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Directed percolation in a two-dimensional stochastic fire-diffuse-fire model.

Y Timofeeva1, S Coombes

  • 1Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom. yulia@ma.hw.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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The stochastic fire-diffuse-fire model, an intracellular calcium release model, belongs to the directed percolation universality class. This finding emerges from numerical experiments on wave propagation and phase transitions.

Area of Science:

  • Complex systems
  • Statistical physics
  • Biophysics

Background:

  • Intracellular calcium release is crucial for cell signaling.
  • Existing models often simplify the discrete and stochastic nature of calcium stores.
  • Spontaneous release events can lead to complex wave dynamics.

Purpose of the Study:

  • To classify the universality class of the two-dimensional stochastic fire-diffuse-fire model.
  • To investigate the phase transition between propagating and non-propagating waves.
  • To determine the critical noise level for this transition.

Main Methods:

  • Extensive numerical experiments were conducted.
  • The model simulates noisy threshold elements coupled by a diffusing signal.
  • Analysis involved examining the local slope of the survival probability to find the critical noise level.

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Main Results:

  • The two-dimensional stochastic fire-diffuse-fire model was found to belong to the directed percolation universality class.
  • The model exhibits spontaneous release events forming circular and spiral waves.
  • A critical noise level was identified for a nonequilibrium phase transition.

Conclusions:

  • The fire-diffuse-fire model provides a framework for understanding intracellular calcium dynamics.
  • Directed percolation universality governs the behavior of this complex system.
  • Noise plays a critical role in the phase transition of wave propagation.