Statistical Analysis of Multiple Ion Channel Data

It is often assumed that ion channels in cell membrane patches gate independently. However, in the present study nicotinic receptor patch clamp data obtained in cell-attached mode from embryonic chick myotubes suggest that the distribution of steady-state probabilities for conductance multiples arising from concurrent channel openings may not be binomial. In patches where up to four active channels were observed, the probabilities of two or more concurrent openings were greater than expected, suggesting positive cooperativity. For the case of two active channels, we extended the analysis by assuming that 1) individual receptors (not necessarily identical) could be modeled by a five-state (three closed and two open) continuous-time Markov process with equal agonist binding affinity at two recognition sites, and 2) cooperativity between channels could occur through instantaneous changes in specific transition rates in one channel following a change in conductance state of the neighboring channel. This allowed calculation of open and closed sojourn time density functions for either channel conditional on the neighboring channel being open or closed. Simulation studies of two channel systems, with channels being either independent or cooperative, nonidentical or identical, supported the discriminatory power of the optimization algorithm. The experimental results suggested that individual acetylcholine receptors were kinetically identical and that the open state of one channel increased the probability of opening of its neighbor.

Section: Resultsmentioning

confidence: 99%

Evidence for Cooperativity Between Nicotinic Acetylcholine Receptors in Patch Clamp Records

Keleshian

Edeson

Liu

et al. 2000

“…Failure to fit a binomial distribution using a goodnessof-fit criterion, would indicate that one of these assumptions is incorrect (Glasbey and Martin, 1988;Dabrowski et al, 1990). However, this may not be a powerful test (Yeramian et al, 1986;Dabrowski et al, 1990;Dabrowski and McDonald, 1991), and the possibility remains that subtle interactions among neighboring channels in a patch, or that microheterogeneity, either in the channels or in the membrane, may invalidate the generality of the binomial distribution.…”

Section: Real Life Considerationsmentioning

confidence: 99%

“…Ion channels have been reported to show a slow switching between modes of gating (e.g., see Hess et al, 1984;Horn et al, 1984), implying that p may not be constant. This is a problem of stationarity, which can be tested, for example, using the methods in Dabrowski and McDonald (1991). Nonstationarity could lead to an underestimation of the number of channels, if recordings are made, fortuitously or deliberately, during a period of high activity (Colquhoun and Hawkes, 1990).…”

Section: Real Life Considerationsmentioning

confidence: 99%

Estimating the number of channels in patch recordings

Horn

1991

113

The estimation of the number of channels in a patch was assumed to be equivalent to the estimation of the binomial parameter n. Seven estimators were evaluated, using data sets simulated for a range of parameters appropriate for single channel recording experiments. No single estimator was best for all parameters; a combination of estimators is a possible option to avoid the biases of individual estimators. All estimators were highly accurate in estimating n in the case that n = 1. For n

“…Here a simplification is presented that can be applied if the channels are independent as can be tested according to Dabrowski and McDonald (1992). Our method makes use of a specific property of the Kronecker product of matrixexponentials (the Kronecker product is also often referred to as tensor product).…”

Section: Extension Of the Single-channel Approach To Multiple Channelsmentioning

confidence: 99%

Estimation of kinetic rate constants from multi-channel recordings by a direct fit of the time series

Albertsen¹,

Hansen²

1994

The maximum-likelihood technique for the direct estimation of rate constants from the measured patch clamp current is extended to the analysis of multi-channel recordings, including channels with subconductance levels. The algorithm utilizes a simplified approach for the calculation of the matrix exponentials of the probability matrix from the rate constants of the Markov model of the involved channel(s) by making use of the Kronecker sum and product. The extension to multi-channel analysis is tested by the application to simulated data. For these tests, three different channel models were selected: a two-state model, a three-state model with two open states of different conductance, and a three-state model with two closed states. For the simulations, time series of these models were calculated from the related first-order, finite-state, continuous-time Markov processes. Blue background noise was added, and the signals were filtered by a digital filter similar to the anti-aliasing low-pass. The tests showed that the fit algorithm revealed good estimates of the original rate constants from time series of simulated records with up to four independent and identical channels even in the case of signal-to-noise ratios being as low as 2. The number of channels in a record can be determined from the dependence of the likelihood on channel number. For large enough data sets, it takes on a maximum when the assumed channel number is equal to the "true" channel number.