Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in COR and OpenCell to reproduce the published results (figure 2c). The units are consistent. This particular version of the model has been translated from equations 4a-4c (Neurospora).
Model Structure
ABSTRACT: We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.
The 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. PubMed ID: 10643740
reaction diagram1
Scheme for the model for circadian oscillations in Drosophila involving negative regulation of gene expression by the PER-TIM protein complex. And beneath this is the 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.
M
Per mRNA
$\frac{d M}{d \mathrm{time}}=\mathrm{vs}\frac{\mathrm{KI}^{n}}{\mathrm{KI}^{n}+\mathrm{FN}^{n}}-\mathrm{vm}\frac{M}{\mathrm{Km}+M}$
FC
non-phopshorylated ER
$\frac{d \mathrm{FC}}{d \mathrm{time}}=\mathrm{ks}M+\mathrm{k2}\mathrm{FN}-\mathrm{vd}\frac{\mathrm{FC}}{\mathrm{Kd}+\mathrm{FC}}+\mathrm{k1}\mathrm{FC}\mathrm{Ft}=\mathrm{FC}+\mathrm{FN}$
FN
non-phopshorylated ER
$\frac{d \mathrm{FN}}{d \mathrm{time}}=\mathrm{k1}\mathrm{FC}-\mathrm{k2}\mathrm{FN}$
circadian rhythms
drosophila
signal transduction
limit cycle
neurospora
gene regulation
James
Lawson
Journal of Biological Rhythms
The University of Auckland
The Bioengineering Institute
Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora
14
433
448
Catherine
Lloyd
May
100
10000
0.1
Limit Cycle Model for Circadian Rhythms in Drosophila and Neurospora (Neurospora model)
The University of Auckland, Bioengineering Institute
c.lloyd@auckland.ac.nz
1999-12-01
Leloup et al.'s 1999 mathematical model of circadian rhythms in Neurospora.
Neurospora
2003-09-24T00:00:00+00:00
Albert
Goldbeter
Jean-Christophe
Leloup
Didier
Gonze
2008-09-05T13:21:26+12:00
keyword
Catherine Lloyd
Added equation for Ft to allow model to replicate Figure 1 of publication.
Added simulation metadata, cmeta:id's to variables
This is the CellML description of Leloup et al.'s 1999 mathematical model of circadian rhythms in Neurospora.
10643740