From peptide chains to chains of peptides - multiscale modelling of self-assembling polypeptides

Promotion on 22 September 2011

Summary of thesis

Amyloid-like fibrils are long, insoluble threads of protein. The fibrils typically consist of two to six protofilaments, each two to five nm in diameter, twisting together to form rope-like fibrils with a length of several tens of nanometers. In each protofilament, the proteins or peptides form β-strands running perpendicular to the fibril axis. The formation of amyloid-like fibrils is related to the process of protein folding. Protein folding is often discussed in terms of a free energy landscape in which minima represent stable or metastable structures. The free energy landscape for a given polypeptide sequence depends largely on the environment. Changes in polypeptide concentration, pH, salt concentration, temperature etc. affect the landscape significantly and can shift the free energy minimum towards the fibril state as was proposed by Astbury. The kinetics of fibril formation is generally thought of as a nucleation-and-growth process. The nucleation step involves the formation of a small, energetically unfavourable aggregate usually called a nucleus or seed. Once this nucleus is formed, fibril growth proceeds downhill.

While amyloid-like fibrils are most famous for their implication in disease (e.g. Alzheimer's, Parkinson's, prion diseases), many examples of functional amyloid fibrils exist. Moreover, peptides forming amyloid-like fibrils have received a lot of attention as potential building blocks for nanomaterials. Amyloid-like fibrils are biocompatible and biodegradable, extremely strong and they form through self-assembly of their peptide-based building blocks. The self-assembly behaviour of these peptides is remarkably robust for modifications of the building blocks, enabling the design of smart, functionalised materials. Moreover, the building blocks can be modified to induce environmental sensitivity. This way, self-assembly will only happen in response to an environmental trigger (pH, temperature) and/or the self-assembled structure disassembles as a result of a change in environment. Potential applications for these materials include self-healing coatings, tissue engineering, generation and degradation of scaffolds for cellular growth, drug delivery and controlled drug release.

In order to facilitate the design of such nanomaterials, a detailed understanding of the physico-chemical processes underlying the self-assembling behaviour is crucial. In this thesis we employed computer simulations to study folding and assembly of fibril-forming peptides at atomistic-to-molecular scale. Although computer power keeps increasing every year, at this time computer simulations are still limited to systems of up to one million particles for several hundreds of ns. Hence it is simply not feasible to simulate certain processes at full-atom resolution and therefore a particular system with its corresponding length- and time scale has a natural description level, going from very detailed (full-atom) for small systems to highly coarse-grained for large systems.

As fibrils are hierarchical structures covering a range of scales going from peptides (about 2 nm), oligomers (1-10 nm) to fibrils (1 to 100 μm) a multiscale modelling approach is essential to elucidate key processes at different stages during fibril formation. Multiscale modelling can be either concurrent or hierarchical. While in concurrent multiscale modelling two levels of description are coupled in one simulation, we have limited ourselves to hierarchical multiscale modelling in which each level is simulated individually. The results at the different levels can subsequently be integrated into one coherent picture.

Apart from changing the description level, it is possible to reach longer timescales for a certain system size and description level through the combination with rare event methods. In a computer simulation, going from one stable state in the free energy landscape to the another can be considered a rare event: most of the simulation time will be spent sampling the (meta-)stable states and crossings are few and far-between. Over the past decades, many techniques have been developed to overcome sampling issues arising from limited simulation time. In this thesis we have used replica exchange MD (REMD), steered MD (SMD), umbrella sampling and transition path sampling (TPS) in combination with both all-atom and coarse-grained simulations.

Chapters 3-6 of this thesis focus on elucidating folding and self-assembly of silk-based block copolymers. These block copolymers consist of a hydrophobic, silk-based block of (Gly-Ala)3Gly-Glu repeats flanked by hydrophilic outer blocks (C-blocks) and form fibrils from solution upon a pH trigger. Where possible we tried to compare our simulation results to experiments done on the silk-based block copolymer as described by Martens et al.

As a first step towards understanding fibril formation of these block copolymers we predicted the structure of the silk-based block in water under fibril-forming conditions (low pH). The experimental silk-based block consists of almost 400 amino acids and is thus too large to simulate at full atomistic resolution. As the silk-based block is highly repetitive, we studied smaller, but representative parts. To obtain a better understanding of possible stable secondary structures in water, we simulated two β-hairpins based on existing structures (PDB 1SLK and 2SLK). One of these hairpins unfolded completely, while the other hairpin rearranged and the resulting ``twisted'' hairpin remained stable for the rest of the simulation. Based on these results a model was constructed for the silk-based block, which is very similar to the β-roll motif. This β-roll is in good agreement with the fibril dimensions as measured in AFM and SAXS experiments and may explain the CD spectra obtained in water. To explore the conformational space of the silk-based block, REMD simulations were performed. These simulations indicate that the β-roll is indeed very stable in water.

When the silk-based block copolymers are solvated in methanol instead of in water, pH-triggered fibril formation has also been observed. Experiments have indicated that the structure of the silk-based blocks in these fibrils is most likely to be an anti-parallel β-sheet. Moreover, these fibrils are unstable in water. To elucidate the solvent-dependency of the molecular conformation of the silk-based block REMD simulations of a stack of two antiparallel β-sheets solvated in water or methanol were performed. A β-roll and a flat, anti-parallel β-sheet can interconvert via a transformation resembling that of an accordeon pleat. In agreement with the experimental evidence, these simulations indicate that in water the β-roll is the most stable structure whereas in methanol an anti-parallel structure is preferred.

All-atom simulations will not allow a study of the self-assembly behaviour of the silk-based block copolymers. Hence, we have developed a coarse-grained model to describe our polymers. Our model is based on earlier models developed in the Head-Gordon and Thirumalai groups. Each amino acid is modelled by one representative bead, located at the c-α position. The solvent is not taken into account explicitly. First, we optimise our model for the silk-based block, with all-atom simulations as a reference. Compared to the HG-model, a new description for the dihedral angles of the turn residues are introduced. Besides, the long-ranged interactions, described by a Lennard-Jones potential, had to be shifted to avoid unphysical attraction between non-neighbouring β-strands. Subsequently, the unknown strength of the non-bonded interactions between the beads is optimised by computing the PMF for unfolding of one outer strand of a β-roll using SMD simulations in combination with Jarzynski's equality. The model was subsequently extended to include a description for the hydrophilic C-blocks.

Compared to an all-atom force field, this coarse-grained model reduces the number of particles to simulate by approximately two orders of magnitude. While the model cannot capture all equilibrium quantities we have shown that several important properties can be reproduced, such as the radius of gyration of the C-block and the persistence length of the fibril.

In order to obtain insight into the exact mechanism of self-assembly we then employed a multiscale modelling approach in combination with rare event simulations. Possible self-assembly mechanisms for the silk-based blocks were assessed at full-atom resolution by forcing this block to behave according to a certain mechanism in an artificially fast manner using SMD simulations. From the SMD results an equilibrium PMF can be obtained using Jarzynski's equality. This facilitates comparing various mechanisms. The coarse-grained model is used to obtain a better understanding of the role of the hydrophilic C-blocks flanking the silk-based block.

Our all-atom simulations indicate that a polypeptide prefolded into a β-roll docks at the growing end of a fibril through the formation of Glu-Glu sidechain contacts. Subsequently it can slide to an optimal position before water is expelled and a dry interface between the attaching β-roll and the growing fibril end is formed. A mechanism where an unfolded polypeptide attaches to the fibril and uses it as a template to fold into a β-roll is highly unlikely due to the high cost of correcting for mismatched rolls. The main role of the C-blocks is in limiting random aggregation of the silk-based block. Moreover, they play a role in pre-aligning the silk-based blocks such that their mismatch is minimised and regular fibrils are formed.

In the last chapter on the silk-based block copolymers we employed a lattice model to study the interplay between folding and assembly. Because of its highly coarse-grained nature, the lattice model allowed us to simulate the entire folding and assembly process starting from two unfolded polypeptides. We investigated how the morphology of the assembled structures depends on the temperature, alanine-solvent interaction and the presence of hydrophilic flanks. We showed that strong hydrophobicity (strong alanine-solvent repulsion) results in misfolded, intertwined aggregates whereas weak hydrophobicity results in structures where two peptides align instead of stack. For low to intermediate hydrophobicity the folding temperature is higher than the aggregation temperature suggesting that upon quenching the temperature folding precedes assembly. Small hydrophilic flanks attached to the termini of the silk-based peptide regulate self-assembly.

In the last chapter the dynamical process of attaching new peptide monomers to a growing amyloid fibril was studied. We focussed on the LVEALYL heptapeptide, which is part of the peptide hormone insulin. This heptapeptide was identified as the main amyloidogenic region of insulin, which forms fibrils under certain conditions. The dynamics of this process is not well understood, but involves docking of the attaching peptide to the growing fibril followed by locking into its correct position. Small peptides are often studied as representatives for their full-length counterparts, but they are also attractive building blocks for amyloid-inspired biomaterials. As the system is relatively small - eight peptides of seven amino acids each - it can be studied using a full-atom description. Using TPS, we showed that there are two possible routes for a docked peptide to attach fully to the fibril. Both involve the formation of backbone hydrogen bonds between the attaching peptide and the fibril and a change of orientation of the central Glu sidechain of the attching peptide but the routes differ in the order in which these key steps take place.

PhD promotion of
Marieke Schor
Prof. Dr. P. Bolhuis
14:00, Tuesday, 20 September 2011
Agnietenkapel, UvA, Amsterdam