Cable analysis with the whole-cell patch clamp. Theory and experiment

Abstract

A theoretical analysis was undertaken of a Rall motoneuron under voltage clamp with a finite access resistance. This model is relevant to the conditions of the whole-cell patch clamp, which to date has been used very little for cable analysis. It was shown that the soma and cable charging currents can be distinguished, and that the soma is charged with a time constant approximately equal to the access resistance times the somatic capacitance. Thus, the charging time of the soma is similar to what it would be if the cell had no process. Simple formulas were derived that can be used to calculate the electrotonic length, the membrane time constant, and the soma-dendrite resistance ratio of a cell with a cylindrical process. With the aid of these formulas, reasonable estimates of parameter values were recovered from simulated transient currents. Tests of the Rall model were proposed to determine when there is an equivalent cylinder that is consistent with observed charging behavior. The analysis was extended to a cable with an open end and to a model in which the soma and dendrite have different membrane time constants. It was shown that with voltage-clamp data estimates of electrical parameters other than rho are relatively insensitive to differences between the membrane properties of the soma and dendrite. The methods of cable analysis introduced here were illustrated by application to charging transients recorded from a hippocampal pyramidal cell and from a neurohypophysial nerve ending. The Rall model provided a good description of the pyramidal cell current transient but was inconsistent with the charging behavior observed for the nerve ending. With the recent technical advance of patch clamp recording in brain slices, the analysis presented here should help neurophysiologists investigate cable properties in a wide variety of systems.