Conceptual Models of Entrainment, Jet Lag, and Seasonality - Tokuda, Isao T.; Schmal, Christoph; Ananthasubramaniam, Bharath; Herzel, Hanspeter (Frontiers in Physiology, 2020)
Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and daylength, govern entrainment ranges and phases of entrainment. We test whether or not simple amplitude-phase models can provide insight into the control of entrainment phases. Using global optimization, we derive conceptual models with just three free parameters (period, amplitude, relaxation rate) that reproduce known phenotypic features of vertebrate clocks: phase response curves (PRCs) with relatively small phase shifts, 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 complex associations between model parameters and entrainment features. Arnold onions of representative models visualize strong dependencies of entrainment on periods, relative Zeitgeber strength, and photoperiod. Our results support the use of oscillator theory as a framework for understanding entrainment of circadian clocks.