Symplectic molecular dynamics simulations on specially designed parallel computers

We have developed a computer program for molecular dynamics (MD) simulation that implements the Split Integration Symplectic Method (SISM) and is designed to run on specialized parallel computers. The MD integration is performed by the SISM, which analytically treats high-frequency vibrational motion and thus enables the use of longer simulation time steps. The low-frequency motion is treated numerically on specially designed parallel computers, which decreases the computational time of each simulation time step. The combination of these approaches means that less time is required and fewer steps are needed and so enables fast MD simulations. We study the computational performance of MD simulation of molecular systems on specialized computers and provide a comparison to standard personal computers. The combination of the SISM with two specialized parallel computers is an effective way to increase the speed of MD simulations up to 16-fold over a single PC processor.     

Molecular dynamics integration and molecular vibrational theory. II. Simulation of nonlinear molecules

A series of molecular dynamics (MD) simulations of nonlinear molecules has been performed to test the efficiency of newly introduced semianalytical second-order symplectic time-reversible MD integrators that combine MD and the standard theory of molecular vibrations. The simulation results indicate that for the same level of accuracy, the new algorithms allow significantly longer integration time steps than the standard second-order symplectic leap-frog Verlet method. Since the computation cost per integration step using new MD integrators with longer time steps is approximately the same as for the standard method, a significant speed-up in MD simulation is achieved.     

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.     

Predictive power of molecular dynamics receptor structures in virtual screening

Molecular dynamics (MD) simulation is a well-established method for understanding protein dynamics. Conformations from unrestrained MD simulations have yet to be assessed for blind virtual screening (VS) by docking. This study presents a critical analysis of the predictive power of MD snapshots to this regard, evaluating two well-characterized systems of varying flexibility in ligand-bound and unbound configurations. Results from such VS predictions are discussed with respect to experimentally determined structures. In all cases, MD simulations provide snapshots that improve VS predictive power over known crystal structures, possibly due to sampling more relevant receptor conformations. Additionally, MD can move conformations previously not amenable to docking into the predictive range.     

On achieving experimental accuracy from molecular dynamics simulations of flexible molecules: aqueous glycerol

The rotational isomeric states (RIS) of glycerol at infinite dilution have been characterized in the aqueous phase via a 1 micros conventional molecular dynamics (MD) simulation, a 40 ns enhanced sampling replica exchange molecular dynamics (REMD) simulation, and a reevaluation of the experimental NMR data. The MD and REMD simulations employed the GLYCAM06/AMBER force field with explicit treatment of solvation. The shorter time scale of the REMD sampling method gave rise to RIS and theoretical scalar 3J(HH) coupling constants that were comparable to those from the much longer traditional MD simulation. The 3J(HH) coupling constants computed from the MD methods were in excellent agreement with those observed experimentally. Despite the agreement between the computed and the experimental J-values, there were variations between the rotamer populations computed directly from the MD data and those derived from the experimental NMR data. The experimentally derived populations were determined utilizing limiting J-values from an analysis of NMR data from substituted ethane molecules and may not be completely appropriate for application in more complex molecules, such as glycerol. Here, new limiting J-values have been derived via a combined MD and quantum mechanical approach and were used to decompose the experimental 3J(HH) coupling constants into population distributions for the glycerol RIS.     

Conformational analysis of six- and twelve-membered ring compounds by molecular dynamics

A molecular dynamics (MD)-based conformational analysis has been performed on a number of cycloalkanes in order to demonstrate the reliability and generality of MD as a tool for conformational analysis. MD simulations on cyclohexane and a series of methyl-substituted cyclohexanes were performed at temperatures between 400 and 1200 K. Depending on the simulation temperature, different types of interconversions (twist-boat–twist-boat, twist- boat–chair and chair–chair) could be observed, and the MD simulations demonstrated the expected correlation between simulation temperature and ring inversion barriers. A series of methyl-substituted 1,3- dioxanes were investigated at 1000 K, and the number of chair–chair interconversions could be quantitatively correlated to the experimentally determined ring inversion barrier. Similarly, the distribution of sampled minimum-energy conformations correlated with the energy-derived Boltzmann distribution. The macrocyclic ring system cyclododecane was subjected to an MD simulation at 1000 K and 71 different conformations could be sampled. These conformations were compared with the results of previously reported conformational analyses using stochastic search methods, and the MD method provided 19 out of the 20 most stable conformations found in the MM2 force field. Finally, the general performance of the MD method for conformational analysis is discussed.     

Application of principal component analysis in protein unfolding: an all-atom molecular dynamics simulation study

We have performed molecular dynamics (MD) simulation of the thermal denaturation of one protein and one peptide-ubiquitin and melittin. To identify the correlation in dynamics among various secondary structural fragments and also the individual contribution of different residues towards thermal unfolding, principal component analysis method was applied in order to give a new insight to protein dynamics by analyzing the contribution of coefficients of principal components. The cross-correlation matrix obtained from MD simulation trajectory provided important information regarding the anisotropy of backbone dynamics that leads to unfolding. Unfolding of ubiquitin was found to be a three-state process, while that of melittin, though smaller and mostly helical, is more complicated.     

Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR T1 measurements

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR T(1) measurements. MD trajectories based on an effective potential are used to calculate the (2)H NMR relaxation time, T(1) via Fourier transform of the relevant rotational time correlation function, C(2R)(t). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of T(1) when an effective charge of ±0.5e is used for the anion and the cation, respectively. The computed C(2R)(t) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the C(2R)(t) is most important to understand frequency and temperature dependencies of T(1) in ILs. On the other hand, the effect of the initial ps relaxation is an increase of T(1) by a constant factor. This is equivalent to an "effective" reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR T(1) analysis, the rotational time correlation function can be modeled analytically in the form of aexp (-t/τ) (Lipari-Szabo model), where the constant a, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and τ represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with a = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since a is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2-3 as a compensation for the neglect of the Lipari-Szabo factor.     

Effects of ionic strength on SAXS data for proteins revealed by molecular dynamics simulations

The combination of small-angle X-ray solution scattering (SAXS) experiments and molecular dynamics (MD) simulations is now becoming a powerful tool to study protein conformations in solution at an atomic resolution. In this study, we investigated effects of ionic strength on SAXS data theoretically by using MD simulations of hen egg white lysozyme at various NaCl concentrations from 0 to 1 M. The calculated SAXS excess intensities showed a significant dependence on ion concentration, which originates from the different solvent density distributions in the presence and absence of ions. The addition of ions induced a slow convergence of the SAXS data, and a ～20 ns simulation is required to obtain convergence of the SAXS data with the presence of ions whereas only a 0.2 ns simulation is sufficient in the absence of ions. To circumvent the problem of the slow convergence in the presence of ions, we developed a novel method that reproduces the SAXS excess intensities with the presence of ions from short MD trajectories in pure water. By applying this method to SAXS data for the open and closed forms of transferrin at 1 M ion concentration, the correct form could be identified by simply using short MD simulations of the protein in pure water for 0.2 ns.     

Rotamer decomposition and protein dynamics: Efficiently analyzing dihedral populations from molecular dynamics

Molecular mechanics methods have matured into powerful methods to understand the dynamics and flexibility of macromolecules and especially proteins. As multinanosecond to microsecond length molecular dynamics (MD) simulations become commonplace, advanced analysis tools are required to generate scientifically useful information from large amounts of data. Some of the key degrees of freedom to understand protein flexibility and dynamics are the amino acid residue side chain dihedral angles. In this work, we present an easily automated way to summarize and understand the relevant dihedral populations. A tremendous reduction in complexity is achieved by describing dihedral timeseries in terms of histograms decomposed into Gaussians. Using the familiar and widely studied protein lysozyme, it is demonstrated that our approach captures essential properties of protein structure and dynamics. A simple classification scheme is proposed that indicates the rotational state population for each dihedral angle of interest and allows a decision if a given side chain or peptide backbone fragment remains rigid during the course of an MD simulation, adopts a converged distribution between conformational substates or has not reached convergence yet. © 2012 Wiley Periodicals, Inc.     

Effect of chain conformational change on micelle structures: experimental studies and molecular dynamics simulations

The effect of chain conformation change on the self-assembly behavior of poly(gamma-benzyl- l-glutamate)-block-poly(ethylene glycol) (PBLG-b-PEG) was studied both experimentally by transmission electron microscopy, laser light scattering, and circular dichroism and computationally using molecular dynamics (MD) simulation. It was found that, by introducing trifluoroacetic acid to the PBLG-b-PEG solution, the conformation of the PBLG chain transforms from alpha-helix to random coil, which results in a change of the micelle structures formed by PBLG-b-PEG from rod to sphere. Meanwhile, the MD simulations were performed by using Brownian dynamics on the self-assembly behavior of model AB-type diblock copolymers with various chain rigidities of the A-block. The results show that, by decreasing the fraction of rigid chain conformation of the A-block, which corresponds to the helix-coil transition in the PBLG-b-PEG sample, the aggregate structure transforms from rod to sphere. The MD simulations also provide chain packing information in the micelles. On the basis of both experimental and MD simulation results, the mechanism regarding the effect of the conformation change of the polypeptide block copolymer on its self-association behavior is suggested.     

Diffusion and viscosity of liquid tin: Green-Kubo relationship-based calculations from molecular dynamics simulations

Molecular dynamics (MD) simulations of liquid tin between its melting point and 1600 °C have been performed in order to interpret and discuss the ionic structure. The interactions between ions are described by a new accurate pair potential built within the pseudopotential formalism and the linear response theory. The calculated structure factor that reflects the main information on the local atomic order in liquids is compared to diffraction measurements. Having some confidence in the ability of this pair potential to give a good representation of the atomic structure, we then focused our attention on the investigation of the atomic transport properties through the MD computations of the velocity autocorrelation function and stress autocorrelation function. Using the Green-Kubo formula (for the first time to our knowledge for liquid tin) we determine the macroscopic transport properties from the corresponding microscopic time autocorrelation functions. The selfdiffusion coefficient and the shear viscosity as functions of temperature are found to be in good agreement with the experimental data.     

A molecular dynamics computer simulation study of room-temperature ionic liquids. II. Equilibrium and nonequilibrium solvation dynamics

The molecular dynamics (MD) simulation study of solvation structure and free energetics in 1-ethyl-3-methylimidazolium chloride and 1-ethyl-3-methylimidazolium hexafluorophosphate using a probe solute in the preceding article [Y. Shim, M. Y. Choi and H. J. Kim, J. Chem. Phys. 122, 044510 (2005)] is extended to investigate dynamic properties of these liquids. Solvent fluctuation dynamics near equilibrium are studied via MD and associated time-dependent friction is analyzed via the generalized Langevin equation. Nonequilibrium solvent relaxation following an instantaneous change in the solute charge distribution and accompanying solvent structure reorganization are also investigated. Both equilibrium and nonequilibrium solvation dynamics are characterized by at least two vastly different time scales--a subpicosecond inertial regime followed by a slow diffusive regime. Solvent regions contributing to the subpicosecond nonequilibrium relaxation are found to vary significantly with initial solvation configurations, especially near the solute. If the solvent density near the solute is sufficiently high at the outset of the relaxation, subpicosecond dynamics are mainly governed by the motions of a few ions close to the solute. By contrast, in the case of a low local density, solvent ions located not only close to but also relatively far from the solute participate in the subpicosecond relaxation. Despite this difference, linear response holds reasonably well in both ionic liquids.     

Molecular dynamics simulation of premelting and melting phase transitions in stoichiometric uranium dioxide

Results of molecular dynamics (MD) simulation of UO2 in a wide temperature range are presented and discussed. A new approach to the calibration of a partly ionic Busing-Ida-type model is proposed. A potential parameter set is obtained reproducing the experimental density of solid UO2 in a wide range of temperatures. A conventional simulation of the high-temperature stoichiometric UO2 on large MD cells, based on a novel fast method of computation of Coulomb forces, reveals characteristic features of a premelting lambda transition at a temperature near to that experimentally observed (T(lambda)=2670 K). A strong deviation from the Arrhenius behavior of the oxygen self-diffusion coefficient was found in the vicinity of the transition point. Predictions for liquid UO2, based on the same potential parameter set, are in good agreement with existing experimental data and theoretical calculations.     

Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: the case of domain motions

Protein dynamics on a long time scale was investigated using all-atom molecular dynamics (MD) simulation and time-structure based independent component analysis (tICA). We selected the lysine-, arginine-, ornithine-binding protein (LAO) as a target protein and focused on its domain motions in the open state. A MD simulation of the LAO in explicit water was performed for 600 ns, in which slow and large-amplitude domain motions of the LAO were observed. After extracting domain motions by rigid-body domain analysis, the tICA was applied to the obtained rigid-body trajectory, yielding slow modes of the LAO's domain motions in order of decreasing time scale. The slowest mode detected by the tICA represented not a closure motion described by a largest-amplitude mode determined by the principal component analysis but a twist motion with a time scale of tens of nanoseconds. The slow dynamics of the LAO were well described by only the slowest mode and were characterized by transitions between two basins. The results show that tICA is promising for describing and analyzing slow dynamics of proteins.     

Identification of the quinolinedione inhibitor binding site in Cdc25 phosphatase B through docking and molecular dynamics simulations

Cdc25 phosphatase B, a potential target for cancer therapy, is inhibited by a series of quinones. The binding site and mode of quinone inhibitors to Cdc25B remains unclear, whereas this information is important for structure-based drug design. We investigated the potential binding site of NSC663284 [DA3003-1 or 6-chloro-7-(2-morpholin-4-yl-ethylamino)-quinoline-5, 8-dione] through docking and molecular dynamics simulations. Of the two main binding sites suggested by docking, the molecular dynamics simulations only support one site for stable binding of the inhibitor. Binding sites in and near the Cdc25B catalytic site that have been suggested previously do not lead to stable binding in 50 ns molecular dynamics (MD) simulations. In contrast, a shallow pocket between the C-terminal helix and the catalytic site provides a favourable binding site that shows high stability. Two similar binding modes featuring protein-inhibitor interactions involving Tyr428, Arg482, Thr547 and Ser549 are identified by clustering analysis of all stable MD trajectories. The relatively flexible C-terminal region of Cdc25B contributes to inhibitor binding. The binding mode of NSC663284, identified through MD simulation, likely prevents the binding of protein substrates to Cdc25B. The present results provide useful information for the design of quinone inhibitors and their mechanism of inhibition.     

RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear ¹H–³¹P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.