We considered an irreversible biochemical intrachain reaction of supercoiled DNA as a random event that occurs, with certain probability, at the instant of collision between two reactive groups bound to distant DNA sites. Using the Brownian dynamics technique, we modeled this process for a supercoiled DNA molecule of 2.5 kb length in dilute aqueous solution at an NaCl concentration of 0.1 M. We calculated the mean reaction time τ∑ as a function of the intrinsic second-order rate constant kI, the reaction radius R, and the contour separation S of the reactive groups. At the diffusion-controlled limit (kI→∞), the kinetics of reaction are determined by the mean time τF of the first collision. The dependence of τF on R is close to inversely proportional, implying that the main contribution to the productive collisions is made by bending of the superhelix axis. At sufficiently small kI, the mean reaction time can be satisfactory approximated by τ∑=τF(app)+1/kIc L, where CL is the local concentration of one reactive group around the other, and τF(app) is an adjustable parameter, which we called the apparent time of the first collision. The value of τF(app) depends on R very weakly and is approximately equal to the mean time of the first collision caused by mutual reptation of two DNA strands forming the superhelix. The quasi-one-dimensional reptation process provides the majority of productive collisions at small kI values.
Klenin, K. V., & Langowski, J. (2001). Intrachain reactions of supercoiled DNA simulated by Brownian dynamics. Biophysical Journal, 81(4), 1924–1929. https://doi.org/10.1016/S0006-3495(01)75843-2