Is the voltage divider ratio a reliable estimate of the resistance ratio of the cell membranes in tubular epithelia?

Abstract

The length dependence of the voltage divider ratio (VDR) was investigated in a double cable model of tubular epithelia with point source current injection into the tubular lumen in order to find out, whether there is a region, in which the VDR — as in flat sheet epithelia — is an appropriate measure of the relative magnitude of the apical (r _a) and basal (r _b) cell membrane resistances. Irrespective of the choice of the cable parameters, we find that VDR, defined as luminal over cellular voltage deflection, overestimates the resistance ratio (r _a+r _b):r _b near the origin, but underestimates it at distances (χ) greater than 1 luminal length constant (β). In the region χ<β there is a crossover point, where VDR is an accurate estimate of the resistance ratio. If the difference between VDR at the origin and at large distances (χ>β) is small, then VDR is a good estimate of the resistance ratio. This is also true, if VDR is constant between χ∼0.5 β and χ>β, (with the exception of some cases, in which the longitudinal resistance in the cell column is exceedingly high). If the latter conditions do not apply, we find that VDR, as measured at χ=β, underestimates the resistance ratio at worst only by 8.8%, provided the cable properties are such that the luminal voltage attenuation exhibits only one single exponential (with maximum tolerable amplitude deviation of 5% at the origin). Cable analysis measurements on rat proximal tubule indicate that VDR is constant in the range between χ∼0.5 β and χ>β. Hence (VDR)_χ=β may be considered as a valid approximation of the ratio of cell membrane resistances in this epithelium.