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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.
To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24h period. Yet, a limit-cycle oscillator is not essential for k
Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellular organisms, often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite t
In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of target genes (partial system) is inse
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigat
Understanding the system level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches such as the constraint-based flux balance analyses (FBA) have