Modelling modal gating of ion channels with hierarchical Markov models.
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 parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. 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.
Systems Biology Laboratory, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia; Centre for Systems Genomics, University of Melbourne, Melbourne, Australia.
Ivo
0000-0002-0706-6307
I
Siekmann
School of Mathematics and Statistics , University of Melbourne , Melbourne, Australia.
Mark
M
Fackrell
Systems Biology Laboratory, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia; Centre for Systems Genomics, University of Melbourne, Melbourne, Australia; School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia; School of Medicine, University of Melbourne, Melbourne, Australia; Australian Research Council Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne, Australia.
Edmund J
EJ
Crampin
School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia; Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Australia.
Peter
P
Taylor
continuous-time hierarchical Markov model; inositol-trisphosphate receptor; ion channels; modal gating