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Stochastic Binding of Ca²⁺ Ions in the Dyadic Cleft; Continuous versus Random Walk Description of Diffusion

Simula Research Laboratory, Lysaker, Norway

Correspondence: Address reprint requests to Johan Hake, Tel.: 47-98-06-0848; E-mail: hake{at}simula.no.

Ca²⁺ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca²⁺ ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca²⁺ signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca²⁺ diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.