Santo, K. P. ; Sebastian, K. L. (2009) The Dynamics of loop formation in a semiflexible polymer Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 80 (6). 061801_1-061801_16. ISSN 1539-3755
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Official URL: http://pre.aps.org/abstract/PRE/v80/i6/e061801
Related URL: http://dx.doi.org/10.1103/PhysRevE.80.061801
Abstract
The dynamics of loop formation by linear polymer chains has been a topic of several theoretical and 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 73, 031923 (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 make use of the "closure approximation" of Wilemski and Fixman [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 878 (1974)], in which a sink function is used to represent the reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain. We show that for short chains, the loop formation time t decreases with the contour length of the polymer. But for longer chains, it increases with length obeying a power law and so it has a minimum at an intermediate length. In terms of dimensionless variables, the closing time is found to be given by τ~Lnexp(const/L), where n=4.5-6. The minimum loop formation time occurs at a length Lm of about 2.2-2.4. These are, indeed, the results that are physically expected, but a multidimensional analysis leading to these results does not seem to exist in the literature so far.
Item Type: | Article |
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Source: | Copyright of this article belongs to The American Physical Society. |
Keywords: | Polymers; Macromolecules; Molecular Biophysics; Diffusion-controlled Reactions |
ID Code: | 52971 |
Deposited On: | 04 Aug 2011 12:15 |
Last Modified: | 18 May 2016 06:18 |
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