Frank Ball (Mathematical Sciences, University of Nottingham, UK)
Abstract:Ion channels are protein molecules embedded in cell membranes. They are fundamental units of the nervous system and contain aqueous pores that may be open or closed. When open, ion channels permit selective flow of ions across the membrane. The patch clamp technique enables the experimenter to record the current flowing across a single ion channel. Over the past three decades, there has been considerable interest in the development and analysis of stochastic models to describe the opening and closing of ion channels, and in methods of inference for such models. The gating mechanism of a single ion channel is usually modelled as a finite state continuous-time Markov chain. The state space is partitioned into two classes, termed open and closed, corresponding to the receptor channel being open or closed, and it is possible to observe only which class, rather than which state, the process is in. A consequence of this aggregation of states is that distinct underlying processes may be equivalent, in that they yield probabilistically indistinguishable aggregated processes. Single-channel models are usually specified in terms of a kinetic scheme which gives the allowable transitions between states. The above equivalence means that (i) a scheme may be unidentifiable, in that there exist equivalent models that satisfy the constraints imposed by the scheme, and (ii) two distinct schemes may be indistinguishable, in that there exist models from the two schemes that are equivalent. In this talk, I will give a brief introduction to ion channel modelling and associated identifiability problems. I will also describe a method for investigating identifiability and distinguishability of a range of practically relevant single channel gating schemes, and illustrate it by application to schemes that have been proposed for glycine receptor channels. Finally, I will outline some future challenges.