A multiple timescales approach to bridging spiking- and population-level dynamics

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Mathematical Biology

Background:

• Bridging spiking-level dynamics and macroscopic quantities in neural populations is crucial.
• Existing methods like the Ott-Antonsen ansatz excel for large, asynchronously firing populations.
• Focus is shifting to understand populations with varying synchronous dynamics.

Purpose of the Study:

• To develop a converse approach predicting synchronization properties of finite neural populations from mean-field dynamics of slow synapses.
• To apply averaging theory and the method of multiple timescales to analyze heterogeneous neural networks.
• To validate the theory using diverse neural models and network configurations.

Main Methods:

• Utilizing averaging theory and the method of multiple timescales for slow synapse dynamics.
• Developing a theory for two heterogeneous populations of excitatory and inhibitory oscillators (n-dimensional and m-dimensional).
• Applying the theory to networks of theta neurons and Traub/Wang-Buzsáki models.

Main Results:

• Accurate prediction of phase drift and phase locking in finite neural populations.
• Demonstrated efficacy across different neural models (theta, Traub, Wang-Buzsáki) and network topologies.
• Validation even when slow synapses exhibit non-trivial mean-field dynamics.

Conclusions:

• The developed theory provides a robust framework for predicting neural synchronization from slow synaptic inputs.
• This approach extends understanding beyond large, asynchronous populations to finite, synchronous networks.
• The findings have implications for modeling complex brain dynamics and neural circuit behavior.