Theory for the nonequilibrium dynamics of flexible chain molecules: Relaxation to equilibrium of pentadecane from an all-trans conformation

Abstract

We extend to nonequilibrium processes our recent theory for the long time dynamics of flexible chain molecules. While the previous theory describes the equilibrium motions for any bond or interatomic separation in (bio)polymers by time correlation functions, the present extension of the theory enables the prediction of the nonequilibrium relaxation that occurs in processes, such as T-jump experiments, where there are sudden transitions between, for example, different equilibrium states. As a test of the theory, we consider the “unfolding” of pentadecane when it is transported from a constrained all-trans conformation to a random-coil state at thermal equilibrium. The time evolution of the mean-square end-to-end distance 〈Rend2(t)〉noneq after release of the constraint is computed both from the theory and from Brownian dynamics (BD) simulations. The lack of time translational symmetry for nonequilibrium processes requires that the BD simulations of the relaxation of 〈Rend2(t)〉noneq be computed from an average over a huge number of independent trajectories, rather than over successive configurations from a single trajectory, which may be used to generate equilibrium time correlation functions. Adequate convergence ensues for the nonequilibrium simulations only after averaging 9000 trajectories, each of 0.8 ns duration. In contrast, the theory requires only equilibrium averages for the initial and final states, which may be readily obtained from a few Brownian dynamics trajectories. Therefore, the new method produces enormous savings in computer time. Moreover, since both theory and simulations use identical potentials and solvent models, the theory contains no adjustable parameters. The predictions of the theory for the relaxation of 〈Rend2(t)〉noneq agree very well with the BD simulations. This work is a starting point for the application of the new method to nonequilibrium processes with biological importance such as the helix-coil transition and protein folding.