The Journal of Membrane Biology

, Volume 34, Issue 1, pp 103–144 | Cite as

Membrane permeability equations and their solutions for red cells

  • Jerome H. Milgram
  • A. K. Solomon


The mathematical equations for the transport of nonelectrolytes across cell membranes are critically examined and cast in forms suitable for solution which involve fewer approximations than has heretofore been commonly done. For the case of red cells, the equations are developed to include the effect of the variation in apparent nonosmotic water owing to the variation in hemoglobin concentration as the cell swells or shrinks. Two methods of solution of the equations are developed and studied and sample calculations are provided. It is shown that the solutions to the linearized equations commonly found in the literature are insufficiently accurate for some purposes and this inaccuracy is avoided by the methods given here. The importance of retaining the effects of variations in apparent nonosmotic water and in solute volume in the cell is demonstrated.


Cell Membrane Human Physiology Membrane Permeability Hemoglobin Concentration Mathematical Equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coddington, E.A., Levinson, N. 1955. Theory of Ordinary Differential Equations. McGraw-Hill, New YorkGoogle Scholar
  2. 2.
    Farmer, R.E.L., Macey, R.I. 1970. Perturbation of red cell volume: Rectification of osmotic flow.Biochim. Biophys. Acta. 196:53PubMedGoogle Scholar
  3. 3.
    Farmer, R.E.L., Macey, R.I. 1972. Perturbation of red cell volume, determination of membrane transport parameters for rapid penetrants.Biochim. Biophys. Acta. 290:290PubMedGoogle Scholar
  4. 4.
    Gary-Bobo, C.M. 1967. Non-solvent water in human erythrocytes and hemoglobin solutions.J. Gen. Physiol. 50:2547PubMedGoogle Scholar
  5. 5.
    Gary-Bobo, C.M., Solomon, A.K. 1968. Properties of hemoglobin solutions in red cells.J. Gen. Physiol. 52:825CrossRefPubMedGoogle Scholar
  6. 6.
    Goldstein, D.A., Solomon, A.K. 1960. Determination of equivalent pore radius for human red cells by osmotic pressure measurement.J. Gen. Physiol. 44:1PubMedGoogle Scholar
  7. 7.
    Hempling, H.G. 1967. Application of irreversible thermodynamics to a functional description of the tumor cell membrane.J. Cell. Physiol. 70:237Google Scholar
  8. 8.
    Johnson, J.A., Wilson, T.A. 1967. Osmotic volume changes induced by a permeable solute.J. Theoret. Biol. 17:304Google Scholar
  9. 9.
    Katchalsky, A., Curran, P.F. 1965. Nonequilibrium thermodynamics in Biophysics. p. 113. Harvard University Press, CambridgeGoogle Scholar
  10. 10.
    Kedem, O., Katchalsky, A. 1958. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes.Biochim. Biophys. Acta 27:229PubMedGoogle Scholar
  11. 11.
    Levitt, D.G. 1974. A new theory of transport for cell membrane pores. 1. General theory and application to red cell.Biochim. Biophys., Acta. 373:115Google Scholar
  12. 12.
    Owen, J.D., Eyring, E.M. 1975. Reflection coefficients of permeant molecules in human red cell suspensions.J. Gen. Physiol. 66:251PubMedGoogle Scholar
  13. 13.
    Rand, R.P., Burton, A.C. 1964. Mechanical properties of the red cell membrane. I. Membrane stiffness and intracellular pressure.Biophys. J. 4:115Google Scholar
  14. 14.
    Robinson, R.A., Stokes, R.H. 1959. Electrolyte Solutions (2nd ed.). Academic Press, New YorkGoogle Scholar
  15. 15.
    Savitz, D., Sidel, V.W., Solomon, A.K. 1964. Osmotic properties of human red cells.J. Gen. Physiol. 48:79CrossRefPubMedGoogle Scholar
  16. 16.
    Sha'afi, R.I., Gary-Bobo, C.M., Solomon, A.K. 1971. Permeability of red cell membranes to small hydrophylic and lipophilic solutes.J. Gen. Physiol. 58:238PubMedGoogle Scholar
  17. 17.
    Sha'afi, R.I., Rich, G.T., Mikulecky, D.C., Solomon, A.K. 1970. Determination of urea permeability in red cells by minimum method.J. Gen. Physiol. 55:427PubMedGoogle Scholar
  18. 18.
    Solomon, A.K., Milgram, J., Kirkwood, D.H. 1975. Observations on Levitt's “New Theory of Transport”.Biochim. Biophys. Acta. 406:157PubMedGoogle Scholar
  19. 19.
    Weast, R.C. (editor), 1966. Handbook of Chemistry and Physics (47th ed.). Chemical Rubber Company, ClevelandGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1977

Authors and Affiliations

  • Jerome H. Milgram
    • 1
  • A. K. Solomon
    • 1
  1. 1.Biophysical Laboratory, Harvard Medical SchoolHarvard UniversityCambridge

Personalised recommendations