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Diffusion in hydrogel-supported phospholipid bilayer membranes
Published online by Cambridge University Press: 16 April 2013
Abstract
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.
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- ©2013 Cambridge University Press
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