Phase response curves and the role of coordinates

Area of Science:

• Dynamical systems theory
• Computational neuroscience
• Nonlinear dynamics

Background:

• The infinitesimal phase response curve (PRC) is crucial for analyzing phase resetting in diverse scientific fields, especially neuroscience.
• Existing methods for PRC calculation can be limited by coordinate dependence, complicating analysis and reconstruction of system dynamics.

Purpose of the Study:

• To address the coordinate dependence of the infinitesimal phase response curve (PRC).
• To develop a coordinate-free definition of the PRC.
• To propose a novel experimental protocol for computing the voltage PRC.

Main Methods:

• Developed a coordinate-free mathematical definition of the infinitesimal phase response curve (PRC).
• Proposed an experimental protocol involving intermittent control of neuron voltage to collect an ensemble of measurements.
• Demonstrated how to compute the voltage PRC using the collected ensemble data for a postulated current carrier dynamic.

Main Results:

• Showed that the infinitesimal phase response curve (PRC) is coordinate-dependent.
• Established that delay embedding reconstruction using a single coordinate is insufficient for computing the PRC.
• Successfully devised a method to compute the voltage PRC from experimental data.

Conclusions:

• The coordinate-free PRC definition clarifies its dependence on coordinate choice.
• The proposed experimental protocol enables accurate PRC computation, even with partial control and measurement of oscillators.
• This approach is extendable to systems with multiple coupled oscillators.