Equations of motion for polymer chains in a thermostat

Abstract

A constrained dynamics method suitable for molecular dynamics simulations is considered to study the long-time dynamics of polymer chains. The method is initially discussed on the basis of the Lagrangian and Hamiltonian formalisms for isolated polymer chains with fixed monomer–monomer links. Subsequently, the corresponding equations of motion are obtained for describing the dynamics of such polymer chains in the presence of a thermostat. The approach is applied to a few typical cases to illustrate how the formalism is implemented numerically and to elucidate its convergence properties when studying such systems in equilibrium. As an example, we consider the problem of reconstructing the backbone structure (chain of Cα atoms) of protein Rubredoxin from its contact matrix. It is shown that the target structure is succesfully reached after a long transient regime (typically in the range from 106 to 108 integration steps). A particular attractive extension of the algorithm presented here is to environment-dependent couplings, which could allow the study of the long-time polymer dynamics in realistic environments. The present method is thus expected to have useful applications in the modelling of the complex dynamics of bio-polymers such as proteins, and also in the context of nanoscale polymer materials.