Membrane Transport: A Mathematical Investigation

  • Nathan A. Busch
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 200)


It is known that the primary constituents of the membranes of cells are lipids. These lipids are arranged in two layers and the membrane is frequently called a bilipid layer. Recent low intensity scanning electron micrographs of the bilipid layer has revealed that the bilipid layer has revealed that the bilipid membrane layer also contains proteins. The proteins in the bilipid membrane layer pass from one side of the layer to the other and thus constitute a “hole” in the membrane layer. The structure of the proteins is such that an essentially void space exists surrounded by the molecular structures of the protein. The exact functioning of the proteins has not yet been determined. The thesis of this paper is that the proteins act as mediators for the transport of specific catabolites. The supporting arguments for the thesis are in the form of mathematical models for the catabolite — protein interactions, and the results of simulations based upon the mathematical models. Physical verifications of the results presented in this paper await physiological experimental data. However the results of this work indicate that modest changes in the membrane proteins result in a significant change in the amount of catabolite transported across the cell membrane. The mediation of the catabolite transport by the proteins has the pathological implications that long term post-disease states of the cells may be linked closely to the altered states of the membrane proteins: which may occur during the period of the disease state.


Brownian Motion Potential Field Oxygen Transport Smoluchowski Equation Oxygen Density 
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  1. Busch, N. and D.F. Bruley, “Approximate-Analytical Solution of the Diffusion, Convection, and Reaction Problem in Homogeneous Media,” In Oxygen Transport to Tissue-VI, Ruston Meeting, (1983).Google Scholar
  2. Busch, N. and D.F. Bruley, “Stochastic Analysis of Oxygen Transport to Tissue,” In Oxygen Transport to Tissue-VII, Nijmegen Meeting, in press (1985).Google Scholar
  3. Chandrasekhar, S., “Stochastic Problems in Physics and Astronomy,” Reviews of Modern Physics, Volume 15, Number 1, 1–89, (1943).CrossRefGoogle Scholar
  4. Doob, J.L., “The Brownian Movement and Stochastic Equations,” Annals of Mathematics, Volume 43, Number 2, 351–368, (1942).CrossRefGoogle Scholar
  5. Kufahl, R., Busch, N. and D.F. Bruley, “Probabilistic Modeling of Oxygen Transport to Tissue,” In Oxygen Transport to Tissue, Dortmund Meeting, (1982).Google Scholar
  6. Lakshminarayanaiah, N., Equations of Membrane Biophysics, Academic Press, (Harcourt Brace Jovanovich, Publ.), New York, (1984).Google Scholar
  7. Lightfood, Jr, E.N., Transport Phenomena and Living Systems, John Wiley and Sons, New York, (1974).Google Scholar
  8. Longmuir, I.S., Knopp, J.A., Tei-Pei Lee, Benson, D and Tang, A. “The Intracellular Heterogeneity of Oxygen Concentrations as Measured by Ultraviolet Television Microscropy of PBA Flourescence Quenching by Oxygen,” In Oxygen Transport to Tissue-III, 93–97, ( 1978 ). Starsak, M.E., The Physical Chemistry of Membranes, Academic Press, Inc, New York, (1984).Google Scholar
  9. Silver, I.A. Personal Communication. (1985).Google Scholar
  10. Uhlenbeck, G.E. and Ornstein, L.S., “On the Theory of Brownian Motion,” Physical Review, Volume 36, 823–841, (1930).CrossRefGoogle Scholar
  11. Uhlenbeck, G.E. and Wang, M.C., “On the Theory of the Brownian Motion II,” Reviews of Modern Physics, Volume 17, Numbers 2 and 3, 323–342, (1945).CrossRefGoogle Scholar
  12. Unwin, N., and Henderson, R., “The Structure of Proteins in Biological Membranes,” Scientific American, Volume 270, Number 2, 56–66. (1984)Google Scholar


  1. Lakshminarayanaiah, N., Transport Phenomena in Membranes, Academic Press, (Harcourt Brace Jovanovich, Publ.), New York, (1969).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Nathan A. Busch
    • 1
  1. 1.University of BristolBristolUK

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