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A Top-Down Multiscale Approach to Simulate Peptide Self-Assembly from Monomers Xiaochuan Zhao, Chenyi Liao, Yong-Tao Ma, Jonathon B Ferrell, Severin T. Schneebeli, and Jianing Li J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b01025 • Publication Date (Web): 24 Jan 2019 Downloaded from http://pubs.acs.org on January 28, 2019
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A Top-Down Multiscale Approach to Simulate Peptide Self-Assembly from Monomers Xiaochuan Zhao, Chenyi Liao, Yong-Tao Ma, Jonathon B. Ferrell, Severin T. Schneebeli, Jianing Li* Department of Chemistry, the University of Vermont, Burlington, VT 05405 *Corresponding author: Jianing Li (
[email protected]) Abstract: Modeling peptide assembly from monomers on large time and length scales is often intractable at the atomistic resolution. To address this challenge, we present a new approach which integrates coarse-grained (CG), mixed-resolution, and all-atom (AA) modeling in a single simulation. We simulate the initial encounter stage with the CG model, while the further assembly and reorganization stages are simulated with the mixed-resolution and AA models. We have implemented this top-down approach with new tools to automate model transformations and to monitor oligomer formations. Further, a theory was developed to estimate the optimal simulation length for each stage using a model peptide, melittin. The assembly level, the oligomer distribution, and the secondary structures of melittin simulated by the optimal protocol show good agreement with prior experiments and AA simulations. Finally, our approach and theory have been successfully validated with three amyloid peptides (β-amyloid 16-22, GNNQQNY fragment from the yeast prion protein SUP35, and α-synuclein fibril 35-55), which highlight the synergy from modeling at multiple resolutions. This work not only serves as proof of concept for multiresolution simulation studies, but also presents practical guidelines for further self-assembly simulations at more physically and chemically relevant scales. Keywords: Multiscale simulation, coarse grain, mixed resolution, all atom, biopolymer
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Introduction Self-assembly or aggregation of peptides is implicated in the development of many human diseases, especially those related to the neurodegenerative processes.1-3 It is also being studied to explore potential treatments for microbial infections4-6 as well as for various cancers.7-8 While computer modeling and simulations have been widely used as an effective means to gain microscopic insight into the conformational changes and pathways,9-12 it remains mostly intractable for all-atom (AA) models to achieve chemically relevant scales for entire assembly processes.9-10,
13-14
Multiscale simulations that combine models at various resolutions — like
coarse-grained (CG) and AA models — represent a promising solution to balance the computational cost and accuracy.15-17 Current methods of multiscale simulation are categorized by how information is transferred between different resolutions18 — in serial or in parallel. The serial multiscale method carries out modeling at different resolutions in sequence, which takes advantages of sampling efficiency at lower resolutions and detailed accuracy at higher resolutions. It has been applied to problems that are currently difficult to simulate with the AA models.19-22 Furthermore, a straightforward setup of the serial simulation is the so-called top-down modeling, which starts from the least detailed model and recovers the details until a fully atomistic model is obtained. However, serial top-down simulations have never been systematically tested with more than two resolutions. Many key issues remain to be investigated, such as transformations between multiple resolutions, effectiveness of sampling, and optimization of the simulation protocol. To address these problems, we have developed a top-down approach of serial multiscale simulations — to study peptide self-assembly using CG, mixed-resolution (also referred to as AACG in this work), and AA models consecutively. While the consistency of these three model resolutions was confirmed in our previous study,23 the simulation protocol — especially to determine the essential or optimal simulation length at each resolution — has remained largely empirical in practice.20-22 Distinct from prior efforts, we present in this work a top-down simulation protocol according to the sampling needs arising during the early steps of peptide self-assembly (also known as pre-polymerization).24-26 Typical peptide concentrations used in current AA molecular dynamics (MD) simulations are much higher than the experimental (micromolar) and the physiological (micromolar to picomolar) ones. Therefore, we designed our top-down approach to better mimic physiological or experimental conditions. Specifically, the CG models are useful to study the initial encounter
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process, due to the large separation of monomers at low concentrations and the high computational cost required to consider their diffusion and initial recognition.27 The mixed-resolution model with atomic detail only for the peptides or proteins provides good efficiency to simulate the further assembly, while allowing for accurate inter/intra-peptide interactions. With the most structural detail, the AA model (including an explicit AA solvent model) is suitable for capturing delicate interactions like hydrogen bonds, hydrophobic packing, and solvation. With reverse mapping tools from prior28 and this work (see the Supporting Information), our top-down approach starts with CG sampling, intermediates with the mixed-resolution model, and ultimately obtains atomistic details of the assembly after AA refinement. Focusing on the top-down simulation approach, we systematically evaluated the accuracy and efficiency of different protocols to combine the CG, mixed-resolution, and AA models. We used a model peptide, melittin, the assembly of which has been extensively studied by various experimental and computational approaches over decades.29-33 The monomer-to-tetramer and coilto-helix transitions of melittin in aqueous solutions have been long known.34-37 On the basis of rich prior knowledge and the finite assembly of melittin, we developed our top-down approach and a theory to optimize the simulation protocol. To validate our approach, we carried out extensive top-down simulations of three amyloid peptides, which show the synergy of models at different resolutions. The top-down approach reported in this work may serve as the proof of concept for future simulation studies to include more model resolutions. It also presents practical guidelines for self-assembly simulations at larger length and time scales. Method and Theory The serial top-down simulation. A serial top-down simulation begins with the CG simulations, followed by mixed-resolution and AA simulations in a sequence (Fig. 1). The CG simulations were carried out with the GROMACS38 package, while the AACG and AA simulations were executed with Desmond (Schrödinger, Inc.). All CG simulations were performed with the MARTINI22p force field.39 Mixed-resolution simulations were performed with our recently developed AACG force field40 where proteins keep atomic details and water molecules are presented as single-site beads. All-atom simulations were performed with the OPLS force field41 with the SPC water model. First, we constructed the CG model with separated peptide monomers in solvent and carried out MD simulations until ~20% of monomers had self-assembled. Then, we changed from the CG
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to the mixed-resolution model for the next simulation stage (through the CG-AA-AACG resolution transformation, see the SI) and simulated the AACG system until the self-assembly process was almost completed (~100%). In the last stage, we converted the AACG model to the AA model with two solvent recovery protocols, which are compared in the discussion below. All the simulations were performed in the NPT ensemble (310 K, 1 bar) and underwent minimization and equilibration before the production stage. Hydrogen atoms were constrained using the SHAKE algorithm in the AA and AACG models, and the LINCS algorithm in the CG models. More information about model preparation and model transformation is presented in the SI.
Figure 1. Cartoon illustration of the CG, AACG, AA serial stages in a top-down multiscale simulation for peptide assembly. Snapshots were taken from the initial model, the final CG model, and the final AA model of the 27-melittin system. The model was equilibrated at the beginning of each stage.
Determination of the assembly cutoffs to switch resolutions. We first performed the AACG+AA simulations of four melittin peptides, which were simulated at the AACG resolution for 12, 18, 40, and 70 ns respectively before 100-ns AA simulations (the length of AA simulations were set to be identical and long enough for fair comparison). With details provided in the Results section, we observed that the AACG model well balanced the simulation efficiency and structural integrity when self-assembly is complete or near complete (with ~100% of peptides present as oligomers). However, excessive sampling in the AACG stage did not improve the overall assembly stability or the folding of individual peptides. We also performed a 400-ns CG simulation with 27 melittin peptides, starting from a model where any two Cα atoms of melittin monomers were separated by over 30 Å. At 15 ns, a melittin heptamer was found to form (Fig. S8). After 70 ns, almost no change in the assembly state was
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observed — with a monomer, a dimer, three trimers, two tetramers and a heptamer (Fig. S8). The “over-aggregation” of melittin in our CG test presumably resulted from the insufficient treatment of electrostatic repulsion among the cationic peptides. We continued to carry out two 40-ns AACG simulations transformed from the snapshots before (5 ns) and after (15 ns) the heptamer formation in the CG simulation (Fig. S6). In the former AACG simulation, we only observed tetramers and smaller oligomers; in the latter, however, we did not observe dissociation of the heptamer. The tetramer is considered the natural and functional state of melittin,34 and oligomers larger than tetramers should be difficult to form.40, 42 After extensive tests, we determine that the early CG stage (corresponding to ~20% of peptides being present in oligomeric states) is optimal to simulate peptide encounter and avoid “over-aggregation”. Optimization of the top-down approach. To determine the optimal length for each simulation stage, we started from a classic theory to describe the standard Wiener process43 (also known as Brownian motion) with a minimum model: two peptides in distance d at time t. The diffusion propagator P(x, t), which represents the probability of finding a peptide at position x at time t with the other peptide as a reference, is a Gaussian function given by 𝑥2
1 ― 𝑃(𝑥,𝑡) = 𝑒 4𝐷𝑡 4𝜋𝐷𝑡
(1)
where D is the diffusion coefficient. The aggregation probability P2 of two peptides is a function of time t 𝑃2(𝑡) =
∫
∞
∫
𝑃1(𝑦,𝑡)𝑦 ―∞
𝑦+𝑟
𝑃1(𝑥,𝑡)𝑑𝑥𝑑𝑦
(2)
𝑦―𝑟
Given that d is on the order of nm, while D and t are on the order of µm2/s and ns respectively, 𝑑/ 𝜋𝐷𝑡 is below 1. Therefore, we can expand the integral of Eq. 2 as a polynomial and Eq. 2 can be approximated with truncation of high-order terms as (the derivation provided in the SI) 𝑃2 ≈
𝑑 𝜋𝐷1𝑡
(3)
We can rearrange Eq. 3 and define the target probability P(t) as a constant, and thus we have the essential simulation length t as a function of peptide separation and diffusion 𝑡=𝑄
𝑑2 𝐷1
(4)
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where d is the minimum distance between two neighboring peptides from the model setup (e.g., for the 27-peptide systems, d is 30 or 60 Å), D1 is the monomer diffusion coefficient, and Q is a universal, dimensionless coefficient (e.g., for the 27-peptide systems, Q has a value of 0.063 for CG or 1.24 for AACG). In particular, the coefficient Q is determined by the peptide concentration, monomeric diffusion coefficient (D1), as well as the time (t) when the assembly level of melittin is ~20% (for CG modeling) or ~100% (for AACG modeling). Generally, Eq. 4 provides a semiquantitative estimation of the essential simulation length, reflecting a realistic physical picture for a situation where the simulation conditions and the target assembly levels remain the same — the smaller the average separation or the faster diffusion of the peptides, the shorter the simulation time needed to simulate the self-assembly. Thus, based on the studies of melittin, we can use Eq. 4 to estimate the optimal lengths for the CG and mixed-resolution simulations for other peptides. The MAP algorithm to identify peptide oligomers. Analyzing and monitoring the oligomer distribution is critical to gain insight into the simulated self-assembly progress. Thus, we developed a machine-learning algorithm to identify peptide oligomers (MAP), implemented as a Python program with the Scikit-learn library (Fig. S7). The core step of the MAP method is based on the K-mean clustering of the peptide centroid (defined as the Cα atom of the centroid residue, e.g. Leu13 of the 26-residue melittin). For each system, the algorithm processes a snapshot from the simulation (taking the periodic boundary condition into consideration) and tests the number of clusters. In each step, our program defines the number of clusters and performs the assignment of clusters. The average distance between any two peptides in a cluster (annotated as the parameter d) is computed. For example, the optimal cluster assignment for melittin is achieved when the parameter d is below a cutoff of 25 Å, which is set according to our prior AA simulations.42 For other peptide systems, we set the cutoff as 2.5 times the monomer radius of gyration. With a given cutoff for inter-cluster distance, MAP finds out the minimum number of clusters, which allows the average distance between two peptides in each cluster to lie within the cutoff. Each cluster assignment is further examined to confirm the oligomeric state, based on the number of backbone contacts within 1.8 times the monomer radius of gyration. Further, a cluster is confirmed when the number of backbone C pair contacts in every peptide pair is higher than the cutoff (twice of the chain length); otherwise, two or more smaller clusters are assigned. Finally, with all the clusters confirmed or adjusted, the overall oligomeric distribution is summarized and reported.
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Alternative Models in the Top-Down Approach. Different from other similar approaches (e.g., the Discrete Molecular Dynamics (DMD) of the four-bead CG model combined with AA simulations for amyloid proteins22, 44), our top-down approach was designed to simulate general peptides under diverse conditions (e.g., peptides that self-assemble into finite structures like melittin). Although only three model resolutions were tested in the current implementation of our top-down simulation approach, it is ready to incorporate a variety of coarser- or finer-grained models.45-49 Moreover, to convert the explicit solvent model from the AACG to the AA resolution, we have tested two solvent recovery protocols: (1) transformation and (2) reconstruction. To transform the single-site AACG water model to the AA model, we directly substituted the coarse-grained water sites with an oxygen atom and also added two hydrogen atoms to each site. On the other hand, an alternative recovery constitutes reconstructing all-atom water molecules from scratch, after removing all the single-site beads of water in the AACG model. In comparison with the reconstruction protocol, the transformation protocol led to more stable melittin tetramers with higher helicity (Figs. 3, S2, and S3). It is clear that direct transformation of the water model reduces the perturbation of the intra- and inter-peptide interactions. Thus, the transformation protocol was chosen in our top-down approach to recover the AA water model. In addition, we attempted to compare our top-down approach with implicit solvent models using the all-atom model with four melittin peptides. Despite many applications of implicit solvent models in protein folding and structure prediction,50-54 few have been reported for peptide assembly systems. We simulated the implicit solvent system using the Generalized Born Molecular Volume (GBMV) model in the CHARMM55 program, and a similar model with the hydrophobic solvent accessible surface area (GBSA) in the GROMACS38 program. In our tests, melittin did not fully assemble in the implicit solvent within comparable lengths of our top-down simulations, mainly due to slow diffusion of the peptides or repulsive interactions between peptides. While future effort is needed to understand these observations in detail, at this point we simply conclude that an explicit solvent model is still essential, especially for peptide encounter and initial recognition. Peptide Diffusion. We observed faster diffusion of the melittin peptides in the AACG models (Table S4), but comparable diffusion coefficients for the CG and AA models for the peptides.
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Importantly, there is a correlation between the order of oligomers (n, as an integer between 2 to 4) and the diffusion coefficient (Dn), which can be described as 𝐷𝑛 = 𝐷1𝑛 ―𝛼
(5).
With the diffusion coefficient not scaling linearly with the coarse grained level, we obtained a universal exponent α at the value of 0.70 ± 0.12 (Fig. 2), in good agreement with a classical theory of polymer self-diffusion using the Rouse-Zimm model.56-58 This theory predicts that the diffusion coefficient D is inversely proportional to M, where M is the molecular mass and
is a temperature-dependent factor. Assuming that the mass of a melittin molecule (M1) is 1.0 in a customized unit system, we can directly derive Eq. 5 from the Rouse-Zimm model. The correlations not only show the consistency of the CG, AACG, and AA models and simulations with prior theory, but also allow for predictions of oligomeric diffusion coefficients of melittin and other peptides that self-assemble.
Figure 2. The linear regression analysis with the diffusion coefficients (µm2/s) calculated from our CG, AACG, and AA simulations. The slopes represent the values of - in each model. = 0.70 ± 0.12.
Results and Discussion Top-down AACG+AA simulations of melittin assemblies suggests an optimal protocol. We first combined the AACG and AA models to simulate the assembly of four separate, partially folded
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melittin peptides. The initial model was obtained from our prior AA simulations.42 To test the assembly process in the AACG model, we carried out a 100-ns MD simulation (Fig. S1). We observed a similar trend of stepwise assembly as in the AA simulations,42 but in a much faster fashion (the dimer and tetramer formed within 10 and 40 ns, respectively). However, the helicity content of the assembly from the AACG simulations tended to be lower (28.2 ± 4.9%) compared to measurements from CD spectra (~60%)35 and our prior AA simulations (47 ± 2%).42
Figure 3. Comparison of four AACG+AA protocols (a), (b), (c), and (d). (A) The AACG snapshots before transformation to AA models in dimeric, didimeric, tetrameric, and tight tetrameric states for protocols (a), (b), (c), and (d), respectively. The geometric centroid distances are labeled. (B) Plots of the average separation over time. The magenta plot represents the smoothed AACG data, while the red, yellow and cyan plots represent the smoothed AA data from three simulation replicas. (C) Histograms of the helicity percentage, the assembly solvent accessible surface area, and the number of inter-peptide hydrogen bonds of different protocols in comparison with 100-ns AACG simulation and pure AA simulations42. The red and cyan bars represent the average value from the last 1 ns in the 100 ns AACG and AA, respectively, while the standard deviations are shown in blue lines.
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To examine if successive AA simulations improve the accuracy of the peptide secondary structures, we carried out successive AA simulations starting from different stages of the AACG simulation. We designed four different protocols, labeled as protocols (a), (b), (c), and (d), by taking the AACG structural snapshots at 12, 18, 40, and 70 ns, transforming into AA models, and then starting 100-ns MD simulations. The time points were chosen so that the melittin peptides were in dimeric, didimeric, tetrameric, and tight tetrameric states for protocols (a), (b), (c), and (d), respectively (Fig. 3A). Each construct (containing peptides, counter ions, and water) was recovered from the AACG to the AA resolution, equilibrated for ~1 ns, and further simulated for 100 ns with three replicas. We compared these four AACG+AA protocols, in terms of the average separation, the melittin helicity, the solvent accessible surface area, and the number of hydrogen bonds (Fig. 3C). In protocol (a), where successive AA simulations were transformed from short AACG simulations of melittins in low assembling states, we observed that a majority of melittin peptides were separate at the end of 100-ns AA simulations (Fig. 3B). As the systems were transformed at longer AACG times with protocols (b), (c), and (d), where melittins mostly had already assembled or aggregated, the melittins were able to maintain their tetrameric state, particularly with protocols (c) and (d). Given the generally lower helical conformations in AACG,40 the overall helicity percentage in (a)–(d) tends to be lower than with previous AA simulated models.59 Protocol (c) maintains a similar helicity percentage as AACG (28.2 ± 4.9%), and exhibits a similar surface area (83.4 ± 4.0 nm2) as our previous AA simulation results (85.4 ± 5.5 nm2).42, 60 However, protocol (d) with a longer AACG time resulted in a lower helicity content and fewer total H-bonds than protocol (c). This is likely because, for the tight tetramer formed at the AACG stage, inter-peptide hydrogen bonds are more favored than the intra-peptide ones (Table S2), leading to the less helical structure which needs much longer AA simulations to equilibrate. In brief, protocol (c) exhibits the highest helicity content and total H-bonds and lowest surface area in all protocols (Fig. 3C), with the best agreement to the AA simulation. Notably, it is important to balance the AACG time to avoid excessive inter-peptide interactions like hydrogen bonds and maintain the peptide structural stability. Therefore, we achieve the maximum accuracy for the AACG+AA protocol with sufficient but not excessive sampling at the AACG stage of the multiscale approach.
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Top-down CG, AACG and AA simulations of 27 melittins assembling show the accuracy and efficiency. To advance our capacity to study larger systems of peptide assembly, we further explored the CG simulation stage in addition to the AACG+AA protocol. To further validate our theory, we tested the top-down simulations at two melittin concentrations: 27 peptides, all of which separated from each other by at least 30 or 60 Å, respectively. Guided by the estimations from Eq. 4, we carried out CG and AACG simulations with pre-calculated simulation times, and then continued with 100 ns AA simulations. The distribution of oligomers was analyzed by our MAP program.
Figure 4. Self-assembly of 27 melittin peptides in a top-down simulation. (A) The integrated oligomer distribution counted by the numbers of monomers in the corresponding states. The snapshots of the initial model, the final CG model, and the final AA model are shown in Fig. 1. Time evolutions of (B) the helicity
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percentage and (C) the surface area of melittin are plotted with the solid lines (smoothed data; CG: blue, AACG: red, and AA: green). The dash lines indicate the extended AACG (red) or CG (blue) stages.
At the high melittin concentration (with the 30-Å peptide separation), we simulated the encounter process with the CG model and obtained the initial assemblies of 4 dimers and 3 trimers. In the following AACG stage, a dominant population of 4 tetramers was observed (Fig. 4A). The helicity (45~50%) was significantly improved during the AA stage, in good agreement with experimental observations35 and our previous simulations42. This result highlights the importance of the AA stage for modeling the maturity process for further stabilization of the melittin assemblies. At the low melittin concentration (with the 60-Å peptide separation), 20 and 140 ns were estimated for the CG and AACG stages by Eq. 4 and the length of the AA stage was set to 100 ns. Our top-down approach is estimated to accelerate the simulation by a factor of 3, in comparison with the AA simulation. The final model obtained from the top-down simulation displayed a tetramer, 6 trimers, 2 dimers and 3 monomers (Fig. 5). It is likely that the disassociation and reorganization of melittin oligomers may need more sampling in the AA stage at the low melittin concentration. Top-down simulations of amyloid peptides validate the generality of our theory and approach. For further tests, we simulated the aggregation of three amyloid peptides (27 peptides with a minimum separation of 30 Å between all of the peptides), including the GNNQQNY segment from the yeast prion protein Sup35 (PDBID: 1YJP), the amyloid-β (Aβ(16-22), PDBID: 2MXU), and the αsynuclein fragment, (α-syn(35-55), PDBID: 2N0A). We measured the diffusion coefficients of the monomers for GNNQQNY peptide, Aβ(16-22), and α-syn(35-55) at different stages in preparation for Eq. 4 (Fig. 2 and Table S4). Accordingly, we estimated the optimized CG simulation lengths as 3, 3, and 4 ns (~20% of peptides in oligomeric states) and the AACG simulation lengths as 13, 16, and 29 ns (~100% of peptides in oligomeric states) for the GNNQQNY peptide, the Aβ(1622), and the α-syn(35-55) system, respectively. After the 3- or 4-ns CG simulations, 18–26% of peptides were present in oligomeric states for the GNNQQNY peptide, the Aβ(16-22), and the α-syn(35-55) system (Fig. 5). Next, the model resolutions were transformed and all three systems were simulated at the AACG stage. At the end of the AACG simulations, the GNNQQNY peptide formed a pentamer and a 22mer; the Aβ(16-
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22) formed a 27mer; and the α-syn(35-55) formed a tetramer, a heptamer, and a 16mer. It is obvious that further aggregation is favorable after initial oligomerization to dimers, trimers, or tetramers, which is consistent with the known aggregation processes of these amyloid peptides.1, 13
Our top-down simulations showed that these peptide monomers were in equilibrium between flexible random coils and ordered β-strand conformations, in line with a rich body of amyloid peptide simulations.62-65 We found that the β contents of GNNQQNY, Aβ(16-22), and syn(35-55) in our final AA models were 5%, ~ 9%, and 8%, respectively, which was also shown in many AA simulation studies63, 65-68 without constraints. Also, we observed that in general, the β content (as well as some α content) increased along with the aggregation process, which agrees with many prior observations (Fig. S4).69-70
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Figure 5. The integrated monomer/oligomer distribution counted by the number of peptide individuals in our top-down simulations of the GNNQQNY peptide, Aβ(16-22), α-syn(35-55) and melittin systems with final snapshots presented on the right. The CG, AACG, and AA stages for each system are marked with blue, red, and green lines on the top frame of each plot. Four colors (red, green, cyan, and orange) are used to represent peptide individuals on the right.
Conclusions We have developed and validated a top-down approach to simulate peptide assembly from dispersed monomers, with model systems of melittin and three amyloid peptides. This innovative approach allows us to simulate one model construct consecutively at the CG, AACG, and AA resolutions, facilitated by transformation tools. A simple equation is also derived based on the classic model of the Wiener process and successfully validated. By optimizing and integrating
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AACG+AA to CG+AACG+AA protocols, we have developed a top-down theory and approach to sample peptides assembly and aggregation with speedups by a factor of 2 to 4 (see the SI). The diffusion coefficients in different resolution simulations of CG, AACG, and AA, were in a good agreement with the classical theory of the polymer self-diffusion model,56-58 which we can use an interpolation method to estimate the diffusion coefficients at higher assembly levels. With the diffusion coefficients and initial conditions, we estimated the simulation lengths for each simulation of different resolutions from Eq. 4, which was derived from the equation of the Wiener process.43 From the applications of the top-down simulation to the self-assembly of peptides, we could estimate the simulation length needed for the CG and AACG stages, and obtain assembled structures with the AA details. We were aware of the hydrogen-bond competition between peptide folding (intramolecular hydrogen bonds) and aggregation (intermolecular hydrogen bonds). The fast process of aggregation may be associated with a slow process of folding. This may explain why a better agreement to the high, experimentally determined α content35 of melittin was obtained with a large system (27-melittin, ~510,000 atoms) than a small system (4-melittin, ~65,000 atoms). Our top-down approach is especially useful for large systems which are challenging for AA simulations alone. Additionally, the AACG stage using the mixed-resolution model plays a key role in correcting the initial aggregation from CG modeling while promoting the folding process, which can be a potential advantage over only CG simulations. We anticipate that our theory will provide a practical guide to utilize a top-down approach to study general peptide assembly phenomena from monomers, and eventually achieve valuable atomic details for future biomedical and materials applications. Acknowledgements We thank Dr. John Shelley (Schrodinger Inc.) for helpful discussions, and NVIDIA for the support of the GPU grant. Supercomputer resources were provided to JL by VACC and Stampede (XSEDE, NSF ACI-1053575). Partial support was also provided by the ACS Petroleum Research Fund (Grant 58219-DNI6 awarded to JL) and the U.S. Army Research Office (Grant 71015-CHYIP awarded to STS).
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References 1.
Irvine, G. B.; El-Agnaf, O. M.; Shankar, G. M.; Walsh, D. M., Protein aggregation in the brain: the
molecular basis for Alzheimer’s and Parkinson’s diseases. Mol. Med. 2008, 14 (7-8), 451. 2.
Aguzzi, A.; O'connor, T., Protein aggregation diseases: pathogenicity and therapeutic perspectives.
Nat. Rev. Drug Discov. 2010, 9 (3), 237. 3.
Murphy, R. M., Peptide aggregation in neurodegenerative disease. Annu. Rev. Biomed. Eng. 2002,
4 (1), 155-174. 4.
Bednarska, N. G.; Van Eldere, J.; Gallardo, R.; Ganesan, A.; Ramakers, M.; Vogel, I.; Baatsen, P.;
Staes, A.; Goethals, M.; Hammarström, P., Protein aggregation as an antibiotic design strategy. Mol. Microbiol. 2016, 99 (5), 849-865. 5.
Zhao, J.; Zhao, C.; Liang, G. Z.; Zhang, M. Z.; Zheng, J., Engineering Antimicrobial Peptides with
Improved Antimicrobial and Hemolytic Activities. J. Chem. Inf. Mod. 2013, 53 (12), 3280-3296. 6.
Chidchob, P.; Offenbartl-Stiegert, D.; McCarthy, D.; Luo, X.; Li, J.; Howorka, S.; Sleiman, H. F.,
Spatial presentation of cholesterol units on a DNA cube as a determinant of membrane protein-mimicking functions. J. Am. Chem. Soc., 2019, 141 (2), 1100–1108. 7.
Rady, I.; Siddiqui, I. A.; Rady, M.; Mukhtar, H., Melittin, a major peptide component of bee venom,
and its conjugates in cancer therapy. Cancer Lett. 2017, 402, 16-31. 8.
Silva, J. L.; Gallo, C. V. D. M.; Costa, D. C.; Rangel, L. P., Prion-like aggregation of mutant p53
in cancer. Trends Biochem. Sci. 2014, 39 (6), 260-267. 9.
Morriss-Andrews, A.; Shea, J.-E., Computational studies of protein aggregation: methods and
applications. Annu. Rev. Phys. Chem. 2015, 66, 643-666. 10.
Wu, C.; Shea, J.-E., Coarse-grained models for protein aggregation. Curr. Opin. Struct. Biol. 2011,
21 (2), 209-220. 11.
Morriss-Andrews, A.; Shea, J.-E., Simulations of protein aggregation: insights from atomistic and
coarse-grained models. J. Phys. Chem. Lett. 2014, 5 (11), 1899-1908. 12.
Sieradzan, A. K.; Liwo, A.; Hansmann, U. H., Folding and self-assembly of a small protein
complex. J. Chem. Theory Comput. 2012, 8 (9), 3416-3422. 13.
Wang, J.; Tan, C.; Chen, H.-F.; Luo, R., All-atom computer simulations of amyloid fibrils
disaggregation. Biophys. J. 2008, 95 (11), 5037-5047. 14.
Carballo-Pacheco, M.; Strodel, B., Advances in the simulation of protein aggregation at the
atomistic scale. J. Phys. Chem. B 2016, 120 (12), 2991-2999. 15.
Zhang, J.; Li, W.; Wang, J.; Qin, M.; Wu, L.; Yan, Z.; Xu, W.; Zuo, G.; Wang, W., Protein folding
simulations: From coarse‐grained model to all‐atom model. IUBMB Life 2009, 61 (6), 627-643.
ACS Paragon Plus Environment
16
Page 17 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Journal of Chemical Theory and Computation
16.
Praprotnik, M.; Site, L. D.; Kremer, K., Multiscale simulation of soft matter: From scale bridging
to adaptive resolution. Annu. Rev. Phys. Chem. 2008, 59, 545-571. 17.
Ekimoto, T.; Ikeguchi, M., Multiscale molecular dynamics simulations of rotary motor proteins.
Biophys. Rev. 2017, 1-11. 18.
Ayton, G. S.; Noid, W. G.; Voth, G. A., Multiscale modeling of biomolecular systems: in serial
and in parallel. Curr. Opin. Struct. Biol. 2007, 17 (2), 192-198. 19.
Rohrdanz, M. A.; Zheng, W.; Lambeth, B.; Vreede, J.; Clementi, C., Multiscale approach to the
determination of the photoactive yellow protein signaling state ensemble. PLoS Comp. Biol. 2014, 10 (10), e1003797. 20.
Rzepiela, A. J.; Sengupta, D.; Goga, N.; Marrink, S. J., Membrane poration by antimicrobial
peptides combining atomistic and coarse-grained descriptions. Faraday Discuss. 2010, 144, 431-443. 21.
Perlmutter, J. D.; Drasler, W. J.; Xie, W.; Gao, J.; Popot, J.-L.; Sachs, J. N., All-atom and coarse-
grained molecular dynamics simulations of a membrane protein stabilizing polymer. Langmuir 2011, 27 (17), 10523-10537. 22.
Barz, B.; Urbanc, B., Dimer formation enhances structural differences between amyloid β-protein
(1–40) and (1–42): an explicit-solvent molecular dynamics study. PloS one 2012, 7 (4), e34345. 23.
Liao, C.; Zhao, X.; Liu, J.; Schneebeli, S. T.; Shelley, J. C.; Li, J., Capturing the multiscale
dynamics of membrane protein complexes with all-atom, mixed-resolution, and coarse-grained models. Phys. Chem. Chem. Phys. 2017, 19 (13), 9181-9188. 24.
Arosio, P.; Knowles, T. P.; Linse, S., On the lag phase in amyloid fibril formation. Phys. Chem.
Chem. Phys. 2015, 17 (12), 7606-7618. 25.
Lomakin, A.; Chung, D. S.; Benedek, G. B.; Kirschner, D. A.; Teplow, D. B., On the nucleation
and growth of amyloid beta-protein fibrils: detection of nuclei and quantitation of rate constants. Proc. Natl. Acad. Sci. 1996, 93 (3), 1125-1129. 26.
Wei, G.; Mousseau, N.; Derreumaux, P., Computational simulations of the early steps of protein
aggregation. Prion 2007, 1 (1), 3-8. 27.
Mansbach, R. A.; Ferguson, A. L., Control of the hierarchical assembly of π-conjugated
optoelectronic peptides by pH and flow. Org. Biomol. Chem. 2017, 15 (26), 5484-5502. 28.
Wassenaar, T. A.; Pluhackova, K.; Böckmann, R. A.; Marrink, S. J.; Tieleman, D. P., Going
backward: a flexible geometric approach to reverse transformation from coarse grained to atomistic models. J. Chem. Theory Comput. 2014, 10 (2), 676-690. 29.
Terwilliger, T. C.; Eisenberg, D., The structure of melittin. J. biol. Chem. 1982, 257 (601), L6015.
30.
Raghuraman, H.; Chattopadhyay, A., Melittin: a membrane-active peptide with diverse functions.
Biosci. Rep. 2007, 27 (4-5), 189-223.
ACS Paragon Plus Environment
17
Journal of Chemical Theory and Computation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
31.
Page 18 of 21
Sun, D.; Forsman, J.; Woodward, C. E., Multistep molecular dynamics simulations identify the
highly cooperative activity of melittin in recognizing and stabilizing membrane pores. Langmuir 2015, 31 (34), 9388-9401. 32.
Schlamadinger, D. E.; Wang, Y.; McCammon, J. A.; Kim, J. E., Spectroscopic and computational
study of melittin, cecropin A, and the hybrid peptide CM15. J. Phys. Chem. B 2012, 116 (35), 10600-10608. 33.
Upadhyay, S. K.; Wang, Y.; Zhao, T.; Ulmschneider, J. P., Insights from micro-second atomistic
simulations of melittin in thin lipid bilayers. J. Membr. Biol. 2015, 248 (3), 497-503. 34.
Miura, Y., NMR studies on the monomer–tetramer transition of melittin in an aqueous solution at
high and low temperatures. Eur. Biophys. J. 2012, 41 (7), 629-636. 35.
Othon, C. M.; Kwon, O.-H.; Lin, M. M.; Zewail, A. H., Solvation in protein (un) folding of melittin
tetramer–monomer transition. Proc. Natl. Acad. Sci. 2009, 106 (31), 12593-12598. 36.
Bello, J.; Bello, H. R.; Granados, E., Conformation and Aggregation of Melittin - Dependence on
Ph and Concentration. Biochemistry 1982, 21 (3), 461-465. 37.
Talbot, J.; Dufourcq, J.; De Bony, J.; Faucon, J.; Lussan, C., Conformational change and self
association of monomeric melittin. FEBS Lett. 1979, 102 (1), 191-193. 38.
Berendsen, H. J.; van der Spoel, D.; van Drunen, R., GROMACS: a message-passing parallel
molecular dynamics implementation. Comput. Phys. Commun. 1995, 91 (1-3), 43-56. 39.
Monticelli, L.; Kandasamy, S. K.; Periole, X.; Larson, R. G.; Tieleman, D. P.; Marrink, S.-J., The
MARTINI coarse-grained force field: extension to proteins. J. Chem. Theory Comput. 2008, 4 (5), 819834. 40.
Shelley, M. Y.; Selvan, M. E.; Zhao, J.; Babin, V.; Liao, C.; Li, J.; Shelley, J. C., A New Mixed
All-Atom/Coarse-Grained Model: Application to Melittin Aggregation in Aqueous Solution. J. Chem. Theory Comput. 2017, 13 (8), 3881-3897. 41.
Harder, E.; Damm, W.; Maple, J.; Wu, C.; Reboul, M.; Xiang, J. Y.; Wang, L.; Lupyan, D.;
Dahlgren, M. K.; Knight, J. L., OPLS3: a force field providing broad coverage of drug-like small molecules and proteins. J. Chem. Theory Comput. 2015, 12 (1), 281-296. 42.
Liao, C.; Esai Selvan, M.; Zhao, J.; Slimovitch, J. L.; Schneebeli, S. T.; Shelley, M.; Shelley, J. C.;
Li, J., Melittin aggregation in aqueous solutions: insight from molecular dynamics simulations. J. Phys. Chem. B 2015, 119 (33), 10390-10398. 43.
Karatzas, I.; Shreve, S., Brownian motion and stochastic calculus. Springer Science & Business
Media: 2012; Vol. 113. 44.
Urbanc, B.; Betnel, M.; Cruz, L.; Bitan, G.; Teplow, D., Elucidation of amyloid β-protein
oligomerization mechanisms: discrete molecular dynamics study. J. Am. Chem. Soc. 2010, 132 (12), 42664280.
ACS Paragon Plus Environment
18
Page 19 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Journal of Chemical Theory and Computation
45.
Madsen, J. J.; Sinitskiy, A. V.; Li, J.; Voth, G. A., Highly Coarse-Grained Representations of
Transmembrane Proteins. J. Chem. Theory Comput. 2017, 13 (2), 935-944. 46.
Yang, L.; Tan, C.-h.; Hsieh, M.-J.; Wang, J.; Duan, Y.; Cieplak, P.; Caldwell, J.; Kollman, P. A.;
Luo, R., New-generation amber united-atom force field. J. Phys. Chem. B 2006, 110 (26), 13166-13176. 47.
Dama, J. F.; Sinitskiy, A. V.; McCullagh, M.; Weare, J.; Roux, B.; Dinner, A. R.; Voth, G. A., The
theory of ultra-coarse-graining. 1. General principles. J. Chem. Theory Comput. 2013, 9 (5), 2466-2480. 48.
Han, W.; Wan, C.-K.; Jiang, F.; Wu, Y.-D., PACE force field for protein simulations. 1. Full
parameterization of version 1 and verification. J. Chem. Theory Comput. 2010, 6 (11), 3373-3389. 49.
Han, W.; Schulten, K., Fibril elongation by Aβ17–42: Kinetic network analysis of hybrid-
resolution molecular dynamics simulations. J. Am. Chem. Soc. 2014, 136 (35), 12450-12460. 50.
Li, J.; Abel, R.; Zhu, K.; Cao, Y.; Zhao, S.; Friesner, R. A., The VSGB 2.0 model: a next generation
energy model for high resolution protein structure modeling. Proteins 2011, 79 (10), 2794-2812. 51.
Zhao, S.; Zhu, K.; Li, J.; Friesner, R. A., Progress in super long loop prediction. Proteins 2011, 79
(10), 2920-2935. 52.
Chen, J.; Brooks Iii, C. L., Implicit modeling of nonpolar solvation for simulating protein folding
and conformational transitions. Phys. Chem. Chem. Phys. 2008, 10 (4), 471-481. 53.
Lee, K. H.; Chen, J., Optimization of the GBMV2 implicit solvent force field for accurate
simulation of protein conformational equilibria. J. Comput. Chem. 2017, 38 (16), 1332-1341. 54.
Kleinjung, J.; Fraternali, F., Design and application of implicit solvent models in biomolecular
simulations. Curr. Opin. Struct. Biol. 2014, 25, 126-134. 55.
Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M.,
CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 1983, 4 (2), 187-217. 56.
Zimm, B. H., Dynamics of polymer molecules in dilute solution: viscoelasticity, flow birefringence
and dielectric loss. J. Chem. Phys. 1956, 24 (2), 269-278. 57.
Doi, M.; Edwards, S. F., The theory of polymer dynamics. oxford university press: 1988; Vol. 73.
58.
Griffiths, M. C.; Strauch, J.; Monteiro, M. J.; Gilbert, R. G., Measurement of diffusion coefficients
of oligomeric penetrants in rubbery polymer matrixes. Macromolecules 1998, 31 (22), 7835-7844. 59.
Liao, C.; Selvan, M. E.; Zhao, J.; Slimovitch, J. L.; Schneebeli, S. T.; Shelley, M.; Shelley, J. C.;
Li, J., Melittin aggregation in aqueous solutions: insight from molecular dynamics simulations. J. Phys. Chem. B 2015, 119 (33), 10390-10398. 60.
Andersson, M.; Ulmschneider, J. P.; Ulmschneider, M. B.; White, S. H., Conformational states of
melittin at a bilayer interface. Biophys. J. 2013, 104 (6), L12-L14.
ACS Paragon Plus Environment
19
Journal of Chemical Theory and Computation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61.
Page 20 of 21
Quay, S. C.; Condie, C. C., Conformational studies of aqueous melittin: thermodynamic parameters
of the monomer-tetramer self-association reaction. Biochemistry 1983, 22 (3), 695-700. 62.
Klimov, D. K.; Thirumalai, D., Dissecting the assembly of Aβ16–22 amyloid peptides into
antiparallel β sheets. Structure 2003, 11 (3), 295-307. 63.
Xie, L.; Luo, Y.; Wei, G., Aβ (16–22) peptides can assemble into ordered β-barrels and bilayer β-
sheets, while substitution of phenylalanine 19 by tryptophan increases the population of disordered aggregates. J. Phys. Chem. B 2013, 117 (35), 10149-10160. 64.
van der Wel, P. C.; Lewandowski, J. R.; Griffin, R. G., Structural characterization of GNNQQNY
amyloid fibrils by magic angle spinning NMR. Biochemistry 2010, 49 (44), 9457-9469. 65.
Mor, D. E.; Ugras, S. E.; Daniels, M. J.; Ischiropoulos, H., Dynamic structural flexibility of α-
synuclein. Neurobiol. Dis. 2016, 88, 66-74. 66.
Reddy, G.; Straub, J. E.; Thirumalai, D., Dynamics of locking of peptides onto growing amyloid
fibrils. Proc. Natl. Acad. Sci. 2009, 106 (29), 11948-11953. 67.
Cheon, M.; Chang, I.; Hall, C. K., Spontaneous formation of twisted Aβ16-22 fibrils in large-scale
molecular-dynamics simulations. Biophys. J. 2011, 101 (10), 2493-2501. 68.
Cao, Y.; Jiang, X.; Han, W., Self-assembly pathways of β-sheet-rich amyloid-β (1–40) dimers:
Markov state model analysis on millisecond hybrid-resolution simulations. J. Chem. Theory Comput. 2017, 13 (11), 5731-5744. 69.
Xu, Y.; Shen, J.; Luo, X.; Zhu, W.; Chen, K.; Ma, J.; Jiang, H., Conformational transition of
amyloid β-peptide. Proc. Natl. Acad. Sci. 2005, 102 (15), 5403-5407. 70.
Okumura, H.; Itoh, S. G., Structural and fluctuational difference between two ends of Aβ amyloid
fibril: MD simulations predict only one end has open conformations. Sci. Rep. 2016, 6, 38422. 71.
Srivastava, A.; Balaji, P. V., Molecular events during the early stages of aggregation of
GNNQQNY: An all atom MD simulation study of randomly dispersed peptides. J. Struct. Biol. 2015, 192 (3), 376-391. 72.
Nasica-Labouze, J.; Mousseau, N., Kinetics of amyloid aggregation: a study of the GNNQQNY
prion sequence. PLoS Comp. Biol. 2012, 8 (11), e1002782.
ACS Paragon Plus Environment
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A Top-Down Multiscale Approach to Simulate Peptide Self-Assembly from Monomers Xiaochuan Zhao, Chenyi Liao, Yong-Tao Ma, Jonathon B. Ferrell, Severin T. Schneebeli, Jianing Li* Department of Chemistry, the University of Vermont, Burlington, VT 05405
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