PRC bisection tests.

Abstract

This communication presents a new method for evaluating phase response curves (PRCs). A PRC describes the phase shifts produced in an oscillator by stimuli applied at different initial phase-states of that oscillator. In the PRC bisection tests, we repeatedly cut in half the circular distribution of the initial phase-states of the oscillator when stimuli are given. Empirically, we locate that optimal diameter which best bisects the circular distribution of phase responses into arcs of relative phase advance and phase delay. We compute a D score reflecting the success of the best bisection. The null hypothesis of a random distribution of phase responses by initial phase is tested with a Monte Carlo procedure, which computes Dr scores from random combinations of phase shifts with initial phases, thus determining the probability, given the null hypothesis, that the observed D score was from a random distribution. The bisection procedure can be extended to examine whether stronger phase shifts are produced in one phase response curve than in contrasting curves. Also, the bisection procedure yields an estimate of the inflection point of the phase response curve. A method is given to estimate the power of the PRC bisection test.