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A Kinetic Model of Single and Clustered IP₃ Receptors in the Absence of Ca²⁺ Feedback

Jianwei Shuai ^*, John E. Pearson , J. Kevin Foskett , Don-On Daniel Mak  and Ian Parker ^*

^* Department of Neurobiology and Behavior, University of California, Irvine, California; Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico; and Department of Physiology, University of Pennsylvania, School of Medicine, Philadelphia, Pennsylvania

Correspondence: Address reprint requests to Dr. Jianwei Shuai, Dept. of Neurobiology and Behavior, University of California, Irvine, CA 92697-4550. Tel.: 949-824-7833; Fax: 949-824-2447; E-mail: shuaij{at}uci.edu.

Ca²⁺ liberation through inositol 1,4,5-trisphosphate receptor (IP₃R) channels generates complex patterns of spatiotemporal cellular Ca²⁺ signals owing to the biphasic modulation of channel gating by Ca²⁺ itself. These processes have been extensively studied in Xenopus oocytes, where imaging studies have revealed local Ca²⁺ signals ("puffs") arising from clusters of IP₃R, and patch-clamp studies on isolated oocyte nuclei have yielded extensive data on IP₃R gating kinetics. To bridge these two levels of experimental data, we developed an IP₃R model and applied stochastic simulation and transition matrix theory to predict the behavior of individual and clustered IP₃R channels. The channel model consists of four identical, independent subunits, each of which has an IP₃-binding site together with one activating and one inactivating Ca²⁺-binding site. The channel opens when at least three subunits undergo a conformational change to an "active" state after binding IP₃ and Ca²⁺. The model successfully reproduces patch-clamp data; including the dependence of open probability, mean open duration, and mean closed duration on [IP₃] and [Ca²⁺]. Notably, the biexponential distribution of open-time duration and the dependence of mean open time on [Ca²⁺] are explained by populations of openings involving either three or four active subunits. As a first step toward applying the single IP₃R model to describe cellular responses, we then simulated measurements of puff latency after step increases of [IP₃]. Assuming that stochastic opening of a single IP₃R at basal cytosolic [Ca²⁺] and any given [IP₃] has a high probability of rapidly triggering neighboring channels by calcium-induced calcium release to evoke a puff, optimal correspondence with experimental data of puff latencies after photorelease of IP₃ was obtained when the cluster contained a total of 40–70 IP₃Rs.

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