Anticipated synchronization in neuronal circuits unveiled by a phase-response-curve analysis

Area of Science:

• Neuroscience
• Computational Neuroscience
• Dynamical Systems

Background:

• Anticipated synchronization (AS) describes systems where a receiver predicts a sender's future dynamics.
• AS has been proposed to explain complex temporal dynamics in primate cortical activity.
• The precise mechanisms generating AS in neuronal circuits remain unclear.

Purpose of the Study:

• To investigate the mechanisms underlying transitions between delayed synchronization, anticipated synchronization, and phase-drift regimes in neuronal circuits.
• To utilize the phase-response-curve (PRC) approach for analyzing neuronal synchronization phenomena.
• To develop a predictive map for phase-locking regimes and their stability.

Main Methods:

• Employing the phase-response-curve (PRC) method on a sender-receiver-interneuron neuronal motif.
• Utilizing a Hodgkin-Huxley model for numerical simulations.
• Constructing a two-variable PRC function to capture simultaneous inputs.

Main Results:

• A two-variable PRC, accounting for sender and interneuron inputs, is crucial for accurately reproducing numerical results.
• The standard approximation using independent single-variable PRCs fails under moderate to high inhibitory coupling.
• The two-variable PRC correctly predicts transitions between synchronization regimes, including delayed to anticipated synchronization.

Conclusions:

• The study highlights the necessity of a multivariate PRC for understanding complex synchronization behaviors in neuronal networks.
• Simple additive PRC approximations are insufficient for capturing key synchronization transitions, particularly with inhibitory interneurons.
• A detailed PRC-based map provides a powerful tool for predicting and understanding neuronal synchronization dynamics.