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.
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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
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
Curran, P.F., MacIntosh, J.R. 1962. A model system for biological water transport.Nature (London) 193:347
Diamond, J.M. 1962. The reabsorptive function of the gall-bladder.J. Physiol. (London) 161:442
Diamond, J.M. 1964a. Transport of salt and water in rabbit and guinea pig gall bladder.J. Gen. Physiol. 48:1
Diamond, J.M. 1964b. The mechanism of isotonic water transport.J. Gen. Physiol. 48:15
Diamond, J.M. 1966. Non-linear osmosis.J. Physiol. (London) 183:58
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
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
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
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
Hill, A.E. 1975b. Solute-solvent coupling in epithelia: Contribution of the junctional pathway to fluid production.Proc. R. Soc. London B. 191:537
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
Hill, A.E., Hill, B.S. 1978a. Sucrose fluxes and junctional water flow acrossNecturus gall bladder epithelium.Proc. R. Soc. London B. 200:163
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
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
Huss, R.E., Stephenson, J.L. 1979. A mathematical model of proximal tubule absorption.J. Membrane Biol. 47:377
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
Lutz, M.D., Cardinal, J., Burg, M.B. 1973. Electrical resistance of renal proximal tubule perfusedin vitro.Am. J. Physiol. 225:729
Mejia, R., Stephenson, J.L., LeVeque, R.J. 1980. A test problem for kidney models.Math. Biosci. 50:129
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
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
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
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
Reuss, L., Finn, A.L. 1977. Effects of luminal hyperosmolality on electrical pathways ofNecturus gallbladder.Am. J. Physiol. 232:C99
Sackin, H., Boulpaep, E.L. 1975. Models for coupling of salt and water transport. Proximal tubular reabsorption inNecturus kidney.J. Gen. Physiol. 66:671
Segel, L.A. 1970. Standing-gradient flows driven by active solute transport.J. Theoret. Biol. 29:233
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
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
Spring, K.R., Hope, A. 1978. Size and shape of the lateral intercellular spaces in a living epithelium.Science 200:54
Spring, K.R., Hope, A. 1979a. Dimensions of cells and lateral intercellular spaces in livingNecturus gallbladder.Fed. Proc. 38:128
Spring, K.R., Hope, A. 1979b. Fluid transport and the dimensions of cells and interspaces of livingNecturus, gallbladder.J. Gen. Physiol. 73:287
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
Tormey, J.M., Diamond, J.M. 1967. The ultrastructural route of fluid transport in rabbit gall bladder.J. Gen. Physiol. 50:2031
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
Welling, L.W., Grantham, J.J. 1972. Physical properties of isolated perfused renal tubules and tubular basement membranes.J. Clin. Invest. 51:1063
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
Whitlock, R.T., Wheeler, H.O. 1964. Coupled transport of solute and water across rabbit gallbladder epithelium.J. Clin. Invest. 48:2249
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
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
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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
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DOI: https://doi.org/10.1007/BF01870828