title: Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.
abstract: The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel models is publicly available.
authors.affiliation: Department of Mathematics, Imperial College London, London, UK; CoMPLEX, University College London, London, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: Epstein
authors.affiliation: Department of Mathematics, Imperial College London, London, UK. Electronic address: b.calderhead@imperial.ac.uk.
authors.forename: Ben
authors.initials: B
authors.lastname: Calderhead
authors.affiliation: Department of Statistics, University of Warwick, Coventry, UK.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Girolami
authors.affiliation: Department of Neuroscience, Physiology & Pharmacology, University College London, London, UK.
authors.forename: Lucia G
authors.initials: LG
authors.lastname: Sivilotti
mesh_terms: D001499:Bayes Theorem; D007473:Ion Channels / Q000378:metabolism*; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method
chemical_list: D007473:Ion Channels