Fluctuating Hydrodynamics in the 13-moment Approximation for Simulating Biomacromolecular Nanomachines

Proteins are nanomachines largely existing in ionic aqueous conditions that perform mechanicochemical work and whose dynamics span femtosecond timescales (i.e., covalent bond oscillations) to beyond the millisecond regime (e.g., glucose transport across a lipid membrane). All-atom molecular dynamics (MD) can fully capture solute-solvent interactions but is currently limited to microsecond timescales—orders of magnitude short of many biophysical timescales of interest. One viable means of overcoming this timescale problem is the hybrid atomistic-continuum (HAC) method where, for example, MD is used in a subdomain requiring atomistic detail while a hydrodynamic representation is used elsewhere to capture solvent dynamics. We are developing a 13-moment fluctuating hydrodynamics model that goes beyond Landau-Lifschitz Navier-Stokes theory—popular in HAC methods. Our numerical model is based on Grad's 13-moment approximation and can capture nonlinear, nanoscale transport phenomena such as emergent viscoelasticity and thermoacoustic effects arising in dense fluids like water. With a view toward understanding large proteins like molecular motors, potential advantages are described and preliminary results are presented.