Delay Model of the Circadian Pacemaker

Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops

“…As there are 44 parameters to be tested (not including three parameters for the number of E-boxes in promoters), it is not possible to explore the behaviour of the system in full dimensional parameter spaces. To investigate the behaviour of the system to parameter variations, we followed the methods used in previous models (Lema, Golombek et al 2000; Leloup and Goldbeter 2003;Smolen, Hardin et al 2004). One parameter was changed at a time while keeping the others at their standard values.…”

“…As TIM stabilises PER in the cytoplasm, the indirect effect of light is to regulate the localisation of PER and in turn to decrease the PER level in the nucleus. Therefore, change in degradation rate of PER has also been used in some models (Scheper, Klinkenberg et al 1999;Lema, Golombek et al 2000;Smolen, Hardin et al 2004). Indeed, experimental findings have shown that tim 01 mutants inducing an absence of TIM lead to a substantial lowering of PER abundance (Vosshall, Price et al 1994;Price, Dembinska et al 1995), an effect that happens to be similar to the result of exposing flies to constant light (Zerr, Hall et al 1990;Price, Dembinska et al 1995).…”

Global attractivity of a circadian pacemaker model in a periodic environment

“…Circadian rhythms are generated by biological clocks that seem to be ubiquitous in nature, ranging from periodic biochemical reactions in molecular organisms to complex structures in the mammalian brain. Several mathematical and physical models have been proposed over the years in order to explain different features of circadian systems in general (see, for example, [1,2,4,5,9,10,13,14,15,22,23,24,26] and the references therein).…”

“…It is difficult to completely understand the dynamics of these models since too many parameters are involved. Lema et al [14] recently proposed a simple model of circadian pacemaker described by the following delay differential equation,…”

“…It has been observed that light, temperature and certain chemicals can affect many circadian rhythms (see, for example, the references in [14]). To study the effects of environment and the photoperiodic (i.e., parametric) entrainment, Lema et al separately perturbed K e , K d , or added to K e the positive half of a sinusoidal function of time.…”