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Diffusion in hydrogel-supported phospholipid bilayer membranes

Published online by Cambridge University Press:  16 April 2013

Chih-Ying Wang
Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 0C5, Canada
Reghan J. Hill*
Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 0C5, Canada
Email address for correspondence:


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: $\Lambda = \eta a/ ({\eta }_{m} h)$ , ${\ell }_{1} / a$ and ${\ell }_{2} / a$ . Here, $\eta $ and ${\eta }_{m} $ are the solvent and membrane shear viscosities, $a$ is the particle radius, $h$ is the membrane thickness, and ${ \ell }_{1}^{2} $ and ${ \ell }_{2}^{2} $ are the upper and lower hydrogel permeabilities. As expected, the dimensionless mobility $4\mathrm{\pi} \eta aU/ F= 4\mathrm{\pi} \eta aD/ ({k}_{B} T)$ (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.

©2013 Cambridge University Press 

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