Amplitude effects allow short jetlags and large seasonal phase shifts in minimal clock models

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jetlag and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of models satisfying certain constraints; here a one-hour pulse PRC with a range of three hours and clock periods between 22h and 26h. Surprisingly, almost all these randomly parameterized models showed a four hour change in phase of entrainment between long and short days and jetlag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jetlag duration and entrainment amplitude and phase. Fast jetlag was realized in this model by means of an interesting amplitude effect: the association between clock amplitude and clock period termed ‘twist’. This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of positive feedback to the model. In summary, the known design principles of rhythm generation – negative feedback, long delay and switch-like inhibition (we review these in detail) – are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.