Molecular modeling of closed circular DNA thermodynamic ensembles

Many modeling studies of supercoiled DNA are based on equilibrium structures from theoretical calculations or energy minimization. Since closed circular DNAs are flexible, it is possible that errors are introduced by calculating properties from a single minimum energy structure, rather than from a complete thermodynamic ensemble. We have investigated this question using molecular dynamics simulations on a low resolution molecular mechanics model in which each base pair is represented by three points (a plane). This allows the inclusion of sequence-dependent variations of tip, inclination, and twist. Three kinds of sequences were tested: (1) homogeneous DNA, in which all base pairs have the helicoidal parameters of an ideal, average B-DNA; (2) random sequence DNA; and (3) curved DNA. We examined the rate of convergence of various structural parameters. Convergence for most of these is slowest for homogeneous sequences, more rapid for random sequences, and most rapid for curved sequences. The most slowly converging parameter is the antipodes profile. In a plasmid with N base pairs (bp), the antipodes distance is the distance dij from base pair i to base pair j halfway around the plasmid, j = i + N/2. The antipodes profile at time tau is a plot of dij over the range i = 1, N/2. In a homogeneous plasmid, convergence requires that the antipodes profile averaged over time must be flat. Even in the small plasmids examined here, the average properties of the ensembles were found to differ from those of static equilibrium structures. These effects will be even more dramatic for larger plasmids. Further, average and dynamic properties are affected by both plasmid size and sequence.