Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events

We present here a maximal likelihood algorithm for estimating single-channel kinetic parameters from idealized patch-clamp data. The algorithm takes into account missed events caused by limited time resolution of the recording system. Assuming a fixed dead time, we derive an explicit expression for the corrected transition rate matrix by generalizing the theory of Roux and Sauve (1985, Biophys. J, 48:149-158) to the case of multiple conductance levels. We use a variable metric optimizer with analytical derivatives for rapidly maximizing the likelihood. The algorithm is applicable to data containing substates and multiple identical or nonidentical channels. It allows multiple data sets obtained under different experimental conditions, e,g,, concentration, voltage, and force, to be fit simultaneously. It also permits a variety of constraints on rate constants and provides standard errors for all estimates of model parameters, The algorithm has been tested extensively on a variety of kinetic models with both simulated and experimental data, II is very efficient and robust; rate constants for a multistate model can often be extracted in a processing time of approximately 1 min, largely independent of the starting values.