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Circadian clocks exhibit the robustness of period and plasticity of phaseagainst environmental changes such as temperature and nutrient conditions. Thusfar, however, it is unclear how both are simultaneously achieved. Byinvestigating distinct models of circadian clocks, we demonstrate reci- procitybetween robustness and plasticity: higher robustness in the period implieshigher plasticity in the phase, where changes in period and in phase follow alinear relationship with a negative coef- ficient. The robustness of period isachieved by the adaptation on the limit cycle via a concentration change of abuffer molecule, whose temporal change leads to a phase shift following a shiftof the limit-cycle orbit in phase space. Generality of reciprocity in clockswith the adaptation mechanism is confirmed with theoretical analysis of simplemodels, while biological significance is discussed.

Reciprocity Between Robustness of Period and Plasticity of Phase in Biological Clocks