Accuracy of circadian entrainment under fluctuating light conditions: Contributions of phase and period responses

The accuracy with which a circadian pacemaker can entrain to an environment al 24-h zeitgeber signal depends on (a) characteristics of the entraining s ignal and (b) response characteristics and intrinsic stability of the pacem aker itself. Position of the sun, weather conditions, shades, and behaviora l variations (eye closure, burrowing) all modulate the light signal reachin g 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 de viation of the clock times at which a reference phase (0) is reached. For t he purpose of this exploration, the authors used a model pacemaker characte rized solely by its momentary phase and momentary velocity. The average vel ocity determines the time needed to complete one pacemaker cycle and, there fore, is inversely proportional to pacemaker period. The model pacemaker re sponds 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 incorporat ed 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 l ight. 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 max imal accuracy, the changes in velocity are such that the average period of the pacemaker under entrained conditions equals 24 h. The results suggest t hat during entrainment, the pacemaker adjusts its period to 24 h, after whi ch daily phase shifts to compensate for differences between the periods of the zeitgeber and the clock are no longer necessary. On average, phase shif ts compensate for maladjustments of phase and velocity changes compensate f or maladjustments of period.