Schedule Aug 31, 2003
Minimal Models for Calcium Waves
Dr. Stephen Coombes, Loughborough University

The De Young Keizer model for intracellular calcium release is based around a detailed description of the dynamics for inositol trisphosphate (IP3) receptors. Systematic reductions of the kinetic schemes for IP3 dynamics have proved especially fruitful in understanding the transition from excitable to oscillatory behaviour. With the inclusion of diffusive transport of calcium ions these reduced models support wave propagation. The analysis of waves, even in reduced models, is typically only possible with the use of numerical bifurcation techniques. Here we review the travelling wave properties of the biophysical De Young Keizer model and show that much of its behaviour can be reproduced by a simpler Fire-Diffuse-Fire (FDF) type model. The FDF model includes both a refractory process and an IP3 dependent threshold. Moreover, the FDF model may be naturally extended to include the discrete nature of calcium stores within a cell, without loss of analytical tractability. By considering calcium stores as idealised point sources we are able to explicitly construct solutions of the FDF model that correspond to saltatory travelling waves.
Finally we introduce a computationally inexpensive model of calcium release based upon a stochastic generalization of the Fire-Diffuse-Fire threshold model. This model incorporates a notion of release probability via the introduction of threshold noise. Apart from belonging to the Directed Percolation universality class this model is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously.

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