title: Statistical properties of ion channel records. Part I: relationship to the macroscopic current.
abstract: Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), through G(t) = P(t) - H(t) * Q(t) where P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.
authors.affiliation: Cardiac Bioelectricity and Arrhythmia Center, Washington University in St. Louis, 290 Whitaker Hall, Campus Box 1097, One Brooking Drive, St. Louis, MO 63130-4899, USA. ali@biomed.wustl.edu
authors.forename: Ali
authors.initials: A
authors.lastname: Nekouzadeh
authors.forename: Yoram
authors.initials: Y
authors.lastname: Rudy
mesh_terms: D015640:Ion Channel Gating; D007473:Ion Channels / Q000378:metabolism*; D051036:Large-Conductance Calcium-Activated Potassium Channels / Q000378:metabolism; D008390:Markov Chains; D008433:Mathematics; D008954:Models, Biological; D018408:Patch-Clamp Techniques; D011336:Probability; D013269:Stochastic Processes
chemical_list: D007473:Ion Channels; D051036:Large-Conductance Calcium-Activated Potassium Channels