Monte Carlo Simulations of Supercoiled DNAs Confined to a Plane

Abstract

Recent advances in atomic force microscopy (AFM) have enabled researchers to obtain images of supercoiled DNAs deposited on mica surfaces in buffered aqueous milieux. Confining a supercoiled DNA to a plane greatly restricts its configurational freedom, and could conceivably alter certain structural properties, such as its twist and writhe. A program that was originally written to perform Monte Carlo simulations of supercoiled DNAs in solution was modified to include a surface potential. This potential flattens the DNAs to simulate the effect of deposition on a surface. We have simulated transfers of a 3760-basepair supercoiled DNA from solution to a surface in both 161 and 10 mM ionic strength. In both cases, the geometric and thermodynamic properties of the supercoiled DNAs on the surface differ significantly from the corresponding quantities in solution. At 161 mM ionic strength, the writhe/twist ratio is 1.20–1.33 times larger for DNAs on the surface than for DNAs in solution and significant differences in the radii of gyration are also observed. Simulated surface structures in 161 mM ionic strength closely resemble those observed by AFM. Simulated surface structures in 10 mM ionic strength are similar to a minority of the structures observed by AFM, but differ from the majority of such structures for unknown reasons. In 161 mM ionic strength, the internal energy (excluding the surface potential) decreases substantially as the DNA is confined to the surface. Evidently, supercoiled DNAs in solution are typically deformed farther from the minimum energy configuration than are the corresponding surface-confined DNAs. Nevertheless, the work ( ΔA int) done on the internal coordinates, which include uniform rotations at constant configuration, during the transfer is positive and 2.6-fold larger than the decrease in internal energy. The corresponding entropy change is negative, and its contribution to ΔA int is positive and exceeds the decrease in internal energy by 3.6 fold. The work done on the internal coordinates during the solution-to-surface transfer is directed primarily toward reducing their entropy. Evidently, the number of configurations available to the more deformed solution DNA is vastly greater than for the less deformed surface-confined DNA.