Solvent effects on supercoiled DNA dynamics explored by Langevin dynamics simulations

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Abstract
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.