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weimann1

weimann1

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Active_BMAL1_degradation

Active_BMAL1_degradation

y7 > ∅

BMAL1_activation

BMAL1_activation

y6 > y7

BMAL1_deactivation

BMAL1_deactivation

y7 > y6

BMAL1_nuclear_export

BMAL1_nuclear_export

y6 > y5

BMAL1_nuclear_import

BMAL1_nuclear_import

y5 > y6

BMAL1_translation

BMAL1_translation

∅ > y5

Bmal1_mRNA_degradation

Bmal1_mRNA_degradation

y4 > ∅

Bmal1_transcription

Bmal1_transcription

∅ > y4

cytoplasmic_BMAL1_degradation

cytoplasmic_BMAL1_degradation

y5 > ∅

cytoplasmic_per2_cry_complex_degradation

cytoplasmic_per2_cry_complex_degradation

y2 > ∅

nuclear_BMAL1_degradation

nuclear_BMAL1_degradation

y6 > ∅

nuclear_per2_cry_complex_degradation

nuclear_per2_cry_complex_degradation

y3 > ∅

per2_cry_complex_formation

per2_cry_complex_formation

∅ > y2

per2_cry_mRNA_degradation

per2_cry_mRNA_degradation

y1 > ∅

per2_cry_nuclear_export

per2_cry_nuclear_export

y3 > y2

per2_cry_nuclear_import

per2_cry_nuclear_import

y2 > y3

per2_cry_transcription

per2_cry_transcription

∅ > y1

Parameters

Global parameters

Fixed species

Initial values

Functions and Rules

Assignment rules

y5_y6_y7 = y5 + y6 + y7

trans_Bmal1 = v4b * pow(y3, r) / (pow(k4b, r) + pow(y3, r))

trans_per2_cry = v1b * (y7 + c) / (k1b * (1.0 + pow(y3 / k1i, hill_coeff)) + y7 + c)

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.


Species:

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Modeling feedback loops of the Mammalian circadian oscillator.

  • Sabine Becker-Weimann
  • Jana Wolf
  • Hanspeter Herzel
  • Achim Kramer
Biophys. J. 2004; 87 (5): 3023-3034
Abstract
The suprachiasmatic nucleus governs daily variations of physiology and behavior in mammals. Within single neurons, interlocked transcriptional/translational feedback loops generate circadian rhythms on the molecular level. We present a mathematical model that reflects the essential features of the mammalian circadian oscillator to characterize the differential roles of negative and positive feedback loops. The oscillations that are obtained have a 24-h period and are robust toward parameter variations even when the positive feedback is replaced by a constantly expressed activator. This demonstrates the crucial role of the negative feedback for rhythm generation. Moreover, it explains the rhythmic phenotype of Rev-erbalpha-/- mutant mice, where a positive feedback is missing. The interplay of negative and positive feedback reveals a complex dynamics. In particular, the model explains the unexpected rescue of circadian oscillations in Per2Brdm1/Cry2-/- double-mutant mice (Per2Brdm1 single-mutant mice are arrhythmic). Here, a decrease of positive feedback strength associated with mutating the Per2 gene is compensated by the Cry2-/- mutation that simultaneously decreases the negative feedback strength. Finally, this model leads us to a testable prediction of a molecular and behavioral phenotype: circadian oscillations should be rescued when arrhythmic Per2Brdm1 mutant mice are crossed with Rev- erbalpha -/- mutant mice.
The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000170). Biomodels notes: "The model reproduces the time profile of the species as depicted in Fig 3A of the paper. Model successfully tested on MathSBML and Jarnac." JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.