From Spikers to Bursters Via Coupling: Help From Heterogeneity

Abstract

It has been shown previously that identical spiking cells, incapable of bursting by themselves, may burst under weak diffusive coupling conditions. With stronger coupling, the coupled system reverts to bursting can be recovered by introducing heterogeneity in the model parameters. For a two-cell system, we explain the phenomenon with bifurcation analysis. For larger clusters of coupled cells, we demonstrate by numerical simulation that the phenomenon carries over. In addition, we use a perturbation analysis to deduce the dependence of the heterogeneity parameter used in the bifurcation analysis on the original heterogeneity parameters and the coupling strength. Implications of the phenomenon of emergent bursting are discussed in the context of electrical activity in pancreatic beta cells.

Synchronization study in ring-like and grid-like neuronal networks

“…It have been observed in many models such as Hindmarsh-Rose model (Wang 1993), models of heart interneurons (Shilnikov and Cymbalyuk 2005a) and b-cells model (De Vries and Sherman 2001) etc. In this paper, a modified version of Hodgkin-Huxley approach (Hodgkin and Huxley 1952), the so-called Huber-Braun model is adopted (Finke et al 2008;Postnova et al 2010).…”

Hybrid discrete-time neural networks

“…Detailed analyses of Rulkov neuron models can be found in Rulkov (2001), de Vries (2001), de Vries & Sherman (2001, Tanaka et al (2006) and Ibarz et al (2007a,b;. In figure 1, we display the main properties of the chaotic model.…”

Mathematical models for insulin secretion in pancreatic β-cells

“…105 In this context, as a different explanation, the heterogeneity hypothesis focuses on the heterogeneous cells, which have different narrow parameter windows for bursting, and consider their coupling as the main reason for the phenomenon. 24,[106][107][108] The introduction of diversity among the elements destabilizes the quiescent state of an excitable medium and leads to global oscillations even when each individual element of the medium is quiescent in isolation.…”

“…89 In contrast to existing studies mostly focused on the synchronizing role of coupling between adjacent cells in the slow oscillation, 106,110 they focused on the effects of the gapjunction coupling in the bursting electrical activity. The rapid firing in the active phase of bursting is asynchronous between neighbors 111 and these fluctuating currents through the gap junction act like noise, enhancing the robust bursting action potential.…”