| Derivation of Unstirred-Layer Transport Number Equations from the Nernst-Planck Flux Equations Biophysical Journal, Volume 74, Issue 6, 1 June 1998, Pages 2903-2905 Peter H. Barry Abstract Since the late 1960s it has been known that the passage of current across a membrane can give rise to local changes in salt concentration in unstirred layers or regions adjacent to that membrane, which in turn give rise to the development of slow transient diffusion potentials and osmotic flows across those membranes. These effects have been successfully explained in terms of transport number discontinuities at the membrane-solution interface, the transport number of an ion reflecting the proportion of current carried by that ion. Using the standard definitions for transport numbers and the regular diffusion equations, these polarization or transport number effects have been analyzed and modeled in a number of papers. Recently, the validity of these equations has been questioned. This paper has demonstrated that, by going back to the Nernst-Planck flux equations, exactly the same resultant equations can be derived and therefore that the equations derived directly from the transport number definitions and standard diffusion equations are indeed valid. Abstract | Full Text | PDF (117 kb) |
| Unstirred layer effects on calculations of the potential difference across an ion exchange membrane Biophysical Journal, Volume 18, Issue 1, 1 April 1977, Pages 53-61 R.J. French Abstract The potential difference between two solutions of the same 1:1 electrolyte bathing an ion exchange membrane has been calculated as the sum of the following components: (a) a Donnan potential at each membrane-solution interface, (b) a diffusion potential within the membrane phase, and (c) a diffusion potential in the unstirred layer on each side of the membrane. For a highly charged ion exchange membrane with at least one surface in contact with a dilute solution, calculated transmembrane potential differences are extremely sensitive to the assumed thickness of the unstirred layers. This sensitivity to unstirred layer thickness is primarily due to changes in the Donnan components of the potential difference. By this approach, it was possible to fit membrane potential data from Gunn and Curran (1971, Biophys. J. 11:559) for a range of bathing solution concentrations from 0.0016 to 4.0 M. If no effort was made to account for the modification of the Donnan potentials by the presence of unstirred layers, the data appeared incompatible with an electrodiffusion equation description. Suggestions for a more stringent experimental test and a brief discussion of possible implications for electrical measurements on fresh-water giant algal cells are presented. Abstract | PDF (515 kb) |
| Osmotic Water Transport with Glucose in GLUT2 and SGLT Biophysical Journal, Volume 94, Issue 10, 15 May 2008, Pages 3912-3923 Richard J. Naftalin Abstract Carrier-mediated water cotransport is currently a favored explanation for water movement against an osmotic gradient. The vestibule within the central pore of Na-dependent cotransporters or GLUT2 provides the necessary precondition for an osmotic mechanism, explaining this phenomenon without carriers. Simulating equilibrative glucose inflow via the narrow external orifice of GLUT2 raises vestibular tonicity relative to the external solution. Vestibular hypertonicity causes osmotic water inflow, which raises vestibular hydrostatic pressure and forces water, salt, and glucose into the outer cytosolic layer via its wide endofacial exit. Glucose uptake via GLUT2 also raises oocyte tonicity. Glucose exit from preloaded cells depletes the vestibule of glucose, making it hypotonic and thereby inducing water efflux. Inhibiting glucose exit with phloretin reestablishes vestibular hypertonicity, as it reequilibrates with the cytosolic glucose and net water inflow recommences. Simulated Na-glucose cotransport demonstrates that active glucose accumulation within the vestibule generates water flows simultaneously with the onset of glucose flow and before any flow external to the transporter caused by hypertonicity in the outer cytosolic layers. The molar ratio of water/glucose flow is seen now to relate to the ratio of hydraulic and glucose permeability rather than to water storage capacity of putative water carriers. Abstract | Full Text | PDF (458 kb) |
Copyright © 1983 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 43, Issue 2, 149-156, 1 August 1983
doi:10.1016/S0006-3495(83)84335-5
Research Article
D.C. Chang
The resting potential in the squid axon has been measured at various concentrations of Cl, K, Na, and Ca ions. The results of these measurements are compared with the Goldman-Hodgkin-Katz (GHK) equation and a modified constant field equation. This modified equation was derived by including currents carried by divalent ions and the effects of the unstirred layer and the periaxonal space. It is shown that, although the GHK equation can fit the V vs. [K]o data well, it has difficulty explaining the observed dependence of V on [Na]o when the axon is bathed in K-free artificial sea water. The use of the modified constant field equation removes this difficulty.