Monte Carlo Simulation of DNA Topological Properties

Abstract

In the scale of hundreds and thousands of base pairs, DNA double helix is very flexible polymer chain that adopts many different conformations in solution. The properties of such molecules have to be analyzed in terms of statistical mechanics. Now these properties can be simulated with very good accuracy. Here we review this simulation technique, with the emphasis on topological properties of circular DNA. We describe the basic concepts related with DNA topological properties and illustrate, by comparing simulation results with the experimental data, how accurately these properties can be computed. We consider DNA model used in the simulation, methods of sampling of the statistical ensemble, simulation of DNA supercoiling, and different problems, related with knots and links in circular DNA. To analyze topological state of closed chain one needs to calculate a topological invariant. We describe the algorithms that allow one to compute one of such invariants, the Alexander's polynomial, which is especially suitable for the Monte Carlo simulation. At the end, we consider special methods of sampling for rare DNA conformations.