Dynamical mechanisms of flexible phase-locking in cortical theta oscillators

Oscillatory activity in auditory cortex is thought to play a central role in auditory and speech processing by synchronizing neural rhythms to external acoustic features of the speech stream. To support this function, cortical oscillators must flexibly phase-lock to inputs spanning a wide range of timescales, including rhythms substantially slower than their intrinsic frequency. Here we identify a general dynamical mechanism by which intrinsic inhibitory currents operating on multiple timescales enable such flexible phase-locking. Using tools from dynamical systems theory, we show that interactions between slow and superslow inhibitory processes generate prolonged post-input recovery delays through delayed Hopf phenomena, thereby substantially expanding the frequency range over which entrainment can occur. We demonstrate this mechanisms in a biophysically grounded cortical theta oscillator model for speech segmentation. Specifically, we show that both a theta-timescale (4-8 Hz) inhibitory current $I_m$ and a slower delta-timescale (1-4 Hz) inhibitory potassium current $I_{\rm K_{SS}}$ are crucial for entrainment flexibility. Their interaction creates a three-timescale structure that gives rise to pronounced delay phenomena associated with a delayed Hopf bifurcation (DHB). Interestingly, the superslow $I_{\rm K_{SS}}$ and the associated DHB play little role in the unforced oscillatory dynamics, but are recruited to support phase locking under external forcing. Moreover, the intermediate-timescale current $I_m$, rather than being redundant, further expands the phase-locking range by prolonging delayed recovery along the superslow manifold. Together, these results suggest that coordination among intrinsic inhibitory currents operating on multiple timescales may represent a key mechanism supporting flexible phase locking to rhythmic inputs in the brain.