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

AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM Methods for Biomolecular Systems

Intermolecular And Surface Forces

HYDROGEN bonds play a crucial role in the behaviour of water1–4; their spatial patterns and fluctuations characterize the structure and dynamics of the liquid5–7. The processes of breaking and making hydrogen bonds in the condensed phase can be probed indirectly by a variety of experimental techniques8, and more quantitative information can be obtained from computer simulations9. In particular, simulations have revealed that on long timescales the relaxation behaviour of hydrogen bonds in liquid water exhibit non-exponential kinetics7,10–13, suggesting that bond making and breaking are not simple processes characterized by well defined rate constants. Here we show that these kinetics can be understood in terms of an interplay between diffusion and hydrogen-bond dynamics. In our model, which can be extended to other hydrogen-bonded liquids, diffusion governs whether a specific pair of water molecules are near neighbours, and hydrogen bonds between such pairs form and persist at random with average lifetimes determined by rate constants for bond making and breaking.

Hydrogen-bond kinetics in liquid water

Four recently proposed intermolecular-potential models have been used in molecular-dynamics simulations of liquid methanol over a temperature range of approximately 70 K. Results are reported for thermodynamic and structural properties, self-diffusion coefficients, and reorientational correlation times. Two of the models are shown to give results in fair agreement with a wide variety of experimental data. The pattern of hydrogen bonding and the distribution of hydrogen-bond lifetimes in the simulated liquids have been investigated. The structure in each case is found to be dominated by winding chains, in agreement with earlier work. For the more realistic models, the mean hydrogen-bond lifetime at room temperature is approximately 1 to 2 ps, which is several times larger than the corresponding time for liquid water.

Molecular-dynamics simulation of liquid methanol

Effective pair‐potential models, parametrized to the properties of the pure liquids, have been used in molecular‐dynamics simulations of aqueous (binary) mixtures containing methanol, ammonia, or acetone. Results are reported for thermodynamic and structural properties, self‐diffusion coefficients, and reorientational correlation times. There is fair agreement with a wide variety of experimental data. The pattern of hydrogen bonding and the distribution of hydrogen‐bond lifetimes in the simulated mixtures have been investigated. The observed anomalous behavior of methanol and acetone solutions appears to be related to specific features of the hydrogen bonding—namely, the ability of these molecules to exhibit enhanced acceptor character. As a consequence of the assumed intermolecular potentials, the balance between the competing effects of hydrophobic hydration of methyl groups and hydrogen bonding to oxygen atoms is tipped towards the latter. A number of interesting structural effects have been noted. In ...

Molecular-dynamics simulation of aqueous mixtures : methanol, acetone, and ammonia

The dynamics of rigid polyatomic systems, either molecules or rigid portions of large molecules, is described by cartesian equations of motion for its atoms. In comparison with the original version of the method of constraints

Molecular dynamics of rigid systems in cartesian coordinates: A general formulation

A constrained molecular dynamics (MD) method for the calculation of the potential of mean force is described, and applied to study the solvent-separated and contact ion pair equilibrium in a polar solvent. The method uses holonomic constraints on the MD to fix ion pair internuclear separation. The average force exerted on the ions by the solvent is computed as a function of ion separation, and the potential of mean force follows from an integration of the mean force. The ion pair mean potential, the reaction equilibrium constant and the solvent structure in the vicinity of the ions are examined for two model solvents with differing molecular dipole moments. The relevance of this study for the dynamics of the contact ion pair-solvent separated ion pair reaction is pointed out.

Constrained molecular dynamics and the mean potential for an ion pair in a polar solvent

The reaction rate and mechanism of the interconversion between a contact ion pair and solvent separated ion pair in model polar solvents is investigated by molecular dynamics (MD) simulation. The full rate constant for the model reaction is estimated from the product of the transition state theory (TST) rate constant, determined from the potential of mean force between the ions in an equilibrium solvent, and the transmission coefficient, which depends on the details of the dynamics. The collective character of the solvent motion in the reaction barrier crossing is examined in some detail, and the important role of solvent dynamics in causing the reaction rate to markedly deviate from the TST rate is discussed. The MD results are compared with the predictions of Kramers and Grote–Hynes theories.

Mauro Ferrario

Papers

Molecular-dynamics simulation of liquid methanol

Molecular-dynamics simulation of aqueous mixtures : methanol, acetone, and ammonia

Molecular dynamics of rigid systems in cartesian coordinates: A general formulation

Constrained molecular dynamics and the mean potential for an ion pair in a polar solvent

Dynamics of ion pair interconversion in a polar solvent