Conceptual models of entrainment, jet-lag, and seasonality

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and day-length, govern entrainment ranges and the phase of entrainment. Using global optimization, we derive conceptual models with just three free parameters (period, amplitude, relaxation rate) that reproduce known phenotypic features of vertebrate clocks: relatively small phase response curves (PRCs), fast re-entrainment after jet-lag, and seasonal variability to track light onset or offset. Since optimization found multiple sets of model parameters, we can study this model ensemble to gain insight into the underlying design principles. We find that amplitudes control the size of PRCs, that fast relaxation supports short jet-lag, and that specific periods allow reasonable seasonal phase shifts. Arnold onions of representative models visualize strong dependencies of entrainment on periods, relative Zeitgeber strength, and photoperiod.