Theoretical analysis of the multicopy sampling method in molecular modeling

Abstract

Langevin Monte Carlo dynamics and equilibrium properties of the multicopy sampling approximation in the modeling of ligand–protein complexes are studied. A perturbation form is derived based on the normal mode analysis, and can be used as a quantitative means to estimate the approximation prior to running a multicopy simulation. The multicopy dynamics is shown to induce an average dynamics of the protein and all the ligand copies, resulting in a well-defined equilibrium with uniform temperature. The induced average dynamics and the equilibrium represent the desired physics of the multicopy approximation, and are extended to include heterogeneous ligand copies. Such an extension presents a natural way to incorporate biologically important information on evolution into energy-based molecular modeling of homologous proteins.