A simple method for introducing a cutoff to hydrodynamic interactions in Brownian dynamics simulations

Brownian dynamics (BD) simulations that include hydrodynamic interactions (HIs) modeled at the Rotne-Prager-Yamakawa (RPY) level of theory are a valuable tool for accurately modeling the translational and rotational diffusion of macromolecules such as proteins and nucleic acids. A major drawback to the inclusion of HIs in BD simulations is their computational expense, and an obvious way to consider reducing the expense of BD-HI simulations is to include a cutoff such that HIs beyond a certain distance are omitted. Unfortunately, a naive attempt to implement such a scheme usually leads to the RPY diffusion tensor becoming non-positive definite, which has the consequence that it becomes impossible to compute the correlated random displacements required by the Ermak-McCammon BD-HI algorithm. Here I show that a simple approach can be used to overcome this problem and implement a distance-based cutoff scheme that is guaranteed to lead to a diffusion tensor that is positive definite. The method involves only a straightforward distance-based scaling of the original RPY terms, and allows a seamless transition to be made between BD simulations that neglect HIs entirely and simulations that include HIs at the full RPY level of theory.