Partition function of a bubble formed in double stranded DNA

TL;DR

This paper calculates the entropic contribution to the partition function of a bubble in double-stranded DNA, incorporating models of chain configurations and self-avoidance effects to refine the loop closure exponent.

Contribution

It introduces a detailed calculation of the bubble's partition function considering chain configurations and self-avoidance, refining the loop closure exponent value.

Findings

Loop closure exponent c is 3 for Gaussian chains.

Including self-avoidance increases c to 3.2.

Distribution of bubble separation follows wormlike chain model.

Abstract

We calculate the entropic part of partition function of a bubble embedded in a double stranded DNA (dsDNA) by considering the total weights of possible configurations of a system of two single stranded DNA (ssDNA) of given length which start from a point along the contour of dsDNA and reunite at a position vector {\bf r} measured from the first point and the distribution function of the position vector {\bf r} which separates the two zipper forks of the bubble in dsDNA. For the distribution function of position vector {\bf r} we use the distribution of the end-to-end vector {\bf r} of strands of given length of dsDNA found from the wormlike chain model. We show that when the chains forming the bubble are assumed to be Gaussian the so called loop closure exponent $c$ is 3 and when we made correction by including self avoidence in each chain the value of $c$ becames 3.2.