A general solution to the time interval omission problem applied to single channel analysis

Abstract

To obtain the open or closed time interval distributions of patch clamp signals, several workers have used a half-amplitude minimum time interval criterion. Within this framework, no transition between states of different conductance levels is considered to have taken place if it leads to a time interval smaller than a certain critical value. This procedure modifies substantially the open or closed time interval distribution of the random signal to be analyzed, since time intervals well above the time resolution of the recording system may be interrupted by short gaps that may or may not satisfy the minimum time interval criterion. We present here a general theoretical framework by means of which the effect of time interval omission on time interval distributions can be taken into account. Based on the mathematical formalism provided by the Kolmogorov forward equation, special matrix operators are first defined. The general solution to the time omission problem in its integral form is then derived. In view of the poor computational feasibility of the resulting solution, a first-order approximation is also presented. This approximation consists essentially in neglecting the contribution of the undetected gaps to the total length of the resulting time interval. The exact and approximate solutions are then applied to two special kinetic schemes commonly found in single-channel studies, namely the O-C and C-O-C models. The applicability of the proposed formalism to the time interval distribution problem of a damped random signal is finally discussed.