Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA

We apply our new algorithms presented in the companion paper (LTID: long-ti me-step inertial dynamics, IBD: inertial Brownian dynamics) for mass-depend ent Langevin dynamics (LD) with hydrodynamics, as well as the standard Brow nian dynamical (BD) propagator, to study the thermal fluctuations of superc oiled DNA minicircles. Our DNA model accounts for twisting, bending, and sa lt-screened electrostatic interactions. Though inertial relaxation times ar e on the order of picoseconds, much slower kinetic processes are affected b y the Brownian (noninertial) approximation typically employed. By comparing results of LTID and IBD to those generated using the standard (BD) algorit hm, we find that the equilibrium fluctuations in writhing number, Wr, and r adius of gyration, R-g, are influenced by mass-dependent terms. The autocor relation functions for these quantities differ between the BD simulations a nd the inertial LD simulations by as much as 10%. In contrast, when the non equilibrium process of relaxation from a perturbed state is examined, all m ethods (inertial and diffusive) yield similar results with no detectable st atistical differences between the mean folding pathways. Thus, while the ev olution of an ensemble toward equilibrium is equally well described by the inertial and the noninertial methods, thermal fluctuations are influenced b y inertia. Examination of such equilibrium fluctuations in a biologically r elevant macroscopic property-namely the two-site intermolecular distance-re veals mass-dependent behavior: The rate of juxtaposition of linearly distan t sites along a 1500-base pair DNA plasmid, occurring over time scales of m illiseconds and longer, is increased by about 8% when results from IBD are compared to those from BD. Since inertial modes that decay on the picosecon d time scale in the absence of thermal forces exert an influence on slower fluctuations in macroscopic properties, we advocate that IBD be used for ge nerating long-time trajectories of supercoiled DNA systems. IBD is a practi cal alternative since it requires modest computational overhead with respec t to the standard BD method. (C) 2000 American Institute of Physics. [S0021 -9606(00)50817-4].