Regulation of Channel and Membrane Currents

Up to this point, we have considered single-ion channels whose currents are given by an equation having the form of Eq. 11. We also observed that a single channel is not open all of the time, but, instead, undergoes spontaneous transitions between open and closed states. It follows that the total current of an ion, i, across a unit area of membrane containing an ensemble of channels selective for i that are opening and closing at random, is given by:

where Ni is the total number of single channels per unit membrane area and Po is the open-time probability. Comparing Eq. 17 with Eq. 13, we see that the total conductance of a membrane to i (Gi) is simply NjPOgi. Furthermore, because (as we will soon see) PO and gi may be functions of Vm, a more general expression of Eq. 17 is:

Now, under steady-state conditions when Co and C\ are constant so that Et is constant (see Eq. 13), changes in It can result only from changes in N, Po, and/or gt. Under conditions where Nt is constant, physiologic regulation of channel activity or (Ji) is the result of changes in Po; that is, the channel is either nonconducting or fully conducting at fixed values of Vm and Et and the parameter that is regulated is the fraction of time that the channel is in either of these two states.

The two major physiologic determinants of Po are Vm and/or chemical regulators. Thus, channels are roughly categorized as voltage-gated or ligand-gated. It should be emphasized, however, that this classification is not ironclad; many channels that are predominantly considered voltage-gated are also influenced by chemical regulators, and some ligand-gated channels are influenced by Vm.

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