Diffusion-assisted long-range reaction between the ends of a polymer: Effective sink approximation

Abstract

We report a Brownian dynamics (BD) simulation study of the Förster energy transfer in a dye-labeled Rouse polymer chain. The simulation method is based on the normal mode BD propagation and numerical path integration of the survival probability. It is shown that a properly constructed truncated normal-mode approximation (TNMA) can speed up the simulations considerably, without essential loss of accuracy. In particular, an effective-sink TNMA scheme is found to be quite efficient. The idea is based on a standard time scale separation ansatz, where all the normal modes are separated into slow and fast, in terms of the corresponding relaxation times. The fast normal modes are assumed to be equilibrated in the course of reaction and thus can be integrated out. Their effect is to modify the reaction sink for the slow modes. The first-order approximation can be handled most easily, without a simulation. Even this simple approximation can be preferable to the well-known Wilemski–Fixman approximation, if the reaction sink is wide, i.e., when the Förster radius exceeds the polymer mean bond length, the condition often chosen in experiments on polymer folding.