Leloup, Goldbeter, 2003

Model Structure

Many living organisms, from bacteria to plants, insects to mammals, display circadian rhythms. These are spontaneously sustained oscillations with a period close to 24 hours. Even in the absence of environment cues such as the light changes associated with day and night, organisms have been shown to retain their circadian behaviour, therefore suggesting that the rhythms are endogenous. Experiments with Drosophila (fruit fly), Neurospora (fungus), cyanobacteria, plants and mammals have improved our understanding of the molecular mechanisms underlying circadian rhythms. It seems that they rely on negative feedback on gene expression. A number of genes involved in circadian rhythms have been identified. These include: Per (period) and Tim (timeless); Cyc (cycle) and Clock; and Cry (cryptochrome).

To date, mathematical models for circadian rhythms have been developed for Drosophila and Neurospora. These models, which are based on experimental data, predict that within a certain parameter range the genetic regulatory network undergoes sustained oscillatory cycles corresponding to circadian rhythmic behaviour. In this 2003 publication, Leloup and Goldbeter develop a deterministic model for the mammalian circadian clock. Their model includes the regulatory effects exerted on gene expression by the proteins PER, CRY, BMAL1, CLOCK and REV-ERB, as well as posttranslational regulation of these proteins by reversible phosphorylation (see the figure below).

Model simulations reveal that their model can account for the autonomous, sustained circadian oscillations in conditions which correspond to continuous darkness (no environmental cues), and also for light-dark cycle entrainment of circadian rhythms - light can entrain circadian rhythms in mammals by inducing the expression of the Per gene. Model simulations also showed that the phase of the oscillations could vary by several hours with relatively small changes in parameter values. This may account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of light-dark entrainment can be related to the non-24 hour sleep-wake syndrome. Further, detailed model analysis suggests that there could be several sources of periodic behaviour in the genetic regulatory network that controls circadian oscillations.

The complete original paper reference is cited below:

Toward a detailed computational model for the mammalian circadian clock, Jean-Christophe Leloup and Albert Goldbeter, 2003, PNAS , 100, 7051-7056. (Full text (HTML) and PDF versions of the article are available on the PNAS website.) PubMed ID: 12775757

Model for circadian oscillations in mammals involving interlocked negative and positive regulations of Per, Cry, Bmal1, and Rev-Erb genes by their protein products.

Please note that the model presented here is the extended version of the model which includes equations to define the role of REV-ERB-alpha in inhibiting the transcription of Bmal1. There are 19 equations and the parameters are listed as part of the Supplementary data set under Figure 8.