Robert D. Skeel

Scalable Molecular Dynamics with NAMD

NAMD is a parallel molecular dynamics code designed for high‐performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high‐end parallel platforms, as well as tens of processors on low‐cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. Features for steering the simulation across barriers and for calculating both alchemical and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomolecular system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the molecular graphics/sequence analysis software VMD and the grid computing/collaboratory software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.

Langevin stabilization of molecular dynamics

In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brunger–Brooks–Karplus–Molly (BBK–M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK–M uses the popular Brunger–Brooks–Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps−1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK–M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein–DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK–M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps−1 is used the dynamics are not significantly distorted.

NAMD: a Parallel, Object-Oriented Molecular Dynamics Program

NAMD is a molecular dynamics program designed for high performance simulations of large biomolecular systems on parallel computers. An object-oriented design imple mented using C++ facilitates the incorporation of new algorithms into the program. NAMD uses spatial decom position coupled with a multithreaded, message-driven design, which is shown to scale efficiently to multiple processors. Also, NAMD incorporates the distributed par allel multipole tree algorithm for full electrostatic force evaluation in O(N) time. NAMD can be connected via a communication system to a molecular graphics program in order to provide an interactive modeling tool for viewing and modifying a running simulation. The application of NAMD to a protein-water system of 32,867 atoms illus trates the performance of NAMD.

A method for the spatial discretization of parabolic equations in one space variable

This paper is concerned with the design of a spatial discretization method for polar and nonpolar parabolic equations in one space variable. A new spatial discretization method suitable for use in a library program is derived. The relationship to other methods is explored. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithm and to compare it with other recent codes.

Scaling for Numerical Stability in Gaussian Elimination

Roundoff error m the solution of hnear algebraic systems is stud,ed using a more reahstsc notion of what st means to perturb a problem, namely, that each datum :s subject to a relatwely small change Th:s ,s particularly appropriate for sparse linear systems The condition number :s determined for th:s approach The effect of scahng on the stabdlty of Gaussmn ellmmat,on is stud:ed, and st is d:scovered that the proper way to scale a system depends on the right-hand s:de However, ff only the norm of the error is of concern, then there ~s a good way to scale that does not depend on the right-hand stde

Multiple grid methods for classical molecular dynamics.

Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of different time steps for different interactions allows longer time steps for many of the interactions, and this can be combined with multiple grids in space. Comparison is made to the fast multipole method, and evidence is presented suggesting that for molecular simulations multigrid methods may be superior to the fast multipole method and other tree methods.

Iterative refinement implies numerical stability for Gaussian elimination

Because of scaling problems, Gaussian elimination with pivoting is not always as accurate as one might reasonably expect. It is shown that even a single iteration of iterative refinement in single precision is enough to make Gaussian elimination stable in a very strong sense. Also, it is shown that without iterative refinement row pivoting is inferior to column pivoting in situations where the norm of the residual is important.

Algorithms for constrained molecular dynamics

In molecular dynamics simulations, the fastest components of the potential field impose severe restrictions on the stability and hence the speed of computational methods. One possibility for treating this problem is to replace the fastest components with algebraic length constraints. In this article the resulting systems of mixed differential and algebraic equations are studied. Commonly used discretization schemes for constrained Hamiltonian systems are discussed. The form of the nonlinear equations is examined in detail and used to give convergence results for the traditional nonlinear solution technique SHAKE iteration and for a modification based on successive overrelaxation (SOR). A simple adaptive algorithm for finding the optimal relaxation parameter is presented. Alternative direct methods using sparse matrix techniques are discussed. Numerical results are given for the new techniques, which have been implemented in the molecular modeling software package CHARMM and show as much as twofold improvement over SHAKE iteration.

An impulse integrator for Langevin dynamics

The best simple method for Newtonian molecular dynamics is indisputably the leapfrog Stormer-Verlet method. The appropriate generalization to simple Langevin dynamics is unclear. An analysis is presented comparing an ‘impulse method’ (kick; fluctuate; kick), the 1982 method of van Gunsteren and Berendsen, and the Brünger-Brooks-Karplus (BBK) method. It is shown how the impulse method and the van Gunsteren-Berendsen methods can be implemented as efficiently as the BBK method. Other considerations suggest that the impulse method is the best basic method for simple Langevin dynamics, with the van Gunsteren-Berendsen method a close contender.

Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics

Numerical experiments are performed on a 36,000‐atom protein–DNA–water simulation to ascertain the effectiveness of two devices for reducing the time spent computing long‐range electrostatics interactions. It is shown for Verlet‐I/r‐RESPA multiple time stepping, which is based on approximating long‐range forces as widely separated impulses, that a long time step of 5 fs results in a dramatic energy drift and that this is reduced by using an even larger long time step. It is also shown that the use of as many as six terms in a fast multipole algorithm approximation to long‐range electrostatics still fails to prevent significant energy drift even though four digits of accuracy is obtained. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1785–1791, 1997