The macroscopic diffusion constant for a charged solute is in part dependent on the volume excluded by diffusional barriers and by electrostatic interactions between those barriers and the solute. Increasing excluded volume reduces diffusive transport of the solute, while electrostatic interactions can alter diffusivity depending on the nature of the potential. We have showed (in review) using homogenization theory that the configuration of molecular-scale barriers can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, the effective distance between molecular barriers approaches the Debye length; this scenario gives rise to a regime in which electrostatic interactions can strongly influence a solute's diffusivity. Here we extend the homogenization methodology to include the contribution of a fixed electrostatic potential, through homogenization of the Smoluchowski equation. We consider the diffusion of Ca2+ in constrained environments at physiological ionic strength and find that electrostatic interactions can substantially influence its macroscopic diffusion properties. We furthermore find that the lateral diffusion of Ca2+ adjacent to the SERCA-containing bilayer of the sarcoplasmic reticulum is hindered by electrostatic interactions, which may serve as a precedent for other trans-membrane proteins. This approach offers new insight into the role of molecular-scale electrostatic interactions on the macroscopic diffusion of calcium.

Homogenization of the Smoluchowski electro-diffusion equation for estimating hindered, anisotropic calcium diffusion in charged environments

246th National Meeting (2013)

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