Small and Large Cosolutes Modulate Enzyme Activity and Protein Folding Kinetics

SMALL AND LARGE COSOLUTES MODULATE ENZYME ACTIVITY AND PROTEIN FOLDING KINETICS

Annelise Hocevar Gorensek

A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Chemistry.

Chapel Hill 2017

Approved by:

Gary J. Pielak

Eric M. Brustad

Sharon L. Campbell

Bo Li

Marcey L. Waters

ABSTRACT

Annelise H. Gorensek: Small and Large Cosolutes Modulate Enzyme Activity and Protein Folding Kinetics

(Under the direction of Gary J. Pielak)

Proteins are the powerhouse of the cell, catalyzing chemical reactions, serving as signaling hubs, and maintaining cellular structure. Recently, several investigators have advanced our understanding of how the crowded cellular interior, and common cytoplasm mimetics such as synthetic polymers and commercially available proteins, affect protein equilibrium stability. These efforts show that attractive chemical interactions between proteins and macromolecular crowding agents, can destabilize proteins, contradicting the long-held idea that steric repulsions under crowded conditions increase protein stability. My work expands on these studies by examining the effect of crowding on enzyme activity and protein folding kinetics. In the first part of my dissertation, I examine the effects of synthetic polymers on the activity of the monomeric enzyme E. coli dihydrofolate reductase as a function of polymer concentration, fractional volume occupancy and viscosity. I compare my results to those in the literature, and find that crowding effects are small, difficult to predict, and depend on the crowder, protein, and even the substrate. To investigate the influence of crowding on folding kinetics, I examined the temperature-dependent folding and unfolding of the small, metastable, N-terminal SH3 domain of the drosophila signaling protein drk. The results contradict classical crowding theory in that osmolytes and polymers alter folding barriers via both enthalpic and entropic contributions. Additionally, the entropic components suggest that solvent and cosolute entropy, rather than configurational entropy, are the dominating effect. Comparing activation parameters from synthetic polymer cosolutes to

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those from the biologically relevant crowder, lysozyme, indicate that synthetic polymers are poor mimics of the cellular interior. However, my results build a foundation for studies to interpret folding landscapes in biologically-relevant crowded conditions.

To my parents, Maximilian Boris Gorensek and Annmarie Hocevar Gorensek.

ACKNOWLEDGEMENTS

I would not be where I am today without the blessing of a lineage of strong mentors who helped shaped me. Thank you to my first mentors: my father, who answered my endless questions about how the world worked, and my mother who encouraged me to read as much as I possibly could. In high school, my chemistry teacher Shannon Williams captured my interest by describing the elements as people (“Francium, he can’t keep his electrons together…”) while Dottie Andreassen showed me how to communicate my thoughts through writing, which has served me well.

As a nervous senior visiting Furman University on accepted students’ day I met Dr.

Karen Buchmueller, who became my academic, research, and essentially life, advisor.

Karen gave me the skills I needed to become a scientist, but the dedication she showed to me and her other students inspired me to become an educator. Thank you, Karen for investing in me even after I graduated, and for talking me through some of my most difficult times both at Furman and at UNC. It was in Karen’s lab at Furman that I met Austin Smith, who at first terrified me (I ‘gave him up for Lent,’ which is still part of departmental lore) but after working together in the Pielak lab at UNC, he became my mentor and personal NMR

911 hotline. Thank you, Austin for teaching me to purify protein, how to not break the NMR, for getting me started on the SH3 project, and finally for challenging me to think deeply about my work.

I joined Gary Pielak’s lab because I wanted to study proteins and thermodynamics was my second-favorite class after biological chemistry, so it seemed like a natural fit. I chose well, even if I ended up studying kinetics instead. Gary taught me the importance of reading the manual first, of thinking before speaking, and in the process constantly kept me on my toes. He has challenged me more than anyone else ever has and helped me realize my own potential as a scientist, teacher, and mentor. But most importantly, he helped me take the first step towards my dream of being a professor by allowing me to mentor two dedicated, hardworking undergraduates. Thank you, Gary for challenging me and supporting me as I prepare for my career after graduation.

Thank you to the Pielak lab members, old and new, for your help and encouragement along the way. Thank you to Will Monteith, Mohona Sarkar and Jillian

Tyrrell for teaching me the ways of the lab. Thank you to Larry Zhou for showing me the ropes of SH3 purification and Michael Senske, for suffering through it along with me. Rachel

Cohen, thank you for encouraging me to stay active, to take my time, to take a chance and apply for an internship and for the countless encouraging conversations we had over coffee, lunch, or at Weaver Street. I would not have made it through Year 4 without you. Thank you to Sam Stadmiller, Pixie Piskiewicsz, Thomas Boothby, Alex Guseman, Candice Crilley and

Shannon Speer for encouragement, for thoughtful conversations about science, and for helping me unwind during this last semester. Finally, I need to recognized my undergraduate mentees, Luis Acosta and Gerardo Perez Goncalves, who worked tirelessly and gifted me with my first opportunity to be a research mentor.

Thank you to the other people who have kept me going outside of the lab: to Greg

Young and Karl Koshlap for keeping me company in the basement and answering my NMR questions and to Reggie Singleton and Karen Gilliam for always being happy to chat and for having a full candy jar.

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Thank you to my sister, Natalie Gorensek, for loving science along with me and for being my first student (she can still recite the Mercury 7 in alphabetical order).

Finally, thank you to my husband, Ryan Benitez for being the ultimate partner and support system during my 5 years here, all while living nearly 150 miles away. Thank you for staying up past your bedtime to talk me through science drama, for helping me figure out my statistical analysis and for working alongside me on weekends when you’d rather play

Ultimate. But most of all thank you for your inexhaustible belief in me, it has made all the difference.

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TABLE OF CONTENTS

LIST OF FIGURES ...... xii

LIST OF TABLES ...... xiii

LIST OF ABBREVIATIONS AND SYMBOLS ...... xiv

CHAPTER 1: A HISTORY OF PROTEIN FOLDING KINETICS IN BUFFER AND IN COSOLUTES ...... 1

Introduction ...... 1 Transition state theory ...... 2 Activation parameters and protein folding ...... 5 Activation parameters in buffer ...... 9 Activation parameters in denaturants ...... 12 Activation parameters in stabilizing osmolytes ...... 16 Activation parameters in synthetic polymers ...... 17 Activation parameters in live cells ...... 19 Conclusions ...... 20 Tables ...... 22 Figures ...... 23 CHAPTER 2: LARGE COSOLUTES, SMALL COSOLUTES AND ENZYME ACTIVITY ...... 27

Introduction ...... 27 Results ...... 29 Polymer and monomer properties ...... 29 DHFR activity ...... 29 Discussion ...... 30 Crowder identity ...... 30 Concentration dependence ...... 31

Overlap concentration (c*) ...... 31 Viscosity ...... 32 Molecular mass ...... 32 Macromolecular effects ...... 32 Cosolute effects are system-specific ...... 33 Materials and Methods ...... 34 Cosolutes ...... 34 Protein preparation and purification ...... 35 Enzyme activity ...... 36 Polymer properties ...... 37 Tables ...... 39 Figures ...... 41 Supplementary Information ...... 44 CHAPTER 3: COSOLUTES, CROWDING AND PROTEIN FOLDING KINETICS ...... 52

Introduction ...... 52 Results ...... 55 Cosolutes and SH3 structure ...... 55 Activation parameters in buffer ...... 56 Activation parameters in cosolutes ...... 57 Viscosity correction ...... 58 Discussion ...... 59 Activation parameters in buffer alone ...... 59 Cosolutes and SH3 structure ...... 60 Activation parameters for cosolutes compared to buffer ...... 61 TMAO and sucrose ...... 63 Ficoll ...... 65 Lysozyme ...... 67 Conclusions ...... 68

Materials and Methods ...... 69 Protein expression and purification ...... 69 NMR ...... 69 Selection of fits for temperature dependence in cosolutes ...... 70 Analysis of uncertainty ...... 71 Viscosity measurements ...... 71 Tables ...... 73 Figures ...... 74 Supplementary Information ...... 78 APPENDIX 1. T1 FITTING SCRIPT WITH MONTE CARLO ERROR SIMULATION ...... 93

APPENDIX 2.1 T1 FITTING SCRIPT WITH MONTE CARLO ERROR SIMULATION ...... 96

APPENDIX 2.2 EVOLUTION EQUATIONS FOR EXCHANGE SPECTROSCOPY ...... 100

APPENDIX 2.3 EXCHANGE SPECTROSCOPY PLOTTING SCRIPT ...... 102

APPENDIX 3. MONTE CARLO ERROR SIMULATION FOR DETERMININATION ACTIVATION PARAMETERS ...... 103

APPENDIX 4. WEIGHTED LINEAR LEAST SQUARES REGRESSION FOR DETERMINATION OF ACTIVATION PARAMETERS ...... 105

REFERENCES ...... 107

LIST OF FIGURES

Figure 1.1. Arrhenius and Eyring plots of a chemical reaction...... 23

Figure 1.2. SH3 stability plot...... 24

Figure 1.3. Temperature dependence of CI2 folding kinetics...... 25

Figure 1.4. Reaction coordinate diagrams for CI2 at 298 K...... 26

Scheme 2.1. DHFR reaction scheme...... 41

Figure 2.1. Cosolute volume occupancy and relative viscosity at 298 K...... 42

Figure 2.2. DHFR activity as a function of concentration, volume occupancy and relative viscosity...... 43

Figure 3.1. Amide proton temperature coefficients...... 74

Figure 3.2. Temperature dependence of folding kinetics in buffer ...... 75

Figure 3.3. Temperature dependence of kinetics in buffer and cosolutes...... 76

Figure 3.4. Changes in the activation parameters in cosolutes...... 77

1 15 Figure S3.1. Changes in composite H- N chemical shift (Δδcomp) at 298 K...... 90

Figure S3.2. Chemical shift perturbations for SH3...... 91

Figure S3.3. Residual plots for SH3 two- and three-parameter fits...... 92

xii

LIST OF TABLES

Table 1.1. Activation parameters of apocytochrome b562 in 85 mg/mL PEG 20K. ... 22

Table 2.1. Partial specific volumes and overlap concentrations ...... 39

Table 2.2. Effects of macromolecular crowding on enzyme kinetics...... 40

Table S2.1 Effects of macromolecular crowding on enzyme activity...... 44

Table S2.2. Effects of macromolecular crowding on Vmax and kcat...... 46

Table S2.3. Effects of macromolecular crowding on Km ...... 49

Table 3.1. Activation parameters for folding and unfolding at 303 K...... 73

Table S3.1. Amide temperature coefficients...... 78

Table S3.2. Composite 1H-15N chemical shift perturbations...... 80

Table S3.3. Average 1H-15N chemical shift perturbations in cosolutes...... 84

Table S3.4. SH3 Longitudinal relaxation and folding rates...... 85

Table S3.5. Changes in activation parameters for SH3 folding and unfolding...... 88

Table S3.6. Equilibrium-from-kinetics parameters for SH3 ...... 89

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LIST OF ABBREVIATIONS AND SYMBOLS

$% ∆"# standard state, equilibrium free energy of unfolding

$% ∆&# standard state, equilibrium enthalpy of unfolding

$% ∆'# standard state, equilibrium entropy of unfolding

$+ ∆(),# standard state, equilibrium heat capacity of unfolding

°%‡ ∆"#,,→#‡ standard state, activation free energy for folding or unfolding

°%‡ ∆",→#‡ standard state, activation free energy for unfolding

°%‡ ∆"#→#‡ standard state, activation free energy for folding

°%‡ ∆&#,,→#‡ standard state, activation enthalpy for folding or unfolding

°%‡ ∆&,→#‡ standard state, activation enthalpy for unfolding

°%‡ ∆&#→#‡ standard state, activation enthalpy for folding

°%‡ ∆'#,,→#‡ standard state, activation entropy for folding or unfolding

°%‡ ∆',→#‡ standard state, activation entropy for unfolding

°%‡ ∆'#→#‡ standard state, activation entropy for folding

ΔΔ'1 standard state, change in excess entropy of unfolding

°+‡ ∆(),,.#→#‡ standard state, activation heat capacity for folding or unfolding

°+‡ ∆(),,→#‡ standard state, activation heat capacity for unfolding

°+‡ ∆(),#→#‡ standard state, activation heat capacity for unfolding

Δδcomp composite chemical shift change

κ transmission coefficient

ℎ Planck’s constant h viscosity h$ viscosity of water

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h456 viscosity of a solution divided by viscosity of water

7(9); temperature dependence of viscosity

A Arrhenius prefactor

Bs CspB Bacillus cereus heat shock protein CspB

Bc CspB Bacillus caldolyticus heat shock protein CspB

°C Celsius

CI2 chymotrypsin inhibitor 2 cm centimeter

DSS 4-,4-dimethyl-4-silapentane-1-sulfonic acid

EXSY exchange spectroscopy

FRET Förster resonance energy transfer

GCN4 general control Nonderepressible protein 4

GuHCl guanidinium hydrochloride

HSQC heteronuclear single quantum coherence hFGF-2 human fibroblast growth factor 2

[>5?] <# unfolding rate in denaturant

ABC <# folding rate in 0 M denaturant kobs observed combined folding and unfolding rate

<,,#→#‡ folding or unfolding rate

<,→#‡ unfolding reate

<#→#‡ folding rate K Kelvin

Kcal/mol kilocalories per mole kDa kilodalton

M molar

D# m-value NEP 1-ethyl-2-pyrrolidone

NMR nuclear magnetic resonance

ppm parts per million ppb/K parts per billion per Kelvin

PEG polyethylene glycol

PGK phosphoglycerate kinase pI isoelectric point

Pr probability of the values arising from uncorrelated data

PVP polyvinyl pyrrolidone

R gas constant

R1 spin-lattice relaxation rate

ReASH resorufin arsenical hairpin binder

RNAse ribonuclease r correlation coefficient

SOD1 superoxide dismutase

TMAO trimethylamine-N-oxide

Tm melting temperature

TS temperature of maximum stability

To reference temperature

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CHAPTER 1: A HISTORY OF PROTEIN FOLDING KINETICS IN BUFFER AND IN COSOLUTES

Introduction

The process by which a protein progresses from an ensemble of unfolded states to its most stable, native conformation is called the folding pathway. A protein’s structure dictates its function,1 and disrupting pathways can lead to aggregation and disease.2-4 To gain the correct conformation, proteins must cross an energy barrier, populating a high- energy transition state before reaching the native folded state.5,6 This activation energy barrier has both a chemical (enthalpic) component and a configurational (entropic) component, which can be extracted by measuring the temperature dependence of the folding and unfolding rates.7 Although the energetic, enthalpic and entropic barriers to folding have been studied in buffer, how a protein’s native environment—the cellular interior—affects folding remains unknown.

One way to understand how the cytoplasm alters protein folding is to determine how the folding landscape changes with the addition of cosolutes that mimic protein- macromolecule interactions that might occur in cells.

In this chapter I describe the history of transition state theory, which when applied to proteins can be used to assess the barriers to protein folding and unfolding. I then review studies that determine activation parameters in dilute buffered solution, denaturants, osmolytes, synthetic polymers, and living cells.

Transition state theory

The relationships that define protein folding equilibria and kinetics were derived for small molecule chemical reactions, in which a single bond was formed or broken. A simple chemical equilibrium between reactants and products is defined as:

Reactants ⇆ Products (1.1)

The extent to which a reaction occurs is determined by the equilibrium constant, Keq.

J5KLMK?MN G = (1.2) 5H O4$>1LMN .

Whether or not the forward reaction occurs spontaneously is determined by the standard state modified standard state equilibrium change in free energy, or ∆"∘%:

∘% ∆" = −R9lnG5H (1.3) where R is the gas constant and T is the temperature. A negative ∆"∘% indicates the forward reaction, and therefore product formation is favored, while a positive ∆"∘ indicates the reverse reaction, and therefore the reactants, is favored. The free energy change can be split into two components through the Gibbs-Helmholtz equation:

∆"∘% = ∆&∘% − 9∆'∘′ (1.4) where ∆&∘% is the modified standard state change in enthalpy and ∆'∘% is the modified standard state change in entropy. The directionality of the reaction is determined by the balance between the entropic and enthalpic components. ∆&∘% is a measure of the change in the heat of the system via bond formation and breakage. A negative ∆&∘′ is favorable for product formation, or exothermic, meaning heat is released. A positive ∆&∘′ is unfavorable, or endothermic, meaning heat must be absorbed from the surroundings. −9∆'∘% is a measure of the change in order of the system. A negative, i.e., favorable −9∆'∘ arises from an increase in the disorder of the system, while a positive, i.e., unfavorable −9∆'∘ accompanies an ordering of the reaction. The equilibrium parameters ∆"∘, ∆&∘, and −9∆'∘

describe the relationship between the products and reactants, and can be determined from the ratio of the forward and reverse reaction rates:

kReactants→Products G5H = (1.5) kProducts→Reactants where kReactants→Products is the rate of the forward reactions and kProducts→Reactants is the rate of the reverse reaction.

In 1889, Svante Arrhenius postulated that before forming product, the reactants must

8 first cross an energy barrier, EA, called the activation energy (Figure 1.1A). Arrhenius derived an equation describing the temperature dependence of reaction rates:

< = _`abc/Je (1.6) where k is the rate constant, EA is the activation energy (or energy barrier between the reactants and activated complex) and A is the pre-exponential factor (prefactor), or the number of collisions per second.8 According to the Arrhenius relationship, rates increase with temperature, because as the temperature increases, the value for the exponent (-

EA/RT) decreases and the frequency of collisions (A) increases.

The activation energy and prefactor can be determined using the linear form of the equation:

b ln < = ln _ − c (1.7) Je

When the natural log of the reaction rate is plotted as a function of inverse temperature, EA can be extracted from the slope, and prefactor A from the y-intercept (Figure 1.1B).

In 1935, Henry Eyring, and, almost simultaneously, Meredith Gwynne Evans and

Michael Polanyi, expanded upon the work of Arrhenius, developing transition state theory.5,6

In this theory, the reactants must cross an energy barrier and populate a high-energy transition state (R‡) before forming the products (P), and vice versa (Figure 1.1C). The products and reactants exist in quasi-equilibria with an activated state, described by the constant, G‡. Therefore, the energy difference between the products or reactants and the

activated state is the activation free energy (∆"‡, Figure 1.1C). Eyring expressed the temperature dependence of the reaction rates, which was defined by the ratio of the activation free energy barrier (∆"‡) to the temperature of the reaction, and the frequency of bond formation:

∆k°+‡ f eh f eh a < = g ∙ G‡ = g ∙ ` lm (1.8) i i

f eh where g is the prefactor, dictated by the frequency of bond formation, the ratio of the i

Boltzmann constant (

The Eyring equation can be expanded into enthalpic and entropic components:

∆p°+‡ ∆r°+‡ f eh a < = g ∙ ` l ∗ ` lm (1.9) i where ∆'°%‡ is the activation entropy and ∆&°%‡ is the activation enthalpy. ∆"°%‡, ∆&°%‡, and

∆'°%‡ are quasi-thermodynamic quantities that describe the pseudo-equilibrium between a ground state and the transition state. These quantities represent the free energy, enthalpy and entropy barriers the molecule must overcome to proceed through the activated complex and form the products or reactants.

To determine the activation parameters for a given reaction, the linear form of this

f s equation is applied to a plot of ln versus (Figure 1.1D). e e

f a∆A°+‡ s f ∆v°+‡ ln = ⋅ + ln g + (1.10) e J e i J

Plotting the natural log of the reaction rate over temperature against inverse temperature yields the ∆&°%‡ from the slope and ∆'°%‡ from the y-intercept.

Five years after the publication of Eyring’s transition state theory, Hans Kramers

f proposed an alternate theory.9 Kramers argued that Eyring’s prefactor, w , the vibration of i bond breakage, developed for elementary gas-phase reactions, was too simplistic for more complex systems.9 As molecules progress through a reaction they are subject to friction from the surrounding solvent (viscosity) and in some cases, within the molecules themselves.10,11 For reactions examined over a range of temperatures, as the temperature of the solution changes, so do the solution properties. Therefore, the temperature dependence of the viscosity must be accounted for. As a result, Kramers modified the Eyring prefactor to incorporate a friction component, assumed to be proportional to the solution viscosity, 7:

x °+‡ < = `az{ /fge (1.11) ?(e)y where 7(9); is the temperature dependence of the viscosity. The Stokes-Einstein relationship predicts a β of unity and therefore a linear dependence of rate on viscosity, but

β values between zero and one, and even deviations from linearity, have been observed.12

Another approach is a viscosity-adjusted Eyring formalism, where the Eyring formalism is used to fit the temperature dependence of viscosity-adjusted rates:13,14

h <$ = < =

Activation parameters and protein folding

A protein undergoing a two-state folding transition exists in an equilibrium between its most stable native, or folded state (F) and an ensemble of unfolded conformations (U):

} ⇆ ~. (1.13)

The equilibrium changes in the free energy of unfolding, i.e., stability of the protein, is determined from the ratio of the concentrations of the folded and unfolded states according to:

[#] ∆"$% = −R9ln . (1.14) # [,]

$% The modified standard state free energy of unfolding ∆"# , of a globular protein is small and positive, favoring the folded state, and typically ranges from 5 -15 kcal/mol near biologically

15 $% relevant temperatures. The conglomeration of interactions that comprise ∆"# can be described by the enthalpic and entropic contributions, and are related to the equilibrium stability according to Equation 1.4.

$% $% $% The molecular components of ∆"# , ∆&# and −9∆'# were elegantly described by

16 $% Walter Kauzmann in his seminal review on protein folding. As a protein unfolds, ∆&# has two contributions: positive, unfavorable changes arising from the breakage of intra-protein bonds and water-water bonds, and a negative, favorable contribution from the solvation of

16 $% $% newly exposed surfaces. The entropic contribution to ∆"# , −9∆'# , is a balance of a favorable, negative change as the protein becomes more disordered with unfolding, and an unfavorable, positive change as water molecules order themselves around the newly exposed protein surfaces.16

The equilibrium changes in enthalpy and entropy can be determined experimentally from the temperature dependence of the equilibrium stability according to the integrated

17 $% Gibbs-Helmholtz equation, which accounts for positive change in heat capacity (∆(),#) when the protein unfolded:

$% $% $+ $% e ∆"#,e = ∆&#,e − 9∆'#,e + ∆(),# 9 − 9Ä − 9ln( ) (1.15) e where the changes in enthalpy and entropy are defined at the so called melting temperature,

+ T ( $% $ ), where $% equals zero (i.e., the folded state and the unfolded m ∆&#,Ä, −9∆'#,e ∆"# ensemble are equally populated).

$+ The temperature-independent change in heat capacity(∆(),#) can be determined from the temperature dependence of the protein’s equilibrium stability. Kauzmann

$% introduced the idea that the non-zero ∆(),#, arises from water molecules solvating hydrophobic residues in the unfolded state that are not exposed in the folded state.16 His assertion was confirmed through calorimetric experiments by Privalov 15 years later,18 who

$% subsequently determined that the ∆(),#is dominated by the hydration of hydrophobic

19,20 $% groups. The result is a noticeably curved stability plot of ∆"# against T (Figure 1.2). At

$% $% the maximum, −9∆'# is zero and all the stability arises from ∆&# . At high temperatures,

$% $% $% 21 ∆"# is dominated by −9∆'# , and at lower temperatures, ∆&# is more influential.

Protein stability curves can elucidate the enthalpic and entropic contributions to a protein’s equilibrium stability. However, equilibrium values provide no insight about the path that a protein takes when it folds or unfolds, i.e. equilibrium parameters cannot describe the formation of the transition state.

Applying transition state theory to protein folding stipulates the protein must cross an activated state, or transition state, to fold or unfold. The activation free energy barriers to

‡ ‡ °%‡ folding (} → } ) and unfolding ~ → } , ∆"#,,→#‡, can be determined from the rates,

<,→#‡ and <#→#‡, using the Eyring-Polanyi equation,

°%‡ fÇ,É→É‡i ∆"#,,→#‡ = −R9Å7 . (1.16) fge

The activation free energies are related to each other through the change in equilibrium free energy of unfolding,

°% °%‡ °+‡ ∆"# = ∆",→#‡ − ∆"#→#‡. (1.17)

°%‡ Although ∆",,#→#‡ represents the energy barrier that a protein must cross to fold or unfold (Figure 1.1C), it provides no insight into the barrier’s composition. The components can be probed by measuring the temperature dependence of the folding and unfolding rates,

°%‡ °%‡ from which ∆&,,#→#‡ and −9∆',,#→#‡ can be extracted using Equation 1.10. For protein

°%‡ °%‡ folding and unfolding, −9∆'#,,→#‡ can be positive or negative, but ∆&#,,→#‡ must be

positive, as an energy input is required to break protein-protein (unfolding) and protein-water

(folding) bonds.

Early studies on the temperature dependence of folding kinetics by Segawa and

Sugihara,22 Chen, Baase and Schellman,23 Chen and Matthews,24 and Oliveberg, Tan and

Fersht25,26 revealed that folding and unfolding rates do not increase linearly with temperature, as predicted by the Arrhenius relationship (Equation 1.7). Instead such plots are curved (Figure 1.3). As with equilibrium stability curves, the curvature arises form a non-

°+‡ zero ∆(),,,#→#‡, due to a difference in the solvent exposure, and consequently reflect the hydration of the unfolded/folded and transition states.23-26

Scalley and Baker explored the possibility of the curvature arising from a higher- order temperature dependence of the prefactor.27 However, they found that once folding rates were corrected for changes in stability that occur with temperature, the plots became linear, indicating the curvature originates from the temperature dependence of the stability (i. e. the change in heat capacity) rather than the prefactor. Subsequent studies on other proeins confirmed Scalley and Baker’s conclusion.14,28

Schellman,23 followed by Matthews24 and Fersht,25,26 applied the integrated Gibbs-

Helmholtz equation for the equilibrium stability of proteins to the activation free energy, which parsed the contributions of the equilibrium free energy 17 to the activation free energy:25

Δ"°′‡ 9 = Δ&°′‡ 9 − 9Δ'°′‡ 9 = Δ&°′‡ 9 + Δ(°%‡ (9 − 9 ) − ,,#⇒#‡ ,,#⇒#‡ ,,#⇒#‡ ,,#⇒#‡ $ ),,,#⇒#‡ $

°%‡ °%‡ e 9[9Δ' ‡ 9$ + Δ( ‡ ln ] (1.18) ,,#⇒# ),,,#⇒# e|

°+‡ where To is the reference temperature, ∆' is the activation entropy at To and ,,#→#‡,e|

°+‡ ∆& is the activation enthalpy at To. ,,#→#‡,e|

Later, the Fersht group inserted Equation 1.18 into the Eyring-Polanyi equation

(Equation 1.8) to yield:26

+ + + + zv° ‡ zA° ‡ zÖ° ‡ eae zÖ° ‡ f f ‡ ‡ ‡ | ‡ e ln É,Ç = [ln w + É,Ç⇒É , m| − É,Ç⇒É , m| − Ü,É,Ç⇒É + Ü,É,Ç⇒É ln . e i J Je Je J e|

(1.19)

Using this equation, the activation enthalpy, entropy and heat capacity could be determined from an Eyring plot (Figure 1.1D) of the folding and unfolding rates. Although Fersht adopted the Eyring method for determining the activation parameters of the model protein chymotrypsin inhibitor 2 (CI2), other groups adapted Kramers’ formalism to account for changes in the reaction prefactor that arise from temperature-dependent changes in viscosity.13,29-31

Both formalisms have been used to determine the activation parameters for protein folding. The Eyring analysis slightly overestimates activation parameters relative to a viscosity-adjusted analysis, such as Kramers’ formalism.13,14 Nevertheless, applying the

Eyring formalism to analyze changes in activation parameters upon adding a perturbant

(such as a mutation or cosolute) provides information on how pathways change.13

Activation parameters in buffer

°% 15 For globular proteins with a ∆"# of between 5-15 kcal/mol, a difference of several orders of magnitude between the folding and unfolding rates renders monitoring both reactions at ambient conditions challenging, if not impossible. Perturbing the system using heat, changing the pH, or adding chemical denaturant such as urea or guanidinium hydrochloride shifts equilibrium so unfolding and refolding rates can be measured. Unfolding rates can be measured as a function of denaturant concentration, and then extrapolated to give the unfolding rate in buffer:32

[>5?] ABC Å7<# = Å7<# + D#[á`7] (1.20)

[>5?] where <# is the unfolding rate in the presence of denaturant, [á`7] is the concentration of

33 ABC denaturant, D# is the denaturant-dependent contribution to the unfolding rate, and Å7<# is the value extrapolated to [á`7]=0, or the rate in buffer alone. The extrapolated rates as a

°+‡ °+‡ °+‡ function of temperature can then be used to determine ∆&,→#‡, ∆",→#‡ and−9∆',→#‡ at 0

M denaturant. In another approach, activation parameters can be determined as a function of denaturant concentration, and then extrapolated back to 0 M.24,34

Others measured these values in the presence of denaturants, but Tan, Oliveberg and Fersht25 were the first to determine the activation enthalpy, entropy and heat capacity of both folding and unfolding at 0 M denaturant. pH-jump experiments, in which acid-denatured protein were added to high pH buffer, were used to measure folding rates of chymotrypsin inhibitor 2 (CI2). Unfolding rates were measured from guanidinium hydrochloride stopped- flow experiments and then extrapolated to 0 M guanidinium chloride.

°+‡ °+‡ For CI2, ∆&,→#‡ and ∆&#→#‡ are both positive, indicating the transition state has a higher enthalpy than either the folded or unfolded state (Figure 1.4B). For the unfolding reaction, the positive enthalpy change is intuitive, resulting from the breaking of native bonds in the folded state to form the transition state. The authors hypothesized that the increase in enthalpy from the unfolded state to the transition state was due to hydration. In other words, they proposed that the breaking of protein-water bonds outweighs the formation of protein-protein bonds in the transition state. For the folding reaction, the positive activation enthalpy suggests the penalty of breaking water-water and water-protein interactions surrounding the unfolded ensemble outweighs the enthalpically favorable formation of native protein-protein interactions in the transition state. With the exceptions of phosphoglycerate kinase (PGK),31 and the GCN4 Leucine Zipper peptide,35 all characterized

°+‡ °+‡ 14,27-29,34 proteins exhibit a positive ∆&#→#‡ and ∆&,→#‡.

°+‡ °+‡ °+‡ Unlike ∆&,,#→#‡, for CI2, −9∆',→#‡ and −9∆'#→#‡ have opposite signs. The

°+‡ °+‡ positive −9∆'#→#‡and negative −9∆',→#‡ and their relative values indicate that the transition state entropy lies between the unfolded and folded states, but is closer to the unfolded state than the folded (Figure 1.4C). While both configurational and solvent entropy

°+‡ influence −9∆'#→#‡, the decrease in entropy with CI2 folding suggests the entropic

°+‡ contribution is dominated by the ordering of the protein as it folds. The −9∆'#→#‡for proteins in subsequent studies suggest that the entropic effect is a delicate (and protein-specific) balance between configurational and solvent entropy.16 In addition to CI2, Protein L, 27

Bacillus subtilis (bs)34 and Bacillus caldolyticus (bc) 13 CspB, GCN4 Leucine Zipper,35 and

36 °+‡ °+‡ PGK have a positive −9∆'#→#‡ and a negative−9∆',→#‡, indicating that the conformational entropy is the driving factor. For the superoxide dismutase monomer

29 28 °+‡ °+‡ (SOD1) and NTL9, both −9∆'#→#‡ and−9∆',→#‡ are negative, indicating the transition state is higher in entropy than both the unfolded and folded states. The positive change

°+‡ −9∆'#→#‡ implies that the system is becoming more disordered with folding, and the solvent entropy is likely the driving force for unfolding. In contrast, hisactophilin14 and FKBP1237

°+‡ °+‡ have positive values for −9∆'#→#‡ and −9∆',→#‡, indicating that the transition state is lower in entropy than both states. In this case, configurational entropy likely dominates the folding reaction, and solvent entropy drives the unfolding reaction.

°+‡ °+‡ °+‡ As with the −9∆',,#→#‡, the signs of ∆(),#→#‡ and ∆(),,→#‡ of CI2 were also

°+‡ °+‡ opposite. The Fersht group observed a negative ∆(),#→#‡, and a positive ∆(),,→#‡,

26 °+‡ approximately equal in magnitude. ∆(),#→#‡, is negative, because the transition state is

°+‡ more solvated than the folded state. ∆(),,→#‡, is positive, because the transition state is less solvent exposed than the unfolded state. Interestingly, the folding reaction displays a strong

curvature (Figure 1.3A) while the unfolding reaction does not (Figure 1.3B). The authors determined, via analysis of residuals, that the temperature dependence of unfolding rates can be fit equally well with a straight line.26 The linearity for the unfolding reaction indicates only a small amount of surface area is exposed from the folded state to the transition state.

°+‡ °+‡ Identical signs for ∆(),#→#‡ and ∆(),,→#‡,, indicating an intermediate solvent exposure of the transition state, were also observed in FKBP12,37 Protein L,27 hisactophilin,14 NTL9, 28 bsCspB, 34 bc CspB,13 the E. coli Trp repressor,38 and SOD1 monomers.29 The one exception is phosphoglycerate kinase, for which negative activation heat capacities were observed for both folding and unfolding.31

Activation parameters in denaturants

Early studies in denaturant, performed by the Sugihara,22 Schellman,7 and

Matthews39 groups, provided important insight into transition state formation, some of which also applies in buffer alone. In their 1984 study of the temperature dependence of lysozyme folding in the presence of four concentrations of three denaturants, Segawa and Sugihara made a key observation that would be repeatedly confirmed: the Arrhenius plots of the folding reaction were steeply curved, while the unfolding reaction was nearly linear. Eyring plots for the folding reaction deviated from the linearity predicted by simple transition state

°+‡ theory because of a negative, nonzero ∆(),#→#‡ resulting from the loss of surface area in

°+‡ the transition state. For the unfolding reaction, ∆(),,→#‡= 0, meaning that the transition state more closely resembled the folded state than the unfolded state. Another important

°+‡ contribution was the assertion that the positive ∆&,→#‡came from breaking long-range intraprotein interactions rather than solvation, which would have resulted in a large, positive

°+‡ ∆(),,→#‡.

The Schellman group, which had published a seminal study on constructing protein equilibrium stability curves via the integrated Gibbs-Helmholtz equation (Equation 1.16),17 applied their equilibrium methodology to kinetics.7 They saw a similar curvature for the temperature dependence of T4 lysozyme folding and unfolding in 3 M guanidine chloride to that reported by Segawa and Sugihara.7 What set their analysis apart, however, is that their application of the integrated Gibbs-Helmholtz equation to transition state formation enabled

°%‡ 7 determination of −9∆'à,â→â‡. The results were surprising; although enthalpy and entropy

°%‡ are known to compensate for each other, for the unfolding reaction, both a positive ∆&à→â‡

°%‡ and −9∆'à→â‡, were observed, which are additive rather than compensatory. They hypothesized that the positive enthalpic barrier arose from an energetically unfavorable breakdown of tertiary structure in the folded state rather than exposure of hydrophobic groups. In a study published two years before, Matthews and coworkers39 also observed a

°%‡ positive −9∆'à→â‡ for the a subunit of Escherichia coli tryptophan synthase, which they attributed to the ordering of solvent and cosolute around surfaces exposed in the transition state (in agreement with a hydrophobic effect-dominated entropic contribution). For the

°%‡ °%‡ °%‡ folding reaction, ∆&â→â‡, and −9∆'â→â‡ had opposite signs, and ∆(),â→â‡ was negative, which the authors ascribed to the hydrophobic effect.

Another important revelation arose from determining how denaturants alter the activation barriers to folding and unfolding. This information is important, because denaturants can serve as a model for purely chemical attractive interactions, which help contextualize and decode the transient chemical interactions that form between proteins in cells.40,41 Changes in activation parameters in the presence of a denaturant or other cosolute were analyzed by whether they lower or raise the barrier to folding. According to the Eyring-

°%‡ Polayni relationship (Equation 1.8), a positive changes in ∆"à,â→â‡ increase the activation free energy barrier, which hinders folding/unfolding, and vice versa.

After initial studies in one or a limited number of denaturant concentrations, several groups studied the denaturant-dependence of protein folding kinetics over a wider concentration range.13,24,34 This approach allowed extrapolation to 0 M denaturant, and consequent comparison of activation parameters in buffer to those in the presence of denaturants.

Chen and Matthews expanded upon the work of Hurle et al.,24 focusing on the temperature dependence of tryptophan synthase unfolding as a function of urea concentration between 4 and 8 M. The authors also extrapolated the activation parameters to 0 M urea to determine the relative contributions of solvent and cosolute, but were cautious in interpreting these results, because the window of urea concentration tested was limited. Therefore, they commented only on the signs of the activation parameters at 0 M urea.

The activation heat capacity for unfolding was positive and increased with increasing urea concentration. The authors attributed the positive value to increasing solvation of the transition state by solvent and urea. When extrapolated to 0 M urea, the value was near

22 °+‡ zero, consistent with the findings of Segawa and Sugihara. ∆&,→#‡ was positive, but decreased with increasing urea concentration, which the authors attributed to the formation of favorable urea-protein hydrogen bonds in the transition state.

°+‡ Finally, Chen and Matthews measured the concentration dependence of −9∆'),,→#‡

°+‡ and found that when extrapolated to 0 M urea, −9∆',→#‡ switched from positive to small to negative at 0 M urea, indicating that the sign change was due to the addition of urea. The positive change, implying an ordering of the protein with increasing urea concentration was proposed either to originate from the ordering of urea molecules around the freshly exposed surface of the transition state or from the conformational restriction of the transition state as urea molecules bound.42

Chen and Matthews were especially cautious when interpreting parameters extrapolated to 0 M urea. However, the signs of the activation parameters they determined for tryptophan synthase were consistent with the activation parameters in buffer for CI2, determined subsequently by the Fersht group,26 and with the urea dependence of the activation parameters for unfolding observed by the Schmid and colleagues.34

The Schmid group was also interested in the denaturant dependence of the barriers to protein folding, and published two studies examining the folding pathways of bsCspB 34 in urea and bcCspB13 in guanidinium chloride. The wide range of concentrations allowed the authors to extrapolate to 0 M urea more accurately than in previous publications. For the initial study in bsCspB, the authors were unable to interpret the denaturant dependence of the activation parameters, which had large uncertainties. In the subsequent study on bcCspB, however, Schmid and coworkers could measure the urea dependence of several activation parameters for both folding and unfolding.

The effect of urea on the activation parameters for unfolding agreed with the findings of the Matthews group24 and observations of the Dirr group on glutathione transferase in 8.3

43 °%‡ °%‡ M urea. Schmid and coworkers determined that both −9∆'â→â‡ and ∆&â→â‡ were positive and increased with increasing denaturant concentration, indicating guanidinium chloride

°%‡ both enthalpically and entropically hinders bcCspB folding. ∆(),â→â‡ was negative, but the concentration dependence could not be determined.13

Estape and Rinas measured the effects of guanidinium hydrochloride on the temperature dependence of human basic fibroblast growth factor (hFGF-2) folding and unfolding.44 Their results for unfolding were consistent with other studies.24,34 For folding,

°%‡ °%‡ however, ∆&â→â‡ was zero. Therefore, the positive ∆"â→â‡, was dominated by an

°%‡ unfavorable, positive −9∆'â→â‡. The sign of the entropic change in denaturant was consistent with the Schmid group’s findings for bcCspB.13

Activation parameters in stabilizing osmolytes

Osmolytes are small molecules that organisms synthesize to protect against stress- induced water loss.45,46 The Bolen group determined the effects of four common osmolytes, glycerol, proline, sarcosine, and trimethylamine-N-oxide (TMAO), on the folding kinetics of the C22A mutant of FKBP12.47 All four osmolytes increase FKBP12 folding rates and decrease unfolding rates, suggesting that although the osmolytes are chemically different, their interactions with proteins are similar. The Bolen group had previously measured transfer free energies of proteins in osmolytes, discovering a phenomenon that they called the osmophobic effect.48,49 The osmolyte TMAO raised the free energy of both the folded and unfolded states for proteins, but raised the free energy of the more solvent-exposed unfolded state to a greater extent than the folded state, resulting in protein stabilization.

From a combination of transfer free energies and solvent accessible surface area studies, they concluded that the stabilization arose from unfavorable osmolyte-protein backbone interactions.49 Bolen and colleagues expanded their studies to activation free energy

°%‡ °%‡ barriers, and determined that TMAO decreased ∆"â→â‡ and increased ∆"à→â‡, consistent with a mechanism in which the protein exposed surface area is minimized to avoid unfavorable interactions with TMAO. The Kanaya and Davidson groups saw similar results in TMAO with T. kodakaraensis RNase HIII50 and fyn SH3.51

The Matthews39 and Fersht52 groups investigated the effects of the osmolyte sucrose on the folding kinetics of the a-subunit fo tryptophan synthase and CI2, respectively. In both

°%‡ cases, sucrose increased the folding rate relative to buffer, implying a decreased ∆"â→â‡. In addition to increasing the folding rate, the Matthews group found that sucrose slowed

°%‡ unfolding, indicative of an increased ∆"à→â‡. In both studies, sucrose was chosen for its ability to increase viscosity, with the idea that increasing the viscosity would slow folding.

The Matthews group determined that the increased folding rate of tryptophan synthase in

sucrose was caused by sucrose-induced equilibrium stabilization. The Fersht group reported the same thing for CI2, but the resulting increase in the folding rate was more complicated.

Sucrose increased the microviscosity of the solution, decreasing CI2 diffusion, which should also slow folding. However, the decrease that should result from reduced diffusion was offset by the equilibrium stabilization by sucrose, resulting in the increased folding rate.

Activation parameters in synthetic polymers

Several studies examined the effects of synthetic polymers, including polyvinyl pyrrolidone (PVP, or povidone),52 Ficoll,53-55 and dextran56 on protein folding and unfolding rates, and consequently, the activation free energies. Synthetic polymers have been predicted to interact with proteins in two ways, both of which are stabilizing: entropically- driven excluded volume effects57,58 and preferential hydration.59,60 Unlike osmolytes, which most studies find to promote folding and hinder unfolding, the results for synthetic polymers are less clear and vary with both polymer and protein. Several studies showed that polymer

°%‡ 55,61 54,56 crowders either increased ∆"à→â‡, slowing unfolding or had no effect. Results for

°%‡ folding reaction results are more complicated; increases in ∆"â→â‡, leading to slower folding

53,61 52 °%‡ 54,56 rates , and decreases in ∆"â→â‡, leading to increased folding rates, have both been observed.

The Wittung-Stafshede group studied the effects of the synthetic sugar-based polymers Ficoll (sucrose) and dextran (glucose) on the folding and stability the football- shaped protein from Borrelia burgdorferi, VIsE54 and apoazurin from Pseudomonas aeruginosa.56 In both cases, the polymers increase folding rates while unfolding rates were unaffected. The authors attributed these effects to polymer-induced increases in excluded volume. Polymer crowders caused unfolded state compaction, promoting unfolding, while the folded and transition states were unaffected, causing little change in the unfolding reaction.

Studies on other proteins generated more complicated results and investigators were forced to consider effects other than excluded volume. Ladurner and Fersht52 found that

°%‡ PVP 10 and PVP 1300 decreased CI2 folding rates, raising ∆"â→â‡. PVP was found not to alter the solution microviscosity. Thus, the authors concluded that the decreased folding rate arose from destabilizing interactions between PVP and CI2 rather than decreased diffusion.

The Winter group found that 30% w/w Ficoll caused a fourfold decrease in the folding rate of another protein, Staphylococcal nuclease (SNase).53 In opposition to the findings of the Fersht group, this change was similar in magnitude to the change in diffusion at that concentration of Ficoll. The authors hypothesized that more than excluded volume effects had come into play. They attributed the decreased rate to viscosity effects plus polymer- protein interactions. Hong and Gierasch55 found that Ficoll slowed the unfolding of cellular retinoic acid-binding protein 1 (CRABP 1). Their conclusions were like those of the Winter

°%‡ group, suggesting that in addition to raising ∆"à→â‡ , the slower unfolding arose from the increased viscosity.

The Choy group examined the temperature dependence of crowding effects by

15 polyethylene glycol (PEG) 20,000 on a mutant apo cytochrome b562 via N relaxation dispersion.62 Addition 85 mg/mL PEG increased the unfolding rate at 25°C, indicative of a

°%‡ decreased ∆"â→â‡, while the folding rate was unaffected. As the temperature was increased, however, the folding rate enhancement decreased. At 35°C, the unfolding rate in

PEG dipped below the unfolding rate in buffer. Measurements were made at only three temperatures (25 °C, 30 °C and 35 °C). Activation parameters were not calculated but application of a weighted linear regression to both sets of data yields the changes in the

°%‡ activation parameters listed in Table 1.1 (∆(),â→â‡ =0 was used in this fit, because the temperature dependence was linear). In this case, PEG enthalpically promotes both folding and unfolding while entropically hindering both reactions.

Interestingly, for this protein, the folding and unfolding rate decrease with

°%‡ temperature, yielding a negative ∆&à,â→â‡ for both reactions. This result may seem counterintuitive, but the apparent negative activation enthalpy is likely due to the activation heat capacity, depending on the location of the curve relative to the Tm and TS (temperature of maximum stability).25 To our knowledge, this is the only study that examines the effects of a synthetic polymer on the temperature dependence of protein folding.

Activation parameters in live cells

The Gruebele group determined the activation parameters for PGK in buffer and in individual U2OS bone tissue cells using FRET. Two schemes were used: PGK labeled with

AcGFP1 as a donor and mCherry as an acceptor31 and a modified construct in which

30 mCherry was replaced with a smaller ReASH tag. Folding rates, unfolding rates, and Tm were calculated from the temperature dependence of the kobs,, the sum of the folding and unfolding rates. Interestingly, plots of the temperature dependence of folding and unfolding

°%‡ °%‡ differed between cells. Although for both cases the authors measured ∆"à,â→â‡, ∆&à,â→â‡,

°%‡ °%‡ −9∆'à,â→â‡ and ∆(),à,â→â‡, their data analysis was parsimonious, and focused on the shapes of the folding and unfolding curves rather than the activation parameters. Guo, Xu and Greubele noted that in some cells, a more negative slope and larger curvature was observed in the temperature dependence of the folding rate than was observed in buffer. In

°%‡ all cases, the folding rates were increased (∆"â→â‡ decreased) relative to buffer, but unfolding rates were decreased. Three explanations were proposed. First, crowding effects are less efficient at higher temperatures. Second, the viscosity of cells decreases less quickly with temperature than buffer. Finally, hydrophobicity increases more rapidly in cells with temperature than in buffer.

Due to the variability between the six individual cells, the authors concluded that some combination these possibilities contribute to the effects of the cellular environment on

folding kinetics. Ultimately, the authors acknowledged that more in-cell data are needed, and that both excluded volume and chemical interactions must be accounted for to describe cellular modulation of protein folding landscapes.

Conclusions

The activation- free energy, -enthalpy and entropy of protein folding have been characterized in dilute buffered solutions.13,25-27,29,34 Similarly, folding pathways have also been studied in the presence of denaturants,7,22,39 and their effects on the temperature dependence of folding and unfolding have been elucidated.13,24,34 Yet, the effects of other cosolutes on folding pathways were unclear. Stabilizing osmolytes, such as TMAO and sucrose, which are upregulated in the cell under stress conditions, raise the free energy barrier to unfolding and lower the free energy barrier to folding via preferential hydration mechanism.39,47,52 Although the effects on free energy barriers to folding and unfolding were established, the enthalpic and entropic components had yet to be determined. Even less was known about synthetic polymers, where the effects on the free energy barriers to folding and unfolding vary with the protein and polymer chosen.53-55 Chapter 3 fills this knowledge

°%‡ °%‡ °%‡ gap, as the ∆"à,â→â‡, ∆&à,â→â‡, and −9∆'à,â→â‡ are determined for the N-terminal SH3 domain of the Drosophila melanogaster protein drk (SH3) in buffer, urea, TMAO, sucrose,

Ficoll, and lysozyme. These results show that in addition to excluded volume effects, chemical interactions between protein and cosolutes influence folding pathways.

Finally, two studies have examined the temperature dependence of folding in living cells.30,31 Although the changes in the parameters were observed, the quality of the data limited their analysis. This lack of information about the kinetics of folding in physiologically relevant environments highlights a need to quantify the enthalpic and entropic contributions of the cellular interior. The effects of cosolutes such osmolytes, synthetic polymers and

physiologically-relevant protein crowders and lysates, provide clues about how chemical interactions in the cytoplasm modulate folding kinetics.

Tables

62 Table 1.1. Activation parameters of apocytochrome b562 in 85 mg/mL PEG 20K.

°%‡ °%‡ Reaction ∆∆&à,â à â‡ (kcal/mol) −9∆'à,â à â‡ 298 K, (kcal/mol) U à U‡ -4 + 1 -4 + 2 F à U‡ -3 + 2 -3 + 2

Figures

Figure 1.1. Arrhenius and Eyring plots of a chemical reaction. A, reaction coordinate according to the Arrhenius formalism. B, Arrhenius diagram of reaction rates. C, reaction coordinate according to Eyring formalism. D, Eyring plot of reaction rates.

Figure 1.2. SH3 stability plot. Adapted from Smith et al.64 Stability plot of the N-terminal SH3 domain of Drosophila melanogaster drk in 50 mM Hepes/bis-Tris propane acetic acid, pH

°% 7.2. The curvature in the plot is due to a nonzero ∆(),â.

Figure 1.3. Temperature dependence of CI2 folding kinetics. Folding, A; Unfolding, B.

26 °%‡ °+‡ °%‡ Adapted from Tan et al. ∆& , −9∆' , and ∆() at with a reference temperature of 298 K

f were used to calculate were used to calculate predicted values of ln Ç,É→É‡ between 278 e and 356 K.

Figure 1.4. Reaction coordinate diagrams for CI2 at 298 K. Adapted from Tan, Oliveberg and Fersht.26 Reaction coordinate diagrams are for the changes in activation ∆"°%‡ (A),

°%‡ °%‡ °%‡ ∆& (B), −9∆' (C) ∆() (D). Gaps between the states are scaled according to the values of the activation parameters.

CHAPTER 2: LARGE COSOLUTES, SMALL COSOLUTES AND ENZYME ACTIVITY Adapted from: Acosta, LH, Perez Goncalves, GM, Pielak, GJ and Gorensek-Benitez, AH. In preparation

Introduction

Most enzymes catalyze reactions inside the cell, where the concentration of proteins and nucleic acids is very high,65-67 exceeding 300 g/L in E. coli.68,69 By contrast, the vast majority of knowledge about enzyme kinetics comes from studies performed in dilute, buffered solutions. Biochemists have attempted to understand how crowded, cell-like environments modulate steady-state enzyme kinetics for almost 50 years.70 A major assumption of many of these early pioneering efforts was to apply excluded volume theory to crowded solutions.58 Essentially, as the concentration of crowding molecules increases, hard-core repulsions between the crowders and the enzyme decreases the space available to the enzyme. The resulting compaction can lead either to decreased activity or a non- monotonic increase with increasing crowder concentration. However, theorists acknowledged early on that crowding effects can change based on the size, mechanism, and oligomeric nature of the enzyme.71

Hard-core repulsions alone cannot fully explain the effects of macromolecular crowding on enzymes. Many investigators report excluded volume effects,72-75 but other effects have been described, including “sieving”, or changes in the effective concentration of enzyme and substrate,70,76 decreased diffusion of the enzyme, the substrate or both,72,73,76 crowder-substrate interactions77 and changes in polymer characteristics with concentration.78,79 These changes in polymer configuration occur at the overlap

concentration (c*), where the polymers cease to act like individual coils (the dilute regime) and form a complex, interwoven mesh (the semidilute regime).80

The effects of crowded environments on enzyme steady-state kinetics have proven difficult to predict. Crowding can raise, lower, and in some instances not significantly change, steady state parameters (Table 2.1). Recent studies highlight the importance of nonspecific chemical interactions between test proteins and cellular components or cytoplasm mimetics can modulate, and even overpower, excluded volume effects.40,41,81-85

Synthetic polymers are often used as crowding agents because they are believed to be chemically inert, although some investigators have demonstrated the existence of nonspecific protein-polymer interactions.59,60,84 Frequently used polymers include the branched sucrose polymer, Ficoll,72,86-88 the glucose polymer, dextran,73-76,89-92 polyvinylpyrrolidone (PVP),73,89 and polyethylene glycol (PEG).77,93-95 To distinguish between chemical effects and those arising from the macromolecular nature of the polymer, the activity in polymer solutions should be compared to activity solutions containing monomers: sucrose, glucose, ethylene glycol and 1-ethyl-2-pyrrolidone (aka N-ethylpyrrolidone, NEP).

Here, we assess the effects of synthetic polymers and their respective monomers on the specific activity of E. coli dihydrofolate reductase (DHFR).96 We analyzed the effects of these cosolutes on activity in terms of mass/volume concentration, the overlap concentration of the polymers, their volume occupancy, and viscosity.

DHFR catalyzes the reduction of dihydrofolate (DHF) to tetrahydrofolate [(THF),

(Scheme 2.1)]. The role of DHFR in carbon metabolism makes it a prime drug target; the human isoform is inhibited by methotrexate in cancer97 while the E. coli enzyme is the target of the anti-microbial therapeutic trimethoprim.96 DHFR begins the cycle bound to reduced

NADPH. After the substrate, DHF, binds, DHFR catalyzes a hydride transfer from NADPH to

DHF, oxidizing NADPH to NADP+ and reducing DHF to THF. The oxidized cofactor is released, NADPH is rebound, and the THF is released, beginning the next cycle. The rate

determining step is the final one, product release,98 which is gated by the movement of a flexible active site loop.99

An advantage of using DHFR as a model enzyme is its monomeric state. Many enzymes examined under crowded studies are oligomeric. In these instances, it can be difficult to determine if crowding alters activity, oligomerization, or a combination of both.71,92

Therefore, any crowding effects on DHFR activity arise from protein-cosolute/protein- solvent, rather than oligomerization, effects.

Results

Polymer and monomer properties

We studied the following polymer families: Ficoll 70, Ficoll 400, and sucrose; Dextran

20 and glucose; PVP 10, PVP 40, PVP 55 and NEP, where the number after the name of the polymer reflects its approximate molecular mass in kDa. We compiled from the literature or measured the partial specific volumes [(n2), Table 2.1] and relative viscosities of the polymers as a function of concentration (Fig. 2.1A-C). Note that we used the value for 1- methyl-2-pyrrolidone in lieu of a value for 1-ethyl-2-pyrrolidone. The n2 values were used to calculate fractional volume occupancies100 as a function of cosolute concentration (Figure

2.1D-F) The viscosity data were used to estimate the overlap concentrations (Table 2.1) by fitting the high and low concentration regimes to lines and finding that concentration at which they intersected (see Materials and Methods).101,102

DHFR activity

To eliminate disulfide formation, a double-cysteine mutant (C85A C152S) that retains the activity of wild type103 was used. Activity was quantified using Eq. 2.1,

µmol/min ((∆OD340/min)sample –(∆OD340/min)blank x d (cm) Activity = mg 2.1 mg DHFR 12.3 mM-1 cm-1 x V x DHFR mL

where (∆OD340/min)sample is the change in absorbance of the sample at 340 nm,

-1 (∆OD340/min)blank is the change in absorbance of the blank, d is the path length, 12.3 mM cm-1 is the extinction coefficient for the DHFR reaction,104 V is the volume of the reaction, and mg/mL DHFR is the enzyme concentration. Initial studies of psWT activity in 100 mM imidazole, pH 7.0, gave a specific activity of 49 +2 µmol/min/mg, where the uncertainty is the standard deviation of the mean, in agreement with the reported value of 47 + 2 µmol/min

/mg under the same conditions.105 DHFR activity is sensitive to inorganic cations.105

Therefore, a HEPES/bis Tris propane buffer was used so the pH could be adjusted without adding salt. In 100 mM HEPES/bis-Tris propane, pH 7.0, the activity of psWT DHFR in 27.9

+ 0.9 µmol/min /mg, where the uncertainty is the standard error of the mean from nineteen samples. To mimic the macromolecule concentrations in cells, we assessed DHFR activity at cosolute concentrations up to 300 g/L of the polymers and their monomers (Figure 2.2A-

C). The PVPs were studied only up to 200 g/L, because the viscosities of PVP 55 and PVP

40 at higher concentrations made mixing difficult.

Discussion

Crowder identity

Classical theory treats crowding agents and test proteins as inert space-filling molecules that interact solely through steric repulsions.100 Consistent with this idea, some studies find that at similar concentrations, polymers with similar molecular weights have indistinguishable effects on enzyme kinetics, as observed for yeast alcohol dehydrogenase

(YADH) in PVP and dextran solutions.73 However, the magnitude of the relative activities observed here for DHFR (i.e., between 0.3 and 2.0, Figure 2.2), are common for studies using Ficoll and dextran,73,76 and small differences between Ficoll and dextran effects, as

observed in Figure 2.2, have been ascribed to differences in polymer shape76,106 and chemical interactions.77

Concentration dependence

Studies of enzyme activity as a function of cosolute concentration also reveal trends that depend on both enzyme and crowder. Monotonic decreases in activity and Vmax are observed for several enzymes,72-74,92 and, in most instances, are attributed to a combination of excluded volume effects and decreased diffusion.

DHFR does not exhibit a monotonic trend in Ficoll and dextran (Figure 2.2A-B).

Instead, the relative activity is greater unity at low concentrations, dips sharply, partially recovers decreases again. Others have observed similar effects. Derham and Harding92 and

Pozdnykova and Wittung-Stafshede72 observed non-monotonic behavior, explaining the trend in terms of an initial rate enhancement from crowding-induced oligomerization92 and electron transfer72 followed by a decrease due to ‘overcrowding’92 or reduced product diffusion.72 For DHFR, oligomerization seems unlikely, because the protein has not been shown to aggregate. Plots of activity against volume occupancy (Figure 2.2D-F) are similar to those against g/L concentration, because the cosolutes have similar partial specific volumes (Table 2.1). The large uncertainties of activity in these polymers make us wary, except to observe that activity general decrease with increasing concentrations and volume occupancy of all the cosolutes.

Overlap concentration (c*)

Ficoll 70 and 400, Dextran 20, and PVP 55 exhibit a dip in activity between 100 and

200 g/L, a region associated with changes in polymer morphology as reflected by the

107 overlap concentration, c*, of the polymer (Figure 2.2A-C). A similar dip in Vmax is observed for horseradish peroxidase in 20% w/w concentration of dextran 20.77 In Ficoll 70, Ficoll 400 and PVP 55, there is a dramatic dip in activity near c*. For PVP 40 the dip occurs well above c*. A monotonic decrease is observed in PVP 10, but for this polymer all the concentrations

tested are below c*. Though it is tempting to suggest a correlation between c* and activity, the relationship is uncertain.

Viscosity

Viscosity increases with weight-to-volume concentration, but the effect is more dramatic for polymers (Figure 2.2G-I).80 Increased viscosity decreases the diffusion of substrates and products,108 and can dampen enzyme motions that are associated catalysis.

All of these outcomes decrease enzymatic rates.73 The general decrease in activity in polymer solutions as a function of viscosity (Figure 2.2G-I) mirrors the observations for concentration (Figure 2.2A-C) and volume occupancy (Figure 2.2D-F), consistent with the idea that increased viscosity affects the rate limiting step of the reaction as described above.

Molecular mass

Simple theories predict that larger crowding molecules of about the same size as or larger than the test protein should have the largest effect, 58,109,110 but we see no pattern with respect to size. Past studies suggest that size-specific crowding effects depend on the identity and size of the protein and the crowder. The Mas group hypothesized that larger enzymes are affected by polymer size but smaller enzymes were not. In agreement with this hypothesis, size-dependence was observed for LDH (105 kDa)74 and alkaline phosphatase

(105 kDa),76 but not for alpha-chymotrypsin (25 kDa) and horseradish peroxidase (42 kDa).74,111 However, this relationship does not hold for all cases. Derham et al. did not observe a size dependence for urease (500 kDa),92 while the size rule also did not hold for studies of MDH89 and YADH.73 In summary, although polymer size modulates DHFR activity, a pattern is not discernable, nor is there an obvious pattern present in data from the literature.

Macromolecular effects

Historically, theory emphasized the role of hard-core excluded volume, but recently the importance of chemical interactions between crowders and proteins has been realized.41

A common test for a macromolecular effect is to compare a polymer to its constituent monomer.

Ficoll 70 increases activity relative to monomers at concentrations less than 200 g/L, then is statistically indistinguishable from the monomer, while Ficoll 400 increases activity relative to the monomer at 100 g/L, and decreases relative to the monomer at the highest concentration. One explanation for the increase in activity at low concentrations of Ficoll 70 relative to sucrose could be nonspecific sucrose-folate interactions. The Howell group demonstrated that osmolytes, such as sucrose, compete with DHFR to bind folate,112,113 which lowers activity. In our experiments, increased activity in Ficoll 70 could arise from the shielding of individual sucrose monomers in the polymer. However, similar trends are observed for PVP, suggesting that a macromolecular effect outside of crowder-substrate interactions is present at low concentrations. Additionally, this hypothesis is contradicted by the observation that the rate enhancement in Ficoll 400, which should more effectively shield monomers, is less than the enhancement in Ficoll 70 and by the observation that in dextran is indistinguishable from glucose (except at 200 g/L). We conclude that there is a macromolecular effect for some polymers at low concentrations that subsides at higher concentrations, but source of the effect remains unclear.

Cosolute effects are system-specific

In summary, the effects of crowding on DHFR activity are complex. The origin for the initial increases observed in Ficoll 70 and PVP are unclear, and may encompass a variety of factors, including a decrease in chemical effects due to monomer shielding,114 a caging effect in polymers leading to increased enzyme-substrate encounters,75 or in the case of

Ficoll, substrate binding present in the monomer but not the polymer.112,113 At higher concentrations, reduction in activity is likely due to a combination of slowed product release arising from dampened conformational fluctuations brought about by increased viscosity or steric-repulsion induced favoring compact conformations. However, trends differ between

polymer families and sizes, suggesting the none of these factors can fully explain our observations.

The complicated nature of macromolecular crowding on DHFR activity is observed for other enzymes (Table 2.2 and Table S2.1-3). Careful consideration of 40 years’ worth of data reveals that crowding effects on enzyme kinetics are specific to the crowder and enzyme. For example, Ficoll 70 decreases the activity of alkaline phosphatase76 but increases the activity of both PGK115 and Ras.36 A similar trend of mixed effects is observed for the effects of Ficoll 70 on enzyme kcat and Km.

Even for the same enzyme, crowding effects can depend on the substrate. Notably, the Slade group showed that dextran lowers the Vmax of YADH for the forward (ethanol) reaction, while Vmax is enhanced for the reverse (isopropanol) reaction (Table S2.2).

Comparison of reactions with deuterated and non-deuterated substrates reveal that for

YADH, crowding effects are linked to the rate-determining step for each reaction.90

Substrate-specific crowding effects are observed for PGK86 and HRP.77

In summary, a great deal of effort has been expended in attempts to understand how and why macromolecular crowding affects enzyme kinetics.72-75,89,90,92,111 However, a clear trend has not emerged, suggesting that steady state kinetics are not the easiest system for understanding macromolecular crowding. To gain a full understanding of crowding effects, enzyme activity studies should be coupled with complementary studies on protein stability, folding, and diffusion.

Materials and Methods

Cosolutes

Dextran from Leuconostoc mesenteroides (~20 kDa) was purchased from Alfa

Aesar. Its monomer, glucose, was purchased from Fisher Scientific. Ficolls (~70 and 400 kDa) were purchased from Sigma Aldrich. Its monomer, sucrose, was acquired from Fisher

Scientific. PVPs (~10, 40, 55 kDa) and NEP were purchased from Sigma Aldrich. The pH of all cosolute solutions was adjusted to pH 7.0 + 0.1 before use.

Protein preparation and purification

Site-directed mutagenesis was performed using the Phusionâ High Fidelity polymerase (New England Biolabs) as specified in the Phusionâ manual on the pET-22 b plasmid containing the gene for E. coli DHFR to create the C85A;C152S variant. The forward primer to produce the C85A change comprised 5’-GGC GGC CGG TGA CGT ACC

AGA AAT CAT G-3’. The reverse primer sequence was 5’-CAC CGG CCG CCG CGA TGG

CTT CGT C-3’.The sequence of the forward primer to produce the C152S mutation was 5’-

GCT ATA GCT TCG AAA TCC TCG AGC GTC G-3’. The reverse primer sequence comprised 5’- CGA AGC TAT AGC TAT GCG AGT TCT GCG C-3’. Plasmids harboring the gene were transformed into BL21 (DE3) Gold cells (Agilent). A single colony was picked to inoculate 50 mL of Lenox broth (LB, 10 g/L tryptone, 5 g/L yeast extract, 5 g/L NaCl). The culture as incubated overnight at 37°C with shaking for 16 h. This culture was added to 950 mL of LB, and the culture was shaken at 37°C. When the optical density at 600 nm reached

0.6, isopropyl β-D-1-thiogalactopyranoside (1 mM final concentration) was added.

Expression was allowed to proceed occurred for 1 h with shaking at 37 oC. Cells were pelleted at 3000 x g, resuspended in 50 mM Tris 1 mM EDTA (pH 7.5) and frozen at -80°C.

Cells were thawed at room temperature and lysed by sonication (Fisher Scientific

Sonic Dismembrator Model 500, 15% amplitude, 15 min, 67% duty cycle) in an ice bath. Cell debris was removed by centrifugation at 16000 x g for 30 min at 10°C, and the supernatant was passed through a 0.45 μm filter.

The DHFR purification involved two chromatography steps using a GE AKTA FPLC.

The first step was anion exchange chromatography (GE column, 0-50% gradient, 50 mM

Tris, 1mM EDTA wash/50 mM Tris, 2 M NaCl, 1mM EDTA eluent, pH 7.5). The second step

was size exclusion chromatography (GE Superdex 75 column, eluted with 50 mM potassium phosphate, 150 mM KCl, 1mM EDTA, pH 6.8). Purified psWT DHFR was dialyzed into 10 mM HEPES/bis-Tris propane, pH 7.0 at room temperature for 6 h. Buffer was refreshed after

3 h. After dialysis and filtration through a 0.22 μm filter, the sample was flash frozen in an ethanol/CO2(s) bath and lyophilized for 12 h (Labconco FreeZone).

Enzyme activity

The buffer comprised 100 mM HEPES/bis-Tris propane, pH 7.0 + 0.1. Cosolute- containing buffers were prepared by weight using an Ohaus PA64 balance. Purified

-1 -1 lyophilized psWT DHFR (e280 = 31,100 M cm ), dihydrofolic acid (DHF, Sigma Aldrich e340 =

-1 -1 116 -1 -1 116 7750 M cm ) and NADPH (Sigma Aldrich, e340 = 6220 M cm ) were resuspended in buffer alone and their concentrations verified by spectrophotometry (NanoDrop ND-1000,

Thermo Scientific). To prevent light-induced degradation, NADPH and DHF were stored in foil-covered amber tubes and stored on ice during activity assays. Fresh aliquots of NADPH and DHF were used for each experiment. Stock solutions of DHF were stored at -20°C for one week and NADPH for one month.

Reaction mixtures were prepared in 10-mm path length plastic cuvettes. psWT

DHFR was added to the reaction mixture to a final concentration of 80 nM, and NADPH was diluted to 100 µM. The solution was mixed by inversion, and pre-incubated in the spectrophotometer (Cary 100, Agilent) at 25°C for 2 min to prevent hysteresis.117 After pre- incubation, DHF was added to a final concentration of 100 µM, and the mixture was shaken by inversion. The reaction was monitored by the decrease in absorbance at 340 nm as DHF was converted to THF and NADPH was oxidized to NADP+. After a 20 s dead time arising from the manually mixing, reaction progress was monitored by measuring the absorbance every 10 sec for 2 min. The slope for the first 60 s was constant. The slope from the no-

enzyme control was then subtracted, and the resulting value used to calculate the specific activity using Eq. 2.1.

For each series, samples were assayed in random order and interleaved with a buffer control. At each concentration, the specific activity for each triplicated sample was calculated using Eq 2.1, and the resulting activities were averaged. Measures were performed in triplicate except for Ficoll 400 at 100, 200 and 300 g/L and PVP-55 at 200 g/L, where 5 measurements were averaged, and 0 g/L dextran where two measurements were averaged. Activity values were rejected for 250 and 300 g/L PVPs and NEP, due to high background. Uncertainties represent the standard deviation of the mean. To account for day-to-day variation, specific activities in cosolutes were divided by the activity in buffer alone. Error propagation for division was performed using the square root of the sum of the squares.118

Polymer properties

The overlap concentration (c*)80 was calculated by plotting the viscosity as a function of polymer concentration.101,102 Two distinct sections of the curve, representing the dilute and semidilute regimes, were fit to lines.80 The polymer concentration at their intersection is c*. Viscosities and partial specific volumes were determined in water. For viscosity measurements, samples were prepared in increments of 10 g/L (PVP-40 and 55), 25 g/L

(Ficoll 70 and 400, and Dextran 20) or 50 g/L (PVP-10), and the viscosities were measured in triplicate using a Viscolite 700 viscometer (Hydramotion Ltd., England). Viscosities were also measured for the monomers sucrose, glucose and 1-ethyl-2-pyrrolidone. All viscosities were normalized to the viscosity of water at 298 K. Temperature was maintained using a

Fischer Scientific Isotemp 210 water bath.

Volume occupancies were calculated for Ficoll 70 and Dextran 20,56 PVP-10, 40 and

55,107 and sucrose and glucose119 by multiplying their partial specific volumes by the g/L concentration.100 We determined the partial specific volume of Ficoll 400 by measuring

solution densities using a vibrating tube densitometer (DMA 5000, Anton Paar) and employing the linear relationship between density and mass fraction.120

Tables

Table 2.1. Partial specific volumes and overlap concentrations. From the literature or measured as described in the Materials and Methods.

Footnotes a Not applicable, monomers do not have an overlap concentration

Cosolute n2 (mL/g) at 25 °C Overlap concentration (g/L) PVP 55 0.80107 350 PVP 40 “ 120 PVP 10 “ 100 1-methyl-2-pyrrolidone 0.91121 NAa Ficoll 400 0.68 150 Ficoll 70 0.65122 250 sucrose 0.61123 NAa dextran 20 0.65122 200 glucose 0.62121 NAa

Table 2.2. Effects of macromolecular crowding on enzyme kinetics. A complete list of effects is provided in Tables S1-S3.

Number of studies reporting Parameter an increase in: a decrease in: no change in: 36,92,93,95,115,124-126 70,76,92,93,95,127 76,92,93,95,128 Activity 8 6 5

72,87,129-131 72,73,86,87,130-134 72,73,86,87,130,131,133,134 kcat 5 9 8

77,88-90,94,95,126,134 73- 77,130,134,135 Vmax 8 12 4 75,77,89,90,93,95,111,130,134,135

72- 73-75,77,86,87,89,90,93- 72- Km 11 14 11 74,77,86,88,89,111,130,134,135 95,132-134 75,77,87,89,90,129,133,134

Figures

Scheme 2.1. DHFR reaction scheme. A hydride is transferred from NADPH to dihydrofolate (DHF), forming the reduced product, tetrahydrofolate (THF), and the oxidized cofactor, NADP+.

Figure 2.1. Cosolute volume occupancy and relative viscosity at 298 K. Viscosity (A-C) and fractional volume occupancy (D-F) are plotted as a function of concentration. A and D: sucrose, black; Ficoll 70, red; Ficoll 400, blue. B and E: glucose, black; Dextran 20, red. C and F: NEP, black; PVP 10, red; PVP 40, blue; PVP 55, green. Uncertainties are smaller than the points.

Figure 2.2. DHFR activity as a function of concentration, volume occupancy and relative viscosity. Viscosity, A-C; volume occupancy, D-F; and relative viscosity, G-I. A, D and G: sucrose, black; Ficoll 70, red; Ficoll 400, blue. B, E and H: glucose, black; Dextran 20, red.

C, F and I: NEP, black; PVP 10, red; PVP 40, blue; PVP 55, green. Asterisks indicate c*, the polymer overlap concentration. Error bars represent standard deviations of the mean from triplicate experiments.

Supplementary Information Table S2.1 Effects of macromolecular crowding on enzyme activity.

Cosolute Concentration Enzyme Crowded/Buffer Ficoll 70 200 g/L PGK115 13 5 % w/w Alkaline phosphatase76, a NS 20 % w/w Alkaline phosphatase76 0.8 200 g/L Cytochrome c127,a 0.8 200 g/L Ras36 2.6 Ficoll 400 20 % w/w Alkaline phosphatase76 0.4 92, a dextran 10 100 g/L Urease 1.4 300 g/L Urease92, a 0.5 dextran 15 20 % w/w Alkaline phosphatase76 0.7 dextran 70 20 % w/w Alkaline phosphatase76 0.4

200 g/L Urease92,a NS 300 g/L Urease92,a 0.7 100 g/L Glutamate decarboxylase92, a 2 300 g/L Glutamate decarboxylase92, a NS 300 g/L Pyruvate decarboxylase92, a 0.8 20 % w/w Alkaline phosphatase76 0.4 dextran 120 300 g/L Urease92, a 0.4 dextran 200 20 % w/w Alkaline phosphatase76 0.2 PEG 83 g/L Hyaluronate lyase70,a 0.5 PEG 200 100 g/L Glucosidase II95, a 0.8 50 g/L Taq DNA polymerase93,a NS 200 g/L Taq DNA polymerase93,a 0.2 60 g/L HptG128, a NS 150 g/L HptG128, a 3.0 PEG 2000 100 g/L Glucosidase II95, a NS PEG 6000 100 g/L AspP126 5 PEG 8000 100 g/L T7 DNA polymerase93,a 1.3 200 g/L T7 DNA polymerase93,a 0.1 100 g/L Taq DNA polymerase93,a 1.3 200 g/L Taq DNA polymerase93,a 0.2 10% RNA helicase eiF4A124 6 Footnotes NS, not significant; within error of buffer value. aestimated. PGK, phosphoglycerate kinase; HptG, bacterial heat shock protein 90 (Hsp90); AspP, ADP-sugar pyrophosphatase; eiF4A, eukaryotic initiation factor-4A; DnaK, bacterial Hsp70; GroEL, bacterial Hsp60; Grp94, mouse Hsp90; Hsp90a, a-subunit of human Hsp90; Hsp82, yeast Hsp82; UGGT, endoplasmic reticulum glycosyl transferase.

Table S2.1, continued.

Cosolute Concentration Enzyme Crowded/Buffer PEG 20000 100 g/L Glucosidase II95, a 2.0 150 g/L DnaK128, a NS 150 g/L GroEL128, a NS 150 g/L HptG128, a 8 100 g/L Grp94128, a 15 100 g/L Hsp90a128, a 6 100 g/L Hsp82128, a 3 lysozyme 300 g/L Pyruvate decarboxylase92,a 5 300 g/L Glutamate decarboxylase92, 92 1.5 300 g/L Urease92, a 7 BSA 100 g/L Glucosidase II95, a 4 400 g/L UGGT95,a NS 400 g/L 1-2-a-mannosidase95,a 0.2 Hemoglobin 300 g/L Pyruvate decarboxylase92,a 6 300 g/L Glutamate decarboxylase92, a 1.2 300 g/L Urease92, a 10 RNAseA 100 g/L Glucosidase II95, a 3 Ethylene 50 g/L HptG128, a NS glycol 150 g/L HptG128, a 1.8 Sucrose 20% w/w Alkaline phosphatase76,a 0.5 Glycerol 300 g/L Urease92, a 0.6 Footnotes NS, not significant; within error of buffer value. aestimated. PGK, phosphoglycerate kinase; HptG, bacterial heat shock protein 90 (Hsp90); AspP, ADP-sugar pyrophosphatase; eiF4A, eukaryotic initiation factor-4A; DnaK, bacterial Hsp70; GroEL, bacterial Hsp60; Grp94, mouse Hsp90; Hsp90a, a-subunit of human Hsp90; Hsp82, yeast Hsp82; UGGT, endoplasmic reticulum glycosyl transferase.

Table S2.2. Effects of macromolecular crowding on Vmax and kcat. Footnotes

Crowder Concentration Enzyme kcat or Vmax Crowded/buffer 72, a Ficoll 70 100 g/L Fet3p kcat 3.5 86 200 g/L PGK (ADP) kcat NS 86 200 g/L PGK (3-PGA) kcat NS 86 200 g/L GAPDH kcat 0.7 86 200 g/L ACP kcat 0.3 87 300 g/L EntC kcat 0.8 87 300 g/L EntB kcat 1.1 87 300 g/L MenF kcat 0.8 87 300 g/L LDH kcat 0.7 133,a 100 g/L Lysozyme kcat NS 133,a 300 g/L Lysozyme kcat 0.9 88 200 gL EcoRV Vmax 1.4 134 100 g/L CaN Vmax 0.7 134 200 g/L CaN Vmax NS 73, a Ficoll 400 300 g/L YADH (ethanol) Vmax 0.8 74 dextran 100 g/L HRP Vmax 0.3 90, a dextran 9-11 300 g/L YADH (ethanol) Vmax 0.5 90, a 300 g/L YADH (isopropanol) Vmax 1.2 77 dextran 10 200 g/L HRP (TMB) Vmax 0.6 77 200 g/L HRP (OPD) Vmax 0.9 73, a dextran 9-20 300 g/L HLADH Vmax 0.3 89, a dextran 20 100 g/L MDH (OAA) Vmax 0.6 89, a 100 g/L MDH (malate) Vmax 0.9 89, a 300 g/L MDH (OAA) Vmax 0.3 72, a 100 g/L Fet3p kcat 2.5 73, a dextran 40 300 g/L HLADH Vmax 0.5 75 dextran 50 100 g/L LDH Vmax 0.7 111 100 g/L a-chymotrypsin Vmax 0.6 133,a dextran 70 300 g/L Lysozyme kcat 0.8 134 100 g/L CaN Vmax 1.7 134 200 g/L CaN Vmax 0.8 89, a dextran 80 300 g/L MDH (OAA) Vmax 0.3 73, a dextran 86 400 g/L YADH (ethanol) Vmax 0.6 NS, not significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

Table S2.2, continued.

Crowder Concentration Enzyme kcat or Vmax Crowded/buffer 90, a dextran 150 300 g/L YADH (ethanol) Vmax 0.5

300 g/L YADH Vmax 1.2 (isopropanol)90, a 73, a 300 g/L HLADH Vmax 0.5 75 100 g/L LDH Vmax 0.3 89, a 300 g/L MDH (OAA) Vmax 0.4 89, a dextran 250 100 g/L MDH (OAA) Vmax 0.4 89, a 100 g/L MDH (malate) Vmax 0.8 75 dextran 410 100 g/L LDH Vmax 0.1 90, a dextran 450- 300 g/L YADH (Forward) Vmax 0.5 650 90, a 300 g/L YADH (Reverse) Vmax 0.9 131 PEG 200 100 g/L Glycoamylase kcat 1.4 77 PEG 400 200 g/L HRP (TMB) Vmax 1.1 77 200 g/L HRP (OPD) Vmax 0.8 126 PEG 6000 50 g/L AspP Vmax 5.9 87 100 g/L EntC kcat 1.2 87 200 g/L EntC kcat 0.8 135 150 g/L β-galactosidase Vmax NS 135 250 g/L β-galactosidase Vmax 0.9

PEG 8000 200 g/L T7 DNA Vmax 0.4 polymerase93 94 150 g/L T4 DNA pol Vmax 3 94 150 g/L DNA pol I Vmax 2.1 77 200 g/L HRP (TMB) Vmax 0.2 77 200 g/L HRP (OPD) Vmax 0.6 129 395 g/L Trypsin kcat 0.4 130 50 g/L PfPNP kcat NS 130 200 g/L PfPNP kcat 0.5 131,a PVP 10 100 g/L Glycoamylase kcat 0.7 89, a BSA 100 g/L MDH (malate) Vmax 1.1 95 400 g/L Glucosidase II Vmax 0.4 132 250 g/L Hexokinase kcat 0.7 Footnotes NS, not significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

Crowder Concentration Enzyme kcat or Crowded/buffer Vmax 89, a lysozyme 100 g/L TaqMDH (OAA) Vmax 0.6 90, a glucose 300 g/L YADH (ethanol) Vmax 0.5 90, a 300 g/L YADH (isopropanol) Vmax 1.4 89, a 300 g/L MDH (OAA) Vmax 0.5 77 200 g/L HRP (TMB) Vmax 0.9 77 100 g/L HRP (OPD) Vmax NS 77 200 g/L HRP (OPD) Vmax 0.9 131 Ethylene glycol 100 g/L Glycoamylase kcat 1.3 72, a Glycerol 100 g/L Fet3p kcat 0.8 130,a 200 g/L PfPNP kcat 1.5 131,a 250 g/L Glycoamylase kcat NS 73, a sucrose 300 g/L YADH (ethanol) Vmax 0.5 72, a 100 g/L Fet3p kcat NS 72, a 300 g/L Fet3p kcat 1.3 Table S2.2, continued. Footnotes NS, not significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

Table S2.3. Effects of macromolecular crowding on Km.

Footnotes NS, Crowder Concentration Enzyme Crowded/buffer not Ficoll 70 150 g/L Fet3p72, a 10 200 g/L PGK (ADP)86 1.3 200 g/L PGK (3-PGA)86 0.6 200 g/L GAPDH86 1.1 200 g/L ACP86 0.8 300 g/L EntC87 0.5 300 g/L EntB87 0.6 300 g/L MenF87 0.4 300 g/L LDH87 0.3 200 g/L EcoRV88 2.3 100 g/L Lysozyme133,a 1.0 300 g/L Lysozyme133,a 0.8 200 g/L CaN134 0.3 Ficoll 400 150 g/L YADH (ethanol)73, a NS 300 g/L YADH (ethanol)73, a 0.7 dextran 100 g/L HRP74 1.0 dextran 9-11 300 g/L YADH (ethanol)90, a 0.6 300 g/L YADH (isopropanol)90, a NS dextran 10 300 g/L HRP (TMB)77 3 300 g/L HRP (OPD)77 1.4 dextran 20 100 g/L MDH (OAA)89, a 0.8 100 g/L MDH (malate)89, a 1.1 300 g/L MDH (OAA)89, a 0.4 150 g/L Fet3p72, a 25 dextran 40 195 g/L LDH (lactate) 70 0.5 195 g/L LDH (NAD+)70 0.6 195 g/L LDH (pyruvate)70 0.5 dextran 50 100 g/L LDH74,75 1 100 g/L a-chymotrypsin111 1.8 dextran 70 100 g/L Lysozyme133,a NS 300 g/L Lysozyme133,a 0.9 200 g/L CaN134 0.3 dextran 75 100 g/L MDH (OAA)89, a 0.8 100 g/L MDH (malate)89, a 2 significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

Table S2.3, continued. Crowder Concentration Enzyme Crowded/buffer dextran 80 300 g/L MDH (OAA)89, a 0.6 dextran 86 300 g/L YADH (ethanol)73, a 0.7 dextran 150 300 g/L YADH (ethanol)90, a 0.7 300 g/L YADH (isopropanol)90, a NS 300 g/L MDH (OAA)89, a 0.5 100 g/L LDH74,75 0.7 dextran 250 100 g/L MDH (OAA)89, a 0.8 100 g/L MDH (malate)89, a 1.4 dextran 410 100 g/L LDH75 0.8 dextran 450-650 300 g/L YADH (ethanol)90, a 0.7 300 g/L YADH (isopropanol)90, a 0.9 PEG 400 200 g/L HRP (TMB)77 5 100 g/L HRP (OPD)77 0.7 200 g/L HRP (OPD)77 NS 300 g/L HRP (OPD)77 2.0 PEG 6000 50 g/L AspP126 0.3 350 g/L β-galactosidase135 5 PEG 8000 200 g/L T7 DNA polymerase93 0.4 150 g/L T4 DNA pol94 0.2 150 g/L DNA pol I94 0.3 200 g/L HRP (TMB)77 11 100 g/L HRP (OPD)77 NS 200 g/L HRP (OPD)77 1.8 395 g/L Trypsin129 NS 50 g/L PfPNP130,a 1.8 200 g/L PfPNP130,a 0.9 lysozyme 100 g/L TaqMDH (OAA)89, a NS 100 g/L mMDH (OAA)89, a 0.7 BSA 100 g/L MDH (malate)89, a 1.5 100 g/L MDH (OAA)89, a 0.8 400 g/L Glucosidase II95 0.3 250 g/L Hexokinase132 0.7 Footnotes NS, not significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

Table S2.3, continued Crowder Concentration Enzyme Crowded/buffer BSA 100 g/L MDH (malate)89, a 1.5 100 g/L MDH (OAA)89, a 0.8 400 g/L Glucosidase II95 0.3 250 g/L Hexokinase132 0.7 glucose 300 g/L YADH (ethanol)90, a 0.5 300 g/L YADH (isopropanol)90, a 0.9 300 g/L MDH (OAA)89, a 0.6 200 g/L HRP (TMB)77 1.5 200 g/L HRP (OPD)77 1.6 glycerol 100 g/L Fet3p72, a 1 200 g/L PfPNP130,a NS sucrose 300 g/L YADH (ethanol)73, a 0.3 100 g/L Fet3p72, a 1 300 g/L Fet3p72, a 4 50 g/L CaN134 NS 150 g/L CaN134 1.4 Footnotes NS, not significant; within error of buffer value. aestimated Fet3p, yeast multi-copper oxidase; PGK, phosphoglycerate kinase; GAPDH, glyceraldehyde 3- phosphate dehydrogenase; ACP, acylphosphatase 1; EntC, isochorismate synthasel EntB, isochorismatase; MenF, monomeric isochorismate synthase; LDH, lactate dehydrogenase; CaN, calcineurin; YADH, yeast alcohol dehydrogenase; HRP, horseradish peroxidase; HLADH, horse liver alcohol dehydrogenase; MDH, malate dehydrogenase; AspP, ADP-sugar pyrophosphatase; PfPNP, Plasmodium falciparum purine nucleoside phosphorylase

CHAPTER 3: COSOLUTES, CROWDING AND PROTEIN FOLDING KINETICS

Adapted from: Gorensek-Benitez, AH, Smith, AE, Stadmiller, SS, Perez Goncalves, GM and Pielak, GJ submitted.

Introduction Historically, descriptions of how the complex, crowded cellular environment affects proteins predicted enhanced folding and diminished unfolding via excluded volume effects resulting from hard core repulsions between the protein and crowding molecules.109,110,136 In these descriptions, protein and crowder are treated as inert particles that interact solely through steric repulsions, with no ‘chemical’ contribution. We test this idea by studying the effects of several small and macromolecular cosolutes on the folding and unfolding kinetics of the metastable 7-kDa N-terminal SH3 domain of the Drosophila signaling protein drk

(SH3), which exists in a two-state equilibrium between a folded (F) state and the unfolded

(U) ensemble.137 Fluorine labeling of its sole tryptophan results in two 19F resonances, one

138 for each state. The transition occurs in seconds, allowing quantification of folding (<â→â‡)

19 and unfolding (<à→â‡) rates using two-dimensional F homonuclear exchange spectroscopy-based NMR experiments.64,139

$% The equilibrium modified standard-state unfolding-free energy (Δ"ä ), -enthalpy

$% $% $% 64 59,60,81,82,140,141 (Δ&ä ), -entropy (Δ'ä ) and -heat capacity (Δ(),ä) of SH3 and other proteins have been determined in buffer, in solutions of small and large cosolutes and in cells. The results reveal that the equilibrium entropic effects of hard-core steric repulsions are balanced, or even dominated, by enthalpic (chemical) interactions, although there are reports of pure entropic effects.142,143 Surprisingly, supposedly “inert” synthetic polymers

such as Ficoll, dextran and their monomers, sucrose and glucose, also exhibit enthalpic

59,60 contributions. Senske et al. even observed a positive ΔΔ'1 for ubiquitin in dextran and glucose solutions, the opposite of what is predicted from a purely excluded-volume point of view.60

Equilibrium measurements, however, only provide information about transitions between F and U. The effects involving the transition state (U‡) remain ill-defined. These poorly populated states determine whether a protein folds or aggregates, and therefore are key to understanding aggregation-related diseases.2-4 It has been stated that protein folding and unfolded needs to be studied under crowded conditions144, but most such studies use synthetic polymers. Our goal is to characterize how small and large cosolutes alter the barriers that define SH3 folding (U à U‡) and unfolding (F à U‡) to define conditions useful for understanding the kinetics of protein folding and misfolding in cells. The free energies

°%‡ required to reach the transition state from the unfolded ensemble, ∆"â→â‡, and the folded

°%‡ 5,6,145 state, ∆"à→â‡, are determined by the Eyring-Polanyi equation (Equation 1.8). Together,

°%‡ °%‡ ∆"à→â‡ and ∆"â→â‡ describe the equilibrium between the thermodynamic states and the transition state (Equation 1.17).

To determine the enthalpic and entropic barriers to transition state formation, we

°%‡ °%‡ measured the folding and unfolding activation enthalpies (∆&à,â→â‡), entropies (∆'à,â→â‡)

°%‡ and heat capacities (∆(),à,â→â‡) from the temperature dependence of <â→â‡ and <à→â‡. Two fitting methods were used. The first method, which we call the three parameter fit, modified the strategy used by Fersht and coworkers (Equation 1.19):26

°+‡ °+‡ °+‡ < Δ'à,â→â‡, å Δ&à,â→â‡, e Δ(),à,â→â‡ 9 − 9$ ln < = [ln ã 9 + ç – | − à,â→â‡ ℎ R R9 R9

°+‡ zÖ e + Ü,è,ê→ê‡ ln ] (3.1) J e|

where To is the reference temperature for the activation enthalpy and entropy. In the second

°%‡ method, which we call the “two parameter fit,” ∆(),à,â→â‡, is set to zero, and there are only

°%‡ two parameters: the assumed temperature-independent activation entropy, ∆'à,â→â‡, and

°%‡ the assumed temperature-independent activation enthalpy, ∆&à,â→â‡.

Activation parameters are analyzed by whether they raise or lower the barriers to folding or unfolding. A decreased folding rate in cosolute results from a positive change in

°%‡ the activation free energy of folding, ∆∆"â→â‡, indicating that the cosolute makes folding more difficult by raising the barrier, and vice versa. The sign convention for the enthalpic

(∆&°%‡ ) and entropic (− 9 ∗ ∆'°%‡ ) contributions is the same as for the changes in à,â→â‡,e| à,â→â‡

+ free energy. ∆&°%‡ and − 9 ∗ ∆'° ‡ values under a particular set of conditions are à,â→â‡,e| à,â→â‡

°%‡ often statistically indistinguishable. That is, ∆"à,â→â‡ is a small difference between larger and

°+‡ °+‡ nearly equal values of ∆&à,â→â‡ and − 9 ∗ ∆'à,â→â‡. In these instances, the sign of each

°%‡ contribution is compared to ∆"à,â→â‡to determine whether the entropy or enthalpy change dominates the free energy barrier.

The metastability of SH3 allowed us to use heat alone as a perturbant. Several groups have reported activation parameters for folding and unfolding from studies that extrapolate the effect of denaturants to the effect of buffer alone. Examples include variation of pH,25,26 urea,13,14,24,29,34,38 and guanidinium chloride.13,27,28 Other studies using only heat include that of Ai et al., who used 15N relaxation dispersion to assess the folding and

62 unfolding of an apocytochrome b562 variant in 85 g/L PEG 20K, and that of the Gruebele group,30,31 who used FRET to measure the temperature dependence of phosphoglycerate kinase folding in buffer and in individual cells. We provide a comprehensive analysis of cosolute effects on folding and unfolding by using 19F labeling, a technique pioneered by the

Frieden lab.146-148 19F NMR reduces experiment time, allowing the exploration of large and

small, stabilizing and destabilizing cosolutes, which is complemented by using 15N enrichment to assess cosolute effects on the structures of the folded state and the unfolded ensemble.

Results

Cosolutes and SH3 structure Amide proton temperature coefficients (the slope of a plot of 1HN upfield shift against increasing temperature) can be used as indicators of intraprotein hydrogen bonding.

Cierpicki and Otlewski analyzed coefficients from a database of 14 proteins of known structure149 and found that amide protons with coefficients greater than -4.6 ppb/K have an

85% likelihood of participating in an intraprotein hydrogen bond.149 Temperature coefficients for the folded and unfolded states of SH3 were determined in buffer and in cosolutes (Figure

3.1, Table S3.1 ). Although 300 g/L Ficoll was used for structural studies, 200 g/L Ficoll was used for determination of activation parameters, because concentrations higher than 200 g/L sucrose are too stabilizing to measure folding (vide infra).

Of the 46 coefficients determined for the folded state in buffer, 36 agree with the

NMR structure [pdb 2A36150]. Of the ten outliers, coefficients for three hydrogen-bonded residues (K4, L17 and K21) fell between -6 and -5 ppb/K, where probability drops from around 70% to 30%. Three nonconforming coefficients come from non-hydrogen-bonded residues with coefficients greater than -4.5 ppb/K (N35, N51, Y52). These residues are, or are adjacent to, aromatic residues, which deshield nearby amide protons to give more positive coefficients.149 Four residues (T12, A13, N35, G43) are located in flexible loops, which can experience abnormal gradients.151 Some of the discrepancies may also arise because the fluorine at position 36 is absent from the structure.

Coefficients for the unfolded state were quantified for 23 residues. Interpretation for the unfolded state must be especially parsimonious, because temperature gradients are

poor predictors of hydrogen bonding in unstructured peptides and in proteins undergoing conformational exchange,151 both of which apply to unfolded SH3.152,153 For both states under crowded conditions, fewer than half of the coefficients of the folded state were significantly altered. The small magnitude of the changes favors the null hypothesis; i.e., hydrogen bonding in the folded state and the unfolded ensemble is largely unaffected by cosolutes.

We also measured composite chemical shift perturbations, Δδcomp caused by the cosolutes:154

1 2 15 2 1/2 Δδcomp= [(Δ Hcosolute - buffer, ppm) + (Δ Ncosolute - buffer, ppm · 0.154) ]. (3.2)

The data are compiled in Table S3.2. The locations of the changes show no obvious pattern with respect to the structure of the folded state (Figure S3.1 and S3.2). Perturbations in sucrose and Ficoll range between 0.01 and 0.11 ppm, indicative of weak cosolute-protein interactions and consistent with observations for another polymer, polyvinylpyrrolidone.155 In urea, the maximum perturbation is slightly larger, 0.14 ppm, while average perturbation in lysozyme (0.08 ppm for both states) was larger than for other cosolutes, with an upper limit of 0.19 ppm, consistent with observations for SOD1 in 50 g/L lysozyme.156 The average perturbation across all cosolutes ranges from 0.02 to 0.05 ppm (Table S3.3). Furthermore, the differences in Δδcomp values between the folded and unfolded states are insignificant

[i.e., <0.02 ppm155]. Ultimately, analysis of both amide proton temperature coefficients and the Δδcomp indicate that the cosolutes do not dramatically affect the structure of either state.

Activation parameters in buffer

Folding and unfolding rates were determined from 19F homonuclear exchange spectroscopy data as described in the Materials and Methods. Equation 1.8 was used to

°%‡ °%‡ determine ∆"â→â‡ and ∆"à→â‡, while rates from 288 K to 313 K were used to determine

°%‡ °%‡ °%‡ ∆&à,â→â‡, −9∆'à,â→â‡ and ∆(),à,â→â‡ (Figure 3.2, Table 3.1). Two- and three-parameter fits were tested. The standard deviations of the rates were used to drive a Monte Carlo analysis of uncertainties for the three-parameter fit, and a weighted linear regression was used for the two-parameter fit (see Materials and Methods).

Analysis of the residuals from the two- and three-parameter fits were used to assess each model. The idea is that an appropriate model will result in random residuals. The concavity of the residuals for the folding data fitted with the two-parameters (Figure S3.3), and the random residuals from the three-parameter fit suggest that inclusion of the third

°%‡ parameter, ∆(),â→â‡, is appropriate for folding. For unfolding, however, both fits give random-looking residuals, perhaps favoring a two-parameter fit, and consistent with the observation that either fit is appropriate for chymotrypsin inhibitor 2 (CI2) unfolding.26 The

°%‡ °%‡ key point is that ∆(),à→â‡is smaller than ∆(),â→â‡because more surface area is buried from the unfolded state to the transition state than from the transition state to the folded state.26

°%‡ °%‡ °%‡ °%‡ ∆"à,â→â‡, ∆&à,â→â‡, −9∆'à,â→â‡ and ∆(),à,â→â‡ in buffer determined from the three-

°%‡ °%‡ and two-parameter fits are compiled in Table 1. Even though the ∆&à,â→â‡ (and −9∆'à,â→â‡) values from the two procedures are not always within the uncertainties of the

°%‡ measurements, the large r and low Pr values indicate that it is reasonable to set ∆() = 0 for unfolding.

Activation parameters in cosolutes

The temperature dependence of folding and unfolding rates in buffer and cosolutes

(Figure 3.3, Table S3.4) were used to determine the activation parameters (Table 3.1, Table

S3.5). The cosolute concentrations and temperatures were selected that allowed quantification of kinetics. These ranges are limited by the equilibrium stability of the protein.

That is, low signal prevents rate quantification when the population of the folded or unfolded state is less than 10%. These limiting conditions restrict the ability to assess curvature and

°%‡ hence the ability to quantify ∆() . Since crowding has only a small effect on the equilibrium

64 °%‡ heat capacity of SH3 unfolding, we set ∆(),à à â‡ to the buffer value for folding, while the

°%‡ large r values and the low Pr values indicated that setting ∆() to zero for unfolding is appropriate (see Materials and Methods). The changes in the activation parameters compared to buffer are given in Table S3.5. The equilibrium values calculated from the kinetic data are given in Table S3.6.

Viscosity correction

A potential shortcoming of Eyring analysis is that the protein is treated as a small molecule in the gas-phase. Kramers’ rate theory accounts for diffusion as the protein crosses the reaction barrier.9 According to the Stokes-Einstein relationship, viscosity is proportional to diffusion,10,11 and, therefore, contributes to the rate according to Equation

1.11. et al. demonstrated a linear decrease of the SH3 folding rate with increasing viscosity in glycerol,157 we assumed a β of unity for the small cosolutes and adjusted the folding rates according to Equation 1.12. Wong et al.14 and Perl et al.13 used similar analyses.

Diffusion of CI2 in Ficoll and lysozyme deviate from Stokes-Einstein behavior because the macroviscosity of the solution does not match the microviscosity felt by the protein.158-160 Therefore, we only considered the viscosity effects for TMAO, urea and sucrose. The adjusted rates are listed in Table S3.4, and the temperature dependence of the adjusted rates was determined as described above. The adjustment lowers the values of

°%‡ °%‡ °%‡ °%‡ ∆&à,â→â‡ and −9∆'à,â→â‡, but the signs of ∆∆&à,â→â‡ and −9∆∆'à,â→â‡ (Table S3.5) in crowded solutions are unchanged. Therefore, and our interpretations are unaffected, and we concentrate the Discussion on the results from the unadjusted Eyring analysis.

Discussion

Activation parameters in buffer alone

We first sought to determine if SH3 is a representative protein for studies of folding

°%‡ and unfolding. ∆&â→â‡,ëíë ì is positive (Table 3.1), suggesting that the cost of breaking water-protein bonds in the unfolded ensemble outweighs the benefit of forming intraprotein

°%‡ interactions in the transition state. ∆&à→â‡,ëíë ì is also positive (Table 3.1), indicating the cost of breaking native intraprotein interactions is greater than the benefit of forming water- protein interactions in the newly exposed surface of the transition state. These suggestions are consistent with data for CI2,26 protein L,27 hisactophilin,14 and NTL9.28

°+‡ −9∆'â→â‡,ëíë ì is positive, meaning that the transition state has a lower entropy than the unfolded state. This observation suggests the lower configurational entropy of the transition state compared to the unfolded ensemble overcomes the increase in entropy as

°+‡ solvent is released upon burial of hydrophobic area. −9∆'à→â‡,ëíë ì is negative (Table 3.1), indicating that the transition state is higher in entropy than the folded state. This observation is consistent with CI226 and CspB,13,34 suggesting that, like folding, the increase in conformational entropy dominates the solvent-ordering effects from exposing hydrophobic surface.

Whether the enthalpy or entropy contribute more to the pathway can be determined

°%‡ °%‡ °%‡ by comparing the signs of ∆&à,â→â‡ and −9∆'à,â→â‡ to that of ∆"à,â→â‡ (Table 3.1). Sign analysis shows that at 303 K, the entropic contribution to folding slightly outweighs the enthalpic contribution, but the enthalpic contribution dominates the free energy barrier to unfolding.

°%‡ ∆(),â→â‡is negative in buffer, indicating a decrease of solvent exposure as the

°%‡ unfolded state forms the transition state. ∆(),,→â‡is positive but small, indicating a small increase in surface area on unfolding. The data indicate that the solvent exposure of the transition state lies between the unfolded and folded states, but more closely resembles the folded state. This observation is consistent with other data indicating that only 25% of SH3 surface exposed in the unfolded state is also exposed in the transition state.157 The signs of

°%‡ 26-29,34 ∆() for folding and unfolding agree with observations for other proteins. Finally, the

°% sign of the measured equilibrium heat capacity change for SH3 unfolding, ∆() , matches the

°%‡ °%‡ 64 prediction from the difference of activation values [∆(),,→â‡ − ∆(),â→â‡ ]. In summary, our activation parameters indicate the folding and unfolding of SH3 resembles that of other small proteins.

Cosolutes and SH3 structure

Next, we considered the feasibility of assigning cosolute effects to the folded state or the unfolded ensemble by adapting ideas from Φ-value analysis.161 To determine if an interaction is present in the transition state, Φ-value analysis compares the change in activation free energy for folding and unfolding to the change in the equilibrium stability of a wild-type protein caused by an amino acid substitution that deletes the potential interaction.161 Interpreting Φ-values is simplified if the free energy of either the folded or the unfolded state can be aligned for the two proteins. The analysis can be expanded to activation enthalpies, entropies and heat capacities. The free energy of the unfolded ensemble is often aligned, under the assumption that substitutions only affect the folded state.162 A similar approach can be applied to crowding effects, where the perturbation is a cosolute, rather than a mutation. Although such comparisons of activation parameters are useful for characterizing the transition state,161,163 it is important to bear in mind that cosolutes may affect structure, and therefore complicate analysis.

For experiments performed in cosolutes, it is tempting to align the folded state, because classic theories assume that stabilizing cosolutes, both large and small, affect only the unfolded ensemble. However, cosolute-induced structural effects differ between proteins and between protein states. Some investigations report cosolute-induced structural changes via unfolded state compaction,55,164 structural rearrangements,115 and increased secondary structure content,54,165 while others report no increase in secondary structure.53,72

Unlike most protein systems, we can observe both the folded state and unfolded ensemble of SH3 in a single experiment, and we tested ideas about structural effect on both states by using amide proton temperature coefficients [Figure 3.1, Table S3.1149], and chemical shift changes [Tables S3.2 and S3.3, Figure S3.1 and S3.2155,166]. Although we know that cosolutes interact with the SH3 unfolded ensemble,64 the cosolute-induced changes in chemical shift perturbations and changes between the folded and unfolded states in the presence of each cosolute are insignificant. Our analysis supports the null hypothesis: neither the structure of the folded state nor unfolded ensemble is greatly changed by the cosolutes we studied. Therefore, we cannot align either end state, and we are forced to interpret cosolute-induced changes only as changes in the barriers to folding and unfolding.

Activation parameters for cosolutes compared to buffer

We quantified the cosolute-induced changes in the activation parameters compared to buffer along with their uncertainties (Figure 3.4, Table S3.5) as well as the equilibrium thermodynamic values calculated from the activation parameters (Table S3.6). Positive cosolute-induced changes (Figure 3.4, Table S3.5) represent increases in the barriers to folding and unfolding, while negative values represent decreases.

Urea

To provide a benchmark, we started with urea, because its effects on equilibrium stability and folding kinetics are well known.24,34,42,60,64,141 Makhatadze and Privalov used

calorimetry to determine that the urea-induced equilibrium thermodynamic destabilization of

°+ RNAse A, lysozyme and cytochrome c arises from a positive, stabilizing, −9∆∆'# that is

°+ 42 °+ overpowered by a destabilizing, negative, ∆∆&# . The negative ∆∆&# may arise from favorable hydrogen bonding between urea and the protein backbone,42,167 while the positive

°+ −9∆∆'# , counterintuitive for a system where the equilibrium stability indicates formation of a disordered unfolded state, arises either from the ordering of solvent around newly exposed protein or from the restriction of protein motion upon hydrogen bonding.24 This early calorimetric work revealed the entropy of the cosolute, urea, and solvent may influence protein equilibrium thermodynamic stability.

°%‡ °%‡ Urea lowers ∆"à→â‡ and raises ∆"â→â‡ (Figure 3.4A), consistent with previous

157 24 °+ studies of SH3 and tryptophan synthase. The ∆"# calculated from these values is negative, in agreement with observations that urea destabilizes proteins,42

°%‡ 24 Urea also lowers ∆&à→â‡, consistent with observations for tryptophan synthase, but

°%‡ its effect on ∆&â→â‡ cannot be resolved (Figure 3.4B). For unfolding, the decrease makes intuitive sense because urea interacts favorably with the backbone,42 and more backbone is exposed and available to interact in the transition state than in the folded state. The

°+ 42,64 derived ∆∆&# is also negative, in agreement with previous studies.

°%‡ °%‡ Entropically, urea raises both −9∆'à→â‡ and −9∆'â→â‡ (Figure 3C, SI Appendix,

Table S5), as was seen for and Bacillus subtilis34 CspB in urea and human fibroblast growth

13 44 °%‡ factor and Bacillus caldolyticus CspB in guanidinium chloride. A more positive −9∆'â→â‡ suggests that the loss of entropy from the conformational ordering of SH3 on its way from the unfolded ensemble to the transition state outweighs the concomitant disordering of urea molecules as they escape. The entropic hindrance to unfolding likely arises because the

unfavorable ordering of urea on the increased urea-attracting surface of the transition state outweighs the gain in conformational entropy of the protein.

°%‡ Analysis of the relative contributions indicates that for unfolding, ∆∆&à→â‡dominates,

°%‡ while for folding, −9∆∆'â→â‡is more important. The good agreement between the effects of urea on SH3 activation parameters and the effect of urea on other proteins indicates that

SH3 is a reasonable model, and that our method is valid for evaluating the effects of other cosolutes. As observed for equilibrium and kinetic measurements of protein folding in urea, both protein-urea interactions and cosolute and solvent entropy influence SH3 folding barriers.

TMAO and sucrose

Lee and Timasheff’s work showed that sucrose168 and other stabilizing osmolytes,169-

171 are preferentially excluded from the protein surface, resulting in preferential hydration of the protein.172 Osmolytes like TMAO and sucrose are more strongly excluded from the unfolded state than the folded state, leading to stabilization, a conclusion compatible with entropically-driven stabilization.173

Liu and Bolen pioneered the idea of an osmophobic effect48 attributed to unfavorable interactions between osmolytes and the protein backbone.49,174-177 The osmophobic effect was subsequently revealed to be dominated by a stabilizing enthalpic contribution balanced by a destabilizing entropic contribution,178,179 directly contradicting entropically-driven stabilization, though entropic stabilization mechanisms have been proposed.142,143,180-182 The origin of the enthalpic contribution is not well understood, although Rose and colleagues suggest that stabilization is inversely related to the fractional polar surface area of the osmolyte.183 In terms of equilibrium thermodynamics, stabilizing osmolytes appear to use a mechanism opposite to that of destabilizing osmolytes.141 Assessing changes in activation parameters, however, will elucidate whether the mechanisms are truly opposite, or point to

other effects undetected at equilibrium. Recent studies indicate stabilization mechanisms may vary between stabilizing osmolytes, emphasizing the need for a kinetic investigation.184,185

Our equilibrium-from-kinetics values for osmolytes (Table S3.6) agree with observations of enthalpic-mediated stabilization,50,60,178 and are the opposite of what is

°%‡ °%‡ observed for urea. TMAO and sucrose increase ∆"â→â‡ (Figure 3.4A) and decrease ∆"à→â‡, consistent with other findings39,47,50-52 and support an “anti-urea” mechanism for stabilizing osmolytes.

Until now, the enthalpic and entropic contributions of osmolytes to protein folding

°%‡ and unfolding were not understood. We observe that TMAO decreases ∆&â→â‡ and

°%‡ increases ∆&à→â‡ (Fig 3.4B). These trends are consistent with the idea of unfavorable enthalpic interactions between these cosolutes and the protein backbone. Folding is likely enthalpically favored because it minimizes unfavorable protein-osmolyte interactions relative

°+ to the more exposed unfolded and transition states. The derived ∆∆&â,åîïñ is stabilizing

(Table S3.5), agreeing with previous observations in TMAO and other stabilizing osmolytes.50,59,60,141

Entropically, TMAO hinders folding and promotes unfolding (Figure 3.4C), the opposite of predictions based exclusively on hard-core repulsions. Therefore, compaction of the unfolded ensemble cannot be the sole driving force. We suggest that analogous to the ordering of urea molecules around unfolded SH3, the entropic effect of TMAO may arise from the increased entropy of the cosolute as it is excluded from the larger unfolded surface, or if the protein is compacted, from water release. The derived change in equilibrium entropy is destabilizing (Table S3.6), consistent with a preferential hydration mechanism.178,179

Sucrose uses a mechanism like TMAO for unfolding, but the activation parameters could not be resolved for folding. At concentrations greater than 20% vol/vol, sucrose has

been shown to switch from preferential hydration to preferential folded-state accumulation, with more protein adhering to the folded state relative to the unfolded ensemble.184

Preferential folded state accumulation has also been observed for RNAse A in sorbitol169,171 and trehalose.170 In preferential accumulation, the folded state is promoted through the entropically favorable release of water from the surface.171 We suspect the effects of preferential hydration in TMAO are counteracted by preferential folded-state accumulation of sucrose.

°%‡ °%‡ °%‡ Sign analysis shows that ∆∆&â→â‡,åîïñ and ∆∆&à→â‡,åîïñand ∆∆&à→â‡,óäòôöóõ

°%‡ dominate ∆∆"à,â→â‡. In agreement with an “anti-urea” mechanism for stabilizing osmolytes,

°%‡ °%‡ °%‡ ∆∆"à→â‡, ∆∆&à→â‡and −9∆∆'à→â‡ in TMAO and sucrose have an effect opposite to that

°%‡ °%‡ °%‡ observed in urea. However, −9∆∆'â→â‡,åîïñ, −9∆∆'â→â‡,óäòôöóõ and −9∆∆'â→â‡,äôõú all have the same sign, weakening the “anti-urea” hypothesis. This observation suggests that although stabilizing and destabilizing osmolytes have opposing affinities for proteins, the contributions are weighted differently. Finally, although stabilizing osmolytes enthalpically promote folded-state repulsion, likely through avoidance of unfavorable interactions, the entropic contributions may arise from increases in cosolute and solvent entropy.

Ficoll

This branched sucrose polymer, and other synthetic polymers, are predicted to interact with proteins in two ways, both of which are stabilizing: entropically-driven excluded volume effects57,58 and preferential hydration.59,60 Although data from equilibrium stability studies of SH3 could not be resolved into changes in enthalpy and entropy,64 Benton et al.59

°+ showed that sucrose and Ficoll increase ∆&# for CI2, supporting a preferential hydration

60 model. Senske et al. also observed a positive ΔΔ&1 for ubiquitin in a similar polymer, dextran. Although these studies suggest that preferential hydration is the stabilization mechanism of synthetic polymers such as Ficoll, the relative contributions of preferential

hydration and steric repulsions remain unclear. Comparing the activation parameters obtained in Ficoll to those obtained in sucrose and TMAO can help unravel the relative contributions.

The effects of Ficoll on the activation free energy of folding and unfolding vary with the protein. For instance, Ficoll has been shown to both decrease54,56 and

53,61 °%‡ 54,55,61 54 °%‡ increase ∆"â→â‡, while increasing or having no effect on ∆"à→â‡ relative to buffer.

°%‡ Another study hinted at more complicated effects, where Ficoll lowers ∆"â→â‡ for a fast-

°%‡ 186 folding step but lowers ∆"â→â‡ for a slow folding step. We observe that Ficoll increases

°+ °%‡ °%‡ the equilibrium stability, i.e., ∆∆"# , of SH3 via a smaller ∆"â→â‡ and a larger ∆"à→â‡ (Figure

3.4A). The signs mirror those observed for TMAO and sucrose.

The signs of the enthalpy and entropy changes in Ficoll compared to buffer are the same as those for TMAO for both folding and unfolding. The signs are also the same for unfolding in sucrose, but for folding in sucrose the values are within uncertainty of zero. In

Ficoll, folding is enthalpically favored, while unfolding is enthalpically hindered, while the opposite is observed for the entropic effects, indicating that the preferential hydration

°%‡ mechanism proposed for TMAO also applies to Ficoll. The negative ∆∆&â→â‡ and positive

°%‡ −9∆∆'â→â‡, which are not observed in the monomer sucrose, indicates the presence of a macromolecular effect in Ficoll. As suggested by Record’s group,114 the appearance of a

°%‡ negative ∆∆&â→â‡ in Ficoll not observed in sucrose may arise from the shielding of sucrose monomers in this branched polymer. This restriction may prevent preferential binding of sucrose monomers to the native state, resulting in the dominance of preferential hydration effects also seen in TMAO.

°%‡ °%‡ For TMAO, sucrose and Ficoll, the trends in ∆∆&à,â→â‡ and −9∆∆'à,â→â‡ conflict with traditional crowding theory in three ways. First, the presence, let alone the dominance, of an

enthalpic contribution contradicts the model based solely on hard-core repulsive entropic effects.58 As stated above, the enthalpic contributions point to preferential hydration.59,60

Second, the entropic effects conflict with stabilization of the folded state predicted by pure steric repulsions;58,181 instead of promoting folding and hindering unfolding, the entropic changes promote unfolding and hinder folding. This contradiction underscores the importance of cosolute and solvent entropy. Third, excluded volume theory predicts that larger molecules should be stronger stabilizers because they exclude more volume, but

64,187 °%‡ equilibrium data have shown that smaller molecules are more stabilizing. Our ∆∆"à,â→â‡ data for TMAO, sucrose and Ficoll show that this trend also applies to the transition state.

Lysozyme

Lysozyme destabilizes CI2188 and SH3,64 but its effect on the equilibrium enthalpy and entropy changes have not been elucidated. Linewidth and tumbling-time data64 indicate that protein destabilization arises, at least in part, from lysozyme-SH3 interactions with the unfolded ensemble. Lysozyme also forms nonspecific, destabilizing interactions with

CI2.160,188 Since lysozyme interacts favorably with proteins, analysis of kinetic data can determine whether lysozyme acts like urea or other contributions, such as excluded volume, come into play. If lysozyme is merely a giant urea molecule, the changes in activation parameters should resemble those induced by urea.

°% °%‡ Like urea, lysozyme decreases ∆"â (Table S3.6) and raises ∆"â→â‡ (Figure 3.4A,

°%‡ Table S3.5). However, the similarity diverges for unfolding; urea decreases ∆"à→â‡, but

°%‡ lysozyme slightly increases this energy (Figure 3.4A). Also unlike urea, for which ∆∆&â→â‡ is

°%‡ °%‡ within the uncertainty of zero, lysozyme increases ∆&â→â‡, as well as ∆&à→â‡and

°%‡ decreases −9∆'à→â‡. Although the contributions to the unfolding reaction resemble

°%‡ osmolytes and Ficoll, ∆∆&â→â‡ is of the opposite sign. These data show that neither the

preferential binding model of urea,42,167 nor the preferential hydration model of TMAO and

Ficoll,59,60 adequately explain SH3-lysozyme interactions. We suspect that in addition to transient chemical interactions, lysozyme exhibits a macromolecular effect. Nevertheless, these effects are diametrically opposed to the macromolecular effect expected from simple theories, which predicts purely entropic stabilization of the native state with no enthalpic contribution.

Conclusions

Our work provides kinetic evidence for a preferential hydration mechanism of stabilization by osmolytes. However, the results reveal nuances that are not detected at equilibrium for stabilizing versus destabilizing osmolytes, and even among stabilizing osmolytes themselves. The kinetic resemblance of Ficoll to TMAO suggests a preferential hydration mechanism, while the presence of an enthalpic effect lacking in sucrose may indicate a macromolecular effect, because the polymeric nature of Ficoll hinders folded state formation. For the stabilizing osmolytes and Ficoll, the entropy changes are opposite to those predicted for pure steric-repulsion based, excluded volume mechanism, suggesting the entropy of the solvent and cosolute, rather than the configurational entropy of the protein, dominate entropic effects. Finally, neither the preferential interaction model of urea nor the preferential hydration model of osmolytes fully explain the mechanism of the biologically-relevant crowder, lysozyme. Although crowding agents are used in reductionism- based efforts to assess the crowding phenomena that occur in cells, the underlying mechanisms are complex and do not these polymers do not act like globular protein crowders. Thus, not only should protein folding and misfolding be studied under crowded conditions, but also the crowding agents themselves should be physiologically relevant.144

Materials and Methods

Protein expression and purification

19F-labeled SH3 was expressed and purified as described previously.189 Briefly, the purification consisted of three steps: anion exchange chromatography and size exclusion chromatography to isolate SH3, followed by hydrophobic interactions chromatography to remove a truncated SH3 contaminant. Sample purity and stability were verified by MALDI

(Thermo LTQ-FTR-ICR-MS, 7T) and 1D 19F NMR experiments.

NMR

Purified, fluorine-labeled protein (1 mg) was resuspended in 450 µL of NMR buffer

(50 mM acetic acid/sodium acetate, HEPES, bis-Tris propane, pH 7.2 + 0.1, 5% vol/vol D2O)

-1 -1 with the stated amount of cosolute. The concentration of lysozyme (e280 = 36 mM cm ) was verified by UV-visible spectrophotometry (NanoDrop ND-1000). Polymers, sugars and urea were weighed (Ohaus PA64). After the protein was resuspended in buffer, the pH was adjusted with small volumes (<1 µL) of 3 M HCl. Fluorine experiments were performed at 15

°C, 20 °C, 25 °C, 30 °C, 35 °C, 40 °C and 45 °C with a Bruker Avance III HD spectrometer operating at a 19F Larmor frequency of 470 MHz running Topspin 3.2 and equipped with a

Bruker QCI cryoprobe.

Spin lattice (R1) relaxation rates for each condition were measured using an inversion recovery sequence [tmix=0, 0.05, 0.1 (x3), 0.25, 0.5, 0.8, 1.0, 1.5 s]. Sixteen transients were used for buffer, 32 for 100 g/L urea, 64 transients for 200 g/L Ficoll and 100 g/L lysozyme, and 64 and 128 transients for 200 g/L sucrose. Acquisition time was 2 s, with a relaxation delay of 4 s, while the sweep width was 70 ppm for both dimensions.

A modified version of the Bruker NOESY library experiment, a pseudo-3D experiment in which the t1 increments for each mixing time [tmix=1.5, 70, 140 (x3), 210, 300,

500, and 800 ms] were interleaved, was used to measure the folding and unfolding rates.

Sweep widths were 70 ppm in both dimensions, with 1,024 complex points collected during t2 with 75 or 100 complex points in t1 for each tmix. Sixteen transients were acquired per increment and a 2 second relaxation delay was used. Data for relaxation and folding experiments were processed using Topspin 3.2 as described previously.64

Fluorine-labeled and 15N-enriched protein samples were prepared identically, and 4-

,4-dimethyl-4-silapentane-1-sulfonic acid (DSS) was added to a final concentration of 0.1%

(vol/vol). Two-dimensional 15N-1H HSQC experiments were performed at 15°C, 20°C, 25°C,

30°C and 35°C on a Bruker Ascend spectrometer operating at an 1H Larmor frequency of

850 MHz and an 15N Larmor frequency of 86 MHz running Topspin 3.2 and equipped with a

Bruker QCI cryoprobe. A sensitivity-enhanced HSQC Bruker Library pulse sequence was used. The sweep widths were 38 ppm (3275 Hz) for F1 and 16 ppm (13587 Hz) for F2. Two- hundred-fifty-six points were collected in t1 and 2048 in t2. Eight transients were acquired per increment. The temperature dependence of the 1HN chemical shifts was determined from the change in the upfield 1HN chemical shifts with increasing temperature.149 Data were processed using Topspin 3.2. The temperature coefficients,149 in ppb/K, and their uncertainties were determined from plots of the 1HN chemical shifts versus temperature, using a linear regression 118.

Assignments for one- and two-dimensional 19F experiments were taken from the data of Evanics et al.138 The addition of fluorine causes minor 1H and 15N chemical shift perturbations relative to the unlabeled protein.138 The chemical shifts of the fluorinated protein were inferred from previous assignments determined at a pH of 7.2190 and by overlaying an HSQC spectrum of wild-type SH3 on a spectrum of the 5-fluorotrytophan- labeled protein.138

Selection of fits for temperature dependence in cosolutes

Four fitting schemes were tested: 1) a three-parameter fit for folding and unfolding, 2)

°%‡ °%‡ a two-parameter fit with ∆(),,,â→â‡= 0, 3) a two-parameter fit with ∆(),,,â→â‡= buffer and 4) a

°%‡ °%‡ two-parameter fit with ∆(),â→â‡ set equal to the value in buffer and ∆(),à→â‡= 0. Scheme 2 was eliminated because of the obvious curvature in the data (Figure 3A). Scheme 1 was ruled out, because the limited number of points restricted the ability of determine the extra

°%‡ °%‡ parameter (∆() ). The large r values and the low Pr values indicate that setting ∆() to zero for unfolding is appropriate, ruling out Scheme 3. Scheme 4 was chosen because crowding has only a small effect on the equilibrium heat capacity of SH3 unfolding64 and because the linear fit was determined suitable for the unfolding reaction (SI Appendix, Figure S3).

Analysis of uncertainty

For determination of relaxation rates, one mixing time was acquired three times. The sample SD was used to drive a Monte Carlo analysis (n = 1,000) to determine R1.

For folding rates, one mixing time was repeated three times. The sample SD was

64,139 used to drive a Monte Carlo analysis (n = 1000), and data were fit as described. R1 was set to values determined by inversion recovery experiments.

For the three-parameter analysis, the folding rate SDs were used to drive another

Monte Carlo analysis in which 10,000 randomly generated datasets were fit to Equation 3 to

°%‡ °%‡ °%‡ ‡ obtain ∆&à,â→â‡, −9∆'à,â→â‡and ∆(),à,â→â‡and their standard deviations. ΔG°’ (303 K) were calculated from the folding and unfolding rates at 303 K using Equation 1.8.

°%‡ °%‡ For the two-parameter analysis, the ∆&à,â→â‡and 9∆'à,â→â‡were determined from weighted linear regression of the sample folding rates and their SD.118 The probability of the values arising from uncorrelated data (Pr) was determined using the correlation coefficient, r.118

Viscosity measurements

The viscosities of water, 100 g/L urea, 50 g/L trimethylamine-N-oxide (TMAO) and

200 g/L sucrose were measured in triplicate at 10 °C, 20 °C, 30 °C and 40 °C K using a

Viscolite 700 (Hydramotion, York, UK). For each condition, the viscosity as a function of T was fit to an exponential function, which was used to extrapolate the viscosities at 15 °C, 25

°C, and 35 °C. Viscosity-adjusted folding rates were determined from the viscosity of the solution relative to water at 30 °C.

Tables

Table 3.1. Activation parameters for folding and unfolding at 303 K.

‡ ΔG°’ ΔH°’‡ -TΔS°’‡ r a P b Condition Reaction r (kcal/mol) (kcal/mol) (kcal/mol) pH 7.2 + 0.1

Buffer U à U‡c 16.85 + 0.01d 8.1 + 0.2d 8.7 + 0.2d NAe

U à U‡f “ 9.0 + 0.2 7.9 + 0.2 0.94 1.4

F à U‡g 17.24 + 0.01 22.8 + 0.2d -5.5 + 0.2d NAe

F à U‡ f “ 22.1 + 0.2 -4.9 + 0.3 0.99 1.4

100 g/L urea U à U‡c 17.85 + 0.01 6 + 2d 12 + 2d NAe

F à U‡ f 16.95 + 0.01 16.7 + 0.9 -0.3 + 0.9 0.96 10

50 g/L TMAO U à U‡c 16.48 + 0.04 6 + 1d 10.3 + 0.9d NAe

F à U‡ f 17.73 + 0.04 28 + 1 -10.0 + 0.9 0.99 10

200 g/L U à U‡c 16.71 + 0.03 8.5 + 0.9d 8.2 + 0.6d NAe sucrose

F à U‡ f 17.71 + 0.03 25.3 + 0.5 -6.9 + 0.6 0.99 10

200 g/L Ficoll U à U‡c 16.76 + 0.02 6.4 + 0.5d 10.3 + 0.7d NAe

F à U‡ f 17.52 + 0.04 26.2 + 0.5 -8.8 + 0.6 0.99 3.7

100 g/L U à U‡c 17.70 + 0.02 9.8 + 0.9d 7.9 + 0.9d NAe lysozyme

F à U‡f 17.32 + 0.03 23.4 + 0.8 -6.1 + 0.9 0.99 10

Footnotes a b 118 c ‡ r, Pearson correlation coefficient Pr, percent probability that r arises from uncorrelated data . ΔCp°’ = -0.59 kcal/mol. dTemperature-dependent with a reference temperature of 303 K eNA, not applicable; f ‡ g ‡ not a linear fit. ΔCp°’ = 0. ΔCp°’ = 0.3 kcal/molK.

Figures

Figure 3.1. Amide proton temperature coefficients. Buffer, black; 100 g/L urea, red; 200 g/L sucrose, green; 300 g/L Ficoll, blue; 100 g/L lysozyme, orange; no bar means no data. RT, reverse turn; DT, diverging turn; n-Src loop; DF, distal loop. Data within blue box have a

>85% probability of participating in an intramolecular hydrogen bond.149 Values were determined using a linear least squares fit of 1H-N chemical shifts from 288 K to 308 K in 5 K increments at pH 7.2. Uncertainties represent one standard deviation.

Figure 3.2. Temperature dependence of folding kinetics in buffer. Folding, black; unfolding,

°+‡ red. Data were fit with Equation 3, incorporating ∆(),à,â→â‡,. The uncertainties (one standard deviation) are smaller than the points, and are listed in the Supporting Information (Table

S3.4).

Figure 3.3. Temperature dependence of kinetics in buffer and cosolutes. A, folding; B, unfolding. Buffer, black; 100 g/L urea, red; 50 g/L TMAO, blue; 200 g/L sucrose, cyan; 200

°%‡ g/L Ficoll, green; 100 g/L lysozyme, magenta. Folding rates in A are fit with ∆ùû,ü→ü‡ = -0.59

°%‡ kcal/molK, while unfolding rates in B are fit with ∆ùû,†→ü‡ = 0. The uncertainties are smaller than the points, and are listed in Table S3.4.

Figure 3.4. Changes in the activation parameters in cosolutes. A, free energy; B, enthalpy;

C, entropy. Folding, black; unfolding, red. Changes in the activation free energy were determined at 303 K. Changes in activation enthalpy and entropy were determined at 303 K for folding, and without a reference temperature for unfolding, as described in the text.

Uncertainties (one standard deviation) in panel A are smaller than the points. Changes in entropy were multiplied by 303 K. All values and uncertainties are listed in Table S3.5.

Supplementary Information Table S3.1. Amide temperature coefficients. Measured at pH 7.2 + 0.1.

Folded state Unfolded state

Amide proton temperature coefficient, ppb/Ka Amide proton temperature coefficient, ppb/Ka

Resi Buffer Urea Sucrose Ficoll Lysozyme Buffer Urea Sucrose Ficoll Lysozym -due 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L e 100 g/L 2 -6.6 + 0.3 -6.3 + 0.4 -6.5 + 0.2 -6.50 + 0.03 3 -2.1 + 0.3 -3.2 + 0.4 -2.2 + 0.2 -2.4 + 0.3 -3.50 + 0.03 -8.1 + 0.4 -8.2 + 0.5 -7.7 + 0.2 -7.70 + 0.04 -8.6 + 0.2 4 -2.1 + 0.3 -2.7 + 0.4 -2.0 + 0.2 -2.9 + 0.4 -2.6 + 0.1 5 -2.7 + 0.3 -3.0 + 0.4 -2.7 + 0.1 -2.1 + 0.3 -2.9 + 0.1 -8.8 + 0.3 -8.9 + 0.4 -8.3 + 0.1 -8.5 + 0.1 -9.3 + 0.2 6 -5.1 + 0.3 -5.2 + 0.5 -4.4 + 0.1 -5.3 + 0.2 -6.1 + 0.3 8 -9.0 + 0.4 -9.7 + 0.6 -8.5 + 0.1 -8.7 + 0.1 -9.3 + 0.1 9 -3.8 + 0.3 -6 + 1 -3.2 + 0.1 -4 + 1 10 -5.6 + 0.3 -7.1 + 0.4 -5.2 + 0.1 -4.8 + 0.1 -5.9 + 0.1 -5.4 + 0.4 -5.9 + 0.4 -4.9 + 0.2 -5.2 + 0.2 -5.9 + 0.2 11 -6.2 + 0.3 -6.8 + 0.4 -5.80 + 0.05 -6.7 + 0.2 -6.7 + 0.4 -6.1 + 0.3 -6.4 + 0.2 -7.2 + 0.2 12 -6.8 + 0.3 -6.4 + 0.4 -6.4 + 0.3 -7.0 + 0.2 -5.6 + 0.1 -6.5 + 0.4 -6.8 + 0.4 -5.8 + 0.2 -6.20 + 0.04 -6.9 + 0.1 13 -1.4 + 0.3 -1.2 + 0.4 -1.0 + 0.1 -1.4 + 0.1 -1.6 + 0.2 -6.5 + 0.3 -5.9 + 0.2 -6.2 + 0.1 -6.7 + 0.1 14 -7.2 + 0.3 -8.7 + 0.5 -6.8 + 0.1 -7.1 + 0.1 -8.1 + 0.4 15 -3.0 + 0.3 -3.2 + 0.4 -3.0 + 0.2 -2.9 + 0.1 -2.8 + 0.1 16 -2.7 + 0.4 -2.8 + 0.5 -2.1 + 0.1 -2.5 + 0.2 -3.1 + 0.1 -3.7 + 0.3 17 -5.7 + 0.3 -5.6 + 0.4 -5.4 + 0.2 -5.70 + 0.04 -6.4 + 0.1 18 -7.2 + 0.3 -7.4 + 0.4 -6.9 + 0.1 -7.4 + 0.2 -4.3 + 0.4 -4.6 + 0.4 -4.0 + 0.2 -4.2 + 0.4 -4.9 + 0.2 19 -3.1 + 0.3 -3.5 + 0.4 -2.7 + 0.2 -3.5 + 0.2 -3.8 + 0.1 20 -6.2 + 0.3 -5.7 + 0.4 -5.3 + 0.2 -5.9 + 0.2 -6.7 + 0.1 Footnotes aSlopes more positive than -4.6 ppb/K are 85% likely to be hydrogen bonded 149.

Table S3.1, continued.

Folded state Unfolded state

Amide proton temperature coefficient, ppb/Ka Amide proton temperature coefficient, ppb/Ka

Resi Buffer Urea Sucrose Ficoll Lysozyme Buffer Urea Sucrose Ficoll Lysozyme -due 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L 100 g/L

21 -5.0 + 0.3 -5.1 + 0.4 -4.7 + 0.1 -5.0 + 0.2 -5.20 + 0.03 22 -2.6 + 0.3 -2.7 + 0.4 -2.5 + 0.1 -1.9 + 0.1 -2.8 + 0.1 -8.2 + 0.4 -7.1 + 0.5 -7.5 + 0.1 -7.1 + 0.4 -6.3 + 0.2 25 -3.5 + 0.4 -3.8 + 0.4 -3.2 + 0.2 -3.8 + 0.4 -3.80 + 0.02 -6.2 + 0.3 -4.8 + 0.1 -5.8 + 0.1 27 -1.9 + 0.3 -2.6 + 0.4 -1.1 + 0.2 -2.1 + 0.2 -2.1 + 0.2 28 -4.2 + 0.4 -4.1 + 0.4 -3.8 + 0.1 -6.6 + 0.1 -4.2 + 0.6 -7.5 + 0.4 -7.80 + 0.02 29 -1.7 + 0.3 -1.8 + 0.4 -1.9 + 0.4 -1.8 + 0.1 30 -7.3 + 0.1 -7.3 + 0.4 -6.9 + 0.1 -7.0 + 0.1 -7.9 + 0.3 34 -7.3 + 0.4 -7.3 + 0.5 -6.5 + 0.2 -6.6 + 0.2 -7.0 + 0.3 -5.0 + 0.3 -5.3 + 0.5 -4.6 + 0.1 -6.6 + 0.2 -5.0 + 0.1 35 -3.6 + 0.4 -4.9 + 0.5 -3 + 2 37 -1.4 + 0.3 -2.0 + 0.4 -0.8 + 0.1 -1.3 + 0.1 -1.7 + 0.2 -6.1 + 0.4 -6.6 + 0.5 38 -4.1 + 0.3 -3.9 + 0.4 -3.8 + 0.1 -3.1 + 0.2 -5.0 + 0.1 -1.8 + 0.3 -1.5 + 0.5 -1.4 + 0.2 -1.6 + 0.1 -2.0 + 0.2 39 -2.3 + 0.4 -2.6 + 0.4 -2.3 + 0.2 -2 + 2 -2.8 + 0.5 -6.5 + 0.5 -2.3 + 0.2 -6.9 + 0.1 40 -3.5 + 0.3 -3.7 + 0.4 -2.9 + 0.1 -4.1 + 0.2 -3.8 + 0.1 41 -3.7 + 0.3 -3.9 + 0.4 -3.2 + 0.1 -3.7 + 0.2 -3.9 + 0.1 42 -10.0 + 0.3 -9.7 + 0.6 -9.50 + 0.02 -9.2 + 0.2 -10.5 + 0.4 43 -7.1 + 0.3 -7.1 + 0.5 -6.9 + 0.1 -6.8 + 0.2 -7.9 + 0.3 -5.0 + 0.3 -5.5 + 0.4 -4.4 + 0.1 -5.1 + 0.4 -5.4 + 0.2 44 -1.7 + 0.3 -1.8 + 0.4 -1.6 + 0.1 -1.6 + 0.1 -2.2 + 0.1 46 -1.8 + 0.3 -2.2 + 0.4 -1.6 + 0.2 -1.7 + 0.1 -5 + 2 -6.0 + 0.3 -6.4 + 0.5 -5.6 + 0.1 -5.6 + 0.4 -6.5 + 0.1

Footnotes aSlopes more positive than -4.6 ppb/K are 85% likely to be hydrogen bonded 149.

Table S3.1, continued.

Folded state Unfolded state

Amide proton temperature coefficient, ppb/Ka Amide proton temperature coefficient, ppb/Ka Resi Buffer Urea Sucrose Ficoll Lysozyme Buffer Urea Sucrose Ficoll Lysozyme -due 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L 100 g/L 47 -4.1 + 0.3 -4.0 + 0.5 48 -3.1 + 0.4 -3.1 + 0.5 -3.0 + 0.1 -3.3 + 0.3 -3.90 + 0.02 -9.1 + 0.4 -9.6 + 0.5 -8.8 + 0.4 -8.6 + 0.4 -9.2 + 0.2 50 -1.2 + 0.3 -1.2 + 0.4 -0.9 + 0.1 -1.4 + 0.2 51 -4.1 + 0.4 -3.8 + 0.4 -4.0 + 0.9 -4.1 + 0.1 -5.1 + 0.2 -8.8 + 0.4 -9.1 + 0.5 -8 + 2 -8.1 + 0.1 -9.6 + 0.2 52 -4.1 + 0.3 -4.1 + 0.4 -3.5 + 0.1 -4.2 + 0.3 -4.5 + 0.2 53 -1.5 + 0.5 -1.4 + 0.5 -1.0 + 0.1 -1.6 + 0.1 -1.6 + 0.1 54 -1.6 + 0.4 -1.9 + 0.5 -1.7 + 0.2 -1.2 + 0.1 -2.0 + 0.4 -6.4 + 0.4 -7.1 + 0.5 -5.9 + 0.1 -5.70 + 0.03 -6.5 + 0.1 55 -7.2 + 0.3 -7.1 + 0.4 -6.6 + 0.1 -7.0 + 0.1 -7.6 + 0.3 -6.7 + 0.4 -7.0 + 0.4 -6.2 + 0.1 -6.0 + 0.2 -7.2 + 0.2 56 -8.4 + 0.7 -8.1 + 0.5 -7.6 + 0.2 -8.1 + 0.1 57 -7.2 + 0.4 -7.2 + 0.4 -9.2 + 0.2 59 -6.1 + 0.4 -6.5 + 0.5 -5.1 + 0.1 -5.6 + 0.1 -6.8 + 0.2 Footnotes aSlopes more positive than -4.6 ppb/K are 85% likely to be hydrogen bonded 149.

Table S3.2. Composite 1H-15N chemical shift perturbations. Measured at 298 K and pH 7.2 + 0.1.

Folded state Unfolded state Δδcomp, ppm Δδcomp, ppm Residue Urea Sucrose Ficoll Lysozyme Urea Sucrose Ficoll Lysozyme 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L 100 g/L 2 0.05 0.01 0.04 0.06 3 0.03 0.00 0.02 0.10 0.01 0.02 0.04 0.07 4 0.04 0.02 0.003 0.09 5 0.04 0.01 0.03 0.08 0.02 0.04 0.06 0.07 6 0.03 0.11 0.02 0.08 7 0.01 0.01 0.03 0.09 8 0.04 0.02 0.03 0.09 9 0.00 0.01 0.02 0.08 0.03 10 0.14 0.02 0.04 0.08 0.03 0.02 0.06 0.08 11 0.04 0.01 0.02 0.08 0.02 0.05 0.08 12 0.01 0.02 0.05 0.09 0.02 0.02 0.06 0.07 13 0.04 0.02 0.05 0.08 0.02 0.09 0.05 0.06 14 0.05 0.01 0.02 0.10 15 0.03 0.01 0.01 0.12 16 0.01 0.01 0.02 0.11 17 0.02 0.02 0.08 18 0.10 0.01 0.03 0.01 0.01 0.02 0.08 19 0.03 0.01 0.02 0.09

Table S3.2, continued.

Folded state Unfolded state Δδcomp, ppm Δδcomp, ppm Residue Urea Sucrose Ficoll Lysozyme Urea Sucrose Ficoll Lysozyme 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L 100 g/L 20 0.03 0.01 0.02 0.08 0.03 21 0.03 0.02 0.03 0.08 0.03 22 0.00 0.01 0.03 0.09 0.09 0.02 0.03 0.10 23 0.03 0.03 0.01 25 0.01 0.01 0.03 0.08 0.12 0.10 0.10 27 0.04 0.01 0.03 0.12 28 0.01 0.01 0.06 0.08 0.10 29 0.03 0.01 0.10 30 0.03 0.03 0.04 31 0.03 34 0.03 0.01 0.02 0.06 0.01 0.01 0.06 0.09 37 0.03 0.01 0.03 0.09 38 0.02 0.01 0.02 0.07 0.02 0.01 0.02 0.09 39 0.03 0.02 0.02 0.07 0.03 0.09 40 0.02 0.01 0.01 0.09 0.08 0.02 0.04 0.09 41 0.03 0.01 0.03 0.08 42 0.06 0.03 0.05 0.08 43 0.01 0.00 0.02 0.07 0.02 0.01 0.03 0.06

Table S3.2, continued.

Folded state Unfolded state Δδcomp, ppm Δδcomp, ppm Residue Urea Sucrose Ficoll Lysozyme Urea Sucrose Ficoll Lysozyme 100 g/L 200 g/L 300 g/L 100 g/L 100 g/L 200 g/L 300 g/L 100 g/L 44 0.01 0.00 0.02 0.08 45 0.02 0.03 0.03 0.08 46 0.01 0.01 0.03 0.08 0.02 0.01 0.04 0.07 48 0.00 0.00 0.02 0.07 0.06 0.06 0.08 0.03 50 0.00 0.03 0.01 0.08 0.04 0.07 0.04 0.19 51 0.01 0.02 0.01 0.12 52 0.00 0.01 0.05 0.07 53 0.01 0.02 0.08 0.09 0.06 0.10 0.08 54 0.02 0.01 0.03 0.08 0.08 0.04 0.06 0.09 55 0.03 0.03 0.02 0.09 56 0.05 0.02 0.03 0.05 57 0.02 0.05 0.08 0.08 0.07 59 0.03 0.06 0.04 0.06

Table S3.3. Average 1H-15N chemical shift perturbations in cosolutes. .

Folded Unfolded Difference Condition Average Δδcomp (ppm) Average Δδcomp (ppm) Δδcomp, U - Δδcomp, F (ppm) 100 g/L urea 0.03 + 0.02 0.04 + 0.03 0.01 + 0.04

100 g/L lysozyme 0.08 + 0.02 0.08 + 0.03 0.00 + 0.04

200 g/L sucrose 0.02 + 0.02 0.04 + 0.03 0.02 + 0.04

300 g/L Ficoll 0.03 + 0.02 0.05 + 0.02 0.02 + 0.03

Table S3.4. SH3 longitudinal relaxation and folding rates.. Longitudinal relaxation (R1)

and reaction rates (k) for SH3 folding (U à U‡) and unfolding (F à U‡) in buffer and

cosolutes were measured various temperatures at pH 7.2 + 0.1.

Temper- Relative Co- ature viscosity, solute (K) η /η R1 (s-1) k (s-1) R1 (s-1) k (s-1) c buffer, 303 K U à U‡ U à U‡ F à U‡ F à U‡ Buffer 283 1.6 2.49 + 0.06 NDa 1.8 + 0.2 NDa 288 1.4 2.52 + 0.09 1.43 + 0.04 1.89 + 0.04 0.40 + 0.01 2.00 + 0.06c 0.73 + 0.01c 293 1.3 2.52 + 0.08 2.15 + 0.05 1.90 + 0.04 0.56 + 0.01 2.79 + 0.07c 0.73 + 0.01c 298 1.1 2.3 + 0.1 3.40 + 0.05 1.76 + 0.08 1.40 + 0.01 3.74 + 0.06c 1.54 + 0.01c 303 1.0 2.3 + 0.1 4.5 + 0.1 1.76 + 0.07 2.36 + 0.03 4.5 + 0.1c 2.12 + 0.03c 308 0.9 2.2 + 0.1 5.3 + 0.1 1.75 + 0.04 4.3 + 0.1 4.77 + 0.09c 3.87 + 0.09c 313 0.9 1.97 + 0.07 6.0 + 0.1 1.7 + 0.1 8.8 + 0.2 5.4 + 0.09c 7.9 + 0.2c 100 g/L urea 293 1.3 2.6 + 0.2 0.49 + 0.03 1.53 + 0.02 1.29 + 0.09

0.64 + 0.04c 1.7 + 0.1c 298 1.2 2.4 + 0.2 0.79 + 0.03 1.52 + 0.05 2.64 + 0.08 0.95 + 0.04c 3.2 + 0.1c 303 1.1 2.4 + 0.1 0.86 + 0.02 1.56 + 0.03 3.79 + 0.09 0.95 + 0.04c 4.2 + 0.1c 308 1.0 1.8 + 0.1 1.0 + 0.2 1.51 + 0.01 7.9 + 0.7 1.0 + 0.2c 7.9 + 0.7c Footnotes aND, not determined; signal to noise too low for peaks to be accurately fit. bFolding and unfolding rates in italics have been adjusted for the viscosity of the solution relative [( ! " #,(&') )*k (s-1)], is to buffer at 303 K according to: F, U U‡ where η T 4 the viscosity of the !)*++,-, /0/ 1 (&') à

solution (buffer or cosolute) at a given temperature, η567789, :;: < is the viscosity of buffer at reference temperature 303 K, and k is the folding or unfolding rate before viscosity F,U à U‡ correction. cND, viscosity-adjusted values not determined, macroviscosity not felt by protein.

Table S3.4, continued.

Co- Temp- Relative solute erature viscosity, R1 (s- R1 (s- U à U‡ F à U‡ (K) η /η 1) k (s-1) 1) k (s-1) c buffer, 303 K U à U‡ F à U‡ 50 g/L 298 1.2 2.51 + 0.03 NDa 2.3 + 0.2 NDa TMAO

303 1.1 2.44 + 0.01 8.3 + 0.5 1.9 + 0.1 1.05 + 0.07 9.1 + 0.5c 1.16 + 0.08c 308 1.1 2.3 + 0.07 8.9 + 0.2 2.1 + 0.1 2.29 + 0.08 9.8 + 0.2c 2.5 + 0.1c 313 1.0 2.2 + 0.1 10.1 + 0.6 1.91 + 0.02 4.4 + 0.2 10.1 + 0.6c 4.0 + 0.2c 318 1.0 1.95 + 0.07 10.0 + 0.6 1.75 + 0.07 10.1 + 0.5 10.0 + 0.6c 10.1 + 0.5c 200 g/L 293 2.5 1.81 + 0.01 NDa 2.0 + 0.5 NDa sucrose

298 2.3 2.28 + 0.01 NDa 1.7 + 0.2 NDa 303 2.1 2.16 + 0.02 5.7 + 0.3 1.7 + 0.2 1.07 + 0.05 10.8 + 0.5c 2.2 + 0.1c 308 2.0 2.19 + 0.04 7.6 + 0.3 2.01 + 0.04 2.22 + 0.06 13.5 + 0.5c 4.4 + 0.1c 313 1.9 2.21 + 0.07 8.4 + 0.3 2.0 + 0.02 4.2 + 0.2 14.2 + 0.5c 8.0 + 0.4c 318 1.8 2.28 + 0.04 8.3 + 0.3 2.03 + 0.04 8.3 + 0.2 13.2 + 0.4c 14.9 + 0.4c 200 g/L 293 ND2 1.97 + 0.03 NDa 1.7 + 0.2 NDa Ficollc

298 ND 2.19 + 0.03 4.1 + 0.1 1.8 + 0.2 0.80 + 0.04 303 ND 2.24 + 0.02 5.2 + 0.2 1.92 + 0.07 1.47 + 0.09 308 ND 2.01 + 0.08 6.2 + 0.2 1.81 + 0.04 3.5 + 0.1 313 ND 2.06 + 0.06 6.5 + 0.3 1.84 + 0.03 6.8 + 0.2 318 ND 1.79 + 0.08 6.5 + 0.3 1.74 + 0.02 13.3 + 0.5 Footnotes aND, not determined; signal to noise too low for peaks to be accurately fit. bFolding and unfolding rates in italics have been adjusted for the viscosity of the solution relative to [( ! " #,(&') )*k (s-1)], is buffer at 303 K according to: F, U U‡ where η T 4 the viscosity of the solution !)*++,-, /0/ 1 (&') à

(buffer or cosolute) at a given temperature, η567789, :;: < is the viscosity of buffer at reference temperature 303 K, and k is the folding or unfolding rate before viscosity correction. F,U à U‡ cND, viscosity-adjusted values not determined, macroviscosity not felt by protein

Table S3.4, continued.

Relative Temp- viscosity, Co- erature ηc/ηbuffer, solute (K) R1 (s-1) k (s-1) R1 (s-1) k (s-1) 303 K U à U‡ U à U‡ F à U‡ F à U‡ 100 g/L 293 ND 1.22 + 0.08 NDa 1.2 + 0.1 NDa lyso- zymec

298 ND 1.5 + 0.2 0.85 + 0.04 1.26 + 0.09 1.09 + 0.03 303 ND 1.4 + 0.1 1.10 + 0.04 1.35 + 0.08 2.05 + 0.09 308 ND 1.6 + 0.1 1.57 + 0.09 1.4 + 0.08 3.6 + 0.2

Footnotes aND, not determined; signal to noise too low for peaks to be accurately fit. bFolding and unfolding rates in italics have been adjusted for the viscosity of the solution relative to [( ! " #,(&') )*k (s-1)], is buffer at 303 K according to: F, U U‡ where η T 4 the viscosity of the solution !)*++,-, /0/ 1 (&') à

(buffer or cosolute) at a given temperature, η567789, :;: < is the viscosity of buffer at reference temperature 303 K, and k is the folding or unfolding rate before viscosity correction. F,U à U‡

Table S3.5. Changes in activation parameters for SH3 folding and unfolding. Activation free energies, enthalpies and entropyiesfor folding (U à U‡) and unfolding (F à U‡) from buffer to cosolutes were measured at pH 303 K and pH 7.2 + 0.1.Green shading indicates a significant decrease and red a significant increase in the barriers to folding and unfolding.

‡ ‡ Cosolute - buffer (ΔCp°’ = buffer, 303 K ) Cosolute – buffer (ΔCp°’ = 0) °+‡ °+‡ °+‡ °+‡ °+‡ °+‡ ∆∆"# à #‡,'(' ) ∆∆", à #‡,'(' ) ∆∆-# à #‡,'(' ) −/∆∆0# à #‡,'(' 1 ∆∆-, à #‡ −/∆∆0, à #‡,'(' 1 Co-solute (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) 100 g/L urea 1.00 + 0.02 -0.29 + 0.02 -2 + 2 3 + 2 -5 + 1 5.2 + 0.9 0.94 + 0.04 -0.35 + 0.02 -2 + 2a 3 + 2 a -5 + 1 a 4 + 1a 50 g/L TMAO -0.37 + 0.04 0.49 + 0.04 -2 + 1 1.6 + 0.9 6 + 1 -5.1 + 0.9 -0.42 + 0.04 0.43 + 0.04 -1 + 1 a 0.5 + 0.6 a 7 + 1a -5.6 + 0.9 a 200 g/L sucrose -0.14 + 0.03 0.48 + 0.03 0.4 + 0.8 0.5 + 0.6 3.2 + 0.5 -2.7 + 0.7 -0.59 + 0.03 0.04 + 0.03 0.9 + 0.7 a -1.6 + 0. 6 a 4.9 + 0.6 a -3.2 + 0.6 a 200 g/L Ficoll -0.09 + 0.03 0.29 + 0.04 -1.7 + 0.5 1.6 + 0.6 4.1 + 0.5 -3.9 + 0.7 100 g/L lysozyme 0.85 + 0.02 0.09 + 0.03 1.7 + 0.9 0.8 + 0.9 1.3 + 0.8 -1.2 + 0.9

Footnotes aUsing viscosity-adjusted rates.

Table S3.6. Equilibrium-from-kinetics parameters for SH3. Parameters derived from activation free energies, enthalpies and entropies of folding and unfolding along with authentic equilibrium data at 303 K and pH 7.2 + 0.1. Green shading indicates significant stabilization and red significant destabilization.

°+‡ °+‡ Cosolute - buffer ( ∆23,# à #‡,'(' 1= -0.59 kcal/molK, ∆23,, à #‡,'(' 1= 0 ) Cosolute – buffer ° °+ °+ ° °+ °+ ∆∆"#, '(' ) ∆∆-# , '(' ) −/∆∆0# , '(' 1 ∆∆"#, '(' ) ∆∆-# , '(' ) −/∆∆0# , '(' 1 Cosolute (kcal/mol) (kcal/mol) (kcal/mol) Cosolute (kcal/mol)a (kcal/mol)a (kcal/mol)a 100 g/L urea -1.3 + 0.01 -3 + 2 2 + 2 100 g/L ureaa -1.25 + 0.07 -2 + 2 1 + 2 50 g/L 0.86 + 0.06 8 + 1 -7 + 1 50 g/L TMAOa 0.45 + 0.05 -1 + 1 1 + 1 TMAO 200 g/L 300 g/L 0.62 + 0.04 4 + 1 -3 + 1 1.1 + 0.1 -1 + 3 2 + 3 sucrose sucrosea 200 g/L 0.37 + 0.04 6 + 1 -6 + 1 300 g/L Ficolla 0.36 + 0.04 -1 + 1 1 + 1 Ficoll 100 g/L 100 g/L -0.76 + 0.04 0 + 1 0 + 1 -0.89 + 0.04 1 + 3 -3 + 3 lysozyme lysozymea Footnotes a 64 From the work of Smith et al. in 0% D2O

RT DT β1 β2 β3 β4 0.2 Folded

0.1

0.0

0.1

Unfolded 0.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

n-Src DL β5 β6 310 β7 0.2 Folded

0.1

0.0

0.1

0.2 Unfolded 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Residue 1 15 Figure S3.1. Changes in composite H- N chemical shift (Δδcomp) at 298 K. Composite chemical shifts were calculated as listed in Davison et al.154 Buffer, black; 100 g/L urea, red; 200 g/L sucrose, green; 300 g/L Ficoll, blue; 100 g/L lysozyme, orange. Δδcomp within the blue box are less than 0.02, the limit of detection as described 155. Changes in composite chemical shift are the absolute value of the change in chemical shift. No bar means no data. Loop and turn names are RT loop (RT); diverging turn (DT); n-Src loop (n-Src); distal loop (DL).

Figure S3.2. Chemical shift perturbations for SH3. Perturbations were calculated from

Δδcosolutes - Δδbuffer at 298 K. folded state structure is used to represent the unfolded ensemble. Chemical shifts were calculated as described 154. Blue, 0.02 > Δδ > 0 ppm; green, 0.1 > Δδ > 0.03 ppm; orange, Δδ > 0.1 ppm. Cosolutes are A) 100 g/L urea B) 100 g/L lysozyme C) 200 g/L sucrose, D) 300 g/L Ficoll.

Figure S3.3. Residual plots for SH3 two- and three-parameter fits. A, folding; B, unfolding.

‡ Data were acquired in buffer and fit with the three-parameter fit [ΔCp°’ ≠ 0 (closed circles)]

‡ and the two parameter fit, [ΔCp°’ = 0 (open circles)].

APPENDIX 1. T1 FITTING SCRIPT WITH MONTE CARLO ERROR SIMULATION clear all close all

%Script to Measure 19F T1 Rates % written by AES, 2015 time = [0;0.1;0.05;0.8;1.5;0.5;1;0.25]; %Input mixing time T1

%Folded State A=[-18142,-19052,-19955]; %Insert 3 repeated delays B=mean(A); Folded = [-33254;B;-26231;26892;35795;15358;31370;-1910]; sigmaF=std(A); covarF=sigmaF^2; %MC uses covariance, which is standard deviation squared CovarF = [covarF covarF covarF covarF covarF covarF covarF covarF]; % Make sure this is the same size as cycles

%Unfolded State C=[-8488,-9160,-8897]; D=mean(C); Unfolded = [-12738;D;-10592;9223;9160;4226;9934;-3381]; sigmaU=std(C); covarU=sigmaU^2; CovarU = [covarU covarU covarU covarU covarU covarU covarU covarU];

%MC stuff, can name files whatever, but need to change below if you do nsamples = 1000; fileIDF = fopen('Folded.dat','w'); fileIDU = fopen('Unfolded.dat','w'); formatSpec = '%d %d %d\n';

%-----STARTS DATA ANALYSIS----- T1fit =fittype('M*(1-V*exp(-x/T))','independent',{'x'},'coefficients',{'M','T','V'}); % Declaring the fit: M is Sz, T is T1, V is fudge factor

[fit1,gof1] = fit(time,Folded,T1fit,'startpoint',[max(Folded),0.05,1],'algorithm','Trust-Region'); [fit2,gof2] = fit(time,Unfolded,T1fit,'startpoint',[max(Unfolded),0.05,1],'algorithm','Trust- Region');

%Values %T1 = fit1.T R1F = 1/fit1.T %gof1.rsquare; %T1 = fit2.T R1U = 1/fit2.T %gof2.rsquare; plot(time,Folded,'rs','MarkerSize',10,'LineWidth',2);

hold on plot(time,Unfolded,'bo','MarkerSize',10,'LineWidth',2); plot(fit1,'black'); hold on plot(fit2,'black'); legend('Folded','Unfolded','Location','Best'); hold off title(['19F drkN SH3'],'fontsize',10); xlabel('Time (s)','fontsize', 10); ylabel('Volume','fontsize',10); %axis([0 1.6 -50000 50000]); % x- axis, y-axis hold off

%-----MONTE CARLO----- %MC FOLDED State fprintf('FOLDED\n'); MC = mvnrnd(Folded,CovarF,nsamples); % Uses covariance... square the STD std(MC); for i=[1:nsamples] DataMC = MC(i,:)'; [fitx]=fit(time,DataMC,T1fit,'startpoint',[fit1.M,fit1.T,fit1.V],'algorithm','Trust- Region','Robust','on'); F= {fitx.M,1/fitx.T,fitx.V}; fprintf(fileIDF,formatSpec,F{1,:}); fprintf('%d ', i); end fclose(fileIDF); fprintf('\n'); fprintf('\nFOLDED\n'); load Folded.dat mean(Folded(:,2)) std(Folded(:,2)) mean(Folded([1:100],2)) std(Folded([1:100],2))

%MC UNFOLDED STATE fprintf('UNFOLDED\n'); MC = mvnrnd(Unfolded,CovarU,nsamples); % Uses covariance... square the STD std(MC); for i=[1:nsamples] DataMC = MC(i,:)'; [fitx]=fit(time,DataMC,T1fit,'startpoint',[fit2.M,fit2.T,fit2.V],'algorithm','Trust- Region','Robust','on'); F= {fitx.M,1/fitx.T,fitx.V}; fprintf(fileIDU,formatSpec,F{1,:}); fprintf('%d ', i); end fclose(fileIDU); fprintf('\n'); fprintf('\nUUNFOLDED\n'); load Unfolded.dat

mean(Unfolded(:,2)) std(Unfolded(:,2)) mean(Unfolded([1:100],2)) std(Unfolded([1:100],2))

APPENDIX 2.1 T1 FITTING SCRIPT WITH MONTE CARLO ERROR SIMULATION

Calls on Appendix 2.2 and 2.3, must be in the same folder.

% Fit for Slow exchange % drkN SH3, F19 % written by AES, 2015 % Can set R1 to value attained from inversion recovery sequence if desired. clear all close all global tmix % exchange time, in seconds global expt_FF_pk expt_UU_pk % experimental self peaks global expt_FU_pk expt_UF_pk % experimental cross peaks global calc_FF_pk calc_UU_pk % obtained by simulations of self peaks global calc_FU_pk calc_UF_pk % obtained by simulations of cross peaks global tmix_plot % array of exchange times used for plotting global err2 % error global calc_FF_pk_plot calc_UU_pk_plot calc_FU_pk_plot calc_UF_pk_plot % plots fits global DataFF DataUU % MC self peaks global DataFU DataUF % MC cross peaks tmix=[0.300 0.140 0.800 0.0015 0.210 0.070 0.500]; % exchange times, in seconds

%invert FU and UF

FF=[927684,927702,926381]; UU=[278379,282835,275108]; UF=[118539,119412,122319]; FU=[154588,154470,157603];

A=mean(FF); % calculates the average of the triplicates B=mean(UU); C=mean(UF); D=mean(FU); expt_FF_pk=[623633 A 176136 1513556 747585 1162224 352975]; % extracting experimental FF points expt_UU_pk=[168451 B 43851 548918 206076 380484 86811]; % extracting experimental UU points expt_UF_pk=[132272 C 63199 -20921 138500 83542 104570]; % extracting cross peaks expt_FU_pk=[165991 D 69563 15138 178927 118670 121468]; %

sigmaFF=std(FF); % calculates the standard deviation of the triplicates sigmaUU=std(UU); sigmaFU=std(FU); sigmaUF=std(UF); covarFF=sigmaFF^2; %MC uses covariance, which is standard deviation squared covarUU=sigmaUU^2; covarFU=sigmaFU^2; covarUF=sigmaUF^2;

CovarFF = [covarFF covarFF covarFF covarFF covarFF covarFF covarFF]; % Make sure this is the same size as tmix CovarUU = [covarUU covarUU covarUU covarUU covarUU covarUU covarUU]; CovarFU = [covarFU covarFU covarFU covarFU covarFU covarFU covarFU]; CovarUF = [covarUF covarUF covarUF covarUF covarUF covarUF covarUF];

%MC stuff, can name files whatever, but need to change below if you do nsamples = 1000; fileIDF = fopen('Dil25176x2.dat','w'); %formatSpec = '%d %d %d %d %d %d %d %d %d\n'; % This will depend on if you %allow R1 to vary or if you set it formatSpec = '%d %d %d %d %d %d %d\n'; % This will depend on if you allow R1 to vary or if you set it

% ------END OF INPUT ------

% --- FIT --- MCFF = mvnrnd(expt_FF_pk,CovarFF,nsamples); % This generates the MC matrix sigmaFF % Actual sample standard deviation std(MCFF) % MC standard deviation, make sure it matches the actual standard deviation MCUU = mvnrnd(expt_UU_pk,CovarUU,nsamples); MCFU = mvnrnd(expt_FU_pk,CovarFU,nsamples); MCUF = mvnrnd(expt_UF_pk,CovarUF,nsamples); for i=[1:nsamples] % Loops and fits DataFF = MCFF(i,:); % reads row by row DataUU = MCUU(i,:); DataFU = MCFU(i,:); DataUF = MCUF(i,:);

Izf = max(DataFF); % Folded decay curve initial amplitude Izu = max(DataUU); % Unfolded decay curve initial amplitude kfu = 1.4; % unfolding rate kuf = 3.5; % folding rate R1f = 2.3; % R1 guess for folded R1u = 1.76; % R1 guess for unfolded Efu = min(DataFU); % Leakage, if the 0ms point gives a buildup peak Euf = min(DataUF); % Leakage, if the 0ms point gives a buildup peak

%x0 = [kfu, kuf, Izf, Izu, Efu, Euf, R1f,R1u]; % declaring variables to minimize x0 = [kfu, kuf, Izf, Izu, Efu, Euf]; % declaring variables to minimize with R1 set

minopt = optimset('TolX',1e-6,'TolFun',1e-6,'MaxFunEvals',1e6,'MaxIter',1e6); x=fminsearch('Dil25_calc176',x0,minopt);

%Ans= {x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),err2}; % vary R1 Ans= {x(1),x(2),x(3),x(4),x(5),x(6),err2}; % dont vary R1 fprintf(fileIDF,formatSpec,Ans{1,:}); %prints to file fprintf('%d ', i); end load Dil25176x2.dat; fprintf('\nkunfold\n'); mean(Dil25176x2(:,1)) std(Dil25176x2(:,1)) fprintf('\nkfold\n'); mean(Dil25176x2(:,2)) std(Dil25176x2(:,2)) fprintf('Entire Dataset') mean(Dil25176x2) std(Dil25176x2) fprintf('Truncated Dataset') mean(Dil25176x2([1:100],:)) std(Dil25176x2([1:100],:)) %fprintf('\nR1F\n'); % comment and uncomment depending on if you vary R1 %mean(Lys30(:,7)) %std(Lys30(:,7)) %fprintf('\nR1U\n'); % comment and uncomment depending on if you vary R1 %mean(Lys30(:,8)) %std(Lys30(:,8))

% Plotting figure(1); plot(tmix,expt_FF_pk,'rs', 'MarkerSize',14,'Linewidth',4); hold on plot(tmix,expt_UU_pk,'bo','MarkerSize',14,'Linewidth',4); hold on plot(tmix,expt_FU_pk,'rs', 'MarkerSize',14,'Linewidth',4); hold on plot(tmix,expt_UF_pk,'bo','MarkerSize',14,'Linewidth',4); tmix_plot=linspace(min(tmix),max(tmix),200);

Izf = mean(Dil25176x2(:,3)); % Decay curve initial amplitude Izu = mean(Dil25176x2(:,4)); % Buildup curve initial amplitude kfu = mean(Dil25176x2(:,1)); % kfu kuf = mean(Dil25176x2(:,2)); % kuf R1f = 2.3; % R1 guess for folded R1u = 1.76; % R1 guess for unfolded

%R1f = mean(Lys30(:,7)); % R1 guess for folded %R1u = mean(Lys30(:,8)); % R1 guess for unfolded Efu = mean(Dil25176x2(:,5)); % Leakage, if the 0ms point gives a buildup peak Euf = mean(Dil25176x2(:,6)); % Leakage, if the 0ms point gives a buildup peak

Dil25_plot176(x); plot(tmix_plot,calc_FF_pk_plot,'k-','Linewidth', 2); plot(tmix_plot,calc_UU_pk_plot,'k-','Linewidth',2); plot(tmix_plot,calc_FU_pk_plot,'k-','Linewidth', 2); plot(tmix_plot,calc_UF_pk_plot,'k-','Linewidth',2); fig_leg=legend('FF','UU','FU','UF','Location','Best'); set(fig_leg,'FontSize',18,'fontweight','bold','Box','off'); hold off tit=[' 19F drkN SH3 ', ' error = ', num2str(err2)]; title(tit,'fontsize',20); xlabel('Time (s)','fontsize', 20); ylabel('Intensity','fontsize',20); set(gca,'fontsize',18);

%fn0 = ['Dilute_EXSY_022315.eps']; %print( gcf, '-depsc2', fn0 ) hold off

APPENDIX 2.2 EVOLUTION EQUATIONS FOR EXCHANGE SPECTROSCOPY

% Equations were taken from Farrow, J. Bio. NMR, 4 (1994) 727-734 function chi2=chi2_simple_Dilil(xarg); global tmix global DataFF DataUU % MC self peaks global DataFU DataUF % MC cross peaks global calc_FF_pk calc_UU_pk calc_FU_pk calc_UF_pk global err2 kfu=xarg(1); kuf=xarg(2); Izf=xarg(3); Izu=xarg(4); Efu=xarg(5); Euf=xarg(6);

R1f=2.3; % Set to value if desired, ie R1f=[2.4]; R1u=1.76; % Set to value if desired. %R1f=xarg(7); % Set to value if desired, ie R1f=[2.4]; %R1u=xarg(8); a11 = R1f + kfu; a22 = R1u + kuf; a12 = -kuf; a21 = -kfu;

L1 = [(1/2)*((a11+a22)+((a11-a22)^2+4*kfu*kuf).^(1/2))]; L2 = [(1/2)*((a11+a22)-((a11-a22)^2+4*kfu*kuf).^(1/2))]; for i=1:length(tmix)

FF=(Izf*(-(L2-a11)*exp(-L1*tmix(i))+(L1-a11)*exp(-L2*tmix(i)))/(L1-L2)); UU=(Izu*(-(L2-a22)*exp(-L1*tmix(i))+(L1-a22)*exp(-L2*tmix(i)))/(L1-L2));

FU=(Efu+Izf*((a21*exp(-L1*tmix(i)))-(a21*exp(-L2*tmix(i))))/(L1-L2)); UF=(Euf+Izu*((a12*exp(-L1*tmix(i)))-(a12*exp(-L2*tmix(i))))/(L1-L2));

calc_FF_pk(i)=FF(1); calc_UU_pk(i)=UU(1); calc_FU_pk(i)=FU(1); calc_UF_pk(i)=UF(1); end;

ChiFF=sum((calc_FF_pk-DataFF).^2); ChiUU=sum((calc_UU_pk-DataUU).^2); ChiFU=sum((calc_FU_pk-DataFU).^2);

100

ChiUF=sum((calc_UF_pk-DataUF).^2); chi2=ChiFF+ChiUU+ChiFU+ChiUF; err2=sqrt(chi2);

101

APPENDIX 2.3 EXCHANGE SPECTROSCOPY PLOTTING SCRIPT function dummy=chi2_simple_plot_Dilil(xarg); global tmix_plot global calc_FF_pk_plot calc_UU_pk_plot calc_FU_pk_plot calc_UF_pk_plot kfu=xarg(1); kuf=xarg(2); Izf=xarg(3); Izu=xarg(4); Efu=xarg(5); Euf=xarg(6); R1f=2.3; % Set to value if desired, ie R1f=[2.4]; R1u=1.76; % Set to value if desired. %R1f=xarg(7); % Set to value if desired, ie R1f=[2.4]; %R1u=xarg(8); a11 = R1f + kfu; a22 = R1u + kuf; a12 = -kuf; a21 = -kfu;

L1 = [(1/2)*((a11+a22)+((a11-a22)^2+4*kfu*kuf).^(1/2))]; L2 = [(1/2)*((a11+a22)-((a11-a22)^2+4*kfu*kuf).^(1/2))]; for i=1:length(tmix_plot)

FF=(Izf*(-(L2-a11)*exp(-L1*tmix_plot(i))+(L1-a11)*exp(-L2*tmix_plot(i)))/(L1-L2)); UU=(Izu*(-(L2-a22)*exp(-L1*tmix_plot(i))+(L1-a22)*exp(-L2*tmix_plot(i)))/(L1-L2));

FU=(Efu+Izf*((a21*exp(-L1*tmix_plot(i)))-(a21*exp(-L2*tmix_plot(i))))/(L1-L2)); UF=(Euf+Izu*((a12*exp(-L1*tmix_plot(i)))-(a12*exp(-L2*tmix_plot(i))))/(L1-L2));

calc_FF_pk_plot(i)=FF(1); calc_UU_pk_plot(i)=UU(1); calc_FU_pk_plot(i)=FU(1); calc_UF_pk_plot(i)=UF(1); end;

102

APPENDIX 3. MONTE CARLO ERROR SIMULATION FOR DETERMININATION ACTIVATION PARAMETERS clear all close all tempfull = [288.15;293.15;298.15;303.15;308.15;313.15]; nsamples = 1000; fileID = fopen('Dil.dat','w'); formatSpec = '%d %d %d\n';

%DATA %Buffer:50 mM acetate, bis-tris propane, HEPES DILUTE = [0.36;0.77;1.22;1.50;1.67;1.79]; %Average of all 5-45 DILERR = [0.03;0.02;0.01;0.02;0.02;0.02]; %SD

DILCOVAR = (DILERR).^2;

MC = mvnrnd(DILUTE,DILCOVAR',nsamples); % Uses covariance... square the STD std(MC);

%FIT DATA lnkft = fittype('log((2.083E10)*x)+((dS-dCp)./1.987)+((x./303.15).*((dCp- (dH./303.15)))./1.987)-((dCp./1.987).*(log(x./303.15)))', 'independent',{'x'},'coefficients',{'dH','dCp','dS'}); %

[fit1,gof1] = fit(tempfull,DILUTE,lnkft,'startpoint',[8000,-610,-30],'algorithm','Trust- Region','Robust','on'); for i=[1:nsamples] DataMC = MC(i,:)'; [fitx]=fit(tempfull,DataMC,lnkft,'startpoint',[fit1.dH,fit1.dCp,fit1.dS],'algorithm','Trust- Region','Robust','on');

F= {fitx.dH,fitx.dCp,fitx.dS}; %F= {fitx.dH,fitx.Ts}; fprintf(fileID,formatSpec,F{1,:}); fprintf('%d ', i); end fclose(fileID); fit1 load Dil.dat fprintf('Entire Dataset') mean(Dil) std(Dil) fprintf('Truncated Dataset')

103

mean(Dil([1:10],:)) std(Dil([1:10],:)) h=errorbar(tempfull,DILUTE,DILERR,'bs','MarkerFaceColor','b','MarkerSize',20); hold on theplot = plot( fit1, tempfull, DILUTE ); set(theplot, 'LineWidth',4) hold off

% Label axes tit=[' SH3 Folding, buffer ']; title(tit,'fontsize',20); legend('buffer','ln(kf, s^-^1/s^-^1)','fit','Location','southeast') xlabel('Temperature, K','fontsize', 20,'fontweight','b'); ylabel('ln(kf, s^-^1/s^-^1)','fontsize',20,'fontweight','b'); set(gca,'fontsize',18,'fontweight','b'); grid on

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APPENDIX 4. WEIGHTED LINEAR LEAST SQUARES REGRESSION FOR DETERMINATION OF ACTIVATION PARAMETERS x = [0.0034704 0.0034112 0.0033540 0.0032987 0.0032452 0.0031934]; y = [-5.31 -4.91 -4.47 -4.21 -4.06 -3.95]; n = numel(x); stdv = [0.03 0.02 0.01 0.02 0.02 0.02]; Invn = 1./n; Invn2 = 1./(n-2); w = (1./(stdv.^2)); Sw = sum(w);

Sx = sum(w.*x); Sy = sum(w.*y); Sxx = sum(w.*(x.^2)); Sxy = sum(w.*(x.*y)); Delta = ((Sw*(Sxx))-(Sx.^2)); A = ((Sxx.*Sy)-(Sx.*Sxy))./Delta; B = ((Sw.*(Sxy))-(Sx.*Sy))./Delta;

%Mid = sum((y-A-(B.*x)).^2); %ErrY = sqrt(Invn2.*Mid);

ErrA = sqrt((Sxx)./Delta); ErrB = sqrt(Sw/Delta);

%SStot = sum((y-MeanY).^2)

deltaH = -B.*1.987 deltaHErr = ErrB.*1.987 deltaS = (1.987*(A-23.76)) deltaSErr = ErrA.*1.987

Syw = sum(y); Sxw = sum(x);

MeanY = Invn.*Syw; MeanX = Invn.*Sxw;

RTop = sum(w.*((x-MeanX).*(y-MeanY))); RTopSquared = (sum(w.*((x-MeanX).^2))).*(sum(w.*((y-MeanY).^2))); RBottom = sqrt(RTopSquared); r=abs(RTop./RBottom) y_fit = A + B*x; clf;set(gcf,'color','w');

105

h=errorbar(x,y,stdv,'rs','MarkerFaceColor','r'); title('SH3 folding, buffer','FontSize',20) hold on; q=plot(x,y_fit,'b.--','linewidth',2); xlabel('x (1/Temperature (1/K)') ylabel('y (ln(ku/T))')

106

REFERENCES

1. Anfinsen CB (1973) Principles that govern the folding of protein chains. Science 181:223-230.

2. Chiti F, Dobson CM (2006) Protein misfolding, functional amyloid, and human disease. Annu Rev Biochem 75:333-366.

3. Liu C, Sawaya MR, Eisenberg D (2011) ₂-microglobulin forms three-dimensional domain-swapped amyloid fibrils with disulfide linkages. Nat Struct Mol Biol 18:49-55.

4. Ruschak AM, Religa TL, Breuer S, Witt S, Kay LE (2010) The proteasome antechamber maintains substrates in an unfolded state. Nature 14:868-71.

5. Eyring H (1935) The activated complex and the absolute rate of chemical reactions. Chem Rev 14:65-77.

6. Evans MG, Polanyi M (1935) Some applications of the transition state method to the calculation of reaction velocities, especially in solution. Trans Faraday Soc 31:875- 894.

7. Chen B, Baase W, Schellman J (1989) Low-temperature unfolding of phage T4 lysozyme. 2. Kinetic investigations. Biochemistry 1989.

8. Arrhenius S (1889) On the reaction rate of the inversion of non-refined sugar upon souring. Z Phys Chem 4:226-248.

9. Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284-304.

10. Einstein A. Investigations on the theory of the Brownian movement. New York, New York: Dover Publications; 1956.

11. Debye PJ. Polar molecules. New York, New York: Chemical Catalog Company; 1929.

12. Rauscher A, Derenyi I, Graf L, Malnasi-Csizmadia A (2012) Internal friction in enzyme reactions. IUBMB Life 65:35-42.

107

13. Perl D, Jacob M, Bano M, Stupak M, Antalik M, Schmid FX (2002) Thermodynamics of a diffusional protein folding reaction. Biophys Chem 96:173-190.

14. Wong H, Stathopulos P, Bonner J, Sawyer M, Meiering E (2004) Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin. J Mol Biol 344:1089-1107.

15. Creighton TE. Proteins: Structures and molecular properties. New York W. H. Freeman and Company; 1993.

16. Kauzmann W (1959) Some factors in the interpretation of protein denaturation. Adv Protein Chem 14:1-63.

17. Becktel WJ, Schellman JA (1987) Protein stability curves. Biopolymers 26:1859- 1877.

18. Privalov PL, Khechinashvili NN (1974) A thermodynamic approach to the problem of stabilization of globular protein structure: A calorimetric study. J Mol Biol 86:665-684.

19. Privalov PL (1979) Stability of proteins. Adv Protein Chem 33:167-236.

20. Privalov PL, Makhatadze GI (1990) Heat capacity of proteins. II partial molar heat capacity of the unfolded polypeptide chain of proteins: Protein unfolding effects. J Mol Biol 213:385-391.

21. Fersht A. Structure and mechanism in protein science: A guide to enzyme catalysis and protein folding. New York: W. H. Freeman and Company; 1999.

22. Segawa S-I, Sugihara M (1984) Characterization of the transition state of lysozyme unfolding. 1. Effect of protein-solvent interactions on the transition state. Biopolymers 23:2473-2488.

23. Chen B-l, Baase WA, Schellman JA (1989) Low-temperature unfolding of a mutant of phage T4 lysozyme. 2. Kinetic investigations. Biochemistry 28:691-699.

24. Chen X, Matthews CR (1994) Thermodynamic properties of the transition state for the rate-limiting step in the folding of the subunit of tryptophan synthase. Biochemistry 33:6356-6362.

108

25. Oliveberg M, Tan Y-J, Fersht A (1995) Negative activation enthalpies in the kinetics of protein folding. Proc Natl Acad Sci USA 92:8926-8929.

26. Tan Y-J, Oliveberg M, Fersht AR (1996) Titration properties and thermodynamics of the transition state for folding; comparison of two-state and multi-state folding pathways. J Mol Biol 264:377-289.

27. Scalley ML, Baker D (1997) Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability. Proc Natl Acad Sci USA 94:10636-10640.

28. Kuhlman B, Luisi DL, Evans PA, Raleigh DP (1998) Global analysis of the effects of temperature and denaturant on the folding and unfolding kinetics of the N-terminal domain of the protein l9. J Mol Biol 284:1661-1670.

29. Kayatekin C, Cohen N, Matthews CR (2012) Enthalpic barriers dominate the folding and unfolding of the human Cu, Zn superoxide dismutase monomer. J Mol Biol 424:192-202.

30. Gelman H, Wirth AJ, Gruebele M (2016) ReASH as a quantitative probe of in-cell protein dynamics. Biochemistry 55:1968-1976.

31. Guo M, Xu Y, Gruebele M (2012) Temperature dependence of protein folding kinetics in living cells. Proc Natl Acad Sci USA 109:17863-17867.

32. Jackson SE, Fersht AR (1991) Folding of chymotrypsin inhibitor 2. 1: Evidence for a two-state transition. Biochemistry 30:10428-10435.

33. Myers JK, Pace CN, Scholtz JM (1995) Denaturant m values and heat capacity changes: Relation to changes in accessible surface areas of protein unfolding. Protein Sci 4:2138-2148.

34. Schindler T, Schmid FX (1996) Thermodynamics of an extremely rapid protein folding reaction. Biochemistry 35:16833-16842.

35. Holtzer ME, Bretthorst GL, d'Avignon DA, Angeletti RH, Mints LH, Alfred (2001) Temperature dependence of the folding and unfolding kinetics of the GCN4 leucine zipper via 13C-NMR. Biophys J 80:939-951.

109

36. Liao J-M, Mo Z-Y, Wu L-J, Chen J, Lang Y (2008) Binding of calcium ions to Ras promotes Ras guanine nucleotide exchange under emulated physiological conditions. Biochim Biophys Acta 1784:1560-1569.

37. Main ERG, Fulton KF, Jackson SE (1999) Folding pathway of FKBP12 and characterisation of the transition state. J Mol Biol 291:429-444.

38. Gloss LM, Matthews CR (1998) The barriers in the bimolecular and unimolecular folding reactions of the dimeric core domain of the escherchia coli trp repressor are dominated by enthalpic contributions. Biochemistry 37:16000-16010.

39. Hurle MR, Michelotti GA, Crisanti MM, Matthews CR (1987) Characterization of a slow folding reaction for the subunit of tryptophan synthase. Proteins 2:54-63.

40. Cohen RD, Pielak GJ (2017) A cell is more than the sum of its (dilute) parts: A brief history of quinary structure. Protein Sci 26:403-313.

41. Sarkar M, Li C, Pielak GJ (2013) Soft interactions and crowding. Biophys Rev 5:187- 194.

42. Makhatadze GI, Privalov PL (1992) Protein interactions with urea and guanidinium chloride. J Mol Biol 226:491-505.

43. Wallace LA, Sluis-Cremer N, Dirr HW (1998) Equilibrium and kinetic unfolding properties of dimeric human glutathione transferase a1-1. Biochemistry 37:5320- 5328.

44. Estape D, Rinas U (1999) Folding kinetics of the all -sheet protein human basic fibroblast growth factor, a structural homolog of interleukin-1. J Biol Chem 274:34083-34088.

45. Yancey PH, Clark ME, Hand SC, Bowlus RD, Somero GN (1982) Living with water stress: Evolution of osmolyte systems. Science 217:1214-1222.

46. Wood JM (1999) Osmosensing by bacteria: Signals and membrane-based sensors. Microbiol Mol Biol Rev 63:230-262.

47. Russo A, Rosgen J, Bolen D (2003) Osmolyte effects on kinetics of FKBP12 C22A folding coupled with prolyl isomerization. J Mol Biol 330:851-866.

110

48. Bolen DW, Baskakov IV (2001) The osmophobic effect: Natural selection of a thermodynamic force in protein folding. J Mol Biol 310:955-963.

49. Liu Y, Bolen DW (1995) The peptide backbone plays a dominant role in protein stabilization by naturally occurring osmolytes. Biochemistry 34:12884-12891.

50. Mukaiyama A, Koga Y, Takano K, Kanaya S (2008) Osmolyte effect on the stability and folding of a hypethermophilic protein. Proteins: Struct, Funct, Bioinf 378:264- 272.

51. Lin SL, Zarrine-Asfar A, Davidson AR (2009) The osmolyte trimethylamine-N-oxide stabilizes the fyn SH3 domain without altering the structure of its folding transition state. Protein Sci 18:526-536.

52. Ladurner A, Fersht A (1999) Upper limit of the timescale for diffusion and chain collapse in chymotrypsin inhibitor 2. Nat Struct Biol 6:28-31.

53. Erlkamp M, Grobelny S, Winter R (2014) Crowding effects on the temperature and pressure dependent structure, stability and folding kinetics of Staphylococcal nuclease. Phys Chem Chem Phys 16:5965-5976.

54. Homouz D, Perham M, Samiotakis A, Cheung MS, Wittung-Stafshede P (2008) Crowded, cell-like environment induces shape changes in an aspherical protein. Proc Natl Acad Sci USA 105:11754-11759.

55. Hong J, Gierasch LM (2010) Macromolecular crowding remodels the energy landscape of a protein by favoring a more compact unfolded state. J Am Chem Soc 132:10445-10452.

56. Christiansen A, Wittung-Stafshede P (2013) Quantification of excluded volume effects on the folding landscape of Pseudomonas aeruginosa apoazurin in vitro. Biophys J 105:189-1699.

57. Chen E, Christiansen A, Wang Q, Cheung MS, Kliger DS, Wittung-Stafshede P (2012) Effects of macromolecular crowding on burst phase kinetics of cytochrome c folding. Biochemistry 51:9836-9845.

58. Minton AP (1981) Excluded volume as a determinant of macromolecular structure and reactivity. Biopolymers 20:2093-2120.

111

59. Benton LA, Smith AE, Young GB, Pielak GJ (2012) Unexpected effects of macromolecular crowding on protein stability. Biochemistry 51:9773-5.

60. Senske M, Tork L, Born B, Havenith M, Herrmann C, Ebbinghaus S (2014) Protein stabilization by macromolecular crowding through enthalpy rather than entropy. J Am Chem Soc 136:9036-9041.

61. Mukherjee S, Waegele MM, Chowdhury P, Guo L, Gai F (2009) Effect of macromolecular crowding on protein folding dynamics at the secondary structure level. J Mol Biol 393:227-236.

62. Ai X, Zhou Z, Bai Y, Choy W-Y (2006) 15N NMR spin relaxation dispersion study of the molecular crowding effects on protein folding under native conditions. J Am Chem Soc 128:3916-3917.

63. Dill KA, Chan HS (1997) From Levinthal to pathways to funnels. Nat Struct Mol Biol 4:10-19.

64. Smith AE, Zhou LZ, Gorensek AH, Senske M, Pielak GJ (2016) In-cell thermodynamics and a new role for protein surfaces. Proc Natl Acad Sci USA 113:1725-1730.

65. Conlon I, Raff M (2003) Differences in the way mammalian cell and yeast cells coordinate cell growth and cell-cycle progression. J Biol 2:7.1-7.10.

66. Zeskind BJ, Jordan CD, Timp W, Trapani L, Waller G, Horodincu V, Erhrlich DJ, Matsudaira P (2007) Nucleic acid and protein mass mapping by live-cell deep- ultraviolet microscopy. Nat Methods 4:567-569.

67. Cheung MC, LaCroix R, McKenna BK, Liu L, Winkelman J, Ehrlich DJ (2013) Intracellular protien and nucleic acid measured in eight cell types using deep- ultraviolet mass mapping. Cytometry A 83:540-51.

68. Zimmerman S, Trach S (1991) Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli. J Mol Biol 222:599- 620.

69. Cayley S, Lewis BA, Guttman HJ, Record MT (1991) Characterization of the cytoplasm of Escherichia coli K-12 as a function of external osmolarity: Implications for protein-DNA interactions in vivo. J Mol Biol 2:281-300.

112

70. Laurent TC (1971) Enzyme reactions in polymer media. Eur J Biochem 21:498-506.

71. Minton AP, Wilf J (1981) Effect of macromolecular crowding on the structure and function of an enzyme: Glyceraldehyde-3-phosphate dehydrogenase. Biochemistry 20:4821-4826.

72. Pozdnyakova I, Wittung-Stafshede P (2010) Non-linear effects of macromolecular crowding on enzymatic activity of multi-copper oxidase. Biochim Biophys Acta 1804:740-4.

73. Schneider SH, Lockwood SP, Hargreaves DI, Slade DJ, LoConte MA, Logan BE, McLaughlin EE, Conroy MJ, Slade KM (2015) Slowed diffusion and excluded volume both contribute to the effects of macromolecular crowding on alcohol dehydrogenase steady-state kinetics. Biochemistry 54:5898-5906.

74. Pastor IP, Laura; Balcells, Cristina; Vilaseca, Eudald; Madurga, Sergio; Isvoran, Adriana; Cascante, Marta; Mas, Francesc (2014) Effect of crowding by dextrans in enzymatic reactions. Biophys Chem 185:8-13.

75. Balcells C, Pastor I, Viladeca E, Madurga S, Cascante M, Mas F (2014) Macromolecular crowding effect upon in vitro enzyme kinetics: Mixed activation- diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase. J Phys Chem B 118:4062-4068.

76. Homchaudhuri L, Sarma N, Swaminathan R (2006) Effect of crowding by dextrans and ficolls on the rate of alkaline phosphatase-catalyzed hydrolysis: A size- dependent investigation. Biopolymers 83:477-486.

77. Aumiller WM, Davis BW, Hatzakis E, Keating CD (2014) Interactions of macromolecular crowding agents and cosolutes with small-molecule substrates: Effect on horseradish peroxidase activity with two different substrates. J Phys Chem B 118:10624-10632.

78. Kozer N, Kuttner YY, Haran G, Schreiber G (2007) Protein-protein association in polymer solutions: From dilute to semidilute to concentrated. Biophys J 92:2139- 2149.

79. Kozer N, Schreiber G (2004) Effect of crowding on protein-protein association rates: Fundamental differences between low and high mass crowding agents. J Mol Biol 336:763-774.

80. Rubinstein M, Colby RH. Polymer physics. Oxford: Oxford University Press; 2003.

113

81. Sarkar M, Smith AE, Pielak GJ (2013) Impact of reconstituted cytosol on protein stability. Proc Natl Acad Sci USA 110:19342-19347.

82. Monteith WB, Cohen RD, Smith AE, Guzman-Cisneros E, Pielak GJ (2015) Quinary structure modulates protein stability in cells. Proc Natl Acad Sci USA 112:1739-1742.

83. Cohen RD, Pielak GJ (2016) Electrostatic contributions to protein quinary structure. J Am Chem Soc 138:13139-13142.

84. Crowley PB, Brett K, Muldoon J (2008) NMR spectroscopy reveals cytochrome c poly(ethylene glycol) interactions. ChemBiochem 9:685-688.

85. Wang Q, Zhuravleva A, Gierasch LM (2011) Exploring weak, transient protein- protein interactions in crowded in vivo environments by in-cell NMR spectroscopy. Biochemistry 50:9225-9236.

86. Vöpel T, Makhatadze G (2012) Enzyme activity in the crowded millieu. PLoS one 7:e39418.

87. Jiang M, Guo Z (2007) Effecs of macromolecular crowding on the intrinsic catalytic efficiency and structure of enterobactin-specific isochorismate synthase. J Am Chem Soc 129:730-731.

88. Wenner JR, Bloomfield VA (1999) Crowding effects on EcoRV kinetics and binding. Biophys J 77:3234-3241.

89. Poggi CS, Kristin M. (2015) Macromolecular crowding and the steady-state kinetics of malate dehydrogenase. Biochemistry 54:260-267.

90. Wilcox AE, LoConte M, Slade K (2016) Effects of macromolecular crowding on alcohol dehydrogenaase activity are substrate-dependent. Biochemistry 55:3350- 3358.

91. Pozdnyakova I, Wittung-Stafshede P (2010) Non-linear effects of macromolecular crowding on enzymatic activity of multi-copper oxidase. Biochim Biophys Acta 1804:740-744.

92. Derham BK, Harding JJ (2006) The effect of the presence of globular proteins and elongated polymers on enzyme activity. Biochim Biophys Acta 1764:1000-1006.

114

93. Sasaki Y, Miyoshi D, Sugimoto N (2006) Effect of molecular crowding on DNA polymerase activity. Biotech J 1:440-446.

94. Zimmerman S, Harrison B (1987) Macromolecular crowding increases binding of DNA polymerase to DNA: An adaptive effect. Proc Natl Acad Sci USA 84:1871-1875.

95. Totani K, Ihara Y, Matsuo I, Ito Y (2008) Effects of macromolecular crowding on glycoprotein processing enzymes. J Am Chem Soc 130:2101-2107.

96. Schnell JR, Dyson HJ, Wright PE (2004) Structure, dynamics and catalytic function of dihydrofoflate reductase. Annu Rev Biophys Biomol Struct 33:119-140.

97. Huennekens FM (1996) In search of dihydrofolate reductase. Protein Sci 5:1201- 1208.

98. Fierke CA, Johnson KA, Benkovic SJ (1987) Construction and evaluation of the kinetic scheme associated with dihydrofolate reductase from Escherichia coli. Biochemistry 26:4085-92.

99. Sawaya MR, Kraut J (1997) Loop and subdomain movements in the mechanism of Escherichia coli dihydrofolate reductase: Crystallographic evidence. Biochemistry 36:586-603.

100. Minton AP (1983) The effect of volume occupancy upon the thermodynamic activity of proteins: Some biochemical consequences. Mol Cell Biochem 55:119-140.

101. Rong Y. Probing the structure of dextran systems and their organization. New Brunswick, NJ: Rutgers, The State University of New Jersey; 2008.

102. Loret C, Meunier V, Frith WJ, Fryer PJ (2004) Rheological characterization of the gelation behavior of maltodextrin aqueous solutions. Carbohydr Polym 57:153-163.

103. Iwakura M, Jones BE, Luo J, Matthews CR (1995) A strategy for testing the suitability of cysteine replacements in dihydrofolate reductase from Escherichia coli. J Biochem 117:480-8.

104. Hillcoat BL, Nixon PF, Blakley RL (1967) Effect of substrate decomposition on the spectrophotometric assay of dihydrofolate reductase. Anal Biochem 21:178-89.

115

105. Baccanari D, Phillips A, Smith S, Sinski D, Burchall J (1975) Purification and properties of Escherichia coli dihydrofolate reductase. Biochemistry 14:5267-73.

106. Venturoli D, Rippe B (2005) Ficoll and dextran vs. Globular proteins as probes for testing glomerular permselectivity: Effects of molecular size, shape, charge and deformability. Am J Physiol Renal Physiol 288:F605-F613.

107. Miklos AC, Li C, Sharaf NG, Pielak GJ (2010) Volume exclusion and soft interaction effects on protein stability under crowded conditions. Biochemistry 49:6984-91.

108. Penner MH, Frieden C (1987) Kinetic analysis of the mechanism of Escherichia coli dihydrofolate reductase. J Biol Chem 262:15908-15914.

109. Hayer-Hartl M, Minton AP (2006) A simple semiemperical model for the effect of molecular confinement upon the rate of protein folding. Biochemistry 45:13356- 13360.

110. Zhou H-X, Rivas G, Minton AP (2008) Macromolecular crowding and confinement: Biochemical, biophysical and potential physiological consequences. Annu Rev Biophys 37:375-397.

111. Pastor I, Vilaseca E, Madurga S, Garces JL, Cascante M, Mas F (2011) Effect of crowding by dextrans on the hydrolysis of n-succinyl-l-phenyl-ala-p-nitroanilide catalyszed by a-chymotrypsin. J Phys Chem B 115:1115-1121.

112. Bhojane PP, Duff MR, Patel HC, Vogt ME, Howell EE (2014) Investigation of osmolyte effects on FolM: Comparison with other dihydrofolate reductases. Biochemistry 53:1330-1341.

113. Duff MR, Grubbs J, Serpersu E, Howell EE (2012) Weak interactions between folate and osmolytes in solution. Biochemistry 51:2309-2318.

114. Shkel IA, Knowles DB, Record MT (2015) Separating chemical and excluded volume interactions of polyethylene glycols with native proteins: Comparisons with PEG effects on DNA helix formation. Biopolymers 103:517-527.

115. Dhar A, Samiotakis A, Ebbinghaus S, Nienhaus L, Homouz D, Gruebele M, Cheung MS (2010) Structure, function and folding of phosphoglycerate kinase are strongly perturbed by macromolecular crowding. Proc Natl Acad Sci USA 107:17586-17591.

116

116. Horecker BL, Kornberg A (1948) The extinction coefficients of the reduced band of pyridine nucleotides. J Biol Chem 175:385-390.

117. Baccanari DP, Joyner SS (1981) Dihydrofolate reductase hysteresis and its effect of inhibitor binding analyses. Biochemistry 20:1710-6.

118. Taylor JR. An introduction to error analysis. Mill Valley, CA: University Science Books; 1996.

119. Batchelor JD, Olteanu A, Tripathy A, Pielak GJ (2004) Impact of protein denaturants and stabilizers on water structure. J Am Chem Soc 126:1958-1961.

120. Sadeghi R, Zafarani-Moattar, Taghi M (2004) Thermodynamics of aqueous solutions of polyvinylpyrrolidone. J Chem Thermodyn 36:665-670.

121. Durchschlag H. Specific volumes of biological macromolecules and other molecules of biological interest. In: Hinz H-J, editor. Thermodynamic data for biochemistry and biotechnology. Berlin: Springer-Verlag; 1986. p 45-182.

122. Christiansen A, Wang Q, Samiotakis A, Cheung MS, Wittung-Stafshede P (2010) Factors defining effects of macromolecular crowding on protein stability: An in vitro/in silico case study using cytochrome c. Biochemistry 49.

123. Weast RC, editor. Handbook fo chemistry and physics. 54 ed. Cleveland, OH: CRC Press; 1973.

124. Akabayov SR, Akabayov B, Richardson CC, Wagner G (2013) Molecular crowding enhanced atpase activity of the RNA helicase eIF4A correlates with compaction of its quaternary structure and association with eif4g. J Am Chem Soc 135:10040-10047.

125. Yadav JK (2013) Macromolecular crowding enhances catalytic efficiency and stability of -amylase. ISRN Biotechnol 2013:1-7.

126. Moran-Zorzano MT, Viale AM, Munoz FJ, Alonso-Casajus N, Eydallin GG, Zugasti B, Baroja-Fernandez E, Pozueta-Romero J (2007) Escherichia coli AspP activity is enhanced by macromolecular crowding by both glucose-1,6-bisphosphate and nucleotide sugars. FEBS Lett 581:1034-1040.

127. Paul SS, Sil P, Chakraborty R, Haldar S, Chattopadhyay K (2016) Molecular crowding affects the conformational fluctuations, peroxidase activity, and folding landscape of yeast cytochrome c. Biochemistry 55:2332-2343.

117

128. Halpin J, Huang B, Sun M, Street T (2016) Crowding activates heat shock protein 90. J Biol Chem 291:6447-6445.

129. Asaad N, Engberts JBFN (2003) Cytosol-mimetic chemistry: Kinetics of the trypsin- catalyzed hydrolysis of p-nitrophenyl acetate upon addition of polyethylene glycol and n-tert-butyl acetoacetamide. J Am Chem Soc 125:6874-6875.

130. Suthar MK, Doharey PK, Verma A, Saxena JK (2013) Behavior of Plasmodium falciparum purine nucleoside phosphorylase in macromolecular crowded environment. Int J Biol Macromolec 62:657-662.

131. Sierks MR, Sico C, Zaw M (1997) Solvent and viscosity effects on the rate-limiting product release step of glycoamylase during maltose hydrolysis. Biotechnol Prog 13:601-608.

132. Olsen S (2006) Applications of isothermal titration calorimetry to measure enzyme kinetics and activity in complex solutions. Thermochim Acta 448:12-18.

133. Shahid S, Ahmad F, Hassan IM, Islam A (2015) Relationship between protein stability and functional activity in the presence of macromolecular crowding agents alone and in mixture: An insight into stability-activity trade-off. Arch Biochem Biophys 584:42-50.

134. Cook EC, Creamer TP (2016) Calcineurin in a crowded world. Biochemistry 55:3092- 3101.

135. Nolan V, Sanchez JM, Perillo MA (2015) PEG-induced molecular crowding leads to a relaxed conformation, higher thermal stability and lower catalytic efficiency of Escherichia coli -galactosidase. Colloids Surf, B 136:1202-1206.

136. Zhou H-X (2008) Protein folding in confined and crowded environments. Arch Biochem Biophys 144:724-732.

137. Zhang O, Forman-Kay JD (1995) Structural characterization of folded and unfolded states of an SH3 domain in equilibrium in aqueous buffer. Biochemistry 34:6784- 6794.

138. Evanics F, Bezsonova I, Marsh J, Kitevski JL, Forman-Kay JD, Prosser RS (2006) Tryptophan solvent exposure in folded and unfolded states of an SH3 domain by 19F and 1H NMR. Biochemistry 45:14120-14128.

118

139. Farrow NA, Zhang O, Forman-Kay JD, Kay LE (1994) A heteronuclear correlation experiment for simultaneous determination of 15N longitudinal decay and chemical exchange rates of systems in slow equilibrium. J Biomol NMR 4:727-734.

140. Miklos AC, Li C, Sharaf NG, Pielak GJ (2010) Volume exclusion and soft interaction effects on protein stability under crowded conditions. Biochemistry 49:6984-6991.

141. Attri P, Venkatesu P, Lee M-J (2010) Influence of osmolytes and denaturants on the structure and enzyme activity of alpha-chymotrypsin. J Phys Chem B 114:1471- 1478.

142. Beg I, Minton AP, Islam A, Hassan IM, Ahmad F (2017) The ph dependence of saccharides' influence on thermal denaturation of two model proteins supports an excluded volume model for stabilization generalized to allow for intramolecular electrostatic interactions. J Biol Chem 292:505-511.

143. Beg I, Minton AP, Hassan IM, Islam A, Ahmad F (2015) Thermal stabilization of proteins by mono- and oligosaccharides: Measurement and analysis in the context of an excluded volume model. Biochemistry 54:3594-3603.

144. Ellis RJ (2001) Macromolecular crowding: An important but neglected aspect of the intracellular environment. Curr Opin Struct Biol 11:114-119.

145. Laidler KJ, King MC (1983) Development of transition-state theory. J Phys Chem 87:2657-2664.

146. Hoeltzli SD, Frieden C (1995) Stopped-flow NMR spectroscopy-real-time unfolding studies of 6-19F-tryptophan-labeled Escherichia coli dihydrofolate reductase. Proc Natl Acad Sci USA 92:9318-9322.

147. Hoeltzli SD, Frieden C (1996) Real-time refolding studies of 6-19F-tryptophan labeled e. Coli dihydrofolate reductase using stopped-flow NMR spectroscopy. Biochemistry 35:16843-16851.

148. Hoeltzli SD, Frieden C (1998) Refolding of 6-19F-tryptophan labeled e. Coli dihydrofolate reductase in the presence of ligand: A stopped-flow NMR spectroscopy study. Biochemistry 37:387-398.

149. Cierpicki T, Otlewski J (2001) Amide proton temperature coefficients as hydrogen bond indicators in proteins. J Mol Biol 21:249-261.

119

150. Bezsonova I, Singer A, Choy W-Y, Tollinger M, Forman-Kay JD (2005) Structural comparison of the unstable drkN SH3 domain and a stable mutant. Biochemistry 44:15550-15560.

151. Andersen NH, Neidigh JW, Harris SM, Lee GM, Liu Z, Tong H (1997) Extracting information from the temperature gradients of polypeptide NH chemical shifts. 1. The importance of conformational averaging. J Am Chem Soc 119:8547-8561.

152. Marsh JA, Neale C, Jack FE, Choy W-Y, Lee AY, Crowhurst KA, Forman-Kay JD (2007) Improved structural characterizations of the drkN SH3 domain unfolded state suggest a compact ensemble with native-like and non-native structure. J Mol Biol 367:1494-1510.

153. Mok Y-K, Kay CM, Kay LE, Forman-Kay JD (1999) NOE data demonstrating a compact unfolded state for an SH3 domain under non-denaturing conditions. J Mol Biol 289:619-638.

154. Davison TS, Nie X, Ma W, Lin Y, Ka C, Benchimol S, Arrowsmith CH (2001) Structure and functionality of a designed p53 dimer. J Mol Biol 307:605-617.

155. Charlton LM, Barnes CO, Li C, Orans J, Young GB, Pielak GJ (2008) Residue-level interrogration of macromolecular crowding effects on protein stability. J Am Chem Soc 130:6826-6830.

156. Iwakawa N, Morimoto D, Walinda E, Sugase K, Shirakawa M (2017) Backbone resonance assignments of monomeric SOD1 in dilute and crowded environments. Biomol NMR Assign 11:81-84.

157. Tollinger M, Neale C, Kay LE, Forman-Kay JD (2006) Characterization of the hydrodynamic properties of the folding transition state of an SH3 domain by magnetization transfer NMR spectroscopy. Biochemistry 45:6434-6445.

158. Roos M, Ott M, Hofmann M, Roessler EA, Balbach J, Krushelnitsky AG, Saalwaechter K (2016) Coupling and decoupling of rotational and translational diffusion of proteins under crowding conditions. J Am Chem Soc 138:10365-10372.

159. Li C, Wang Y, Pielak GJ (2009) Translational and rotational diffusion of a small globular protein under crowded conditions. J Phys Chem B 113:13390-13392.

160. Wang Y, Li C, Pielak GJ (2010) Effects of proteins on protein diffusion. J Am Chem Soc 132:9392-9397.

120

161. Fersht AR, Leatherbarrow RJ, Wells TNC (1986) Quantitative analysis of structure- activity relationships in engineered proteins by linear free-energy relationships. Nature 322:284-286.

162. Matouschek A, Kellis JT, Serrano L, Bycroft M, Fersht AR (1990) Transient folding intermediates characterized by protein engineering. Nature 346:440-445.

163. Matthews CR (1993) Pathways of protein folding. Annu Rev Biochem 63:653-683.

164. Mikaelsson T, Aden J, Johansson L, Wittung-Stafshede P (2013) Direct observation of protein unfolded state compaction in the presence of macromolecular crowding. Biophys J 104:694-704.

165. Perham M, Stagg L, Wittung-Stafshede P (2007) Macromolecular crowding increases structural content of folded proteins. FEBS Lett 581:5065-5069.

166. Sarkar M, Pielak GJ (2014) An osmolyte mitigates the destabilizing effect of protein crowding. Protein Sci 23:1161-1164.

167. Timasheff SN, Xie G (2003) Preferential interactions of urea with lysozyme and their linkage to protein denaturation. Biophys Chem 105:421-448.

168. Lee JC, Timasheff SN (1981) The stabilization of proteins by sucrose. J Biol Chem 256:7193-7201.

169. Xie G, Timasheff S (1997) Mechanism of the stabilization of Ribonuclease A by sorbitol: Preferential hydration is greater for the denatured than for the native protein. Protein Sci 6:211-221.

170. Xie G, Timasheff S (1997) The thermodynamic mechanism of protein stabilization by trehalose. Biophys Chem 64:25-43.

171. Xie G, Timasheff SN (1997) Temperature dependence of the preferential interactions of ribonuclease A in aqueous co-solvent systems: Thermodynamic analysis. Protein Sci 6:222-232.

172. Davis-Searles PR, Saunders AJ, Erie DA, Winzor DJ, Pielak GJ (2001) Interpreting the effects of small uncharged solutes on protein-folding equilibria. Annu Rev Biophys Biomol Struct 30:271-306.

121

173. Bhat R, Timasheff S (1992) Steric exclusion is the principal source of the preferential hydration of proteins in the presence of polyethylene glycols. Protein Sci 1:1133- 1143.

174. Bolen DW (2001) Protein stabilization by naturally occurring osmolytes. Methods Mol Biol 168:17-36.

175. Auton M, Rosgen J, Sinev M, Holthauzen LMF, Bolen DW (2011) Osmolyte effects on protein stability and solubility: A balancing act between backbone and side- chains. Biophys Chem 159:90-99.

176. Auton M, Bolen D (2005) Predicting the energetics of osmolyte-induced protein folding/unfolding. Proc Natl Acad Sci USA 102:15065-15068.

177. Bolen D, Rose G (2008) Structure and energetics of the hydrogen-bonded backbone in protein folding. Annu Rev Biochem 77:339-362.

178. Politi R, Harries D (2010) Enthalpically driven peptide stabilization by protective osmolytes. Chem Commun 46:6449-6451.

179. Gekko K, Morikawa T (1981) Preferential hydration of bovine serum albumin in polyhydric alcohol-water mixtures. J Biochem 90:39-50.

180. Cho SS, Reddy G, Straub JE, Thirumalai D (2011) Entropic stabilization of proteins by TMAO. J Phys Chem B 115:13401-13407.

181. Linhananta A, Hadizadeh S, Plotkin SS (2011) An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability. Biophys J 100:459-468.

182. Ratnaparkhi GS, Varadarajan R (2001) Osmolytes stabilize Ribonuclease S by stabilizing its fragments s protein and s peptide to compact folding-competent states. J Biol Chem 276:28789-28798.

183. Street TO, Bolen DW, Rose G (2006) A molecular mechanism for osmolyte-induced protein stability. Proc Natl Acad Sci USA 103:17064-17065.

184. Barnett GV, Razinkov VI, Kerwin BA, Blake S, Qi W, Curtis RA, Roberts CJ (2016) Osmolyte effects on monoclonal antibody stability and concentration-dependent protein interactions with water and common osmolytes. J Phys Chem B 120:3318- 3330.

122

185. Liao Y-T, Manson AC, DeLyser MR, Noid WG, Cremer PS (2017) Trimethylamine N- oxide stabilizes proteins via a distinct mechanism compared with betaine and glycine. Proc Natl Acad Sci USA 114:2479-2484.

186. van der Berg B, Wain R, Dobson CM, Ellis RJ (2000) Macromolecular crowding perturbs protein refolding kinetics: Implications for folding inside the cell. EMBO J 19:3870-3875.

187. Sharp K (2015) Analysis of the size dependence of macromolecular crowding shows that smaller is better. Proc Natl Acad Sci USA 112:7990-7995.

188. Miklos AC, Sarkar M, Wang Y, Pielak GJ (2011) Protein crowding tunes protein stability. J Am Chem Soc 133:7116-7120.

189. Stadmiller SS, Gorensek-Benitez AH, Guseman AJ, Pielak GJ (2017) Osmotic-shock induced protein destabilization in living cells and its reversal by glycine betaine. J Mol Biol 429:1155-1161.

190. Lee JH, Zhang D, Hughes C, Okuno Y, Sekhar A, Cavagnero S (2015) Heterogeneous binding of the SH3 client protein to the DnaK molecular chaperone. Proc Natl Acad Sci USA 112:4206-4215.

123