Evaluating Partition Functions for Multiscale Models of DNA

Abstract

Multiscale modeling has become a major focus in computational chemistry and biology in order to simulate systems of ever-increasing complexity. To properly treat such systems on multiple length scales, it is necessary to rigorously treat the momenta and coordinates of the individual entities that make up the system of interest. We use principles of polymer physics to model DNA on two different length scales: individual DNA base pairs and rigid cylinders composed of many base pairs. Our results yield rigorous expressions for the partition functions of these systems, from which equilibrium thermodynamic properties can be obtained. * )

The thermodynamics of DNA loop formation, from J to Z

“…where h is Planck's constant and β = 1/(k B T). Here H{x, p, θ, l} = N k=1 T k ( p k , l k ) + U tot {x, θ} is the sum of kinetic energy terms plus the total potential energy U tot expressed as functions of non-canonical momenta {p,l} and co-ordinates {x,θ }, with the Jacobian for the transformation from canonical to non-canonical variables [39]. The integration is performed over all segments of the chain k and the three degrees of freedom for each segment a.…”