Abstract
The burgeoning interest in membrane research reflects the central role played by membranes in physiological processes, together with the fact that most of the important membrane transport problems remain unsolved. These unsolved problems are frequently based on complex molecular interactions which are poorly understood. One of the first tasks confronting an investigator is to separate out those portions of transport processes that can be adequately described in elementary terms, e. g., in terms of diffusion and osmosis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fick, A. 1855. Phil. Mag. 10 (4): 30.
Crank, J. 1957. The Mathematics of Diffusion. Oxford Univ. Press, London and New York.
Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. Oxford Univ. Press, London and New York.
Abramowitz, M., and I. A. Stegun. 1964. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics. Series 55.
Helfferich, F. 1962. Ion Exchange. McGraw-Hill, New York.
Dainty, J., and C. R. House, 1966. “Unstirred layers” in frog skin. J. Physiol. 182:66–78.
Wright, E. M., A. P. Smulders, and J. M. Tormey. 1972. The role of the lateral intercellular spaces and solute polarization effects in the passive flow of water across the rabbit gallbladder. J. Membr. Biol. 7:198– 219.
House, C. R. 1974. Water Transport in Cells and Tissues. Arnold, London.
Finkelstein, A., and A. Cass. 1968. Permeability and electrical properties of thin lipid membranes. J. Gen. Physiol. 52: 145s.
Foster, M., and S. McLaughlin. 1974. Complexes between uncouplers of oxidative phosphorylation. J. Membr. Biol. 17: 155 – 180.
Diamond, J. M., and E. M. Wright. 1969. Molecular forces governing nonelectrolyte permeation through cell membranes. Proc. R. Soc. Lond. B. 172: 273 – 316.
Diamond, J. M., and E. M. Wright. 1969. Biological membranes: The physical basis of ion and nonelectrolyte selectivity. Anna. Rev. Physiol. 31: 581 – 646.
Diamond, J. M., and Y. Katz. 1974. Interpretation of nonelectrolyte partition coefficients between dimyristoyl lecithin and water. J. Membr. Biol. 17: 121 – 154.
Cass, A., and A. Finkelstein. 1967. Water permeability of thin lipid membranes. J. Gen. Physiol. 50:1765– 1784.
Gutknecht, J. 1968. Permeability of Valonia to water and solutes: Apparent absence of aqueous membrane pores. Biochim. Biophys. Acta 163: 20.
Mauro, A. 1957. Nature of solvent transfer in osmosis. Science 126, Series 2: 252 – 253.
Paganelli, C. V., and A. K. Soloman. 1957. The rate of exchange of tritiated water across the human red cell membrane. J. Gen. Physiol. 41: 259.
Kedem, O., and A. Katchalsky. 1958. Thermodynamic analysis of the permeability of biological membranes to nonelectrolytes. Biochim. Biophys. Acta 27: 229 – 246.
Kedem, O., and A. Katchalsky. 1961. A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 45: 143 – 179.
Ginzburg, B. Z., and A. Katchalsky. 1963. The fric- tional coefficients of the flows of nonelectrolytes through artificial membranes. J. Gen. Physiol. 47:403– 408.
Landahl, H. D. 1953. Note on the Donnan equilibrium. Bull. Math. Biophys. 15: 153.
Goldman, D. E. 1944. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27: 37 – 60.
Cole, K. S. 1965. Electrodiffusion of models for the membrane of squid giant axon. Physiol. Rev. 45:340– 379.
Agin, D. 1967. Electroneutrality and electrodiffusion in the squid axon. Proc. Natl. Acad. Sci. U.S.A. 57: 1232 – 1238.
Adrian, R. H. 1969. Rectification in muscle membrane. In: Progress in Biophysics and Molecular Biology, Vol. 19, Pt. 2. J. A. V. Butler and D. Noble, eds. Pergamon, Oxford, pp. 339 – 369.
MacGillivary, A. D., and D. Hare. 1969. Applicability of Goldman’s constant field assumption to biological systems. J. Theor. Biol. 25: 113 – 126.
Teorell, T. 1953. Transport processes and electrical phenomena in ionic membranes. In: Progress in Biophysics and Biophysical Chemistry, Vol. 3. J. A. V. Butler and D. Noble, eds. Pergamon, Oxford, pp. 305– 369.
Jacquez, J. A., and S. G. Schultz. 1974. A general relation between membrane potential, ion activities, and pump fluxes for symmetric cells in a steady state. Math. Biosci. 20: 19.
Stein, W. D., and J. F. Danielli. 1956. Structure and function in red cell permeability. Discuss. Faraday Soc. 21: 238 – 251.
LeFevre, P. G. 1975. A comparison of recent suggestions for the functional organization of red-cell sugar- transport sites based on kinetic observations. Ann. N.Y. Acad. Sci. 264: 398 – 413.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Plenum Publishing Corporation
About this chapter
Cite this chapter
Macey, R.I. (1978). Mathematical Models of Membrane Transport Processes. In: Andreoli, T.E., Hoffman, J.F., Fanestil, D.D. (eds) Physiology of Membrane Disorders. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3958-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3958-8_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3960-1
Online ISBN: 978-1-4613-3958-8
eBook Packages: Springer Book Archive