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Many ion channels spontaneously switch between different levels of activity.Although this behaviour known as modal gating has been observed for a long timeit is currently not well understood. Despite the fact that appropriatelyrepresenting activity changes is essential for accurately capturing time coursedata from ion channels, systematic approaches for modelling modal gating arecurrently not available. In this paper, we develop a modular approach forbuilding such a model in an iterative process. First, stochastic switchingbetween modes and stochastic opening and closing within modes are representedin separate aggregated Markov models. Second, the continuous-time hierarchicalMarkov model, a new modelling framework proposed here, then enables us tocombine these components so that in the integrated model both mode switching aswell as the kinetics within modes are appropriately represented. A mathematicalanalysis reveals that the behaviour of the hierarchical Markov model naturallydepends on the properties of its components. We also demonstrate how ahierarchical Markov model can be parameterised using experimental data and showthat it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlyingmolecular properties of the channel protein, it is likely that biophysicalprocesses are better captured by our new approach than in earlier models.

Modelling modal gating of ion channels with hierarchical Markov models