Diffusion-controlled intrachain reactions of supercoiled DNA: Brownian dynamics simulations

The Brownian Dynamics technique was used to model a diffusion-controlled in tramolecular reaction of supercoiled DNA (2500 basepairs) in 0.1 M sodium c hloride solution. The distance between the reactive groups along the DNA co ntour was 470 basepairs. The reaction radius was varied from 6 to 20 nm. Th e results are presented in terms of the probability distribution P-F(t) of the first collision time. The general form of the function P-F(t) could be correctly predicted by a simple analytical model of one-dimensional diffusi on of the superhelix ends along the DNA contour. The distribution P-F(t) is essentially non-exponential: within a large initial time interval, it scal es as P-F(t) similar to t(-1/2), which is typical for one-dimensional diffu sion. However, the mean time of the first collision is inversely proportion al to the reaction radius, as in three dimensions. A visual inspection of t he simulated conformations showed that a considerable part of the collision s is caused by the bending of the superhelix axis in the regions of the end loops, where the axis is most flexible. This fact explains why the distrib ution P-F(t) combines the features of one- and three-dimensional diffusion. The simulations were repeated for a DNA chain with a permanent bend of 100 degrees in the middle position between the reactive groups along the DNA c ontour. The permanent bend changes dramatically the form of the distributio n P-F(t) and reduces the mean time of the first collision by approximately one order of magnitude.