  Many ion channels spontaneously switch between different levels of activity.
Although this behaviour known as modal gating has been observed for a long time
it is currently not well understood. Despite the fact that appropriately
representing activity changes is essential for accurately capturing time course
data from ion channels, systematic approaches for modelling modal gating are
currently not available. In this paper, we develop a modular approach for
building such a model in an iterative process. First, stochastic switching
between modes and stochastic opening and closing within modes are represented
in separate aggregated Markov models. Second, the continuous-time hierarchical
Markov model, a new modelling framework proposed here, then enables us to
combine these components so that in the integrated model both mode switching as
well as the kinetics within modes are appropriately represented. A mathematical
analysis reveals that the behaviour of the hierarchical Markov model naturally
depends on the properties of its components. We also demonstrate how a
hierarchical Markov model can be parameterised using experimental data and show
that it provides a better representation than a previous model of the same data
set. Because evidence is increasing that modal gating reflects underlying
molecular properties of the channel protein, it is likely that biophysical
processes are better captured by our new approach than in earlier models.
