The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected
- 15 September 1990
- journal article
- Published by The Royal Society in Philosophical Transactions A
- Vol. 332 (1627), 511-538
- https://doi.org/10.1098/rsta.1990.0129
Abstract
The openings and shuttings of individual ion channel molecules can be described by a Markov process with discrete states in continuous time. The predicted distributions of the durations of open times, shut times, bursts of openings, etc., are all described, in principle, by mixtures of exponential densities. In practice it is usually found that some of the open times, and/or shut times, are too short to be detected reliably. If a fixed dead-time r is assumed then it is possible to define, as an approximation to what is actually observed, an ‘ extended opening ’ or e-opening which starts with an opening of duration at least r followed by any number of openings and shuttings, all the shut times being shorter than r ; the e-opening ends when a shut time longer than r occurs. A similar definition is used for e-shut times. Several authors have derived approximations to the distribution of durations of e-openings and e-shuttings. In this paper the exact distributions are derived. They are defined piecewise over the intervals r to 2r, 2r to 3 r ,..., etc., the distribution in each interval being a sum of products of polynomials in t with exponential terms. The number of terms is finite, but increases as intervals get further from t = r. An asymptotic form for large t (for which the exact solution becomes difficult to compute) is given for the two state case. The exact solution is compared with several approximations, some of which are shown to be good enough for use in most practical applications.Keywords
This publication has 30 references indexed in Scilit:
- Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordingsProceedings of the Royal Society of London. B. Biological Sciences, 1989
- The use of dwell time cross-correlation functions to study single-ion channel gating kineticsBiophysical Journal, 1988
- Single-channel autocorrelation functions: the effects of time interval omissionBiophysical Journal, 1988
- A note on correlations in single ion channel recordsProceedings of the Royal Society of London. B. Biological Sciences, 1987
- Correcting single channel data for missed eventsBiophysical Journal, 1986
- The Principles of the Stochastic Interpretation of Ion-Channel MechanismsPublished by Springer Science and Business Media LLC ,1983
- On the stochastic properties of bursts of single ion channel openings and of clusters of burstsPhilosophical Transactions of the Royal Society of London. B, Biological Sciences, 1982
- On the stochastic properties of single ion channelsProceedings of the Royal Society of London. B. Biological Sciences, 1981
- Relaxation and fluctuations of membrane currents that flow through drug-operated channelsProceedings of the Royal Society of London. B. Biological Sciences, 1977
- Commutative ordinary differential operators. II.—The identity P n = Q mProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1931