Skip to main content
SpringerLink
Log in

Mathematical Models of Membrane Transport Processes

  • Chapter
Physiology of Membrane Disorders

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Sten-Knudsen, O. 1978. Passive transport processes. In: Membrane Transport in Biology, Volume 1. G. Giebisch, D. C. Tosteson, and H. H. Ussing, eds. Springer-Verlag, Berlin, pp. 5–114.

    Google Scholar 

  2. Crank, J. 1957. The Mathematics of Diffusion. Oxford University Press, London.

    Google Scholar 

  3. Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. Oxford University Press, London.

    Google Scholar 

  4. Fick, A. 1855. Ueber diffusion. Ann. Phys. Chem. 94: 59–86.

    Article  Google Scholar 

  5. Eisenberg, D., and D. Carothers. 1979. Physical Chemistry. Benjamin-Cummings, Menlo Park, Calif.

    Google Scholar 

  6. Hardt, S. L. 1981. The diffusion transit time; a simple derivation. Bull. Math. Biol, 41: 89–99.

    Google Scholar 

  7. Abramowitz, M., and I. A. Stegun. 1964. Handbook of Mathe¬matical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics, Series 55.

    Google Scholar 

  8. Helfferich, F. 1962. Ion Exchange. McGraw-Hill, New York.

    Google Scholar 

  9. Dainty, J., and C. R. House. 1966. “Unstirred layers” in frog skin. J. Physiol. (London) 182:66–78.

    Google Scholar 

  10. Wright, E. M., A. P. Smulders, and J. M. Tormey. 1972. The role of the lateral intracellular spaces and solute polarization effects in the passive flow of water across the rabbit gallbladder. J. Membr. Biol. 7: 198–219.

    Article  Google Scholar 

  11. House, C. R. 1974. Water Transport in Cells and Tissues. Arnold, London.

    Google Scholar 

  12. Finkelstein, A., and A. Cass. 1968. Permeability and electrical properties of thin lipid membranes. J. Gen. Physiol. 52: 145s.

    Article  CAS  Google Scholar 

  13. Foster, M., and S. McLaughlin. 1974. Complexes between uncouples of oxidative phosphorylation. J. Membr. Biol. 17: 155–180.

    Article  PubMed  CAS  Google Scholar 

  14. Diamond, J. M., and E. M. Wright. 1969. Molecular forces governing nonelectrolyte permeation through cell membranes. Proc. R. Soc. London Ser. B 172: 273–316.

    Article  CAS  Google Scholar 

  15. Diamond, J. M., and E. M. Wright. 1969. Biological membranes: The physical basis of ion and nonelectrolyte selectivity. Annu. Rev. Physiol. 31: 581–646.

    Article  PubMed  CAS  Google Scholar 

  16. Diamond, J. M., and Y. Katz. 1974. Interpretation of nonelectrolyte partition coefficients between dimyristoyl lecithin and water. J. Membr. Biol. 17: 121–154.

    Article  PubMed  CAS  Google Scholar 

  17. Cass, A., and A. Finkelstein. 1967. Water permeability of thin lipid membranes. J. Gen. Physiol. 50: 1765–1784.

    Article  PubMed  CAS  Google Scholar 

  18. Gutknecht, J. 1968. Permeability of Valonia to water and solutes: Apparent absence of aqueous membrane pores. Biochim. Biophys. Acta 163: 20.

    Article  PubMed  CAS  Google Scholar 

  19. Mauro, A. 1957. Nature of solvent transfer in osmosis. Science 126: 252–253.

    Article  PubMed  CAS  Google Scholar 

  20. Paganelli, C. V., and A. K. Solomon. 1957. The rate of exchange of tritiated water across the human red cell membrane. J. Gen. Physiol. 41: 159.

    Article  Google Scholar 

  21. Kedem, O., and A. Katchalsky. 1958. Thermodynamic analysis of the permeability of biological membranes to nonelectrolytes. Biochim. Biophys. Acta 27: 229–246.

    Article  PubMed  CAS  Google Scholar 

  22. Kedem, 0., and A. Katchalsky. 1961. A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 45: 143–179.

    Article  Google Scholar 

  23. Ginzburg, B. Z., and A. Katchalsky. 1963. The frictional coefficients of the flows of nonelectrolytes through artificial membranes. J. Gen. Physiol. 47: 403–408.

    Article  PubMed  CAS  Google Scholar 

  24. Schultz, S. G. 1980. Basic Principles of Membrane Transport. Cambridge University Press, London.

    Google Scholar 

  25. McLaughlin, S. 1976. Electrostatic potentials at membrane-solution interfaces. Curr. Top. Membr. Transp. 9: 71–94.

    Article  Google Scholar 

  26. Patlak, C. S., K. D. Pettigrew, and S. I, Rapoport. 1980. Use of transient and steady state measurements of the unidirectional flux ratio for the determination of free energy change of chemical reactions and active transport systems. Bull. Math. Biol. 42: 529–537.

    PubMed  CAS  Google Scholar 

  27. Landahl, H. D. 1953. Note on the Donnan equilibrium. Bull. Math. Biophys. 15: 153.

    Article  CAS  Google Scholar 

  28. Goldman, D. E. 1944. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27: 37–60.

    Article  Google Scholar 

  29. Cole, K. S. 1965. Electrodiffusion models for the membrane of squid giant axon. Physiol. Rev. 45: 340–379.

    PubMed  CAS  Google Scholar 

  30. Agin, D. 1967. Electroneutrality and electrodiffusion in the squid axon. Proc. Natl. Acad. Sci. USA 57: 1232–1238.

    Article  PubMed  CAS  Google Scholar 

  31. Adrian, R. H. 1969. Rectification in muscle membrane. Prog. Biophys. Mol. Biol. 19: 339–369.

    Article  PubMed  CAS  Google Scholar 

  32. MacGillivary, A. D., and D. Hare. 1969. Applicability of Golman’s constant field assumption to biological systems. J. The or. Biol. 25: 113–126.

    Google Scholar 

  33. de Levie, R., and H. Moreira. 1972. Transport of ions of one kind through thin membranes. J. Membr. Biol. 9: 241–260.

    Article  Google Scholar 

  34. de Levie, R. 1978. Mathematical modeling of transport of lipid- soluble ions and ion-carrier complexes through lipid bilayer membranes. Adv. Chem. Phys. 37: 99–137.

    Article  Google Scholar 

  35. Walz, D., E. Bamberg, and P. Laiiger. 1969. Nonlinear electrical effects in lipid bilayer membranes. I. Ion injection. Biophys. J. 9: 1150–1159.

    Article  PubMed  CAS  Google Scholar 

  36. Patlak, C. S. 1956. Contributions to the theory of active transport. Bull. Math. Biophys. 18: 271.

    Article  Google Scholar 

  37. Teorell, T. 1953. Transport processes and electrical phenomena in ionic membranes. Prog. Biophys. Biophys. Chem. 3: 305–369.

    CAS  Google Scholar 

  38. Patlak, C. S. 1960. Derivation of an equation for the diffusion potential. Nature (London) 188: 944–945.

    Article  CAS  Google Scholar 

  39. Barr, L. 1965. Membrane potential profiles and the Goldman equation. J. Theor. Biol. 9: 351–359.

    Article  PubMed  CAS  Google Scholar 

  40. Mullins, L. J., and K. Nöda. 1963. The influence of sodium-free solutions on the membrane potential of frog muscle fibers. J. Gen. Physiol. 47: 117–132.

    Article  PubMed  CAS  Google Scholar 

  41. 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.

    Article  CAS  Google Scholar 

  42. Laüger, P., R. Benz, G. Stark, E. Bamberg, P. C. Jordan, A. Fahr, and W. Brock. 1981. Relaxation studies of ion transport systems in lipid bilayer membranes. Q. Rev. Biophys. 14: 513–598.

    Article  PubMed  Google Scholar 

  43. Hille, B. 1975. Ionic selectivity of Na and K channels of nerve membranes. In: Membranes—A Series of Advances. G. Eisenman, ed. Dekker, New York. pp. 256–316.

    Google Scholar 

  44. Lieb, W. R. 1982. A kinetic approach to transport studies. In: Red Cell Membranes—A Methodological Approach. J. C. Ellory and J. D. Young, eds. Academic Press, New York. pp. 135–164.

    Google Scholar 

  45. Heinz, E. 1978. Mechanics and Energetics of Biological Transport, Springer-Verlag, Berlin.

    Google Scholar 

  46. Cornish-Bowden, A. 1976. Principles of Enzyme Kinetics. Butterworths, London.

    Google Scholar 

  47. Segel, I. H. 1975. Enzyme Kinetics. Wiley, New York.

    Google Scholar 

  48. Wong, J. T. 1975. Kinetics of Enzyme Mechanics. Academic Press, New York.

    Google Scholar 

  49. Schachter, H. 1972. The use of steady-state assumption to derive kinetic formulations for the transport of a solute across a membrane. In: Metabolic Pathways, 3rd ed., Volume VI. L. E. Hokin, ed. Academic Press, New York. pp. 1–15.

    Google Scholar 

  50. Laiiger, P. 1980. Kinetic properties of ion carriers and channels. J. Membr. Biol. 57: 163–178.

    Article  Google Scholar 

  51. Hodgkin, A. L., and R. D. Keynes. 1955. The potassium permeability of a giant nerve fiber. J. Physiol. (London) 128: 61–88.

    CAS  Google Scholar 

  52. Heckmann, K. 1972. Single file diffusion. In: Passive Permeability of Cell Membrane. F. Kruezer and J. F. G. Siegers, eds. Plenum Press, New York. pp. 127–153.

    Google Scholar 

  53. Hladky, S. B. 1965. The single file model for diffusion of ions through a membrane. Bull. Math. Biol. 27: 79.

    CAS  Google Scholar 

  54. Macey, R. I., and R. M. Oliver. 1967. The time dependence of single file diffusion. Biophys. J. 7: 545–554.

    Article  PubMed  CAS  Google Scholar 

  55. Dick, D. A. T. 1966. Cell Water. Butterworths, London.

    Google Scholar 

  56. Levitt, D. G. 1974. A new theory for cell membrane pores. 1. General theory and application to red cells. Biochim. Biophys. Acta 373: 115–131.

    Article  PubMed  CAS  Google Scholar 

  57. Rosenberg, P. A., and A. Finkelstein. 1978. Water permeability of gramacidin A treated lipid bilayer membranes. J. Gen. Physiol. 72: 341–350.

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physiology-Anatomy, University of California, Berkeley, California, 94720, USA

    Robert I. Macey

Authors
  1. Robert I. Macey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Texas Health Science Center at Houston, Houston, Texas, USA

    Thomas E. Andreoli M.D.  & Stanley G. Schultz M.D.  & 

  2. Yale University School of Medicine, New Haven, Connecticut, USA

    Joseph F. Hoffman Ph.D.

  3. University of California, San Diego La Jolla, California, USA

    Darrell D. Fanestil M.D.

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Plenum Publishing Corporation

About this chapter

Cite this chapter

Macey, R.I. (1986). Mathematical Models of Membrane Transport Processes. In: Andreoli, T.E., Hoffman, J.F., Fanestil, D.D., Schultz, S.G. (eds) Physiology of Membrane Disorders. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2097-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2097-5_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9242-5

  • Online ISBN: 978-1-4613-2097-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation