Multibaric-multithermal ensemble molecular dynamics simulations

We present new generalized-ensemble molecular dynamics simulation algorithms, which we refer to as the multibaric-multithermal molecular dynamics. We describe three algorithms based on (1) the Nosé thermostat and the Andersen barostat, (2) the Nosé-Poincaré thermostat and the Andersen barostat, and (3) the Gaussian thermostat and the Andersen barostat. The multibaric-multithermal simulations perform random walks widely both in the potential-energy space and in the volume space. Therefore, one can calculate isobaric-isothermal ensemble averages in wide ranges of temperature and pressure from only one simulation run. We test the effectiveness of the multibaric-multithermal algorithm by applying it to a Lennard-Jones 12-6 potential system.     

Partial rigid-body dynamics in NPT, NPAT and NPgammaT ensembles for proteins and membranes

A partial rigid-body method of molecular dynamics simulations for proteins and membranes is presented. In this method, the symplectic integrator for rigid bodies is combined with the equations of motion for the NPT ensemble. The standard NPT ensemble is extended to the membrane-specific ensembles, the NPAT (constant normal pressure and lateral surface area of membranes and constant temperature) and NPgammaT (constant normal pressure and lateral surface tension of membranes and constant temperature) ensembles. By more than 30-ns simulations of aqueous proteins and hydrated lipid bilayers, the results of the partial rigid-body method demonstrated excellent conservation of total energy and consistent behavior with the traditional constraint method in terms of structural distribution and fluctuation of proteins and lipids. The efficient implementation of the partial rigid-body method in parallel computation is presented, which is shown to work well in large-scale molecular dynamics simulations.     

Molecular dynamics simulation in the grand canonical ensemble

An extended system Hamiltonian is proposed to perform molecular dynamics (MD) simulation in the grand canonical ensemble. The Hamiltonian is similar to the one proposed by Lynch and Pettitt (Lynch and Pettitt, J Chem Phys 1997, 107, 8594), which consists of the kinetic and potential energies for real and fractional particles as well as the kinetic and potential energy terms for material and heat reservoirs interacting with the system. We perform a nonlinear scaling of the potential energy parameters of the fractional particle, as well as its mass to vary the number of particles dynamically. On the basis of the equations of motion derived from this Hamiltonian, an algorithm has been proposed for MD simulation at constant chemical potential. The algorithm has been tested for the ideal gas, for the Lennard-Jones fluid over a wide range of temperatures and densities, and for water. The results for the low-density Lennard-Jones fluid are compared with the predictions from a truncated virial equation of state. In the case of the dense Lennard-Jones fluid and water our predicted results are compared with the results reported using other available methods for the calculation of the chemical potential. The method is also applied to the case of vapor-liquid coexistence point predictions.     

On the influence of charged side chains on the folding-unfolding equilibrium of beta-peptides: a molecular dynamics simulation study

The influence of charged side chains on the folding-unfolding equilibrium of beta-peptides was investigated by means of molecular dynamics simulations. Four different peptides containing only negatively charged side chains, positively charged side chains, both types of charged side chains (with the ability to form stabilizing salt bridges) or no charged side chains were studied under various conditions (different simulation temperatures, starting structures and solvent environment). The NMR solution structure in methanol of one of the peptides (A) has already been published; the synthesis and NMR analysis of another peptide (B) is described here. The other peptides (C and D) studied herein have hitherto not been synthesized. All four peptides A-D are expected to adopt a left-handed 3(14)-helix in solution as well as in the simulations. The resulting ensembles of structures were analyzed in terms of conformational space sampled by the peptides, folding behavior, structural properties such as hydrogen bonding, side chain-side chain and side chain-backbone interactions and in terms of the level of agreement with the NMR data available for two of the peptides. It was found that the presence of charged side chains significantly slows down the folding process in methanol solution due to the stabilization of intermediate conformers with side chain-backbone interactions. In water, where the solvent competes with the solute-solute polar interactions, the folding process to the 3(14)-helix is faster in the simulations.     

Many-body effects on structure and dynamics of aqueous ionic solutions

We performed several molecular dynamic studies of metal cations in aqueous solution. The alkali metal ion Li(+) and the first-row transition metal ion Mn(2+) have been chosen as model systems. Two different three-body corrections are proposed to mimic the crucial many-body effects of electrolyte solutions. The correction function, which includes attractive features of the three-body potential, performs considerably better than the purely repulsive interaction function. Structural and dynamic results show that this simple enhancement is able to satisfactorily reproduce experimental and higher-level results for the first hydration shell.     

Energy exchange network of inter‐residue interactions within a thermally fluctuating protein molecule: A computational study

Protein function is regulated not only by the structure but also by physical dynamics and thermal fluctuations. We have developed the computer program, CURrent calculation for proteins (CURP), for the flow analysis of physical quantities within thermally fluctuating protein media. The CURP program was used to calculate the energy flow within the third PDZ domain of the neuronal protein PSD‐95, and the results were used to illustrate the energy exchange network of inter‐residue interactions based on atomistic molecular dynamics simulations. The removal of the α3 helix is known to decrease ligand affinity by 21‐fold without changing the overall protein structure; nevertheless, we demonstrated that the helix constitutes an essential part of the network graph. © 2015 Wiley Periodicals, Inc.     

Molecular dynamics study of polymer crystallization in the presence of a particle

We have used molecular dynamics simulations with a coarse‐grained model to study the effect of a particle on the crystallization of polymer melt. We analyzed in particular a bond order parameter to characterize the nucleation and crystallization process. Our calculations show that the presence of a particle modifies the free energy landscape of polymer melts, locally induces the ordering of polymer melts near the particle surface, and thus enhances the polymer crystallization. Because the interaction between the particle and polymers is repulsive, our results suggest that the origin of the enhancement for polymer crystallization is entropic. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2161–2166, 2007     

The absorption and diffusion of polyethylene chains on the carbon nanotube: The molecular dynamics study

Classical molecular dynamics simulations have been used to investigate the absorption and diffusion behavior of polyethylene (PE) chains on the surface of the side‐wall of the carbon nanotube (CNT). Different degrees of polymerization from 50 to 80 at separate temperatures of 300, 400, 500, and 600 K are considered. Through the simulation, it is examined that the PE chains are absorbed on the surface of CNT and form stable composites with the nanotube as capsules. It is found that the most probable distance between the CNT and the C atoms in backbone of PE molecules only attribute to the temperature, and at T = 300 K, this distance is about 3.8 Å. Furthermore, the pattern of the composites mainly depends on the temperature and the length matching of the chains and the CNT. In particular, the PE chains keep approximately linear conformation, and extend along the axis of the CNT at the room temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 272–280, 2008     

Structure and dynamics of liquid water with different long-range interaction truncation and temperature control methods in molecular dynamics simulations

We have used molecular dynamics simulations to study the physical properties of modified TIP3P water model included in the CHARMM program, using four different methods-the Ewald summation technique, and three different spherical truncation methods-for the treatment of the long-range interactions. Both the structure and dynamics of the liquid water model were affected by the methods used to truncate the long-range interactions. For some of the methods artificial structuring of the model liquid was observed around the cutoff radius. The model liquid properties were also affected by the commonly applied temperature control methods. Four different methods for controlling the temperature of the system were studied, and the effects of these methods on the bulk properties for liquid water were analyzed. The system size was also found to change the dynamics of the model liquid water. Two control simulations with the SPC/E water model were carried out. The self-diffusion coefficient (D), the radial distribution function (g(OO)), the distance dependent Kirkwood G-factor [G(k)(r)] and the intermolecular potential energy (E(pot)) were determined from the different trajectories and compared with the experimental data.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Combination of COSMOmic and molecular dynamics simulations for the calculation of membrane–water partition coefficients

The importance of membrane‐water partition coefficients led to the recent extension of the conductor‐like screening model for realistic solvation (COSMO‐RS) to micelles and biomembranes termed COSMOmic. Compared to COSMO‐RS, this new approach needs structural information to account for the anisotropy of colloidal systems. This information can be obtained from molecular dynamics (MD) simulations. In this work, we show that this combination of molecular methods can efficiently be used to predict partition coefficients with good agreement to experimental data and enables screening studies. However, there is a discrepancy between the amount of data generated by MD simulations and the structural information needed for COSMOmic. Therefore, a new scheme is presented to extract data from MD trajectories for COSMOmic calculations. In particular, we show how to calculate the system structure from MD, the influence of lipid conformers, the relation to the COSMOmic layer size, and the water/lipid ratio impact. For a 1,2‐dimyristoyl‐sn‐glycero‐3‐phosphocholine (DMPC) bilayer, 66 partition coefficients for various solutes were calculated. Further, 52 partition coefficients for a 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3‐phosphocholine (POPC) bilayer system were calculated. All these calculations were compared to experimental data. © 2013 Wiley Periodicals, Inc.     

Molecular dynamics in the isothermal-isobaric ensemble: the requirement of a "shell" molecule. I. Theory and phase-space analysis

Current constant pressure molecular-dynamics (MD) algorithms are not consistent with the recent reformulation of the isothermal-isobaric (NpT) ensemble. The NpT ensemble partition function requires the use of a "shell" molecule to identify uniquely the volume of the system, thereby avoiding the redundant counting of configurations [e.g., G. J. M. Koper and H. Reiss, J. Phys. Chem. 100, 422 (1996); D. S. Corti, Phys. Rev. E, 64, 016128 (2001)]. So far, only the NpT Monte Carlo method has been updated to allow the system volume to be defined by a shell particle [D. S. Corti, Mol. Phys. 100, 1887 (2002)]. A shell particle has yet to be incorporated into MD simulations. The proper modification of the NpT MD algorithm is therefore the subject of this paper. Unlike Andersen's method [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] where a piston of unknown mass serves to control the response time of volume fluctuations, the newly proposed equations of motion impose a constant external pressure via the introduction of a shell particle of known mass. Hence, the system itself sets the time scales for pressure and volume fluctuations. The new algorithm is subject to a number of fundamentally rigorous tests to ensure that the equations of motion sample phase space correctly. We also show that the Hoover NpT algorithm [W. G. Hoover, Phys. Rev. A. 31, 1695 (1985); 34, 2499 (1986)] does sample phase correctly, but only when periodic boundary conditions are employed.     

MDAnalysis: A toolkit for the analysis of molecular dynamics simulations

MDAnalysis is an object‐oriented library for structural and temporal analysis of molecular dynamics (MD) simulation trajectories and individual protein structures. It is written in the Python language with some performance‐critical code in C. It uses the powerful NumPy package to expose trajectory data as fast and efficient NumPy arrays. It has been tested on systems of millions of particles. Many common file formats of simulation packages including CHARMM, Gromacs, Amber, and NAMD and the Protein Data Bank format can be read and written. Atoms can be selected with a syntax similar to CHARMM's powerful selection commands. MDAnalysis enables both novice and experienced programmers to rapidly write their own analytical tools and access data stored in trajectories in an easily accessible manner that facilitates interactive explorative analysis. MDAnalysis has been tested on and works for most Unix‐based platforms such as Linux and Mac OS X. It is freely available under the GNU General Public License from http://mdanalysis.googlecode.com . © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Comparison of the accuracy of periodic reaction field methods in molecular dynamics simulations of a model liquid crystal system

A periodic reaction field (PRF) method is a technique to estimate long‐range interactions. The method has the potential to effectively reduce the computational cost while maintaining adequate accuracy. We performed molecular dynamics (MD) simulations of a model liquid‐crystal system to assess the accuracy of some variations of the PRF method in low‐charge‐density systems. All the methods had adequate accuracy compared with the results of the particle mesh Ewald (PME) method, except for a few simulation conditions. Furthermore, in all of the simulation conditions, one of the PRF methods had the same accuracy as the PME method. © 2015 Wiley Periodicals, Inc.     

Simulated tempering based on global balance or detailed balance conditions: Suwa–Todo,heat bath,and Metropolis algorithms

Simulated tempering (ST) is a useful method to enhance sampling of molecular simulations. When ST is used, the Metropolis algorithm, which satisfies the detailed balance condition, is usually applied to calculate the transition probability. Recently, an alternative method that satisfies the global balance condition instead of the detailed balance condition has been proposed by Suwa and Todo. In this study, ST method with the Suwa–Todo algorithm is proposed. Molecular dynamics simulations with ST are performed with three algorithms (the Metropolis, heat bath, and Suwa–Todo algorithms) to calculate the transition probability. Among the three algorithms, the Suwa–Todo algorithm yields the highest acceptance ratio and the shortest autocorrelation time. These suggest that sampling by a ST simulation with the Suwa–Todo algorithm is most efficient. In addition, because the acceptance ratio of the Suwa–Todo algorithm is higher than that of the Metropolis algorithm, the number of temperature states can be reduced by 25% for the Suwa–Todo algorithm when compared with the Metropolis algorithm. © 2015 Wiley Periodicals, Inc.     

Balancing target flexibility and target denaturation in computational fragment‐based inhibitor discovery

Accounting for target flexibility and selecting “hot spots” most likely to be able to bind an inhibitor continue to be challenges in the field of structure‐based drug design, especially in the case of protein–protein interactions. Computational fragment‐based approaches using molecular dynamics (MD) simulations are a promising emerging technology having the potential to address both of these challenges. However, the optimal MD conditions permitting sufficient target flexibility while also avoiding fragment‐induced target denaturation remain ambiguous. Using one such technology (Site Identification by Ligand Competitive Saturation, SILCS), conditions were identified to either prevent denaturation or identify and exclude trajectories in which subtle but important denaturation was occurring. The target system used was the well‐characterized protein cytokine IL‐2, which is involved in a protein–protein interface and, in its unliganded crystallographic form, lacks surface pockets that can serve as small‐molecule binding sites. Nonetheless, small‐molecule inhibitors have previously been discovered that bind to two “cryptic” binding sites that emerge only in the presence of ligand binding, highlighting the important role of IL‐2 flexibility. Using the above conditions, SILCS with hydrophobic fragments was able to identify both sites based on favorable fragment binding while avoiding IL‐2 denaturation. An important additional finding was that acetonitrile, a water‐miscible fragment, fails to identify either site yet can induce target denaturation, highlighting the importance of fragment choice. © 2012 Wiley Periodicals, Inc.     

Adsorption of a single polymer chain on a surface: A molecular dynamics simulation study

We performed simulations of the physical adsorption of a single globular chain on a surface of hemispherical shape by means of molecular dynamics simulations. For the chain, we took advantage of a united atom model. Interactions within the chain were limited to stretching, bending, and torsional as well as nonbonded interactions between the nonadjacent atoms. The interaction between each chain element and the surface formation are reigned by a Lennard–Jones potential. In this article, we focused on differences in the behavior of the adsorbed globule to the free unadsorbed one particularly in two different zones of the immediate vicinity of the surface. There were strong indications for a localized acceleration of the dynamics as compared with the bulk that appears in an increase of trans–gauche switches. For explanation we came up with an adsorption scenario. Special attention was given to the shift of the percentage of trans and gauche conformations within the globule in dependence on the strength of the adsorption potential that might be related to crystallization or glass transition. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2333–2339, 2001     

Structure and Thermodynamics of Mg:Phosphate Interactions in Water: A Simulation Study

The association of Mg²⁺ and H₂PO₄^? in water can give insights into Mg:phosphate interactions in general, which are very widespread, but for which experimental data is surprisingly sparse. It is studied through molecular dynamics simulations (>100 ns) by using the polarizable AMOEBA force field, and the association free energy is computed for the first time. Explicit consideration of outer‐sphere and two types of inner‐sphere association provides considerable insight into the dynamics and thermodynamics of ion pairing. After careful assessment of the computational approximations, the agreement with experimental values indicates that the methodology can be extended to other inorganic and biological Mg:phosphate interactions in solution.     

Pulling Polymers on Energetically Disordered Surfaces: Molecular Dynamics Tests of Linear and Non‐linear Response

Equilibrium and non‐equilibrium molecular dynamics simulations of flexible polymer chains absorbed on heterogeneous surfaces are presented. The surfaces are flat but energetically disordered, consisting of a random mixture of weakly and more strongly absorbing sites (94 and 6%, respectively). For comparison, the two corresponding homogeneous surfaces are also simulated. This apparently weak energetic disorder can produce significant changes of the chain statistics, equilibrium dynamics, and non‐equilibrium response to a horizontal pulling force. On the disordered surfaces, the polymer–surface effective friction coefficient becomes strongly force‐dependent, as the dominant mode of motion changes from localized stick–slip events to smooth and continuous sliding. This is strongly reminiscent of the Schallamach model of rubber friction and the Maier–Göritz picture of the Payne effect in filled elastomers.

     

Correlated motions analysis from molecular dynamics trajectories: Statistical accuracy on the determination of canonical correlation coefficients

A numerical study of the accuracy on the determination of a unique global canonical correlation coefficient C between two groups of random variables is presented as a function of the number of variables of both groups (n and m, respectively), of the sampling size N and of the actual level of correlation C between the groups. The method used to estimate C has been already described (Briki, F.; Genest, D. Biophys Chem 1994, 52, 35–43; and J Biomol Struct Dynam 1995, 12, 1063–1082), and is implemented in the home made program TECOR. To check the accuracy on the estimation of C for given values of n, m, N, and C, samples of the random variables are synthesized (with known C), then TECOR is used to get an estimated value M of the global canonical coefficient, which is compared to the actual value C. Special attention is paid to the application of the method to the analysis from molecular dynamics simulation trajectories of concerted motions of two groups of atoms (not larger than about 20 atoms) in the course of internal deformation of biopolymers. It is found that there is a good agreement between M and C for moderate and high correlation (C≥0.35), provided that at least about 2000 configurations are stored during the molecular dynamics simulation. If C is smaller than 0.35, the method can overestimate its value if the number of configurations is not increased, especially for larger groups. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1571–1576, 1999