Cyclization of a polymer with charged reactive end groups

We calculate the cyclization rate k(t) of a single polymer chain with charged end groups, where cyclization takes place with probability of one when the ends approach each other at a distance smaller than the reaction radius R. Using Monte Carlo simulations in a kink-jump model we show that the long-time asymptotic value of k for longer chains and attractive Coulomb interaction does not depend on R, but depends strongly on the Onsager radius, which characterizes the strength of electrostatic interaction. This result relies only on the large-scale behavior of the chain and is reproduced within a simple harmonic-spring approximation. The harmonic-spring model leads to a diffusion equation which is solved numerically. The solution for long chains is confirmed with analytical approximations.