Approach to Monte Carlo calculation of the buckling of supercoiled DNA loops

The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A Monte Carlo algorithm is developed to alleviate the problem of "ergodicity breaking'' of the glassy systems, in which the Markov process is driven by an explicitly analytic weight factor with enhanced probability in both low- and high-energy regions. To characterize the degree of puckering of the supercoiled DNA loops, a different quantity of aplanarity is introduced as the shortest principal axis of configurational ellipsoid of DNA. With the suggested Monte Carlo method, the quantitative correlation between supercoiling degree and buckling of DNA is attained. With supercoiling stress increasing, the conformational transition from a circle to mono-, diplo-, or triple interwound superhelical structure will take place in a successive but decreasingly abrupt mode.