A Scalar Poincaré Map for Anti-phase Bursting in Coupled Inhibitory Neurons With Synaptic Depression

Area of Science:

• Neuroscience
• Computational Neuroscience
• Systems Neuroscience

Background:

• Short-term synaptic plasticity, specifically synaptic depression, is crucial in central nervous system networks.
• Inhibitory half-center central pattern generators (CPGs) utilize synaptic depression for burst termination, enabling anti-phase bursting essential for locomotion.

Purpose of the Study:

• To investigate burst generation mechanisms in CPGs by analyzing a minimal two-neuron network with depressing synapses.
• To understand how synaptic conductance strength influences the dynamics and period of anti-phase bursting patterns.

Main Methods:

• Development of a reduced eight-dimensional network model to a scalar Poincaré burst map, focusing on synaptic depression dynamics.
• Analysis of the Poincaré map to identify fixed points corresponding to stable burst solutions and predict bifurcations.
• Derivation of conditions for predicting transitions between n:n and (n+1):(n+1) bursting patterns.

Main Results:

• The minimal network generates symmetric n:n anti-phase bursts, with periods increasing proportionally to synaptic conductance strength.
• The Poincaré burst map accurately captures the network's complex bursting dynamics and predicts bifurcations.
• The derived conditions successfully predict transitions between different bursting patterns, validated by numerical simulations.

Conclusions:

• The simplified Poincaré map effectively models synaptic depression and bursting dynamics in CPGs.
• The study provides a framework for understanding and predicting rhythm generation in neural networks.
• This approach allows for detailed analysis of parameter sensitivity in neural rhythm generation.