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This paper presents a new algorithm for the detection of channel openings and closures from noisy current signals, especially for the correct generation and interpretation of open-time and closed-time histograms. The Hinkley detector is a nonlinear off-line jump detection algorithm from the field of fault detection. Here, an improved version, the higher-order Hinkley detector H.O.H.D., is developed. A general description of the sensitivity of a detector is introduced by the time resolution tres. This allows a comparison of the nonlinear detectors with the standard threshold detectors preceded by a low-pass filter for noise suppression. By means of application to simulated and real data, the performance of the detection algorithms is investigated. The higher-order Hinkley detector gave the best results with respect to correct reconstruction of the event length, to a small amount of missed brief events as well as to the ability to achieve short time resolution without pretending false events, especially in the presence of colored noise.

Spontaneous cooperatively of K+ channels is studied in excised patches of Chara corallina tonoplasts. Bar histograms (dwell time versus number of open channels) are constructed from the time series of current by means of the higher-order Hinkley detector (R. Schultze and S. Draber. 1993. J. Membr. Biol. 132:41-52). A statistical test, based on these bar histograms, shows that the channels are not independent. Further analysis reveals that the channels are cooperatively changing their open probability, which leads to the idea of cooperative mode shifting.

Patch-clamp studies have been employed in order to check whether the assumption of a multi-ion single-file pore is necessary for the explanation of the anomalous mole fraction effect or whether this effect can also be explained by a single-barrier enzyme kinetic model. Experiments in the cell-attached configuration were done on the tonoplast membrane of cytoplasmic droplets of Nitella in solutions containing 150 mol m-3 of K+ plus Tl+ with seven different K+/Tl+ ratios. At first sight, the results seem to support the multi-ion single-file pore, because apparent open channel conductivity displays the anomalous mole fraction effect, whereas open-probability has not been found to be dependent on the K+/Tl+ ratio. Changes in open probability would be expected for a single-barrier enzyme kinetic model with a lazy state. On the other hand, the lazy-state model is more successful in explaining the measured I-V curves. The entire slope of the apparent open channel current-voltage curves rotates with changing K+/Tl+ ratios in the whole voltage range between -100 and +80 mV. Numerical calculations on the basis of multi-ion single-file pores could create the anomalous mole fraction effect only in a limited voltage range with intersecting I-V curves. The apparent absence of an effect on open probability which is postulated by the lazy-state model can be explained if switching into and out of the lazy state is faster than can be resolved by the temporal resolution of 1 msec.