Abstract
Some neurons generate endogenous rhythms with a period of a few hundred milliseconds,while others generate rhythms with a period of a few tens of seconds. Sometimes rhythms appear chaotic. Explaining how these neurons can generate various modes of oscillation with a widely ranging frequency is a challenge. In the first part of this review, we illustrate that such rhythms can be generated from simple yet elegant mathematical models. Chaos embedded in rhythmic activity has interesting characteristics that are not seen in other physical systems. Understanding of how these neurons utilizes endogenous rhythms to communicate with each other is important in elucidating where the brain gets various rhythms and why it can pervert into abnormal rhythms under diseased conditions. Using the islet of Langerhans in pancreas as an example, in the second part of this review, we illustrate how insulin secreting β‐cells communicate with glucagon secreting α‐cells to achieve an optimal insulin release.
Highlights
Neurons generate action potentials upon receiving synaptic input or external stimuli
Two types of chaos have been discovered in the models presently reviewed: period-reducing chaos that leads to spindle oscillations (Figs. 7 and 13) and period-adding chaos that leads to an inverse period-doubling sequence (Figs. 9 and 14)
In the period-reducing scenario exhibited by thalamocortical neuron (TCN) (Fig. 7), the spikes are reduced one by one at first
Summary
Neurons generate action potentials upon receiving synaptic input or external stimuli. The delta oscillation consists of fast spikes that appear on the top of a slow wave, as can be seen more clearly in an expanded scale on the lower right trace. The burst typically consists of groups of 2-10 spikes separated by a long duration of postburst hyperpolarizations (0.5-2 s) This can be seen more clearly in an expanded scale on the right. To explain endogenous rhythmic activity, our group has developed a one-compartment neuronal model (Chay, 1983; 1984; 1985a; 1990a,b; 1993a,b; 1996a,b; Chay and Fan, 1993; Chay and Cook, 1988; Chay and Lee, 1990; Chay et al, 1995) This compartmental model is a model that lumps the dendritic membrane with the soma, and all the inputs are delivered to the lumped membrane. These models utilize three distinct mechanisms in order to burst the first model utilizes an oscillating T-type Ca+ current, the second model utilizes a Ca:+-sensitive K+ channel that is modulated by oscillating intracellular Caz+ concentration, and the third model utilizes a voltage-independent Ca2+ channel that is modulated by the calcium concentration in the ER
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