Brownian dynamics of double-stranded DNA in periodic systems with discrete salt

Abstract

Numerical models of mesoscale DNA dynamics relevant to in vivo scenarios require methods that incorporate important features of the intracellular environment, while maintaining computational tractability. Because the explicit inclusion of ions leads to electrostatic calculations that scale as the square of the number of charged particles, such models typically handle these calculations using low-potential, mean-field approaches, rather than by considering the discrete interactions of ions. This allows approximation of the long-range, screened self-repulsion of DNA, but is unable to capture detailed electrostatic phenomena, such as short-range attractions mediated by ion-ion correlations. Here, we develop a dynamical model of explicitly double-stranded, sequence-specific DNA in a bulk environment consisting of other polyions and explicitly represented counterions and coions. DNA is represented as two interwound chains of charged Stokes spheres, and ions as free, monovalently charged Stokes spheres. Brownian dynamics simulations performed at salt concentrations of 0.1, 1, 10, and 100 mM demonstrate this model captures anticipated behaviors of the system, including increasing compaction of the polyion by the ionic atmosphere with increasing ionic strength. The decay of the distance dependence of the ion concentrations as one moves away from the polyion approaches their equilibrium values in quantitative agreement with predictions of Poisson-Boltzmann theory. The simulation results also demonstrate quantitative agreement with experimental measurements of the persistence length of B-DNA, which increases significantly at low ionic strengths. The model also captures behaviors intimating the importance of explicitly representing ionic and polyionic structure. These include penetration of the polyion interior by both coions and counterions, and counterion-mediated accumulation of coions near the surface of the polyion. Such phenomena are likely to play an important role in the formation of alternative DNA secondary structures, suggesting the present methods will prove valuable to dynamic models of superhelical stress-induced DNA structural transitions.