Statistics of loop formation along double helix DNAs.

We compute relative position distributions of distant sites along discretized semiflexible polymers, focusing on encounter statistics for pairs of sites along a double-stranded DNA molecule (dsDNA), using a transfer-matrix approach. We generalize the usual semiflexible polymer, considering nonlinear elasticity effects arising from inhomogeneities which either appear at any position via thermal fluctuation, or which occur at specific "quenched" locations. We apply our theory to two problems associated with dsDNA looping. First, we discuss how local flexible defects in double-helix structure facilitate cyclization of short dsDNA molecules. Flexible defects greatly enhance cyclization rate, and strongly modify its dependence on the closure orientational boundary condition. This effect is relevant to free-solution cyclization experiments, and to loop formation in vivo. Second, we present calculations of force dependence of the probability of formation of loops along single dsDNAs which show how the probability of loop formation is suppressed by tension.