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Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection
1Courant Institute, Center for Neural Science.
Communications on Pure and Applied Mathematics
|November 14, 2014
Summary
This review explores mathematical models of neuronal firing dynamics, focusing on single-cell excitability and bursting. It highlights how mathematical neuroscience aids understanding of neuronal computation, like sound localization.
Area of Science:
- Mathematical Neuroscience
- Computational Neuroscience
- Dynamical Systems Theory
Background:
- Neuronal systems exhibit complex firing dynamics at single-cell and network levels.
- Mathematical neuroscience and dynamical systems offer powerful tools for studying these phenomena.
- Single-cell excitability and bursting are long-standing areas of interest for mathematicians.
Purpose of the Study:
- To review widely studied models and firing dynamics in neuronal systems.
- To focus on mathematical frameworks for single-cell excitability and bursting.
- To demonstrate the application of fast/slow analysis in neuronal modeling.
Main Methods:
- Review of mathematical frameworks for neuronal excitability types.
- Analysis of Hodgkin's classification of repetitive firing properties.
- Application of fast/slow analysis for dissecting bursting oscillations.
- Demonstration using single-cell and mean-field network models.
Main Results:
- Detailed review of three types of excitability and repetitive firing onset.
- Illustration of Type III excitability, characterized by response to rapid stimuli.
- Application of fast/slow analysis to understand bursting dynamics.
- Case study on auditory brain stem neurons for sound localization.
Conclusions:
- Mathematical approaches provide deep insights into neuronal excitability and bursting.
- Fast/slow analysis is a key technique for dissecting complex neuronal dynamics.
- Understanding neuronal firing properties is crucial for deciphering computations like coincidence detection in sound localization.
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