Cluster-based model for calcium excitations from coupled IP3R channels

Abstract

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as puffs, waves and oscillations that occur on various spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release puffs, waves and spikes respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. Further, we extend our approach to a stochastic reaction-diffusion model with the IP3 dependent randomly distributed clusters of channels. Our model reveals how the main characteristics of the activity of clusters, namely inter-puff intervals (IPIs), depend on the IP3 loads. Furthermore, by performing a correlation analysis of [Ca²⁺] traces at the neighbouring clusters, we obtain the principal characteristics of the membrane which define the possibility of Ca²⁺ wave initiation and propagation. Using given approach, we aim to link the local properties of IP3R channels and clusters, such as channel type or coupling between channels, with the global patterns which may emerge from these channels, e. g. spikes, waves or oscillations. We study the effect of cooperative behaviour of the IP3 clusters found by Tauq-Ur-Rahman et al. [2009] and also introduce insight into the clustering of the channels using the Ising-like approach.

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