A Functional Analysis of Circadian Pacemakers in Nocturnal Rodents. IV. Entrainment:Pacemaker as Clock

1. In the first part of the paper, the model of non-parametric entrainment of circadian pacemakers is tested for the case of nocturnal rodents. The model makes use of the available data on freerunning period (τ) in constant darkness and on phase response curves (PRC) for short light pulses. It is tested in experiments using 1 or 2 light pulses per cycle. 2. Mesocricetus auratus and Peromyscus leucopus entrain to Zeitgebers involving 1 pulse (15' or 60') per cycle. The phase angle differences between rhythm and light cycle depends on the periods (τ and T) as predicted by the model. Entrainment of P. leucopus is unstable due to the after effects on τ created by the light pulse. 3. The limiting values of Zeitgeber period to which the animals entrain are much closer to 24 h than in Drosophila pseudoobscura, as the model predicts. However, frequent failures to entrain to T = 23 and T = 25 h are only explained if we take considerable interindividual variation in both τ and PRC into account. 4. With 2 pulses per cycle, the model predicts that entrainment will be more stable when activity is in the longer interval between the pulses than when it is in the shorter interval. This is true in the experimental data, where the phase relationships match predictions for skeleton photoperiods up to ca. 14 h. Increasing asymmetry forces animals into a "phase jump", so that activity shifts from the shorter to the longer interval. These ψ-jumps are accurately predicted in the hamster, but they occur at much longer photoperiods than predicted in P. leucopus. 5. Thus, the unqualified model, using a rigidly fixed species τ and PRC, is surely inadequate to explain entrainment. The extent to which variations in τ and PRC-shape, both "spontaneous" and induced by the entrainment process, can be known or inferred restricts the validity of the predictions. Yet we conclude, from a good deal of agreement between experiment and prediction (i), from the close correspondence between complete and skeleton photoperiods (ii), and on behavioural grounds (iii), that non-parametric entrainment by short light signals has a major share in the entrainment of nocturnal rodent rhythms in nature. 6. With these restrictions in mind, we analyse in the second part of the paper how the empirical regularities concerning τ and PRC contribute to the stabilization of the phase angle difference (ψ) between the pacemaker and the external world. Use is made of computer simulations of artificial pacemakers with variable τ and PRC. 7. ψ is most sensitive to instabilities in τ when ¯τ is close to 24 h. Thus the very circadian nature of these pacemakers helps to conserve ψ. Selection pressure for homeostasis of τ has been large in a species (M. auratus) where ¯τ = 24 h. The effect of ψ-instability is further reduced by entrainment with 2 pulses (dawn and dusk), made possible by the PRC's having both an advance and a delay section. 8. To analyze the contributions to ψ-conservation with seasonally changing photoperiod, we have assumed that it is of functional significance to conserve the phase of activity with respect to dusk (nocturnal animals) or to dawn (diurnal animals). We distinguish three contributions of nocturnal pacemaker behaviour to this type of ψ-conservation: increased amplitude of the PRC (i), asymmetry in the PRC, such that the slope of the delay-part is steeper than the slope of the advance-part (ii), and a short freerunning period in DD (iii). 9. A further contribution must derive from parametric effects of light, which are not traceable by the model, but certainly effective in preventing in complete photoperiods the ψ-jump which is seen in skeleton photoperiods. The existence of parametric effects is further demonstrated by the change of τ with light intensity in LL, described by Aschoffs Rule, which presumably reflects differences in PRC-shape between nocturnal and diurnal animals. 10. The paper concludes with an attempt to distinguish the features of circadian clocks that are analytically necessary for entrainment to occur (i), or have functional meaning, either in the measurement of the lapse of time (ii) or in the identification of local time (iii)