Amplitude histograms can identify positively but not negatively coupled channels

We investigated the ability of amplitude distributions to determine if the gating of a pair of channels is coupled. These distributions are expressed as probability density amplitude histograms with peaks corresponding to zero, one, or two open channels. If the channels gate independently, the areas under these peaks (A, B, and C, respectively) determine the open probabilities of the two channels (p(1) and p(2)). Manivannan et al. (Biophys J 1994;61:216) showed that if Delta=B(2)/AC was less than 4 then the channel gating is coupled. We defined a similar parameter, D=(B(2)/4)-AC. If D<0 then channel gating is coupled. However, amplitude histograms with D0 are consistent with both independent and coupled gating. We further present a simple model in which channels are assumed to be identical and can be positively or negatively coupled. Here, amplitude histograms determine q=(B+2C)/2 (open probability of the coupled channels) and r=-D (the coupling parameter). Thus, positively coupled channels (r0) produce amplitude histograms with D<0 whereas negatively coupled channels (r<0) produce amplitude histograms with D0.