Macroscopic equations governing noisy spiking neuronal populations with linear synapses

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Mathematical Biology

Background:

• Deriving simplified equations for large biological neural networks is a significant challenge.
• Understanding macroscopic dynamics of neuronal sub-populations requires tractable models.

Purpose of the Study:

• To propose a reduction method for large-scale multi-population stochastic neural networks.
• To derive differential equations describing macroscopic population activity using mean-field theory.
• To provide a framework applicable to various spiking neuron models.

Main Methods:

• Application of mean-field theory to stochastic neural networks.
• Derivation of a system of differential equations for population dynamics.
• Analytical and numerical determination of the effective non-linearity function.
• Parameterization for McKean, Fitzhugh-Nagumo, and Hodgkin-Huxley neuron models.

Main Results:

• A system of differential equations analogous to Wilson-Cowan models was derived.
• The effective non-linearity depends on cell properties and noise levels.
• The reduced model accurately simulates macroscopic dynamics for McKean and Fitzhugh-Nagumo models.

Conclusions:

• The proposed mean-field reduction provides a tractable approach for modeling large neural networks.
• The method successfully captures macroscopic dynamics, validated against specific neuron models.
• This framework advances computational neuroscience by simplifying complex network analysis.