Dynamical phase separation on rhythmogenic neuronal networks.

Area of Science:

• Computational neuroscience
• Network dynamics
• Mathematical modeling

Background:

• The pre-Bötzinger complex generates rhythmic breathing patterns.
• Neuronal firing-rate models with dendritic adaptation are used to study neural circuits.
• Network structure significantly impacts collective neural activity.

Purpose of the Study:

• To investigate the dynamics of excitatory neurons with dendritic adaptation on Erdős-Rényi networks.
• To model the pre-Bötzinger complex and its role in respiratory rhythm generation.
• To analyze how network connectivity and structure influence neural oscillations and firing patterns.

Main Methods:

• Utilized the Feldman-Del Negro firing-rate model for excitatory neurons.
• Simulated neuronal interactions on fixed, directed Erdős-Rényi networks.
• Analyzed network properties such as k-cores and their influence on dynamics.

Main Results:

• Observed spontaneous symmetry breaking leading to distinct firing and quiescent neuronal clusters.
• Demonstrated that clustering persists in sparsely connected networks, influenced by network k-cores.
• Found that stable oscillations do not persist in the high-sensitivity limit, contradicting mean-field predictions.
• Showcased remarkable robustness of oscillations in sparse networks, surviving significant neuron loss.

Conclusions:

• The firing-rate model on sparse networks exhibits dynamics not captured by mean-field theory.
• Neuronal network structure plays a critical role in respiratory rhythm generation.
• Simulated network robustness aligns with experimental findings on neural circuit resilience.