Membrane-Related Diseases - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 161

Fig. 7.7 Elements in Horis-
berger's model [ 18 ]

tight junctions

Gb K

Ga Na

Gb Cl

Ga Cl

P

Na-K-
2Cl

apical
membrane

basolateral
membrane

then defined by an equation giving the flux of ions or the current flowing through
this transporter as a function of ion concentrations on both sides of the membrane,
and the membrane potential.
Horisberger's model involved the following quantities:
In the apical membrane:

Na + conductance ( Ga Na ) provided by ENaC, •

Cl − conductance ( Ga Cl ) provided by CFTR,

•

K + conductance ( Ga K ).
In the basolateral Membrane:

•

K + and Cl − conductances ( Gb K and Gb Cl ), •

• Na-K pump,

• Na/K/Cl cotransporter.

Furthermore, tight junctions between cells correspond to a paracellular “shunt” path-
way.
The equation defining the pump is:

I p max

I p = (7.1)

1 + ( k Na i / c Na i )

n Hill

and it uses a predefined parameter, the I p max , k N a and the steep Hill equation constant
( n Hill ), which is determined experimentally. Horisberger found that the average value
for this parameter is somewhere between 2 and 3, and judiciously chose 3 in the
model.
The passive channels including the ENaC, CFTR, and the basolateral Cl − channels
were modeled by the Goldman-Hodgkin-Katz (GHK) equation.