Single-channel autocorrelation functions: the effects of time interval omission

Abstract

We present a general mathematical framework for analyzing the dynamic aspects of single channel kinetics incorporating time interval omission. An algorithm for computing model autocorrelation functions, incorporating time interval omission, is described. We show, under quite general conditions, that the form of these autocorrelations is identical to that which would be obtained if time interval omission was absent. We also show, again under quite general conditions, that zero correlations are necessarily a consequence of the underlying gating mechanism and not an artefact of time interval omission. The theory is illustrated by a numerical study of an allosteric model for the gating mechanism of the locust muscle glutamate receptor-channel.

The α1K276E Startle Disease Mutation Reveals Multiple Intermediate States in the Gating of Glycine Receptors

“…A linear sequence of shut and open states would predict no correlations. The observed correlation is unlikely to result from distortions introduced by finite time resolution (Ball and Sansom, 1988). In fact, missing brief events as a consequence of limited time resolution may tend to obscure such correlations (Schorge et al, 2005).…”

Hurst Analysis Applied to the Study of Single Calcium-activated Potassium Channel Kinetics

“…This fact indicates that models which assume that the channelprotein makes transitions only between discrete states of energy are not completely adequate to describe the kinetic process of single-ion channels, at least similar to the one shown here. Markovian models which assume the presence of more than one gate state may show memory and can generate correlations in the open and closed time records (McManus et al, 1985;Ball & Sansom, 1988;Colqhoun & Hawkes, 1987;Steinberg, 1987;Labarca et al, 1985;Jackson et al, 1983). The problem with them is that they are not able to describe fractal long-term correlation, as the Hurst analysis does.…”

“…The switching between these states is considered random and the probabilities per unit time (rate constants) of transitions between them depend only on the present state, and not on the previous history of the channel (Colquhoun & Hawkes, 1981, 1982. However, short-term correlation in experimental and simulated data has been shown to exist in some channels (McManus et al, 1985;Ball & Sansom, 1988;Colqhoun & Hawkes, 1987;Steinberg, 1987;Labarca et al, 1985;Jackson et al, 1983) and this can be interpreted to indicate that the channel kinetics is a process with short-term memory. The studies of Toib et al (1998) have shown direct experimental evidence for the existence of memory in the function of ion channels.…”

Activation of N‐methyl‐D‐aspartate receptors by L‐glutamate in cells dissociated from adult rat hippocampus.

“…However, examination of the NMDA RECEPTOR ACTIVATION data at each individual glutamate concentration shows no obvious trend related to glutamate concentration in the adjacent interval analysis which could have enhanced the correlations observed here. In addition, although the effects of limited time resolution may change the magnitude of any observed correlation, limited time resolution is unlikely to generate an artifactual correlation (Ball & Sansom, 1988).…”