Stochastic modeling of the structure and mechanical properties of the DNA

Abstract

Decades of experimentation on the DNA, including recent micromanipulations at the single-molecule level, have provided information that could guide and constrain theoretical models for the DNA. In an effort to understand better the mechanical properties of DNA, an experimentally inspired model is presented in this talk which accommodates the following observed features:

1. an underlying Brownian motion of a DNA;
2. the formation of a helical structure for the DNA;
3. information embodied by the sequence of DNA bases;
4. the presence of left-handed and right-handed DNA; and
5. a DNA molecule which overwinds when stretched.

Various experiments have validated the modeling of polymer configurations as Brownian paths. In a polymer entanglement scenario, the basic helical structure of a DNA strand can also be induced by a radial-dependent potential V(r) (in circular cylindrical coordinates) for low temperatures. In the present model, we augment this picture by simulating the data encoded by the sequence of bases along the DNA strand by a potential, U(s)=(df/ds)q, where f(s) is a modulating function. Using white noise analysis, one can explicitly calculate the probabilities for various winding configurations of a DNA strand which are significantly influenced by f(s). Moreover, a proper choice of the modulating function f(s) allows one to model the recently reported overwinding of the DNA when stretched until a critical value is reached.