Mathematical Models of Membrane Transport Processes

  • Robert I. Macey

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.

Keywords

Sugar Permeability Migration Glycerol Convection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fick, A. 1855. Phil. Mag. 10 (4): 30.Google Scholar
  2. 2.
    Crank, J. 1957. The Mathematics of Diffusion. Oxford Univ. Press, London and New York.Google Scholar
  3. 3.
    Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. Oxford Univ. Press, London and New York.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    Helfferich, F. 1962. Ion Exchange. McGraw-Hill, New York.Google Scholar
  6. 6.
    Dainty, J., and C. R. House, 1966. “Unstirred layers” in frog skin. J. Physiol. 182:66–78.Google Scholar
  7. 7.
    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.Google Scholar
  8. 8.
    House, C. R. 1974. Water Transport in Cells and Tissues. Arnold, London.Google Scholar
  9. 9.
    Finkelstein, A., and A. Cass. 1968. Permeability and electrical properties of thin lipid membranes. J. Gen. Physiol. 52: 145s.CrossRefGoogle Scholar
  10. 10.
    Foster, M., and S. McLaughlin. 1974. Complexes between uncouplers of oxidative phosphorylation. J. Membr. Biol. 17: 155 – 180.PubMedCrossRefGoogle Scholar
  11. 11.
    Diamond, J. M., and E. M. Wright. 1969. Molecular forces governing nonelectrolyte permeation through cell membranes. Proc. R. Soc. Lond. B. 172: 273 – 316.CrossRefGoogle Scholar
  12. 12.
    Diamond, J. M., and E. M. Wright. 1969. Biological membranes: The physical basis of ion and nonelectrolyte selectivity. Anna. Rev. Physiol. 31: 581 – 646.CrossRefGoogle Scholar
  13. 13.
    Diamond, J. M., and Y. Katz. 1974. Interpretation of nonelectrolyte partition coefficients between dimyristoyl lecithin and water. J. Membr. Biol. 17: 121 – 154.PubMedCrossRefGoogle Scholar
  14. 14.
    Cass, A., and A. Finkelstein. 1967. Water permeability of thin lipid membranes. J. Gen. Physiol. 50:1765– 1784.Google Scholar
  15. 15.
    Gutknecht, J. 1968. Permeability of Valonia to water and solutes: Apparent absence of aqueous membrane pores. Biochim. Biophys. Acta 163: 20.PubMedCrossRefGoogle Scholar
  16. 16.
    Mauro, A. 1957. Nature of solvent transfer in osmosis. Science 126, Series 2: 252 – 253.PubMedCrossRefGoogle Scholar
  17. 17.
    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.PubMedCrossRefGoogle Scholar
  18. 18.
    Kedem, O., and A. Katchalsky. 1958. Thermodynamic analysis of the permeability of biological membranes to nonelectrolytes. Biochim. Biophys. Acta 27: 229 – 246.PubMedCrossRefGoogle Scholar
  19. 19.
    Kedem, O., and A. Katchalsky. 1961. A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 45: 143 – 179.PubMedCrossRefGoogle Scholar
  20. 20.
    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.Google Scholar
  21. 21.
    Landahl, H. D. 1953. Note on the Donnan equilibrium. Bull. Math. Biophys. 15: 153.CrossRefGoogle Scholar
  22. 22.
    Goldman, D. E. 1944. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27: 37 – 60.CrossRefGoogle Scholar
  23. 23.
    Cole, K. S. 1965. Electrodiffusion of models for the membrane of squid giant axon. Physiol. Rev. 45:340– 379.Google Scholar
  24. 24.
    Agin, D. 1967. Electroneutrality and electrodiffusion in the squid axon. Proc. Natl. Acad. Sci. U.S.A. 57: 1232 – 1238.PubMedCrossRefGoogle Scholar
  25. 25.
    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.Google Scholar
  26. 26.
    MacGillivary, A. D., and D. Hare. 1969. Applicability of Goldman’s constant field assumption to biological systems. J. Theor. Biol. 25: 113 – 126.CrossRefGoogle Scholar
  27. 27.
    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.Google Scholar
  28. 28.
    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.CrossRefGoogle Scholar
  29. 29.
    Stein, W. D., and J. F. Danielli. 1956. Structure and function in red cell permeability. Discuss. Faraday Soc. 21: 238 – 251.CrossRefGoogle Scholar
  30. 30.
    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.PubMedCrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Robert I. Macey
    • 1
  1. 1.Department of Physiology-AnatomyUniversity of CaliforniaBerkeleyUSA

Personalised recommendations