Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

Inference of macromolecular assemblies from crystalline state.

We describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a number of powerful tools of modern computational chemistry, focused on molecular dynamics and free energy calculations of proteins, nucleic acids, and carbohydrates.

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The Amber biomolecular simulation programs

Evaluation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to elucidate the electrostatic potential is the Poisson-Boltzmann equation; however, existing methods for solving this equation have limited the scope of accurate electrostatic calculations to relatively small biomolecular systems. Here we present the application of numerical methods to enable the trivially parallel solution of the Poisson-Boltzmann equation for supramolecular structures that are orders of magnitude larger in size. As a demonstration of this methodology, electrostatic potentials have been calculated for large microtubule and ribosome structures. The results point to the likely role of electrostatics in a variety of activities of these structures.

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Electrostatics of nanosystems: Application to microtubules and the ribosome

Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program

Electrostatics in biomolecular structure and dynamics

Numerical solutions of the Poisson-Boltzmann equation (PBE) have found wide application in the computation of electrostatic energies of hydrated molecules, including biological macromolecules. However, solving the PBE for electrostatic forces has proved more difficult, largely because of the challenge of computing the pressures exerted by a high dielectric aqueous solvent on the solute surface. This paper describes an accurate method for computing these forces. We begin by presenting a novel derivation of the forces acting in a system governed by the PBE

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Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation

Comparisons have been made between relaxation methods and certain preconditioned conjugate gradient techniques for solving the system of linear equations arising from the finite-difference form of the linearized Poisson-Boltzmann equation. The incomplete Cholesky conjugate gradient (ICCG) method of Meijerink and van der Vorst has been found to be superior to relaxation methods, with at least a factor of two improvement in speed, and only a 50% increase in storage.

Solving the finite difference linearized Poisson‐Boltzmann equation: A comparison of relaxation and conjugate gradient methods

We compare the Particle-Particle Particle-Mesh (PPPM) and Ewald methods for calculating electrostatic interactions in periodic molecular systems. A brief comparison of the theories shows that the methods are very similar differing mainly in the technique which is used to perform the “k-space” or mesh calculation. Because the PPPM utilizes the highly efficient numerical Fast Fourier Transform (FFT) method it requires significantly less computational effort than the Ewald method and scales almost linearly with system size.

Malcolm E. Davis

Papers

Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program

Electrostatics in biomolecular structure and dynamics

Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation

Solving the finite difference linearized Poisson‐Boltzmann equation: A comparison of relaxation and conjugate gradient methods

A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods for Calculating Electrostatic Interactions in Periodic Molecular Systems