Equilibrium Configurations of the Noncircular Cross-Section Elastic Rod Model with the Elliptic KB Method

Abstract

The mechanical deformation of DNA is very important in many biological processes. In this paper, we consider the reduced Kirchhoff equations of the noncircular cross-section elastic rod characterized by the inequality of the bending rigidities. One family of exact solutions is obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behavior of the system in response to changes in physical parameters that concern asymmetry. The effects of the factor on the DNA conformation are discussed. A qualitative analysis is also conducted to provide valuable insight into the topological configuration of DNA segments.