Multiple Time Step Molecular Dynamics Research Articles

Multiscale Methods Framework with the 3D-RISM-KH Molecular Solvation Theory for Supramolecular Structures, Nanomaterials, and Biomolecules: Where Are We Going?

3D-RISM-KH molecular solvation theory based on statistical mechanics has been an engine of the multiscale methods framework, which also includes molecular simulation techniques. Its applications range from the solvation energy of small molecules to the phase behavior of polymers and biomolecules. Molecular solvation theory predicts and explains the molecular mechanisms and functioning of a variety of chemical and biomolecular systems. This includes the self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), the aggregation of peptides and proteins related to neurodegeneration, the binding of ligands to proteins, and the solvation properties of biomolecules related to their functions. The replica RISM-KH-VM molecular solvation theory predicts and explains the structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous carbon supercapacitor electrodes, and is part of recent research and development efforts. A new quasidynamics protocol couples multiple time step molecular dynamics (MTS-MD) stabilized with an optimized isokinetic Nosé–Hoover (OIN) thermostat driven by 3D-RISM-KH mean solvation forces at gigantic outer time steps of picoseconds, which are extrapolated forward at short inner time steps of femtoseconds with generalized solvation force extrapolation (GSFE). The OIN/3D-RISM-KH/GSFE quasidynamics is implemented in the Amber Molecular Dynamics package. It is validated on miniprotein 1L2Y and protein G in ambient aqueous solution, and shows the rate of sampling 150 times faster than in standard MD simulations on these biomolecules in explicit water. The self-consistent field version of Kohn–Sham DFT in 3D-RISM-KH mean solvation forces is implemented in the Amsterdam Density Functional (ADF) package. Its applications range from solvation thermochemistry, conformational equilibria, and photochemistry to activation barriers of different nanosystems in solutions and ionic liquids.

A Stochastic, Resonance-Free Multiple Time-Step Algorithm for Polarizable Models That Permits Very Large Time Steps.

Molecular dynamics remains one of the most widely used computational tools in the theoretical molecular sciences to sample an equilibrium ensemble distribution and/or to study the dynamical properties of a system. The efficiency of a molecular dynamics calculation is limited by the size of the time step that can be employed, which is dictated by the highest frequencies in the system. However, many properties of interest are connected to low-frequency, long time-scale phenomena, requiring many small time steps to capture. This ubiquitous problem can be ameliorated by employing multiple time-step algorithms, which assign different time steps to forces acting on different time scales. In such a scheme, fast forces are evaluated more frequently than slow forces, and as the former are often computationally much cheaper to evaluate, the savings can be significant. Standard multiple time-step approaches are limited, however, by resonance phenomena, wherein motion on the fastest time scales limits the step sizes that can be chosen for the slower time scales. In atomistic models of biomolecular systems, for example, the largest time step is typically limited to around 5 fs. Previously, we introduced an isokinetic extended phase-space algorithm (Minary et al. Phys. Rev. Lett. 2004, 93, 150201) and its stochastic analog (Leimkuhler et al. Mol. Phys. 2013, 111, 3579) that eliminate resonance phenomena through a set of kinetic energy constraints. In simulations of a fixed-charge flexible model of liquid water, for example, the time step that could be assigned to the slow forces approached 100 fs. In this paper, we develop a stochastic isokinetic algorithm for multiple time-step molecular dynamics calculations using a polarizable model based on fluctuating dipoles. The scheme developed here employs two sets of induced dipole moments, specifically, those associated with short-range interactions and those associated with a full set of interactions. The scheme is demonstrated on the polarizable AMOEBA water model. As was seen with fixed-charge models, we are able to obtain large time steps exceeding 100 fs, allowing calculations to be performed 10 to 20 times faster than standard thermostated molecular dynamics.

MTS-MD of Biomolecules Steered with 3D-RISM-KH Mean Solvation Forces Accelerated with Generalized Solvation Force Extrapolation.

We developed a generalized solvation force extrapolation (GSFE) approach to speed up multiple time step molecular dynamics (MTS-MD) of biomolecules steered with mean solvation forces obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model with the Kovalenko-Hirata closure). GSFE is based on a set of techniques including the non-Eckart-like transformation of coordinate space separately for each solute atom, extension of the force-coordinate pair basis set followed by selection of the best subset, balancing the normal equations by modified least-squares minimization of deviations, and incremental increase of outer time step in motion integration. Mean solvation forces acting on the biomolecule atoms in conformations at successive inner time steps are extrapolated using a relatively small number of best (closest) solute atomic coordinates and corresponding mean solvation forces obtained at previous outer time steps by converging the 3D-RISM-KH integral equations. The MTS-MD evolution steered with GSFE of 3D-RISM-KH mean solvation forces is efficiently stabilized with our optimized isokinetic Nosé-Hoover chain (OIN) thermostat. We validated the hybrid MTS-MD/OIN/GSFE/3D-RISM-KH integrator on solvated organic and biomolecules of different stiffness and complexity: asphaltene dimer in toluene solvent, hydrated alanine dipeptide, miniprotein 1L2Y, and protein G. The GSFE accuracy and the OIN efficiency allowed us to enlarge outer time steps up to huge values of 1-4 ps while accurately reproducing conformational properties. Quasidynamics steered with 3D-RISM-KH mean solvation forces achieves time scale compression of conformational changes coupled with solvent exchange, resulting in further significant acceleration of protein conformational sampling with respect to real time dynamics. Overall, this provided a 50- to 1000-fold effective speedup of conformational sampling for these systems, compared to conventional MD with explicit solvent. We have been able to fold the miniprotein from a fully denatured, extended state in about 60 ns of quasidynamics steered with 3D-RISM-KH mean solvation forces, compared to the average physical folding time of 4-9 μs observed in experiment.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

Multiple time scale molecular dynamics for fluids with orientational degrees of freedom. I. Microcanonical ensemble

We propose a new approach to eliminate the resonance instabilities inherent in multiple time step molecular dynamics simulations. The approach is developed within the microcanonical ensemble on the basis of an energy-constrained technique in the presence of orientational degrees of freedom. While the single and standard multiscale methods are restricted to small time steps of 5 and 8 fs, respectively, it is shown in simulations of water that the algorithms we have derived postpone the appearance of the instabilities to larger steps of about 16 fs. Such steps are close to the upper theoretical limit of 20 fs peculiar to the microcanonical ensemble and can be used without affecting static and dynamical properties.

Multiple time step molecular dynamics simulation for interaction between dislocations and grain boundaries

A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries.

Computer Simulation Studies of Finite Temperature Conformational Equilibrium in Alanine-Based Peptides

Conformational equilibria in two poly-alanine and one lysine-doped poly-alanine peptide, [Ala8]+, [Ala16]+, and [Ac−(AAAAK)3A−NH2]3+, respectively, has been examined in both gas and water solution phase by computer simulation. The simulations studies were carried out using recently developed two-dimensional umbrella sampling techniques coupled to novel extended system multiple time step molecular dynamics methods. The efficiency of the latter method permitted run lengths greater than 30 ns to be used in the studies. The in vacuo simulation results are compared to recent novel gas-phase experimental studies employing drift tubes coupled to mass spectrometers (the injected-ion mobility/MS technique). Simulation studies of the peptides and neutralizing chloride anions solvated in computer water are compared to solution-phase NMR and ESR experimental work. Solvent effects are elucidated through a comparison of in vacuo and solution-phase simulation results. Comparisons between the results generated for the three different peptides are performed in order to assess the effect of the lysine side-chain and the position of the positive charge on peptide conformational equilibria in the two environments. The results indicate that the 3K peptide is roughly helical in a vacuum as well as in solution. The [Ala16]+ and [Ala8]+ form compact states in a vacuum in order to solvate the charge on the N-terminus. In water solution, the [Ala16]+ uncompacts but does not become strongly α-helical.

Two dimensional umbrella sampling techniques for the computer simulation study of helical peptides at thermal equilibrium: The 3K(I) peptide in vacuo and solution

New computational techniques are developed to study conformational equilibrium in helical peptides at finite temperature. Two dimensional umbrella sampling methods involving coordinate systems which incorporate the α-helical hydrogen bonding distances along the peptide backbone as collective variables are presented. The umbrella sampling techniques are combined with new extended system multiple time step molecular dynamics simulation methods to allow peptide equilibria to be examined on a realistic potential energy surface. In particular, this combination of methods is employed to study a sixteen residue alanine-based peptide, Ac−(AAAAK)3A−NH2, at T=300 K in vacuo and solution, under the all-atom CHARMM22 force field. The efficiency of the multiple time step integration methodology permitted a minimum total run length of 30 ns to be employed in each umbrella sampling calculation reported.

Classical molecular simulations of complex, industrially-important systems on the intel paragon

Advances in parallel supercomputing now make possible molecular-based engineering and science calculations that will soon revolutionize many technologies, such as those involving polymers and those involving aqueous electrolytes. We have developed a suite of message-passing codes for classical molecular simulation of these industrially-important systems on the Intel Paragon and summarize some of the results. Nonequilibrium, multiple time step molecular dynamics lets us investigate the rheology of molecular fluids. Chain molecule Monte Carlo simulations in the Gibbs ensemble permit calculation of phase equilibrium of long-chain molecular systems. Complementary equilibrium molecular dynamics yields fundamental insight into the technologically-important problem of liquid-liquid phase separation in polymer blends. Parallel codes for quaternion dynamics using techniques for handling long-range Coulombic forces allow study of ion pairing in supercritical aqueous electrolyte solutions.

Computer simulation of a model 2–2 electrolyte: Multiple time-step molecular dynamics

A popular model of a 2–2 electrolyte is simulated using a multiple time-step molecular dynamics algorithm. Many authors have used this particular model to test approximate statistical mechanical theories. The ions are assumed to be the same size, and to interact via a continuous potential which behaves as a Coulomb potential at large distances and as an inverse ninth power repulsion at short distances. The ions are embedded in a dielectric continuum of fixed dielectric constant, here taken to be 78.358 to model water at 25 °C. The multiple time-step algorithm outlined here is essential to the success of the simulation. The structure, thermodynamics, and clustering of ions in the electrolyte are examined over the full range of concentrations. Significant corrections are found to earlier Monte Carlo simulations at the concentration 0.005 M, and new results are presented at the concentration 0.001 M.