Period-Adding Bifurcation with Chaos in the Interspike Intervals Generated by an Experimental Neural Pacemaker

Abstract

The dynamics of the generation of the various spike trains in neural pacemakers is of fundamental importance to the understanding of neural coding. Recent studies have demonstrated, theoretically and experimentally, that neural pacemakers produce chaotic oscillations. Deeper analyses in several neuronal models have revealed many nonlinear phenomena including periodadding bifurcations whose existence has not been experimentally confirmed. In this letter, we reported that the period-adding bifurcation with chaos was observed in the interspike interval (ISI) series generated by an experimental neural pacemaker when the extracellular calcium concentration was changed or a potassium channel blocker was administered at the site of the pacemaker. We also simulated our experimental discoveries by computing a generalized model of excitable cells. The chaotic phenomenon in the experiment and that in the model were demonstrated and compared using the nonlinear forecasting and surrogate data methods.

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

“…These experimental results showed that periodic firing and chaotic firing, bifurcation to chaos could be generated in biological system and in nerve system [7]. After these pioneering studies, many experiments performed on different assembles of animals, such as neural pacemaker in rats [8][9][10][11][12][13] , neurons including isolated neuron of pyloric central pattern generating (CPG) in the lobster stomatogastric ganglion [14][15][16][17][18], dopamine neurons [19][20][21][22], extracellular and intracellular measurements from small assembles in hippocampal slices [23], sensory receptors including cold receptors, caudal photoreceptor of crayfish and electroreceptors of the catfish [24][25][26][27], living β-cells in the mouse pancreatic islet [28], dorsal root ganglion (DRG) of rats [29], teleost Mauthner cells' synaptic noise [30], epileptic activity [31,32] and so on, were done to identify the deterministic dynamics underlying complex and irregular firing patterns. The bifurcation routes to chaos and the nonlinear time series analysis method played important roles in identifying chaotic firings.…”

“…In a series of experimental studies, chaotic bursting and spiking were observed. The chaotic bursting lay within a period-doubling bifurcation cascade from period 1 bursting to period 2, period 4, chaotic burstings [10], or lay in a period-adding bifurcation scenario from period 1 bursting to period 2 , chaotic, period 3, chaotic, period 4 burstings [8][9][10][11], as shown in Fig. 5.…”

Models Wagging the Dog: Are Circuits Constructed with Disparate Parameters?

“…It has, however, been observed that neurons can have chaotic regimes (Elson et al 1999;Ren 1997;Schiff et al 1994) and it is known that self-organized systems often approach such instable parameter regions for greater flexibility (Bak et al 1988;Bertschinger and Natschlager 2004;Kauffman and Johnsen 1991). In this light, disregarding models solely based on the observation of sensitive and/or irregular dynamics appears to be somewhat presumptuous.…”

Analysis of the noise-induced bursting-spiking transition in a pancreaticβ-cell model

“…We have studied this model as a paradigmatic example of electrophysiologically bursting cell models, as we are interested in developing an approach to obtain as much information as possible from a biological system in a noisy environment. In the literature several tools have been suggested for studying irregular biological phenomena, such as heart rate variability [29] or neural spiking signals [30], both in noiseless and in noisy environments. We believe, however, that ␤-cell models warrant a thorough study all by themselves, and our work points in this direction.…”