Estimation of open dwell time and problems of identifiability in channel experiments

Abstract

Membrane channels can open or close in response to a change in membrane voltage. An important neurophysiological problem is the estimation of the duration of a channel opening, called the open dwell time. In many experiments, however, the recorded measurement is often a summation of several open dwell times from multi-channels. Under a standard kinetic model, this would give rise to a distribution of the total open dwell time which is a mixture of gamma distributions with binomial weights. For such a mixture, the maximum likelihood estimates are difficult to compute. We illustrate an easily implementable estimation method introduced by Le Cam. The method produces asymptotically optimal estimates. We also discuss problems of parameter identification and the potential bias associated with using a continuous-time model to analyze discrete-time data.