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Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Modeling the network dynamics of pulse-coupled neurons
Sarthak Chandra1, David Hathcock2, Kimberly Crain3
1University of Maryland, College Park, Maryland 20742, USA.
Chaos (Woodbury, N.Y.)
|April 3, 2017
Summary
This study introduces a mean-field approximation for pulse-coupled theta neuron networks, revealing how network structure impacts collective behavior. Network degree distributions and correlations significantly influence neuronal firing patterns and phase transitions.
Area of Science:
- Computational Neuroscience
- Complex Systems
- Network Science
Background:
- Understanding the macroscopic dynamics of large neuronal networks is crucial for neuroscience.
- Previous studies often focused on simplified network structures or lacked efficient analytical tools.
- The influence of specific network topologies, like degree distributions and correlations, on emergent dynamics remains an active area of research.
Purpose of the Study:
- To develop and apply a mean-field approximation for large networks of pulse-coupled theta neurons.
- To investigate the impact of varying network degree distributions and degree correlations (assortativity) on macroscopic neuronal dynamics.
- To enable efficient analysis of phase transitions and attractors in these complex systems.
Main Methods:
- Derivation of a mean-field approximation using the Ott and Antonsen ansatz.
- Reduction of the system's dimensionality to a set of ordinary differential equations.
- Comparison of the reduced model's dynamics with the full network dynamics for validation.
Main Results:
- The reduced mean-field model accurately captures the macroscopic dynamics of large neuronal networks.
- Tightly peaked degree distributions lead to behavior similar to fully connected networks.
- Highly skewed distributions and degree correlations (assortativity/disassortativity) significantly alter macroscopic dynamics, including the suppression of synchronous firing.
Conclusions:
- The derived mean-field approximation provides a computationally efficient method to study neuronal network behavior.
- Network topology, specifically degree distribution and correlations, plays a critical role in shaping emergent neuronal activity.
- This approach facilitates a deeper understanding of how network structure influences macroscopic dynamics in biological and artificial neural systems.
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