A Mathematical Model for Basepair Opening in a DNA Double Helix

Abstract

In this paper, we consider a mathematical model that draws an analogy between a DNA molecule and a mechanical system consisting of two chains of interconnected pendulums. This model is designed to explore the dynamics of the system determined by rotational movements of nucleobases around a double-stranded pentose phosphate backbone. The workability of this model is assessed with respect to various factors: inhomogeneity of the chain of nucleobases, the properties of bonds in complementary pairs, and the formation of open states. It has been shown that simplified models for averaging the characteristics of the chain of nucleobases or simplification of the type of hydrogen bond in their complementary pairs influence the type of solution significantly, impairing the validity of the results. Therefore, the approach to the solution of rotational DNA molecule dynamics developed here is more consistent with its actual biomechanics. It is shown that the emergence of open states within nucleobase pairs and restoration of the closed structure may occur in the tested mathematical model.