Wormlike chain statistics with twist and fixed ends

Department of Chemical Engineering, Stanford University - Stanford, CA, USA

Received: 17 October 2005
Accepted: 5 January 2006

Abstract

We present the exact solution for the end-to-end statistics of a wormlike chain including twist stiffness and fixed-end orientations. Our results are expressed in Fourier-Laplace space as infinite continued fractions, which are concisely stated and easily employed in a wide range of problems involving semiflexible polymers that oppose twist deformation. We then apply our results to the J-factor or ring-closure probability of DNA. As our results are exact (i.e. non-perturbative), we find a measurable difference between the J-factor calculated from our results and approximate, perturbative theory; the error in the approximate theory stems in part from the absence of non-trivial topoisomers that are accounted for in our exact treatment.