Calculating hydrodynamic interactions for membrane-embedded objects

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-Delbrück length of the membrane.

Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

“…Differences between the two result from the different values for both monomer diffusion and the membrane Oseen tensor between the two hydrodynamic geometries. The Kirkwood approximation will break down in the limit where the separation r approaches the size of the protein; 34,35 in fact,T(r) diverges as r → 0. For numerical simplicity in converging the sum in Eq.…”

“…If one were inclined to refine the IB calculations here to quantitatively reproduce no-slip boundary value solutions for D, methods have been introduced to do this, both in 3D [30][31][32] and in the membrane geometry. [33][34][35] Implementing the IB scheme to calculate D is straightforward. A force density is applied to the IB "particle," assumed radially symmetric and located at the origin: f(r) = Fδ R (r), where δ R is a "finite delta" function (i.e.,  d 2 r δ R (r) = 1, and δ R has a characteristic envelope size R).…”

Motion of objects embedded in lipid bilayer membranes: Advection and effective viscosity

“…This paper extends the interfacial regularized Stokeslet scheme 24,25 to allow simulating the motion of torque-and force-free objects advected and rotated by an ambient flow field. These calculations reproduce, in the appropriate limits, approximate Faxén relationships developed in Ref.…”

“…We have previously worked on extending the Saffman-Delbrück model beyond its base assumptions, including the introduction of an interfacial regularized Stokeslet (RS) method to allow for numerical computations of diffusion coefficients and pair diffusion coefficients for membraneembedded objects of arbitrary shape 24,25 . The focus of this earlier work centered around the computation of drag and mobility coefficients, i.e.…”

Geodesic curvature driven surface microdomain formation

“…Various dynamical scaling rates were summarized to related the microdomain size and the time when the domain size is far way from the Saffmann-Delbruck length L sd determined by the relative viscosity of the lipid membrane with respect to the surrounding fluid field. This approach has been recently extended to model multicomponent membranes with embedded proteins [30,31].…”