Adjustments for the Display of Quantized Ion Channel Dwell Times in Histograms with Logarithmic Bins

J. Alex Stark and Stephen B. Hladky

Accepted by the Biophysical Journal, October 1999.

Dwell time histograms are often plotted as part of patch clamp investigations of ion channel currents. The advantages of plotting these histograms with a logarithmic time axis were demonstrated by A.L. Blatz, K.L. Magleby and O.B. McManus (1986, J. Physiol. [Lond.], 378:141-174 and 1987, Pfluegers Arch. 410:530-553) and F.J. Sigworth and S.M. Sine (1987, Biophys. J. 52:1047-1054). Sigworth and Sine argued that the interpretation of such histograms is simplified if the counts are presented in a manner similar to a probability density function. However, when ion channel records are recorded as a discrete time series, the dwell times are quantized. As a result, the mapping of dwell times to logarithmically spaced bins is highly irregular: bins may be empty and significant irregularities extend beyond 100 samples duration. Using simple approximations based on the nature of the binning process and the transformation rules for probability density functions, we develop adjustments for the display of the counts to compensate for this effect. Tests with simulated data suggest that this procedure provides a faithful representation of the data.