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A stochastic fire-diffuse-fire model of $$Ca^{2+}$$ release. (English) Zbl 1031.92011
Summary: Calcium ions are an important second messenger in living cells transmitting signals in the form of waves. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs) from spatially localised calcium stores. We develop a mathematical model of calcium release based upon a stochastic generalisation of the fire-diffuse-fire (FDF) threshold model for calcium release. Our model retains the discrete characteristics of the FDF model (spatially localised stores) but also incorporates a notion of release probability, via the introduction of threshold noise. It is possible to identify a critical level of noise defining a non-equilibrium phase-transition between abortive and propagating waves. This transition is shown to belong to the directed percolation universality class.

##### MSC:
 92C37 Cell biology 60K35 Interacting random processes; statistical mechanics type models; percolation theory