Phase response curves and the role of coordinates

Wilshin, S; Kvalheim, MD; Revzen, S

Abstract

The "infinitesimal phase response curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences in general and neuroscience in particular. We make the observation that the PRC with respect to a coordinate v actually depends on the choice of other coordinates. As a consequence, a complete delay embedding reconstruction of the dynamics using v which would allow phase to be computed still does not allow the v PRC to be computed. We give a coordinate-free definition of the PRC making this observation obvious. This leads to an experimental protocol: first collect an appropriate ensemble of measurements by intermittently controlling neuron voltage. Then, for any suitable current carrier dynamic postulated, we show how the ensemble can be used to compute the voltage PRC with that current carrier. The approach extends to many oscillators measured and controlled through a subset of their coordinates.

Citation

Wilshin, S., Kvalheim, M., & Revzen, S. (2024). Phase response curves and the role of coordinates. Biological Cybernetics, https://doi.org/10.1007/s00422-024-00997-w

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2024
• Publication Date: 2024
• Deposit Date: Nov 11, 2024
• Journal: Biological Cybernetics
• Print ISSN: 0340-1200
• Electronic ISSN: 1432-0770
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s00422-024-00997-w
• Keywords: Phase response; Dynamical systems; Neural oscillator; Fitzhugh-Nagumo; Delay coordinates