Mathematics, Department of
Date of this Version
2010
Citation
Journal of Integrative Neuroscience, 9(2010), pp.31–47.
Abstract
For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in opposite transmembrane directions to materialize, and if only one ion pump is left to operate, the plastic states will be lost to a rigid asymptotically stable state either as a resting potential, or a limit cycle with a fixed pulse frequency, or a spike-burst with a fixed spike-per-burst number. These metastable-plastic pulses and spike-bursts may be used as information-bearing alphabet for a communication system that neurons are thought to be.
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Computational Neuroscience Commons, Dynamic Systems Commons, Molecular and Cellular Neuroscience Commons, Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons, Systems Neuroscience Commons