Diffusion in phospholipid bilayer membranes: dual-leaflet dynamics and the roles of tracer–leaflet and inter-leaflet coupling

Abstract

A variety of observations—sometimes controversial—have been made in recent decades when attempting to elucidate the roles of interfacial slip on tracer diffusion in phospholipid membranes. Evans–Sackmann theory (1988) has furnished membrane viscosities and lubrication-film thicknesses for supported membranes from experimentally measured lateral diffusion coefficients. Similar to the Saffman and Delbrück model, which is the well-known counterpart for freely supported membranes, the bilayer is modelled as a single two-dimensional fluid. However, the Evans–Sackman model cannot interpret the mobilities of monotopic tracers, such as individual lipids or rigidly bound lipid assemblies; neither does it account for tracer–leaflet and inter-leaflet slip. To address these limitations, we solve the model of Wang and Hill, in which two leaflets of a bilayer membrane, a circular tracer and supports are coupled by interfacial friction, using phenomenological friction/slip coefficients. This furnishes an exact solution that can be readily adopted to interpret the mobilities of a variety of mosaic elements—including lipids, integral monotopic and polytopic proteins, and lipid rafts—in supported bilayer membranes.

Transmembrane Protein Diffusion in Gel-Supported Dual-Leaflet Membranes

“…The left panel is for bilayers sandwiched between gels having equal permeabilities (' 2 /' 1 ¼ 1), whereas the right panel is for bilayers supported on a single gel (' 2 /' 1 ¼ 1000). As expected, the solid-supported model of Hill and Wang (30) breaks down when a/' 1 is sufficiently small and L 1 is sufficiently large. For example, if we take the radius of a protein to be a~2.5 nm, and estimate the Brinkman screening length from the mesh size of a weakly cross-linked gel with storage modulus G 0~1 00 Pa, then '~(k B T/G 0 ) 1/3 z 3.5 nm ((37), where k B T~10 À21 J is the thermal energy), therefore, a/'~1.…”

“…More importantly, these calculations demonstrate a relatively weak influence of interleaflet friction. As the solid-supported dual-leaflet model of Hill and Wang (30) has shown, the effects of interleaflet slip are accentuated when there is strong coupling (of one leaflet) to a single support.…”

“…Wang and Hill (14) developed a single-leaflet model to quantify how varying the hydrogel porosity bridges the pure-fluid and solid-supported regimes. This has been advanced to elucidate the roles of interfacial slip for monotopic and transmembrane tracers in bilayers with finite interleaflet slip (30). However, the model adopted a phenomenological lubrication interaction between the leaflets and an impenetrable support (neglecting the threedimensional hydrodynamic disturbances in the porous supports), thereby leaving open the question as to how porous such a support must be for the lubrication approximation to break down.…”

“…Results and Discussion presents the results as tracer mobilities, which are typically measured as lateral self-diffusion coefficients, and 1), quantifies how the dimensionless mobility depends on the interleaflet friction; 2), furnishes theoretical predictions of transmembrane-protein diffusion coefficients; and 3), identifies the reduced parameter space for the analytical theory of Hill and Wang (30). In the absence of suitable data for gel-supported membranes, we apply the model to interpret the transmembrane protein diffusion coefficients of Peters and Cherry (17) and Gambin et al (23), concluding with a brief Summary section.…”

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

“…A particularly relevant case involves including the two-leaflet structure of the bilayer explicitly; friction between the two leaflets then can influence the dynamics of bodies localized within a single leaflet, such as a monotopic protein or individual lipid. 34,[80][81][82] A generalization to the two-leaflet case is provided in Appendix B. Should these single-leaflet results be applied to lipids?…”