The dynamics of loop formation in a semiflexible polymer

TL;DR

This paper models the loop formation dynamics in semiflexible polymers using a multidimensional diffusion approach, providing new insights into the process that are more realistic than previous flexible chain models.

Contribution

It introduces a detailed multidimensional analysis of loop formation in semiflexible polymers, extending previous work on chain opening dynamics.

Findings

Calculated closing times for semiflexible chains

Provided a physically consistent model for loop formation

Extended understanding of semiflexible polymer dynamics

Abstract

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical/experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study (K. P. Santo and K. L. Sebastian, Phys. Rev. E, \textbf{73}, 031293 (2006)), we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit, based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain which leads to results that are physically expected. Such a multidimensional analysis leading to these results does not seem to exist in the literature so far.