Brownian dynamics study of a polymer chain of linked rigid bodies

Abstract

A Brownian dynamics model for the backbone chain of a macromolecule is developed as a system of linked rigid bodies so that constraints on valence angles and bond lengths are satisfied exactly. For comparison, a corresponding flexible model is developed in which bond lengths and valence angles are held nearly constant by strong harmonic potentials. Equilibrium properties and barrier crossing rates are examined theoretically and by computer simulation of both models, with differences arising due to the presence of constraints in the rigid case. A compensating potential based on the metric determinant of unconstrained coordinates in the rigid model is found to eliminate the effect of constraints. Barrier crossing rates in the transition state approximation are studied when a force fixed in space is applied to the end atoms of the three-bond chain. An exact transition state rate formula developed for this case predicts curved Arrhenius plots of barrier crossing rates; this result is confirmed by computer simulation.