| A new model for simulating dynamic properties of long DNA is presented, combining features of both wormlike chain and bead models. Our goal is to use the model for millisecond Langevin dynamics simulations of both linear and closed circular DNA. The energy of the model chain includes stretching, bending, twisting, and electrostatic components. Beads are associated with each vertex of the chain and specify hydrodynamic properties of the DNA. Careful parameterization of the model is presented, and efficient algorithm are designed and applied. In particular, our modified second-order Brownian dynamics (BD) algorithm offers at a timestep {dollar}Delta t{dollar} = 600 ps about the same numerical accuracy as the Ermak & McCammon algorithm with {dollar}Delta t{dollar} = 300 ps and yields a factor of 8 saving in CPU time. Equilibrium properties obtained from our dynamic simulations are compared with results of Monte Carlo simulations, showing very good agreement for distributions of writhe and the radius of gyration of DNA. Our BD results for the translational and rotational diffusion constant agree very well with the experimental results as well.; Our model offers for the first time the possibility of associating physical timescales with juxtaposition of supercoiled DNA, namely the spatial approach of two linearly-distant DNA segments. We find the collision time {dollar}(Tsb{lcub}c{rcub}){dollar} of two designated sites on supercoiled DNA to be two orders of magnitude smaller than in relaxed DNA. This explains why supercoiling is often a prerequisite for efficient synapsis and site-specific recombination reactions. In addition, we explore systematically the dependence of {dollar}Tsb{lcub}c{rcub}{dollar} on DNA length, site separation, and the superhelical density. Our BD results regarding the dependence of {dollar}Tsb{lcub}c{rcub}{dollar} on superhelical density match excellently available experimental data from recombination experiments. Our studies further point to specific conditions that enhance juxtaposition rates and offer detailed configurational views to help interpret juxtaposition processes, important components in fundamental DNA and DNA/protein reactions. |
