  Circadian clocks exhibit the robustness of period and plasticity of phase
against environmental changes such as temperature and nutrient conditions. Thus
far, however, it is unclear how both are simultaneously achieved. By
investigating distinct models of circadian clocks, we demonstrate reci- procity
between robustness and plasticity: higher robustness in the period implies
higher plasticity in the phase, where changes in period and in phase follow a
linear relationship with a negative coef- ficient. The robustness of period is
achieved by the adaptation on the limit cycle via a concentration change of a
buffer molecule, whose temporal change leads to a phase shift following a shift
of the limit-cycle orbit in phase space. Generality of reciprocity in clocks
with the adaptation mechanism is confirmed with theoretical analysis of simple
models, while biological significance is discussed.
