Frank G. Ball

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 25-30 years, 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, after a brief introduction to ion channel modelling, I will develop 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 recently for glycine receptor channels.

**Keywords:** Ion channel models; Aggregated Markov processes; Identifiability

**Biography:** Frank Ball is a Professor of Applied Probability at the University of Nottingham. His research is concerned mainly with applications of stochastic processes and statistics to problems in biology, in particular to epidemic modelling and to ion channel modelling. He has published extensively in both of these areas and he is currently on the editorial boards of Mathematical Biosciences and Mathematical Medicine and Biology.