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Spontaneous secondary spiking in excitable cells
1Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada.
Journal of Theoretical Biology
|June 30, 2000
Summary
Researchers simplified a crab neuron model to understand spontaneous secondary spikes. A reduced three-dimensional model, including a slow inward current, successfully replicated this electrical activity, revealing crucial parameters for spiking behavior.
Area of Science:
- Computational neuroscience
- Mathematical biology
- Neuronal electrical activity modeling
Background:
- Kepler & Marder (1993) proposed a model for crab neuron electrical activity.
- This model described action potentials sometimes followed by spontaneous secondary spikes.
Purpose of the Study:
- To gain insight into the mechanism underlying spontaneous secondary spikes.
- To reduce a five-dimensional model to three dimensions for analysis.
- To provide a qualitative explanation using phase-plane and bifurcation analysis.
Main Methods:
- Reduced a five-dimensional crab neuron model to three dimensions.
- Treated a slowly varying current as a parameter.
- Employed phase-plane and bifurcation analysis.
- Utilized the AUTO software for numerical bifurcation analysis.
Main Results:
- A three-dimensional model with a two-dimensional excitable system and a slow inward current is sufficient to reproduce spontaneous secondary spikes.
- The relative time constant and amplitude of the slow inward current are critical for the observed behavior.
- Bifurcation diagrams showed a stable resting potential and the emergence of a stable tonic firing mode via a saddle-node of periodics bifurcation at a critical parameter value.
Conclusions:
- The simplified three-dimensional model captures the essential dynamics of spontaneous secondary spikes.
- The occurrence of transient or continuous spontaneous spiking depends on parameter space positioning relative to the saddle-node of periodics bifurcation.