Peptide In Explicit Water Research Articles

Replica permutation with solute tempering for molecular dynamics simulation and its application to the dimerization of amyloid-β fragments.

We propose the replica permutation with solute tempering (RPST) by combining the replica-permutation method (RPM) and the replica exchange with solute tempering (REST). Temperature permutations are performed among more than two replicas in RPM, whereas temperature exchanges are performed between two replicas in the replica-exchange method (REM). The temperature transition in RPM occurs more efficiently than in REM. In REST, only the temperatures of the solute region, the solute temperatures, are exchanged to reduce the number of replicas compared to REM. Therefore, RPST is expected to be an improved method taking advantage of these methods. For comparison, we applied RPST, REST, RPM, and REM to two amyloid-β(16-22) peptides in explicit water. We calculated the transition ratio and the number of tunneling events in the temperature space and the number of dimerization events of amyloid-β(16-22) peptides. The results indicate that, in RPST, the number of replicas necessary for frequent random walks in the temperature and conformational spaces is reduced compared to the other three methods. In addition, we focused on the dimerization process of amyloid-β(16-22) peptides. The RPST simulation with a relatively small number of replicas shows that the two amyloid-β(16-22) peptides form the intermolecular antiparallel β-bridges due to the hydrophilic side-chain contact between Lys and Glu and hydrophobic side-chain contact between Leu, Val, and Phe, which stabilizes the dimer of the peptides.

Dimerization of α-Synuclein Fragments Studied by Isothermal-Isobaric Replica-Permutation Molecular Dynamics Simulation.

Aggregates and fibrils of intrinsically disordered α-synuclein are associated with Parkinson's disease. Within a non-amyloid β component (NAC) spanning from the 61st to the 95th residue of α-synuclein, an 11-residue segment called NACore (68GAVVTGVTAVA78) is an essential region for both fibril formation and cytotoxicity. Although NACore peptides alone are known to form aggregates and amyloid fibrils, the mechanisms of aggregation and fibrillation remain unknown. This study investigated the dimerization process of NACore peptides as the initial stage of the aggregation and fibrillation processes. We performed an isothermal-isobaric replica-permutation molecular dynamics simulation, which is one of the efficient sampling methods, for the two NACore peptides in explicit water over 96 μs. The simulation succeeded in sampling a variety of dimer structures. An analysis of secondary structure revealed that most of the NACore dimers form intermolecular β-bridges. In particular, more antiparallel β-bridges were observed than parallel β-bridges. We also found that intramolecular secondary structures such as α-helix and antiparallel β-bridge are stabilized in the pre-dimer state. However, we identified that the intermolecular β-bridges tend to form directly between residues with no specific structure rather than via the intramolecular β-bridges. This is because the NACore peptides still have a low propensity to form the intramolecular secondary structures even though they are stabilized in the pre-dimer state.

Extended diffusion theory: Recovering dynamics from biased/accelerated molecular simulations.

Dynamical properties are of great importance in determining the behavior of synthetic and natural molecules, but capturing them by computational methods is a nontrivial task. Very often the time scales of the relevant phenomena are far beyond the typical time windows accessible by classical Molecular Dynamics (MD) simulations, currently limited to the order of microseconds on standard laboratory workstations. On the other hand, biased and accelerated simulations allow for fast and thorough exploration of the molecular conformational space, but they lose the dynamic information. The problem of recovering dynamics from biased/accelerated simulations is a very active field of research, but no totally robust/reliable solutions have been given yet. In this paper it is shown how the Smoluchowski equation, in the framework of Diffusion Theory (DT), can be used to bridge this gap, and dynamical properties, in the form of time correlation functions (TCFs), can be extracted also from such kind of simulations. DT is first extended (EDT) to express the mobility tensors entering the Smoluchowski operator in terms of a recently introduced unified and regularized Rotne-Prager-Yamakawa approximation, [P. J. Zuk, E. Wajnryb, K. A. Mizerski, P. Szymczak, J. Fluid. Mech. 2014, 741, R5, 1-13] also involving mixed rotation-translation contributions, and rotation-rotation terms beside the classical translation-translation ones, so far used in DT. Then, the method is applied to recover the dynamics of a nontrivial example of a peptide in explicit water from the first 200 ns of a Replica Exchange Molecular Dynamics simulation, which is a popular computational method that destroys the long time dynamics. EDT dynamics were found to favorably compare against those coming from a standard MD simulation of the same system, requiring a time window of 30 μs to converge. This result shows that EDT is a tool of practical value to recover the long time dynamics of systems in diffusive regimes from biased/accelerated simulations, to be exploited in those cases when direct evaluation by standard MD is unfeasible.

Dynamic stability of nano-fibers self-assembled from short amphiphilic A6D peptides.

Self-assembly of A6D amphiphilic peptides in explicit water is studied by using coarse-grained molecular dynamics simulations. It is observed that the self-assembly of randomly distributed A6D peptides leads to the formation of a network of nano-fibers. Two other simulations with cylindrical nano-fibers as the initial configuration show the dynamic stability of the self-assembled nano-fibers. As a striking feature, notable fluctuations occur along the axes of the nano-fibers. Depending on the number of peptides per unit length of the nano-fiber, flat-shaped bulges or spiral shapes along the nano-fiber axis are observed at the fluctuations. Analysis of the particle distribution around the nano-fiber indicates that the hydrophobic core and the hydrophilic shell of the nano-structure are preserved in both simulations. The size of the deformations and their correlation times are different in the two simulations. This study gives new insights into the dynamics of the self-assembled nano-structures of short amphiphilic peptides.

Communication: Multiple atomistic force fields in a single enhanced sampling simulation.

The main concerns of biomolecular dynamics simulations are the convergence of the conformational sampling and the dependence of the results on the force fields. While the first issue can be addressed by employing enhanced sampling techniques such as simulated tempering or replica exchange molecular dynamics, repeating these simulations with different force fields is very time consuming. Here, we propose an automatic method that includes different force fields into a single advanced sampling simulation. Conformational sampling using three all-atom force fields is enhanced by simulated tempering and by formulating the weight parameters of the simulated tempering method in terms of the energy fluctuations, the system is able to perform random walk in both temperature and force field spaces. The method is first demonstrated on a 1D system and then validated by the folding of the 10-residue chignolin peptide in explicit water.

Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins

Development of the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and side chain torsional parameters were determined by comparing to gas-phase QM (RI-TRIM MP2/CBS) conformational energies of dipeptides and to statistical distributions from the Protein Data Bank. Molecular dynamics simulations are reported for short peptides in explicit water to examine their conformational properties in solution. Overall the calculated conformational free energies and J-coupling constants are consistent with PDB statistics and experimental NMR results, respectively. In addition, the experimental crystal structures of a number of proteins are well maintained during molecular dynamics (MD) simulation. While further calculations are necessary to fully validate the force field, initial results suggest the AMOEBA polarizable multipole force field is able to describe the structure and energetics of peptides and proteins, in both gas-phase and solution environments.

Conformational Ensemble and Polymorphism of the All-Atom Alzheimer’s Aβ37–42 Amyloid Peptide Oligomers

Although the Aβ(37-42) peptide has two opposite terminal charges, counterintuitively its current fibril amyloid structure reveals in register parallel β-strands, as formed by the full length Aβ peptide. In this study, we carried out a replica exchange molecular dynamics simulation of 16 all-atom Aβ(37-42) peptides in explicit water starting from randomized and dispersed chains. The extensive conformational sampling (48 replicas, 460 ns/replica) with a total simulation time of 23 μs allows us to obtain a full picture on the equilibrium conformational distribution of oligomers and β-sheet sizes and gain some insights into the oligomerization process at 300 K. At the peptide concentration of 12 mM, self-assembly is described by the condensation-polymerization mechanism with conversion from micelle-like to high β-sheet structures. At equilibrium, the oligomer distribution consists of large aggregates and free monomers, representing 70% and 25% of all species, respectively. Though the formation/dissociation of β-strand is high, the population of 4-5 fully parallel β-strands, consistent with the arrangement in the current fibril, is marginal and that of 4-5 fully antiparallel β-strands, consistent with amyloid polymorphism, is non-negligible. However, the system adopts essentially mixed parallel/antiparallel β-strands. This indicates that a system of 16 Aβ(37-42) chains in explicit solvent still does not form more stable species that will irreversibly grow to a fibril, independently of polymorphism. Our results also suggest that the Aβ(37-42) fibril may display packing polymorphism with antiparallel β-strands, in addition to the experimentally observed in register parallel β-strands.

Non-Markov state model of peptide dynamics

A hidden Markov state model has been applied to classical molecular dynamics simulated small peptide in explicit water. The methodology allows increasing the time resolution of the model and describe the dynamics with the precision of 0.3ps (comparing to 6ps for the standard methodology). It also permits the investigation of the mechanisms of transitions between the conformational states of the peptide. The detailed description of one of such transitions for the studied molecule is presented.

Aggregated yet Disordered: A Molecular Simulation Study of the Self-Aggregation of Elastin

Elastin is the protein responsible for the elastic recoil of skin, arteries, and lungs. Elastin exhibits high resilience and remarkable durability; it also undergoes phase separation and self-organization into a fibrillar structure upon increasing temperature. These properties make elastin ideal for biomaterials applications. In order to investigate the molecular basis for elastin self-aggregation, we performed extensive atomistic molecular dynamics simulations of a monomer and an aggregate of eight elastin-like peptides in explicit water. These simulations required a total time of nearly 0.5 ms, and utilized simulated tempering distributed replica sampling, a method that relies on a random walk in temperature to enhance conformational sampling. We obtain a configurational ensemble of the elastin-like aggregate that resembles a “polymer melt” in which the chains are completely entangled with each other, but retain significant hydration and do not form a water-excluding hydrophobic core. Within the aggregate, the chains act to “solvate” each other: intramolecular interactions present in the monomer in aqueous solution are largely replaced by intermolecular interactions in the aggregate. As a result, the overall chain dimensions are similar to the expected dimensions of chains in an ideal solvent, a state in which chain entropy is maximized. This is the prediction of the Flory theorem for generic polymer chains within a polymer melt, but has never, to our knowledge, been observed before for an aggregate of polypeptide chains in atomistic detail. Finally, we note that our results are not consistent with the current model of elastin self-aggregation, which involves a conformational transition of a monomer towards a more “ordered” aggregation-prone state. Instead, we propose a model in which both the hydrophobic effect and the enhanced chain entropy afforded by the interactions with other peptides within the aggregate favour elastin self-aggregation.

Molecular dynamics study of aggregation of amyloidogenic peptides in explicit water

AbstractThe presence of amyloid fibrils is associated with a number of degenerative and serious human diseases. Nonetheless, the process of fibrillogenesis is still poorly understood. In this study, we present the results of a molecular dynamics investigation into the self‐aggregation of the amyloidogenic peptide FLVHSS, a six‐residue peptide belonging to the sequence of human islet amyloid polypeptide (hIAPP), capable of self‐association to form amyloid‐like fibrils. The simulations were performed at T = 300 K, using multiple replicas of FLVHSS monomer with random initial spatial distribution and orientation, in explicit water, set in a confined space volume (simulation box). Different simulations were carried out by varying initial atomic coordinates or initial atomic velocities and simulation box size. The formation of a unique aggregate (cluster) was observed within few nanoseconds from the beginning of all simulations. Structural analysis of the clusters clearly showed an elongated scalene ellipsoidal shape and a preferential parallel alignment of the peptides, roughly perpendicular to the main axis of the cluster and in extended conformation. The spatial arrangement of peptides in the simulated clusters appears to be similar to the spatial disposition of molecules in amyloid fibrils. An elongated scalene ellipsoidal shape was observed also in the final aggregate of the cluster growth simulation we also reported herein, indicating a tendency of cluster to grow along its major geometrical axis. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:1844–1851, 2012

Computational study of bound water in a human collagen II model peptide and its variants

The human collagen II sequence P02458 (GFO GER GSO GAQ GLQ GPR GLO GTO GTD GPK) was obtained from the UniProtKB/Swiss‐Prot database and was used to construct collagen II trimers based on the 1CGD.pdb crystal structure. This sequence is of interest because it contains two human mutations at residue 717 (the GPR triplet above) that cause congenital bone disorders. The G717S mutation causes femoral head necrosis, a degenerative disease, while G717V causes achondrogenesis; neonatally lethal. The AMBER10 molecular dynamics package was used to simulate the resulting peptides in explicit water at 310 K. Sites of bound water were identified using VMD (Visual Molecular Dynanics), a visualization package used to observe the trimeric protein and its bound waters. These bound waters are sequestered by polar amino acid residues that form cage‐like structures that contribute to the stability of the trimer via hydrogen bonding. In the second and third nanosecond of the wild type (G717G), three cages were found. Nanosecond two of G717S and G717V had two cages and one cage, respectively. These findings suggest that the G→S and G→V mutations both lead to decreased stability, but the G717V shows a higher degree of unfolding at the C‐terminus. Department of Chemistry and Pharmaceutical Science, Becton College, Fairleigh Dickinson University, Madison, NJ

Free Energy Landscapes of Alanine Dipeptide in Explicit Water Reproduced by the Force-Switching Wolf Method.

Precise and rapid calculation of long-range interactions is of crucial importance for molecular dynamics (MD) and Monte Carlo simulations. Instead of the Ewald method or its high speed variant, PME, we applied our novel method, called the force-switching Wolf method, to computation of the free energy landscapes of a short peptide in explicit water. Wolf and co-workers showed that long-range electrostatic energy under a periodic boundary condition can be well reproduced even by truncating the contribution from the distant charges, when the charge neutrality is taken into account. We recently applied the procedure proposed by Wolf and co-workers to a mathematically consistent MD theory by means of a force-switching scheme, and we show that the total electrostatic energy for sodium chloride liquid was well conserved and stable during the MD simulation with the force-switching Wolf method. Our current results for an aqueous peptide solution with a series of canonical and multicanonical molecular dynamics simulations show that the force-switching Wolf method is not only in good accordance with the energies and forces calculated by the conventional PME method but also properly reproduces the solvation and the free energy landscapes of the peptide at 300 K.

Simulated tempering distributed replica sampling: A practical guide to enhanced conformational sampling

Simulated tempering distributed replica sampling (STDR) is a generalized-ensemble method designed specifically for simulations of large molecular systems on shared and heterogeneous computing platforms [Rauscher, Neale and Pomès (2009) J. Chem. Theor. Comput. 5, 2640]. The STDR algorithm consists of an alternation of two steps: (1) a short molecular dynamics (MD) simulation; and (2) a stochastic temperature jump. Repeating these steps thousands of times results in a random walk in temperature, which allows the system to overcome energetic barriers, thereby enhancing conformational sampling. The aim of the present paper is to provide a practical guide to applying STDR to complex biomolecular systems. We discuss the details of our STDR implementation, which is a highly-parallel algorithm designed to maximize computational efficiency while simultaneously minimizing network communication and data storage requirements. Using a 35-residue disordered peptide in explicit water as a test system, we characterize the efficiency of the STDR algorithm with respect to both diffusion in temperature space and statistical convergence of structural properties. Importantly, we show that STDR provides a dramatic enhancement of conformational sampling compared to a canonical MD simulation.

Development of molecular simulation methods to accurately represent protein-surface interactions: The effect of pressure and its determination for a system with constrained atoms

When performing molecular dynamics simulations for a system with constrained (fixed) atoms, traditional isobaric algorithms (e.g., NPT simulation) often cannot be used. In addition, the calculation of the internal pressure of a system with fixed atoms may be highly inaccurate due to the nonphysical nature of the atomic constraints and difficulties in accurately defining the volume occupied by the unconstrained atoms in the system. The inability to properly set and control pressure can result in substantial problems for the accurate simulation of condensed-phase systems if the behavior of the system (e.g., peptide/protein adsorption) is sensitive to pressure. To address this issue, the authors have developed an approach to accurately determine the internal pressure for a system with constrained atoms. As the first step in this method, a periodically extendable portion of the mobile phase of the constrained system (e.g., the solvent atoms) is used to create a separate unconstrained system for which the pressure can be accurately calculated. This model system is then used to create a pressure calibration plot for an intensive local effective virial parameter for a small volume cross section or "slab" of the system. Using this calibration plot, the pressure of the constrained system can then be determined by calculating the virial parameter for a similarly sized slab of mobile atoms. In this article, the authors present the development of this method and demonstrate its application using the CHARMM molecular simulation program to characterize the adsorption behavior of a peptide in explicit water on a hydrophobic surface whose lattice spacing is maintained with atomic constraints. The free energy of adsorption for this system is shown to be dramatically influenced by pressure, thus emphasizing the importance of properly maintaining the pressure of the system for the accurate simulation of protein-surface interactions.

Simulated Tempering Distributed Replica Sampling, Virtual Replica Exchange, and Other Generalized-Ensemble Methods for Conformational Sampling.

Generalized-ensemble algorithms in temperature space have become popular tools to enhance conformational sampling in biomolecular simulations. A random walk in temperature leads to a corresponding random walk in potential energy, which can be used to cross over energetic barriers and overcome the problem of quasi-nonergodicity. In this paper, we introduce two novel methods: simulated tempering distributed replica sampling (STDR) and virtual replica exchange (VREX). These methods are designed to address the practical issues inherent in the replica exchange (RE), simulated tempering (ST), and serial replica exchange (SREM) algorithms. RE requires a large, dedicated, and homogeneous cluster of CPUs to function efficiently when applied to complex systems. ST and SREM both have the drawback of requiring extensive initial simulations, possibly adaptive, for the calculation of weight factors or potential energy distribution functions. STDR and VREX alleviate the need for lengthy initial simulations, and for synchronization and extensive communication between replicas. Both methods are therefore suitable for distributed or heterogeneous computing platforms. We perform an objective comparison of all five algorithms in terms of both implementation issues and sampling efficiency. We use disordered peptides in explicit water as test systems, for a total simulation time of over 42 μs. Efficiency is defined in terms of both structural convergence and temperature diffusion, and we show that these definitions of efficiency are in fact correlated. Importantly, we find that ST-based methods exhibit faster temperature diffusion and correspondingly faster convergence of structural properties compared to RE-based methods. Within the RE-based methods, VREX is superior to both SREM and RE. On the basis of our observations, we conclude that ST is ideal for simple systems, while STDR is well-suited for complex systems.

Association of Helical β-Peptides and their Aggregation Behavior from the Potential of Mean Force in Explicit Solvent

Helical β-peptides have been shown to fold into well-defined structures. In aqueous solution, some β-peptides self-assemble into nanoscale fibers, aggregates, and liquid crystalline phases. Molecular simulations, at an atomistic level, are used to examine, in a systematic manner, the interactions between distinct β-peptide molecules. The relationship between side-chain chemistry (and position along the backbone) and, in particular, aggregation behaviors, is assessed by calculating the potential of mean force or dimerization free energy of two peptides in explicit water. The free energy profiles as a function of separation for helical, amphiphilic β-peptides are consistent with experimental observations, and help explain the origins of aggregate or fiber formation in solution. Close examination of the energetic and entropic contributions to the free energy reveals that, depending on the position of certain side groups along the molecule, the tendency of two peptides to aggregate can be driven by entropy or by energy, respectively. In contrast to findings from previous works that employed a coarse representation of the solvent, it is shown that water-peptide interactions play key roles in the association behavior of β-peptides.

Verifying trivial parallelization of multicanonical molecular dynamics for conformational sampling of a polypeptide in explicit water

Multicanonical molecular dynamics (McMD) simulation is an enhanced conformational sampling method. For more accelerated sampling, we examined a trajectory-parallelization method, which trivially integrates multiple McMD trajectories into one. This method decreases communications between computing nodes largely. We applied this method to conformational sampling of a seven-residue peptide in explicit water. Physical quantities converged well with those from a long McMD simulation in a wide temperature range. Thus, the integration can generate a canonical ensemble without performing the long simulation. The current method is useful for folding study of long polypeptides (proteins) in explicit water with massive parallelism.

Molecular dynamics simulations of an apoliprotein A–I derived peptide in explicit water

Molecular dynamics simulations have been performed for the 104–117 α-helical fragment of apoliprotein A–I using the CHARMM22 force field and the N amd simulation engine. Simulation (50 ns in explicit water) resulted in significant appearance of π-helix conformation, which was totally diminished when the CMAP correction of the CHARMM force field was applied. This is consistent with other similar studies which suggest that the observation of π-helix in peptide conformation was force field biased rather actually existed. This study suggests that the 104–117 fragment of apoliprotein A–I has a stable α-helical conformation in water.

Dynamical frustration of protein's environment at the nanoseconds time scale

A 21-residue peptide in explicit water has been simulated using classical molecular dynamics. The system's trajectory has been analysed with a novel approach that quantifies the process of how atom's environment trajectories are explored. The approach is based on the measure of Statistical Complexity that extracts complete dynamical information from the signal. The introduced characteristic quantifies the system's dynamics at the nanoseconds time scale. It has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the exploration of the dynamically allowed configurations of the environment. During these periods the rates remain the same but different from other periods and from the rate for water. Periods of dynamical frustration are detected when only limited routes in the space of possible trajectories of the surrounding atoms are realised.

Peptide folding kinetics from replica exchange molecular dynamics

We show how accurate kinetic information, such as the rates of protein folding and unfolding, can be extracted from replica-exchange molecular dynamics (REMD) simulations. From the brief and continuous trajectory segments between replica exchanges, we estimate short-time propagators in conformation space and use them to construct a master equation. For a helical peptide in explicit water, we determine the rates of transitions both locally between microscopic conformational states and globally for folding and unfolding. We show that accurate rates in the approximately 1(100 ns) to approximately 1(1 ns) range can be obtained from REMD with exchange times of 5 ps , in excellent agreement with results from long equilibrium molecular dynamics.