Accuracy of Circadian Entrainment under Fluctuating Light Conditions: Contributions of Phase and Period Responses

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Abstract
The accuracy with which a circadian pacemaker can entrain to an environmental 24-h zeitgeber signal depends on (a) characteristics of the entraining signal and (b) response characteristics and intrinsic stability of the pacemaker itself. Position of the sun, weather conditions, shades, and behavioral variations (eye closure, burrowing) all modulate the light signal reaching the pacemaker. A simple model of a circadian pacemaker allows researchers to explore the impact of these factors on pacemaker accuracy. Accuracy is operationally defined as the reciprocal value of the day-to-day standard deviation of the clock times at which a reference phase (0) is reached. For the purpose of this exploration, the authors used a model pacemaker characterized solely by its momentary phase and momentary velocity. The average velocity determines the time needed to complete one pacemaker cycle and, therefore, is inversely proportional to pacemaker period. The model pacemaker responds to light by shifting phase and/or changing its velocity. The authors assumed further that phase and velocity show small random fluctuations and that the velocity is subject to aftereffects. Aftereffects were incorporated mathematically in a term allowing period to contract exponentially to a stable steady-state value, with a time constant of 69 d in the absence of light. The simulations demonstrate that a pacemaker reaches highest accuracy when it responds to light by simultaneous phase shifts and changes of its velocity. Phase delays need to coincide with slowing down and advances with speeding up; otherwise, no synchronization to the zeitgeber occurs. At maximal accuracy, the changes in velocity are such that the average period of the pacemaker under entrained conditions equals 24 h. The results suggest that during entrainment, the pacemaker adjusts its period to 24 h, after which daily phase shifts to compensate for differences between the periods of the zeitgeber and the clock are no longer necessary. On average, phase shifts compensate for maladjustments of phase and velocity changes compensate for maladjustments of period.