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Am J Physiol Heart Circ Physiol (September 23, 2005). doi:10.1152/ajpheart.00695.2005
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Submitted on June 26, 2005
Accepted on September 19, 2005

The Mechanism of Osmotic Flow in a Periodic Fiber Array

Xiaobing Zhang1, Fitz-Roy E Curry2, and Sheldon Weinbaum1*

1 Department of Biomedical Engineering, Graduate School, The City College of The City University of New York, New York, NY, USA
2 Department of Physiology & Membrane Biology, University of California, Davis, Davis, CA, USA

* To whom correspondence should be addressed. E-mail: weinbaum{at}ccny.cuny.edu.

The classical analysis of Anderson and Malone (Biophys J 14: 957-982, 1974) for the osmotic flow across membranes with long circular cylindrical pores is extended to a fiber matrix layer wherein the confining boundaries are the fibers themselves. The equivalent of the well known result for the reflection coefficient {sigma}0=(1-{phi})2, where {phi} is the partition coefficient, is derived for a periodic fiber array of hexagonally ordered core proteins. The boundary value problem for the potential energy function describing the solute distribution surrounding each fiber is solved by defining an equivalent fluid annulus in which the pressures and osmotic forces are determined. This model is of special interest in the osmotic flow of water across a capillary wall where recent experimental studies suggest that the endothelial glycocalyx is a quasi-periodic fiber array that serves as the primary molecular sieve for plasma proteins. Results for the reflection coefficient are presented in terms of two dimensionless numbers, {alpha}=a/R and {beta}=b/R, where a and b are the solute and fiber radii and R is the outer radius of the fluid annulus. In general, the results differ substantially from the classical expression for a circular pore due to the large difference in the shape of the boundary along which the osmotic force is generated. However, as in circular pore theory, one finds that the reflection coefficients for osmosis and filtration are the same.




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