Emergence of ion channel modal gating from independent subunit kinetics

Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca2+ concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.

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.

Statistical analysis of modal gating in ion channels

Ion channels regulate the concentrations of ions within cells. By stochastically opening and closing its pore, they enable or prevent ions from crossing the cell membrane. However, rather than opening with a constant probability, many ion channels switch between several different levels of activity even if the experimental conditions are unchanged. This phenomenon is known as modal gating: instead of directly adapting its activity, the channel seems to mix sojourns in active and inactive modes in order to exhibit intermediate open probabilities. Evidence is accumulating that modal gating rather than modulation of opening and closing at a faster time scale is the primary regulatory mechanism of ion channels. However, currently, no method is available for reliably calculating sojourns in different modes. In order to address this challenge, we develop a statistical framework for segmenting single-channel datasets into segments that are characteristic for particular modes. The algorithm finds the number of mode changes, detects their locations and infers the open probabilities of the modes. We apply our approach to data from the inositol-trisphosphate receptor. Based upon these results, we propose that mode changes originate from alternative conformational states of the channel protein that determine a certain level of channel activity.