Single-Channel Data and Missed Events: Analysis of a Two-State Markov Model
Patch-clamp recording permits investigation of the gating kinetics of single ion channels. Careful statistical analysis of kinetic data can yield clues as to the molecular events underlying channel gating. However, it is important that such analysis should take full account of the limitations that arise from the finite time resolution of patch-clamp recording techniques. Single-ion-channel data are generally interpreted in terms of Markov process models of channel gating mechanisms. Experimental channel records suffer from time interval omission, i.e. failure to detect brief channel openings and closings. This leads to an identifiability problem when analysing single-channel data, i.e. different gating mechanisms provide equally convincing descriptions of the same experimental data. We consider a two-state Markov model of receptor-channel gating in which the channel opening rate is proportional to the agonist concentration, [Note: See the image of page 61 for this formatted text] C --OA. By using computer-simulated data, the approximate likelihood of the data is maximized to yield parameter estimates for the model. At a single agonist concentration there is an identifiability problem in that two pairs of parameter estimates are obtained. The `true' parameter estimates cannot be distinguished from the `false' ones. By considering data corresponding to a range of agonist concentrations one may identify the `true' parameter estimates as those that do not change as the agonist concentration is increased. Alternatively, one may identify the `true' parameter estimates directly by maximizing a global likelihood, the latter being obtained by simultaneous consideration of data obtained at several different agonist concentrations. Three different approximations to the likelihood function are shown to yield comparable results. This overall approach appears to be valid provided that the degree to time interval omission is not unreasonably high.
Proceedings of the Royal Society of London Series B
- Pub Date:
- October 1990