Benchmark of Schemes for Multiscale Molecular Dynamics Simulations.

In multiscale molecular dynamics simulations the accuracy of detailed models is combined with the efficiency of a reduced representation. For several applications - namely those of sampling enhancement - it is desirable to combine fine-grained (FG) and coarse-grained (CG) approaches into a single hybrid approach with an adjustable mixing parameter. We present a benchmark of three algorithms that use a mixing of the two representation layers using a Lagrangian formalism. The three algorithms use three different approaches for keeping the particles at the FG level of representation together: 1) addition of forces, 2) mass scaling, and 3) temperature scaling. The benchmark is applied to liquid hexadecane and includes an evaluation of the average configurational entropy of the FG and CG subsystems. The temperature-scaling scheme achieved a 3-fold sampling speedup with little deviation of FG properties. The addition-of-forces scheme kept FG properties the best but provided little sampling speedup. The mass-scaling scheme yielded a 5-fold speedup but deviated the most from FG properties.

Stochastic Dynamics with Correct Sampling for Constrained Systems.

In this paper we discuss thermostatting using stochastic methods for molecular simulations where constraints are present. For so-called impulsive thermostats, like the Andersen thermostat, the equilibrium temperature will differ significantly from the imposed temperature when a limited number of particles are picked and constraints are applied. We analyze this problem and give two rigorous solutions for it. A correct general treatment of impulsive stochastic thermostatting, including pairwise dissipative particle dynamics and stochastic forcing in the presence of constraints, is given and it is shown that the constrained canonical distribution is sampled rigorously. We discuss implementation issues such as second order Trotter expansions. The method is shown to rigorously maintain the correct temperature for the case of extended simple point charge (SPC/E) water simulations.

Efficient Algorithms for Langevin and DPD Dynamics.

In this article, we present several algorithms for stochastic dynamics, including Langevin dynamics and different variants of Dissipative Particle Dynamics (DPD), applicable to systems with or without constraints. The algorithms are based on the impulsive application of friction and noise, thus avoiding the computational complexity of algorithms that apply continuous friction and noise. Simulation results on thermostat strength and diffusion properties for ideal gas, coarse-grained (MARTINI) water, and constrained atomic (SPC/E) water systems are discussed. We show that the measured thermal relaxation rates agree well with theoretical predictions. The influence of various parameters on the diffusion coefficient is discussed.

Completion and refinement of 3-D homology models with restricted molecular dynamics: application to targets 47, 58, and 111 in the CASP modeling competition and posterior analysis.

A method is presented to refine models built by homology by the use of restricted molecular dynamics (MD) techniques. The basic idea behind this method is the use of structure validation software to determine for each residue the likelihood that it is modeled correctly. This information is used to determine constraints and restraints in an MD simulation including explicit solvent molecules, which is used for model refinement. The procedure is based on the idea that residues that the validation software identifies as correctly positioned should be strongly constrained or restrained in the MD simulations, whereas residues that are likely to be positioned wrongly should move freely. Two different protocols are compared: one (applied to CASP3 target T58) using full structural constraints with separate optimization of each short fragment and the other (applied to T47) allowing some freedom using harmonic restraining potentials, with automatic optimization of the whole molecule. Structures along the MD trajectory that scored best in structural checks were selected for the construction of models that appeared to be successful in the CASP3 competition. Model refinement with MD in general leads to a model that is less like the experimental structure (Levitt et al. Nature Struct Biol 1999;6:108-111). Actually, refined T47 was slightly improved compared to the starting model; changes in model T58 led not to further enhancement. After the X-ray structure of the modeled proteins became known, the procedure was evaluated for two targets (T47 and the CASP4 target T111) by comparing a long simulation in water with the experimental target structures. It was found that structural improvements could be obtained on a nanosecond time scale by allowing appropriate freedom in the simulation. Structural checks applied to fast fluctuations do not appear to be informative for the correctness of the structure. However, both a simple hydrogen bond count and a simple compactness measure, if averaged over times of typically 300 ps, correlate well with structural correctness and we suggest that criteria based on these properties may be used in computational folding strategies.