Kinetics of intrachain reactions of supercoiled DNA: Theory and numerical modeling

We considered an irreversible biochemical intrachain reaction of supercoile d DNA as a random event that occurs, with some probability, at the instant of collision between two reactive groups attached to distant sites of the D NA molecule. For sufficiently small intrinsic rate constant k(I), the domin ant process contributing to the productive collisions is the quasione-dimen sional reptation of the strands forming the superhelix. The mean reaction t ime is then given by tau (F) + 1/k(I)c(L), where tau (F) is the mean time o f the first collision caused by reptation, and c(L) is the local concentrat ion of one reactive group around the other. The internal reptation of DNA s trands was simulated by the repton model, in which a superhelix branch is a pproximated by a string of beads placed in a row of cells. This simple mode l allows semiquantitative estimation of tau (F) and c(L) (in some arbitrary units) for a large range of the DNA lengths L. The repton chain was calibr ated with the help of the data available for small supercoiled plasmids fro m Monte Carlo and Brownian dynamics simulations. The repton model and the B rownian dynamics give the same form of the distribution of the first collis ion time. Our estimations show that, for opposite sites of the chain, the m ean first collision time tau (F) varies from 5 ms (L = 2.5 kb) to 1 s (L = 20 kb). The corresponding c(L) values (for the reaction radius 10 nm) are 3 x 10(-6) and 2 x 10(-7) M. (C) 2001 American Institute of Physics.