A framework for macroscopic phase-resetting curves for generalised spiking neural networks

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Systems Neuroscience

Background:

• Brain rhythms arise from synchronized activity in interconnected spiking neurons.
• The phase-resetting curve (PRC) is crucial for understanding these rhythms.
• Systematic phase reduction theory for large-scale brain rhythms is a significant challenge.

Purpose of the Study:

• To present a theoretical framework and methodology for computing the PRC of generic spiking networks with emergent collective oscillations.
• To bridge the gap between individual neuron properties and macroscopic network dynamics.

Main Methods:

• Utilized a renewal approach describing neurons by time since the last action potential.
• Employed a continuity equation (refractory density equation) for large neural populations.
• Developed an adjoint method to derive a semi-analytical expression for the infinitesimal PRC.

Main Results:

• Successfully computed the PRC for generic spiking networks with emergent oscillations.
• Validated the framework using specific neural network examples.
• Demonstrated the ability to link single-neuron properties to macroscopic oscillatory network behavior.

Conclusions:

• The developed theoretical framework provides a robust method for calculating the PRC in large-scale spiking neural networks.
• This approach advances the understanding of brain rhythm generation and phase reduction theory.
• The methodology is applicable to diverse systems exhibiting renewal processes.