A novel Method for Coarse Graining of Atomistic Simulations Using Boltzmann Inversion

Abstract

Molecular dynamics (MD) simulations play an important role in many physical, chemical and biological applications. To allow MD methods to be applied to sufficiently large systems and sufficiently long timescales, coarse grained (CG) molecular dynamics methods have been developed in which groups of atoms are represented by a single pseudo-atom, or coarse grained bead. In general, two groups of coarse-grained force-fields for molecular simulation exist, one in which standard form potentials are tuned to reproduce certain thermodynamic properties of a system of interest, and a second group in which potentials are chosen to reproduce simulation results from an atomistic MD simulation. This second procedure to develop a CG force field depends on the ability to map coarse grained particles on atoms in an atomistic simulation. An example of this is the Boltzmann inversion method, in which radial distribution functions are calculated between the mapped CG particles. For (macro)molecules that are mapped onto multiple CG centers this mapping is relatively straightforward. However, for small molecules, like water which is the basic component of most biophysically relevant systems, one must map a group of molecules onto a single CG particle. Finding the optimal division of molecules into groups for each frame of the atomistic trajectory is far from trivial. Here, a novel method is introduced that allows for this mapping of CG particles on a pre-fixed amount of molecules. Our coarse graining algorithm involves the optimization of the division of the molecules, using simulated annealing. The feasibility of the method is demonstrated on various systems containing either pure water, a water-octanol mixture or a solution of sodium chloride in water and may be very useful for large biological systems such as membranes in the future.