Application of Computational Modelling to Protein Folding and Aggregation Studies

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1 Application of Computational Modelling to Protein Folding and Aggregation Studies NEVENA TODOROVA, ANDREW HUNG AND IRENE YAROVSKY School of Applied Sciences RMIT University GPO Box 2476V Melbourne Victoria 3001 AUSTRALIA Abstract: - This paper describes computer modelling studies using classical Molecular Dynamics techniques and their derivative methods such as umbrella sampling and bias-exchange metadynamics to study protein behavior in various environments causing folding, unfolding and aggregation of proteins. We present applications related to two important proteins insulin and apolipoprotein C-II (ApoC-II). Key-Words: Protein Folding, Protein Aggregation, Molecular Dynamics Simulations, Umbrella Sampling 1 Introduction 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 dynamics of insulin and apoc-ii. 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 threedimensional, biologically active conformation is poorly understood and theoretical prediction of the folding pathways remains a challenge. Using a methodology called bias-exchange metadynamics (BE-META) we were able to identify the structural transitions and possible folding pathways of insulin. A brief summary of our results is presented in section When a protein is subjected to external stresses (e.g. thermal, electric or chemical) it can experience conformational changes that can cause the protein to misfold. Such structural changes have been linked with many debilitating diseases, therefore improved understanding of the protein response to an external stress is required. Recently, the proliferation of radio-frequency electromagnetic devices has raised concerns regarding the effects of electric and magnetic radiation on human health. We used a prototype protein insulin, to investigate the variance in its structure, when subjected to static and oscillating fields at different strengths and frequencies using all-atom MD simulations. Brief summary of our findings is reported in section of this article. Another interesting phenomena is the misfolding of protein that may lead to formation of either amorphous compounds or structures of elongatedunbranched 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 ISSN: ISBN:

2 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. Interestingly, insulin and apoc-ii belong to the family of unrelated proteins that are prone to form amyloid fibrils under different conditions. Fibrillation in insulin has created difficulties in production, storage and therapeutic use. 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. We have performed computational studies to investigate the influences of phospholipids, mutations and ph on 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 (see sections 3.2, 3.3 and 3.4). In this article we present an overview of computational modelling techniques we have applied to 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. 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: V( r N ki 2 ki 2 Vn ) = ( li li 0) + ( θi θi,0) + n bonds 2 angles 2 dihedrals 2 N N σ ij + 4ε ij i= j= i+ rij 12 ( 1+ cos( ω )), δ 6 σ ij q iq j + rij 4πε rij (1) where V(r N ) 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 insulin [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. 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, ISSN: ISBN:

3 specifically, configurational changes that involve the crossing of large free energy barriers. Few novel techniques capable of exploring wider conformational space have recently been developed. They include the BE-META method and umbrella sampling, described below. 2.2 BE-META Bias exchange metadynamics is a recently introduced methodology [3], which allows free energy reconstruction in a virtually unlimited number of variables, and as such can be considered for investigating complex processes like protein folding, protein-protein interactions and enzyme reactions. This novel theoretical tool incorporates two previously reported powerful techniques, replica exchange [4] and metadynamics [5]. In BE-META approach, the dynamics of the system is biased by a history dependent potential constructed as a sum of gaussians centred on the trajectory of a selected set of collective variables (CV). After transient period, the gaussian potential compensates the free energy, allowing the system to efficiently explore the space defined by the CVs. All replicas are evolved at the same temperature and allowed to periodically exchange the metadynamics potential, where an exchange is accepted or rejected according to a Metropolis criterion. As a result, the system of interest is capable of efficiently exploring a free energy landscape in several dimensions due to the multidimensional nature of the bias applied. New tools of analysis have been introduced [6] that exploit the outcomes of a BE-META simulation for constructing a thermodynamic and kinetic model of a biomolecular process being investigated. Using these techniques we investigated the folding pathways of chain B and the results are summarized in section of this article. 2.3 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 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 [7] 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. [8]. 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 Protein dynamics: case studies 3.1 Insulin Folding of insulin chain B Explicit solvent BE-META simulations were performed to effectively sample the conformational space available to chain B of insulin and to shed some light on the complex structural transitions this important protein undergoes upon folding. To exploit the statistics accumulated using this powerful technique, a recently developed analytical method was used to construct a model describing the complex conformational transitions chain B experiences. We identified a three state model for the folding pathway of insulin chain B. Starting from an extended structure, at first the protein is governed by electrostatic interactions (moltenglobule 1, figure 1). This finding is supported by experimental studies which suggested this type of conformation to be biologically active. Progressive building of hydrophobic core is initiated by the burial of Y16, followed by further packing of F24 and F25 (molten-globule 2, figure 1), resulting in stable compact structures. Furthermore, the hydrogen bonding interactions between the buried backbone groups commence the formation of an α- helix at the core of the protein. An unfolded N- terminal region is found in the structures at the ISSN: ISBN:

4 border of molten-globule 2 and the folded basin, suggesting that the last stage of the folding of chain B is the complete formation of the α-helix. The transformation from molten-globule 2 to a folded state requires crossing of a high energy barrier, and as a consequence of this tens of microseconds are required to make this transition. The calculated transition times gave further insight into the dynamics between the three wells, suggesting that the residence time of the three wells is of the order of a several microseconds. We believe that the native disulfide pairing of chain A with chain B (A7-B7 and A2-B19) plays an important part in the stability of the α-helix, which effectively prevents the protein from unfolding and becoming a moltenglobule. Molten globule 1 (electrostatic interactions) Molten globule 2 (hydrophobic interactions) Folded state Fig. 1. Schematic representation of the insulin chain B folding dynamics Electric field effects on insulin. MD simulations were performed on chain B of insulin under the influence of static and oscillating fields, ranging from 10 7 to 10 9 V/m [9]. We have found that both variants have an effect on the normal behavior of the protein, with oscillating fields being more disruptive to the structure as compared to static fields of similar effective strength. Fig. 2. Change in structure of native chain B (blue) when exposed to strong static electric field stress (gold). The application of a static field had a stabilizing effect on the secondary structure, restricting the inherent flexibility that is crucial for insulin s biological activity (Fig. 2). This inherent flexibility was also observed in our computational study of possible thermal and chemical effects on the dynamics of chain B [10]. Studies performed by Legge et al. [11], yielded information clarifying uncertainties about the structure and dynamics of insulin with respect to its biological behavior by performing multiple MD simulations as an alternative way to improve the conformational sampling. 3.2 ApoC-II monomers 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. Our recent 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 [12]. Furthermore, we investigated the effect of single-point mutations at Met60 to Val and Gln on the dynamics and structure of apoc-ii(56-76) and (60-70). 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 V60M and Q60M mutated peptides do form fibrils. We have also applied computational simulations to investigate the influences of phospholipids, methionine oxidation (known to be fibril-inhibiting) and acidic ph (fibrillogenic) on the derived apoc- II(60-70) peptide [13]. 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 3, with the aromatic sidechain orientations illustrated. We observe a distinct bias towards symmetric distribution of aromatic surface for the fibrillogenic peptides (Fig. 3A), 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 (3B). We propose that orientation of the rings on opposite faces of the hairpin renders them capable of ISSN: ISBN:

5 rapid formation of an energetically-favourable linear oligomeric complex (Fig. 3A), 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. 3B). 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. A) B) OR Fig. 3. Proposed mechanism of initial aggregate formation for apoc-ii(60-70) peptide under, A) favourable fibrillization conditions, and B) fibrilinhibiting, 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. PMF profiles indicating the dimerisation free energies of a stable complex with and without di-5-phosphatidylcholine (D5PC) lipids are shown in figure 4. 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 peptidebound 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 reassociate 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). G (kcal/mol) Centre-of-mass Separation (nm) Pure water D5PC lipids Fig. 4. PMF profiles for the dimerisation of apoc- II(60-70), in D5PC lipid-free (black line) and lipidrich (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 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. a) c) Fig. 5. a) Trimer rmsd of backbone atoms; b) Tetramer rmsd of the backbone atoms; c) Screenshot of the parallel trimer (1-3-P) at 70 ns; d) and antiparallel tetramer (1-4-AP) at 70 ns. b) d) ISSN: ISBN:

6 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. 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 antiparallel arrangement (see Fig. 5d, top strand). This result gives further insight into the orientation preference for fibril formation in apoc-ii(60-70) peptide. 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 insulin and apoc-ii in different environments. The effects of chemical, thermal and electric field (static and oscillating) stresses were modeled using classical MD technique to identify the conformational changes experienced by protein when exposed to external stresses. Using the novel methodology BE-META we were able to identify the folding mechanisms of chain B of insulin, with good agreement to experiment. 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 antiparallel orientation between the strands was determined to be the most favourable. 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: [1] MacKerell Jr., A.D. Empirical force fields for biological macromolecules: Overview and issues. Journal of Computational Chemistry, Vol. 25, 2004, pp [2] Todorova, N., Legge, F.S., Treutlein, H., Yarovsky, I. Systematic Comparison of Empirical Forcefields for Molecular Dynamic Simulation of Insulin. Journal of Physical Chemistry B, Vol. 112, 2008, pp [3] Piana, S., Laio, A. A Bias-Exchange Approach to Protein Folding. Journal of Physical Chemistry B, Vol. 111, 2007, pp [4] Sugita, Y., Okamoto, Y. Replica-exchange molecular dynamics method for protein folding. Chemical Physics Letters, Vol. 314, 1999, pp [5] Laio, A., Parrinello, M. Escaping free-energy minima. Proceedings of the National Academy of Sciences of the United States of America, Vol. 99, 2002, pp [6] Marinelli, F., Pietrucci, F., Laio, A., Piana, S. A kinetic model of Trp-cage folding from multiple biased molecular dynamics simulations. Plos Computational Biology, submitted, [7] Torrie, G.M., Valleau, J.P. Non-Physical Sampling Distributions in Monte-Carlo Free-Energy Estimation - Umbrella Sampling. Journal of Computational Physics, Vol. 23, 1977, pp [8] Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., Kollman, P.A. THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. Journal of Computational Chemistry, Vol. 13, 1992, pp [9] Budi, A., Legge, F.S., Treutlein, H., Yarovsky, I. Electric Field Effects on Insulin Chain-B Conformation. Journal of Physical Chemistry B, Vol. 109, 2005, pp [10] Budi, A., Legge, S., Treutlein, H., Yarovsky, I. Comparative study of insulin chain-b in isolated and monomeric environments under external stress. Journal of Physical Chemistry B, Vol. 112, 2008, pp [11] Legge, F.S., Budi, A., Treutlein, H., Yarovsky, I. Protein Flexibility: Multiple Molecular Dynamics Simulations of Insulin Chain B. Biophysical Chemistry, Vol. 119, 2006, pp [12] Legge, F.S., Treutlein, H., Howlett, G.J., Yarovsky, I. Molecular dynamics simulations of a fibrillogenic peptide derived from apolipoprotein C- II. Biophysical Chemistry, Vol. 130, 2007, pp [13] Hung, A., Griffin, M.D., Howlett, G.J., Yarovsky, I. Effects of oxidation, ph and lipids on amyloidogenic peptide structure: implications for fibril formation? European Biophysics Journal, Vol. 38, 2008, pp ISSN: ISBN: