BiophysicalInvestigationsof Allostery in E.coli ...

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Biophysical Investigations of Allostery in E.coli Adenylate Kinase Using Entropy Enhancing Mutations by Harry Gustavo Saavedra Espinoza A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy Baltimore, Maryland May, 2015 2015 Harry G. Saavedra Espinoza All Rights Reserved

Transcript of BiophysicalInvestigationsof Allostery in E.coli ...

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Biophysical Investigations of Allostery in

E.coli Adenylate Kinase Using Entropy

Enhancing Mutations

by

Harry Gustavo Saavedra Espinoza

A dissertation submitted to Johns Hopkins University

in conformity with the requirements for the degree of

Doctor of Philosophy

Baltimore, Maryland

May, 2015

2015 Harry G. Saavedra Espinoza

All Rights Reserved

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Abstract

Allostery is the regulatory effect that a perturbation in one region has on an-

other distal site of the same macromolecule. Although allostery has been studied

extensively, understanding of how a perturbation in one region can affect other

region(s) is still incomplete. For a long time, allostery has been regarded as a

structural-based phenomenon. However, it is currently known that allostery can

also be manifested without perturbation in the crystal structure. Also, it has

been demonstrated from studies of thermal adapted enzymes, that enzyme func-

tion regulation can be promoted by increasing the conformational flexibility in

regions other than the active site. To understand these different facets of allostery,

we used Escherichia coli adenylate kinase as a model system. This enzyme is

composed of three distinct domains: The LID, CORE and AMPbd domains. To

answer the question of how conformational perturbations regulate enzyme func-

tion, entropy-enhancing Gly substitutions were used on distal uncharged solvent

exposed residues located far from the active site. Mutations on the three do-

mains were chosen in order to avoid or minimize structural distortions. Subse-

quently, the impact of increased conformational flexibility on the ensemble, bind-

ing affinity and catalytic activity were investigated with DSC, ITC and catalytic

activity assays. In addition, ensemble modulation was characterized by combin-

ing HX-NMR and ITC techniques. Together, the results show that enzymes can

use local unfolding in regions distal to the active site to regulate macromolec-

ular function. This regulation arises predominantly from the redistribution of

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the probabilities of states promoted by local destabilization of the enzyme. Also,

this work indicates that allostery can also be understood from a thermodynamic

point of view. Finally, it is shown that the LID interacts with the other domains.

Advisor: Prof. Vincent Hilser

Reader: Prof. Doug Barrick

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To my beloved mother, Zoraida, wife, Alicia, and son Rodrigo.

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Preface

Life as well as scientific research are not traveled alone. During my years in gradu-

ate school, I was very fortunate to be surrounded by great and supporting people.

Above all, I would like to thank my advisor, Dr. Vincent Hilser for giving me the

opportunity to carry out research in his laboratory. The knowledge I have acquired

from him is invaluable. Not only at the scientific level but also at the personal

level. I really appreciate his efforts in transmitting the value of clear writing and

effective presentations.

I am also indebted to my thesis committee members: Dr. Richard Cone, Dr.

Bertrand Garcia-Moreno, Dr. Doug Barrick and Dr. Greg Bowman. The guidance

and suggestions they gave in every thesis review were really helpful to overcome

different obstacles I faced out during my research journey. Their mentorship com-

plemented Dr. Hilser’s guidance that provided me a wide scientific perspective.

The other person to whom I am eternally grateful is Dr. James Wrabl. He was

always ready to share with me not only insightful ideas but also research expe-

rience. In addition, I would like to thank present and previous students in the

lab, especially Dr. Travis Schrank, who trained me on protein expression and pu-

rification, Dr. William Elam, who showed my how to use the ITC calorimeter,

Dr. Jing Li, who shared with me her expertise on mutagenesis, Jeremy Anderson,

who shared with me 15N-labeled V142G; and, Andrew Martens, Hesam Motlagh,

Jordan White, Alex Chin and James Rives for their useful feedback on my research.

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I also like to thank our great collaborators -and great people- who played impor-

tant roles in my research. Dr. Arne Schon for sharing his extensive knowledge of

the experimental nuances associated with DSC experiments. Dr. Ananya Majun-

dar for training me on the operation of the NMR spectrometer, and, Dr. Katherine

Tripp for her logistic support on the ITC and DSC calorimeters.

Last, but certainly not least, I would like to acknowledge my mother, Zoraida,

my wife, Alicia, and my son Rodrigo for their love, patience and support during

my years in graduate school.

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Table of Contents

Table of Contents vi

List of Tables x

List of Figures xii

List of Abbreviations xix

1 Introduction 1

1.1 Allostery, structural and ensemble views . . . . . . . . . . . . . . . 1

1.2 Thermal adaptations of enzymes . . . . . . . . . . . . . . . . . . . . 3

1.3 E. coli adenylate kinase as a model system . . . . . . . . . . . . . . 4

1.4 Mutational strategy employed to investigate allostery . . . . . . . . 5

1.5 Previous results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5.1 Glycine mutation promotes local unfolding . . . . . . . . . . 5

1.5.2 One mutation in the LID does not distort the crystallo-

graphic structure . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5.3 Allostery can occur in the absence of structural distortion . 6

1.6 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Materials and methods of AK preparation 14

2.1 Selection of entropy enhancing glycine mutations . . . . . . . . . . 14

2.2 Site directed mutagenesis . . . . . . . . . . . . . . . . . . . . . . . . 15

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2.3 LIDLESS plasmid construction . . . . . . . . . . . . . . . . . . . . 16

2.4 Protein expression,purification, and storage . . . . . . . . . . . . . . 17

3 Calorimetric determination of interdomain interactions and sta-

bility of AK constructs 21

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.1 Protein preparation . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.2 DSC experimental design . . . . . . . . . . . . . . . . . . . . 23

3.3.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4.1 The CORE-AMPbd unfolds as a single domain and it is cou-

pled to the LID . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4.2 Single and double mutants promote local unfolding . . . . . 30

3.4.3 Coupling interactions are still present even though the LID

is unfolded . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.4 Local unfolding mechanism for stability change . . . . . . . 31

3.4.5 Local unfolding modulates the conformational ensemble . . . 32

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Calorimetric determination of inhibitor binding affinity of AK

constructs 49

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3.1 Protein preparation . . . . . . . . . . . . . . . . . . . . . . . 51

4.3.2 ITC experimental design . . . . . . . . . . . . . . . . . . . . 51

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4.3.3 Linkage analysis between local unfolding and ensemble mod-

ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3.4 Prediction of ∆Ha and ∆Ga . . . . . . . . . . . . . . . . . . 54

4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4.1 Local unfolding promoted by mutations modulates binding

affinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4.2 The CORE-AMPbd can also bind Ap5A in the absence of

the LID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.4.3 Trends of free energy and enthalpy of binding as functions

of temperature can be predicted using EAM . . . . . . . . . 56

4.4.4 Double mutations in the LID completely depopulate the

folded state at 40 . . . . . . . . . . . . . . . . . . . . . . . 57

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Measurement of catalytic rate of AK constructs 69

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3.1 Measurements of catalytic activity in the reverse reaction . . 71

5.3.2 Transition state characterization . . . . . . . . . . . . . . . . 72

5.3.3 Exploration of kcat modulation through a random Bi Bi mech-

anism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.4.1 Mutational effects are temperature dependent . . . . . . . . 73

5.4.2 Local unfolding modulates kcat . . . . . . . . . . . . . . . . . 74

5.4.3 LIDLESS exhibits marginal catalytic activity . . . . . . . . 75

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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6 Characterization of the ensemble modulation using HX-NMR and

ITC 83

6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . 85

6.4 Data acquisition and processing . . . . . . . . . . . . . . . . . . . . 86

6.5 Domain stabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.6 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.6.1 The CORE is the most stable domain. . . . . . . . . . . . . 89

6.6.2 V142G modulates the conformational ensemble. . . . . . . . 89

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7 Concluding remarks 100

7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.2 Future directions and experiments . . . . . . . . . . . . . . . . . . . 101

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List of Tables

3.1 Summary of the thermodynamic parameters obtained from DSC. . . 43

3.2 Stability perturbation of AK domains promoted by Gly mutations. 44

4.1 Intrinsic enthalpy of binding (∆CP,o) of AK constructs. . . . . . . . 68

5.1 Representative values of kcat at 25 . . . . . . . . . . . . . . . . . . 79

5.2 Characterization of the transition state using the linear Eyring-

Polanyi equation, see Eq. 5.3. . . . . . . . . . . . . . . . . . . . . . 80

6.1 ∆GHX of L83 and V106 in WT. . . . . . . . . . . . . . . . . . . . . 91

6.2 ∆GHX of residues L83 and V106 in V142G. . . . . . . . . . . . . . 94

6.3 ∆Ga and ∆GHX values for WT and V142G at 37 . . . . . . . . . . 97

6.4 Domain stabilities in WT and V142G at 37 . . . . . . . . . . . . . 97

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List of Figures

1.1 E. coli AK: domains and catalytic scheme. . . . . . . . . . . . . . . 10

1.2 Local unfolding promoted by V142G affects neighboring residues. . 11

1.3 V142G can destabilize the entire LID domain . . . . . . . . . . . . 12

1.4 Mutational effects introduced by one mutation do not affect the

crystallographic structure. . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Modulation of binding affinity at different temperatures. . . . . . . 13

2.1 Selected Gly mutations on uncharged solvent exposed residues. . . . 19

2.2 LIDLESS plasmid construction. . . . . . . . . . . . . . . . . . . . . 20

3.1 Mutation positions in AK used for DSC experiments shown in red. . 34

3.2 Thermal unfolding simulation of the CORE-AMPbd and the LID

based on Eq. 3.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Corrected 〈∆CP,tr〉 of LIDLESS upon removing the stability effects

of the flexible linker, see Eq. 3.12 . . . . . . . . . . . . . . . . . . . 36

3.4 Comparison of 〈∆CP,tr〉 profiles of WT and LIDLESS. Decreased

Tm of LIDLESS is clearly evident. . . . . . . . . . . . . . . . . . . . 37

3.5 〈∆CP,tr〉 profiles of WT, A55G and A73G. Single mutants exhibit a

small decrease in Tm as compared to WT. . . . . . . . . . . . . . . 38

3.6 〈∆CP,tr〉 profiles of WT, V135G, V142G and V135G/V142G. . . . . 39

3.7 〈∆CP,tr〉 profiles of WT, A73G, V142G and A73G/V142G. . . . . . 40

3.8 ∆CP associated with the unfolding of the CORE-AMPbd . . . . . . 41

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3.9 ∆CP associated with the unfolding of the LID . . . . . . . . . . . . 42

3.10 Thermal stabilities calculated according to thermodynamic param-

eters from Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.11 Coupling interaction (φ)between the LID and CORE-AMPbd in

WT at 37 , based on Fig. 3.10 (b) . . . . . . . . . . . . . . . . . 46

3.12 Theoretical state probabilities vs temperature plots determined us-

ing values from Table 3.1 and Eq. 3.1 . . . . . . . . . . . . . . . . . 47

3.13 Probabilities of the folded state of different constructs calculated at

37 using values from Table 3.1. . . . . . . . . . . . . . . . . . . . 48

4.1 Simulations of ∆Ha as a function of temperature of AK mutants

using Eq. 4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Simulation of ∆Ga at different temperatures of AK mutants using

Eq. 4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 Apparent enthalpies of binding of AK constructs vs temperature

(∆Ha vs T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4 Apparent free energies of binding of AK constructs vs temperature

(∆Ga vs T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.5 Representative ITC titration curves at 37 with respective fitting

parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.6 Representative binding signatures at 37 . . . . . . . . . . . . . . 64

4.7 Simulated ∆Ha of V135G/V142G as a function of temperature using

Eq. 4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.8 Simulated ∆Ga of V135G/V142G as a function of temperature using

Eq. 4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.9 Simulated probabilities of states of simulated V135G/V142G in the

absence of Ap5A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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5.1 Kinetic model for AK. . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.2 Expected ln(kcat/T ) vs 1000/T using Eq. 5.4. . . . . . . . . . . . . 77

5.3 Experimental data fitted to the linear form of the Eyring-Polanyi

equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.4 Simulation of mutational effects of A55G and A73G on kcat. . . . . 81

5.5 Simulation of mutational effects of V135G and V142G on kcat. . . . 82

6.1 Location of residues in the EX2 in WT. . . . . . . . . . . . . . . . . 91

6.2 The apparent rate constant (kex) of residues L83 and V106 in WT. 92

6.3 Residues in the EX2 regime in WT. . . . . . . . . . . . . . . . . . . 93

6.4 Location of residues in the EX2 regime in V142G. . . . . . . . . . . 94

6.5 The apparent rate constant (kex) of residues L83 and V106 in V142G. 95

6.6 Residues in the EX2 regime in V142G. . . . . . . . . . . . . . . . . 96

6.7 Graphical representation of ∆GLID and ∆gmut. . . . . . . . . . . . 98

6.8 Probabilities of the folded state of WT and V142G at 37 using

values from Table 6.4. . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.1 Comparisson between the area under the data points (∆Hcal) and

the van’t Hoff enthalpy (∆HvH) . . . . . . . . . . . . . . . . . . . . 119

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List of Abbreviations

ADP Adenosine diphosphate

AMP Adenosine monophosphate

ATP Adenosine triphosphate

Ala Alanine

AK Escherichia coli adenylate kinase

AMP Adenosine monophosphate

Ap5A P1, P5-Di-(adenosine- 5’)-pentaphosphate

ATP Adenosine triphosphate

CA CORE-AMPbd domain

ddH2O Double-distilled water

DSC Differential scanning calorimetry

DMSO Dimethyl sulfoxide

EAM Ensemble Allosteric Model

F Folded state

Gly Glycine

HX-NMR Hydrogen/deuterium exchange NMR

HSQC Heteronuclear single quantum coherence spectroscopy

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ITC Isothermal titration calorimetry

IPTG Isopropyl-D-thiogalactopyranoside

K Equilibrium constant

kcat Catalytic rate

KNF Koshland-Nemethy-Filmer

LU Locally unfolded state

MWC Monod-Wyman-Changeux

NADP Nicotinamide adenine dinucleotide phosphate

NADPH Nicotinamide adenine dinucleotide phosphate reduced

NMR Nuclear magnetic resonance

PCR Polymerase chain reaction

Q Conformational partition function

R Gas constant, (1.986 cal/mol*K)

SDS-PAGE Sodium dodecyl sulfate polyacrylamide gel electrophoresis

T Temperature

Tm Melting temperature

U Unfolded state

Val Valine

WT Wild type

∆CP Change in heat capacity at constant pressure

∆H Change in standard-state enthalpy

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∆G Change in standard-state free energy

∆S Change in standard-state entropy

∆∆G Difference in change in standard-state free energy

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Chapter 1

Introduction

1.1 Allostery, structural and ensemble views

Allostery is the regulation of protein function by remote perturbations such as, but

not restricted to, ligand binding, mutations, change in temperature, and change

in pH. The understanding of this action-at-a-distance regulation is fundamental

to elucidating thermal adaptation, cell signaling and diseases. Overall, functional

regulation in one protein can affect the entire homeostasis of the cell [1]. Allostery

was first described by Monod and Jacob [2] in 1961 and mathematically formulated

by Monod, Wyman, and Changeux in 1965 [3] and by Koshland, Nemethy and

Filmer in 1966 [4]. Theories of allostery can be viewed as belonging to one of two

broad classes: structure-based allostery or ensemble-based (dynamic) allostery.

Structural views of allostery often fall into one of two subcategories. In the

concerted MWC (Monod-Wyman-Changeux) model, proteins can only visit two

states, one having only high affinity subunits and the other having only low con-

formational affinity subunits. Also, binding affinity depends only on the state of

the subunit. The underlying assumption of this model is that there is coupling

between subunits; that is, the conformational change in one subunit promotes

conformational changes in another one. On the other hand, the KNF (Koshland-

Nemethy-Filmer) model states that proteins visit sequential states from the un-

bound to the fully bound state as sites fill with ligand. This model assumes that

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ligand binding induces conformational changes in the whole protein that increases

the binding affinity of the unbound subunits. In both models, allostery is the re-

sult of mass action between low- and high-affinity states, taking proteins as static

structural macromolecules.

Since the realization that proteins are dynamic macromolecules, the concept of

dynamic allostery has been emerging. Cooper and Dryden [5] introduced the idea

of allostery in the absence of structural change. In other words, allostery can be

an entropic effect that results from conformational fluctuations around the mean.

The importance of fluctuations in regulation of enzyme functions is also stated in

the work of Somero et al. [6, 7]. They observed that ortholog lactate dehydroge-

nases (LDHs) from cold adapted fish have higher activity and lower affinity than

those from warm adapted fish. Interestingly, they also observed that cold adapted

LDHs present more Gly residues outside the active site. Based on their findings,

they hypothesized that proteins adapted their functions by modulating the confor-

mational flexibility (i.e. modulating the conformational entropy) in regions other

than the active site.

Recently, several observations cannot be explained by models based on confor-

mational changes. For example, it has been shown that allostery can exclusively

arise due to changes in conformational motions [8] and in the absence of commu-

nicating structural pathway [9]. Furthermore, allostery can manifest in disordered

domains [10] and intrinsically disordered proteins [11]. In order to reconcile these

results, our lab has developed the Ensemble Allosteric Model (EAM) [13] in which

allostery emerges as the conformational ensemble is modulated by, but not lim-

ited to, ligand binding or mutations. According to the EAM, allostery can be

described simply in terms of domain stabilities and energetic interactions between

them. Thus, crystallographic structure is not necessary a priori although a struc-

tural model of allostery can be considered a special case of EAM. The models and

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analysis presented in this thesis are based on the ensemble redistribution stand-

point.

1.2 Thermal adaptations of enzymes

Cold adapted organisms do not produce more enzyme to survive at lower tem-

peratures. Instead, they adapt enzyme function because no extra metabolic cost

is involved. Enzymes have evolved to function at different temperatures without

extreme changes in their amino acid sequence [6]. Therefore, more flexible en-

zymes would visit binding competent states more easily and counterbalance lower

thermal energy and higher viscosity.

Studies led by Somero and colleagues [6, 7] on enzyme function of ortholog LDH

molecules from cold and warm adapted fish have shed some light on the thermal

adaptation of enzymes. Analysis of amino acid sequences of cold adapted LDHs

revealed more Gly residues in regions outside the active site [6]. Interestingly,

these enzymes presented lower affinity (higher Km) and higher catalytic activity

(kcat) than those of warm adapted LDHs. Based on their findings, Somero and col-

leagues hypothesized that enzymes thermally adapt their function by modulating

their conformational flexibility through sequence changes in region other than the

active site. Since it is known that enzymes exist as a ensemble of states [14, 21, 22],

Somero and colleagues explained their results in the context of ensemble modu-

lation. Higher flexibility increases the population of binding incompetent states,

thus decreasing the observed binding affinity, and increases the speed of catalytic

steps, increasing the catalytic activity. Because less energy is needed to promote

rate-limiting conformational changes and more ordered enzyme-substrate complex

are involved, lower ∆H‡ and more negative ∆S‡ are expected to be observed. As

a result, the activation energy barrier decreases (involving higher kcat) but not at

the same extent as ∆H‡ due to compensating effects.

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To investigate the relationship between conformational fluctuations and en-

zyme function, i.e. dynamic allostery, we took the ideas presented by Somero

and colleagues as a starting point. The flexibility was increased through entropic

enhancing mutations that avoid or minimize structural distortions in our model

system (E. coli adenylate kinase). Mutations were introduced according to a strat-

egy developed in our lab. Then, stabilities were characterized and enzyme function

of wild type (WT) and mutants at different temperatures. The model system and

the mutational strategy are explained in detail in the next two sections.

1.3 E. coli adenylate kinase as a model system

Escherichia coli adenylate kinase (AK) is a 214 residue enzyme that catalyzes

the interconversion of ATP and AMP into two molecules of ADP. Its function is

essential to maintaining the homeostais of the cell. AK is composed of three specific

domains, the LID, the CORE and AMPbd domains, see Fig. 1.1. During catalysis,

the LID and AMPbd undergo large conformational changes, forming the active site.

Interestingly, these two regions are highly dynamic before binding, allowing the

enzyme to visit conformations similar to the ligand-bound state [15]. This results

suggest that ligands select the binding competent states (conformational selection)

without inducing any significant conformational change. It has been proposed that

residues exist that function as hinges of the LID and AMPbd domains, based on

a close inspection of the crystallographic structures of the apo and holo states

of the Aquifex AK [16]. However, previous studies [9], as well as data analysis

in this thesis, show that regulation of enzyme function is instead promoted by

conformational fluctuations. Therefore, the idea of residues working as molecular

hinges can be discarded.

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1.4 Mutational strategy employed to investigate

allostery

Glycine promotes local unfolding and hence increases conformational flexibility,

due to the elimination of steric constraints. This residue confers increased flexibility

because it only has a hydrogen as a side chain, presenting a broader φ, ψ space in

the Ramachandran plot. This characteristic allows Gly to be in turns, loops and

in crowded regions forbidden for other larger residues.

Based on the Somero hypothesis, our lab developed a strategy to promote

conformational fluctuations avoiding or minimizing structural perturbations [9].

That is, the conformational entropy is increased while the crystallographic struc-

ture is not perturbed. For that purpose, selected residue positions are mutated

to entropy-enhancing Gly residues. Residues to be mutated should be uncharged,

solvent exposed residues that are not involved in any intramolecular interaction.

In addition, side chains of the chosen residues should be far from the active site

and they should avoid any contact with ligand(s).

To investigate allostery, amino acid substitutions are made in different domains

of AK and their effects on stability and enzyme function, which involves binding

and catalysis, are measured through calorimetric techniques, NMR hydrogen ex-

change and catalytic activity assays. Mutational impact on the conformational

ensemble is determined by comparing the probability of states of the WT with

those of mutants.

1.5 Previous results

1.5.1 Glycine mutation promotes local unfolding

Val to Gly mutations in the LID domain have higher impact on the conforma-

tional entropy. For that reason, 1H-15N HSQC NMR spectra from WT and V142G

5

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were collected at 21 and at 33 [9]. At 21 , peaks corresponding to residues

surrounding V142G mutation become undetectable. In addition, no new peaks

appear, indicating extreme broadening of peaks due to a fast chemical exchange

process induced by local unfolding. The almost perfect overlap of spectra, indicates

very similar folded states at this temperature, see Fig. 1.2. When temperature

is increased to 33 , residues from position 109 to 165 become undetectable. It

is clearly observed that temperature affects the extent of local unfolding. Also,

mutational effects of V142G are located not only on the entire LID domain but

also on some residues of the CORE, see Fig. 1.3.

1.5.2 One mutation in the LID does not distort the crys-

tallographic structure

Comparison of the crystal structure of the complex WT-Ap5A with that of V148G-

Ap5A shows that one solvent exposed Val to Gly mutation does not perturb the

protein structure in the bound state. In other words, this result points out that a

single mutation only perturbs the dynamics of the unbound state, increasing the

population of partially unfolded and unfolded states. However, this perturbation

is negligible at low temperature according to the overlap of 1H-15N HSQC NMR

spectra of WT and V142G at 21 .

1.5.3 Allostery can occur in the absence of structural dis-

tortion

V148G does not perturb the crystallographic structure. However, V148G, along

with V135G and V142G, modulate binding affinity [9]. These three single mutants

have the same effect on binding affinity of Ap5A, see inset Fig. 1.5. In addition,

allostery in the absence of conformational changes has been observed in other en-

zymes. Popovych and colleagues found that cAMP binds the two subunits of the

catabolite activator protein (CAP) following a negative cooperativity process. The

6

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binding of the first cAMP is associated with higher protein motions. Neverthe-

less, the binding of the second cAMP has a dampening effect on protein motions.

Interestingly, the binding of one cAMP does not induce conformational change in

the other subunit [8].

1.6 Thesis overview

Allostery can be the result of higher flexibility in regions other than the active site

in the absence of any structural alteration. To answer the question of how allostery

arises, we proposed the hypothesis that proteins modulate enzyme function by pro-

moting local unfolding without any structural distortion in distal regions from the

catalytic site. To test, this hypothesis, we used Gly substitutions in the LID, CORE

and AMPbd according to the mutational strategy previously introduced. Then we

investigated the effect of mutations in binding affinity and catalytic activity.

In Chapter 2, Gly mutations were selected according to the strategy developed

in our lab. Substitutions were done in solvent exposed residues that are distal

from the active site. For that purpose, we inspected the crystallographic structure

of WT AK in the apo and holo forms. Details of plasmid preparations, protein

expression, and purification of Gly and LIDLESS mutants are also described.

In Chapter 3, the effect of Gly mutations on stability and ensemble modulation

was investigated through differential scanning calorimetry in the absence of any

ligand. Also, the energetic coupling between the LID and CORE-AMPbd domains

were investigated by replacing the whole LID with a short Gly-rich linker (LID-

LESS construct). It was found that mutations affected stability, especially those

located in the LID domain. The effect of local unfolding was directly observed

as shifts in unfolding transitions. The ensemble probability of states was then

calculated according to a sequential three-state model. It was determined that

the population of the folded state in WT represents 95% of all the states visited

7

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by AK at 37 . The other 5% corresponds to an intermediate state whereby the

LID is unfolded. As expected, the population of the folded state was reduced by

mutations. For instance, the probability of the folded state dropped to 54% in

V135G at the same temperature. Furthermore, it was also found that the stability

of the CORE-AMPbd increases in the absence of the LID (LIDLESS) and that

the CORE and AMPbd unfold as a single domain, suggesting positive coupling

between them. This result shows that coupling interactions are present in WT.

In Chapter 4, the impact of local unfolding on binding affinity was studied using

isothermal titration calorimetry (ITC). Binding experiments were carried out in the

presence of saturating conditions of the non-hydrolyzable inhibitor Ap5A. It was

found that local unfolding promoted by Gly mutations decreases binding affinity to

different extents. This effect can be explained by the modulation of the ensemble

of states, whereby the population of low-affinity state is increased. Moreover, even

though the LID was removed, AK could marginally bind Ap5A.

In Chapter 5, the catalytic activity of the different AK constructions were

characterized in the direction of the formation of ATP and AMP (reverse reaction)

under saturating concentrations of substrates. It was found that local unfolding

can regulate the catalytic rate (kcat). Single mutations in the LID (V135G and

V142G) do not change kcat between 15 and 40 . However, two simultaneous

mutations in the LID (V134G/V142G) decrease kcat. On the other hand, mutations

in the CORE (A73G) and AMPbd (A55G) domains increase kcat. Interestingly, the

kcat of A73G is increased to the value observed in A55G, when V142G is present.

In general, these results can be explained by the redistribution of the ensemble

induced by local unfolding, changes in the release rate of Mg2+.ATP, and binding

affinity of Mg2+.ADP associated with the LID.

In Chapter 6, the redistribution of the ensemble induced by local unfolding was

investigated by comparing the probabilities of the folded state in WT and V142G

8

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in the absence of ligand at 37 by combining HX-NMR and ITC techniques.

This method was previously developed in our lab to determine the stability of

domains not detected by HX-NMR, as is the case for the LID and AMPbd that

have the amide hydrogens completely exchanged to deuterium during the sample

preparation. The results show that the LID and AMPbd are very flexible and

the CORE is the most stable domain. According to this method, the folded state

in WT represents 90% of the ensemble. On the other hand, V142G decreases

the population of the folded state to 43%. Although the determined probability

values in this Chapter differ from those values determined by DSC (specially those

associated with V142G), the conclusions are the same: Gly mutations induced

local unfolding that, in turn, caused the redistribution of the ensemble.

Finally, in Chapter 7, the principal findings were discussed, future directions

were outlined and experiments were proposed. A final remark: unless indicated,

plots and simulations in this dissertation were generated with the R programming

language [73].

9

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Mg2+ · ATP + AMPforward−−−−−−−−reverse

Mg2+ · ADP + ADP

Figure 1.1: E. coli AK: domains and catalytic scheme. This figure was made usingthe 4AKE.pdb file [17] and PyMOL Molecular Graphics System Version 1.4.1.Schrodinger, LLC

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Figure 1.2: Local unfolding promoted by V142G affects neighboring residues. 1H-15N HSQC NMR spectra of WT (black) and V142G (red) at 21 C [9]

11

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(a) 1H-15N HSQC NMR spectra of WT (black) andV142G (red) at 33 [9]

(b) Propagation of mutational effects at 33 [9]

Figure 1.3: V142G can destabilize the entire LID domain. (a) Local unfoldingincreases with temperature. (b) Affected residues are in yellow.

12

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Figure 1.4: Mutational effects introduced by one mutation do not affect the crys-tallographic structure. Alignment of WT and V148G from position A (red) andposition B (black) within the asymmetric unit (ASU). The RMSD values betweenWT and V148G from the same position are less than the RMSD between twocopies of the same construct inside the ASU [9].

Figure 1.5: Modulation of binding affinity at different temperatures [9].

13

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Chapter 2

Materials and methods of AK

preparation

2.1 Selection of entropy enhancing glycine mu-

tations

Mutations in the three domains of AK that satisfy our mutational strategy were

selected: V135G, V142G in the LID, A55G in the AMPbd and A73G in the

CORE domain, see Fig. 2.1. In addition to these single mutants, we also se-

lected double mutations such as V135G/V142G, V135G/V148G, V142G/V148G

and A73G/V142G. In addition to the above mutants, the entire LID domain was

removed and replaced with a flexible linker (LIDLESS) in order to investigate the

coupling between the LID and the CORE-AMPbd domains. The reasons for selec-

tion of double mutants were to determine whether AK can function having the LID

severely unfolded, and whether these effects on function are position dependent.

The purposes of LIDLESS characterization were to dissect the coupling between

the LID and CORE-AMPbd and to determine whether the CORE and AMPbd

domains unfold as a single domain.

Target residues to be mutated were selected after close inspection of the apo,

4AKE.pdb [17], and holo, 1AKE.pdb [18], crystallographic structures. Val to Gly

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mutations were expected to produce the largest conformational entropy change be-

cause a β-branched side chain is effectively reduced to one hydrogen. On the other

hand, Ala to Gly mutation should promote a smaller change in conformational en-

tropy since a methyl group is replaced. Consistent with this expectation, D’aquino

and colleagues computationally determined the unfolding conformational entropy

changes for 19 residues [20]. According to their results, Val to Gly mutation in-

creases the conformational entropy by 2.9 cal/mol*K and Ala to Gly substitution

by 2.4 cal/mol*K.

2.2 Site directed mutagenesis

AK WT plasmid (DNA 2.0, Menlo Park, CA) was optimized for E. coli expression

and then synthesized and inserted into the pJ414 bacterial expression vector. This

vector was designed with a IPTG-inducible T7 promoter and no affinity tag codons.

WT plasmid was used as template to obtain single and double mutations through

site directed mutagenesis employing polymerase chain reactions (PCR) with Phu-

sion High-Fidelity DNA Polymerase (NEB, Ipswich, MA) and specifically designed

primers. Complimentary primers, synthesized by IDT (Coralville,IA) had between

15 and 20 nucleotides on each side of the targeted mutation. This sequence length

ensures selectivity and an a effective Tm of the primers. Tm should be within

the range of 70 to 80 for best results. Reaction setup that includes 3% DMSO

and thermocycling conditions were performed according to the PCR Phusion DNA

Polymerase protocol from NEB. When the thermocycling steps were done, diges-

tion of parental plasmid was achieved by the addition of 2 !l of DpnI for every 10

!l of PCR product and posterior incubation of the product for at least 4 hours at

37 . The digested product was then transformed into homemade DH5 competent

cells. Transformed cells were spread on LB agar plates with 100 !g/ml ampi-

cillin. Plates were incubated for 18-24 hours at 37 . Then, single colonies were

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gathered for plasmid extraction. Plasmid concentration was increased by using

a GeneJET Plasmid Miniprep Kit (Thermo Fisher Scientific, Rockville, MD) for

subsequent plasmid sequence verification and protein expression. Plasmids were

stored in aliquots at -20 .

2.3 LIDLESS plasmid construction

Amino acids 121-160 corresponding to the LID domain were replaced by the flexible

linker GTGGSGGS, which is composed of eight residues. Threonine and serine

were in the linker to make it soluble without adding bulkier side chains. LIDLESS

plasmid was made from WT plasmid. Complimentary primers were used on the

WT plasmid to remove the LID codons and to add one KpnI and one BamHI

restriction site. A duplex DNA oligomer, which carried the codon sequence for the

flexible linker, replaced the sequence of the LID.

Phosphates were added to the 5’-ends of the duplex before ligation. The primers

and duplex were synthesized by IDT. Deletion of the LID was done using PCR

with Phusion High-Fidelity DNA Polymerase following the corresponding proto-

col. The reaction product was inoculated with 2!l of DpnI for every 10uL to digest

the parental plasmid. The solution was then incubated for 4 hours at 37 . Af-

ter incubation, the plasmid was purified with the GeneJet PCR purification kit.

Afterwards, 47 !l of purified PCR solution was mixed with 2 !l of KpNI, 2 !l

BamHI and 5 !l of 10xCutSmart buffer. This step was necessary to make sticky

ends for ligation. The restriction enzymes and related buffers were from NEB. The

solution was incubated at 37 for at least 1 hour to achieve complete digestion.

Agarose electrophoresis gel was carried out to check the plasmid length. The gel

was made with 40 ml 1xTAE buffer and 0.3 gr of UltraPure"Agarose 16500 Invit-

rogen (Thermo Fisher Scientific). After microwaving the agarose solution for two

minutes, 1 !l of ethidium bromide was added. The ladder solution was made by

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mixing 1.5 l of 2-Log-DNA marker (NEB) with 5 l of nucleic acid sample buffer

5x (Bio-Rad, Hercules, CA). The plasmid solution was made by mixing 14 l of

nucleic acid sample buffer 5x with 56 l of purified solution for ligation. The gel

was then inspected using UV light in a dark room, wearing proper UV glasses. The

target plasmid was removed from the gel using a clean sterile razor. The plasmid

was extracted from the gel using the GeneJET gel extraction kit.

Addition of 5’-phosphates to the duplex DNA oligomer for subsequent ligation

was achieved by mixing 3 l of duplex solution (50uM), 1 l of T4 Polynuclotide

Kinase (NEB), 10x T4 ligase buffer, 8 l of PEG 8000 (30%) and 33 l of ddH20.

The solution was incubated for 12 hours at 37 !. Ligation between the duplex

DNA oligomer and the cut plasmid was carried out by T4 DNA ligase (NEB).

The concentration of the duplex was three times the extracted concentration of

PCR product. The ligation solution was left at room temperature for 1 hour.

The ligated plasmid was transformed into homemade DH5 competent cells [19].

Transformed cells were spread on LB agar plates with 100 g/ml ampicillin. Plates

were incubated for 18-24 hours at 37!. Afterwards, single colonies were collected

for plasmid extraction. Plasmid concentration was increased by using a GeneJET

Plasmid Miniprep Kit for subsequent plasmid sequence verification and protein

expression. Plasmids were stored in aliquots at -20!.

2.4 Protein expression,purification, and storage

Rosetta"2(DE3)pLysS Singles"competent cells Novagen (EMD millipore, Biller-

ica, MA) were transformed with AK plasmids and plated on LB plates with

100ug/mL ampicillin and incubated for 18-24 hours at 37!. A single colony was

gathered and inoculated into 50 mL 2xYT medium with 60 g/mL ampicillin and

grown for 8 hours at 37! in an incubator shaker at 250 rpm. 5 ml of grown cells

were inoculated for every liter of 2xYT medium containing 60 g/ml. Cells grew

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at 37 in an incubator shaker at 250 rpm until they reached an OD between 0.6

and 0.8. Then, the culture was induced by 1mM IPTG and continued growing in

the incubator shaker for 5 hours. The pellets were collected and washed with soni-

cation buffer (50 mM Tris, 0.1 NaCl, 2mM EDTA, 2mM DTT, pH 8.0) and stored

at -80 . Sonication was carried out using sonication buffer and protease inhibitor

cocktail (Sigma-Aldrich, St.Louis, MO) in a 4 room. Cell lysate was centrifuged

at 30,000g at 4 for 1 hour. The supernatant containing AK was collected and

filtered several times with 0.2 !m sterile filters (Nalgene). The next purification

steps were taken from [9] and performed using FPLC. The supernatant was diluted

3x with diluting buffer (10mM Tris, 1 mM DTT, pH 8.0) and then loaded into a

column containing Cibacron Blue F3GA dye (Bio-Rad) suspended in buffer A-blue

(50 mM Tris, 0.1 mM EDTA, 1 mM DTT, pH 7.5). AK was gathered through a

linear gradient elution employing buffer A-blue and B-blue (50 mM Tris, 0.1 mM

EDTA, 1 mM DTT, 2M NaCl, pH 7.5). Fraction collections with the highest AK

concentration were selected. Concentrations were determined by measuring the

absorbance at 277 nm. The extinction coefficient (ε) used for WT, single and dou-

ble mutants was 13750 M-1cm-1 and for LIDLESS was 11653 M-1cm-1. Collections

purity was examined on SDS-PAGE. The protein solution was dialyzed against

buffer A (20 mM Tris, 0.1 mM EDTA, 1mM DTT, pH 8.0) for 24 hours at 4 .

Dialyzed AK was then loaded into a Resource Q resin suspended in buffer A. AK

was collected using a linear gradient elution by mixing buffer A and buffer B (20

mM Tris, 0.1 mM EDTA, 1mM DTT, 0.3 M NaCl, pH 8.0). Fraction collections

were monitored at 277 nm and the ones with the highest concentration were gath-

ered and purity was examined on 12% SDS SDS-PAGE. Finally, AK was dialyzed

against calorimetric buffer (60 mM PIPES, 1 mM EDTA, pH 7.85) for 24 hours.

This step was repeated three times. PIPES buffer was acquired from AmericanBio

Inc., Natick, MA. and EDTA from Sigma-Aldrich.

18

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(a) Apo state, view 1 (b) Apo state, view 2

(c) Holo state, view 1 (d) Holo state, view 2

Figure 2.1: Selected Gly mutations on uncharged solvent exposed residues. Theseresidues are far from the active site and have no contact with the ligand. Therefore,our mutational strategy is satisfied both in the apo,(a) and (b), and in the holostate, (c) and (d). This figure was made using the 4AKE.pdb [17] and 1AKE.pdb[18] files and PyMOL Molecular Graphics System Version 1.4.1, Schrodinger, LLC.Mutations are shown in red. The active site is approximated by the location ofAp5A (brown).

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Figure 2.2: LIDLESS plasmid construction.

20

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Chapter 3

Calorimetric determination of

interdomain interactions and

stability of AK constructs

3.1 Abstract

NMR hydrogen exchange experiments demonstrated that proteins are flexible en-

tities and exist as an ensemble of conformational states [21]. This technique was

also used to determine the local and global stability of AK at 19 [12]. The results

show that the CORE is the most stable domain of the enzyme. In addition, it has

been suggested that the three domains folds uncooperatively [12]. In other words,

that there is no interdomain (coupling) interactions between domains. However,

our differential scanning calorimetry (DSC) data show that the LID and CORE-

AMPbd are negatively coupled and the coupling is temperature dependent. The

coupling is zero at about 30 and positive at lower temperature. Most impor-

tantly, DSC also allowed us to observed the effects of local unfolding regulation,

promoted by mutations, on the subdomain stabilities, and consequently, to deter-

mine the redistribution of the conformational ensemble.

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3.2 Introduction

Probabilities of conformational states have been previously determined using differ-

ent techniques such as HX-NMR [21, 22], CD combined with ITC [9] and residual

dipolar coupling (RDC) [23]. In this chapter, we investigated the modulation of

the conformational ensemble promoted by local unfolding regulation. For that

purpose, DSC experiments were performed on WT, A55G, A73G ,V135G,V142,

A73G/V142G, V135G/V142G and on LIDLESS. DSC is a thermodynamic tech-

nique that measures the apparent molar heat capacity (CP ) of proteins as temper-

ature is changed. Thermodynamic parameters such as Tm and ∆HvH of transitions

can be obtained running only one experiment. In addition, ∆CP can be obtained

by measuring ∆HvH and Tm at different pH conditions. Subsequently, the partition

function (Q) and conformational states probabilities can be calculated. Modula-

tion of the conformational ensemble promoted by mutations and LID deletion was

determined and the probabilities of the folded state between WT and mutants were

compared at 37 . The coupling between the LID and CORE-AMPbd was also

studied by comparing the unfolding transition of LIDLESS with those observed in

the other constructs.

3.3 Materials and methods

3.3.1 Protein preparation

Thermal unfolding experiments were carried out onWT, A55G, A73G ,V135G,V142,

A73G/V142G, V135G/V142G and on LIDLESS. Constructs were expressed and

purified according to protocols described in Chapter 2. Experiments were per-

formed with freshly prepared AK solutions dialyzed against calorimetric buffer

(60 mM PIPES, 1 mM EDTA pH 7.85). Protein concentrations were measured

with a UV spectrometer at 277 nm using ε = 13750 M−1cm−1 for WT, single and

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double mutants and ε = 11653 M−1cm−1 for LIDLESS. Afterwards, the protein

concentration was corrected by multiplying the n value obtained from isothermal

titration calorimetry (ITC) experiments run at 25 by the protein concentration

previously measured (i.e., [AK]corrected = n[AK]UV). The inhibitor Ap5A [18] was

used as ligand in ITC experiments. DSC and ITC runs used protein solution from

the same preparation to minimize random errors. Protein concentrations of 20 !M

(≈ 0.5 mg/ml) were used in all the experiments. To determine ∆CP s accurately,

pH was lowered to pH 7.2. In this way, we observed change in Tm and ∆Hm. When

pH was lower than 7.2, proteins aggregated at temperatures higher than Tm. ITC

experiments were run according to details given in Chapter 4.

3.3.2 DSC experimental design

The heat capacity (CP ) as a function of temperature was measured by a high preci-

sion differential scanning microcalorimeter MicroCal VP-DSC (Malvern, Westbor-

ough, MA). The running parameters were selected as follows: starting temperature

= 10 ; final temperature = 80 ; scan rate = 60 /h; prescan thermostat= 15

min; postscan = 0 min; filtering period = 20 seconds and FB Mode/Gain = none.

Protein solution and calorimetric buffer were degassed and loaded into the sample

and reference cells, avoiding bubbles as much as possible. The cells were cleaned

before each experiment. For this purpose, nitric acid (70%) was left in the cells for

2 hours at 80 . Then, the temperature was lowered to 30 and the nitric acid

was discarded. Subsequently, the cells were cleaned up with filtered contrad 70

(1x) and rinsed with ddH2O. CP was processed at temperatures higher than 15

to eliminate perturbations associated with the instrument equilibration. It was

empirically observed that starting temperatures lower than 10 produced noisy

data. To determined the extent of reversibility, protein the sample was reheated

(10-80 ). Then, the unfolding profile areas of the two scans were compared. The

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reversibility was also tested by heating the sample 3 more than the melting tem-

perature of the last transition. The sample was cooled down and then reheated

again. According to the first method, the extent of reversibility was between 72%

(A73G/V142G) and 82% (WT). However, the second method showed that unfold-

ing is highly reversible and that irreversibility arises because of high temperature

effects, [24, 25, 26], see Appendix 4.

3.3.3 Data analysis

To investigate the modulation of conformational ensemble promoted by entropy en-

hancing mutations, the probabilities of states for every construct were determined.

In general, the probability that a protein visits state i is given by

Pi =e−

∆GiRT

Q(3.1)

with the partition function defined as :

Q =n

i=1

e−∆GiRT (3.2)

where ∆Gi is the stability of the state i, whereby the folded state is the reference

state (∆G1 = 0):

∆Gi = −RTln(Ki) = ∆Hi − T∆Si (3.3)

∆Hi is the enthalpy associated with the state i and it is described by the van’t

Hoff equation:

∆Hi = RT 2dlnKi

dT= ∆HvH,i +∆CP,i(T − Tm,i) (3.4)

∆Si is the entropy of the state i and it is expressed as:

∆Si =∆HvH,i

Tm,i

+∆CP,ilnT

Tm,i

(3.5)

Using the last two equations, ∆Gi can be expanded to the well-known Gibbs-

Helmholtz equation:

∆Gi = ∆HvH,i(1−T

Tm,i

) + ∆CP,i(T − Tm,i − lnT

Tm,i

) (3.6)

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T and Tm are absolute temperatures. ∆CP s are assumed to be constant over the

temperature range used [27]. Stabilities and probabilities were calculated by ob-

taining ∆HvH,i, ∆CP,i and Tm,i from the transition excess heat capacity (〈∆CP,tr〉)

profiles. 〈∆CP,tr〉 was obtained by subtracting the sigmoidal (i.e. progressive)

baseline CP,bl from the apparent molar heat capacity (CP ), thus:

〈∆CP,tr〉 = CP − CP,bl (3.7)

where CP,bl was calculated according to:

CP,bl = (1− α)CP,N + αCP,U (3.8)

α is the probability of the unfolded state calculated following the method described

in [32] and [33]. CP,N and CP,U are the heat capacity of the native and unfolded

states respectively. Although equation 3.8 is only mathematically correct for a

two-state transition [27], it was also used for non-two-state transitions because the

progressive baseline was the method that produced the less perturbed 〈∆CP,tr〉.

Finally, the 〈∆CP,tr〉 profile is fitted according to [27]:

〈∆CP,tr〉 =n

i=1

∆HidPi

dT(3.9)

To obtain thermodynamic parameters from 〈∆CP,tr〉 profiles of WT and mu-

tants (excepting V135G/V142G), a sequential three-state model was proposed

whereby the coupling parameter, φ, accounts for the interdomain interaction, and

therefore communication, between the LID and CORE-AMPbd, see Eq. 3.16 and

related reaction scheme. The three-state model was based on the observation that

the LID unfolds cooperatively [9], see Fig. 1.3 and that the CORE and AMPbd un-

folding as a single domain, see Fig. 3.4. Interaction between the LID and the rest

of the enzyme was evident when the removal of the LID (LIDLESS) decreased the

stability of the CORE-AMPbd, see Fig. 3.4. In addition, it was observed that in-

terdomain interactions are present although the LID is unfolded (V135G/V142G),

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see Fig. 3.6. Close inspection of 〈∆CP,tr〉 profiles of WT and single mutants indi-

cates that thermal unfolding of the LID is not accompanied simultaneously by the

break of interdomain interactions. Actually, they are still acting on the CORE-

AMPbd as shown by thermal unfolding of V135G/V142G. Therefore, φ was placed

on the transition associated with the CORE-AMPbd unfolding. Following these

observations, unfolding of LIDLESS was analyzed using a two-state model, see Eq.

3.10. Unfolding of V135G/V142G was also characterized with a two-state model

incluiding φ, see Eq. 3.14.

In general, coupling interactions can contribute to the stabilization or destabi-

lization of associated domains when ∆Gφ = −RTlnφ 6= 0. For the case ∆Gφ > 0,

it is energetically more favorable to unfold one of the interacting domains when

the other is unfolded or removed. This situation could arise when the interface

between domains is composed of two complementary hydrophobic surfaces that in-

teract energetically more favorable with each other than with solvent [13]. On the

other hand, ∆Gφ < 0 means that unfolding or removal of one domain would make

the other more stable. This is the case when interfaces would prefer to interact

with solvent rather than with each other. This situation could arise for a specific

arrangement of charge residues or for complementary hydrophobic surfaces at low

temperature [13].

It has been shown that thermodynamic parameters can be estimated using the

accessible surface areas [34]. Since the interface area associated with φ is assumed

to be small, and therefore the accessible surfaces areas, compared with those of

the LID and CORE-AMPbd domain; ∆CP,φ was assumed to be zero.

The thermal unfolding of LIDLESS was analyzed using the following two-state

reaction scheme :

FCORE-AMPbdKCA−−−−−−−−−−−−−−−−−− UCORE-AMPbd

26

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which gives the partition function:

QLIDLESS = 1 +KCA (3.10)

where KCA is the equilibrium constant related to the unfolding of the CORE-

AMPbd. The associated 〈∆CP,tr〉 function was determined by using Eq. 3.10 into

Eq. 3.9, giving:

〈∆CP,tr〉 =1

RT 2[PU(1− PU)∆H

2CA] (3.11)

PU is the related probability of the unfolded state. The effect of the flexible linker

of the stability of LIDLESS is corrected according to the expression:

Tm,New =∆HvH

∆HvH/Tm +∆Slinker

(3.12)

with

∆Slinker = −Rln[(3

2πNL2)3/2

1

6πd3] (3.13)

where d is the distance between the first and last residues of the loop, N is the

number of residues of the loop, and L is the statistical length of an amino acid,

see [35]. For our case, d=5.6 a, N=8 and L=3.8 a.

Since unfolding of V135G/V142G showed coupling effects between the LID and

CORE-AMPbd domains even though the LID is unfolded (LU). The unfolding

reaction was modeled according to a two-state model that includes φ:

LUφKCA−−−−−−−−−−−−−−−− U

with the partition function:

QV 135G/V 142G = 1 + φKCA (3.14)

and:

〈∆CP,tr〉 =1

RT 2[PU(1− PU)(∆Hφ +∆HCA)

2] (3.15)

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It was determined that the folded state of AK is composed of compact and

extended coexisting conformations. The compact conformation is populated even

in the absence of substrates [15]. In our model, it is assumed that these two con-

formations have the same stability and therefore they are treated as one single

state, the folded state. In addition, it was shown that V142G and V148G muta-

tions promote marginal perturbations in the NMR spectra of unligated and crystal

structure of ligated AK respectively [9], see Chapter 1. Therefore, the folded state

was assumed to be conserved by mutants.

WT and mutants showing two transitions were studied with the sequential

reaction:

FKLID−−−−−−−−−−−−−−−−−− LU

φKCA−−−−−−−−−−−−−−−− U

giving rise to the partition function:

Q = 1 +KLID +KLIDφKCA (3.16)

and:

〈∆CP,tr〉 =1

RT 2[ PF (1− PF )∆H

2LID + 2PFPU∆HLID(∆Hφ +∆HCA) (3.17)

+PU(1− PU)(∆Hφ +∆HCA)2]

PF and PU are the probabilities of the folded and unfolded states calculated from

Q, see Eq. 3.16. The ∆CP s associated with KLID and KCA were set to zero

to obtain 〈∆CP,tr〉 because progressive baseline subtraction makes CP,N and CP,U

equal to zero. Since ∆Cp was assumed to be constant [27], it was taken as the slope

of the linear function of the plot ∆Hm vs Tm. Therefore, ∆CP,CA was determined

by calculating the slope associated to the ∆Hm and Tm values obtained at pH of

7.2 and 7.85, see Fig. 3.8. ∆CP,LID was the calculated slope related to the ∆Hm

and Tm values from the thermal characterization of the LID from WT, V135G and

28

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V142G, see Fig. 3.9. As mentioned above, ∆Cp,φ was assumed to be zero in our

calculations. Our experimental data were analyzed using software written in our

lab, see Appendices 1 and 2.

3.4 Results and discussion

3.4.1 The CORE-AMPbd unfolds as a single domain and

it is coupled to the LID

The effect of the flexible linker on the stability of LIDLESS was corrected accord-

ing to Eq. 3.12, see Fig. 3.3. Comparison between the heat capacity function of

WT and the corrected one of LIDLESS is shown in Fig. 3.4. It reveals that the

CORE-AMPbd region unfolds as a cooperative domain, as previously suggested

by NMR experiments, see Fig. 1.3. This result also suggests that the CORE and

AMPbd are positively (or favorably) coupled. In addition, the apparent Tm is

shifted downwards by 2.5 when the LID is removed, indicating that the LID and

CORE-AMPbd are also positively coupled. 〈∆CP,tr〉 of WT exhibits an asymmet-

ric shape, showing that at least one other transition is present. The presence of

additional state(s) was also confirmed by the van’t Hoff to calorimetric enthalpy ra-

tio (∆Hcal/∆HvH = 1.15), see Appendix 3. On the other hand, thermal unfolding

of LIDLESS follows a two-state mechanism (∆Hcal/∆HvH = 1.00). The thermal

unfolding is characterized by an enthalpy change (∆HCA) of 109.1 kcal/mol and a

melting temperature (Tm,CA) of 53.4 . 〈∆CP,tr〉 of WT was fitted according to

Eq. 3.17 using the ∆HCA and Tm,CA obtained from LIDLESS. Unfolding of the

LID was described by a ∆HvH,LID of 43.6 kcal/mol11, Tm,LID of 51.0 , ∆HvH,φ

of 22.6 kcal/mol and Tm,φ of 67.8 . ∆CP,LID and ∆CP,CA were determined to be

0.4 and 2.7 kcal/mol*K respectively for WT and mutants, see the Data analysis

section. These results indicate that the LID and CORE-AMPbd are positively

29

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coupled at temperatures lower than 67.8 , see Fig. 3.11. The coupling interac-

tion between the LID and CORE as well as the stabilities of AK domains also were

studied through HX-NMR [12]. Rundqvist and colleagues showed that the CORE

is the most stable region and that LID and AMPbd exhibit low stability (exchange

of amide protons in the LID and AMPbd were too fast to be detected). They con-

cluded that the stabilities of the LID and AMPbd do not affect the stability of the

CORE. However, our thermal unfolding analysis of WT and LIDLESS revealed the

presence of coupling between the LID and CORE-AMPbd regions. Furthermore,

unfolding of the CORE and AMPbd as a single domain suggests the presence of

positive coupling. Coupling characterization in AK can be further investigated by

removing the AMPbd as well as the LID and AMPbd simultaneously.

3.4.2 Single and double mutants promote local unfolding

It is clearly observed that our entropy enhancing mutations promote local unfolding

and their impact is higher in the LID than in the CORE, see Fig. 3.5 and 3.6.

Direct evidence of local unfolding regulation is given by the downward shift of

Tm of the LID transition promoted by V135G and V142G. Moreover, A55G and

A73G also destabilize the CORE but not to the same extent as Gly mutations

do to the LID. Destabilizing effects of mutations are relative to the stability of

the affected region. In other words, the more stable the region, the less impact

on stability mutations will have. Moreover, mutations in the CORE-AMPbd have

no appreciable impact, if any, on the stability of the LID, Fig. 3.5. The reverse

is also valid. Mutations in the LID do not perturb the stability of the CORE-

AMPbd, see Fig. 3.7, and Table 3.1. Importantly, these results are not predicated

on a communicating pathway between domains. Only stabilities and coupling

interactions are necessary to explain our DSC data.

30

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3.4.3 Coupling interactions are still present even though

the LID is unfolded

V135G, V142G, V135G/V142G and A73G/V142G reduce the unfolding transition

area associated with the CORE-AMPbd by the same extent. However, the center

peak corresponding to the CORE-AMPbd transition of WT, single and double

mutants present small but significant differences in Tm, meaning that coupling

interactions are still present. Fitted values, Table 3.1, that characterized the un-

folding profiles of WT, V135G, V142G and V135G/V142G in Fig. 3.6 show how

one mutation in the LID such is enough to reduce the coupling enthalpy change by

≈ 19 kcal/mol. Moreover, the coupling Tm is increase to be temepratures higher

than 130 . When two mutations are present in the LID, the enthalpy loss is 14.4

kcal/mol and the coupling Tm is decreased to 102.5 . This result suggests that

local unfolding can induce compensatory effects. Interestingly, the coupling is only

perturbed by mutations in the LID (Fig. 3.6) but not by those in the CORE or

AMPbd (Fig. 3.5), probably because A55G and A73G are distal mutations to the

LID-CORE interface.

3.4.4 Local unfolding mechanism for stability change

Thermodynamic parameters were obtained from DSC, Table 3.1. ∆CP,LID and

∆CP,CA were calculated according to the Data analysis section, see Fig. 3.8 and

3.9. ∆CP,φ was assumed to be zero. Stabilities were calculated at 37 according

to the Gibs-Helmholtz equation, see Eq. 3.3. Modulation of thermal stabilities

of constructs are shown in Fig. 3.10. The total stability of WT is 8.1 kcal/mol.

∆∆GTotal,37 indicates the degree of mutational effects on stability. Gly mutations

in a specific domain promote similar effects. A55G and A73G decrease the global

stability by 0.5 and 0.6 kcal/mol respectively. However, V135G and V142G de-

crease stability by 2.6 and 2.8 kcal/mol respectively. These results can be explained

31

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by the increased conformational flexibility produced by Val to Gly substitutions.

A73G/V142G decreased stability by 2.8 kcal/mol. This value shows that muta-

tional effects are not additive. The stability of the CORE-AMPbd (LIDLESS) was

4.3 kcal/mol, 1.4 kcal/mol lower than the stability of V135G/V142G. The differ-

ence is the consequence of the positive coupling interaction between the LID and

CORE-AMPbd.

3.4.5 Local unfolding modulates the conformational en-

semble

Probabilities of states were calculated according to Eq. 3.1 using the thermody-

namic values obtained from DSC, see Table 3.1. Probabilities of states were plotted

(Fig. 3.12) and the folded state probabilities were calculated at 37 and then com-

pared with those of the mutants, see Fig. 3.13. V135G/V142G and LIDLESS are

two special cases. In the former, unfolding of the LID was not detected by the

calorimeter at the range of the experimental scan (10 to 80 ), Fig 3.6, and in the

latter, LIDLESS has a different native state because the LID was removed. Un-

folding of V135G/V142G is computationally explored in the Chapter 4. Changes

of probabilities of the folded state show clearly how local unfolding promoted by

Gly mutations modulates the conformational ensemble. In WT, A55G and A73G,

95% of the total enzyme is folded at 37 . The population of the folded state goes

down to 54%, 71% and 75% in V135G, V142G and A73G/V142G respectively.

According to the model used in this chapter, the population of the folded state is

zero in V135G/V142G.

3.5 Conclusions

Local unfolding promoted by Gly mutations modulates the conformational ensem-

ble. At 37 , the folded state population represents 95% of the ensemble. While

32

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the other 5% is populated by the locally unfolded state (LU), defined as having

the LID unfolded. AK unfolds following a three-state process. The LID is the

less stable domain. On the other hand, the CORE-AMPbd, which unfold as a

single domain, is the most stable region of the enzyme. In addition, the LID and

CORE-AMPbd are positively coupled. In the next chapters, we will investigate

the impact of local unfolding in protein function.

33

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Figure 3.1: Mutation positions in AK used for DSC experiments shown in red.Double mutants V135G/V142G and A73G/V142G, as well as LIDLESS, were alsotested.

34

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(a) LIDLESS

(b) WT

Figure 3.2: Thermal unfolding simulation of the CORE-AMPbd and the LID basedon Eq. 3.17. Parameters used in the simulations: ∆HvH,LID=43.0 kcal/mol,∆HvH,CA= 109.0 kcal/mol, ∆HvH,φ=22.0 kcal/mol, Tm,φ=68 , ∆CP,CA =∆CP,LID = ∆CP,φ= 0.0 kcal/mol*K. In (a), Tm,LID = 51.0; Tm,CA was set to 53.4 (black), 52.4 (green) and 51.4 (blue). In (b), Tm,CA = 53.4 . Tm,LID was setto 51.0 (black), 41.0 (orange) and 36.0 (dark red). *CA = CORE-AMPbd

35

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Figure 3.3: Corrected 〈∆CP,tr〉 of LIDLESS upon removing the stability effects ofthe flexible linker, see Eq. 3.12. Tm is decreased by 7.2 .

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Figure 3.4: Comparison of 〈∆CP,tr〉 profiles of WT and LIDLESS. Decreased Tmof LIDLESS is clearly evident.

37

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Figure 3.5: 〈∆CP,tr〉 profiles of WT, A55G and A73G. Single mutants exhibit asmall decrease in Tm as compared to WT.

38

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Figure 3.6: 〈∆CP,tr〉 profiles of WT, V135G, V142G and V135G/V142G. Theunfolding of the LID is observed in single mutants (see small unfolding transitions)but not in the double mutant. Mutants present small decrease in Tm of the CORE-AMPbd as compared to WT.

39

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Figure 3.7: 〈∆CP,tr〉 profiles of WT, A73G, V142G and A73G/V142G. All mutantsclearly demonstrate decrease in Tm.

40

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Figure 3.8: ∆CP associated with the unfolding of the CORE-AMPbd (CA). Calcu-lated from the thermal unfolding characterization of LIDLESS at two pH values.Itis assumed that the flexible linker has no effect on ∆CP,CA. *Estimated valuedetermined with COREX [38], based on accessible surface areas.

41

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Figure 3.9: ∆CP associated with the unfolding of the LID. Calculated from the LIDunfolding characterization of WT, V135G and V142G, see Table 3.1. *Estimatedvalue determined with COREX [38], based on accessible surface areas.

42

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AK Tm,LID ∆HvH,LID ∆CP,LID Tm,φ ∆HvH,φ Tm,CA∗ ∆HvH,CA∗ ∆CP,CA∗ ∆GTotal,37 ∆∆GTotal,37

Construct (kcal/mol) (kcal/mol ∗ K) (kcal/mol) (kcal/mol) (kcal/mol ∗ K) (kcal/mol) (kcal/mol)

LIDLESS NA NA NA NA NA 53.4!0.1 109.1!0.1 2.7!0.4 4.3!0.2 -3.8!0.3

WT 51.0!0.1 43.6!0.7 0.4!0.1 67.8!0.2 22.6!0.5 53.4!0.1 109.1!0.1 2.7!0.4 8.1!0.2 0.0!0.0

A55G 51.0!0.1 43.6!0.7 0.4!0.1 67.8!0.2 22.6!0.5 52.0!0.1 103.0!0.1 2.7!0.4 7.6!0.2 -0.5!0.3

A73G 51.0!0.1 43.6!0.7 0.4!0.1 67.8!0.2 22.6!0.5 51.2!0.1 105.5!0.1 2.7!0.4 7.5!0.2 -0.6!0.3

V135G 37.8!0.1 38.0!0.4 0.4!0.1 163.0!0.8 4.0!0.1 53.4!0.1 109.1!0.1 2.7!0.4 5.6!0.2 -2.6!0.3

V142G 41.3!0.1 41.0!0.7 0.4!0.1 133.3!0.9 2.0!0.1 53.4!0.1 109.1!0.1 2.7!0.4 5.3!0.2 -2.8!0.3

A73G/V142G 42.2!0.3 42.0!1.0 0.4!0.1 109.9!2.0 4.5!0.2 51.2!0.1 105.5!0.1 2.7!0.4 5.3!0.2 -2.8!0.3

V135G/V142G NA NA NA 102.5!2.2 8.2!0.3 53.4!0.1 109.1!0.1 2.7!0.4 5.7!0.2 -2.4!0.3

Table 3.1: Summary of the thermodynamics parameters obtained from DSC. ∆GTotal = ∆GCA + ∆GLID + ∆Gφ. ∆CP,φ wasfixed to zero. Errors are from three replicates. NA = Not aplicable. *CA = CORE-AMPbd.

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Affected ∆∆GA55G ∆∆GA73G ∆∆GV 135G ∆∆GV 142G ∆∆GA73G/V 142G ∆∆GV 135G/V 142G

Domain (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol)

LID 0.0 0.1 0.0 0.1 -1.7 0.1 -1.2 0.1 -1.1 0.1 -1.8 0.1

*CA -0.5 0.2 -0.6 0.2 0.0 0.3 0.0 0.3 -0.6 0.2 0.0 0.3

φ 0.0 0.1 0.0 0.1 -0.9 0.1 -1.6 0.1 -1.2 0.1 -0.6 0.1

∆∆GTotal -0.5 0.3 -0.6 0.3 -2.6 0.3 -2.8 0.3 -2.8 0.3 -2.4 0.3

Table 3.2: Stability perturbation of AK domains promoted by Gly mutations.∆∆G were calculated at 37 using values from Table 3.1. Errors in ∆∆G weredetermined by propagation of errors associated with ∆G.*CA = CORE-AMPbd

44

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(a) LIDLESS (b) WT

(c) A55G (d) A73G

(e) V135G (f) V142G

(g) A73G/V142G (h) V135G/V142G

Figure 3.10: Thermal stabilities calculated according to thermodynamic parame-ters from Table 3.1. ∆GTotal = ∆GCORE−AMPbd + ∆GLID + ∆Gφ

45

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Figure 3.11: Coupling interaction (φ) between the LID and CORE-AMPbd in WTat 37 , based on Fig. 3.10 (b)

46

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(a) LIDLESS (b) WT

(c) A55G (d) A73G

(e) V135G (f) V142G

(g) A73G/V142G (h) V135G/V142G

Figure 3.12: Theoretical state probabilities vs temperature plots determined usingvalues from Table 3.1 and Eq. 3.1. Since the unfolding of the LID in V135G/V142Gwas not detected by DSC experiments (h), it was assumed that the folded state wasnot populated at the temperature range of the experiment. States probabilities ofthe double mutant were calculated using to Eq. 3.14.

47

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Figure 3.13: Probabilities of the folded state of different constructs calculated at37 using values from Table 3.1. Mutants reduce the population of the foldedstate. According to model used in V135G/V142G, the folded state population iszero in this construct.

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Chapter 4

Calorimetric determination of

inhibitor binding affinity of AK

constructs

4.1 Abstract

The impact of induced local unfolding on binding affinity is investigated in this

chapter at temperatures ranging from 7 to 47 . Binding affinity was character-

ized with isothermal titration calorimetry (ITC) [54], using the non-hydrolyzable

inhibitor Ap5A [18] as ligand. Ap5A is composed of ATP covalently bound to

AMP by the last phosphate group. ITC is an efficient technique that determines

the apparent change in enthalpy (∆Ha) and apparent free energy (∆Ga) associ-

ated with the binding process in one single experiment. Our results show that a

state with little affinity for the ligand is also present in WT at physiological tem-

perature (37 ). Moreover, the increase of the population of the this low-affinity

state promoted by Gly mutations is responsible for the modulation of ∆Ha and

∆Ga. Interestingly, AK can also bind Ap5A in the absence of the LID (LID-

LESS). However, the binding affinity is marginal (Ka,WT/Ka,LIDLESS = 37.2 at

21 ). ∆Ha of this construct followed a linear relationship with temperature, indi-

cating a binding process in the absence of any binding incompetent state between

49

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7 and 47 . Intriguingly, when the LID possessed two simultaneous Gly muta-

tions (i.e. V135G/V142G), ∆Ha showed small change at temperatures higher than

30 . Our simulations suggested that this unexpected trend can be reconciled if

it is assumed that the ensemble is highly populated by the state having the LID

unfolded (LU) at the investigated temperatures and if it is assumed that binding

affinity of LU is equal to that of LIDLESS. Overall, our ITC experiments indicate

that local unfolding events modulate binding affinity through modulation of the

conformational ensemble.

4.2 Introduction

Binding affinity is the propensity of a enzyme to bind a specific ligand. Modulation

of binding affinity promoted by local unfolding was characterized by determining

∆Ha and ∆Ga of different constructs at different temperatures between 7 and

47 . The inhibitor Ap5A was used as ligand instead of original substrates be-

cause heat released during ATP hydrolysis obscures the heat evolution related to

the binding process. ∆Ha and ∆Ga of WT and mutants were investigated using a

thermodynamic model at which AK can visit three states, as indicated by DSC ex-

periments. In this model, it is assumed that the folded, and at much lesser extent,

the LU state are able to bind ligand. For WT, single mutants and A73G/V142G,

it is safe to assume that the presence of LU has no effect on apparent affinity.

However, in V135G/V142G, the marginal affinity of LU has to be considered to

reconcile experimental observations. Binding affinity of LIDLESS was also inves-

tigated between 7 and 47 . Finally, to investigate V135G/V142G trend, it is

assumed that LU present the same binding parameters as LIDLESS.

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4.3 Materials and methods

4.3.1 Protein preparation

ITC experiments were performed onWT, A55G, A73G ,V135G,V142, A73G/V142G,

V135G/V142G, V135G/V148G, V142G/V148G and on LIDLESS. Constructs were

expressed and purified according to protocols described in Chapter 2. Binding

affinity experiments were carried out with freshly prepared AK solutions dialyzed

against calorimetric buffer (60 mM PIPES, 1 mM EDTA pH 7.85). PIPES buffer

was selected because of its small heat of ionization. The number of protons

(nH+) transfered from the buffer to the protein-inhibitor complex was negligi-

ble (-0.04±0.07 for WT and 0.17±0.17 for V142G) [40], AK concentrations were

measured with a UV spectrometer at 277 nm using ε = M-1cm-1 for WT, single

and double mutants and ε = 11653 M-1cm-1 for LIDLESS. The inhibitor Ap5A

(Sigma-Aldrich) solution was prepared using the same buffer used to dialyze the

AK solution. Ap5A concentration was measured with ε259 = 30882 M-1cm-1. Initial

protein concentrations of ≈ 40 M and inhibitor concentration ≈ 400 Mwere used

for WT, A55G, A73G, V135G and V142G and A73G/V142G. For V135G/V142G,

V135G/V148G and V142G/V148G, protein and inhibitor concentrations of ≈ 80

M and 1200 M were used. For LIDLESS, the protein and inhibitor concentration

were ≈ 80 M and ≈ 2100 M respectively. Since constructs with double muta-

tions in the LID and LIDLESS presented lower binding affinity constants (Ka), the

protein and inhibitor concentrations were increased to obtain complete titration

curves.

4.3.2 ITC experimental design

Binding parameters were obtained by measuring the heat released or absorbed

while a ligand was titrated into the sample cell containing the AK solution to be

studied. The initial ligand concentration was at least ten times the concentration of

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the enzyme to ensure a complete saturation. The area generated by every injection

of ligand under the heat evolution was recalculated as function of the molar ratio

of ligand to enzyme. Subsequent analysis of the resulting titration curves gave the

apparent change of free energy (∆Ga), apparent enthalpy (∆Ha), and apparent

entropy (∆Sa) of binding as well as the binding stoichiometry number (n) of the

binding process. The n value gives the number of ligand molecules bound to

the enzyme. The expected n value for our experiments is one because one AK

molecule binds only one Ap5A molecule. Binding parameters were measured at

different temperatures (from 7 to 47 ) with a VP-ITC (Malvern, Westborough,

MA). Injection parameters were selected as follows: total number of injections =

55; volume injection = 5 !l ; spacing between injections = 220 or 300 seconds ;

duration= 10 seconds; filter period = 2 seconds. The stirring speed and Feedback

Mode/gain option were set up to 307 rpm and high respectively. Reference and

sample cells were cleaned extensively before every running. The reference cell was

filled with ddH2O. Protein solutions were degassed for at least 30 minutes. Binding

parameters (∆Ga,∆Ha,∆Sa and n) were determined from titration binding curves

using the software Originr version 7.0 (Malvern, Westborough, MA).

4.3.3 Linkage analysis between local unfolding and ensem-

ble modulation

Effects of local unfolding promoted by Gly mutations on the free energy ∆Ga and

enthalpy ∆Ha of binding were studied using the following reaction scheme:

We assumed that the folded and LU states are the only states able to bind

inhibitor and that AK unfolds through a three-state process. LU, which is regarded

to be have little affinity for the inhibitor, is the state having the LID unfolded.

As we mentioned in Chapter 3, the folded state is composed of a extended and

a compact conformation that is also populated in the absence of substrates, [15].

Due to the addition of inhibitor, the compact conformation is populated while

52

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the extended is depopulated. Based on the scheme, the apparent binding affinity

constant is defined as:

Ka =[F − I] + [LU − I]

([F ] + [LU ] + [U ])[I]=

Ko +KLUKLID

1 +KLID +KLIDφKCA

=Ko +KLUKLID

Q(4.1)

where Ko is the intrinsic binding constant between the folded and the inhibitor

and it was expected no to be affected by mutants because the crystallographic

structure is not perturbed. KLU is the intrinsic binding constant between LU and

the inhibitor. KLID, φ and KCA are the equilibrium constants associated to the

unfolding of the LID, coupling and CORE-AMPbd respectively. Q is the parti-

tion function in the absence of inhibitor, see chapter 3. Therefore, the apparent

enthalpy of binding ∆Ha is defined as

∆Ha = RT 2dln(Ka)

dT=

1

(1 +KLUKLID

Ko

)

[

∆Ho +KLUKLID

Ko

(∆HLU +∆HLID)]

− (PLU + PU)∆HLID − PU(∆Hφ +∆HCA) (4.2)

where ∆HLID, ∆Hφ and ∆HCA are the changes of enthalpies related to the un-

folding of the LID, coupling and CORE-AMPbd respectively. PLU and PU are the

probability of the state at which the LID is unfolded and the probability of the

unfolded state, respectively, in the absence of inhibitor. They were calculated from

the partition function Q. When Ko ≫ KLUKLID, Eq. 4.2 is reduced to:

∆Ha = ∆Ho − (PLU + PU)∆HLID − PU(∆Hφ +∆HCA) (4.3)

53

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The apparent free energy of binding (∆Ga) is defined as:

∆Ga = −RTln(Ko(1 +KLUKLID

Ko

)) +RTln(Q) (4.4)

When Ko ≫ KLUKLID, Eq. 4.4 is reduced to:

∆Ga = ∆Go +RTln(Q) = ∆Go +∆GConf (4.5)

4.3.4 Prediction of ∆Ha and ∆Ga

Since it is expected that Ko ≫ KLUKLID, ∆Ha and ∆Ga trends as function of

temperature were calculated using Eqs. 4.3 and 4.5, see Figs. 4.1 and 4.2. These

equations carry the assumptions that Ko ≫ KLUKLID. Therefore, the effect of

low affinity of LU on the measured affinity is considered to be negligible. Since it

is expected that mutations do not disturb the protein structure, only the equilib-

rium between the folded and locally unfolded state (LU), simulated curves were

determined by assuming that the intrinsic enthalpy (∆Ho) and intrinsic free en-

ergy (∆Go) are not perturbed. ∆Ho and ∆Go were calculated from actual WT

titration curves. ∆Ho was determined by using ∆Ha at 7 and 11 to calculate

the intrinsic heat capacity of binding, ∆CP,o, and therefore to determine ∆Ho up

to 47 , see dashed line in Fig. 4.1. ∆Go was calculated between 20 and 47

by using Eq. 4.5. This temperature range was used because ∆Ga measurements

become noisy at lower temperatures. ∆Ha and ∆Ga for V135G/V142G were de-

termined by assuming that the LID is 50% unfolded at 10 (Tm,LID = 10 ).

This assumption was included because unfolding of the LID was not observed in

DSC experiments performed on V135G/V142G between 10 and 80 . ∆HvH,LID

was determined by extrapolating ∆HvH,LID of WT to 10 . The thermodynamic

parameters of the coupling interaction and CORE-AMPbd in V135G/V142G were

taken from DSC experiments, see Table 3.1.

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4.4 Results and discussion

4.4.1 Local unfolding promoted by mutations modulates

binding affinity

Local unfolding promoted by mutations affects ∆Ha and ∆Ga. Our data show

the temperature dependence of mutational effects, see Figs. 4.3 and 4.4(b)-(d).

According to our model, the presence of the low-affinity LU state, which also pop-

ulates the WT ensemble at physiological temperature, it is principal responsible

for deviations from ∆Ho, see Fig. 4.1. Mutations in the CORE-AMPbd (A55G

and A73G) exhibit similar effects on binding affinity of AK. A55G decreases ∆Ga

by 0.4 kcal/mol at 37 . On the other hand, A73G has statistically no effects on

∆Ga. However, both mutations do not affect ∆Ha between 7 and 47 . This

small change on binding affinity can be explained by the small perturbation of

the ensemble exerted by A55G and A73G, see Figs. 3.5, 3.12 and 3.13. However,

V135G and V142G promote larger and similar effects on ∆Ha and ∆Ga. This

can be explained by lower stability of the LID and the higher capacity of Gly

substitution to promote local unfolding, and therefore, the low-affinity state (LU),

especially at temperatures higher than 20 . Consequently, larger population of

LU state induces larger deviations from ∆Ho and ∆Go, see Eq. 4.3. It is shown

that A73G/V142G presents statistically the same effects on binding as V142G

because A73G has negligible effects on binding affinity and does not destabilize

the LID. V135G and V142G exhibit similar effects on binding affinity. However,

V135G/V142G trend is different from our predictions. Experimental ∆Ha de-

creases monotonically from 7 to 30 ; then, ∆Ha presents small changes with

temperature. To understand this behavior, a computational parameter exploration

was performed using Eqs. 4.2 and 4.4.

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4.4.2 The CORE-AMPbd can also bind Ap5A in the ab-

sence of the LID

LIDLESS was also able to bind Ap5A but to a much lower extent than WT, see

Fig. 4.4 (a) and (b). At 37 , ∆∆Ha is -7.5 kcal/mol and ∆∆Ga is 2.8 kcal/mol.

This value corresponds to ratio of Ka,WT/Ka,LIDLESS ≈ 95. ∆Ha follows a linear

relationship with temperature between 7 and 47 . This trend is characteristic

of a enzyme with only one state that is binding competent at that range of temper-

ature. This observation is consistent with the two-state unfolding of the CORE-

AMPbd observed in Chapter 3. The intrinsic heat capacity of binding (∆CP,o) of

AK constructs, excepting simultaneous mutation in the LID, corresponds to -0.6

kcal/mol*K, implying that the area buried during inhibitor binding belongs to the

CORE-AMPbd, see Table 4.1. This result is a strong evidence that the short linker

that replaces the LID does not perturb the structure of the CORE-AMPbd. The

assumption that the low affinity of LU have negligible effect on the observed affin-

ity on WT, single mutants and A73G/V142G was tested by determining the value

of KLUKLID/Ko at 21 . It was assumed that KLU = KLIDLESS. KLID values

were determined from Table 3.1. Additionally, it was considered that Ko = Ka,WT

because the WT ensemble is only populated by the folded states (Q = 1) at 21 .

Calculated values of KLUKLID/Ko at 21 supported the above assumption and

they were: 6.4×10−5, 6.4×10−5, 6.4×10−5, 6.4×10−5, 1.0×10−3, 4.2×10−4 and

3.2× 10−4 for WT, A55G, A73G, V135G, V142G and A73G/V142g respectively.

4.4.3 Trends of free energy and enthalpy of binding as

functions of temperature can be predicted using EAM

In general, simulated ∆Ha and ∆Ga curves agree with those obtained by ITC

experiments. This similarity in trends indicates that modulation of the ensemble

plays an important role in the regulation of ∆Ha and ∆Ga. According to Eqs.

4.3 and 4.5, the decrease of ∆Ha and increase of ∆Ga can be explained by the

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larger population of the low-affinity LU state promoted by Gly mutations, see

Figs. 4.1 and 4.2. Although our model predicts the binding signature trends of

single mutants and A73G/V142G, it does not completely capture the trend of ΔGa

and ΔHa of mutants having two simultaneous Gly mutations on the LID. After a

steady decrease of ΔHa as temperature was raised, ΔHa presented small changes

at temperature higher than 30, crossing the ΔHa profiles of V135G and V142G,

see Figs. 4.1 and 4.3 (c). In addition, experimental ΔGa exhibits more positive

values when compared with the simulated curve specially at temperatures higher

than 30 , see Figs. 4.2 and 4.4 (c). A plausible explanation for this unexpected

trend is presented below.

4.4.4 Double mutations in the LID completely depopulate

the folded state at 40.

Effects of two simultaneous mutations in the LID on binding affinity, see Figs.4.7

and 4.8, could be explained if double mutations in the LID promotes high depopu-

lation of the folded state at temperatures higher than 20. Our simulations shows

that the ensemble is populated by the LU state, which is regarded a low-affinity

state, at temperatures between 40 and 47. On the other hand, the popula-

tion of the folded state is 50% at 13 and 1% at 37, see Fig. 4.9. Simulation

also suggest that double mutantions in the LID do not change the crystallographic

structure. They just modulate the ensemble as expected. This simulation also

suggests that DSC experiments were not able to detect the unfolding of the LID

in V135G/V142G because of the low stability promoted by two simultaneous Gly

mutations in the LID.

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4.5 Conclusions

Our ITC experiments support the view that the redistribution of the conforma-

tional ensemble promoted by local unfolding is the principal mechanism in binding

affinity regulation. The population of the low-affinity LU state, which is present on

the WT ensemble, is increased by Gly mutations. Surprisingly, AK can marginally

bind Ap5A although the LID is removed. Furthermore, computational investi-

gation of ∆Ha and ∆Ga of V135G/V142G strongly suggests that simultaneous

mutations in the LID do not change the structure. They only modulate the en-

semble.

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(a) Apparent (∆Ha) and intrinsic (∆Ho) binding enthalpies ofWT

(b) Simulations of ∆Ha of Gly mutants

Figure 4.1: Simulation of ∆Ha as a function of temperature of AK mutants usingEq. 4.3. (a) ∆Ho,WT as a function of temperature was determined by using∆Ha,WT at 7 and 11 to calculate ∆CPo,WT . Then, ∆Ha,WT at 7 was taken asreference and it was extrapolated up to 47 . (b) In mutants, ∆Ha was determinedby using ∆Ho,WT and associated partition function calculated from DSC, see Table3.1. Since DSC experiments performed on V135G/V142G did not detect unfoldingof the LID between 10 and 80 , it was assumed that the associated Tm,LID is10 . ∆HvH,LID of V135G/V142G was calculated using ∆HvH,LID of WT and∆Cp,LID.

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(a) Apparent (∆Ga) and intrinsic (∆Go) free energies of bindingof WT

(b) Simulation of ∆Ga of AK mutants

Figure 4.2: Simulation of ∆Ga at different temperatures of AK mutants using Eq.4.5. (a) ∆Go,WT as function of temperature was calculated by rewriting Eq. 4.5.That is, ∆Go,WT = ∆Ga,WT −RTln(QWT ). (b) ∆Ga of mutants were determinedby using ∆Go,WT and the associated partition function (Q) calculated from DSC,see Table 3.1. For V135G/V142G, it was assumed that the associated Tm,LID is10 . ∆HvH,LID of V135G/V142G was calculated using ∆HvH,LID of WT and∆Cp,LID.

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(a) LIDLESS (b) Mutations in the CORE-AMPbd

(c) Mutations in the LID (d) Mutations in the LID and CORE-AMPbd

Figure 4.3: Apparent enthalpies of binding of AK constructs vs temperature (∆Ha

vs T). Temperature varies from 7 to 37 . The inhibitor Ap5A was used asligand. (a) LIDLESS is also able to bind the inhibitor. (b)-(d) Gly mutations in-crease the population of the low-afinity state (LU), especially at high temperatures.Larger population of LU results in lower values of ∆Ha.

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(a) LIDLESS (b) Mutations in the CORE-AMPbd

(c) Mutations in the LID (d) Mutations in the LID and CORE-AMPbd

Figure 4.4: Apparent free energies of binding of AK constructs vs temperature(∆Ga vs T). Temperature varies from 7 to 37 . The inhibitor Ap5A was usedas ligand. (a) LIDLESS binds the inhibitor at much less extent than WT does,approximately 37 fold less at 21 . (b)-(d) Gly mutations increase the popula-tion the binding incompetent (LU) state, especially at high temperatures. Largerpopulation of LU results in more positive values of ∆Ga.

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(a) LIDLESS (b) WT (c) A55G

(d) V135G (e) V142G (f) V135G/V142G

Figure 4.5: Representative ITC titration curves at 37 with respective fittingparameters.

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(a) LIDLESS (b) WT (c) A55G

(d) V135G (e) V142G (f) V135G/V142G

Figure 4.6: Representative binding signatures at 37 . These plots show the effectsof entropy-enthalpy compensation on AK constructs. Relative small changes in∆Ga are accompanied by large changes in ∆Ha and −T∆Sa, which show opposingeffects.

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(a) Simulated ∆Ha of V135G/V142G. ∆Ho,WT and ∆HLIDLESS

are shown as comparison

(b) Comparison of ∆Ha constructs with simulated ∆Ha ofV135G/V142G

Figure 4.7: Simulated ∆Ha of V135G/V142G as a function of temperature usingEq. 4.2 (dotdash line). (a) Simulated curve of ∆Ha involves the terms Ho,WT

and ∆HLU . It was assumed that KLU = KLIDLESS and ∆HLU = ∆HLIDLESS

(b) Simulated ∆Ha was calculated using the following values: ∆HvH,LID = 28.4kcal/mol, ∆CP,LID = 0.4 kcal/mol*K , Tm,LID = 13 , ∆HvH,φ = 8.1 kcal/mol,∆CP,φ = 0.0 kcal/mol*K , Tm,φ = 102.5 , ∆HvH,CA = 109.1 kcal/mol, ∆CP,CA =2.7 kcal/mol*K , Tm,CA = 53.4 . ∆Ha of WT, V135G, V142G and V135G/V142Gwere plotted for comparison.

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(a) Simulated∆Ga of V135G/V142G. ∆Go,WT and ∆GLIDLESS

is shown as comparison

(b) Comparison of ∆Ga of constructs with simulated ∆Ga ofV135/V142G

Figure 4.8: Simulated ∆Ga of V135G/V142G as a function of temperature usingEq. 4.4 (dotdash line). (a) Simulated curve of ∆Ga involves the terms ∆Go,WT

and ∆GLU . It was assumed that ∆GLU = ∆GLIDLESS. (b) Simulated ∆Ga wascalculated using the following values: ∆HvH,LID = 28.4 kcal/mol, ∆CP,LID = 0.4kcal/mol*K , Tm,LID = 13 , ∆HvH,φ = 8.1 kcal/mol, ∆CP,φ = 0.0 kcal/mol*K ,Tm,φ = 102.5 , ∆HvH,CA = 109.1 kcal/mol, ∆CP,CA = 2.7 kcal/mol*K , Tm,CA =53.4 . ∆Ga of WT, V135G, V142G and V135G/V142G were plotted for compar-ison (b).

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Figure 4.9: Calculated probabilities of states of simulated V135G/V142G in theabsence of Ap5A. Probabilities of states as function of temperature were calculatedusing values in Fig. 4.7 on Eq. 3.1. According to our simulations, V135G/V142Gdoes not change intrinsic affinity, only depopulates the folded state to at largerextent than V135G and V142G.

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AK constructs: LIDLESS WT A55G A73G V135G V142G A73G/V142G

∆CP,o (kcal/mol*K) -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6

Table 4.1: Intrinsic enthalpy of binding (∆CP,o) of AK constructs, calculated ac-cording to: ∆CP,o = (∆Ha,11 − ∆Ha,7 )/(11 − 7 ). Although the LID wasremoved, LIDLESS exhibits the same ∆CP,o as WT.

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Chapter 5

Measurement of catalytic rate of

AK constructs

5.1 Abstract

Catalytic rate (kcat) describes how fast a enzyme converts substrates into products.

In this chapter, we investigate the effects of promoted local unfolding by Gly

mutations on kcat associated with the reverse catalytic reaction [41] (Mg2+ADP +

ADP →Mg2+ATP+AMP ) between 15 and 50 . Our data indicate that single

mutations in the CORE-AMPbd (A55G and A73G) cause an increase in kcat by a

factor of 29% and 16% at 37 respectively. On the other hand, single mutations in

the LID (V135G and V142G) have no impact in kcat between 15 and 40 . After

40 , kcat was lower in V135G and V142G, implying that mutational effects increase

with temperature. However, two simultaneous mutations in the LID, promoted

lower values of kcat at any temperature. Surprisingly, when A73G and V142G

were simultaneously present, kcat reached similar values to those observed in A55G.

This result suggests that mutational effects are not necessarily additive. Removal

of the LID dramatically decreases kcat by a factor of 52 at 25 , indicating that

the CORE-AMPbd by itself is also able to poorly catalyze nucleotides. Overall,

our data show that promoted local unfolding outside the active site can modulate

kcat, and the magnitude of the effect depends on the location of the perturbation.

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5.2 Introduction

Enzymes speed up reactions without altering the equilibrium between the sub-

strates and products, meaning that the depletion rate of substrate and formation

rate of products are increased by the same factor. According to the transition

state theory (TST), enzymes catalyze reactions by decreasing the activation en-

ergy barrier, by binding more tightly the transition state than the ground state,

[60]. Thus, higher binding propensity of enzymes for transition states favors the

crossing of the barrier, increasing the formation of products. Catalytic activity is

characterized by the catalytic rate (kcat) and the activation energy barrier (∆G‡).

kcat is defined as the rate of substrate-to-product conversion when the enzyme is

saturated with substrate. As stated by the Eyring-Polanyi equation [61, 62], kcat

can be described as a function of temperature and ∆G‡, see Eq. 5.1. In this chap-

ter, we study the impact of induced local unfolding on kcat on the reverse catalytic

reaction (Mg2+ADP + ADP → Mg2+ATP + AMP ) at different temperatures.

kcat was measured at saturating concentration of Mg2+ and ADP . Then, the

enthalpy (∆H‡) and entropy (∆S‡) of the transition state, and therefore ∆G‡,

were determined by using the linear Eyring-Polanyi equation, see Eq. 5.3. It has

been proposed that AK catalysis follows a random Bi Bi mechanism [58] at which

two different substrates bind their corresponding site randomly. In addition, it

has been determined that the rate-limiting step in AK catalysis is the conforma-

tional change of the LID related to the release of the products (kLID)[29]. This

conformational change is also regarded as the opening of the LID to release the

products. Simulations based on the random Bi Bi mechanism, see Fig. 5.1, were

also employed to improve our understanding of the effects of local unfolding on

kcat.

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5.3 Materials and methods

5.3.1 Measurements of catalytic activity in the reverse re-

action

Reverse reaction was measured by coupling the formation of Mg2+ATP to the

hexokinase and glucose-6-phosphate dehydrogenase reactions [40]. The reaction

mixture was composed of 50 mM HEPES, 10 mM D-Glucose, 20 mM MgCl2,

100 mM KCl, 15 mM ADP, 1.2 mM NADP and 0.5 mg/ml BSA, 10 UN/ml of

hexokinase and glucose-6-phosphate dehydrogenase (diluted in 50% w/v glycerol),

pH 8.0. The reaction was equilibrated at the desired temperature for at least 5

min. and then started by the addition of 10 l of 0.4 M AK. The total mixture

volume was 1 ml. The rate of increase in absorbance produced by the formation of

NADPH (kNADPH) was measured at 340 nm. To test that Mg2+ADP +ADP →

Mg2+ATP + AMP was the slowest reaction, 1.5 mM of ATP was added to the

reaction mixture at 25!. The rate of NADPH conversion was more than 10 times

greater than the fastest AK rate measured at the same temperature. Finally, kcat

was determined according to:

kcat =kNADPH

2 εNADPH [E]T(5.1)

where, εNADPH is the extinction coefficient of NADPH and is equal to 6220 AU

M−1cm−1 and [E]T is the final concentration of AK in the reaction solution. En-

zyme concentrations were determined with a UV spectrometer and corrected by

using the number of sites (n) obtained from Ap5A-ITC experiments run at the

same temperature as the activity assay. All the chemical compounds used in this

assay were acquired from Sigma-Aldrich.

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5.3.2 Transition state characterization

According to the TST, a reaction rate k is a function of temperature and a high-

energy barrier, [61] and it is described by the Eyring-Polanyi equation as follows:

k =kBT

he−

∆G‡

RT (5.2)

where, ∆G‡ is free energy of the transition state and corresponds to the highest

point in the energy profile. For enzyme kinetics, kcat is the apparent rate in a

catalytic process and it can be linked to the TST parameters by linearizing the

Eyring-Polanyi equation, thus:

ln(kcatT

) = −∆H‡

R

1

T+

∆S‡

R+ ln(

kBh) (5.3)

In this equation, ∆H‡ and ∆S‡ are assumed to be temperature independent. The

transition state of every AK construct was characterized by taking the linear region

of the ln(kcat/T ) vs 1000/T plot, see Table 5.2 and Fig. 5.3.

5.3.3 Exploration of kcat modulation through a random Bi

Bi mechanism

kcat was modeled according to the reaction scheme shown in Fig. 5.1. The model

assumes that substrates and the enzyme bind very fast compared with the phos-

phate transfer and the release of products. Therefore, substrates and the enzyme

achieve a state of quasi-equilibrium, [63]. This model also assumes that the con-

formational change of the LID (kLID) associated with the release of the product

is the rate-limiting step in AK catalysis. In other words, the conversion of ADP

into ATP and AMP and the release of AMP are regarded as fast compared with

kLID. All the AK species formed after the phosphate transfer were assumed to be

negligible. The folded state was assumed to be the only binding competent state,

see Chapter 4. Mg2+ADP and Mg2+ATP bind to residues in the LID and CORE

(ATP site) and the ADP and AMP bind to residues in the CORE and AMPbd

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(AMP site), [18]. Although, there is evidence that either AMP or Mg2+ can bind

to the ATP site at high concentrations, [58, 64], this model does not consider those

effects. Thus, the expression used to simulate kcat as function of temperature was:

kcat =kLIDKMg2+ADPKADP [Mg2+ADP ][ADP ]

Q+KMg2+ADP [Mg2+ADP ]+KADP [ADP ]+KMg2+ADPKADP [Mg2+ADP ][ADP ](5.4)

where, KMg2+ADP and KADP are the binding affinity constant related to the as-

sociation of AK with Mg2+ADP and AK with ADP respectively. [ADP ] and

[Mg2+ADP ] were calculated as follows:

[ADP ]=−(KMg2+ ([Mg2+]T−[ADP ]T )+1)+

(KMg2+ ([Mg2+]T−[ADP ]T )+1)2+ 4KMg2+ [ADP ]T

2KMg2+

(5.5)

[Mg2+ADP ]=[ADP ]T−[ADP ] (5.6)

KMg2+ is the association constant for Mg2+ and ADP. [Mg2+]T and [ADP ]T are

the total concentration of Mg and ADP. kLID was assumed to follow Eq. 5.2.

Binding constants (KMg2+ADP and KADP ) were calculated assuming free energies

of binding as constants with temperature. Prediction of ln(kcat/T ) vs 1000/T for

AK constructs were determined by assuming that Gly mutations do not change

kLID,KMg2+ADP and KADP , see Fig. 5.2. Partition functions were calculated accord-

ing to thermodynamic values from Table 3.1, with the exception of V135G/V142G.

For this double mutant, we used the partition function used to explain the trend

of ∆Ha and ∆Ga observed in ITC experiments, see Figs. 4.7 and 4.8. The propose

model was also used to analyze our experimental data, see Figs. 5.4 and 5.5.

5.4 Results and discussion

5.4.1 Mutational effects are temperature dependent

All constructs increase kcat with temperature, indicating the importance of thermal

motion in protein function. However, kcat drops dramatically at high temperatures.

It was observed that the catalytic activity ceases at 55 in all the AK constructs.

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While some mutants maintain or decrease kcat, others such as A55G, A73G and

A73G/V142G increase it. The dramatic drop of kcat observed in AK constructs at

high temperatures, see Fig. 5.3, can be reconciled by inspection of Eq. 5.4. This

equation indicates that the partition function (Q) becomes the dominant term in

the denominator at high temperatures. Higher values of Q are associated with

larger population of low-affinity (LU) and unfolded states (U).

5.4.2 Local unfolding modulates kcat

A55G and A73G increase kcat by 36% and %9 respectively at 25 , see Fig. 5.3(a)

and Table 5.1 by lowering the activation energy, see Table 5.2. The increase is ob-

served for the whole temperature range (15-55 ). According to our kinetic model,

see Fig. 5.1, higher kcat values can be achieved by faster kLID, by higher binding

affinity between AK and substrates (KMg2+ADP , and KADP ) or combination of both

effects. ITC experiments show that our mutants do not increase binding affinity

(Ka). In fact, A55G slightly decreases it. Therefore, the simplest explanation is

that higher kcat can be the result of faster release of [Mg2+ATP ] (that is, higher

kLID), see Fig 5.4. Single mutations in the LID have no impact in kcat between

15-40 , see Fig. 5.3(b). After this temperature, single mutants exhibit higher

drops in kcat. Our model can explain this trend by the larger population of LU

induced by Gly mutations without any change in kLID, KMg2+ADP or KADP . In

other words, single mutants do not perturb the folded state. Double mutations

in the LID decreases kcat. This trend can be explained if double mutations only

lower kLID, see Fig 5.5. Finally, simultaneous single mutations in the LID and

CORE-AMPbd (A73G/V142G) increase kcat to the same extent as A55G does,

see Fig. 5.3(c). Again, this result can be the effect of higher kLID. This result

indicates that mutational effects are not necessarily additive.

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5.4.3 LIDLESS exhibits marginal catalytic activity

LIDLESS also catalyzes substrates. However, the catalytic activity is dramatically

reduced by the absence of the LID, see Fig. 5.3(c). The observed trend can be

described considering only that KMg2+ADP is close to zero and the transfer of the

phosphate group is the rate-limiting step. This result raises the question of what

is the catalytic function of the LID. It has been suggested that the LID protects

the phosphate-group transfer from water during catalysis [52]. However, AKs from

different organisms have a short (e.g. porcine AK, domain: eukaryota, pdb file:

3ADK) or no LID domain (e.g. sulfolobus solfataricus AK, domain: archaea, pdb

file: 3HOK).

5.5 Conclusions

Local unfolding can modulate kcat. Single mutations in the LID maintain catalytic

activity. Single mutations in the CORE and AMPbd increase it; and, two simul-

taneous mutations in the LID decrease it. According to our kinetic model, kcat

modulation can result by slowing down or increasing the release of the products

(kLID modulation). Unexpectedly, AK can also catalyze nucleotides without the

LID (LIDLESS), but to a marginal extent.

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Figure 5.1: Kinetic model for AK. The model is based on the random Bi Bi mechanism [58]. In this model, the LID only bindsMg2+ADP andMg2+ATP , [18]. The AMPbd only binds ADP and AMP. It was assumed that a there AK and substrates reacha state of quasi-equilibrium followed by a slow catalytic event [63]. In this model, the rate-limiting step is the conformationalchange of the LID (kLID) before the release of Mg2+ATP, [29, 15]. KMg2+ADP and KADP are the binding affinity constants relatedto the association of AK with Mg2+ADP and AK with ADP respectively. F, LU and U are the folded, LID unfolded andunfolded states respectively.

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Figure 5.2: Expected ln(kcat/T ) vs 1000/T using Eq. 5.4. It was assumed thatmutations did not change KMg2+ADP , KADP and kLID. Values used in our simu-lation were: [ADP ]T = 4 mM, [Mg2+]T = 2 mM, ∆H‡ = 11.7 kcal/mol, ∆S‡ =-0.01 kcal/mol*K, KMg2+ = 4000 M−1, KMg2+ADP = 30303 M−1, KADP = 3570 M−1.Binding affinity constants were taken from [59]. Temperature varies from 15 to60 . Partition functions, with the exception of V135G/V142G, were calculatedusing values in Table 3.1 in Chapter 3. Since DSC experiments performed onV135G/V142G did not detect unfolding of the LID between 15 and 80 . Parti-tion functions were calculated using the values to simulate the trend of ∆Ha and∆Ga observed in ITC experiments. In sum, ∆HvH,LID = 28.4 kcal/mol, ∆CP,LID =0.4 kcal/mol*K , Tm,LID = 13 , ∆HvH,φ = 8.1 kcal/mol, ∆CP,φ = 0.0 kcal/mol*K,Tm,φ = 102.5 , ∆HvH,CA∗ = 109.1 kcal/mol, ∆CP,CA∗ = 2.7 kcal/mol*K, Tm,CA∗= 53.4 . *CA = CORE-AMPbd.

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(a) Mutations in the CORE-AMPbd (b) Mutations in the LID

(c) Mutations in the LID and CORE-AMPbd (d) LIDLESS

Figure 5.3: Experimental data fitted to the linear form of the Eyring-Polanyiequation, see Eq. 5.3. Temperature varies from 15 to 50 .

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AK kcat,25

Construct (1/s)

WT 124.6 4.0

A55G 169.9 4.0

V135G 135.2 4.0

V142G 132.0 4.0

A73GV142G 174.2 4.0

V135GV142G 69.8 2.0

V135GV148G 101.3 2.0

V142GV148G 102.7 4.0

LIDLESS 2.4 0.1

Table 5.1: Representative values of kcat at 25!.

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AK ∆H‡ −T∆S‡ ∆G‡25

Construct (kcal/mol) (kcal/mol) (kcal/mol)

WT 10.6 0.3 4.1 0.3 14.6 0.4

A55G 10.9 0.2 3.7 0.2 14.4 0.3

A73G 10.9 0.4 3.7 0.4 14.5 0.6

V135G 10.7 0.3 3.9 0.3 14.5 0.5

V142G 10.7 0.3 4.0 0.3 14.6 0.4

A73GV142G 10.9 0.3 3.7 0.3 14.4 0.5

V135GV142Ga 12.8 1.3 2.3 1.3 14.9 1.8

V135GV148Gb 10.1 0.7 4.9 0.7 14.8 1.0

V142GV148Gc 10.9 0.2 4.0 0.2 14.7 0.3

LIDLESS 8.2 1.1 9.1 1.1 16.9 1.5

Table 5.2: Characterization of the transition state using the linear Eyring-Polanyiequation, see Eq. 5.3. Activation free energy barrier at 25!. Curve fitting wasperfomed on data collected between 15! and 40!, excepting (a) V135G/V142G(15!-25!), (b) V135G/V148G (15!-35!) and (c) V142G/V148G (15!-30!)∆H‡ and −T∆S‡ and related errors were obtained from least square fitting. Errorsin ∆G‡37 were calculated by propagation of errors associated to ∆G‡ and −T∆S‡.

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Figure 5.4: Simulation of mutational effects of A55G and A73G on kcat. It isassumed that these mutations only lower ∆G‡ by decreasing ∆S‡. Similar effectscan be explained if it is assumed that mutations increase binding affinity. However,this effect is not supported for ITC binding experiments. Partition functions werecalculated from Table 3.1. The binding constants, KMg2+ADP and KADP , wereassumed not to be affected by mutations. Parameter used in this simulation were:[ADP ]T = 4 mM, [Mg2+]T = 2 mM, ∆H‡ = 11.7 kcal/mol, KMg2+ = 4000 M−1,KMg2+ADP = 30303 M−1, KADP = 3570 M−1. ∆S‡ for WT, A55G and A73G were-0.01, -0.094 and -0.097 kcal/mol*K respectively. Temperature varies from 15 to60 .

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Figure 5.5: Simulation of mutational effects of V135G and V142G on kcat. It isassumed that single mutations do not change kLID, KMg2+ADP andKADP . See valuesin Fig. 5.2. V135G/V142G only decreases kcat by decreasing kLID (∆S‡ = -0.11).Temperature varies from 15 to 60 .

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Chapter 6

Characterization of the ensemble

modulation using HX-NMR and

ITC

6.1 Abstract

The ensemble modulation was investigated using hydrogen/deuterium exchange

NMR (HX-NMR) and ITC at 37 . Stability of the LID (∆GLID) and stability of

the CORE-AMPbd, including the coupling interaction, (∆Gφ+∆GCA) were deter-

mined at 37 by using a method previously developed in our lab, [65]. According

to this method, ∆GLID and ∆Gφ +∆GCA were 1.3 and 7.3 kcal/mol respectively.

In V142G the stability of the LID was reduced to -0.2 kcal/mol. Subsequently,

the probability of the folded state of WT and V142G were calculated. Our results

show that the population of the folded state in WT represents 90% of the ensem-

ble. As expected, V142G modulates the ensemble by depopulating the folded state

from 90% to 43% and by increasing the locally unfolded state from 10% to 57%.

Although, the values obtained by this method slightly differ from those determined

by DSC, they also show the effect of a Gly mutation on the ensemble modulation.

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6.2 Introduction

Hydrogen/deuterium exchange NMR (HX-NMR) [21] is used to determined the

stability (∆GHX) at 37 of different regions and to describe partially folded states.

Because of conformational fluctuations, exchange-incompetent amide protons (due

to burial or hydrogen bonding) are exposed to the solvent and become susceptible

to be exchanged with deuterium (D2O). If the rate of the amide proton to become

exchange-incompetent again is much larger than the rate to exchange with D2O

(condition known as the EX2 regime), the equilibrium constant (KHX) between

the exchange-competent (HX-C) and the exchange-incompetent (HX-I) state can

be determined. The equilibrium constant in turn gives the stability (∆GHX) asso-

ciated with the corresponding conformational fluctuation, [36]. HX-NMR exper-

iments have been previously performed on E. coli AK at 20 , [12]. It has been

reported that the CORE is the most stable region. It was also observed that the

residues in the LID and the AMPbd exchanged during the dead time for exchange,

which is the time between the very first exposure of AK to D2O and the very

first NMR measurement. Consequently, they were not observed during the actual

experiment. To determine the modulation of the ensemble, ∆GLID, ∆Gφ +∆GCA

as well as the impact of Gly mutation on the LID stability (∆gmut) were deter-

mined by using a method developed in our lab, [65]. This method combines ∆GHX

measured in the absence of ligand and ∆Ga from HX-NMR and ITC experiments,

respectively, to access domains stabilities. In this chapter, the probability of the

folded states for WT and V142G were measured at 37 and compared with those

values obtained from DSC experiments.

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6.3 Materials and methods

6.3.1 Sample preparation

WT and V142G were 15N-labeled using the protocol presented in [37] and pu-

rified according to details described in Chapter 2. Protein samples were then

concentrated to ≈ 1mM using centrifugal filter units Amicon Ultra-15 30K (EMD

millipore) at 900xg (2500 rpm) in a Sorvall GS-3 rotor at 4 . A D2O solu-

tion was made using deuterium 99 atom % D from Sigma-Aldrich with 30 mM

PIPES buffer (AmericanBio). The pH was then measured using sodium deuterox-

ide (Sigma-Aldrich) at 37 . Subsequently, the pD was calculated according to

the formula pD = pH + 0.4, [12]). Concentrated AK solutions were exchanged to

D2O using the above-mentioned filter units under the same temperature and rotor

speed. The filter units were previously washed with D2O through centrifugation.

To ensure that the solution contained more than 90% of deuterium, the AK solu-

tion (≈ 600 !l) was mixed with the D2O (≈ 1800 !l) solution with a volume ratio

of 1 to 3. The mixed solution was then centrifuged until getting the same volume

of the initial AK solution. Then, the resulting mixed solution was again mixed

with the D2O solution with the same volume ratio. The new mixed solution was

centrifuged again to recover the initial AK solution volume. The exchange to D2O

took around 1 hour. The percent of D2O in the final solution was determined to

be 96% and it was calculated according to:

%D2O = [(Vratio + 1)n − 1

(Vratio + 1)n] · 100% (6.1)

where Vratio is the volume ratio of D2O solution to AK solution. n is the number

of repetitions. The pD of the AK exchanged solution was measured at 37 .

Thereafter, the solution was transfered to a NMR tube and immediately sent to

the NMR spectrometer. The corresponding pD values were measured again after

the NMR data was acquired. As expected, pD did not change.

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6.4 Data acquisition and processing

Data were acquired in the Varian Inova 800 MHz NMR spectrometer at 37 . Ap-

parent hydrogen exchange rates (kex) were determined by collecting 1H-15N HSQC

NMR spectra for 48-60 hours. NMR data were processed using NMRPipe [68] and

Sparky [69] for Linux. Peak intensities were measured by volume integration and

kex was determined by fitting the function:

I = Ioe−kext + C (6.2)

where I is the intensity as a function of time, Io is the initial intensity and C

is a constant that corresponds to the baseline noise caused by residual H2O in

the sample, see [70]. Experiments were performed at different pD conditions to

determine the exchange regime (EX2 or EX1). WT Spectra were collected at pD

values of 6.8 and 7.2, and V142G spectra at pD values of 6.9 and 7.3. Then,

the slope of the log10(kex) vs ∆pD curve was determined. A slope equal to one

is associated with the EX2 regime, assuming that the equilibrium constant KHX

is pD independent, and slope of zero with the EX1 regime. ∆GHX values were

calculated only in residues that exchanged under the EX2 regime according to :

∆GHX = −RTln(kexkrc

) (6.3)

where krc is the intrinsic rate exchange. It corresponds to the rate at which an

solvent-exposed amide hydrogen is exchanged to deuterium. krc is pD and tem-

perature dependent and it was calculated at 37 according to [70], [71] and [72].

6.5 Domain stabilities

Since the stability of the LID cannot be monitored by HX-NMR, our lab developed

a method [65] to access the LID stability and therefore the probability of the folded

state. For this purpose, ∆Ga (free energy of binding) along with ∆GHX of WT

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and V142G were combined to determine the stability of the LID and the CORE,

and subsequently, the probabilities of the folded states at 37 . The unfolding

reaction scheme for WT is similar to the scheme used in DSC experiments, see

Chapter 3, and it is defined as:

FKLID−−−−−−−−−−−−−−−−−− LU

φKCA−−−−−−−−−−−−−−−− U

F is the folded state, LU is the locally unfolded state whereby the LID is unfolded,

and U is the unfolded state. For V142G, the unfolded reaction is:

FΩKLID−−−−−−−−−−−−−−−−−−−− LU

φKCA−−−−−−−−−−−−−−−− U

where Ω represents the effect of the Gly mutation in the stability of the LID by

increasing the conformational entropy. Since it is assumed that single mutations

introduce only entropic perturbations, Ω is constant and is equal to:

Ω = e−∆gmut

RT = e∆SR (6.4)

We assumed that the unfolded state is the only exchange-competent state. F and

LU states were regarded as exchange-incompetent states. Thus the equilibrium

between the exchange-competent and exchange-incompetent state is for WT:

KHX,WT =[U ]

[F ] + [LU ]=KLIDφKCA

1 +KLID

(6.5)

and for V142G:

KHX,V 142G =ΩKLIDφKCA

1 + ΩKLID

(6.6)

thus,

∆∆GHX = −RTln(Ω(1 +KLID)

1 + ΩKLID

) (6.7)

More relationships between Ω, KLID and KCA were obtained from ∆Ga through

the following binding scheme:

In this scheme used for WT, it is assumed that the folded state (F) is the only

state able to bind the inhibitor Ap5A, see Chapter 4. For V142G, the scheme

reaction was:

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F-I represents the bound state and Ko is the intrinsic affinity and it is the same

for WT and V142G. It was assumed that V142G substitution did not change Ko

and that the probability of the unfolded state is close to zero at 37 , therefore:

∆∆Ga = −RTln(1 +KLID

1 +ΩKLID

) (6.8)

By using Eqs. 6.5, 6.7 and 6.8, we obtained the mutational perturbation ∆gmut,

∆GLID and ∆Gφ + ∆GCA, thus:

∆gmut = ∆∆GHX −∆∆Ga (6.9)

∆GLID = −RTln(e−

∆∆GaRT − 1

1− e−∆∆GHX

RT

) (6.10)

∆Gφ +∆GCA = ∆GHX,WT −∆GLID −RTln(1 + e−∆∆GLID

RT ) (6.11)

It is assumed that ∆Gφ + ∆GCA is the same for both WT and V142G. However

the stability of the LID in V142G was calculated according to:

∆GLID,V 142G = ∆GLID +∆gmut (6.12)

Finally, the probability of the folded state (F) was determined using Eq. 3.1.

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6.6 Results and discussion

6.6.1 The CORE is the most stable domain.

HX-NMR experiments clearly showed that residues L83 and V106 in the CORE

are the most stable residues in E.coli AK at 37 . see Figs. 6.1 and 6.4 and Tables

6.1 and 6.2. It is important to mention that only residues in the CORE were

detected and that L83 and V106 were the only residues in the EX2 regime, see Figs.

6.3 and 6.6. Residues in the LID and AMPbd were not detected during the data

acquisition, indicating the high conformational flexibility of both domains. Similar

conclusions were reached by Rundqvist and colleagues, see [12], by measuring

∆GHX through urea denaturation at 20 . Overall, amide hydrogen/deuterium

exchange experiments clearly show the intrinsic flexibility of proteins whereby the

most buried residues can also visit the solvent.

6.6.2 V142G modulates the conformational ensemble.

According to the methods employed in the material and methods section of this

Chapter, V142G depopulates the folded state (F) from 90% to 43%, and at the

same time, it increases the population of the locally unfolded state (LU) from

10% to 57% at 37 . This results also show that the LU state is also populated

at the physiological temperature of AK (37 ). At this temperature, ∆GLID is

1.3!0.2 kcal/mol and ∆Gφ + ∆GCA is 7.3!0.2 kcal/mol in WT. In V142G, the

Gly substitution decreases ∆GLID to -0.2!0.2 kcal/mol entropically. Although

the probabilities of the folded state in WT and V142G determined by HX-NMR

and ITC differ from those determined using DSC (95% and 71% respectively), the

effect of promoted local unfolding in the ensemble modulation is clearly evident.

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6.7 Conclusions

Gly substitutions can modulate the ensemble of states by depopulating the folded

state and populating the locally unfolded state. Interestingly, the locally unfolded

state (LU), at which the LID is unfolded, is also visited by AK at physiological

temperatures. Finally, high flexibility, and therefore the low stability, of the LID

and AMPbd domains as well as the higher stability of the CORE were all confirmed.

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Figure 6.1: Location of residues in the EX2 in WT.

Residues ∆GHX,37 (kcal/mol)

L83 8.7 0.1

V106 8.7 0.1

∆GHX,WT (average) 8.7 0.1

Table 6.1: ∆GHX of L83 and V106 in WT. Values were calculated according toEq. 6.3.

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(a) L83, pD=6.8 (b) L8, pD=7.2

(c) V106, pD=6.8 (d) V106, pD=7.2

Figure 6.2: The apparent rate constant (kex) of residues L83 and V106 in WT.Data points were fitted to Eq.6.2.

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Figure 6.3: Residues in the EX2 regime in WT. A value of log10(kex)/pD = 1indicates that kex can be used to determine ∆GHX .

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Figure 6.4: Location of residues in the EX2 regime in V142G.

Residues ∆GHX,37 (kcal/mol)

L83 7.5 0.1

V106 7.7 0.1

∆GHX,V 142G (average) 7.6 0.1

Table 6.2: ∆GHX of residues L83 and V106 in V142G. Values were calculatedaccording to Eq. 6.3.

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(a) L83, pD=6.9 (b) L8, pD=7.3

(c) V106, pD=6.9 (d) V106, pD=7.3

Figure 6.5: The apparent rate constant (kex) of residues L83 and V106 in V142G.Data points were fitted to Eq.6.2.

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Figure 6.6: Residues in the EX2 regime in V142G. A value of log10(kex)/pD = 0.9indicates that L83 and V142 are just leaving the EX2 regime.

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AK ∆Ga ∆GHX

Constructs (kcal/mol) (kcal/mol)

WT -9.3 0.1 8.7 0.1

V142G -8.9 0.1 7.6 0.1

Table 6.3: ∆Ga and ∆GHX values for WT and V142G at 37!. ∆Ga values weretaken from ITC experiments, see Chapter 4.

∆G (kcal/mol) WT V142G

∆GLID 1.3 0.2 -0.2 0.2*

∆Gφ + ∆GCA∗∗ 7.3 0.2 7.3 0.2

∆GTotal 8.6 0.2 7.1 0.2

Table 6.4: Domain stabilities values in WT and V142G at 37!. Values weredetermined by using experimental values from Table 6.3 in Eqs. 6.10, 6.11,6.9 and 6.12. *The stability of the LID in V142G was calculated according to∆GLID,V 142G = ∆GLID + ∆gmut, where ∆gmut = -1.5 0.2 kcal/mol. **CA =CORE-AMPbd

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Figure 6.7: Graphical representation of ∆GLID and ∆gmut. ∆∆Ga (∆Ga,V 142G −∆Ga,WT ) and ∆∆GHX (∆GHX,V 142G−∆GHX,WT ) at 37 were plotted accordingto Eqs. 6.8 and 6.7. ∆gmut is always constant between the two curves.

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Figure 6.8: Probabilities of the folded state of WT and V142G at 37 using valuesfrom Table 6.4. V142G reduces the population of the folded state from 90% to43%.

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Chapter 7

Concluding remarks

7.1 Summary

Allostery was investigated by biophysical characterization of the effects promoted

by entropy enhancing mutations. Our fundamental conclusion is that proteins

can use local unfolding to regulate enzyme function, whereby the redistribution of

the probability of states promoted by local unfolding is the predominant mecha-

nism. Although, it was reported [12] that the LID and AMPbd are not coupled

to the CORE, our DSC experiments clearly shows that coupling interaction be-

tween the domains exists, see Fig. 3.4. The coupling between the LID and the

CORE-AMPbd is favorable (positive) at functional temperatures, and according

to our model, unfavorable (negative) at temperatures higher than 67.8 . Since

the CORE and AMPbd unfold as a single domain, it is possible that they are also

favorably coupled. The folded state is not the only state populated at physiological

temperature (37 ). At this temperature, the folded state represents 95% of the

ensemble, while the other 5% corresponds to the state having the LID unfolded.

The population of the folded state was decreased by mutations and high tempera-

tures. Another important observation is that binding affinity and catalytic rate can

be decoupled. Higher catalytic rates can arise even if binding affinity is maintained

(A73G). Last but not least, our research supports the view of allostery as the ef-

fect of structural flexibility modulation rather than the effect of crystallographic

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distortion. That is, allostery can arise by affecting the excited states without any

crystallographic distortion.

7.2 Future directions and experiments

In this dissertation, we investigated allostery and its mechanisms. However, one

question arises, how local unfolding can promote higher kcat values? What is(are)

the mechanisms behind this effects? Our simulations suggest that faster release

of products is the underlying mechanism. To answer the above questions and test

our prediction, CPMG relaxation dispersion NMR experiments (to determine kLID)

along with enzyme kinetics assays (to measure kcat) can be performed in WT and

compared with results of A55G, A73G and A73G/V142G.

Our data also show a trend regarding binding affinity constants (Ka) and cat-

alytic activity rates (kcat) in AK. It is observed that mutations in the LID change

Ka but not kcat; and, that mutations in the CORE and AMPbd have little or no

effect on Ka but the increase kcat. Characterization of A99G (CORE) and A37G

(AMPbd) can confirm this trend. Finally, to characterize the coupling between

the AMPbd and the rest of the enzyme, a DSC experiment can be performed in a

construct at which the AMPbd has been removed.

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Appendix 1. Code in R to fit a

DSC profile using a three state

model

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To run this code, we should type:

> R> source( DSC 3s!)The following steps show how to use the R code:

(a) Select for points to determine the baseline (b) The baseline is plotted

(c) The < ∆Cp,Tr > is plotted (d) Fitting parameters are determined

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Appendix 2. Code in R to fit a

DSC profile using a two state

model

This code is run in the same way as the previous code.

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Appendix 3. Two state model

test in WT

Figure 7.1: Comparisson between the area under the data points (∆Hcal) andthe van’t Hoff enthalpy (∆HvH), determined from a two state model. The ratio∆Hcal/∆HvH greater than one indicates the presence of at least one intermediatestate.

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Appendix 4. Reversibility test

Reversibility was tested by determining the percentage of the DSC profile arearecovered after reheating the protein sample. If the area is completely recovered,the thermal unfolding is reversible. If no area is recovered after the second scan,the unfolding is therefore irreversible. The extent of reversibility of AK constructswere between 70-82%.

(a) WT (b) A73G/V142G

(c) V135G/V142G (d) LIDLESS

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To know whether irreversibility is the effect of high temperatures or is inherentto the unfolding process [24, 25], AK was heated up to a temperature equal to 3 higher than the melting temperature of the last peak. Then the sample is cooleddown and reheated up to a high temperature (≈ 80 for AK). Our results indicatethat irreversibility is caused by the effects of high temperatures and predominatelyappears after the AK was unfolded. High temperature effects include misfoldedstructure, peptide bond hydrolysis and other chemical alteration of residues, [25,26].

(a) WT (b) A73G/V142G

(c) V135G/V142G (d) LIDLESS

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