Interfacing molecular dynamics with continuum dynamics in computer simulation: Toward an application to biological membranes

A clear challenge in the field of computer simulation of biological systems is to develop a simulation methodology that incorporates the vast temporal and spatial scales observed in living systems. At present, simulation capabilities generally operate in either microscopic or macroscopic regimes. Microscopic molecular dynamics simulations can examine systems up to the order of 100000 atoms on time scales of the order of nanoseconds. This is still orders of magnitude below the scales required to model complete biological structures such as a living cell. Continuum-based simulations, frequently employed in mechanical engineering problems, can model complete biological assemblies but do not contain any explicit molecular information. To fully capture the intricate interplay between microscopic processes and macroscopic events, a method of "information transfer" between these two disparate time and length scales is required. We present a new simulation methodology based on fundamental aspects of statistical and continuum mechanics that allows microscopic fluctuations to propagate to macroscopic scales and vice versa. A feedback mechanism is developed in which microscopic-level molecular dynamics simulations are coupled to corresponding macro-scale continuum-level simulations. The techniques of non-equilibrium molecular dynamics are used to create the micro-to-macro interface, where transport coefficients that are required input at the continuum level are calculated from detailed microscopic models. We present results for a model membrane in which the material is modeled at both spatial and temporal levels. The effect of non-elastic perturbations at the molecular level on macroscopic material properties is examined as a demonstration of the viability of the technique.