Embedded in cell membranes are specialised proteins, called ion channels, which regulate many aspects of cell function. Data on channel current is routinely collected by the patch clamp technique. Suitable stochastic models, commonly finite state Markov chains with superimposed noise, are used to describe the channel behaviour, and hence the current, over time. Inference based on such models is important in assessing the usually extensive data, and a variety of approaches have been considered. These include: methods based on sojourn times derived by idealization from the original data; maximization of the likelihood directly, by Markov chain Monte Carlo, or by use of hidden Markov models. Many challenging problems arise, e.g. from low-pass filtering during data collection, missed brief events, aggregation, identifiability, and from attempts to fit such complex models to large quantities of data.
This talk reports on joint work with Nazim Khan, Barry Madsen and Boris Martinac (all of UWA), Geoff Yeo (Murdoch) and Rob.Edeson (Sir Charles Gairdner Hospital). We studied high quality mulitlevel data from the large conductance mechanosensitive channel (MscL) in E. coli with the initial aim of determining the number of conductance levels of the channel, together with the mean current, mean dwell time and equilibrium probability of occupancy for each level. Statistical analysis was based on hidden Markov models (HMMs) incorporating state-dependent white noise and moving average adjustment for filtering, with maximum likelihood parameter estimates obtained using a EM (expectation-maximisation) based iteration. Implementation of the above approach for such multiconductance data required care in order to avoid misleading results. The brevity of intermediate level sojourns indicated high bandwidth data was required to deal adequately with the data, a view supported also by simulation studies.