The Stochastic Elastica and Excluded-Volume Perturbations of DNA Conformational Ensembles

A coordinate-free Lie-group formulation for generating ensembles of DNA conformations in solution is presented. In this formulation, stochastic differential equations define sample paths on the Euclidean motion group. The ensemble of these paths exhibits the same behavior as solutions of the Fokker-Planck equation for the stochastically forced elastica. Longer chains for which the effects of excluded volume become important are handled by piecing together shorter chains and modeling their interactions. It is assumed that the final chain lengths of interest are long enough for excluded volume effects to become important, but not so long that the semi-flexible nature of the chain is lost. The effect of excluded volume is then taken into account by grouping short self-avoiding conformations into 'bundles' with common end constraints and computing average interaction effects between bundles. The accuracy of this approximation is shown to be good when using a numerically generated ensemble of self-avoiding sample paths as the baseline for comparison.