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¹ Departments of Mathematics at Universidad Simón Bolívar and Instituto Venezolano de Investigaciones Científicas (IVIC), Caracas 1020-A, Venezuela
² Department of Physiology, Loyola University of Chicago, Maywood, IL 60153
³ Department of Physiology, Texas Tech University HSC, Lubbock, TX 79430

Address correspondence to Ariel L. Escobar, Department of Physiology, Texas Tech University HSC, 3601 4th Street, Lubbock, TX 79430. Fax: (806) 743-1512; email: ariel.escobar{at}ttuhsc.edu

Type-II ryanodine receptor channels (RYRs) play a fundamental role in intracellular Ca²⁺ dynamics in heart. The processes of activation, inactivation, and regulation of these channels have been the subject of intensive research and the focus of recent debates. Typically, approaches to understand these processes involve statistical analysis of single RYRs, involving signal restoration, model estimation, and selection. These tasks are usually performed by following rather phenomenological criteria that turn models into self-fulfilling prophecies. Here, a thorough statistical treatment is applied by modeling single RYRs using aggregated hidden Markov models. Inferences are made using Bayesian statistics and stochastic search methods known as Markov chain Monte Carlo. These methods allow extension of the temporal resolution of the analysis far beyond the limits of previous approaches and provide a direct measure of the uncertainties associated with every estimation step, together with a direct assessment of why and where a particular model fails. Analyses of single RYRs at several Ca²⁺ concentrations are made by considering 16 models, some of them previously reported in the literature. Results clearly show that single RYRs have Ca²⁺-dependent gating modes. Moreover, our results demonstrate that single RYRs responding to a sudden change in Ca²⁺ display adaptation kinetics. Interestingly, best ranked models predict microscopic reversibility when monovalent cations are used as the main permeating species. Finally, the extended bandwidth revealed the existence of novel fast buzz-mode at low Ca²⁺ concentrations.

Key Words: ryanodine channel gating • adaptation • hidden Markov models • Bayesian statistics • Markov chain Monte Carlo

Abbreviations used in this paper: BIC, Bayes information criterion; CICR, Ca²⁺-induced Ca²⁺ release; HMM, hidden Markov model; MCMC, Markov chain Monte Carlo.

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