Advances in the Simulation of Protein Aggregation at the Atomistic

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Review Article

Advances in the Simulation of Protein Aggregation at the Atomistic Scale Martín Carballo-Pacheco, and Birgit Strodel J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00059 • Publication Date (Web): 10 Mar 2016 Downloaded from http://pubs.acs.org on March 15, 2016

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The Journal of Physical Chemistry

Advances in the Simulation of Protein Aggregation at the Atomistic Scale Mart´ın Carballo-Pacheco†,‡ and Birgit Strodel∗,†,¶ Institute of Complex Systems: Structural Biochemistry, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany, AICES Graduate School, RWTH Aachen University, Schinkelstraße 2, 52062 Aachen, Germany, and Institute of Theoretical and Computational Chemistry, Heinrich Heine University D¨ usseldorf, Universit¨ atsstrasse 1, 40225 D¨ usseldorf, Germany E-mail: [email protected] Phone: +49 (0)2461 613670. Fax: +49 (0)2461 619497

Abstract Protein aggregation into highly-structured amyloids fibrils is associated with various diseases including Alzheimer’s disease, Parkinson’s disease and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize ∗

To whom correspondence should be addressed Forschungszentrum J¨ ulich ‡ RWTH Aachen University ¶ Heinrich Heine University D¨ usseldorf †

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experimentally, and to understand the difference in aggregation behaviour between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.

Introduction Protein aggregation into amyloid fibrils One of the grand challenges of biophysics and biochemistry is to understand the principles that govern protein aggregation. 1–5 Protein aggregation is an intricate process which operates on a large range of timescales and results in complexes that range from dimers to highly-structured fibrils. Aberrant aggregation is associated with a range of diseases such as Alzheimer’s, Parkinson’s, Huntington’s, type II diabetes and spongiform encephalopathies (e.g., Mad cow disease). A characteristic of these diseases is that normally soluble proteins assemble into structured aggregates called amyloid fibrils, which are insoluble and resistant to degradation. The fibrillar assemblies are characterized by a β-sheet structure where the β-strands lay perpendicular to the fibril axis. 1,2 They are normally formed by two or more β-sheets which aggregate laterally to form the final fibrils. This structure is called cross-β because of its characteristic X-ray diffraction pattern with a reflection at 4.8 ˚ A corresponding to the distance between β-strands in a sheet, and a second reflection at ∼ 10 ˚ A corresponding to the distance between β-sheets. While it has been hypothesized that most proteins can form amyloids under the right conditions, 6 most proteins under physiological conditions do not aggregate. Protein sequences that form amyloids under physiological conditions have high hydrophobicity, high β-sheet propensity and low net charge. Even though amyloids are normally associated with diseases, a number of amyloids have been discovered with physiological roles. 1,2 These functional amyloids can be found in almost every kingdom 2 and have diverse functions, including storage of peptides, 7 scaffold for melanin formation, 8 or in biofilm formation. 9 In addition, scientists have started to take 2


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advantage of the amyloid fold to create amyloid-based nanomaterials. 10 Since amyloids assemble from soluble precursors, they can be built in a bottom-up fashion from simple building blocks and can also be combined with traditional nanomaterials such as carbon nanotubes to produce hybrid materials. 11 These properties make functional amyloids very appealing for many industrial applications. The aggregation process Two of the fundamental questions are what pathways do aberrant and functional protein aggregation follow, and whether there are major differences between the aggregation of different primary sequences. Several algorithms have been developed to elucidate the link between primary sequence and aggregation propensity and speed, which mainly depend on hydrophobicity, charge and secondary structure propensity of the sequence. 12–17 These algorithms are useful in determining the regions of a protein that are directly involved in fibril formation. However, they cannot predict the mechanism of amyloid fibril formation. It is believed that the conversion of soluble proteins into amyloid fibrils requires the production of an unfolded peptide as a first step. 18 Hence, amyloid diseases are also called protein misfolding diseases. Indeed, many proteins involved in amyloid diseases are either intrinsically disordered or have intrinsically disordered regions (e.g., Alzheimer’s amyloid-β (Aβ), type II diabetes’ islet amyloid polypeptide (IAPP), Parkinson’s α-synuclein, and spongiform encephalopathies’ prions). 1 The unfolded or misfolded peptides coalesce into transient oligomers, which, after having overcome a free energy barrier, rapidly progress to the stable amyloid form. The kinetics of this process displays three characteristic stages: a lag phase, a growth phase and a final plateau regime (see figure 1). It has been recently discussed that during the lag phase a large number of primary nuclei assemble from monomers in solution. 19 For the growth phase, several kinetic models have been proposed. The simplest one, which assumes linear growth at the fibril ends, would underestimate the extreme autocatalysis and strong concentration dependence of amyloid self-assembly giving rise to an exponential mass accumulation during the initial aggregation phase observed for

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the presence of soluble Aβ oligomers correlates better with disease symptoms. 33,34 Thus, the aggregation of monomers of amyloidogenic peptides into oligomers has received much attention in the last years. The definition of oligomer in the amyloid field is still under debate. 35 Hence, we define what we will refer to as oligomers in this review. An oligomer is a non-covalent assembly of amyloidogenic peptides that comprise from dimers up to N -mers with N . 100. Oligomers could be either unstructured or highly structured. Due to the difficulty in studying oligomers experimentally, their formation has been intensely studied using simulations 5 and kinetic models. 36,37 Molecular simulations of amyloid aggregation Molecular simulations have helped tremendously in understanding the underlying physics and chemistry behind protein dynamics. 38 The standard method for simulating proteins is molecular dynamics (MD) simulations, in which the positions and velocities of atoms are calculated using classical mechanics. Because of the many length- and timescales that are involved in protein aggregation, both coarse-grained and atomistic models have been used to simulate protein aggregation. In coarse-grained models, a certain number of atoms are simulated as a single bead, allowing to simulate the aggregation of hundreds of peptides on the millisecond time scale. The application of coarse-grained models to protein aggregation has been reviewed recently. 4,5,39–41 With the improved parallelization of widely used MD codes, 42,43 the advent of special purpose parallel architectures 44 and the implementation of various MD codes into graphical processing units (GPUs), 45,46 simulations which were impossible a few years ago have become a reality. Thus, it is now possible to study the aggregation of up to twenty or so amyloidogenic peptides by means of explicit solvent atomistic simulations on the microsecond timescale. Here, we review the use of atomistic simulations to study the oligomer formation of amyloidogenic peptides. First, we briefly discuss atomistic simulations of amyloidogenic peptide monomers, and then concentrate on aggregation simulations with and without enhaced sampling techniques. We also emphasize on the need to design new methods that take into account the

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low concentrations of these peptides in vivo.

Simulations of monomer dynamics Proteins that aggregate into fibrils are usually disordered or have disordered regions. Thus, a detailed understanding of the aggregation process starts with an understanding of the free energy landscape of the monomer. Moreover, simulations of monomers are easier to converge. Finally, it has been argued that the propensity to form fibrils is encoded in the conformational dynamics of the monomer. 47,48 In particular, Lapidus 47 has argued that aggregation is controlled by the reconfiguration kinetics of protein monomers. Under this model, monomers can be in two different states: M or M*, where M is not aggregation competent and M* is aggregation competent. The reconfiguration between these two states is controlled by internal diffusion. If two M* monomers come close by diffusion, they may aggregate or come apart. If reconfiguration is too fast, the monomer does not live in M* long enough to form stable oligomers. If reconfiguration is slow compared to the kinetics of aggregation, the likelihood of two M* finding each other is too low for aggregation to occur. However, if the rates of both processes are similar, aggregation into oligomers can proceed. For α-synuclein Lapidus and co-workers demonstrated that when intramolecular diffusion is slow aggregation is promoted, while fast intramolecular diffusion prohibit aggregation. 49 The existence of a M* monomer state that is aggregation competent has also been hypothesised by other researchers. 48 Atomistic simulations have been extensively used to study the monomer dynamics of amyloidogenic peptides. 50–60 One of the most commonly used enhanced sampling algorithms, namely replica exchange molecular dynamics (REMD), 61 is often used for scanning the conformational space of the amyloidogenic monomers. In this algorithm, one runs multiple replicas of the system under study at different temperatures. Then, based on the Metropolis criterion, one periodically exchanges configurations between replicas at different temper-

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atures. High temperature replicas are used to enhance the sampling of the free energy surface, whereas low temperature replicas are used to sample the system at a relevant temperature. For example, Garc´ıa and collegues 50–52 have performed long REMD simulations of Alzheimer’s Aβ. They observe that Aβ samples a very heterogeneous ensemble with changing populations of secondary structure. They detect that Aβ partially forms β-hairpin conformations that could function as aggregation seeds. Qiao et al. 59 have also seen that hIAPP, which is associated with type II diabetes, is mostly disordered but also samples populations with β-hairpin structures and extended hydrophobic surfaces exposed to the solvent. Again, these regions are hypothesised to seed aggregation.

Atomistic simulations of protein aggregation Molecular dynamics simulations of protein aggregation The most straightforward way of studying protein aggregation is by placing a number of peptides in a solvated box and allowing them to aggregate. 28,62–67 The first study of protein aggregation using an explicit water all-atom force field was performed by Klimov and Thirumalai. 62 They studied the aggregation of a fragment of Alzheimer’s Aβ, Aβ16−22 and used a harmonic constraint between the center of the water box and the oligomer center of mass in order to speed up the aggregation process. They observed that Aβ16−22 forms antiparallel β-sheets, after passing through an α-helical intermediate. Later, many similar studies were performed in which different amyloidogenic peptides were allowed to aggregate without constraints. In most of these studies, 64–67 it is observed that the peptides first collapse to form only partially ordered aggregates and later, these aggregate evolve into ordered β-sheet structures. A particularly interesting study is the one by Matthes et al. 65 in which they study the driving forces behind protein aggregation for various peptides. They observe a two-step mechanism in which the peptides first aggregate into partially ordered aggregates driven by solvation free energy, and later these aggregates reorder into β-sheets driven by the optimization of inter-peptide

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interactions. Enhancing the sampling of protein aggregation simulations Even though it is now possible to simulate larger systems for longer times, protein aggregation simulations are hard to converge. Hence, enhanced sampling techniques are normally used to accelerate the convergence of these simulations. REMD simulations have been used extensively to study protein aggregation. 68–76 For example, REMD was used to study the aggregation of 16 Alzheimer’s Aβ37−42 peptides by Nguyen and Derreumaux. 72 They observed that the global free energy minimum is characterized by 2- or 3-stranded β-sheets. However, they also observed a non-negligible amount of 5- and 6-stranded antiparallel sheets. One of the problems of REMD simulations is that, because of the exchanges between replicas, kinetic information is lost and, hence, it is hard to have a detailed understanding of the dynamics of the aggregation process. Also, because the number of replicas depend on the number of atoms of the system, REMD can easily become expensive. The latter problem can be alleviated by using the Hamiltonian REMD (HREMD) method, in which the different replicas have different Hamiltonians but are simulated (in most cases) at a constant temperature. 77–79 The idea behind this approach is that the system is trapped in a local minimum because of strong bonded and non-bonded interactions. Thus, if these interactions are weakened by applying a scaling factor, the energy landscape is sampled more efficiently. Such scaling factor is chosen in a way so that the number of replicas does not depend on the number of solvent molecules. In HREMD different scaling factors are used for the different replicas, including one replica with the unmodified Hamiltonian. Compared to temperature REMD, fewer replicas are required if only the Hamiltonian of the aggregating peptides but not the solvent is modified. Laghaei et al. 80 used the combination of temperature and Hamiltonian REMD to characterize the structure and thermodynamics of the full-length hIAPP dimer. Another algorithm used to enhance sampling is metadynamics. 81 In this method, a history dependant bias acts in a number of collective variables on the system. The system is then

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forced to leave the areas of the free energy landscape that have already been visited and, hence, the sampling is enhanced. In the case of studying protein aggregation, bias-exchange metadynamics, 82 in which replica exchange and metadynamics are combined, was used. 83–86 Using this methodology, Baftizadeh et al., 83 for example, showed that the aggregation of polyvaline starts with the formation of antiparallel β-sheets. When enough antiparallel sheets are formed, parallel β-sheets begin to appear. The system then falls into a free energy minimum mostly formed by parallel β-sheets. Kinetics of protein aggregation determined by atomistic simulations A number of methods are available for studying rare events which can accurately estimate the kinetics of the processes in question, 87 such as transition path sampling (TPS) 88 and forward flux sampling (FFS). 89 Even though they have not yet been used to study oligomer formation using explicit-solvent atomistic simulations, they have been applied to similar systems. In particular, Schor et al. 90 studied the mechanism of monomer addition to an amyloid fibril of a fragment of the insulin peptide hormone using TPS. TPS calculates the equilibrium path ensemble between two predefined states using a Monte Carlo random walk in trajectory space. Using TPS, Schor et al. 90 proposed a detailed mechanism of the docking of monomers to a growing fibril. In a different study, Luiken and Bolhuis 91 applied FFS to elucidate the aggregation of different amyloidogenic peptides into amyloids represented with a coarsegrained model. In FFS, the initial and final state are separated in terms of an order parameter λ. FFS starts with a normal MD simulation, in which configurations at the initial state are generated. Trial runs are generated from these configurations that reach the next interface defined by λ or return to the initial state. The algorithm then generates configurations from the following interface and the procedure is repeated until the final state is reached. Luiken and Bolhuis 91 used order parameters dependant on the number of in-register contacts between peptides to study amyloid formation. They found that the nucleation pathway changes from a one-step to a two-step nucleation mechanism with increasing hydrophobicity.

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In the last years, it has become popular to construct kinetic models of long-time protein dynamics from multiple MD simulations using so-called Markov state models (MSMs). 92,93 MSMs not only use the information of multiple short simulations but also allow to sample the energy landscape more efficiently by adaptive sampling. 94 Kelley et al. 95 used MSMs to analyze atomistic MD simulations of the aggregation of Alzheimer’s Aβ21−43 into small oligomers (up to tetramers). By analytically considering the diffusion of peptides, they could estimate the aggregation of these peptides at in vitro concentrations. Perkett and Hagan 96 used MSMs to study the aggregation of virus proteins using a coarse-grained model. They created a theoretical framework in which aggregates are considered as undirected graphs which are then used to construct the MSM. However, neither of these two MSM studies considered the intramolecular dynamics that drive aggregation. Finally, Schor et al. 97 used MSMs to understand the mechanism of monomer addition of transthyretin TTR105−115 to a growing TTR105−115 fibril. In this case, the intramolecular dynamics was considered and a detailed mechanistic model of the process of monomer addition established. The concentration problem of protein aggregation studies Even though studies on the aggregation of amyloidogenic peptides have provided important information about the driving forces behind aggregation and the differences in aggregation between different peptides, they all suffer from one important limitation: they all were performed at concentrations much higher than physiological ones. Explicit solvent all-atom studies are performed at concentrations of at least 1 mM, 28,64–67 while the in vivo concentrations of most relevant amyloidogenic peptides are in the pM to nM range (see table 1 and figure 2) and in vitro experiments are typically performed in the µM range. The problem is that at such high in silico concentrations, encounter oligomers, i.e., oligomers that have just formed, do not have enough time to equilibrate into a stable oligomer, i.e., into a free energy minimum before colliding with other monomers or oligomers. The formation of an encounter oligomer is diffusion controlled, and the rate of its formation is equal to the encounter frequency of

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the peptides. Assuming that the reacting peptides A and B are spheres with no interactions between them, an analytical solution of the Smoluchowski coagulation equation 98 exists, which allows the diffusion-controlled encounter frequency kenc to be determined. If one further introduces the Stokes-Einstein expression for the diffusion constant D of a sphere with radius r in a continuous medium of viscosity η,

D = kB T /6πηr,

(1)

where kB is Boltzmann’s constant and T is the absolute temperature, the Smoluchowski coagulation equation reduces to 99

kenc =

2RT 3000η

8RT (rA + rB )2 ≈ rA rB 3000η

(2)

with R being the gas constant. The last approximation is valid if the spheres have similar radii rA and rB . For two molecules of the same radius in water at 298 K, the encounter frequency is equal to 7 × 109 s−1 M−1 . In a typical MD simulation with a concentration of 1 mM, the average time that two peptides encounter each other is then 140 ns, whereas at concentrations of 1 µM and 1 nM these times are 0.14 ms and 0.14 s, respectively. This numerical exercise demonstrates the very short time scale that MD simulations currently allow oligomers to equilibrate before growing into larger oligomers, compared to the time scales that rule oligomer formation in in vitro experiments and in vivo. This calls into question the validity of the aggregation pathways observed in atomistic simulations. It is worth mentioning that also the validity of in vitro studies has been challenged because they are usually performed at concentrations orders of magnitude higher than the physiological values. 100 However, it should be noted that there is experimental evidence that Aβ can reach a µM concentration in acidic vesicular compartments in cell cultures. 101 Another problem of protein aggregation simulations is that the accuracy of atomistic force fields to represent protein-protein interactions has been questioned; 102–104 most force fields have been shown 11




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However, with the advance of new technologies and software, atomistic simulations of the aggregation of small amyloidogenic peptides are now possible. These simulations are normally performed at mM concentrations, while the concentration of amyloidogenic peptides in vivo is in the pM to nM range and in vitro studies are performed at µM concentrations. Since high peptide concentrations do not give the newly formed oligomers enough time to equilibrate before the attachment of another monomer or oligomer, new approaches or methodologies should be developed in order to enable simulations at much lower concentrations. Brute force simulations at such low concentrations are currently not feasible. Considering that a simulation at mM concentration requires thousands up to one million atoms, 28 the same simulation at nM concentration would require a hundred billion atoms, which is orders of magnitude more than the current biggest simulations. 115 Even though eventually such large simulations will probably become possible, most of the simulation time would be wasted on the diffusion of the peptides and the simulation of the solvent. Thus, methods that take into account the low concentration implicitly by means of analytical or multiscale methods 116,117 are needed. Moreover, in the future we expect more aggregation studies of the entire peptides or even proteins associated with diseases and not only sections of them. These simulations, studying aggregation beyond dimers, are currently only possible using approximations such as an implicit representation of the solvent. 118 Finally, future aggregation simulations should consider the different environments which are essential in modulating amyloid formation, such as membranes, 119 transition metal ions 58 or macromolecular crowding. 120 Such simulations will provide an enhanced understanding of the aggregation of disease-related and functional amyloids, and will help in the design of drugs to fight disease-related amyloids and in the development of novel amyloid-based nanomaterials.

Acknowledgement M.C.-P. acknowledges financial support from the Deutsche Forschungsgemeinschaft (German Research Foundation, DFG) through Grant No. GSC 111. 14


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(119) Bucciantini, M.; Rigacci, S.; Stefani, M. Amyloid Aggregation: Role of Biological Membranes and the Aggregate-Membrane System. J. Phys. Chem. Lett. 2014, 5, 517–527. (120) Ellis, R.; Minton, A. Protein Aggregation in Crowded Environments. Biol. Chem. 2006, 387, 485–497.

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Biographies Mart´ın Carballo-Pacheco is a Ph.D. student at RWTH Aachen University and Forschungszentrum J¨ ulich. He received a B.Eng. in Chemical Engineering from the Complutense University of Madrid and a M.Sc. in Simulation Sciences from RWTH Aachen University. He studies the aggregation of functional amyloids using atomistic molecular dynamics simulations. Birgit Strodel studied Chemistry at the universities of D¨ usseldorf and North Carolina at Chapel Hill, and received her Ph.D. from the University of Frankfurt/Main in 2005 under the supervision of Prof. Gerhard Stock. She then joined the group of Prof. David J. Wales in the Chemistry Department at Cambridge University as a post-doctoral research associate. Since 2009 she heads the Computational Biochemistry Group at the J¨ ulich Research Centre and in 2011 was appointed to an Assistant Professorship in D¨ usseldorf. Her research interests primarily involve the thermodynamics and kinetics of protein aggregation.

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Advances in the Simulation of Protein Aggregation at the Atomistic

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