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Bifurcation, bursting, and spike frequency adaptation
J Guckenheimer1, R Harris-Warrick, J Peck
1Mathematics Department, Cornell University, Ithaca, NY 14853, USA. gucken@cam.cornell.edu
Journal of Computational Neuroscience
|July 1, 1997
Summary
This study mathematically models spike frequency adaptation in neural systems, revealing two distinct mechanisms that cause neurons to stop firing. These findings offer insights into neural plasticity and firing termination.
Area of Science:
- Computational neuroscience
- Dynamical systems theory
- Mathematical biology
Background:
- Neural systems exhibit adaptive properties on slow time scales, distinct from rapid action potential firing.
- Spike frequency adaptation (SFA) is a key neural process reducing action potential firing frequency, potentially leading to quiescence.
Purpose of the Study:
- To mathematically investigate the mechanisms underlying spike frequency adaptation.
- To analyze the role of singularly perturbed dynamical systems in SFA.
- To differentiate bifurcation mechanisms based on interspike interval dynamics.
Main Methods:
- Utilized singularly perturbed dynamical systems to model neural adaptation.
- Focused analysis on the lengths of successive interspike intervals during adaptation.
- Compared theoretical predictions with experimental data from a model of the lobster LP cell.
Main Results:
- Identified two distinct bifurcation mechanisms responsible for firing termination in neural systems.
- Characterized these mechanisms by the rate at which interspike intervals lengthen near termination.
- Found theoretical predictions align with SFA measurements in the LP cell model.
Conclusions:
- Singularly perturbed systems provide a framework for understanding SFA.
- The rate of interspike interval slowing distinguishes different firing termination mechanisms.
- Mathematical modeling successfully captures key aspects of neural adaptation in biological systems.