## 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-time-step inertial dynamics, IBD: inertial
Brownian dynamics) for mass-dependent Langevin dynamics (LD) with hydrodynamics, as well as the standard Brownian
dynamical (BD) propagator, to study the thermal fluctuations of supercoiled DNA minicircles. Our DNA model accounts
for twisting, bending, and salt-screened electrostatic interactions. Though inertial relaxation times are on the order of
picoseconds, much slower kinetic processes are affected by the Brownian (noninertial) approximation typically employed.
By comparing results of LTID and IBD to those generated using the standard (BD) algorithm, we find that the equilibrium
fluctuations in writhing number, Wr, and radius of gyration, Rg, are influenced by mass-dependent terms. The
autocorrelation functions for these quantities differ between the BD simulations and the inertial LD simulations by as
much as 10%. In contrast, when the nonequilibrium process of relaxation from a perturbed state is examined, all methods
(inertial and diffusive) yield similar results with no detectable statistical differences between the mean folding pathways.
Thus, while the evolution of an ensemble toward equilibrium is equally well described by the inertial and the noninertial
methods, thermal fluctuations are influenced by inertia. Examination of such equilibrium fluctuations in a biologically
relevant macroscopic property-namely the two-site intermolecular distance-reveals mass-dependent behavior: The rate
of juxtaposition of linearly distant sites along a 1500-base pair DNA plasmid, occurring over time scales of milliseconds
and longer, is increased by about 8% when results from IBD are compared to those from BD. Since inertial modes that
decay on the picosecond time scale in the absence of thermal forces exert an influence on slower fluctuations in
macroscopic properties, we advocate that IBD be used for generating long-time trajectories of supercoiled DNA systems.
IBD is a practical alternative since it requires modest computational overhead with respect to the standard BD method.

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