Phase response curves and the role of coordinates

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 c...

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Bibliographic Details
Published inBiological cybernetics
Main Authors Wilshin, Simon, Kvalheim, Matthew D, Revzen, Shai
Format Journal Article
LanguageEnglish
Published Germany 30.10.2024
Subjects
Phase response
Neural oscillator
Delay coordinates
Fitzhugh–Nagumo
Dynamical systems
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Summary: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.
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ISSN:1432-0770
1432-0770
DOI:10.1007/s00422-024-00997-w