Luận án tiến sĩ: Computational study of amyloid beta protein in implicit and explicit solvent models: Probing the initial stages of aggregation

The ensemble of dimer structures are evaluatedusing rapidly computed estimates of the desolvation and electrostatic interaction energies to identify a putative stable dimer structure.. .

GRADUATE SCHOOL OF ARTS AND SCIENCES

Dissertation

COMPUTATIONAL STUDY OF AMYLOID BETA PROTEIN

IN IMPLICIT AND EXPLICIT SOLVENT MODELS: PROBING THE INITIAL STAGES OF AGGREGATION

BOGDAN TARUS

B.S., Iasi University, 1993M.A., Boston University, 2004

Submitted in partial fulfillment of therequirements for the degree ofDoctor of Philosophy

2007

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I would like to thank my advisor, Prof John E Straub, for his generous support andpatience over my entire period of doctoral studies at Boston University His sustained ded-ication as research advisor and enthusiastic teacher will constitute a permanent example forme.

I thank all the professors on my thesis committee, Prof Rosina Georgiadis, Prof TomKeyes, Prof Sandor Vajda and Prof John Snyder I also thank Prof Devarajan Thiru-malai from University of Maryland for being a constant source of help and inspiration for myresearch

I thank all my professors at Boston University I would like to thank Prof David Coker

for sharing his research enthusiasm with us I am sincerely grateful to all the colleagues I hadover the years in the Straub group

Finally, I would like to thank my family, especially my wife, Dana, for all her love and

unconditioned support

1V

IN IMPLICIT AND EXPLICIT SOLVENT MODELS:

PROBING THE INITIAL STAGES OF AGGREGATION

(Order No )

BOGDAN TARUS

Boston University Graduate School of Arts and Sciences, 2007

Major Professor: John E Straub, Professor of Chemistry

ABSTRACT

It has been proposed that the amyloid đ-protein (Ađ-protein) plays a crucial role in thedevelopment of Alzheimer’s Disease (AD) This dissertation presents the results of computa-tional studies of the initial stages of AG-protein association The objective of this work was

to determine the stability and role of the ÀØ-protein monomers and low-order oligomers asmetastable intermediates on the pathway for formation of larger aggregates and fibrils Aprotocol based on shape complementarity is used to generate an assortment of possible dimer

structures of the A@jpo_35-protein congener The ensemble of dimer structures are evaluatedusing rapidly computed estimates of the desolvation and electrostatic interaction energies to

identify a putative stable dimer structure Using the umbrella sampling method and classicalmolecular dynamics, the potential of mean force (PMF) associated with the dimerization ofthe peptide in aqueous solution is computed The profiles of the PMF corresponding to theformation of the two putative dimer structures are compared Molecular dynamics trajectories

originating from the two putative dimer structures are used to analyze their stability

Significant attempts are made to increase the time over which the association of the

Afi9—35-protein can be simulated In this respect, conformations generated by the protein simulated using an explicit TIP3P solvent model are compared to conformations re-sulting from simulations employing one empirical and two continuum electrostatics solventmodels Inspired by recent experimental results, the dynamics of the D23-K28 “salt-bridge”

A@io_35-of Ø-structure characteristic A@io_35-of amyloid fibrils.

The behavior of the Àại_ao-protein fragment is studied using molecular dynamics tions employing an explicit aqueous solvent model Special attention is paid to the VGSN(24-

simula-27) region of the protein where experimental solid-state nuclear magnetic resonance (NMR)measurements indicate that formation of a turn may play a crucial role in stabilizing theAfØi-4a-protem in fibril structure The influence of two mutations, E22Q and D23N, on thethermodynamics properties of the Ai ao fragment is analyzed and related to the possible

roles played by these two naturally occurring mutations in amyloidosis

vi

2.3.1 Dimer structure generation using a docking protocol 102.3.2 Desolvation energy screening 000.20 10

2.3.3 Molecular Dynamics 2 2 Q Q à Qv va 11

2.3.4 Secondary Structure Analysis 0.0 2000-00008 13

2.4 Results and Discussion 00.00.0000 eee ee 13

2.4.2 Generation of dimer structures 2 0 eee ee 15

2.4.38 Potential of Mean Force 0 0.0 00 eee es 24

2.4.5 Dynamical fluctuations in the y-dimer 0.0000 32

2.4.6 Time dependence of secondary structure fluctuations in the homodimer 36

3 A comparative study of the structure and thermodynamics of the

A{io_35-protein in different hydration models 39

vil

3.2 Background 2 vn gà gà lv lv vn à và và và3.38 Computational Models and Methods 0.00000 eee3.3.1 Explicit solvent molecular dynamics 0 cv pees3.3.2 Implicit solvent molecular dynamics 0 00000004

3.3.3 Computational estimation of pK, 2 0 Q2

3.4 Results and analySlS cv ng gà gà g kg v va

3.4.1 Radius of gyration c ee3.4.2 Root-mean-square Ñuctuations ee es

3.4.3 Lipari-Szabo generalized order parameter 200,43.4.4 Solvationenergy 2 2 a.aK<<.3.4.5 Solvation self-energy ch vu ng ee na3.4.6 Intra-peptide hydrogen bonds 0 Q.2

3.4.7 Computational estimation of pK, 6 LH ee

Dynamics of Asp23—Lys28 salt bridge formation in Ađịo_ss monomers

viii

K28 ee 824.4.6 Burial of K28 involves a large free energy cost - 834.4.7 The structure of water around residues D23 and K28 844.5 Summary and Conclusions 1 c Q c Q k Q kg và gà va 86

The competition between the electrostatic and hydrophobic intra-peptideinteractions in the Às¡_so-protein 91

5.2 Background kg vn gà v g kg kg kg A 925.38 Computational Methods and Models 0.000004 0 | 95

5.3.1 Simulation model and methods 0 0004 955.3.2 Computational estimation of pK, 1 2 ee 96

5.3.3 Freeenergy analysis 2 0 ee k k k k KV 985.4 Results and analysis 2 Q g gà và TT va 995.4.1 pK, values indicate weak intra-peptide electrostatic interactions 995.4.2 Inter-titratable side-chain distances 0 0.0000 106

5.4.3 Intra-peptide hydrophobic contacts 2004 108

5.4.4 Lys28 makes transitive contacts with the peptide backbone 109

5.4.5 Intra-peptide folding elements 0.000000 08 110

Bibliography 121Curriculum Vitae 137

1X

of e = 4 was used as the protein dielectric constant .00.

Computational pK, values are compared with the experimental! (in sis) pK, values for titratable residues Glu22, Asp23, and Lys28 in the A21~30-peptide The isolated residues and the residues in the peptide structure aresimilar, indicating that the pK, shifts result from weak intra-peptide electro-

parenthe-static interactions 2 6 c Q Q LH nu nu cà na vn g V NV k k k vUAThe number of nodes, N, and direct transitions among nodes, Ni, associated

with the free energy transition disconnectivity graphs of the WT, E22Q, D23N,

and K28A peptides Na, is reduced to N—1 using the minimum-cut algorithm.?

Ng nodes with free energies higher than —0.6 kcal/mol define the entropic

73

is referred to as the “e-dimer” (b) The “desolvation energy”— corresponding to

the energy change on going from separated monomeric À/Øo_ss to AZ dimericdecoy structure — was used as a measure of the degree of hydrophobic surfaceburial The decoy sets were obtained using two shape complementarity proto-

cols, GRAMM (a) and ZDOCK (b) The energy of desolvation was calculatedbased on an atom contact energy (ACE) method A bin of 0.2 kcal/mol was

used to compute the distribution of the interaction energy

The putative dimer structures derived by minimization of the functions S,(Eq (2.4)) and S, (Eq (2.6)), corresponding to the y-dimer (a) and e-dimer(b), respectively The side chains at the dimer interface are depicted explicitly.The green and yellow colored residues belong to monomer A (left) and those

in red and orange are part of monomer B (right),

Xi

of the atomic root-mean-square distance between each decoy structure and thestructure of the y-dimer (a) and the e-dimer (b) In general, the unfavorable

dimer structures are well differentiated from the most favorable structures The

desolvation energy distribution (a) has a “funnel-like” character, indicating

that structures more similar to the reference structure tend to be structures

of minimal energy The contribution of the electrostatic interaction energy

determines a discontinuous distribution (b), the structure of most of the decoy

dimers being very different from the structure of the e-dimer The sidechain-sidechain contact matrices averaged for the ten decoy structures

corresponding to the y-dimer (a) and e-dimer (b), respectively The selection

of the y-dimer is produced by a scoring function which is composed by the

de-solvation energy only (a), while the e-dimer is selected by a function defined as

the sum of the desolvation energy, the van der Waals and the electrostatic

inter-actions (b) (see text for details) The interface of the ¿-dimer is dominated bycontacts which involve hydrophobic residues, while the presence of the polar and

charged residues is evident at the interface of the e-dimer The amino acid

se-quence of the A@i9_3, monomer is Y!'EVHHQ!5KLVFF?AEDVG25°SNKGA*®

TIGLM®, 6 -ỗ q.IaẶặ a a aAa_¬Ặẽ A aaa ẶẼ

xH

2.7

tations of the monomeric peptide within the dimer The PMF is computed as

a function of the surface separation, 6 = € — €sø„;, along the distance between

the centers-of-mass (DCOMs) of the two monomers, where € and £,on: are the

DCOMs of the two monomers when they are at an arbitrary separation and incontact, respectively The profile in blue corresponds to the free energy surfacecomputed using the e-dimer as the starting structure The red curve is similarly

computed using the y-dimer as the starting structure The difference between

the two surfaces suggests that hydrophobic interactions may be more essential

to stabilization of the dimer structure than electrostatic interactions

The distribution of the surface buried area at the interface between the AGio_35monomers during the molecular dynamics simulation of the dimer indicates thatthe set of the principal contacts at the dimer interface are maintained for the

y-dimer (a), and that the e-dimer is not stable (b) A bin of 15 A? was used

to compute the distribution of the interface surface area .The comparison of the electrostatic (red) and the hydrophobic (green) inter-action energies between the A@jo_35 monomers during the molecular dynamics

simulation implies that the stability of the y-dimer is given by contacts betweenhydrophobic residues In black is shown that the contribution of the fragment

15-30 plays a dominant role to the overall stability of the y-dimer

xiii

action energies between the À/ịo_as monomers during the molecular dynamics

simulation implies that the stability of the e-dimer cannot be assured by theelectrostatic interaction between the monomers, and that the e-dimer tends toreduce the exposure to solvent of the the hydrophobic residues The behav-

ior of the interface surface area (black) implies that the e-dimer is not stable

in the first three trajectories (T1, T2, and T3) For the remaining two (T4and T5), it appears that the reorganization of the interface, by reducing theunfavorable exposure of the hydrophobic residues to the solvent, stabilizes the

é-dimer Due to the screening effect induced by the polar solvent, the strength

of the transient interpeptide salt-bridges is reduced, and, thus, the electrostaticinteraction between the monomers cannot assure the stability of the e-dimer .The root mean square displacement of the entire A@jo_35 fragment for the

monomers A (a) and B (b) during the NPT molecular dynamics simulation,

in the absence of restraints, indicates that the monomers undergo

reorgani-zation from the initial dimer configuration Under the same conditions, the

distribution of the root mean square displacement of the hydrophobic fragment

LVFEA(17-21) suggests a more conservative structure for both monomers A

(c) and B (d) A bin of 0.01 A was used to compute the distribution of the

xiv

31

experimen-perience considerable reorganization in structure over the course of the 10 ns

NPT molecular dynamics simulation The tendency of the monomer A (c) to

have a more extended conformation compared with the monomer B (d) is

ev-ident Bins of 0.1 A and 0.3 A were used to compute the distributions of the

radius of gyration and end-to-end distance, respectively

The time evolution of the secondary structure of monomer A (a) and monomer

B (b), corresponding to the first trajectory T1 of the y-dimer, shows strong

signs of formation of đ-strands preceded or accompanied by formation of traceamounts of a-helical structural motifs Random coil is represented in blue,a-helical structure in green, and G-strandinred

Distribution of the radius of gyration of the AG,9_35-protein simulated in foursolvent models The peptide structure is unrealistically compacted in all sim-

ulations employing an implicit solvent model The greatest compactness isobserved in simulations employing the ACE and GBORN models The radius

of gyration in the empirical EEF 1 solvation model is intermediate to resultsderived from the explicit and the continuum-electrostatics solvation models

The RMS fluctuations of the Aj9_35-protein backbone during its dynamics in

four solvent models The A@j9_3; peptide adopts very compact structures in

the implicit GBORN and ACE solvation models In simulations employing the

empirical solvent EEF 1, the peptide is more flexible In explicit water, TIP3P,the termini show large fluctuations relative to the peptide core

51

3.5

peptide backbone For A(19_35-protein simulated in the TIP3P solvent model,the low values of S? indicate that the peptide samples very different conforma- tions over the course of the simulation The large values of 92 of the peptidesimulated in the ACE and GBORN solvent models suggest that A@jp-35 sam-ples rigid conformations The empirical solvent model, EEF 1, generates flexiblestructures of the À/a_as-protein, leading to intermediate values of the orderparameters 2 ẶẼÈ L TH ẶA

The polar component of the solvation energy is underestimated by the implicitsolvation models, which induces the unrealistic bias toward small values of the

The atomic solvation self-energies computed in the continuum electrostatics

im-plicit solvents ACE and GBORN are compared with values obtained in PBEQreference solvation Simulations in the implicit solvents systematically underes-

timate the atomic solvation energy, leading to an overestimation of the atomicBorn radius These values were obtained by averaging over five one-nanosecondtrajectories of the À/Øqo_ss protein simulated in explicit solvent TIP3P

Xvi

56

3.8

the radius of gyration of the A19_35-protein simulated in implicit solvent

mod-els is strongly correlated with an increased intra-peptide force Implicit solvent

models favor intra-peptide hydrogen bonding as opposed to peptide-water

hy-drogen bonding when compared with explicit solvation models A salt-bridgebetween D23 and K28 has a transitory presence in the peptide structure sim-

ulated in the TIP3P solvent model (a), is diminished in the energy effectivefunction EEF 1 (b), and is totally disrupted in the continuum-electrostatics sol-vent models, ACE and GBORN (c and d) The peptide structure simulated

in the EEF1 solvent model is dominated by short-range and low-probability

long-range hydrogen bonds (b) In the continuum-electrostatics solvent

mod-els, ACE and GBORN, the stability of the peptide core is increased by the

hydrogen bonds between the D23 carboxylate and the backbone amides of theN-terminus and the hydrophobic core LVFFA(17-21) (candd)

The Aịo sz-protein simulated in the TIP3P explicit solvent model generateshighly solvated structures, with charged residues hydrogen-bonded to the sol-vent The backbone oxygen and nitrogen atoms are colored in red and blue,respectively The positively and negatively charged, polar, and hydrophobicresidues are colored in blue, red, purple, and green, respectively Hydrogen-bonds are shown in black dashed line 2 0.0 0 0 00000

The A(io-35-protein simulated in the implicit solvent models EEF1 (a), ACE(b), and GBORN (c) generates conformations with increased number of intra-

peptide hydrogen-bonds The same color scheme as in Figure 3.7 was used

xvi

61

experi-increased tendency for favorable electrostatic interactions with the rest of the

AG io—-35-protein when simulated in the continuum-electrostatics solvent modelscompared to the explicit solvent model The very low pK, values associatedwith the D23 residue (d) simulated in the continuum electrostatic solvent mod-els indicate that the carboxylate group of the D23 side-chain is favorably buried

in the peptide interior The K28 pK, values are close to the pK, values of theisolated K28 residue, indicating that the K28 side-chain is well solvated

Measures of global structural fluctuations (a) The distribution of the radius of

gyration for the five independent trajectories labeled T1, T2, T3, T4, and T5

(b) The root-mean-square fluctuations (measured with respect to the initialconformation) of the backbone atoms (c) The Lipari-Szabo order parameter,

Se

The distribution of the pK, values indicates that E22, D23, and K28 are highly

solvated in the Afj9_35 protein The D23 residue makes small favorable

elec-trostatic interactions with the peptide The small distribution in the positive

pk, shift for K28 indicates that the side-chain of this residue tends to make

favorable electrostatic interaction with the rest of the AGj9_35-protein Theexperimental values are taken from ref.t eeThe distributions of the distance between the C,(D23) and N¢(K28) atoms as

a measure of the salt-bridge D23-K28 stability There are substantial to-sample variations which is indicative of the dynamic heterogeneity of the

sample-MONOMELr 26 we ee

xvin

63

4.6

leads to a large separation between the D23 and K28, three solvation shells in

(a) Decrease of the contact between V24 and K28 reduces the distance betweenD23 and K28 to two solvation shells (b) and less that one solvation shell (c) Thebackbone oxygen and nitrogen atoms are colored in red and blue, respectively

The positively and negatively charged, polar, and hydrophobic residues are

colored in blue, red, purple, and green, respectively Water molecules around

D23 and K28 are colored in cyan, while water molecules which separate thetwo residues are shown in yellow Hydrogen-bonds are shown in black dashedline The figures were made by using VMDð and rendered with POV-Ray.®

The process of formation and disruption of the D23-K28 salt-bridge is

repre-sented as a free energy disconnectivity graph Two super-basins characterizethe states with the D23-K28 salt-bridge formed or broken Two possible con-formations of the residue K28, solvated or buried, are represented as sub-basins.The disrupted salt-bridge is the more favorable state and a large barrier makesthe transition between the formed and disrupted substates improbable Bury-ing the K28 in the peptide interior is an unfavorable process The number ofmicrostates associated with each of the four basins is indicated in parenthesis

“D23-K28 on” stands for salt-bridge present, while “D23-K28 off” stands forsalt-bridge broken The table includes the free energy values corresponding toeach basin and to the transition point between two basins .Structure indicating that the side-chain of the K28 residue is buried in theinterior of the peptide The electrostatic interactions between the ammonium

group of K28, on one side, and the backbone carbonyl oxygen atoms of F20 andE22 and the side-chain carboxylate of D23, on the other side, are supplemented

by the hydrophobic interaction between the aliphatic part of the K28 side-chain

and the side-chains of V24 and I31 The same color scheme as in Figure 4.4was used we

Xix

76

dis-in Figure 4.4 was used 2 eeThe distribution of the hydrogen-bonds reveals that the D23 side-chain is highlysolvated during the entire period of simulation while the K28 side-chain can

make transient hydrogen-bonds with the peptide backbone

Discrete water molecules play substantially different structural role that pends on the peptide basin The structure of water around the D23 and K28

de-is analyzed in terms of radial dde-istribution functions between the pairs of the

O¿(D23) and Nc(K28) atoms with the water oxygen atoms The fully solvated

D23 and K28 side-chains, characterizing the conformations in basin 4, have on

average 3.7 water molecules in the first solvation shell around the O;(D23) andN¿(K28) atoms Once the D23 and K28 side-chains are in electrostatic contact,but still solvated (basin 2), the number of water molecules decreases to 3.0 and2.7 around the O;(D23) and N¿(K28) atoms, respectively In basin 4, buryingthe K28 side-chain in the peptide interior is possible after its desolvation, while

the weak electrostatic contact between the D23 and K28 side-chains allows to

the OD atoms to maintain the waters forming the first solvation shell

The D23-K28 salt-bridge and hydrophobic interactions keep the fragments

17-21 and 30-34 in contact The same color scheme as in Figure 4.4 was used

Time dependence of the pK, values of the titratable residues in the AG@2i_39

WT and the E22Q, D23N, and K28A mutants are computed with two values, 4and 20, of the peptide interior dielectric coefficient, e¿ The lower £¿ attempts tocapture the infrequent favorable electrostatic interaction between the chargedresidues ©

88

d The vertical and horizontal correlation dots in the panels a-c corresponds

to electrostatic interactions between the corresponding charged residue and the

backbone and/or uncharged residues Most of the correlations correspond to

small favorable and unfavorable electrostatic interactions The E22Q mutation

increases the frequency of the D23-K28 pK, shift correlations

The electrostatic interaction energy distributions between the residues E22-K28

and D23-K28 indicate that the titratable residues in the AGo1_39 peptide are

highly solvated during the simulation Hydrated electrostatic contacts ated with weakly favorable interactions are of low favorable energies, explainingtheir instability In the WT peptide, the D23-K28 electrostatic interaction is

associ-more frequent in a low favorable energy domain (around -2.0 kcal/mol), whilethe E22-K28 is more frequent in a larger favorable energy domain (around -3.5kcal/mol) The E22Q mutation increases the probability of electrostatic inter-action between the D23 and K28 residues The D23N mutation decreases theprobability of electrostatic interaction between the E22 and K28 residues inthe low-value domain (-2.0 kcal/mol), while it increases the probability in thelarger-value domain (around -3.5 keal/mol)

XXi

5.7

N¿(K28) indicate the weak electrostatic interaction between these titratable

residue pairs The hydrogen-bonded salt-bridge of the E22-K28 and D23-K28

pairs are equally populated in the A{o:-30(WT) peptide, while the

water-mediated salt-bridge is more populated for the E22-K28 pair The E22Q tion increases the D23-K28 close-interaction probability The D23N mutationdoes not change the probability of the hydrogen-bonded E22-K28 salt-bridge

muta-compared to the WT, while the water-mediated E22-K28:salt-bridge is lessprobable DB1 indicates the first desolvation barrier, while DB2 indicates the

The distance between the centers of mass of the V24 side-chain and the drophobic portion of residue 28 reveals the distribution of the hydrophobicintra-peptide interactions The position 28 is occupied by Lys in the WT andE22Q, and D23N variants, and by Ala in the K28A mutant Two distinct basinscharacterize the distributions The distances between the side-chain V24 and

hy-the residue 28 in contact are centered around 5.0 A The solvated side-chains 24

and 28 have their centers-of-mass separated by at least one solvation shell, with

a minimum distance of 7.54 The E22Q mutation increases the intra-peptide

hydrophobic interaction while the D23N decreases it The K28A mutationmaximizes the population of the 24-28 hydrophobic contacts

The distance between the Nc(K28) and the backbone oxygen atoms is used as ameasure of interaction between the K28 residue and the peptide backbone The

WT and the E22Q mutant of the Affo1_39 peptide increases the contact

proba-bility between the K28 side-chain and peptide backbone The D23N mutationreduces the probability of the K28-backbone contact

xxii

between the center-of-mass of the V24 side-chain (SC) and the hydrophobic part

of the K28 side-chain (SCH) (the X axis) and the distance between the C, atoms

of the residues V24 and N27 (the Y axis) Three hyper-basins are observed inthe C,(V24)-C,(N27) vs SC(V24)-SCH(K28) projection of the free energy.Basin I is characterized by a compact structure of the VGSN(24-27) segment of

the AGo,-39 peptide The peptide structures in basin II are described by stronghydrophobic interaction between the V24 and K28 side-chains, while the ends

of the VGSN(24-27) backbone are well separated The flexible structures of

the AGo1_39 peptide have large values of the X and Y coordinates and define

Basin III Basin II is deeper than Basin I in the WT (panel a), contrary tothe E22Q mutant (panel b) The D23N mutation makes the decapeptide moreflexible, with Basin I almost canceled and Basin III deeper and wider (panelc) The K28A mutation enhances the hydrophobic interaction between theV24 side-chain and the side-chain of A28, particularly through cancellation

of the electrostatic interaction of K28 side-chain with the neighboring watermolecules Basins I and II are deep and equally populated (panel d)

XxxII1

in the Afo;_39 peptide induces pronounced changes in the TRDS tions of the peptide free energy The grey color defines the entropic basin of

representa-unstructured configurations The colors blue, green, and red corresponds tostructures belonging to Basins I, II, and III, respectively, defined in Figure 5.8

(see the legend) The hydrophobic interaction between the V24 and K28

chains and the electrostatic interactions within the E22-K28 and D23-K28

side-chain pairs generate a rough free energy surface (multiple on-path basins) in theA$01-30(WT) peptide (panel a) The roughness aspect of the free energy surface

is accentuated by the E22Q mutation (panel b), especially due to the increasedelectrostatic interaction between D23 and K28 side-chains (see Fig 5.5) TheD23N mutation (panel c) does not increase the intra-peptide electrostatic inter-actions (see Fig 5.5), generating a smoother free energy surface, with a weak

convergence towards a configuration stabilized by the V24-K28 hydrophobic

in-teraction (Basin II in Figure 5.8(c)) The K28A mutation (panel d) generates

a deep and relatively smooth free energy funnel 114

XXIV

atomic contact energyanalytical continuum electrostaticsAlzheimer’s disease

circular dichroism

Chemistry at HARvard Molecular Mechanicsdistance between centers-of-mass

effective energy function

free energy transition disconnectivity graph

fast Fourier transform

generalized Borngeneralized Born solvation energy

Global Range Molecular Matching

low molecular weight

Poisson-Boltzman equationpotential of mean force

radius of gyrationroot-mean-square

transition disconnectivity graphweighted histogram analysis method

XXvi

It has been proposed that the amyloid đ-protein (Ađ-protein) plays a crucial role in the opment of Alzheimer’s Disease (AD) This dissertation presents the results of computationalstudies of the initial stages of AG-protein association The objective of this work was to de-

devel-termine the stability and role of AG-protein monomers and low-order oligomers as metastable

intermediates on the pathway for formation of larger aggregates and fibrils Characterization

of the early stages of peptide aggregation is of fundamental importance in elucidating themechanism of formation of deposits associated with amyloid disease

This dissertation is divided into four parts Chapter 2 presents a study of the initial step inthe pathway of aggregation of the À/o_ss-protein, whose monomeric NMR structure is known,through the simulation of the structure and stability of the peptide dimer in aqueous solution

A protocol based on shape complementarity was used to generate an assortment of possibledimer structures The structures generated based on shape complementarity were evaluated,using rapidly computed estimates of the desolvation and electrostatic interaction energies,

to identify a putative stable dimer structure The potential of mean force associated withthe dimerization of the peptides in aqueous solution was computed for both the hydrophobic

and the electrostatic driven forces using umbrella sampling and classical molecular dynamicssimulation at constant temperature and pressure with explicit solvent and periodic boundary

conditions The comparison of the two free energy profiles suggests that the structure of

the interface Molecular dynamics trajectories originating from two putative dimer structures

indicate that the peptide dimer is stabilized primarily through hydrophobic interactions, while

the conformations of the peptide monomers undergo substantial structural reorganization in

the dimerization process The finding that the y-dimer may constitute the ensemble of stable

A@io-35 dimer has important implications for fibril formation In particular, the expulsion

of water molecules at the interface might be a key event, just as in the oligomerization ofAGig—22 fragments We conjecture that events prior to the nucleation process might involve

crossing free energy barriers that depend on peptide-peptide and peptide-water interactions.Consistent with existing experimental studies, the peptides within the ensemble of aggregatedstates show no signs of formation of secondary structure

Chapter 3 presents the comparison of À/đo_ss-protein simulations in four different vent models: explicit water, using the TIP3P model, an empirical model, EEF1, and two

sol-continuum-electrostatics models, GBORN and ACE In explicit water, the peptide assumes

a structure characterized as a “collapsed coil” with a hydrophobic core, đ-turn, and

disor-dered N- and C-termini regions The GBORN and ACE solvent models induce a compactstructure in the peptide that is inconsistent with the experimentally derived NMR structuresand Lipari-Szabo amide bond order parameters Use of the EEF 1 solvent model led to a pep-

tide with compactness and flexibility intermediate to those observed in explicit, TIP3P, andimplicit, GBORN and ACE, models The solvation of the A@j9_35-protein is underestimated

in simulations employing these implicit solvents In explicit solvent, there is an equilibriumbetween the solvent-solute and intra-peptide hydrogen bonds; implicit solvents favor the for-mation of intra-peptide hydrogen bonds, biasing the protein toward unrealistically compactstructures It appears this is due to the underestimation of the solvation self-energy by theimplicit solvent models, causing the peptide to compensate through exaggerated intra-peptide

hydrogen bonding

Chapter 4 presents a study of the dynamics of the contact between the Asp23 and Lys28residues in the A@io_35-protein In the amyloid fibrils formed from long fragments of the

The structure of the monomers satisfies the Amyloid Self-Organization Principle (ASOP): thelow free energy state of the monomer maximizes the number of intra- and inter-peptide con-tacts and salt-bridges The formation of the intra-molecular salt-bridge between Asp(D)23-Lys(K)28 ensures that unpaired charges are not buried in the low dielectric interior We

investigated, using all atom molecular dynamics simulations in explicit water, if the D23-K28interaction forms spontaneously in the isolated A/Øop_s; monomer To validate the simula-

tion, five independent trajectories spanning a total of 100 ns were used to compute the pK,

values of the titratable groups, which were found to be in good agreement with experimentalmeasurements The computed free energy disconnectivity graph shows that the ensemble ofcompact random coil conformations can be clustered into four basins that are separated by

free energy barriers ranging from 0.3 kcal/mol to 2.7 kcal/mol Significant residual structurewas observed in the conformation of the peptide in each of the basins Due to the desolvationpenalty, the structural motif consisting of a turn involving the residues VGSN stabilized by apreformed D23-K28 contact was found to be a minor component of the simulated structures.The extent of solvation of the peptides in the four basins varies greatly which underscores the

dynamical fluctuations in the monomer Our results suggest that the expulsion of discretewater molecules must be an early event in the oligomerization process that facilitates theformation of inter-peptide interaction-driven stable structures with intra-molecular D23-K28salt-bridge and intact VGSN turn

In Chapters 5, the competition between hydrophobic and electrostatic interactions in thebehavior of the Á/¡_so-peptide was analyzed Intra-peptide electrostatic interactions were

connected to pA, values estimated through molecular dynamics simulations The computed

pK, estimates compare well with the experimental estimates The influence of titratableresidues on the stability of the structure of the VGSN region was dissected by successive

mutations of the E22, D23, and K28 residues Computed pK, values of the titratable residueswere found to be close to the model pK, values, consistent with solvent-exposure of thecorresponding side-chains Both the E22 and D23 side-chains were found to infrequently form

WT and E22Q peptides were estimated Negligible pK, shifts of the E22 and K28 residueswere observed in the D23N mutant peptide Small positive (unfavorable) shifts of the pK, for

the E22 and D23 residues were observed in the K28A mutant The E22-K28 contacts wereobserved to be more probable in “dried” salt-bridges The D23-K28 contacts were found to

be more probable in solvated salt-bridges A one-barrier desolvation process was observedfor the E22-K28 pair in the WT peptide, in contrast to the D23N peptide, were desolvationinvolves crossing two barriers The D23-K28 pair desolvates in two activated steps in the WT

and E22Q mutant peptides The populations of the intra-peptide hydrophobic interactionsincrease as D23N < WT < E22Q < K28A Increased contacts of the K28 ammonium group

with the backbone oxygen atoms were observed in the WT and E22Q peptides compared tothe D23N peptide The hydrophobic interactions cluster the AGo,_39-peptide into two basins,differentiated by the relative position of the DVG(23-25) and GSN(25-27) fragments about

the G25 residue The E22Q mutation increased the population in Basin I, compared to the WT

peptide, from 9% to 19% Basin II was depopulated from 13% to 7% by the E22Q mutation

The D23N mutation dramatically reduced the intra-peptide interactions, with populations of

3% and 5% of Basins I and II, respectively The K28A mutation increased the intra-peptidehydrophobic interactions, with populations of 23% for Basin I and 12% for Basin II The

intra-peptide electrostatic interactions in the WT and E22Q peptide roughened the computedfree energy surface compared to the K28A peptide The D23N mutation generated a flat

free energy surface, corresponding to an increased population in Basin III The 27) fragment converged to a helix-like motif in Basin I, driven by V24-K28 hydrophobic

DVGSN(23-interactions and stabilized by D23-K28 salt-bridge and intra-peptide hydrogen-bonds.Our results suggest that that the structure of the A/ịo_as dimer is determined by thefavorable desolvation of the hydrophobic residues at the monomer-monomer interface The

inter-peptide hydrophobic interactions were shown to stabilize the AGio_35 dimer, while the

conformations of the peptide monomers undergo substantial structural reorganization in the

dimerization process The Àịog_ss-protein monomers simulated in implicit solvent models

monomers simulated in explicit solvent model The underestimation of the solvation

self-energy by the implicit solvent models caused the peptide to compensate through exaggeratedintra-peptide hydrogen bonding The expulsion of discrete water molecules must be an earlyevent in the oligomerization process that facilitates the formation of inter-peptide interaction-

driven stable structures with intra-molecular D23-K28 salt-bridge and intact VGSN turn

We showed that the intra-peptide hydrophobic interactions drive the A/¡_aso-peptide to energy conformations The profile of the free energy surface was shown to be modulated byintra-peptide electrostatic interactions in the A(o1~39-peptide

low-Probing the initial stage of aggregation

of the A/ịo_as-protein: Assessing the propensity for peptide dimerization

2.1 Summary

Characterization of the early stages of peptide aggregation is of fundamental importance inelucidating the mechanism of the formation of deposits associated with amyloid disease Theinitial step in the pathway of aggregation of the Ểịoa ss-protein, whose monomeric NMRstructure is known, was studied through the simulation of the structure and stability of thepeptide dimer in aqueous solution A protocol based on shape complementarity was used togenerate an assortment of possible dimer structures The structures generated based on shapecomplementarity were evaluated using rapidly computed estimates of the desolvation andelectrostatic interaction energies to identify a putative stable dimer structure The potential of

mean force associated with the dimerization of the peptides in aqueous solution was computed

for both the hydrophobic and the electrostatic driven forces using umbrella sampling andclassical molecular dynamics simulation at constant temperature and pressure with explicitsolvent and periodic boundary conditions The comparison of the two free energy profiles

of the hydrophobic residues at the interface Molecular dynamics trajectories originating

from two putative dimer structures indicate that the peptide dimer is stabilized primarily

through hydrophobic interactions, while the conformations of the peptide monomers undergosubstantial structural reorganization in the dimerization process The finding that the ¿-dimer

may constitute the ensemble of stable A@io_35 dimer has important implications for fibril

formation In particular, the expulsion of water molecules at the interface might be a key

event, just as in the oligomerization of AGig_22 fragments We conjecture that events prior tothe nucleation process themselves might involve crossing free energy barriers which depend

on the peptide-peptide and peptide-water interactions Consistent with existing experimental

studies, the peptides within the ensemble of aggregated states show no signs of formation of

secondary structure

2.2 Background

Amyloid Øđ-protein (A) is involved in the pathogenesis of Alzheimer’s disease (AD).”Š Earlystudies illustrated the presence of amyloid plaques in the human brain of AD victims, andthese conglomerates have been related to the evolution of AD.° It is still not establishedwhether amyloid protein aggregates, fibrils or plaques are causative agents of the pathologicalmanifestations or whether they are only collateral products of this disease.? However, the toxic influence of the amyloid plaques on the proximate neurons has been demonstrated.!0-12Recent studies have found that the neurotoxicity may be provoked even by mobile low molec-ular weight (LMW) aggregates of Ađ.!#!5 The oligomeric structures of A@ are also involved

in the early steps of fbrilization.!8 Teplow and co-workers have analyzed the role of A@ in the

nucleation phase, showing that two alloforms, A/đị_ao and A(;_42, follow different pathways

in the fibril formation process.!” They hypothesized that the peptides initially form clei and that those nuclei further form, through a linear aggregation mechanism, amyloidicfbrils.! These observations give rise to the question of how the structure of the monomer will

paranu-tions of AGio_35 wild-type with the more amyloidogenic Dutch mutant of the same fragment

using molecular dynamics simulation They concluded that there is not much difference in theintrapeptide interactions corresponding to the two peptides and that the enhanced amyloido-genic propensity of the Dutch mutant results from its decreased hydrophilicity.!# Recently,

Bitan et al.!° analyzed the differences in oligomerization of two alloforms, A/¡_¿o and AGj_22.

It is known that the fibrilization kinetics of A@,_49 is faster than that of A(@y_49.2%?! Theyobserved that the oxidation of Met35 in AG@,_42 reduced the rate of fibril formation, rendering

it comparable to that of AGi_49 It was postulated that the increased hydrophilicity of the idized mutant will result in a larger free energy barrier to oligomerization.!? These studies allpoint to the essential role of intermonomeric interactions, in the formation of LMW aggregates,and the role of LMW aggregates as essential intermediates in the process of amyloidogenesis.?2Solid-state NMR studies of amyloid fibrils have revealed that AG adopts a parallel in-

ox-register organization in đ-sheets for both A/o_ss;?3 and AGy_49.24?> Those structures raise

the question, by what mechanism does the native collapsed random coil structure of the

monomeric Af undergo conformational transition to the G-strand conformation characteristic

of the fibrils? Recent experimental and computational studies have led to the conjecture that atransient a-helical phase is a necessary on-pathway intermediate?? connecting the monomeric

peptide with the đ-strand conformations of the fibrils for AG,—~497° and AGig_22.2” These data

suggest a central role for LMW aggregates in the A@ aggregation pathway and possibly the

evolution of AD itself It may be that an efficient therapy for AD is to prevent the formation

of LMW aggregation of AQ

In the present work, we study the initial step in the oligomerization process of A/ịo sz,

which is the process of A@io_35 dimerization The initial configuration of the system wasobtained using a protein docking protocol Two possible initial structures were obtained,

and the best one was selected based on energetic considerations Finally, the stability of the

dimer and the secondary structure elements’ fluctuations were analyzed via classical moleculardynamics

NMR structure for this fragment of the protein.?? Knowledge of the starting structure for such

a large peptide represents an important advantage in our in silico experiment Guessing thestructure of the AG)_49, starting from A@io-35 will add uncertainty to our results The lack of

a 3D structure for the A@,_42 is not the only impediment for an atomic resolution dimerizationstudy The experimental observations report a high flexibility of the AG,_42 termini in aqueoussolvent, and, consequently, it is very difficult to find an initial dimer structure The flexiblestructure of the A@i_42 will also increase the size of the system studied (the protein andthe explicit solvent) to such an extent that the simulations become prohibitive We note

28, 29

that besides Maggio’s studies of the AGjo_35 structure and properties, Lynn showed thatAGio-35 adopts a parallel in-register organization in đ-sheets.?3

2.3 Computational Model and Methods

In the protocol for generating the decoy sets, the dimer structures were generated using a

shape-complementarity based algorithm The dimer structures were discriminated by

com-paring estimates of the desolvation energy using an atomic contact energy protocol Starting

from the putative dimer structure, molecular dynamics trajectories were simulated with brella sampling to compute the potential of mean force The stability of the dimer structure

um-was demonstrated through the computation of the potential of mean force, that shows that

the dimer represents a minimum in the free energy The simulation of 10 ns trajectories,further shows the stability of the contact dimer The potential of mean force and dynamical

trajectories were analyzed and used to characterize the ensemble of peptide dimer

configura-tions The amino acid sequence of the A@jo_35 is Y!CEVHHQUKLVFF~AEDVG“SNKGA”

IIGLM®.

2.3.1 Dimer structure generation using a docking protocol

Decoy structures of the AGjo_35 dimer were generated using the shape-complementarity basedalgorithm Global Range Molecular Matching (GRAMM).°° The surface of a macromolecularstructure depends on the Cartesian coordinates of the atoms composing the macromolecule.The surface is not planar (bi-dimensional, N2) but irregular, having a 3D profile Consequently, the surface will be an N? order function The atomic coordinates of the two molecules areprojected onto a grid of Nx NxN points, allowing each molecule to be described by adiscrete function As a measure of the intermolecular contact, the correlation between thediscrete representation of the two macromolecules is calculated A good contact is represented

by a high value of the correlation function The penetration of two molecules is penalized

with a negative-value contribution to the correlation function In its most straightforward

form, this calculation scales as N? x NŠ To make the calculation of the correlation function

computationally feasible, the projected representations of both the protein and the ligand are

discrete Fourier transformed As a result, a N® order sum is reduced to N*In(N°) order A total

of 2000 dimer decoy structures were generated We used only the coordinates of the heavyatoms With the position of one peptide fixed, all positions and orientations of the second

peptide were searched The result of the dimer decoy set will not be influenced by whichmonomer is held fixed and which is moved around the other to match their surfaces Evenwith both monomers mobile during the search, the decoy set will have the same composition

A grid step of 1.7 A, and a step for the search through the rotational coordinates of 10 degrees,

were used The resulting structures were further minimized using the program CHARMM?!

version c29b1 with the PARAM22*? all-atom potential function.

2.3.2 Desolvation energy screening

An extension of the residue-residue potential contact method proposed by Miyazawa andJernigan®? was used to calculate the contribution of the desolvation energy to the bindingfree energy The resolution of the calculation of the desolvation energy was increased byestimating the work necessary to transfer different types of atoms from water to the non-

polar protein interior.3t The Atomic Contact Energy (ACE) involves the calculation of the

number of different atom-atom pair types at the dimer interface using a 6.0 A cutoff Only

the heavy atoms are considered and they are grouped in 18 classes.”t The backbone, Ơaand C., atoms were grouped based on energetic and chemical similarities, while the remainingatoms were grouped according to their chemical properties and cooperative interactions.*4The desolvation energy is written as

within a reutos (= 6.0 A) distance This simple estimation was used to discriminate between

well formed and weakly associated dimer structures

2.3.3 Molecular Dynamics

The molecular dynamics simulations were carried out using the program

CHARMM®* version c29b1 with the PARAM22* all-atom force field The solvent was treated

explicitly using the TIP3P three-site rigid model for water molecules.*° For the initial dinates of the unstructured monomers, the NMR structure of ÄÀịo_as—NHa (410 atoms) wasused.*8 The protonation state of the titratable amino acids was fixed to the expected values

coor-at neutral pH in all simulcoor-ations The dimer was centered in a trunccoor-ated octahedron cell thcoor-at

was carved from a larger pre-equilibrated cell of pure water The size of the primary cell

was set according to the minimum-image convention and periodic boundary conditions Thepotential energy of the system was minimized until the RMS gradient of the potential energy

was less than 0.1 kcal/mol/A while the dimer atoms were fixed in their positions To remove

steric clashes between atoms, the steepest descent energy minimization algorithm was usedfor an initial 200 minimization steps; to achieve a desired maximum potential gradient, theadopted basis Newton-Raphson algorithm was applied for the remainder of the minimization

The system was linearly heated to 300 K for 120 ps followed by an equilibration phase

involving two steps The system was equilibrated for 80 ps using NVE molecular dynamics

with a leapfrog integrator, followed by an additional 70 ps of NPT molecular dynamics.

The pressure was restrained to 1 atm using a variant of the extended system method, theLangevin piston algorithm.°8 The temperature was restrained to 300 K using the Nosé-

Hoover thermostat.?? During the heating and the NVE equilibration phases, the velocities

were assigned according to a Gaussian distribution In order to prevent any conformationalchange of the peptide during the heating and equilibration phases, the dimer atoms were

harmonically restrained To assure a gradual equilibration of the water surrounding the dimer,

the restraints were gradually reduced to zero The center of mass of the dimer was constrained

to the center-of-mass of the box of water using the MMFP utility implemented in CHARMM.

The electrostatic interactions were calculated with no truncation, using the particle mesh

Ewald summation algorithm®® with a FFT grid point spacing of 0.95 A, and a fifth-degree B-spline interpolation The width of the Gaussian distribution in real-space was 0.32 Ä~1,

The real-space electrostatic and van der Waals interactions were smoothly shifted to zero at

10 A, using an atom-based cutoff The list of the non-bonded interactions was truncated

at 12 A The lengths of the bonds containing hydrogen atoms were fixed with the SHAKE

algorithm®? and the equation of motion was iterated using a time step of 2 fs in the leapfrogintegrator

The umbrella sampling method*? was used to determine the profile of the potential of

mean force (PMF)*! along a coordinate € This method implies the constraint of the chosen

coordinate in narrow, successive windows i centered on €?, in order to improve the tical sampling In this case, the distance between the centers-of-mass (DCOMs) of the two

statis-monomers was adopted as the coordinate € A harmonic potential was used to bias the

dynamics of the system

ile) = 5h (EB) = 5h (6 — Soom — 8)’, (2.2)

where cont is the DCOMs between the two monomers when they are in contact, and 6?

is the surface separation along the coordinate £, corresponding to different windows The

time evolution of the DCOMs was saved every 20 fs while the coordinates of the system

were saved every 0.2 ps A force constant of 20 kcal/mol was used for each window TheUMBRELLA facility*? of CHARMM was used to bias the distance between the centers-of-

mass The constrained dynamics was computed in 19 windows centered on 6?=0.0, 0.5, 1.0, ,

9.0 A The unphysical contribution of the constraining potential on the overall evolution of

the system gives the PMF corresponding to each window

W,(§) = —kT In(ø(§)) ~ UI(€) + Gi, (2.3)

where p;(€) is the density probability of DCOMs in the i*” window, and C; is a constant that

was computed using the weighted histogram analysis method (WHAM).*?:44

2.3.4 Secondary Structure Analysis

The random coil, a-helix, and đ-strand structures were determined according with the specific

values of the dihedral ¢ and w angles We used the “broad” definition of Mufioz and Serrano**

for the secondary structure motifs They assume that the a-helix domain is included in apolygon defined by the ¢-y coordinates {(—90, 0), (—90, —54), (—72, —54), (—72, —72),(—36, —72), (—36, —18), (—54, —18), (—54, 0)}, while the đ-strand is given by the polygon{(—180, 180), (—180, 126), (—162, 126), (—162, 108), (—144, 108), (—144, 90), (—50, 90),(—50, 180)}

2.4 Results and Discussion

2.4.1 Outline

As our study consists of a number of parts, and both atomistic and coarse-grained models are

employed, an overview of the study is provided as an outline