Intrachain reactions of supercoiled DNA simulated by Brownian dynamics

We considered an irreversible biochemical intrachain reaction of supercoile d DNA as a random event that occurs, with certain probability, at the insta nt of collision between two reactive groups bound to distant DNA sites. Usi ng the Brownian dynamics technique, we modeled this process for a supercoil ed DNA molecule of 2.5 kb length in dilute aqueous solution at an NaCl conc entration of 0.1 M. We calculated the mean reaction time tau (Sigma) as a f unction of the intrinsic second-order rate constant k(I), the reaction radi us R, and the contour separation S of the reactive groups. At the diffusion -controlled limit (k(I) --> infinity), the kinetics of reaction are determi ned by the mean time tau (F) of the first collision. The dependence of tau (F) on R is close to inversely proportional, implying that the main contrib ution to the productive collisions is made by bending of the superhelix axi s. At sufficiently small k(I), the mean reaction time can be satisfactory a pproximated by tau (Sigma) = tau ((app))(F) + 1/k(I)C(L), where C-L is the local concentration of one reactive group around the other, and tau ((app)) (F) is an adjustable parameter, which we called the apparent time of the fi rst collision. The value of tau ((app))(F) depends on R very weakly and is approximately equal to the mean time of the first collision caused by mutua l reptation of two DNA strands forming the superhelix. The quasi-one-dimens ional reptation process provides the majority of productive collisions at s mall k(I) values.