DNA looping is the name given to a biological process in which short segments of DNA (40-400 basepairs) deform to meet some boundary conditions; cyclization is the special case of periodic boundary conditions. Several recent cyclization experiments have revealed special DNA sequences with unusually high flexibility, out of sync with current models. We consider two discrete models of DNA---one that treats the basepairs as rigid and one that treats the individual bases as rigid---with an eye toward new flexibility parameters that may be able to explain the high-flexibility experiments.

A key mathematical quantity to model DNA looping or cyclization is an end-to-end probability density function (pdf) on R^3 x SO(3), the configuration space for one end of the DNA, once the other hand is fixed by choice of coordinates. Monte Carlo simulations allow direct sampling of this pdf, although the typical values of the pdf are small enough that it can be challenging to get decent statistics. A semiclassical approach, which finds local minimizers of the DNA energy and computes contributions to the pdf based on a quadratic expansion about the minimizer, is much faster, but its accuracy largely unexplored.

We present some preliminary results, including a comparison to classical DNA results of the dependence of cyclization probability on the number of basepairs and the consideration of all possible boundary conditions for "2D looping" of an elastic rod. For these examples, we assess the accuracy of the semiclassical approximation and consider possible improvements.