Rapid changes in synchronizability in conductance-based neuronal networks with conductance-based coupling.

Area of Science:

• Computational neuroscience
• Network dynamics
• Mathematical biology

Background:

• Neuron connectivity is non-random and influences network synchronization.
• The impact of connectivity on conductance-based neuron models, like Hodgkin-Huxley and Morris-Lecar, remains unclear.
• The master stability function (MSF) is a powerful tool for analyzing network synchronizability.

Purpose of the Study:

• To apply and extend the MSF to conductance-based Morris-Lecar neuron networks.
• To determine parameters and graph structures that ensure stable synchronous solutions.
• To investigate conductance-based synapses beyond diffusive coupling.

Main Methods:

• Extended the master stability function (MSF) approach for conductance-based coupling.
• Analyzed networks of Morris-Lecar neurons with constant non-zero row sum connectivity graphs.
• Investigated synchronous solutions as self-coupled neurons (autaptic).

Main Results:

• Reversal potential is the primary determinant of synchronous solution stability.
• A narrow voltage range rapidly transitions synapses between excitatory and inhibitory.
• Islands of synchronizability appear in inhibitory networks for specific global synaptic conductance values.

Conclusions:

• The MSF effectively analyzes synchronizability in conductance-based networks.
• Reversal potential critically controls network synchrony stability.
• Specific inhibitory coupling strengths can promote network synchronization, a finding supported by simulations.