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  • Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in drosophila
  • Leloup JC, Goldbeter A
  • Journal of theoretical biology , 6/ 1999 , Volume 198 , pages: 445-459 , PubMed ID: 10366496
  • Unite de Chronobiologie Theorique, Faculte des Sciences, Universite Libre de Bruxelles, Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.
  • In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila. Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyse the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems. Copyright 1999 Academic Press.
Submitter of the first revision: Nicolas Le Novère
Submitter of this revision: Nicolas Le Novère
Modellers: Nicolas Le Novère

Metadata information

is (3 statements)
BioModels Database MODEL6617834203
BioModels Database BIOMD0000000021
KEGG Pathway dme04710

isDerivedFrom (1 statement)
BioModels Database BIOMD0000000171

isDescribedBy (1 statement)
PubMed 10366496

hasTaxon (1 statement)
isVersionOf (1 statement)

Curation status

Connected external resources

Name Description Size Actions

Model files

BIOMD0000000021_url.xml SBML L2V1 representation of Leloup1999_CircClock 49.54 KB Preview | Download

Additional files

BIOMD0000000021-biopax2.owl Auto-generated BioPAX (Level 2) 29.66 KB Preview | Download
BIOMD0000000021-biopax3.owl Auto-generated BioPAX (Level 3) 45.69 KB Preview | Download
BIOMD0000000021.m Auto-generated Octave file 12.62 KB Preview | Download
BIOMD0000000021.pdf Auto-generated PDF file 226.87 KB Preview | Download
BIOMD0000000021.png Auto-generated Reaction graph (PNG) 126.76 KB Preview | Download
BIOMD0000000021.sci Auto-generated Scilab file 8.56 KB Preview | Download
BIOMD0000000021.svg Auto-generated Reaction graph (SVG) 47.71 KB Preview | Download
BIOMD0000000021.vcml Auto-generated VCML file 65.68 KB Preview | Download
BIOMD0000000021.xpp Auto-generated XPP file 7.76 KB Preview | Download
BIOMD0000000021_urn.xml Auto-generated SBML file with URNs 48.47 KB Preview | Download

  • Model originally submitted by : Nicolas Le Novère
  • Submitted: Sep 13, 2005 2:24:15 PM
  • Last Modified: Feb 25, 2015 1:16:43 PM
  • Version: 2 public model Download this version
    • Submitted on: Feb 25, 2015 1:16:43 PM
    • Submitted by: Nicolas Le Novère
    • With comment: Current version of Leloup1999_CircClock
  • Version: 1 public model Download this version
    • Submitted on: Sep 13, 2005 2:24:15 PM
    • Submitted by: Nicolas Le Novère
    • With comment: Original import of Leloup1999_CircClock

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

: Variable used inside SBML models

Reactions Rate Parameters
T1 => T0 Cell*V_2T*T1/(K_2T+T1) V_2T=1.0; K_2T=2.0
T0 => T1 Cell*V_1T*T0/(K_1T+T0) V_1T=8.0; K_1T=2.0
T2 => T1 Cell*V_4T*T2/(K_4T+T2) V_4T=1.0; K_4T=2.0
CC => Cn Cell*k1*CC-compartment_0000002*k2*Cn k1=0.6; k2=0.2
P1 => P0 Cell*V_2P*P1/(K_2P+P1) V_2P=1.0; K_2P=2.0
Mt => Cell*k_d*Mt+Cell*V_mT*Mt/(K_mT+Mt) V_mT = 0.7; K_mT=0.2; k_d=0.01
P1 => P2 Cell*V_3P*P1/(K_3P+P1) V_3P=8.0; K_3P=2.0
Cn => compartment_0000002*k_dN*Cn k_dN=0.01
P1 => Cell*k_d*P1 k_d=0.01
T1 => Cell*k_d*T1 k_d=0.01
P0 => Cell*k_d*P0 k_d=0.01
=> P0; Mp Cell*k_sP*Mp k_sP=0.9
Curator's comment:
(added: 19 Oct 2006, 21:49:27, updated: 19 Oct 2006, 21:49:27)
Figure 2A reproduced by COPASI 4 build 19