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General method for the derivation and numerical solution of epithelial transport models

The Journal of Membrane Biology volume 82, pages 67–82 (1984)Cite this article

Summary

A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.

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Author notes

  1. Richard Latta

    Present address: School of Medicine, Medical College of Pennsylvania, Philadelphia, Pennsylvania

Affiliations

  1. Department of Physiology and Biophysics, Health Sciences Center, State University of New York at Stony Brook, 11794, Stony Brook, New York

    Richard Latta, Chris Clausen & Leon C. Moore

Authors
  1. Richard Latta
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  2. Chris Clausen
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  3. Leon C. Moore
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Latta, R., Clausen, C. & Moore, L.C. General method for the derivation and numerical solution of epithelial transport models. J. Membrain Biol. 82, 67–82 (1984). https://doi.org/10.1007/BF01870733

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  • DOI: https://doi.org/10.1007/BF01870733

Key Words

  • Epithelial transport
  • mathematical models
  • cell volume
  • intracellular composition
  • sodium transport
  • Ussing model
  • tight epithelia
  • mammalian urinary bladder