Do circadian oscillators ever stop in constant light?

Abstract

A TWO-DIMENSIONAL limit cycle model (Fig. 1) predicts the behaviour in darkness of both the Drosophila pseudoobscura circadian eclosion rhythm^1,2 and the mosquito Culex pipiens quinquefasciatus Say (C p. fatigans Wied.) flight activity rhythm^3,4. This model has been extended to explain features of rhythms in very dim light, but in constant ‘bright’ light it has been suggested that the dynamics are fundamentally different, with the system having a globally stable equilibrium point and hence no stable oscillation¹. We propose here a simplifying modification: for each light intensity the dynamics are topologically equivalent, and thus for each there is a limit cycle, its position and amplitude being continuous functions of intensity. This interpretation avoids the awkward discontinuity between ‘light’ and ‘dark’ dynamics and emphasises the possibility of time-keeping at all light intensities. Furthermore, it provides a simple explanation for novel features of the Culex rhythm described here and previously³, and allows us to treat some important differences between Culex and Drosophila as merely quantitative. Finally, it suggests a new general strategy for the analysis of circadian rhythms and allows extensions of established theory that explain previously paradoxical results obtained for the two species (E.L.P. in preparation).