Summary of physics doctoral thesis: The role of hydrophobic and polar sequence on folding mechanisms of proteins and aggregation of peptides

The objectives of the thesis: The aim of the studies is to gain fundamental understanding of the role of hydrophobic and polar sequence on folding mechanism of proteins and aggregation of peptides

MINISTRY OF EDUCATION VIETNAM ACADEMY

GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY

———————

NGUYEN BA HUNG

THE ROLE OF HYDROPHOBIC AND POLAR SEQUENCE

ON FOLDING MECHANISMS OF PROTEINS AND

The problem of protein folding has always been of prime concern in molecularbiology Under normal physiological conditions, most proteins acquire well definedcompact three dimensional shapes, known as the native conformations, at whichthey are biologically active When proteins are unfolding or misfolding, theynot only lose their inherent biological activity but they can also aggregate intoinsoluble fibrils structures called amyloids which are known to be involved inmany degenerative diseases like Alzheimer’s disease, Parkinson’s disease, type

2 diabetes, cerebral palsy, mad cow disease etc Thus, determining the foldedstructure and clarifying the mechanism of folding of the protein plays an importantrole in our understanding of the living organism as well as the human health.Protein aggregation and amyloid formation have also been studied extensively

in recent years Studies have led to the hypothesis that amyloid is the generalstate of all proteins and is the fundamental state of the system when proteinscan form intermolecular interactions Thus, the tendency for aggregation and for-mation amyloid persists for all proteins and is a trend towards competition withprotein folding However, experiments have also shown that possibility of aggre-gation and aggregation rates depend on solvent conditions and on the amino acidsequence of proteins Some studies have shown that small amino acid sequences

in the protein chain may have a significant effect on the aggregation ability As

a result, knowledge about the link between amino acid sequence and possibility

of aggregation is essential for understanding amyloid-related diseases as well asfinding a way to treat them

Although all-atom simulations are now widely used molecular biology, theapplication of these methods in the study of protein folding problem is not feasibledue to the limits of computer speed A suitable approach to the protein foldingproblem is to use simple theoretical models There are quite a number of modelswith different ideas and levels of simplicity, but most notably the Go model andthe HP network model and tube model

Considerations of tubular polymer suggest that tubular symmetry is a damental feature of protein molecules which forms the secondary structures ofproteins (α and β) Base on this idea, the tube model for the protein was de-veloped by Hoang and Maritan’s team and proposed in 2004 The results of thetube model suggest that this is a simple model and can describes well many of thebasic features of protein The tube model is also the only current model that cansimultaneously be used for the study of both folding and aggregation processes

fun-In this thesis, we use a tube model to study the role of hydrophobic andpolar sequence on folding mechanism of proteins and aggregation of peptides.Spatial fill of the tubular polymer and hydrogen bonds in the model play therole of background interactions and are independent of the amino acid sequence.The amino acid sequence we consider in the simplified model consists of twotypes of amino acids, hydrophobic (H) and polar (P) To study the effect of HPsequence on the folding process, we will compare the folding properties of thetube model using the hydrophobic interaction (HP tube model) with tube modelusing the pairing interaction which is similar to the Go model (Go tube model).This comparison helps to clarify the role of non-native interactions in non-nativeinteractions To study the role of the HP sequence on aggregation of protein, wewill compare the possibility of aggregation of peptide sequences with different HPsequences including the consideration of the shape of the aggregation structuresand the properties of aggregation transition phase In addition, in the study ofprotein aggregation, we propose an improved model for hydrophobic interaction

in the tube model by taking into account the orientation of the side chains ofhydrophobic amino acids Our research shows that this improved model allowsfor obtaining highly ordered, long-chain aggregation structures like amyloid fibrils

1 The objectives of the thesis:

The aim of the studies is to gain fundamental understanding of the role ofhydrophobic and polar sequence on folding mechanism of proteins and aggre-gation of peptides

2 The main contents of the thesis:

The general understanding of protein and protein folding, protein aggregation

is introduced in chapters 1, 2 of this thesis Chapter 3 presents the methodsused to simulate and analyze the data The obtained results of role of HPsequence for protein folding are presented in chapter 4 The results of role of

HP sequence for protein aggregation are presented in chapter 5

Chapter 1

Protein folding

1.1 Structural properties of proteins

Proteins are macromolecules that are synthesized in the cell and responsiblefor the most basic and important aspects of life Proteins are polymers (polypep-tides) formed from sequences of 20 diffirent types of amino acids, the monomers

of the polymer The amino acids in the protein differ only in their side chainsand are linked together through peptide bonds that form a linear sequence in aparticular order

Under normal physiological conditions, most proteins acquire well definedcompact three dimensional shapes, knows as the native conformations, at whichthey are biologically active

The amino acid sequence in the protein determines the structure and function

of the protein Proteins has four types of structure

Primary structure: It is just the chemical sequence of amino acids along thebackbone of the protein These amino acid in chain linked together by peptidebonds

Secondary structure is the spatial arrangement of amino acids There are twosuch types of structures: the α-helices and the β-sheets This kind of structurewhich maximize the number of hydrogen bonds (H-bonds) between the CO andthe NH groups of the backbone

Tertiary structure: A compact packing of the secondary structures comprisestertiary structures Usually, theses are the full three dimensional structures ofproteins Tertiary structures of large proteins are usually composed of severaldomains

Quaternary structure: Some proteins are composed of more than one tide chain The polypeptide chains may have identical or different amino acidsequences depending on the protein Each peptide is called a subunit and has itsown tertiary structure The spatial arrangement of these subunits in the protein

polypep-is called quaternary structure

There are a number of semi-empirical interactions that are introduced bychemists and physicists to describe interactions in proteins: disulfide bridges,

Coulomb interactions, Hydrogen bonds, Van der Waals interactions, Hydrophobicinteractions.

1.2 Protein folding phenomenon

Once translated by a ribosome, each polypeptide folds into its characteristicthree-dimensional structure from a random coil Since the fold is maintained by anetwork of interactions between amino acids in the polypeptide, the native state

of the protein chain is determined by the amino acid sequence (hypothesis ofthermodynamics)

1.3 Paradox of Levinthal

Levinthal paradox which addresses the question: how can proteins possiblyfind their native state if the number of possible conformations of a polypeptidechain is astronomically large?

1.4 Folding funnel

Based on theoretical and empirical research findings, Onuchic and his leagues have come up with the idea of the folding funnel as depicted in Figure1.1 The folding process of the protein in the funnel is the simultaneous reduc-tion of both energy and entropy As the protein begins to fold, the free energydecreases and the number of configurations decreases (characterized by reducedwell width)

col-N

folding

entropy g

Figure 1.1: The diagram sketches of funnel describes the protein folding energy lanscape

Figure 1.2: Free energy lanscape in the two-state model In this model, ∆F is the diference between the free energy of the folded and unfolded states ∆FN and , ∆FD, ∆F are the height of barrier from the unfolded and folded states and free energy difference between the N and U states , respectively

In the canonical depiction of the folding funnel, the depth of the well sents the energetic stabilization of the native state versus the denatured state, andthe width of the well represents the conformational entropy of the system Thesurface outside the well is shown as relatively flat to represent the heterogeneity

repre-of the random coil state

1.5 The minimum frustration principle

The minimum frustration principle was introduced in 1989 by Bryngelsonand Wolynes based on spin glass theory This principle holds that the amino acidsequence of proteins in nature is optimized through natural selection so that thefrustrated caused by interaction in the natural state is minimal

1.6 Two-state model for protein folding

Experimental observations suggest that the two-state model is a commonmechanism used to characterize folding dynamics of the majority of small, globuarproteins In a two-state model of protein folding, the single domain protein canoccupy only one of two states: the unfolded state (U) or the folded state (N).The free energy diagram for two-state model is characterized by a large barrierseparating the folded state and the unfolded state corresponding minima of thefree energy of a reaction coordinate The free energy difference between the Nand U states (∆F ) characterize the degree of stability of the folding state calledfolding free energy Rates of folding kf and unfolding ku obey the law Vant Hoff-

1.7 Cooperativity of protein folding

Cooperativity is a phenomenon displayed by systems involving identical ornear-identical elements, which act dependently of each other The folding ofproteins is cooperative process In the protein, cooperativity is applied to the two-state process and is understood as the sharpness of thermodynamic transitions

In practice, cooperativity is determined by the parameter measured by the ratiobetween the enthalpy van’t Hoff and the thermal enthalpy

High cooperativity means that the system satisfies the two-state standard and

κ2 is closer to 1, the higher the co-operation and vice versa

1.8 Hydrophobic interaction

The hydrophobic effect is the observed tendency of nonpolar substances (such

as oil, fat) to aggregate in an aqueous solution and exclude water molecule Thetendency of nonpolar molecules in a polar solvent (usually water) to interact withone another is called the hydrophobic effect In the case of protein folding, thehydrophobic effect is important to understanding the structure of proteins Thehydrophobic effect is considered to be the major driving force for the folding ofglobular proteins It results in the burial of the hydrophobic residues in the core

of the protein

1.9 HP lattice model

In the HP lattice model, there are two types of amino acids with respect totheir hydrophobicity: polar (P), which tend to be exposed to the solvent on theprotein surface, and hydrophobic (H), which tend to be buried inside the globule

protein The folding of the protein is defined as a random step in a 2D or 3Dnetwork Using this model, Dill had design some HP sequence that the minimalenergy state in the tight packet configurations was unique The phase transition

of the sequences is designed to be well cooperative Research shows that aggregatedue to hydrophobic interaction is the main driving force for folding

1.10 Go model

The Go model ignores the specificity of amino acid sequences in the proteinchain and interaction potential is build based on the structure of the folded state.The basis of the Go model is the maximum consistent principle of protein interac-tions in the folded state The results of the study show that the Go model for thefolding mechanism is quite good with the experiment, especially in determiningthe contribution of amino acid positions in the polypeptide chain to the transi-tion state during protein folding Because the model is based on a native statestructure, the Go model can not predict the protein structure from the aminoacid sequence that is only used to study the folding process of a known structure

1.11 Tube model

Considerations of symmetry and geometry lead to a description of the tein backbone as a thick polymer or a tube At low temperatures, a homopoly-mer model as a short tube exhibits two conventional phases: a swollen essen-tially featureless phase and and a conventional compact phase, along with a novelmarginally compact phase in between with relatively few optimal structures made

pro-up of α-helices and β-sheets The tube model predicts the existence of a fixedmenu of folds determined by geometry, clarifies the role of the amino acid se-quence in selecting the native-state structure from this menu, and explains thepropensity for amyloid formation

2.2 Mechanism of amyloid aggregation

The formation of amyloid can be considered to involve at least three stepsand are generally referred to as lag phase, growth phase (or elongation) phaseand an equilibration phase Seeding involves the addition of a preformed fibrils to

a monomer solution thus increasing the rate of conversion to amyloid fibrils dition of seeds decreases the lag phase by eliminating the slow nucleation phase

Ad-Chapter 3

Methods and Models for simulations

3.1 HP tube model

The backbone of the protein is models as a string of Cα atoms separated by

an interval of 3.8˚A, forming a flexible tube of 2.5˚A also has a constraint with boththe tube’s three radii (local and non-local) Potential 3 objects describing thiscondition are given in figure 3.1)

(3.3)

The same for a non-local hydrogen bond:

Non local radius

of curvature Hydrophobic

eW denotes the hydrophobic interaction energy for each contact, depending

on the hydrophobicity of the amino acids i and j In the most studies, thesevalues were selected by eHH = −0.5 , eHP = eP P = 0

3.2 Go tube model

The Go tube model is a tube model in which hydrophobic interaction energy

is replaced by the same energy interaction as the Go-like interaction model:

Thus, the Go tube model retains the geometric and symmetric properties, the

bending energy and hydrogen bonds as in tube model Go-type energy is built onthe structure of the given native state Interactive Go is given by:

3.3 Tube Model with correlated side chain orientations

we apply an additional constraint on the hydrophobic contact by taking intoaccount the side chain orientation: ni · cij < 0.5 and −ni · cij < 0.5 Where niand nj are the normal vectors of the Frenet frames associated with bead i and

j, respectively, cij is an unit vector pointing from bead i to bead j The newconstraint is in accordance with the statistics drawn from an analysis of PDBstructures

3.4 Structural protein parameters

To study the protein folding to the native state, we examine the properties

of the protein configurations obtained from the simulation through a number

of characteristic features including folding contacts, root mean square deviation(rmsd) and radius of gyration (Rg)

3.5 Monte Carlo simulation method

For studying the folding and aggregation of protein, we carry out multiple dependent Monte Carlo (MC) simulations with Metropolis algorithm The trans-fer of states of the systems in the models used is made by pivot, crank-shaftand tranlocation motion for protein aggregation and pivot, crank-shaft motionfor protein folding

in-3.6 Parallel tempering

Parallel tempering , also known as replica exchange MCMC sampling, is asimulation method aimed at improving the dynamic properties of Monte Carlo

method simulations of physical systems, and of Markov chain Monte Carlo (MCMC)sampling methods more generally by exchanges configurations at different tem-peratures.

Using Metropolis algorithm to swap two configurations

kBA = min {1, exp [(βi − βj) (Ei− Ej)]} (3.8)For kBA is the probability of moving from A to B This method is veryeffective to find the basic state simultaneously at each temperature still obtainedbalanced set and they are easily applied on parallel computers

3.7 The weighted histogram analysis method

The Weighted Histogram Analysis Method (WHAM) allows for optimal ysis of data obtained from MC simulations as well as other simulations over awide range of parameters by combining multiple histograms together

anal-The probability is found system at the temperature T

fm are calculated from Eqs 3.9 and 3.10 self-consistently Normally, fm

converge quickly when the histograms balance and overlap Determining thevalues of fk completely determines P (E, β) at any temperature

Chapter 4

The role of hydrophobic and polar sequence on folding

mechanisms of proteins

In this chapter we study the folding process of protein in two models: the

HP tube Model and the Go tube Model In this study, we construct the tube Gomodel for the two strutures in such a way that the total hydrophobic energy ofeach structure are the same in the two models The study was conducted withtwo proteins of the same length of N = 48: a three helix bundle (3HB) and aGB1-like structure (GB1) Figure 4.1 shows the native state of protein GB1 and3HB

Figure 4.1: Ground state conformations of two HP sequences considered in our study: a three-helix bundle (a) and a GB1-like structure (b)

In the HP tube model, eHH = −0.5, eHP = eP P = 0 and the unit  sponds to the energy of a local hydrogen bond

corre-4.1 Thermodynamics of protein folding in HP tube model

Figure 4.2a–c show the temperature dependence of the averaged radius ofgyration, hRgi, average energy E and the specific heat of 3HP protein in the HPtube model Average energy, radius decreases as the temperature decreases Thespecific heat graph has a maximum Cmax = 1526kB at Tf = 0, 296/kB It can

be seen that for the tube HP model there is a small shoulder on the right ofthe specific heat peak at T ≈ 0.5 /kB corresponding to a sharp decrease in theaverage radius of motion as the temperature decreases At T ≈ 0.5 /kB there

is a sharp decrease in the size of the protein while the energy does not decreasemuch.This shoulder corresponds to a collapse transition

Figure 4.2: Temperature dependence of the averaged

radius of gyration, hR g i, average energy E and the

specific heat of 3HP protein in the HP tube model

-60 -40 -20 0

Figure 4.3: similar as figure 4.2 in the tube Go model.

Same with GB1 protein (fig 4.2d–f), the transition temperature of the specificheat maximum of GB1 protein is Tf = 0.243 /kB and maximum of the specificheat Cmax = 509.7 kB, both significantly lower than 3HB, showing that the phasetransition of GB1 is less sharp and less cooperative

4.2 Thermodynamics of protein folding in Go tube model

Figure 4.3 show the temperature dependence of the averaged energy E, erage radius of gyration, hRgi and the specific heat of 3HP and GB1 protein inthe Go tube model The folding transition phase and collapse transition phaseare sharper than the HP tube model For both proteins, the change of the av-erage energy and the average radius of gyration were significantly greater at thetransition temperature with greater slope than the HP tube model Specific heathas only a single peak at the transition temperature Tf and in particular, noshoulder appears at temperatures greater than the transition temperature In thetube Go model, the collapse and folding transitions coincide at temperature Tmax.Collapse phase in the Go tube model is the same as the folding phase

av-The folding transition temperature Tf is also slightly higher in the tube Gomodel: 0.345 /kB versus 0.296 /kB for 3HB protein and 0.291 /kB versus 0.243

/kB for GB1 protein The maximum of the specific heat,Cmax, are roughly 2.8and 4.1 times higher in the tube Go model comparing to the tube HP modelcorresponding to 3HB and GB1 protein (4269 kB versus 1526 kB for 3HB proteinand 2104 k versus 509.7 k for GB1 ) These observations suggest that the tube

Go model is significantly more cooperative than the tube HP model and the latteralso yields a higher stability of the native state.

4.3 Folding transition phase in HP tube model and Go tube model

0 0.05 0.1 normalized histogram (d)

0 0.1 0.2 normalized histogram (e)

0 0.05 0.1 0.15 normalized histogram (f)

Figure 4.4: trajectories and normalized histograms of

3HB protien in HP tube model obtained at a large

time of 2 × 10 9 MC steps at the folding transition

temperature T f = 0.296 /k B

-50 -40 -30 -20 -10

0 4 8 12

8 10 12

0 0.03 0.06 normalized histogram (d)

0 0.04 0.08 normalized histogram (e)

0 0.05 0.1 0.15 normalized histogram (f)

Figure 4.5: Same as 4.4 but for GB1 in HP tube model at T f = 0.243 /k B

0 0.02 0.04 normalized histogram (d)

0 0.03 0.06 normalized histogram (e)

0 0.1 0.2 normalized histogram (f)

Figure 4.6: Trajectories and normalized histograms

of 3HB protien in Go tube model obtained at a large

time of 2 × 10 9 MC steps at the folding transition

temperature Tf = 0.345 /kB

-40 -20 0

0 5 10 15 20 25

8 12 16 20 24 28

0 0.03 0.06 normalized histogram (d)

0 0.03 0.06 normalized histogram (e)

0 0.05 0.1 0.15 normalized histogram (f)

Figure 4.7: Same as 4.6 but for GB1 in Go tube model at Tf= 0.291 /kB

Figure 4.4 and figure 4.5 describes long trajectories 2 × 109 MC steps at