Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to properly respond to external stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist because better entrainability favors higher sensitivity, which may sacrifice the regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase-response curve with a variational method. Our result indicates an existence of a dead zone, i.e., a time during which external stimuli neither advance nor delay the clock. This result is independent of model details and a dead zone appears only when the input stimuli obey the time course of actual insolation . Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle . Our result also explains the lack of a dead zone in oscillators of mammalian somatic cells, and justifies more effective entrainment by dawn and dusk than by on/off lighting protocols in animals including humans .
Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist because better entrainability favors higher sensitivity, which may sacrifice the regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase-response curve with a variational method. Our result indicates an existence of a dead zone, i.e., a time period during which input stimuli neither advance nor delay the clock. A dead zone appears only when input stimuli obey the time course of actual solar radiation but a simple sine curve cannot yield a dead zone . Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle .
R
properly respond to external
synchronize internal time with periodic
R
during which external
period during which input
R
This result is independent of model details and a
A
D
the
R
insolation
solar radiation but a simple sine curve cannot yield a dead zone
D
. Our result also explains the lack of a dead zone in oscillators of mammalian somatic cells, and justifies more effective entrainment by dawn and dusk than by on/off lighting protocols in animals including humans