Limit Cycle Model for Circadian Rhythms in Drosophila and Neurospora

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 a negative feedback on gene expression. A number of genes involved in circadian rhythms have been identified. These include two which are considered in the current model: Per (period) and Tim (timeless).

In order to better understand the genetic mechanisms underlying the regulation of rhythms, scientists have developed mathematical models of the oscillatory periods. Initially, these models described ultradian (less than 24 hour period) oscillations, which are typically characterised by periods from seconds to minutes. These early molecular models predicted that negative feedback on gene expression generated the limit cycles. This principle was subsequently applied to the study of circadian rhythms. During the past decade, improved experimental techniques have lead to the elucidation of much genetic and biochemical data relating to mechanisms controlling circadian rhythms. Concurrent with this increase in data availability, more detailed theoretical models can be developed.

In this 1999 study, Leloup et al. develop mathematical models of the genetic regulation underlying circadian oscillations in Drosophila and Neurospora. Experimental observations indicate that a similar genetic control underlies circadian rhythm generation in both Drosophila and Neurospora. In each case, circadian oscillations arise from the negative autoregulation of gene expression (see Figure 1 and Figure 2 below). In Drosophila, a PER-TIM protein complex migrates to the nucleus and represses the transcription of the per and tim genes. Similarly in Neurospora, FRQ protein enters the nucleus where it represses the transcription of its gene frq. Together with the negative, autoregulatory feedback loops just discussed, the models also take into account the specific effects of light in these two systems. In Drosophila, light controls the circadian rhythm by inducing the degeneration of TIM. In Neurospora, light controls the circadian system by inducing the transcription of frq.

The model has been described here in CellML (the raw CellML description of the Leloup et al. 1999 model can be downloaded in various formats as described in the section “Download This Model”).

The complete original paper reference is cited below:

Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora, Jean-Christophe Leloup, Didier Gonze, and Albert Goldbeter, 1999, Journal of Biological Rhythms, 14, 433-448. (A PDF version of the article is available on the Journal of Biological Rhythms website.) PubMed ID: 10643740

Figure 1. Scheme for the model for circadian oscillations in Drosophila involving negative regulation of gene expression by the PER-TIM protein complex.

Figure 2. Scheme for the model for circadian rhythms in Neurospora. This model is based on negative feedback exerted by the protein FRQ on the transcription of the frq gene.