The dynamics of chain closure in semiflexible polymers

The mean first passage time of cyclization τ of a semiflexible polymer with reactive ends is calculated using the diffusion-reaction formalism of Wilemski and Fixman [J. Chem. Phys. 60, 866 (1974)]. The approach is based on a Smoluchowski-type equation for the time evolution, in the presence of a sink, of a many-body probability distribution function. In the present calculations, which are an extension of work carried out by Pastor et al. [J. Chem. Phys. 105, 3878 (1996)] on completely flexible Gaussian chains, the polymer is modeled as a continuous curve with a nonzero energy of bending. Inextensibility is enforced on average through chain-end contributions that suppress the excess fluctuations that lead to departures from the Kratky–Porod result for the mean-square end-to-end distance. The sink term in the generalized diffusion equation that describes the dynamics of the chain is modeled as a modified step function along the lines suggested by Pastor et al. Detailed calculations of τ as a function of the chain length N, the reaction distance a, and the stiffness parameter z are presented. Among other results, τ is found to be a power law in N, with a z-dependent scaling exponent that ranges between about 2.2–2.4.