The dynamical effects of solvent on supercoiled DNA are explored through a simple, macroscopic energy model for DNA in the Langevin dynamics framework. Closed circular DNA is modeled by B splines, and both eleastic and electrostatic (screened Coulomb) potentials are included in the energy function. The Langevin formalism describes approximately the influence of the solvent on the motion of the solute. The collision frequency γ determines the magnitude of the friction and the variance of the random forces due to molecular collisions. Thus, as a first approximation, the Langevin equation of motion can be parametrized to capture the approximate dynamics of DNA in a viscous medium. Solvent damping is well known to alter the dynamical behavior of DNA and affect various hydrodynamic properties. This work examines these effects systematically by varying the collision frequency (viscosity) with the goal of better understanding the dynamical behavior of supercoiled DNA. By varying γ over ten orders of magnitude, we identify three distinct physical regimes of DNA behavior: (i) low γ, dominated by globally harmonic motion; (ii) intermediate γ, characterized by maximal sampling and high mobility of the DNA; and (iii) high γ, dominated by random forces, where all of the global modes are effectively frozen by extreme overdamping. These regimes are explored extensively by Langevin dynamics simulations, offering insight into hydrodynamic effects on supercoiled DNA. At low γ, the DNA exhibits small, harmonic fluctuations.

Transitions to other configurational regions are more difficult to capture in finite simulations. In the intermediate γ regime, the DNA exhibits maximal sampling of the writhe. Transition times are accelerated and more readily captured in the simulations. A preferential lowering of the writhe from the value at the potential energy minimum is noted, reflecting entropic effects. Only beyond a specific value of γ in this regime do we find reasonable convergence of the translational diffusion constants and velocity autocorrelation functions. This brackets the biologically relevant regime. At high γ the DNA supercoil fluctuates about two distinct regions of configuration space, one near the tightly wound potential energy minimum, the other related to more open configurations. Transitions between the two regions are infrequent. This behavior suggests two regions of free-energy minima (potential and entropically favored) separated by a barrier. Indeed, the general dependence of the extent of configurational sampling on the collision frequency is analogous to the isomerization behavior of a particle in a bistable potential modeled by the Langevin equation of motion. This intriguing parallelism suggests a favorable viscosity medium where specific internal modes, namely, global twisting, are activated. It is possible that physiological solvent densities correspond to this region of optimal mobility for the DNA.

• Received 4 November 1994

DOI:https://doi.org/10.1103/PhysRevE.51.6188