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PoreTransport

Transport of a hard spherical solute through a cylindrical pore. import nsrunit; unit uM = 1e-6 M; unit conversion on;

Model number: 0279

Description

   OBJECTIVE: The equations for transport of hydrophilic solutes through aqueous pores
 provide a fundamental basis for examining capillary-tissue exchange and water and
 solute flux through transmembrane channels, but the theory remains incomplete for
 ratios, alp, of sphere diameters to pore diameters greater than 0.4. Values for
 permeabilities, P, and reflection coefficients, sigma, from Lewellen [18], working
 with Lightfoot et al. [19], at alp = 0.5 and 0.95, were combined with earlier values
 for alp < 0.4, and the physically required alp < 1, to provide accurate expressions
 over the whole range of 0 < alp < 1. (alp =rs/rpore & stands for the greek alpha in the text.)

 METHODS: The "data" were the long-accepted theory for alp < 0.2 and the computational
 results from Lewellen and Lightfoot et al. on hard spheres (of 5 different alp's)
 moving by convection and diffusion through a tight cylindrical pore, accounting
 for molecular exclusion, viscous forces, pressure drop, torque and rotation of
 spheres off the center line (averaging across all accessible radial positions),
 and the asymptotic values at alp = 1.0. Coefficients for frictional hindrance to
 diffusion, F(alp), and drag, G(alp), and functions for sigma(alp) and P(alp), were
 represented by power law functions and the parameters optimized to give best
 fits to the combined "data".

 RESULTS: The reflection coefficient sigma = {1 - (1 - (1-PHI)^2)*G'(alp)} + 2*alp^2*PHI*F'(alp),
 and the reloative permeabiltiy P/Omax = PHI*F'(alp)*(1 + 9* alp^5.5 * (1 -alp^5)^(0.02)],
 where PHI is the partition coefficient or volume fraction of the pore available to solute.
 The new expression for the diffusive hindrance is
 F'(alp) = (1-alp^2)^(3/2)*PHI / (1 + 0.2 alp^2 *(1 - alp^2)^16), and for the drag factor is
 G'(alp) = (1-(2/3)*alp^2 - 0.20217*alp^5) / (1 - 0.75851*alp^5) - 0.0431*[1 - (1 - alp^10)].
 All of these converge monotonically to the correct limits at alp = 1.

 CONCLUSION: These are the first expressions providing hydrodynamically based estimates
 of SIGMA(alp) and P(alp) over 0 < alp < 1. They should be accurate to within 1 t0 2%.

• 2006 paper on Porous transport (pdf)

Equations

 Bassingthwaighte JB. A practical extension of hydrodynamic theory of porous
 transport for hydrophilic solutes. Microcirculation 13: 111-118, 2006.

 Bean CP. The physics of porous membranes: neutral pores. In: Membranes:
 Macroscopic Systems and Models, edited by Einsenman G. New York: Dekker, 1972, p. 1-54

 Biber TUL and Curran PF. Coupled solute fluxes in toad skin.
 J Gen Physiol 51: 606-620, 1968.

 Curry FE. Mechanics and thermodynamics of transcapillary exchange..
 In: Handbook of Physiology, Sec. 2 The Cardiovascular System. Vol. 4, Microcirculation,
 edited by Renkin EM and Michel CC. American Physiological Society: Bethesda, Maryland, 1984, p. 309-374.

 Katchalsky A and Curran PF. Nonequilibrium Thermodynamics in Biophysics.
 Cambridge, MA: Harvard University Press, 1965. 

 Kedem O and Katchalsky A. Thermodynamic analysis of the permeability of
 biological membranes to non-electrolytes. Biochim Biophys Acta 27: 229-246, 1958.

 Kedem O and Katchalsky A. A physical interpretation of the phenomenological
 coefficients of membrane permeability. J Gen Physiol 45: 143-179, 1961.

 Kellen MR and Bassingthwaighte JB. An integrative model of coupled water
 and solute exchange  in the heart. Am J Physiol Heart Circ Physiol 285: H1303-H1316, 2003.

 Kellen MR and Bassingthwaighte JB. Transient transcapillary exchange of water
 driven by osmotic forces in the heart. Am J Physiol Heart Circ Physiol 285: H1317-H1331, 2003.

 Apelblat A, Katzir-Katchalsky A, and Silberberg A. A mathematical analysis
 of capillary-tissue fluid exchange. Biorheology 11: 1-49, 1974.

 Ginzburg BZ and Katchalsky A. The frictional coefficients of the flows of
 non-electrolytes through artificial membranes. J Gen Physiol 47: 403-418, 1963.