Diffusion in hydrogel-supported phospholipid bilayer membranes

We model a cylindrical inclusion (lipid or membrane protein) translating with velocity U in a thin planar membrane (phospholipid bilayer) that is supported above and below by Brinkman media (hydrogels). The total force F, membrane velocity, and solvent velocity are calculated as functions of three independent dimensionless parameters: Lambda = eta a/(eta(m)h), l(1)/a and l(2)/a. Here, eta and eta(m) are the solvent and membrane shear viscosities, a is the particle radius, h is the membrane thickness, and l(1)(2) and l(2)(2) are the upper and lower hydrogel permeabilities. As expected, the dimensionless mobility 4 pi eta aU/F = 4 pi eta aD/(k(B)T) (proportional to the self-diffusion coefficient, D) decreases with decreasing gel permeabilities (increasing gel concentrations), furnishing a quantitative interpretation of how porous, gel-like supports hinder membrane dynamics. The model also provides a means of inferring hydrogel permeability and, perhaps, surface morphology from tracer diffusion measurements.