Abstract
A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells.
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This work was supported by the National Science Foundation Grant DMS-97-04-966.
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Pernarowski, M. Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells. Bull. Math. Biol. 62, 101–120 (2000). https://doi.org/10.1006/bulm.1999.0143
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DOI: https://doi.org/10.1006/bulm.1999.0143