We study the system-size dependence of translational diffusion coefficients and viscosities in molecular dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coefficients increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N -1/3, where N is the number of particles. For a cubic simulation box of length L, the diffusion coefficient corrected for system-size effects is D 0 = D PBC + 2.837297k B T/(6πηL), where D PBC is the diffusion coefficient calculated in the simulation, k B the Boltzmann constant, T the absolute temperature, and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quantitatively accounts for the system-size dependence of the calculated self-diffusion coefficients. In contrast to diffusion coefficients, the shear viscosities of water and the LJ fluid show no significant system-size dependences.

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

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End-to-end contact formation rates of several peptides were recently measured by tryptophan triplet quenching (Lapidus et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 7220). Motivated by these experiments, we study loop-closure kinetics for two peptides of different lengths, Cys-(Ala-Gly-Gln)n-Trp (n = 1, 2), in multiple all-atom explicit-solvent molecular dynamics simulations with different initial conditions and force fields. In 150 simulations of approximately 20 ns each, we collect data covering 1.0 and 0.8 micros for the penta-peptide simulated with the AMBER and CHARMM force fields, respectively, and about 0.5 micros each with the two force fields for the octa-peptide. These extensive simulations allow us to analyze the dynamics of peptides in the unfolded state with atomic resolution, thus probing early events in protein folding, and to compare molecular dynamics simulations directly with experiment. The calculated lifetimes of the tryptophan triplet state are in the range of 50-100 ns, in agreement with experimental measurements. However, end-to-end contacts form more rapidly, with characteristic times less than 10 ns. The contact formation rates for the two force fields are similar despite differences in the respective ensembles of peptide conformations.