Modeling Electrodynamic Interactions in Brownian Dynamics Simulations

Abstract

There is a great deal of interest in interactions between biomolecules and high frequency electromagnetic (EM) fields. To investigate these interactions, a variety of simulation methods are available. For small length and time scales (approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1 \,\mathrm{\mu }\mathrm{s}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$100 \,\mathrm{n}\mathrm{m}$</tex-math></inline-formula> ), All-Atom Molecular Dynamics simulates every atom in the system. This captures the relevant physics to a high degree of accuracy. Phenomena such as electric field screening by counter-ions are emergent properties from the collective interactions of these atoms. For larger systems on longer time scales, however, this method is too computationally expensive. To reduce complexity, other simulation techniques such as Brownian Dynamics treat the solvent as a continuum, instead of explicitly. One typical assumption is that electric field interactions are electrostatic and subjected to Debye screening. Once charges start moving at high frequencies and velocities, however, charges are able to outrun the counter-ion cloud and this assumption breaks down. We propose a method of removing the electrostatic assumption without explicitly modeling the solvent or imposing a grid on the simulation. We demonstrate the charged wake can be modeled using a finite trail of charges. Interactions can be computed using electrostatic expressions only, but still capture electrodynamics.