A Subsequent Fit of Time Series and Amplitude Histogram of Patch-Clamp Records Reveals Rate Constants up to 1 per Microsecond

Abstract

Fast gating in time series of patch-clamp current demands powerful tools to reveal the rate constants of the adequate Hidden Markov model. Here, two approaches are presented to improve the temporal resolution of the direct fit of the time series. First, the prediction algorithm is extended to include intermediate currents between the nominal levels as caused by the anti-aliasing filter. This approach can reveal rate constants that are about 4 times higher than the corner frequency of the anti-aliasing filter. However, this approach is restricted to time series with very low noise. Second, the direct fit of the time series is combined with a beta fit, i.e., a fit of the deviations of the amplitude histogram from the Gaussian distribution. Since the "theoretical" amplitude histograms for higher-order Bessel filters cannot be calculated by analytical tools, they are generated from simulated time series. In a first approach, a simultaneous fit of the time series and of the Beta fit is tested. This simultaneous fit, however, inherits the drawbacks of both approaches, not the benefits. More successful is a subsequent fit: The fit of the time series yields a set of rate constants. The subsequent Beta fit uses the slow rate constants of the fit of the time series as fixed parameters and the optimization algorithm is restricted to the fast ones. The efficiency of this approach is illustrated by means of time series obtained from simulation and from the dominant K+ channel in Chara. This shows that temporal resolution can reach the microsecond range.