Calculating hydrodynamic interactions for membrane-embedded objects

TL;DR

This paper extends a numerical scheme to calculate hydrodynamic interactions between multiple membrane-embedded objects, validating analytical predictions and demonstrating the significance of these interactions in membrane protein dynamics.

Contribution

The authors develop and validate a numerical method for computing hydrodynamic interactions among multiple objects in membranes, surpassing previous analytical limitations.

Findings

Method converges to near-field lubrication results for close objects.

Hydrodynamic interactions significantly affect membrane protein diffusion.

Maximum diffusion change occurs for objects comparable to the Saffman-Delbrück length.

Abstract

A recently introduced numerical scheme for calculating self-diffusion coefficients of solid objects embedded in lipid bilayer membranes is extended to enable calculation of hydrodynamic interactions between multiple objects. The method is used to validate recent analytical predictions by Oppenheimer and Diamant [Biophys. J., 96, 3041, 2009] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near-field lubrication results as objects closely approach one another, however the present methodology also applies outside of the limiting regimes where analytical results are available. Multiple different examples involving pairs of disk-like objects with various constraints imposed on their relative motions demonstrate the importance of hydrodynamic interactions in the dynamics of proteins and lipid domains on membrane surfaces. It is demonstrated that the relative change in self-diffusion of a membrane embedded object upon perturbation by a similar proximal solid object displays a maximum for object sizes comparable to the Saffman-Delbr\"uck length of the membrane.