Skip to main content
SpringerLink
Log in

Models of coupled salt and water transport across leaky epithelia

  • Articles
  • Published:
The Journal of Membrane Biology Aims and scope Submit manuscript

Summary

A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

M :

Mucosal bath

S :

Serosal bath

E :

Extracellular channel

A :

Tight junction

L :

Lateral membrane bounding the intercellular space

M :

Composite mucosal membrane comprised of tight junction and lateral membrane

B :

Basement membrane

C 0 :

Reference salt concentration, mOsm/cm3

C α :

Difference from reference,C 0, of salt concentration in compartment α, mOsm/cm3

P α :

Hydrostatic pressure, mmHg

C i :

Mucosal impermeant species concentration, mOsm/cm3

A β :

Membrane area, cm2

L p β :

Hydraulic conductivity, cm/sec mmHg

L β :

(=A β ·L p β) Hydraulic conductivity, cm3/sec mmHg

< β :

Reflection coefficient

h β :

Salt permeability, cm/sec

H β :

(=A β ·h β) Salt permeability, cm3/sec

\(\bar C_\beta \) :

Difference of mean membrane salt concentration from the referenceC 0, mOsm/cm3

L p :

Epithelial hydraulic conductivity, cm3/sec mmHg

σ:

Epithelial reflection coefficient

H :

Epithelial salt permeabilty, cm3/sec

$$L_{LB} = \frac{{L_L L_B }}{{L_L + L_B }}L_{MB} = \frac{{L_M L_B }}{{L_M + L_B }}$$
J v β :

Transmembrane volume flow, cm3/sec

J s β :

Transmembrane salt flux, mOsm/sec

N :

Metabolically driven salt transport into the lateral intercellular space, mOsm/sec

J v :

Transepithelial volume flow, cm3/sec

J v :

Transepithelial salt flux, mOsm/sec

C R :

Ratio of transepithelial salt flux to water flow (reabsorbate concentration), mOsm/cm3

γ:

Osmotic coupling coefficient, (C 0/C R )

C *M :

Mucosal equilibrium concentration-mucosal deviation from reference for which reabsorbate concentration is equal to mucosal bath concentration (serosa at reference), mOsm/cm3

C * S :

Serosal equilibrium concentration- serosal deviation from reference for which reabsorbate concentration is equal to serosal bath concentration (mucosa at reference), mOsm/cm3

C * :

Mucosal deviation from reference for which reabsorbate concentration is equal to the reference concentration (serosa at reference), mOsm/cm3

\(\hat C\) :

Strength of transport-maximum salt gradient against which volume can be transported, mOsm/cm3

References

  • Andreoli, T.E., Schafer, J.A. 1978. Volume absorption in the pars recta. III. Luminal hypotonicity as a driving force for isotonic volume absorption.Am. J. Physiol. 234:F349

    Google Scholar 

  • Andreoli, T.E., Schafer, J.A., Troutman, S.L. 1978. Perfusion rate-dependence of transepithelial osmosis in isolated proximal convoluted tubules: Estimation of the hydraulic conductance.Kidney Int.14:263

    Google Scholar 

  • Curran, P.F., MacIntosh, J.R. 1962. A model system for biological water transport.Nature (London) 193:347

    Google Scholar 

  • Diamond, J.M. 1962. The reabsorptive function of the gall-bladder.J. Physiol. (London) 161:442

    Google Scholar 

  • Diamond, J.M. 1964a. Transport of salt and water in rabbit and guinea pig gall bladder.J. Gen. Physiol. 48:1

    Google Scholar 

  • Diamond, J.M. 1964b. The mechanism of isotonic water transport.J. Gen. Physiol. 48:15

    Google Scholar 

  • Diamond, J.M. 1966. Non-linear osmosis.J. Physiol. (London) 183:58

    Google Scholar 

  • Diamond, J.M. 1978. Solute-linked water transport in epithelia.In: Membrane Transport Processes. J.F. Hoffman, editor. pp. 257–276. Raven Press, New York

    Google Scholar 

  • Diamond, J.M., Bossert, W.H. 1967. Standing-gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia.J. Gen. Physiol. 50:2061

    Google Scholar 

  • Henin, S., Cremaschi, D., Schettino, T., Meyer, G., Donin, C.L.L., Cotelli, F. 1977. Electrical parameters in gallbladders of different species. Their contribution to the origin of the transmural potential difference.J. Membrane Biol. 34:73

    Google Scholar 

  • Hill, A.E. 1975a. Solute-solvent coupling in epithelia: A critical examination of the standing-gradient osmotic flow theory.Proc. R. Soc. London B. 190:99

    Google Scholar 

  • Hill, A.E. 1975b. Solute-solvent coupling in epithelia: Contribution of the junctional pathway to fluid production.Proc. R. Soc. London B. 191:537

    Google Scholar 

  • Hill, A.E. 1977. General mechanisms of salt-water coupling in epithelia.In: Transport of Ions and Water in Animals. B. Gupta, R. Moreton, J. Oschman, and B. Wall, editors. pp. 183–214. Academic Press, Inc., New York

    Google Scholar 

  • Hill, A.E., Hill, B.S. 1978a. Sucrose fluxes and junctional water flow acrossNecturus gall bladder epithelium.Proc. R. Soc. London B. 200:163

    Google Scholar 

  • Hill, B.S., Hill, A.E. 1978b. Fluid transfer byNecturus gall bladder epithelium as a function of osmolarity.Proc. R. Soc. London B. 200:151

    Google Scholar 

  • Huss, R.E., Marsh, D.J. 1975. A model of NaCl and water flow through paracellular pathways of renal proximal tubules.J. Membrane Biol. 23:305

    Google Scholar 

  • Huss, R.E., Stephenson, J.L. 1979. A mathematical model of proximal tubule absorption.J. Membrane Biol. 47:377

    Google Scholar 

  • Lin, C.C., Segel, L.A. 1974. Illustration of techniques on a physiological flow problem.In: Mathematics Applied to Deterministic Problems in the Natural Sciences. pp. 244–276. Macmillan, New York

    Google Scholar 

  • Lutz, M.D., Cardinal, J., Burg, M.B. 1973. Electrical resistance of renal proximal tubule perfusedin vitro.Am. J. Physiol. 225:729

    Google Scholar 

  • Mejia, R., Stephenson, J.L., LeVeque, R.J. 1980. A test problem for kidney models.Math. Biosci. 50:129

    Google Scholar 

  • Mikulecky, D.C. 1977. A simple network thermodynamic method for series-parallel coupled flows: II. The non-linear theory, with applications to coupled solute and volume flow in a series membrane.J. Theoret. Biol. 69:511

    Google Scholar 

  • Mikulecky, D.C., Thomas, S.R. 1978. A simple network thermodynamic method for series-parallel coupled flows: III. Application to coupled solute and volume flows through epithelial membranes.J. Theoret. Biol. 73:697

    Google Scholar 

  • Mikulecky, D.C., Wiegand, W.A., Shiner, J.S. 1977. A simple network thermodynamic method for modeling series-parallel coupled flows: I. The linear case.J. Theoret. Biol. 69:471

    Google Scholar 

  • Patlak, C.S., Goldstein, D.A., Hoffman, J.F. 1963. The flow of solute and solvent across a two-membrane system.J. Theoret. Biol. 5:426

    Google Scholar 

  • Reuss, L., Finn, A.L. 1977. Effects of luminal hyperosmolality on electrical pathways ofNecturus gallbladder.Am. J. Physiol. 232:C99

    Google Scholar 

  • Sackin, H., Boulpaep, E.L. 1975. Models for coupling of salt and water transport. Proximal tubular reabsorption inNecturus kidney.J. Gen. Physiol. 66:671

    Google Scholar 

  • Segel, L.A. 1970. Standing-gradient flows driven by active solute transport.J. Theoret. Biol. 29:233

    Google Scholar 

  • Sha'afi, R.I., Rich, G.T., Sidel, V.W., Bossert, W., Solomon, A.K. 1967. The effect of the unstirred layer on human red cell water permeability.J. Gen. Physiol. 50:1377

    Google Scholar 

  • Smulders, A.P., Tormey, J.M., Wright, E.M. 1972. The effect of osmotically induced water flows on the permeability and ultrastructure of the rabbit gallbladder.J. Membrane Biol. 7:164

    Google Scholar 

  • Spring, K.R., Hope, A. 1978. Size and shape of the lateral intercellular spaces in a living epithelium.Science 200:54

    Google Scholar 

  • Spring, K.R., Hope, A. 1979a. Dimensions of cells and lateral intercellular spaces in livingNecturus gallbladder.Fed. Proc. 38:128

    Google Scholar 

  • Spring, K.R., Hope, A. 1979b. Fluid transport and the dimensions of cells and interspaces of livingNecturus, gallbladder.J. Gen. Physiol. 73:287

    Google Scholar 

  • Thomas, S.R., Mikulecky, D.C. 1978. A network thermodynamic model of salt and water flow across the kidney proximal tubule.Am. J. Physiol. 235:F638

    Google Scholar 

  • Tormey, J.M., Diamond, J.M. 1967. The ultrastructural route of fluid transport in rabbit gall bladder.J. Gen. Physiol. 50:2031

    Google Scholar 

  • Weinstein, A.M., Stephenson, J.L. 1978. Transport across a simple epithelium.FASEB, 62nd Annual Meeting. Atlantic City, N.J., April 9–14. Abstract, p. 569

  • Weinstein, A.M., Stephenson, J.L. 1979. Electrolyte transport across a simple epithelium. Steady-state and transient analysis.Biophys. J. 27:165

    Google Scholar 

  • Welling, L.W., Grantham, J.J. 1972. Physical properties of isolated perfused renal tubules and tubular basement membranes.J. Clin. Invest. 51:1063

    Google Scholar 

  • Welling, L.W., Welling, D.J. 1975. Surface areas of brush border and lateral cell walls in the rabbit proximal nephron.Kidney Int 8:343

    Google Scholar 

  • Whitlock, R.T., Wheeler, H.O. 1964. Coupled transport of solute and water across rabbit gallbladder epithelium.J. Clin. Invest. 48:2249

    Google Scholar 

  • Wright, E.M., Diamond, J.M. 1968. Effects of pH and polyvalent cations on the selective permeability of gall-bladder epithelium to monovalent ions.Biochim. Biophys. Acta 163:57

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Section on Theoretical Biophysics, National Heart, Lung and Blood Institute, and Mathematical Research Branch, National Institute of Arthritis, Metabolism, and Digestive Diseases, National Institutes of Health, 20205, Bethesda, Maryland

    Alan M. Weinstein & John L. Stephenson

Authors
  1. Alan M. Weinstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Stephenson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weinstein, A.M., Stephenson, J.L. Models of coupled salt and water transport across leaky epithelia. J. Membrain Biol. 60, 1–20 (1981). https://doi.org/10.1007/BF01870828

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01870828

Key words

Search

Navigation