Modelling modal gating of ion channels with hierarchical Markov models

TL;DR

This paper introduces a hierarchical Markov model framework for accurately representing modal gating in ion channels, capturing both mode switching and within-mode kinetics, and demonstrates its superiority over previous models using experimental data.

Contribution

The paper presents a novel modular hierarchical Markov model framework for modal gating, enabling better representation of ion channel activity changes and their underlying molecular processes.

Findings

Hierarchical Markov models effectively capture modal gating behavior.

The new model outperforms previous models in fitting experimental data.

Mathematical analysis links model behavior to component properties.

Abstract

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.