Laplace approximation of J factors for rigid base and rigid basepair models of DNA cyclization

Abstract

We apply the Laplace approximation to a mathematical formulation of DNA cyclization J factors, leading to a formula that involves energies of local minima of the DNA energy, factors coming from the Hessian of the energy near each minimum, and geometric factors arising from the orientational portion of J. The approximation is derived in a quite general setting that encompasses both rigid base and rigid basepair models common in the literature. The approximation is applied to several families of 200-400 bp DNA, some relatively straight (fragments of λ-phage) and others quite bent (constructs that include up to 10 A tracts). The accuracy of the approximation is assessed by comparing with (more time-consuming) Monte Carlo computations: Laplace is within 20% of Monte Carlo for most 200 bp molecules and undershoots Monte Carlo by about 30% for 300 bp and 50% for 400 bp. We explore length and sequence dependence, both for our overall approximation of J and for its energy and entropic components, and make comparisons to a different approximation of J proposed in the literature.