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

  • Transport Processes, Metabolism and Endocrinology; Kidney, Gastrointestinal Tract, and Exocrine Glands
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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.

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Abbreviations

r a :

resistance per unit length of luminal membrane (Ω cm)

r b :

resistance per unit length of basal membrane (Ω cm)

r s :

resistance per unit length of shunt pathway (Ω cm)

r i :

core resistance of luminal cable per unit length (Ω/cm)

r c :

core resistance of cellular cable per unit length (Ω/cm)

χ:

distance from current source (cm)

V i :

the change in the lumen potential due to current injection (V)

V c :

the change in the cellular potential due to current injection (V)

I o :

injected current (A)

λi :

length constant of the luminal cable if isolated from the cellular cable (cm)

λc :

length constant of the cellular cable if isolated from the luminal cable (cm)

α, β:

length constants actually observed in the double cable (cm)

i a :

current flow through the apical resistance at χ (A/cm)

i b :

current flow through the basal resistance at χ (A/cm)

i s :

current flow through the shunt pathway at χ (A/cm)

i c :

current flow along the cellular cable at χ (A)

i i :

current flow along the luminal cable at χ (A)

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Authors and Affiliations

  1. Department of Physiology, University of Sydney, Sydney, New South Wales, Australia

    D. I. Cook

  2. Zentrum der Physiologie, Klinikum der J. W. Goethe-Universität, Theodor-Stern-Kai 7, D-6000, Frankfurt am Main 70, Federal Republic of Germany

    E. Frömter

Authors
  1. D. I. Cook
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  2. E. Frömter
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Additional information

Dedicated to Prof. T. Hoshi, Dept. of Physiology, University of Tokyo, Japan, a pioneer in renal tubular resistance analysis

This work was supported by the Deutsche Forschungsgemeinschaft

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Cook, D.I., Frömter, E. Is the voltage divider ratio a reliable estimate of the resistance ratio of the cell membranes in tubular epithelia?. Pflugers Arch. 403, 388–395 (1985). https://doi.org/10.1007/BF00589251

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  • DOI: https://doi.org/10.1007/BF00589251

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