Yulia Timofeeva* and Stephen Coombes
Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, U.K.
(Received November 27, 2002; Accepted December 11, 2002)
Keywords: Calcium Sparks, Noise, Non-equilibrium Phase-Transition, Directed-Percolation
Abstract. 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. Here 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 characteristic 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.