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leloup1

leloup1

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Mp_degradation

PER mRNA degradation

Mp > ∅

Mp_production

PER mRNA production

∅ > Mp

Mt_degradation

TIM mRNA degradation

Mt > ∅

Mt_production

TIM mRNA production

∅ > Mt

P0_degradation

PER degradation

P0 > ∅

P0_production

PER production

∅ > P0

P0_to_P1

First Phosphorylation of PER

P0 > P1

P1_degradation

PER-1 degradation

P1 > ∅

P1_to_P0

Dephosphorylation of PER (1st P)

P1 > P0

P1_to_P2

Second Phosphorylation of PER

P1 > P2

P2_degradation

PER-2 degradation

P2 > ∅

P2_to_P1

Dephosphorylation of PER (2nd P)

P2 > P1

PT_complex_degradation

PER-TIM complex degradation (cytosol)

CC > ∅

PT_complex_formation

PER-TIM complex formation

P2 + T2 = CC

PT_complex_nucleation

PER-TIM complex nucleation

CC = Cn

PTnucl_complex_degradation

PER-TIM complex degradation (nuclear)

Cn > ∅

T0_degradation

TIM degradation

T0 > ∅

T0_production

TIM production

∅ > T0

T0_to_T1

First Phosphorylation of TIM

T0 > T1

T1_degradation

TIM-1 degradation

T1 > ∅

T1_to_T0

Dephosphorylation of TIM (1st P)

T1 > T0

T1_to_T2

Second Phosphorylation of TIM

T1 > T2

T2_degradation

TIM-2 degradation

T2 > ∅

T2_to_T1

Dephosphorylation of TIM (2nd P)

T2 > T1

Parameters

Global parameters
Mp_degradation
Mp_production
Mt_degradation
Mt_production
P0_degradation
P0_production
P0_to_P1
P1_degradation
P1_to_P0
P1_to_P2
P2_degradation
P2_to_P1
PT_complex_degradation
PT_complex_formation
PT_complex_nucleation
PTnucl_complex_degradation
T0_degradation
T0_production
T0_to_T1
T1_degradation
T1_to_T0
T1_to_T2
T2_degradation
T2_to_T1

Fixed species

Initial values

Functions and Rules

Assignment rules

Tt = CC + Cn + T0 + T1 + T2

Pt = CC + Cn + P0 + P1 + P2

Function definitions

Events

Constraints

Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.


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Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in drosophila

  • Jean-Christophe Leloup
  • Albert Goldbeter
J. Theor. Biol. 1999; 198 (3): 445-459
Abstract
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.
The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000021) Biomodels notes: This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.