A general mathematical version of the cell model of a leaky epithelium
for the NaCl absorption is presented, analysed and integrated numeric
ally. The model consists in the adequate differential equations that d
escribe the rate of change of the intracellular ion concentrations and
are expressed in strict accordance with the law of mass conservation.
The model includes many state variables representing ion concentratio
ns, the cell volume, and membrane potentials. Ion movements are descri
bed by the Michaelis-Menten kinetics or by the constant field flux equ
ation (Goldman-Hodgkin-Katz). In this paper, we model the intracellula
r ion concentrations, change in the cell volume, the transmembrane flu
x and membrane potentials of intestinal epithelium of both fresh water
and sea water fish, and generate several simulations (in both the ste
ady state and the transient slate analysis) that appear to accord with
prior experimental data in this area. For the ion movements of the se
a water fish intestine, there were included a Na+/K+ pump, a K+-Cl- sy
mport system, the K+ and Cl- channels in the basolateral membrane, whe
reas a Na+-K+-2Cl(-) cotransporter for NaCl absorption and K+ channels
are located in the apical membrane. In the fresh water fish intestina
l cells, the NaCl absorption is performed by two coupled antiporters N
a+/H+ and Cl-/HCO3- presumably responsible for the intracellular pH re
gulation. In this type of cells, Na+ and K+ channels are located withi
n the apical membrane, whereas Cl- channels are located within the bas
olateral membrane. The osmotically induced water transport across the
apical and basolateral membranes has been taken into account as well.
The simulations plot the steady state values for membrane potential di
fference, short-circuit current and intracellular ionic concentrations
using the magnitude of the transmembrane flux through the Na+/K+ pump
and Na+ -K+ 2Cl(-) cotransporter, or the basolateral Cl- permeability
as dependent variables. The model behaves appropriately with regard t
o several experimental studies regarding the hyperpolarization (sea wa
ter fish intestine) and depolarization (fresh water fish intestine) of
the apical membrane potential and inhibition of the short-circuit flu
x with reduced NaCl absorption. The model is also used to make several
analytical predictions regarding the response of the membrane potenti
al and ionic concentrations to variations in the basolateral Cl- flux.
Furthermore, maintaining conservation of both mass and electroneutral
ity and taking into account the osmolar forces is an important advanta
ge, because it allows a rigorous analysis of the relationship between
membrane potential difference, volume and flux. The model can be used
in the analysis and planning of the experiments and is capable of pred
icting the instantaneous values of ionic fluxes and intracellular conc
entrations and of cell volume. (C) 1998 Elsevier Science Ireland Ltd.
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