
equilibria determined by a variety of spectroscopic methods yields a wide range of
thermodynamic parameters for protein L (Table 3.3), which may mean that a simple

two-state transition model is not appropriate for protein L.

60

Short Loop Long Loop

 

 

 

 

 

 

 

 

 

 

 

 

1.0’ 0 - 0
° A
A
O
u- - ‘
3 .
'2“. ’ _
1% A
D
,8 ' .
3w _
“-1 ‘ ‘
A
u- ' » '
O
A 0 Proteinl.
A ProteinG
”1 A o - a IAA
Siiiiffr 3?:13332:
[GdnHCl] (M) [GdnHCl] (M)

Figure 3.10: Fraction of unfolded molecules as measured by the relative fast phase
amplitudes. The equilibrium stability of both proteins and all mutants appear to
be essentially the same. The red points correspond to the protein L data and dark
points to protein G.

3.6 Contact Formation Kinetics

Figure 3.11 shows the fast and slow rates of both proteins grouped by loop length.

For protein G, the slow rate is similar at all concentrations of denaturant signify-

61

 

 

type method AG (kcal / moi ) m(kcal/mol)
WT Fluor, A31; = 280,Aem = 3200' 4.6 1.85
WT Fluor, A31; = 280,Aem = 334 3.86 :I: 1.01 1.73 :I: 0.44
WT Fluor, A63 = 297,).em = 334 1.26 :I: 0.66 0.69 :l: 0.26
WT Fluor, max wavelengthb 5.15 :l: 1.23 1.78 :I: 0.43
WT CD, A31; = 220 2.24 :l: 0.42 0.88 :I: 0.16
T57C Fluor, A69; = 297,Aem = 334 1.18 :l: 0.95 0.82 i 0.41
T57C Fluor, max wavelength 5.13 :l: 1.01 2.12 :I: 0.41
T57C CD, A355 = 220 1.75 :l: 0.33 1.02 :l: 0.14
T57C intramolecular contactC 2.61 :l: 0.33 0.96 :l: 0.12

 

 

 

 

 

 

Table 3.3: Thermodynamic Parameters for protein L Wildtype (Trp only) and T57C
Mutant. “All measurements were made at room temperature in 0.1 M potassium
phosphate buffer (pH 7). The diflerence between exciting fluorescence at 280 and
297 nm is that the 297 nm excites only tryptophan while 280 nm also excites tyrosine

emission. bThe peak fluorescence intensity wavelength, A33; = 297nm. CData from
Figure 3.10 (triangles).

ing that the tryptophan remains hydrophobically buried until the protein unfolds
completely. However, for protein L, the slow rate decreases from ~22000 s-1 to
~5000 s-1 in an apparently cooperative transition. This is observed in both the
protein L mutants and in the control protein, Trp-only protein L (black circles in
figure 3.11). The higher protein L rate is approximately equal to that measured for
N—Acetyltryptophan amide in water whereas the lower rate is consistent with rates
for tryptophan triplet measured in the hydrophobic core of a protein [44]. Neither

rate is fast enough to reflect an intramolecular contact.

These observations suggests that proteins L and G each have a structurally differ-
ent “intermediates”. In architecture of protein G, formation of the second fl-hairpin
is the first step in its folding event [68]. Hairpin 2 forms a stable intermediate that

effectively buries the tryptophan at position 43. Formation of hairpin 1 is the rate—

62

 

Short Loop Rates Long Loop Rates

   

 

 

 

 

 

106 .
105 .

E"

13

0

5 water

hydrophobic
103...... ......
0123456701234567
[GdnHCll (M) [GdnHCl] (M)

Figure 3.11: Fast and slow triplet decay rates measured at various concentrations of
GdnHCl. Graph on the left correspond to the short loop mutants (T57C and T51C),
and graph on the right is for the long loop mutants (K230 and E190). The dark
points are the measured tryptophan triplet rates in the control protein L Trp—only
mutant, which has no cysteine.

limiting step in this well characterized sequence of folding events. Since the W43 on
hairpin 2 remains hydrophobically buried until the complete unfolding of the protein,
triplet contact quenching is insensitive to the rate limiting step and does not capture
the kinetic intermediate. In contrast, hairpin 1 forms first in protein L. This results
in a compact, partially folded intermediate and leaves the tryptophan at position 47
on hairpin 2 of protein L solvent exposed. The rate limiting step here, is formation

of hairpin 2 which hydrophobically buries the tryptophan eventually. This kinetic

63

intermediate in protein L is therefore captured as a decrease in the slow rate from
~22000 s-1 to ~5000 8'1. Could this be an indicator of the partially collapsed
unfolded chain, hinted by fluorescence-quenching experiments with sodium iodide by
Scalley et.al. [66]? A definitive answer to questions such as this can be obtained by
closer inspection of the equilibrium data and well resolved kinetic experiments. A
detailed analysis of thermodynamics and kinetics of unfolding/ refolding of protein
L will expose any stabilized intermediates that may have significant accumulation

during folding.

Further evidence for deviation of protein L folding kinetics fi'om a simple two-
state model is obtained from microfluidic ultrarapid mixer experiments performed
in this lab. Improved mixing techniques have enabled us to unravel the fast folding
events and phases that previously remained obscured in the long (>1 ms) dead time
of the stopped-flow instrument. Kinetic measurements using FRET and tryptophan
fluorescence on a 2-4 as mixing time scale discerns, in addition to a slow phase,
a faster phase of about 50 as [47]. Presence of two phases in the folding kinetic of
protein L suggests that a simple two-state model may not offer a complete description
of the folding characteristics. The dynamics of the unfolded state may be marked by
multiple energy barriers and hence a multidimensional energy landscape is necessary
to describe the folding of protein L. Figure 3.12 shows a conceptual representation
of such a folding energy landscape. Between the unfolded and the native state
basins, there exists a large energy barrier. The fast phase of 50 as, corresponds to
energy roughness fluctuations of the order of 1 kcal/mol and also corresponds to

the medium phase triplet rates at moderate [GdnHCl]. From figure 3.12, it appears

64

that denatured or unfolded states close to points such as “a” will tend to exhibit a
cooperative folding transition while those near the region marked “unfolded” could

show a more complex behavior deviating from two-state model.

Free Energy

# of native
contacts

 

 

 

radius of gjration

 

Native

Figure 3.12: Energy landscape representation under the final folding conditions. The
unfolded basin reflects the roughness that slows down the relaxations and intramolec-

ular diffusion.

65

3.7 Dynamics of Proteins L and G

The contact formation (fast) rate of the unfolded state for both proteins increases
slightly with decreasing denaturant concentration but then decreases significantly
below 3 M GdnHCl (fast rates in Figure 3.11). This contrasts sharply with similar
measurements of the cold shock protein of Thermotoga maritime in which the fast
rate increased monotonically as denaturant decreased to at least 1 M GdnHCl [71].
Ffom the measurements made at varying viscosities and temperatures, the reaction-
limited rate, kR(T), and diffusion-limited rate, k D + (7), T) are extracted through a
plot of l/kobs versus viscosity. Figure 3.13 shows such a data set.

The dynamics of the unfolded states of proteins L and G are remarkably simi-
lar. The reaction-limited and diffusion—limited rates for both proteins and all mutants
appear to have opposing trends. As depicted in figure 3.14, as the denaturant concen-
tration is decreased and solvent conditions become favorable for folding, the reaction
limited rate increases and the difl‘usion-limited rate decreases. At 6 M GdnHCl, the
difl‘usion-limited rate is 2—5 times faster than the reaction-limited rates for all mu-
tants. Comparing it to the AGQ peptides under the same conditions, the measured
rates are found to be very similar. To understand this behavior of the reaction-
limited and diflhsion-limited rates of proteins L and G quantitatively, we employ
Szabo, Schulten, and Schulten (SSS) theory and model the proteins as wormlike
chain with excluded volume. k R and k D +, according to SSS theory are given by
equations (2.18) and (2.19) respectively.

To give a qualitative description of the observed rates, we can model the unfolded

protein as a Gaussian chain. The reaction-limited and diflusion-limited rate is in-

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3e-5
3&5‘
2:3
2:61
le-Sl ’.
M A A A A A A A A 5&6‘ . .
02468l0|21416180
,mmm 01234567
(a) E190 6M GdnHCl (b) E190 3M GdnHCl
8c-6
. 1c-5
96” 9 6
93M 0.
3 ° 6e-6
‘ 2e-6 . °
3e—6
o .
o 1 2 3 4 s 0 . . - - .
“mm,” 0 5 10 15 20 25
(c) T57C 6M GdnHCl (d) T57C 2.3M GdnHCl

Figure 3.13: Temperature and viscosity dependence of observed quenching rates of
protein L T57C at 6 M GdnHCl. Lines are fits to equations (2.11), and (2.12).
The y-intercept gives the reaction-limited rate 1 / k R and slope gives 1 /nk D +. For
the lowest [GdnHCl] in which the unfolded state was observed, the temperature
dependence of k R disappeared. Errors of these measurements are typically less than
10%.

67

short loop long loop

 

 

G k,
c 1.0,
L k,
L km 0

>>00

 

 

 

 

 

 

 

 

 

0 l 2 3 4 5 6 0 l 2 3 4 5 6
[GuHCI](M) [GuHCI](M)

Figure 3.14: Reaction-limited and diffusion-limited rates for the short loop (left
panel) and long loop (right panel) in proteins L and G determined by equa-
tions (2.11), and (2.12). Based on the sum of squares of the fit, the error of these
rates is typically less than 10%.

versely proportional to the chain volume (equations (2.21) and (2.22)). The k R being
larger at the lower denaturant concentrations implies that the chain volume is lower
in conditions that favor folding. The ratio of the measured reaction-limited rates
at two denaturant concentrations gives an approximate change in the volume of the
unfolded chain. For the long loops, E190 and K230, the ratio of kR(2.3M)/kR(6M)
is 2.4 and 4.7 respectively. This means that the chain volume decreases by a factor
of 2 (4) for the loop E190 (K230) at 2.3 M GdnHCl as compared to that at 6M
GdnHCl. Since we are measuring the unfolded fractions, this denotes a compact
unfolded state under folding conditions. The diffusion—limited rate k D +, is observed

to be decreasing with denaturant concentration. For the mathematical consistency,

68

an observed decrease in k D + and a concomitant decrease in average chain volume
must correspond to a significant decrease in the diflusion coefficient D. Taking the
ratio (kR/kD+)2.3M x (kD+/kR)6M E D6M/D2.3M we find that the effective
diffusion coeficient decreases by 8—10—fold for the long loops and 15—30—fold for the
short loops. This suggests that the unfolded fractions of the protein have lower rate

of intramolecular diflusion, i.e., the chain is more viscous under folding conditions.

To further investigate the polymer dynamics of the unfolded state under folding
conditions, we modeled the protein as a wormlike chain with excluded volume and
use Szabo, Schulten, and Schulten (SSS) theory to estimate the effective persistence
length and intramolecular diffusion constant at various concentrations of GdnHCl.
We assume that the persistence length, lp, is an intrinsic property of the chain and
does not change with solvent conditions, but that the excluded volume diameter,
da, and diflusion constant, D, depend on solvent and intramolecular interactions
and therefore depend on the concentration of denaturant. For each loop length (8,
10, and 24 residues), 2 x 106 wormlike chains were generated for each persistence and
contour length. The simulated tails were always set to 5 residues since Buscaglia et
al. found that reaction limited rates were depressed by about a factor of 1.7 for each
tail due to excluded volume and that the effect was very insensitive to the length of
the tail [52]. A normalized histogram (0.1 A binning) of Trp-Cys distances was used
as P(r) in equations (2.18) and (2.19). The P(r) in conjunction with equation (2.18)
was used to calculate the reaction-limited rate for a variety of persistence lengths and
excluded volume diameters and compared to the measured rates at 6 M GdnHCl.

We observed that the calculated rates were much more sensitive to da than to lp.

69

Therefore the persistence length was kept fixed at 4 A as was found for unstructured
AGQ peptides [52], and the excluded volume radius was allowed to vary. As shown
in Table 3.4, for each mutant at 6 M GdnHCl, the best fits of da are very close
to 4 A, indicating that the polymer properties of the fully denatured proteins are
very similar to the completely unstructured peptides from [52] in 6 M GdnHCl.
Chains were then generated for smaller da to match the measured reaction-limited
rates at 2.3 M GdnHCl (see Table 3.4). Column 6 of Table 3.4 gives the root mean
squared 'Il‘p-Cys distance calculated using these probability distributions. Between
6 and 2.3 M GdnHCl, the average 'I‘t‘p-Cys distance decreases by 10 percent at lower

denaturant concentration.

70

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team was: 8386 5 assess 2: ea. .ao_aa§m s26 586.3 5 e8: assassin a.” sea.

 

 

 

 

 

 

71

 

 

 

 

 

 

 

 

 

a: x 3 a: x 3 3s 3 3 Oman
a: x 3 a: x 3 Rm 3 as 3. ea
m3 x as. m3 x on. how new md 03m
a: x 3 a: x 3 as.” an as 3. an
as x 3 a: x 3. a: an ms 039
m3 x as we x v.» «.3 Qm ed on. 3
a: x 5 ea x on 1.; as 2 05.
m3 x w.w n3 x o.w QB no.“4 ed on. w

:35 38. :35 a... 8 fig as... 35:82 E... a .843

 

Using equation (2.19), the effective diffusion coefficient, D, was calculated from
the wormlike chain probability distributions given in Table 3.4 and the measured
diffusion-limited rates. These values are given in Table 3.5. They vary quite sub-
stantially by mutant and, except for K23C, are significantly lower than that reported
for unstructured AGQ polypeptides in 6 M GdnHCl. We conclude that the diffusion
coeflicient is a local property of the loop sequence and support this claim by two
observations. First, the sequences measured by Buscaglia et al. are 33 % glycine, so
intramolecular diffusion should be faster than the sequences in this study. Second,
the diffusion coeficients for the T510 and T57C loops, which form fl — strands,
are much lower than for the K230 and E190 loops, which form mostly a — helix;
this difference likely reflects the propensity for extended structure in the [3 — strand
sequences. From table 3.5, the calculated effective difi'usion coeficients in 2.3 M
GdnHCl for all mutants decrease by about a factor of 6 relative to 6 M GdnHCl.
This uniformity of scaling for each mutant suggests that this trend is a global prop-
erty of the chain. Thus, the loss of denaturant in a real protein yields an unfolded
state that is less diffusive than the fully denatured state and reflects transient in-
teractions throughout the entire chain. A 6-fold decrease in D represents a very
significant change in the internal dynamics of the proteins. This decrease in D is
completely different than the trend observed by Buscaglia et al. on unstructured
AGQ peptides in which the coefficient increases by about a factor of two between 6
and O M GdnHCl [52]. We attribute this qualitatively different behavior to the fact
that the peptides measured previously were completely unstructured and contained

no hydrophobic residues.

72

 

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73

The intramolecular diflusion rate of unstructured peptides has been used as a
measure of the protein folding “speed limit” [7 2]. Low intramolecular difl‘usivity of
the unfolded state ultimately limits the folding process. The D values measured
in this work under folding conditions are up to 20 times lower than measured for
unstructured AGQ peptides. Our extrapolation of k D + to 0 M GdnHCl in figure 3.14
indicates that this internal friction time is on the order of microseconds, in good
agreement with measurements by Hagen et al. of fast folding protein rates as a
ftmction of viscosity and temperature [73]. This low difllisivity could arise through
formation of backbone-backbone interaction (hydrogen bonds). A decrease in the
diffusion coefficient has been observed by other research groups too. Using single
molecule fluorescence correlation spectroscopy, a two-fold decrease in D from 6 M
to 2.3 M GdnHCl was reported for the unfolded state of the cold shock protein [74].
Using bulk FRET on Gly-Ser unstructured peptides, the average end-to-end distance
and the diflusion coefficient seemed to be lower in water as compared to high levels
of denaturant [75]. Except for the AlarGly-Gln measurements of Buscaglia et al., it
does appear that presence of hydrophobes have an ubiquitous eflect of lowering the
diffusion coeflicient and also the average end—to-end distance in conditions that favor
folding. This degree of compaction and the extent of diffusion coeflicient lowering
varies from sequence to sequence and will be expected to also depend on solution
conditions such as temperature, nature of denaturant chemical used, solvent pH

conditions, solution viscosity and molecular crowding.

In conclusion, we have investigated the contact formation rates in amyloidogenic

peptides - polyglutamine - as well as proteins that are not very prone to aggrega-

74

tion (proteins L and G). While the proteins that do not easily aggregate have an
unfolded state fraction that is relatively more collapsed and less diffusive compared
to the typical denatured states, the same is not necessarily true for the aggregation
prone peptides. A further detailed atomic level characterization can be obtained
using molecular modeling and simulations. The unfolded fractions of protein can
be observed at higher temporal and structural resolution, generally inaccessible to
experiments. This could lay a strong foundation to directly relate experimental data

and simulation results.

75

Chapter 4

Protein L Simulations and
Experiment

4.1 Introduction

Molecular dynamics (MD) is a computational technique for modeling time evolution
of a molecular system. The central governing equation of motion is provided by New-
tonian mechanics and statistical mechanics. Each atom in the system experiences a
net force due to the potential created by all other atoms. The direction of motion is
thus determined and atomic motions simulated as a function of time by integrating
the Newton’s equations of motion. Trajectories of all the atoms are saved as the

molecular system progresses in time.

In the previous chapter we observed the significance of characterizing the unfolded
states of a protein to understand its folding landscape. A number of experimental
and computational tools have helped better our understanding of protein folding.
The various experimental techniques provide a wealth of information (structural,

dynamic, kinetic and thermodynamic) on a macroscopic length and time scales.

76

Molecular dynamics simulations complement the experiments by providing the in-
formation at atomic scales too. In spite of numerous advances in techniques and
computational throughput, there is no settled doctrine on the pathways and mecha—
nisms of protein folding or the exact nature of the folding landscape. Lack of better
connectivity between experimental results and computational modeling is one reason
there is still no comprehensive understanding of the problem of protein folding and
misfolding. In this chapter we present a comparison of experimental results with
simulation data to characterize the structure and dynamics of unfolded states of

protein.

Experimentally, we observe the unfolded states in proteins L and G to be more
viscous and compact under folding conditions [44]. Using a wormlike chain model
with these results, the diffusion coeflicients in both proteins appear to decrease by a
factor of about 6 at 2.3 M GdnHCl as compared to that at 6 M GdnHCl. Also, the
average end-to-end distance decreases by almost 10% for both the proteins at lower
denaturant (GdnHCl) concentration exhibiting the dynamic coil-to-globule transi-
tion. Identification of the primary contributors to this attenuated dynamics is neces-
sary to break the protein folding code. For a better understanding of the molecular
basis and origin of the observed nature of unfolded state, we compute the sampling
of the configuration space using molecular dynamics simulations and compare it to
experimental results. In the following sections we present a study of the B1 domain of
protein L using molecular simulations and Trp/Cys contact quenching experiments
to characterize its folding dynamics and unfolded states. The simulations reveal

a coil-to-globule transition with decreasing temperature that closely resembles the

77

results found with decreasing GdnHCl concentration.

4.2 Methods: Simulations and Experiment

A typical MD simulation using AMBER molecular dynamics package involves the

following:

1. Obtain or create the starting structure (typically a PDB structure file).

2. From the standardized PDB file, create the topology and parameters files.

3. Perform an initial energy minimization to remove steric hindrances and find
the local energy minimum.

4. Perform an optional equilibration to overcome low energy barriers and escape
the local minima.

5. Do the final production run for the protein to sample the thermally and kinet-

ically accessible configuration space.

The starting extended structure for protein L can be constructed using the molec-
ular visualization program Pymol. Generally, the starting structures do not have
hydrogens atoms in them. However, AMBER offers that functionality through the
program tleap. All our initial simulations are done with AMBER9 Molecular Dy-
namics package. For the protein representation, we have adopted the AMBER ff99
force field [76] in all the runs. The solvation effect was modeled by choosing the
standard pairwise Born continuum solvent (igb=1) [77]. The MD simulations were
carried out at 9 diflerent temperatures: 250, 300, 350, 400, 500, 600, 700, 800, and
1000K. For all simulations, I started with the fully extended initial conformation of

78

 

1"

the 63 residue protein L mutant T57C. This was then energy minimized with an
initial minimization of 500 steps. This energy minimized state formed the starting
structure for all our further production runs. Initial velocities are assigned randomly
from a Maxwell-Boltzman distribution. To maintain the temperature of our system,
we used the Langevin thermostat with a collision frequency of 1 ps’l. The time
step of our simulation was set to 1fs. Coordinates of the entire system is saved every
picosecond. The Tfp-Cys end-to-end distance was obtained as the distance between
the sulfur atom of cysteine side chain and the center of mass of tryptophan. The
production run was for 40 ns at all the temperatures except 300K. We performed
70 independent 10 ns simulation runs at 300K. This makes for a total accumulated

time of 0.94 as.

For temperatures below 500K, the simulation trajectories do not appear to con-
verge to a stationary state (discussed below) even in about 40 ns. Therefore, to
achieve a more accurate description further runs were performed in collaboration
with Folding@Home research group at Stanford. Longer trajectories were obtained
using graphical processing units (GPU) accelerated GROMACS. For the protein rep—
resentation, they have used the AMBER fl96 and ff03 forcefields with the generalized
Born/ surface area (GBSA) implicit solvent model of Onufriev, Bashford and Case
(igb=5) [78]. Simulations were performed at temperatures of 300K, 330K, 370K and
450K. The simulations produced multiple independent trajectories of 10 microsec-

onds starting from native, extended and random coil conformations.

For a direct comparison between experiments and simulations, we performed

further rIrp/Cys contact quenching experiments with a destabilized protein L mu-

79

 

tant: F22A, K23C. A substitution of the hydrophobic core residue of phenylalanine
with alanine considerably destabilizes the protein. This makes for a better model for
studying the nature of unfolded protein segments using both molecular dynamics and
experiments since various conformations from native to denatured states can now be
accessed and studied using minimal inclusion of non-physical entities (chemical de-
naturants). This destabilization results in unfolded state ensembles for denaturant
concentrations even below 0.5M GdnHCl. Figure 4.1 shows the normalized observed
tryptophan triplet kinetics in GM denaturant (green) and 1M Gdanl (red) at 20
degree C. The observed rates appear to be very similar at this viscosity and denat-
urant concentrations and can both be fit to first order decays. This shows that the
mutation F22A does in fact destabilize the protein because we would have normally
seen, at 1M GdnHCl, a slow rate corresponding to natural tryptophan decay; we now
observe a fast decay signifying an intramolecular contact. Figure 4.2 shows a plot
of 1 / kobs against viscosity for protein L F22A, K23C in 1M GdnHCl. As discussed

earlier, the slope in figure 4.2 gives 1/nkD+ and y-intercept gives 1/kR.

4.3 Results and Discussion

By comparing the experimentally obtained parameters for protein L with that of the
computed ones from MD trajectories, we can quantify and benchmark the accuracy of
the simulations and also characterize the nature of unfolded proteins at atomic level.
We also intend to check the effectiveness of the MD simulations in sampling of the

configuration space and the degree to which the sampling is realistic. We observe

80

 

‘Z‘I.-‘ '

 

 

 

 

 

 

 

 

1.2
1.0« O 1MGdnHCI
o 6MGdnHCl

0.8a

8 06

a: ' ‘

E

g 0.4+ ‘\
0.2«
0.0-1 I I §
'0.2 F I I 1' l I

1e—8 1e-7 1e-6 1e-5 10-4 10-3 10-2 1e-1
Tlme(s)

Figure 4.1: Protein L F22A, K23C, W47 Observed Tryptophan Triplet Kinetics: A
fast decay even at 1M Gdanl (red points) caused by significant protein destabiliza-
tion as a consequence of deleting a hydrophobic core residue.

that at higher temperatures, the end-to-end distance distribution from simulation
trajectories can be fit well to a Gaussian model indicating that the protein behaves
like an ideal freely-jointed chain at higher temperatures.

Figure 4.3 shows a plot of the root mean square deviation (RMSD) of the back-
bone Ca atoms at 400K with respect to various conformational states with the MD

performed on high performance computing cluster (HPCC) using AMBER9. There

81

 

2.40-5
2.2c-5 -
2.0c-5 ‘
1.8c-5 ‘
1.6c-5 ‘
1.4c-5 ‘
1.2e-5 -
1.0e-5 -
8.09-6 ‘
6.0c-6 ‘
4.0c-6 ‘
2.0c-6

l"(obs (S)

 

 

 

 

o s 10 15 20 25
Viscosity (cP)
(a)

l .4c-5

 

1.2c-5 ‘

l.0c-5 4

8.0e-6 «

1lkobs (S)

6.0c-6 ‘

 

4.0c-6 ‘

 

 

 

2.0e-6 . . . . .
0 1 2 3 4 5 6
Viscosity (cP)

(b)

Figure 4.2: Temperature and viscosity dependence of quenching rate for protein L
F22A, K23C, W47 mutant at 0 C (red), 10 C (green), 20 C (blue), 30 C (pink), and
40 C (cyan). (a) Protein L F22A K23C in GM GdnHCl, (b) Protein L F22A K23C
in 1.5M GdnHCl

82

is no indication of relaxation through multiple local minima as would be indicated
by distinct jumps representing spatial deviation between the structures in time with
respect to the reference structure [79]. This is yet another indication of limited and
narrow conformation sampling for simulations below 500K, the protein remains stuck

in local energy minima even till about 40 us.

I d

«ifw'wtt‘l‘tu [4]“sz

RMSD (Angst)

N

 

A L A A

"o 5 no 15 20 25 3o 35 40
Time (as)

Figure 4.3: Time evolution of backbone (Ca) RMSD with respect to various confor-
mations for protein L simulations at 400K. The deviation is obtained with respect to
conformations at: starting extended structure(red), 0.1ns (black), 0.5ns (blue), 2ns
(pink), and 35ns (green).

Figure 4.4 shows the probability distribution of W47-T57C distances for temper-
atures from 400K to 1000K. The distribution gets broader at higher temperatures.

Figure 4.5 shows the autocorrelation fimction at 800K for various parameter mear

83

surements all of which seem to exhibit exponential relaxation kinetics. The estimated
distribution of relaxation time constants was found to vary from 7 ps for the dihedral
angle ¢(6) to about 0.30 ns for the radius of gyration. The global chain relaxation
will be a convolution of different local relaxations. At very large simulation times,
all the diflerent relaxation rates should collapse into a single global rate constant.
Figure 4.6 shows the relaxation time as estimated from the autocorrelation of radius

of gyration measurements at various temperatures.

1.2

 

P“)

 

 

 

 

r (nm)

Figure 4.4: Protein L T57C probability distribution of W47-T57C distances from
400K (extreme left, black) to 1000K (extreme right, dark red).

For temperatures below 500K, we obtained narrower sampling distributions in-

84

1.2

 

1.0 J
0.8 4

C(t)

0.4 a

0.2 s

0.0 a

 

-0.2 ‘

 

 

 

0.4 r V V
0&1 0.00: 0.01 0.1 1 10 100

Tim. (m)

Figure 4.5: Protein L autocorrelation function for various parameters measures at
800K: dihedral angle 45(6) (green), RMSD from configuration at 35 ns (pink), W47-
T57C distance (red), and radius of gyration (black).

dicative of a range of energy barriers on many different scales. The ensemble of
unfolded states appear to be stuck in the rugged topography of folding energy land-
scape. Figure 4.7 shows the probability distribution of W47-T57C end-to—end dis-
tance of protein L T57 C mutant at 300 K for various independent random coil

starting configurations.

For 300K simulation runs, each of the starting configuration was randomly picked
from the runs at 600, 700, and 800K. Each 10 ns simulation results in a different end-

to-end average distance as shown in figure 4.7. Clearly, the protein is not sampling

85

 

10

Relaxation Time (as)

 

 

 

0.1 V U V V
200 400 600 800 1000 1200

Temperature (K)

Figure 4.6: Protein L characteristic relaxation time constant estimated at various
temperatures from single exponential fits to the autocorrelation function of radius of
gyration estimates.

a broad configurational space and is rather immobile or trapped in one of the many
local energy minima. Since the probability distributions of the intramolecular W47-
T57 C distances are not broad enough for the states to interconvert and converge, we
conclude that the 10ns simulations at 300K does not produces an ergodic sampling.
The net probability distribution over the 7 0 independent runs at 300K could not be

be fit to a Gaussian curve suggesting that the protein does not behave like a freely

86

 

  
  

   

   

 

 

 

0.10
0.004
0.00 .
a 004« ‘.'.’l.l‘3 .‘ [
0.02 ‘ ”1' ‘\r“'
'lt’ .v A\ \ (I
0.004 """
0 5 10 1'5 20 2'5 30

r (nm)

Figure 4.7: Simulated probability distributions of W47—T57C distances over time, for
various starting configurations at 300K. Each 10 ns trajectory produces a completely
independent and nonergodic distribution of distances.

jointed chain at 300 K.

Further evidence for a complex behavior of the chain at 300K emerges from the
'Ii'p-Cys distance autocorrelation plot shown in figure 4.8. An ergodic behavior would
be reflected in this autocorrelation flmction rapidly converging to zero. On the time
scale of our simulations, this end-to—end distance autocorrelation does not converge.
Absence of any non-converging regime suggests that there is a very strong correlation
between the Trp—Cys distances over the range of the trajectories averaged over 70

runs of 10 ns each. That is, each ensemble of states is bound and constrained to

87

difl‘use in its own local potential well and cannot cross over the energy barriers within

our simulation time.

 

1.2

1.0 d

0.0 4

0.0 s

C (t)

0.4 a

0.2 4

0.0 -

‘02 I

 

 

 

-0.4

q
d

V V

0 1 2 3 4 5 0
Time (n3)

1
1

Figure 4.8: Autocorrelation fimction of W47-T57C distances in protein L T57C MD
simulations at 300K. This is an average over 70 independent 10 ns simulation runs.

The relaxation to the equilibrium state is established much faster at higher tem-
peratures. This suggests that the protein molecules are more diflusive at higher tem-
peratures. At lower temperatures the average kinetic energy per molecule is small
enough that intramolecular non bonded interactions begin to dominate. These domi-
nating interactions (H—bonding, disulfide, aromatic-aromatic, charge-charge, van der

Waals) define the kinetic and thermodynamical properties of the protein and conse-

88

quently structure of native states. The multiple energy barriers created by various
interactions attenuate the protein chain dynamics. The energy required to cross over
these barriers and escape the local minima are again obtained from Brownian motion
and through these very interactions. Therefore, to accurately capture the protein dy-
namics through the rough energy landscape, one needs large enough simulation time
to first relax the protein into equilibrium and then sample this equilibrium phase to
obtain ergodic behavior/ sampling. This cannot be easily accomplished on CPU’s,
but a GPU offers a better performance of up to about 300 ns/ day as against about
9 ns / day achieved on the high performance computing cluster.

Taking advantage of the GPU accelerated GROMACS molecular dynamics sim-
ulation via the Folding@Home distributed computing platform, tens of thousands of
all-atom MD trajectories spanning ~10ps was generated. Simulations are performed
from starting configurations of native, extended and coil states. The plots of W47-
T57 distance P(r) over time suggests that the simulation starting from random-coil
and extended conformation produces ensembles that begin to converge at about 100
ns and are completely converged by about 1 us (figure 4.9). Convergence of the
distributions can be quantified by computing the relative entropies of extended con-
formation probability distribution Peat (r) and native state probability distribution

Pnat (r) with respect to the reference distribution of coil conformation Pcoil (r):

 

S = / drP(r) log [1922”] , (4.1)

here Pam-[(1') forms the reference distribution. According to the relative entropy

89

metric, the unfolded states are converged on the 100ns-1us time scale (figure 4.10).
The smaller the value of relative entropy, the more similar are the distributions. An
identical distribution will have zero relative entropy. The relative entropy metric de-
cays roughly exponentially to small values only after about 100 ns; this explains why

shorter 10 ns trajectories at 300K (Figure 4.7) fail to produce converged ensembles.

300K 450K

Log P( r)

 

 

 

 

0 IO 20 30400.

IO ZI) L 30 40
distance (A distance (A

Figure 4.9: Simulated distributions of W47-T57C distances of protein L over time
for various starting states at 300K and 450K. The unfolded state trajectories appear
to converge over a as time scale.

90

relative entropy (bits)

 

 

 

time (ns)

Figure 4.10: Relative entropy: A measure of convergence. The relative entropy
of Perth") (dashed line) and Pnatz've (r) (solid line) with respect to Pom-[(1‘) over
time, at various temperatures. Smaller values of relative entropy reflect more similar
distributions. For protein L T57 C, the unfolded states converge on ~100ns-1ps time
scale.

To draw a comparison between experiments and MD simulations, we have to
compare denaturant (GdnHCl) concentration and temperature. While temperatures
induces conformational changes by adding kinetic energy to the molecules and thus
higher temperatures favor entropy of unfolding. Chemical denaturants, on the other
hand, are understood to act by competing with protein-solvent interactions and in-

tramolecular protein—protein interactions by binding along the protein surface thus

91

making the protein more soluble. It disrupts the hydrophobic core and induces dis-
order in the protein configuration. Monte Carlo simulation studies by Choi et a1. [80]
suggest that denaturant-induced unfolding exhibits a wider conformational sampling
than temperature-induced unfolding. Although the destabilizing mechanism for tem-
perature and GdnHCl are different, we would expect a qualitatively similar behavior
of the unfolded states of protein under similar conditions. If the conformational
sampling is broad enough and truly ergodic, the relaxation kinetics, thermodynam-
ics and structural information would become independent of the type of denaturant
(chemical, temperature, pH, or pressure). Consequently, nature and characteristics
of the unfolded state will be context invariant. This is where the computing power
of GPU’s significantly overwhelms CPU’s to easily achieve an ergodic sampling of

the configuration space.

In our experimental measurements and results on proteins L and G, we observe
an unfolded state that is less diflusive and more compact under folding conditions
as compared to the denaturing condition (6M GdnHCl). Figure 4.11 shows the
reaction-limited and diffusion-limited rates for the destable protein L mutant F22A,
K23C. The trend observed in the destable mutant is mirrored in the other protein
L mutants studied (T570 and K230). Below 2 M GdnHCl, the reaction-limited rate
increases rapidly with decreasing denaturant and the difl‘usion-limited rate decreases.
At higher denaturant concentration (> 2M GdnHCl), the reaction limited rate de-
creases with increasing denaturant and diffusion-limited rate increases. In contrast,
the rates of protein L K23C indicate that it is more compact than the destabilized
protein L mutant (F22A,K23C). This suggests that deletion of the hydrophobic core

92

causes significant expansion and increased diffusion in unfolded protein states com-

pared to the original protein sequences at higher denaturant concentrations.

 

1046']

Rates (3")

 

1.45 v

 

 

[ GdnHCl 1

Figure 4.11: Reaction-Limited and Diffusion-Limited Rates for Protein L: The data
points marked in red correspond to reaction-limited rates and the blue data points
are the diffusion-limited rates. The “x” is for protein L K230 mutant and the circles

represent the destabilized protein L F22A, K230 mutant. The rates of K2300
mutant are bounded by the F22A rates.

4.4 Comparison: Simulation and Experiment

A platform for comparing the simulated ensembles with experimental results in the

context of intramolecular contact quenching experiments is provided by the SSS

93

theory. Probability distributions P(r), generated from MD simulations at different
temperatures was used to evaluate the reaction-limited rates using equation (2.18).
These rates are compared to experimental rates as shown in figures 4.12 and 4.13.
There is a very good agreement between the k R measured as a function of GdnHCl
and that computed from simulations using equation (2.18) in the higher denaturing
regime (high temperature and high GdnHCl). The comparison reveals an intriguing
relationship between temperature and chemical denaturant from the perspective of
protein dynamics. For the estimation of 1612, simulated temperatures of 300K corre-
sponds to GM GdnHCl, 370K corresponds to 2.3M and 450K to ~3M. Simulations at
lower temperatures corresponding to lower denaturant concentrations predict a very
high I: R increasing by an order of magnitude indicating a compact globular state at
lower denaturing conditions. The measured 10R values for F22A show an expanded
ensemble at equivalent denaturant concentrations. However, simulations of the F22A
mutant predict k R values with little difference from wild—type k R values except at

lower simulation temperatures (300K and 330K).

Yet another calibration of the simulated ensemble with experimental measure-
ments of protein L is obtained using two similar polymer theory approaches [81,82].
Based on this analysis we conclude that the simulated unfolded ensembles at low
temperatures correspond to unfolded ensembles near zero concentration of denatu-
rant, whereas the 450K ensembles correspond to [GdnHCl] ~ 3.2M i 1M (for details

see Appendix B).

Figures 4.14 and 4.15 show a comparison of the intramolecular diflusion coef-

ficients D as obtained from experiments and simulations. The blue points in the

94

[GdnHCl] (M)
0 2 4 6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

le+7 ’
: \k7\
32' le+6 : &<¥/ 1§§ .
.4: I \\§§
\\ \rt///\\
\/”\\\\ \
“~\\‘ \\p
\\v
1e+5 - - -
300 400 500 600

T(K)

Figure 4.12: Reaction-Limited rate for protein L W47-K23 loop from experiment
and MD simulation. Blue points are measured using Trp—Cys contact quenching in
GdnHCl. Red points are calculated using equation (2.18) and the MD simulated
P(r). The “x” are for F22A mutant of protein L K230.

figure show the diffusion coefficient calculated using worm like chain modeling of
the experimental data, as discussed in chapter 4. The red points correspond to the
diffusion coeflicients calculated using equation (2.19) from the SSS theory, experi-
mental values of kD+a and P(r) obtained from MD simulations. Experimentally
deduced k D + at 2.3M GdnHCl was used with simulated P(r) at 370K to obtain D
and the measured k D + at 3M GdnHCl is used with P(r) simulated at 450K. The

95

[ GdnHCl ]

 

 

 

 

 
    

 

O 2 4 6
:16‘1'8 I ' r ' r '
'm I I
.. I I
O
H I I
2 I \N I
3 I I
x: ' '

I I
.§ I I I
7; I... a — -I ------+
3 I I I
‘g I I I
o I I I
04 1e+5 1- ! !

 

 

 

 

 

250 350 450 550 650
'l‘cmperaturc (K)

Figure 4.13: Reaction-Limited rate for protein L W47-T57 loop from experiment
and MD simulation. Blue points are measured using 'I‘I‘p—Cys contact quenching in
GdnHCl. Red points are calculated using equation (2.18) and the MD simulated
P(r).

green points in the plot represent the diffusion coefficients calculated directly from
the simulated trajectory data by fitting the mean square displacements of Trp-Cys
distances over time in 50-ns windows. At greater denaturing conditions (high T of
450K and excess GdnHCl of 3M) the agreement for D is quite good for all three
methods. But at lower temperatures and [GdnHCl], the three methods seem to be

exhibit differing absolute values of D. However the trend of decreasing diffusion coef-

96

raga—w

ficient is captured fairly well. Since there is good agreement for k R at low simulated
temperatures and [GdnHCl], we conclude that the differing diffusion coeficients from
mean square displacement is an artifact arising from GBSA solvation model, possibly

due to lack of hydrodynamic interactions.

These techniques (MD and Contact Quenching) of measurements and character-
ization through two different methods (temperature and chemical denaturant) and
a comparison between them on at least two diflerent scales provides an estimate on
the realistic nature of the computational sampling methods. We find the probability
distribution of 'Ii‘p-Cys distances as sampled experimentally by denaturant and in
simulations by temperature to exhibit similar conformational ensembles of the un-
folded states in elevated denaturing regime (high T and [GdnH01]) as measured by
kR. Equation (2.18) suggests that k R is directly related to the probability distribu-
tion but is scaled by the distance dependent quenching rate. Since I: R is sensitive
only to the lower end of P(r), the comparison of the conformational ensembles with
the yardstick of k R will only be relevant to the tail of the distributions. However,
the intramolecular diffusion coefficients incorporate more global dynamics and there-
fore compares the unfolded states on a larger length scale. In elevated denaturing
regimes (450K, 3M GdnHCl), the diffusion coefficient estimated by MD simulations
and contact quenching experiments seem to agree quite well. But in lower denatur-
ing conditions of temperatures and chemical denaturants, the values of D obtained
are quite diflerent. This could be because in mild denaturing conditions of temper-
ature and [GdnHCl], the unfolded fractions are observed to be less diffusive, more

viscous and compact as compared to the fully denaturing conditions. Consequently

97

 

[GdnHCl]

 

O 2 4 6 8
1 ’ I I I I I
O 0.1 r
0 5
CD
\
N
E
0 0.01 f
A I
*9 :
o b
V .
O 0.001 ,-
o.0001 . - ' .

 

 

 

200 300 400 500 600 700 800
I‘u<)

Figure 4.14: Comparing experimental and computationally deduced diffusion coef-
ficient (D) for W47-T57C loop of B1 domain of protein L. The green points are
calculated from the simulated mean squared displacement over time, blue points are
calculated using worm-like chain model with equation (2.19) and experimentally ob-
tained k D +, the red points are calculated using equation (2.19), the MD simulated
P(r), and the measured 1: D + at the equivalent [GdnHCl].

the average kinetic energy per protein molecules is smaller under folding conditions.

Therefore, the amino acids have a long enough time to interact and influence each

98

 

[GdnHCl ] (M)

 

 

0 2 4 6
ma . . . .
811’
me',’
/
Ole-2r
‘5
£13
ne'i
1e-4 ‘ ‘ ‘ ‘

 

 

T(K)

Figure 4.15: Comparing experimental and computationally deduced diffusion co-
efficient (D) for the K230 and the F22A mutants of B1 domain of protein L. The
triangles are for the F22A mutant of protein L K230. The green points are calculated
from the simulated mean squared displacement over time, blue points are calculated
using worm—like chain model with equation (2.19) and experimentally obtained k D +,
the red points are calculated using equation (2.19), the MD simulated P(r), and the
measured 1: D + at the equivalent [GdnHCl].

other’s motion causing roughness in the potential of the free energy landscape in
which the proteins diffuse. It appears that for proteins to adopt the right native
state, it is essential for it to have this low diffusivity to instigate the folding process.

This may be the only way local interactions can take dominant effect and define

99

 

 

the kinetic and thermodynamical properties to lead the process of protein folding.
But in elevated denaturing regimes, the kinetic energy per protein molecule is large
enough that they can easily overcome and negate most of the local and nonlocal in-
teractions (H-bonding, disulfide, aromatic-aromatic, charge-charge, Van der Waals)
thus rendering the otherwise rugged landscape itself rather flat and planar.

To obtain a better understanding of protein folding, it is necessary to mark its
characteristics at length and time scales (femtoseconds to seconds; angstroms to
microns) that encompasses all of the relevant protein folding events. This can be
accomplished only through a good connect between experimental results and molec-
ular simulations. Since we observe a very slow equilibration of unfolded states on the
timescales of a as, this translates to, in the current scenario of computing power and
throughput, adopting and further developing of parallel processing with increased
number of graphical processing units (GPU).

100

Chapter 5

Summary

Anfinsen’s experiment proved that all the information needed for the protein to
adopt its native three-dimensional structure is embedded in its amino acid sequence.
Although there are exceptions to this rule, but it holds true for most small fast
folding single domains. Every protein synthesized in vivo has a function - either
as an antibody or a catalytic enzyme or some other specific physiological fimction.
The biological fimction of the protein therefore, is strongly dependent on its na-
tive conformation. To confront and successfully solve the protein folding problem
of predicting the three-dimensional structure from its amino acid sequence, we need
appropriate models for the initial unfolded state ensemble of the protein that is
sufl‘used with all the information necessary to spontaneously seek the viable native
state through kinetic and thermodynamic considerations. Recent evidences from
N MR experiments [30, 83] and results presented in this thesis have challenged the

earlier perspectives of random coil nature of the unfolded state ensembles of a pro-

101

tein under folding conditions and have emphasized presence of residual structure
in unfolded states. The dynamic and heterogeneous nature of the unfolded state
conformations has proven to be an intriguing hindrance to its characterization.

The growmg interest in the nature of a protein’s unfolded state has resulted in
rapidly developing methodologies to study them. Using experimental and computa
tional techniques to study the early events of protein folding I have presented in this

thesis -

1. Characteristics of polyglutamine polypeptides that are prone to aggregation.
A possible pathway for this aggregation is proposed.

2. Early events in the folding process of well behaved proteins L and G that are
not aggregation prone under normal physiological conditions.

3. An attempt to bring together the results from experiments, molecular simula-
tion and polymer modeling to ofler deeper and far reaching insights into the

mechanisms of protein folding.

Aggregation Mechanism in Polypeptides: Using the experimental technique
of transient intramolecular Ti‘p/Cys contact quenching on polyglutamine polypep-
tides and modeling the length dependence of contact formation rates with a worm-
like chain, we determined the persistence length of polyglutamine polypeptides to
be ~ 13.0.21. This corresponds to ~3.4 amino acid residues. Considering the obser-
vations reported for other peptide sequences and denatured proteins to be typically
about ~4A, the polyglutamine sequences appear to be much more stiffer. This poly-
mer “stiffness” possibly suggests the polyglutamine sequence prefers an extended

conformation that hinders the host protein in adopting its intrinsic native state.

102

Consequently the destabilized misfolded state forms a nucleus for aggregation and

amyloid formation.

A Primordial Hydrophobic Collapse: The technique of Trp/Cys contact
quenching to measure intramolecular difllision and rate of end-to-end contact forma-
tion, revealed for B1 domains of proteins L and G, a compact and viscous unfolded
state under conditions that favor folding. This suggests that the primordial event
after protein synthesis is the hydrophobic collapse of the relevant hydrophobic side
chain amino acid residues. This entropy driven collapse is responsible for close in-
tramolecular contacts between various chain segments triggering the interplay of ther-
modynamic, electrostatic forces and mechanical steric effects that induces ruggedness
of the free energy landscape. For proteins L and G, the difl‘usion coefficient dropped
by a factor of almost 6 at 2.3M GdnHCl compared to that at 6M GdnHCl, and the
average end-to—end distance dropped by ~10%. Similar compaction in the unfolded
states of the protein has been reported by other research groups. Both proteins L and
G share the same native topology with a central a—helix resting on a four-stranded
fl-sheet composed of N- and C-terminal ,B-hairpins, however, they follow diflerent
folding pathways. This is suggestive of at least two characteristics of proteins en
route the folding - firstly of existence of a hydrophobic collapse as the precursor
to the actual folding event, and secondly sequence dependent pathways for protein

folding inspite of similar native topology.

Synthesis of Experiments, Molecular Simulation and Polymer Mod-
eling: It is currently impossible to identify all the conformational variations in a

protein as it progresses spontaneously towards its native basin on the energy land-

103

scape. The experimental techniques and protocols lack the fine temporal and spatial
resolution. The simulations are deficient in their description of force fields, poten-
tials and solvation. The polymer theory lacks the necessary chemical heterogeneity
and other salient information on local structural ordering based on electrostatics
and bond formations. A more complete understanding of the folding mechanism
and pathways requires a union of all these techniques. Experiment ally deciphered
characteristics of early events of protein folding can be mapped onto the polymer
models and the biochemical and physical characteristic ascribed to the respective lo-
cal groups in molecular simulations so that they sample the required configurational

space and adopt the accurate biologically fimctional native state conformation.

For a comprehensive underst anding of the protein folding problem through a
harmonious synthesis of the various fragments of folding characteristics, it is neces-
sary to achieve a close collaboration between experimental techniques, computational
simulations, and theoretical modeling. The computational simulations can be bench-
marked by experimental results for providing the folding principles at a molecular
level. Details of the molecular mechanism can be delved into only through computa-
tional techniques. For the simulations to be realistic and accurate, it should have a
good overlap with predictions of experimental results and be well substantiated. The
folded native conformation of a protein being unique, distinct and relatively rigid, its
characterization is well accomplished through the recorded atomic coordinates, the
local secondary structure elements defined by the network of hydrogen-bonds and
well characterized dihedral angles. However, the unfolded state ensembles do not

submit themselves for such a representation owing to their conformational hetero-

104

geneity. Therefore, the only way to characterize the distribution of unfolded fractions
of the protein under folding conditions is to use physics based polymer models which

use a statistical mechanics based depiction.

As a preliminary step the distribution of unfolded state conformations was sought
by tuning the end-to—end distance probability distributions to the experimentally ob-
tained reaction-limited rates and the diffusion coeflicient deciphered through worm-
like chain modeling. The simulations reveal a coil-to-globule transition with decreas-
ing temperature that closely resembles the results found with decreasing GdnHCl
concentration. The degree of such a chain collapse would depend on the nature of the
hydrophobic pattern distribution along the chain length. As the protein is formed in
the ribosome, the hydrophobic residues begin sequestering in an entropically driven
process. Any polymer model that seeks to accurately describe the unfolded state
fraction must incorporate this sequence dependent hydrophobic collapse which is re—
sponsible for bringing together in close contact various segments of the chain for short
and long range forces to then start taking effect. Depending on the local short range
and long range interactions, the protein adopts one of the multiple routes towards

the native conformation basin.

In these molecular dynamics simulations, we observe a very slow equilibration
of unfolded states on the timescales of a microsecond. To make more meaningful
comparison between the experimental results and computational data, it would be
essential to obtain a broad sampling of the configuration space that is essentially
ergodic. The quest for the fundamental principles of protein folding will find its

consummation in the synthesis of the experimental techniques, the molecular sim-

105

ulations and polymer modeling to define the free energy landscape on which the

protein molecules diffuse to adopt their native conformation.

106

Appendix A

Polymer Models for Describing

Unfolded State Conformations

A simple two-state kinetic model may not completely describe the folding characteris-
tic of some proteins. Presence of compact non-native states under folding conditions
are suggestive of transient “intermediate” states seemingly difl‘using on a rugged en-
ergy landscape. The structural and dynamic characteristics of such states cannot
easily be captured unless we adopt physics based polymer models. Many polymer
models have developed that seek to describe various characteristics of the unfolded
state ensembles in proteins and polypeptides. Here, I present a few polymer models

that I have used in this work.

107

A.1 Freely-Jointed Chain

The freely- jointed chain model [84] of polymers is among the simplest model for
polymer conformations. This model treats the polymer chain as being constituted
of N rigid rods (monomers) of fixed length l as shown in figure A.1. The adjacent
monomers have no orientational correlation and the pivot point is absolutely flexible.
Therefore, there is no excluded volume in this model and different chain segments can

occupy the same volume in space. The total contour length of the chain is L = N x 1.

n=1

 

n=N

Figure A.1: Freely-Jointed Chain: Each monomer of length I has no orientational
correlation with other monomers. There is no excluded volume interaction and two
chain segments can occupy the same volume.

For an unbiased chain conformation, the ensemble average of end-to—end position
vector is zero since the links are uncorrelated. The average of end-to-end distance

squared, known as the mean squared displacement is

108

.L‘ numum __

 

N
< 1‘2 >= <| Z zn|2> = Nl2 (A.1)
n=1

therefore, the approximate size of the freely-jointed chain (as given by the root mean
square of end-to-end distance, ml) grows as square root of the number of monomers.
For large N, size of the polymer would be much smaller than its contour length. For
a large N, the probability density P(r) such that P(r)dr gives probability of finding
the polymer chains with the end-to-end distance between 1' and r + dr is given by a

Gaussian distribution

7, 2 -3/2 r2
P(r) = P(~'0)1"(I/)1"(Z) = (LEI—Z) exp (-—3—-—) (A?)

3 2<r2>

where the factor (27r < r2 > /3)_3/2 is obtained from the normalization condition
f P(r)d3r = 1. For a freely-jointed chain of N segments each of length l, the radius

if gyration is given by

 

1/2
129 = %) ><l (A.3)
2 2
2 _ EL = < I" >
R9 _ 6 _ 6 (AA)

and hence the ratio between radius of gyration and end-to-end distance is a constant

109

 

= __ = 6 (A.5)

The freely- jointed chain does not take into account any excluded volume. But real
polymers do have an excluded volume interaction and also a stiffness. Chain stiffness
is parametrized through either a Kuhn length or a persistence length. This model
assumes that chemical bonds are free to rotate and posses a uniform distribution of
bond angles. The uniform distribution of bond angles necessitates that the average
chain vector over all conformations is zero. Flory used this relation to define the

characteristic ratio (0n) of a polymer

C _<r2>
7'” N12

 

(A.6)

By definition C'n is unity for freely jointed chains, for other models, such as the
worm-like chain (WLC), which do not assume that the bond angle is free to rotate,

Cn exceeds unity.

A.2 Gaussian Chain

In this model the length of the monomers (bond vectors) is no longer a constant, and
the ideal polymer is treated as an efl’ective freely jointed chains of Kuhn segments [85,
86]. Each link vector has a probability distribution given by

110

7r2 "W2 ,2
P(r) = (~2—3L) exp (:2?) (A.7)

where < 1'2 >= 12

 

Figure A.2: Gaussian Chain Model: The length of each bond vector li is not a
constant but has a Gaussian probability distribution.

The probability density of end-to—end distance distribution is given by

27r<122>'3/2 3%

111

The Gaussian chain model gives a better description of the chain statistics for
long chains. An important property in the chain characterization is the excluded
volume, but the Gaussian chain ignores this. Local excluded volume interactions
will play a large role at smaller chain lengths by constraining the backbone dihedral
angles. Although the probability density may not be very accurately depicted, most
denatured proteins and polypeptide chains do exhibit a Gaussian statistics for large

chains lengths.

A.3 Worm-Like Chain Model

Also referred to as the Kratky-Porod worm-like chain model, it is the simplest model
that incorporates stiffness to describe the behavior of semi-flexible polymers. The
model describes the whole spectrum of chains with different degrees of chain stiffness
from rigid rods to random coils. Proteins and polypeptides are typically inextensi-
ble unlike the Gaussian chain considered above. For short peptide chain lengths,
the polymer exhibits memory effect in the chain direction. Persistence length is the
distance over which the polymer begins to loose memory of the direction. Mathe-
matically, it is expressed by the correlation between the tangent vectors at different

points along the chain

_ I
(0(8) '£2(8')) = exp (J37?) (A-9)

where f1(s) and 52(3’) are the unit tangent vectors at points TI and r2 respectively

112

separated by a distance Is — s’ I along the chain segment, and lp is the persistence
length. For Is — s’l << lpl, {1(3) and f2(s’) will be approximately collinear and
the chain segment will appear like a stiff rod. For |s — s’l >> lpl, the unit vectors
would be fully independent (no memory) of each other and the chain segment would
appear absolutely flexible. The mean square distance between two points for a chain

of length la is given

(72) = zzpzc — 21,2,[1 — exp(—lc/lp)] (A.10)

There is no one single expression that describes the P(r), but to obtain the
probability distribution of end-to-end distances, wormlike chain model is constructed
with a Monte Carlo algorithm using the method of Hagerman and Zimm. Chains
with a persistence length, lp, are randomly generated by sequentially adding random
links to the C-terminus. Each link in the chain is 0.38 A long, and is related to the
previous link by two spherical angles, 0 and (I), where the polar angle 9 is a Gaussian
distributed random number with a variance 41c / lp around zero, and the azimuthal
angle 43 is a random number between 0 and 27r . To account for excluded volume
effects, the pairwise distance between the last link added and every tenth link in the
chain is computed. If a clash of less than the excluded volume diameter of do, is
detected, the chain is truncated 3 persistence lengths before the clash and the chain
is regenerated. Millions of chains can be thus simulated and the end-to—end distance
for each chain is calculated to create a normalized histogram with 0.11:1 binning. This

normalized histogram is used as the probability distribution of distances P(r).

113

I=L

Figure A.3: Worm-Like Chain Polymer Model: This model incorporates an intrinsic
polymer stiffness characterized by persistence length lp. the excluded volume inter-
actions are invoked by checking for spatial clash of the chain segments. The tangent
vector at each point along the chain can be used to estimate the persistence length.

114

 

Appendix B

Calibrating Simulated Unfolded
Ensembles with Experiment:

Polymer Theory Approach

Protein stability is quantified by studying the denaturation-renaturation curve under
different conditions of the denaturant - chemical (GdnHCl or urea), temperature or
pH, etc. The molecular simulations most often employ temperature as the parameter
of choice while many experimental techniques rely on a chemical denaturant. To be
able to make a comparison between experiments and simulations and place them on
a common platform, it is therefore necessary to establish a link between the unfolded

state ensembles obtained with these two processes of denaturation.

A polymer-theory approach is used to examine the coil-globule transition in both

experimental results and simulation data. The estimated radius of gyration (R9)

115

 

is a good indicator of free volume occupied by the polymer chain (chain expansion
and compaction). In the coil-globule reconfiguration process of the chain, some of
the monomer residues undergo a shift in its physiochemical environment from the
hydrophobic core to being solvent exposed. The free energy associated with this
shift is referred to as the transfer free energy. A key features of the polymer theory
is that this mean-field transfer free energy is independent of the molecular mecha-
nism involved in protein destabilization. Therefore, the free energy for transfer of a
monomer into solvent can be computed based on estimated By and compared across
different [GdnH Cl] and temperatures in order to map the unfolded state ensembles

with respect to the two denaturing parameters.

To estimates the free energy of transfer (a), two different polymer-models are
used for fitting Rg vs temperature and a comparison is made with the experimentally
obtained conformation. We refer to the first polymer model as the “Dill” model and

the second as “Ziv” model:

B.1 Dill Polymer-Model

This model was proposed by Ken A. Dill [81,87]. In this model, the free energy
diflerence AFDz’ ll with respect to the maximally compact polymer state is modeled

as

116

AFDz'll_ 7 2/3 2/3 2 I—p
air-”5600 ‘(PO/P) +5111P+ —p_ 111PP+§,;—T(1’P)

(13.1)

where n is the chain length, k B is the Boltzmann constant, T is temperature, p is
volume density of the monomers and is defined such that p = 1 in the maximally
compact state (usually assumed to be the native state), p0 is the volume density
at the coil-globule transition, and 5 reflects a mean-field transfer energy across all

residues. The value of po is fixed to be

p0 = [717:]1/2 ‘ (B2)

B.2 Ziv Polymer-Model

The second of the models is the modified-Sanchez model of Ziv and Haran [82] which
we refer to as the “Ziv” model. This model starts with the empirical ideal-chain
Flory-Fisk distribution [88] of the radius of gyration Rg =< R3 >1/2 and weights

it by a Boltzmann factor capturing the transfer free energy of the chain:

 

7R2
6 9 "9(PI5))
P R ~R ex —— ex — B.3
( g) g p( 2R3) p( [0351' ( )

117

where

gas) = -5). + 1.341%] 1n(1 — p) (3.4)

Here, R0 is the radius of gyration of the ideal chain and is fixed by the relation

P0 = —RT' (35)

B.3 Fitting Polymer Theory Models to Simulated

Data

Since the equilibration of the unfolded states occurs on the timescale of about a mi-
crosecond, the radius of gyration is calculated using the simulated ensemble sampled
after 1 microsecond. The ensemble corresponding to the starting structure as the
extended conformation is used for estimation of Rg for the simulations at temper-
atures T = 300K, 330K, 370K and 400K. The calculated mean radius of gyration
for ensembles started from the extended state at various simulated temperatures is
shown in table RI. The radius of gyration of the maximally compact state Rnatz'vev
was set to the lowest value of mean Rg observed in our simulations (11.521). The

free energy for the Dill and Ziv models is minimized by numerical evaluation of the

118

volume density (p). A least-squares fit to the R9 vs T data is then performed to

obtain the best estimate of transfer free energy 5.

 

Temperature (K) Average Rg (after 1 ,us) (A)

 

300 12.42
330 12.32
370 12.63
450 21.99

 

Table B.l: Simulated temperature and mean radius of gyration for ensembles started
from the extended state.

As is evident in figure 3.1, the trend in R9 vs T cannot be accurately represented
by fitting it with constant values for s.

Therefore, a temperature dependent linear model of the transfer free energy,
s(T) = so — (T — To)AS, is used for produce a more satisfactory and accurate fit
to the data. For both the Dill and Ziv models, values of so and AS are obtained
by least-squares fitting. Such a fit is shown in figure B.2. The fitting parameters
obtained for Dill models is found to be so ~ 4.0kcal/mol and AS ~ 20.4kcal/mol
and that for Ziv mdoel is found to so ~ 3.7kcal/mol and AS ~ 20.8kcal/mol. There
is a very good agreement between both the Dill and Ziv models for transfer energy

estimation.

B.4 Comparing Simulated and Experimental Un-
folded Ensembles

From histograms of FRET efficiencies published in two different single-molecule

FRET studies of protein L by Sherman et al. [89] and Merchant et al. [90], Ziv

119

Dill II model

 

 

24 ' ’ -

22 ~ -

20 r <
<3 13- , 0 extended
a? 16 - - -

O COII

14 - “I’M/,- .

12 ~ ' .

10 '

 

 

 

300 3§0 400 4530
temperature (K)

 

 

 

Ziv model

24 - l T '

22 - e ‘ 6 =1.0 (k1)
A 20 ~ 4;? e 21.1
S. 18 - 1:_____€ :12
g 16’ / .

14- /§ 4’ 6 = 2,0

12- , -

10

 

300 350 400 450
temperature (K)

Figure RI: The trend in By vs T cannot be accurately represented by fitting it
with constant values for 5. Various constant values of s(T) = so yield poor polymer
theory fits to the data.

120

DHlmodd

 

 

1.

l

 

 

24'
22'
20'
518-
01
K16.
14-
12-

A

A

300

350 460 450
temperature (K)

Ziv model

 

 

_ I"

1'

 

 

 

U

300

350 400 450
temperature (K)

Figure B.2: A temperature dependent linear model of the transfer free energy, s(T) =
so — (T — To)AS, yields a robust fit to the average Rg versus temperature.

and Haran [82] computed free energies of transfer s([GdnHCl]) and expansion fac-
tors 012([GdnHCl]).

121

The plot is shown in figure B.3. The expansion factor is equivalent to a2 =

123/R3, where R9 is the radius of gyration of the ensemble, and Ro is the radius of
gyration for the ideal chain at the coil-globule transition. Using Rnatz’ve = 11.521,
Rg(450K) = 21.99 and n = 64, we compute the expansion factor for our 450K
ensemble to be a2 ~ 0.81. As seen in figure B.3 the value of [GdnHCl] with an
equivalent expansion factor is ~ 2.45M for the Merchant et al. data, and ~ 3.8M
for the Sherman et al. data. Thus for purposes of comparing the simulated and
experimental unfolded ensembles, we conclude that the 450K ensemble is comparable
to an experimental GdnHCl concentration of ~ 3.2M :1: 1M .

The simulated unfolded states at low temperatures (300K, 330K and 370K) ex-
hibit a high degree of compaction, becoming even more compact than the native
ensembles beyond 1 as. This observation, combined with the large free energies of
transfer predicted by the polymer theory, and small values of the expansion fac-
tors for the observed R9, indicate that the low-temperature simulations can best be

compared to experimental conditions in the absence of denaturant.

122

 

 

 

 

 

 

5
0'0 I ' I . I I I ' F
O 2 4 6 8
deCl or urea [M]
AB:-
1.5__ (—4a
79'
.g -'
210—
w -
0.5—

 

 

 

 

] ' I ' I ' l '
0 2 4 6 8
deCl or urea [M]

Figure B.3: Coil-Globule transition in denatured proteins obtained from smFRET
experiments by analysis using Sanchez polymer theory. The plot in light blue (4a)
corresponds to the Sherman et al. data and that in brown (4b) is for the Merchant
et al. data for protein L. (A) The expansion factor (12 as a function of denaturant
concentration. (B) the mean-field interaction energy E as a function of denaturant
concentration. This plot is adopted from [82].

123

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