Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise

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Abstract
(1) Analysis of the durations of open and shut intervals measured from single channel currents provides a means to investigate the mechanisms of channel gating. Durations of open and shut intervals are conveniently measured from single channel data by using a threshold level to indicate transitions between open and shut states. This paper presents a detailed characterization of sampling, binning, and noise errors associated with 50% threshold analysis, provides criteria to reduce these errors, methods to correct for them, and presents an efficient means of data handling for binning and plotting interval durations. (2) Measuring interval durations by sampling at a fixed rate introduces two types of errors, (a) the number of intervals of a given measured duration are increased (promoted) over that expected in the absence of sampling, producing a sampling promotion error, (b) sampling decreases the total fraction of true intervals that are detected, producing a sampling detection error. Sampling errors can be reduced to negligible levels if the actual or effective (after interpolation) sampling period is less than 10–20% of both the dead time and fastest time constant in the distribution of intervals. Dead time is given by the duration of a true interval that has a filtered amplitude equal to 50% of the true amplitude. (3) Methods are presented to correct for sampling promotion error during least squares and maximum likelihood fitting. Sampling detection error is more difficult to correct, but an empirical description of the sampling detection error can be used to calculate the effective fraction of detected events with sampling. (4) Noise in the single channel current record can produce two types of error. (a) If noise peaks in the absence of channel activity exceed the threshold for detection, then false channel events of brief duration are produced. Sufficient filtering will prevent this type of error. (b) Noise can also increase the total fraction of true intervals that are detected, producing a noise detection error. Increased filtering over that required to prevent false events is not necessarily the best method for reducing noise detection error, as increased filtering can prevent detection of the faster exponential components. (5) Noise detection error can be reduced in two ways: (a) an empirical description of the noise detection error can be used to calculate the effective fraction of detected events in the presence of noise. (b) The sampling period can be selected so that the sampling detection error cancels the noise detection error. (6) Combining (binning) intervals with a range of durations into single bins promotes the amplitudes of the bins, producing a binning promotion error similar to the sampling promotion error, but of smaller magnitude. Binning promotion error can be avoided if bin width is less than 20–30% of the fastest time constant. Methods are presented to correct for binning promotion error for interval durations measured with continuous time resolution or by sampling. (7) Storing and plotting intervals from single channels is often difficult because interval durations and frequency of occurrence can range over many orders of magnitude. Binning intervals based on the logarithms of their durations provides a convenient method to overcome these difficulties, as several hundred bins are sufficient to bin any number of intervals of any expected duration with essentially no errors associated with fitting and plotting the distributions of intervals. Log binning can reduce the time required to fit the data by orders of magnitude for large numbers of events, and log binning provides increasing bin widths as interval durations increase to combine the necessary number of intervals for plotting of data without excessive fluctuation. (8) Plotting distributions of intervals on log-log plots is an effective way to present distributions of intervals that span orders of magnitude in frequency of occurrence and duration. Each bump in the distributions on log-log plots indicates an exponential component. (9) Using the techniques described above for efficient data handling and for the prevention or reduction of errors associated with sampling, binning, and noise, true rate constants and expected distributions of intervals were determined from sampled, log binning, filtered, and noisy data with errors of typically less than 1–2% for two and four state models.