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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
Published on: June 21, 2022
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Mean-field equations for neuronal networks with arbitrary degree distributions
Duane Q Nykamp1, Daniel Friedman1, Sammy Shaker1
1School of Mathematics, University of Minnesota 127 Vincent Hall, Minneapolis, Minnesota 55455, USA.
Physical Review. E
|May 17, 2017
Summary
Networks of spiking neurons exhibit complex dynamics influenced by their structure. This study reveals that more structured neuronal connectivity, beyond random networks, leads to richer network dynamics.
Area of Science:
- Computational Neuroscience
- Network Science
- Systems Neuroscience
Background:
- Emergent dynamics in spiking neural networks depend on single-cell properties and network topology.
- Theoretical studies often simplify network topology (e.g., Erdös-Rényi networks).
- Cortical neuron connectivity exhibits more structure than random networks.
Purpose of the Study:
- To investigate how higher-order statistical structure in neuronal connectivity affects network dynamics.
- To explore the impact of joint degree distributions on neural network behavior.
- To compare dynamics in structured networks versus random networks.
Main Methods:
- Derivation of mean-field equations for homogeneous and heterogeneous neuronal networks.
- Analysis of mean-field equations for networks with arbitrary degree distributions.
- Simulations of integrate-and-fire neuron networks with specified degree distributions.
Main Results:
- Networks with structured connectivity (joint degree distributions) exhibit richer dynamics than Erdös-Rényi networks.
- Mean-field analysis and simulations confirm enhanced dynamic complexity.
- Degree distributions can be related to specific cortical motifs.
Conclusions:
- Neuronal network topology significantly shapes emergent dynamics.
- Incorporating realistic structural features, like joint degree distributions, is crucial for understanding brain function.
- Structured connectivity provides a richer repertoire of network dynamics compared to random models.
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