Circadian rhythms are acquired through evolution to increase the chances for survival by synchronizing to the daylight cycle. Reliable synchronization is realized through two trade-off properties: regularity to keep time precisely, and entrainability to synchronize the internal time with daylight. Since both properties have been tuned through natural selection, their adaptation can be formalized in the framework of mathematical optimization. By using a succinct model , we found that simultaneous optimization of regularity and entrainability entails  inherent features of the circadian mechanism irrespective of model details . At the behavioral level we discovered the existence of a dead zone, a time during which light pulses neither advance nor delay the clock. At the molecular level we demonstrate the role-sharing of two light inputs, phase advance and delay, as is well observed in mammals. We also reproduce the results of phase-controlling experiments and predict molecular elements responsible for the clockwork . Our results indicate that circadian clocks function optimally and that a simple mathematical model can illuminate many complex phenomena observed in nature .
Circadian rhythms are acquired through evolution to increase the chances for survival through synchronizing with the daylight cycle. Reliable synchronization is realized through two trade-off properties: regularity to keep time precisely, and entrainability to synchronize the internal time with daylight. We found by using a phase model with multiple inputs that achieving the maximal limit of regularity and entrainability entails many inherent features of the circadian mechanism . At the molecular level, we demonstrate the role sharing of two light inputs, phase advance and delay, as is well observed in mammals. At the behavioral level, the optimal phase-response curve inevitably contains a dead zone, a time during which light pulses neither advance nor delay the clock. We reproduce the results of phase-controlling experiments entrained by two types of periodic light pulses . Our results indicate that circadian clocks are designed optimally for reliable clockwork through evolution .
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by synchronizing to
through synchronizing with
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Since both properties have been tuned through natural selection, their adaptation can be formalized in the framework of mathematical optimization. By using a succinct model , we found that simultaneous optimization
We found by using a phase model with multiple inputs that achieving the maximal limit
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many
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irrespective of model details
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behavioral level we discovered the existence of a dead zone, a time during which light pulses neither advance nor delay the clock. At the molecular level
molecular level,
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role-sharing
role sharing
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We also
At the behavioral level, the optimal phase-response curve inevitably contains a dead zone, a time during which light pulses neither advance nor delay the clock. We
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and predict molecular elements responsible for the clockwork
entrained by two types of periodic light pulses
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function optimally and that a simple mathematical model can illuminate many complex phenomena observed in nature
are designed optimally for reliable clockwork through evolution