On the Response of Neurons to Sinusoidal Current Stimuli: Phase Response Curves and Phase-Locking

A powerful technique for analyzing mathematical models for biological oscillators is to reduce them to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. From this reduction, one obtains the oscillator's phase response curve (PRC), which determines its response to weak stimuli. In this paper, we show how properties of the PRC determine the parameter regimes for which the response of an oscillator is phase-locked to a sinusoidal stimulus. Furthermore, we show how knowledge of an oscillator's phase-locking behavior can be used to deduce useful properties of the PRC. Our focus is on neural oscillators described by conductance-based models and stimulated by a sinusoidal current, although the results are expected to be relevant to other biological oscillators