Abstract
We establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a nonequilibrium phase transition between propagating and nonpropagating waves is obtained by an examination of the local slope delta (t) of the survival probability Pi(t) proportional exp [-delta(t)] for a wave to propagate for a time t .
Highlights
In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class
The fluorescent imaging of localized Ca2+ release events has made it clear that Ca2+ release dynamics is a stochastic process that occurs at spatially discrete sites that are clusters of IP3 receptors in the endoplasmic reticulum or ryanodine receptors in the sarcoplasmic reticulum [3, 4]
In this paper we describe the two dimensional stochastic fire-diffuse-fire (FDF) model of Ca2+ release and use extensive numerical simulations to highlight the interesting statistical properties for the waves generated by the model
Summary
In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. Cellular calcium signals generally do not occur uniformly throughout a cell but are initiated at specific sites and spread in the form of saltatory waves [2].
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