Computer Simulation Studies of Abnormal Protein …wseas.us/e-library/conferences/2009/moscow/BEBI/BEBI06.pdfgain an insight into the protein folding mechanisms and the environmental

Computer Simulation Studies of Abnormal Protein Aggregation

ANDREW HUNG, NEVENA TODOROVA AND IRENE YAROVSKY

School of Applied Sciences

RMIT University

GPO Box 2476V Melbourne Victoria 3001

AUSTRALIA

[email protected] http://www.rmit.edu.au/staff/irene-yarovsky

Abstract: - This paper describes computer modelling studies using classical Molecular Dynamics techniques

and their derivative methods such as umbrella sampling and coarse grain simulations to study protein

behaviour in various environments causing their partial unfolding and aggregation. We present an overview of

a series of theoretical studies which provided fundamental insights into the molecular mechanisms of self-

assembly of apolipoprotein C-II (ApoC-II) which is involved in blood lipid transport and shows a tendency to

misfold and aggregate into insoluble amyloid fibrils.

Key-Words: Protein Misfolding, Protein Aggregation, Molecular Dynamics simulations, Amyloid Fibrils

1 Introduction One of the most fundamental phenomena in

nature is the capability of proteins to fold de novo to

their native conformation, also known as their

biologically functional state. Significant advances

have been made in the understanding of protein

folding through experimental and theoretical

approaches. However, to this day the folding process

of a linear polypeptide strand to its three-

dimensional, biologically active conformation is

poorly understood and theoretical prediction of the

folding pathways remains a challenge.

The misfolding of proteins may lead to formation

of either amorphous compounds or structures of

elongated-unbranched morphology, known as

amyloid fibrils, containing β-sheets with strands

perpendicular to the fibril axis. An accumulation of

these fibrils can result in a range of human diseases,

such as Alzheimer’s, variant Creutzfeldt-Jakob

disease, Parkinson’s, type II diabetes and many

others. Little is known of the mechanism of fibril

formation. It is believed to be a multistage process

driven by hydrophobic interactions where a variety

of intermediate structures are formed. Fibrillation

may be enhanced by the local environment, such as

changes in the metal ion concentration, temperature,

pH conditions, organic solvents, or cosolvents.

Other factors include mutations, transmitted prion

proteins, or simply the inevitable aging process.

The apoC-II protein belongs to the family of

apolipoproteins proteins that are prone to form

amyloid fibrils under lipid free conditions. The

aggregates of apoC-II are a major component of

human atherosclerotic plaques and are known to

affect the macrophage inflammatory response which

is detrimental to the human health. Fibril formation

is believed to follow a series of steps:

monomerisation, formation of partially folded

intermediates, nucleation, and fibril growth. All the

models proposed so far involve significant

conformation changes during the fibrillation

process; however, the exact structural mechanism

continues to remain ambiguous.

Over the last few decades molecular dynamics

(MD) simulations have emerged as a powerful tool

for the characterization of biomolecular structure

and dynamics at the atomic level. This technique has

helped us understand complex molecular processes

associated with protein conformational changes,

ranging from studies of enzyme-reaction

mechanisms and ligand binding to problems of

protein folding and denaturation. With continuing

advances in methodology and computer power,

molecular dynamics studies are being applied to

larger systems, longer time scales and can reveal

molecular mechanisms of more complex

phenomena. Molecular dynamics enables sampling

of structural states of a protein under controlled

conditions and has been shown to be a

complementary technique to experiments for

studying protein dynamics, such as folding,

unfolding and aggregation. We have recently

implemented different computational techniques to

gain insight into these important areas of protein

behavior, with specific applications to the

conformational dynamics and self-assembly of

apoC-II derivative peptides.

In this paper we present a summary of our

computational studies which investigated the

influences of phospholipids, mutations and pH on

Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 41 ISBN: 978-960-474-110-6

amyloid formation by peptides derived from apoC-

II. The structural stability of pre-formed oligomeric

composites of different sizes and arrangements was

also analyzed. Based on our results we identified the

peptide conformations with aggregation and

fibrillization propensities. In this article we also

present an overview of computational modelling

techniques we have applied in several case studies to

gain an insight into the protein folding mechanisms

and the environmental conditions that can lead to

misfolding and aggregation of proteins in general.

2 Methodology 2.1 Molecular dynamics The molecular dynamics simulation method is based

on Newton’s second law or the equation of motion,

F=ma, where F is the force exerted on the particle,

m is its mass and a is its acceleration. From a

knowledge of the force on each atom, it is possible

to determine the acceleration of each atom in the

system. Integration of the equations of motion then

yields velocities and trajectories that describe the

atomic positions as they vary with time. From this

trajectory, a thermodynamic ensemble of the system

configurations can be obtained for a given

temperature and average values of a number of

properties can be determined. Fundamental to MD

simulations are the forces that govern the atomic

motions, derived from a pairwise atom-atom

interaction function usually referred to as an

empirical potential energy function or a forcefield

[1]. One functional form of such forcefield can be

represented as:

( ))cos(12

)(2

)(2

)( 20,

20, δωθθ −+∑+−∑+−∑= n

Vkll

kV

dihedrals

nii

angles

iii

bonds

iNr

∑ ∑

+

−

+

= +=

N

i

N

ij ij

ji

ij

ij

ij

ij

ijr

qq

rr1 1 0

612

44

πε

σσε

(1)

where V(rN) denotes the potential energy, which is a

function of the positions (r) of N particles. The first

three terms in Equation 1, model the bonded or

intramolecular interactions, where the interatomic

bonds and angles are represented by a harmonic

potential and the dihedrals by torsional potential.

The forth contribution is the non-bonded interaction

term, which in a simple forcefield is usually

modelled using a Coulomb potential term for the

electrostatic interactions and a Lennard-Jones

potential for the van der Waals interactions. The

terms contain parameters that are either determined

empirically or from high level ab-initio calculations.

The choice of mathematical function and the

parameters describing a forcefield is important,

since it will ultimately determine the quality of the

results.

We recently performed a systematic comparison

of multiple simulations of insulin chain B using five

different forcefields to gain an improved

understanding of the forcefield influences on the

representation of the conformational behavior of

proteins [2]. The effect of these widely used

forcefields on the secondary structure of insulin and

its dynamics were investigated in detail by

comparison of our results with X-ray

crystallographic structures, calculating the

conformational evolution, solvent accessible surface

area, radius of gyration and interproton distance

violations for each forcefield simulation. We have

observed that different forcefields favour different

conformational trends, which is important to be

aware of for the interpretation of classical simulation

results of proteins in general.

Insufficient sampling of the conformational space

available to a biological system remains a problem

for theoreticians even with the significant

improvements in computer technology. The

complexity and ruggedness of the free energy

surface, comprised of numerous minima induces

difficulties in using classical MD for studying

complex processes such as protein folding as the

system can easily get trapped in one of the local

minima and fails to properly sample the rest of the

conformational space. In order to overcome this

complexity it is necessary to employ a methodology

that is capable of accelerating rare events,

specifically, configurational changes that involve the

crossing of large free energy barriers. Few novel

techniques capable of exploring wider

conformational space and longer timescales have

recently been developed. They include umbrella

sampling and coarse grained simulations, described

below.

2.2 Umbrella Sampling Characterization of the early stages of molecular

aggregation (dimer formation from initially solvated

monomers) is of fundamental importance in

elucidating the mechanism of crystallization. In the

case of fibril-forming peptides, calculation of the

free energy of dimerisation can lend insights into the

effects which various factors may exert on the

earliest stages of fibril-formation. The dimerisation

free energy may be represented as a potential of

mean force (PMF), i.e. free energy as a function of

the distance between the centers-of-mass of the two

monomers: A(x) = -kTln[P(x)] where P(x) is the

probability density over the coordinate x,

intermolecular separation. Although this quantity

may in principle be obtained from long timescale

Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 42 ISBN: 978-960-474-110-6

MD simulation, in practice P(x) is very slow to

converge, as the peptides might be unable to cross a

barrier (a local maximum in A(x)) to explore

conformational space beyond the barrier. This leads

to poor sampling of conformations along

dimerisation pathways, and a poor quantification of

dimerisation free energy. The umbrella sampling

method of Valleau and Torrie [3] overcomes the

problem of insufficient sampling for certain regions

on the reaction coordinate x by introducing an

additional biasing potential w(x) which forces the

peptides to sample prescribed separation distances.

Typically, a number of simulations with different

biasing potentials are carried out, each one confining

the variations in the position of the particle to a

particular region or “window” i on x. The resultant

probability density over the reaction coordinate is

the biased density P(x’). A common algorithm to

obtain the unbiased density, P(x), and thereby

retrieve the unbiased PMF, is the weighted

histogram analysis method (WHAM) of Kumar et

al. [4]. In our work, we have applied umbrella

sampling with WHAM to obtain PMF profiles of

amyloidogenic peptide dimerisation, and the results

from these calculations are discussed in section 3.3.

2.3 Coarse-grained simulations Although advanced methods of conformational

sampling such as umbrella sampling have enabled

the study of the formation of dimers and small

oligomeric clusters, aggregation phenomena at

larger, biologically relevant length and time-scales

are still difficult to access at the atomistic level

computationally. To bridge this gap, coarse-grained

molecular models have been developed, in which

multiple atoms are grouped together into single

interaction sites. In the case of proteins, one

common approach is to reduce the level of detail of

each amino acid into a single “backbone” and

between 1 to 3 “sidechain” beads, as implemented in

the MARTINI forcefield [5]. These methods are

appropriate to the study of mesoscopic phenomena

in which atomic-level details do not play direct, vital

roles, such as prediction of peptide-micelle

interactions and membrane protein-lipid self

assembly [6]. Significant computational speed-up is

possible due to a number of factors. Firstly, the

coarse-graining scheme produces a reduction in the

total number of particles, and therefore a significant

reduction in the number of non-bonded interactions,

in the simulation system, Secondly, larger

simulation timesteps may be used as a result of the

removal of fast degrees of freedom such as

individual bond length/angle vibrations and torsion

angle rotations. Furthermore, there is a “smoothing”

of the potential as a result of combining several

atoms into single sites, which in turn produces

smoother free energy landscapes which are more

easily explored by unbiased simulation dynamics (in

contrast to rugged, atomistic landscapes, which

contain multitudes of local energy minima). In

preliminary work carried out in our laboratory, we

have applied the MARTINI forcefield to study the

effects of lipids on aggregation of several tens of

copies of an amyloidogenic peptide. This forcefield

was applied due to its demonstrated success in

simulating peptide-lipid interactions, and further

work is currently in progress to develop a coarse-

grained model capable of describing fibril

formation.

3 Protein aggregation: case studies 3.1 ApoC-II (56-76) peptide: effect of Met60

oxidation and mutation

The human plasma apolipoprotein (ApoC-II) is a 79

residue protein involved in lipid metabolism. In the

presence of lipids, apoC-II is composed of α-helical

elements, however in lipid-free environment it folds

into cross-β sheet structure to form amyloid fibrils.

Using hydrogen/deuterium exchange and proteolysis

studies, peptide fragments composed of residues 60

to 70 and 56 to 76 have been shown to exhibit an

inherent propensity for amyloid fibril formation in

solution. MD simulations of the apoC-II(56-76)

peptide have demonstrated the peptide populated an

ensemble of turn structures, stabilized by hydrogen

bonds and hydrophobic interactions enabling the

formation of a strong hydrophobic core which may

provide conditions required to initiate aggregation

[7]. Legge et al. have also recently investigated the

effect of single-point mutations at Met60 to Val and

Gln on the dynamics and structure of apoC-II(56-76)

[8]. Based on the analysis performed on these

simulations, the two mutations show qualitative

similarity to the native structure. Therefore, it is

reasonable to suggest that the mutants may form

fibrils also, but likely with different kinetics and/or

fibril morphology. Recent thioflavin T (ThT)

fluorescence time course results of the apoC-II(56-

76) peptide showed that the M60V and M60Q

mutated peptides do form fibrils.

3.2 ApoC-II (60-70) peptide: effect of lipids,

pH and mutations

We have also applied computational simulations to

investigate the influences of phospholipids,

methionine oxidation (known to be fibril-inhibiting),

Met60 to Val and Gln mutation and acidic pH

(fibrillogenic) on the derived apoC-II(60-70) peptide

Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 43 ISBN: 978-960-474-110-6

[9]. Our results indicate that MD simulations may be

used as a qualitative predictor of fibrillogenicity in

this peptide. We focused on the orientations of the

two aromatic residues in the peptide, Y63 and F67,

under both fibrillogenic and fibril-inhibiting

conditions. Our results correlate well with

experimentally-determined fibrillization propensity.

The major conformations sampled during

simulations under different conditions are shown in

figure 1, with the aromatic sidechain orientations

illustrated. We observe a distinct bias towards

symmetric distribution of aromatic surface for the

fibrillogenic peptides (Fig. 1A), with Y63 and F67

sidechains situated on opposite sides of the hairpin

structure, while asymmetric distributions are

observed for the lipid-bound and ox-M60 peptides,

with both rings located on the same face (Fig. 1B).

We propose that orientation of the rings on

opposite faces of the hairpin renders them capable of

rapid formation of an energetically-favourable linear

oligomeric complex (Fig. 1A), stabilised by strong

inter-molecular hydrophobic contacts between the

aromatic sidechains, in which the constituent

monomers may then undergo translational,

rotational or internal structural conversion to the

fibrillar form. In the case of lipid- and ox-M60, there

are more oligomer-forming pathways involving

hydrophobic ring interactions, leading to the

possible formation of large assemblies with

hydrophobic cores which are not elongated (Fig.

1B). The existence of multiple, competing,

energetically favourable aggregation pathways may

be one manner in which the oxidation of M60

influences fibrillation propensity via alteration to the

monomer structure.

Fig.1. Proposed mechanism of initial aggregate

formation for apoC-II(60-70) peptide under, A)

favourable fibrillization conditions, and B) fibril-

inhibiting, oxidised M60 conditions.

3.3 ApoC-II dimers ThT fluorescence and ultracentrifugation

sedimentation experiments demonstrate the effects

of lipids in inhibiting fibrillization and enabling the

formation of stable, soluble, oligomeric peptide-lipid

complexes which do not proceed to fibril elongation.

Nevertheless, the atomic mechanisms of peptide

aggregation and the influences of lipids are currently

not fully understood. To address this deficiency, we

have applied computer simulations and umbrella

sampling (section 2) to examine the effects of

solvated lipids on the association energies between

peptide monomers [10]. PMF profiles indicating the

dimerisation free energies of a stable complex with

and without di-5-phosphatidylcholine (D5PC) lipids

are shown in figure 2. The presence of lipids

enhances the association free energy of dimers by

~4 kcal/mol, indicating the enhanced stability of the

dimer complex due to interactions between the

peptides and the lipids. Based on our simulations,

we propose that one mechanism by which peptide-

bound lipids inhibit fibrillization is via trapping of

dimers (and other oligomeric species) in arbitrary

conformations, including fibril-disfavouring ones,

reducing their likelihood to dissociate and re-

associate into conformations more prone to fibril

nucleation and growth. Such lipid-trapped

intermediates may contribute to the toxic nature of

oligomeric amyloid intermediates. The “trapping”

effect of lipids on the peptides structure was also

observed in our most recent work on the lipid

concentration effects on the conformation of apoC-

II(60-70).

Fig. 2. PMF profiles for the dimerisation of apoC-

II(60-70), in D5PC lipid-free (black line) and lipid-

rich (grey line) environments. Insets show typical

system configurations at indicated separations.

Aromatic residues in CPK format, peptide

backbones as ribbons, and lipids as thin lines.

3.4 ApoC-II oligomers

It is postulated that the oligomeric intermediates are

possible cytotoxic species in diseases associated

with amyloid deposit, therefore insight into the

mechanism of fibril formation at its initial stages is

crucial. Continuing from our extensive monomer

and dimer dynamics studies, we extend our work by

OROR

A) B)

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2

Centre-of-mass Separation (nm)

∆G

(k

ca

l/m

ol)

Pure water

D5PC lipids

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2

Centre-of-mass Separation (nm)

∆G

(k

ca

l/m

ol)

Pure water

D5PC lipids

Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 44 ISBN: 978-960-474-110-6

performing MD simulations of apoC-II(60-70)

oligomeric seeds of various sizes and arrangements.

Specifically, we investigated the structural stability

of trimer and tetramer single β-sheet formations in

parallel (P) and anti-parallel (AP) strand

orientations. The effect of different terminal states,

e.g. charged, NH3+…COO-, and neutral,

NH2…COOH (T) was also investigated.

Fig. 3. A) Trimer rmsd of backbone atoms; B)

Tetramer rmsd of the backbone atoms; C)

Screenshot of the parallel trimer (1-3-P) at 100 ns;

D) and anti-parallel tetramer (1-4-AP) at 100 ns.

Our simulations showed that the increase in number

of strands, improves the stability of the oligomers

dramatically, regardless of the strands orientation.

However, the AP arrangement between the strands

was more favourable, as indicated by the lower rmsd

compared to the P oligomers (Fig. 3A,B).

Interestingly, rearrangement between the strands

was observed from the trimer simulation starting

from a parallel arrangement, where the outer strand

separated from the oligomers and rotated to reattach

back in an anti-parallel arrangement (see Fig. 3C,D).

This result gives further insight into the orientation

preference for fibril formation in apoC-II(60-70)

peptide.

3.5 ApoC-II aggregation: coarse-grained

simulations

In addition to atomistic simulations, we have applied

the MARTINI [5] coarse-grained potential to study

the aggregation behaviour of the apoC-II(60-70)

peptide, both in the absence and in the presence of

dihexanoylphosphocholine (DHPC) lipids. We

performed 200ns unbiased simulations of 27 copies

of the peptide, initially separated from each other by

~4nm, both in the absence and presence of 125

lipids. The backbone dihedral potentials of the

peptide were assigned assuming random coil

conformations, based on our earlier atomistic

simulations of the peptide [9]. In pure water, the

peptide formed disordered aggregates within 5ns,

and all 27 peptides aggregated into a single

elongated cluster by ~160ns (illustrated in Fig. 4A).

The rapid kinetics of aggregation can be seen in a

plot of the number of distinct peptide clusters in the

solution as a function of simulation time (Fig. 4C,

black); note the rapid drop between 0-10ns

indicating fast aggregation. In contrast, in the

presence of lipids, peptide aggregation proceeds

much slower. Instead of a single large cluster, a

suspension of solvated lipid micelles with peptide

aggregates partially buried in the micellar core is

formed (an example is shown in Fig. 4B).

A) B)

C)

0123456789

101112131415161718192021222324252627

0 50 100 150 200

Simulation Time (ns)

Nu

mb

er

of

Pep

tid

e C

luste

rs

Pure water

DHPC lipids

Fig. 4 Graphics of A) coarse-grained apoC-II(60-70)

peptide aggregate in pure water, viewed along a

plane perpendicular to the principal axis and B) one

peptide-micelle complex in DHPC-rich solution at

200ns. Peptide backbone beads in green, sidechain

beads in yellow. DHPC lipids in CPK, with choline

(blue), phosphate (bronze) and carbon tail beads

(cyan). C) Number of peptide clusters with respect

to time for lipid-free (black) and lipid-rich (grey)

solvents.

Three such peptide-micelle complexes are formed

by the end of the simulation. The marked reduction

in aggregation kinetics in the presence of lipids is

evident by inspection of Fig. 4C (grey), in which the

A) B)

C) D)

Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 45 ISBN: 978-960-474-110-6

reduction in total number of clusters is

approximately linear up to ~100ns, as opposed to the

exponential decrease exhibited (black line) when

lipids are absent. These results are in good

agreement with experiments, which demonstrated

the aggregation-inhibition effects of lipids [11].

They are also in qualitative agreement with our

umbrella sampling simulations, in which we showed

that lipids can stabilize peptide dimers [10]; in the

case of our coarse-grained simulations, we found

suspensions of peptide clusters partly buried inside

lipid micelles. Thus, the lipids appear to stabilize

such small, disordered oligomeric clusters.

However, we note that in its present form, the

MARTINI forcefield is incapable of producing

amyloid fibril formation, although it appears to

predict the initial stages of peptide aggregation

which are driven by inter-peptide sidechain-

sidechain interactions. We are pursuing further work

to develop a model capable of describing the entire

pathway of fibrillogenesis, from initial

oligomerisation through to the structural

transformations required for mature fibril formation.

4 Conclusion Theoretical molecular simulations have been

demonstrated to be a useful complementary

technique to experiments which enable molecular

mechanisms, dynamics and structure-function

relationship to be revealed at the atomic level. We

have applied molecular dynamics technique and

several derivative methods to gain insight in the

folding, misfolding and aggregation mechanisms of

apoC-II in different environments. Umbrella

sampling algorithm was applied to determine the

free energies of dimerisation of apoC-II peptides and

the effects of environment and mutations, in order to

gain a better understanding of the initial stages of

amyloid fibril formation. We identified key

structural changes in apoC-II derived peptides under

fibril favoring conditions (neutral and low pH) and

fibril disruptive conditions (lipid-rich and oxidized

Met). The structural stability and dynamics of pre-

formed apoC-II oligomers with various sizes and

arrangements was also investigated where the anti-

parallel orientation between the strands was

determined to be the most favourable. We also

applied coarse-grained simulations to study longer

time scales and larger aggregates of the peptides.

The capability of classical MD simulations to

explore the molecular-motion or evolution of a

system over time and under controlled conditions in

explicit solution is very useful for studying various

protein behaviors.

References:

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biological macromolecules: Overview and issues.

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[6] Sansom, MSP; Scott, KA; Bond, PJ Coarse-

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apolipoprotein C-II. Journal of Physical Chemistry

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[9] Hung, A., Griffin, M.D., Howlett, G.J.,

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[10] Hung, A., Griffin, M.D., Howlett, G.J.,

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derived amyloidogenic peptide oligomerisation but

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[11] Griffin, M.D., Mok, M.L., Wilson, L.M., Pham,

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Proceedings of the 2nd WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS

ISSN: 1790-5125 46 ISBN: 978-960-474-110-6