Membrane potential and time requirements for detection of weak signals by voltage-gated ion channels

The question of minimum detection limits for biological processes sensitive to membrane potential perturbations has arisen in various contexts. Of special interest are the prediction of theoretical limits for sensory perception processes and for possible biological effects of environmental or therapeutic electric and magnetic fields. A new method is presented here, addressing the particular case in which perturbations of membrane potential affect the gating rate probability of voltage-sensitive ion channels. Using a two-state model for channel gating, the influence of the perturbing potential on the mean fraction of open channels is approximated by a Boltzmann distribution, and integrated over time to obtain a quantity proportional to the net change in expected charge transfer through the membrane. This change in net charge transfer (the signal, S) is compared to the expected root mean variance in charge transfer (the noise, N) due to random channel gating. Using a nominal criterion of S/N = 1, a model is developed for predicting the minimum time and number of ion channels necessary to detect a given membrane potential. Example calculations, carried out for a gating charge of 6, indicate that a 1 microV induced membrane potential can be detected after 10 ms by an ensemble of less than 10(8) ion channels.