modelContainer
Extends from BioChem.Compartments.MainCompartment (Main compartment (constant volume)).
Information
Circadian Oscillator
This example is the modelica version of the model presented in
Modeling feedback loops of the Mammalian circadian oscillator by
Becker-Weimann S, Wolf J, Herzel H, Kramer A. (Biophysical Journal Volume 87 November 2004 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.
Simulations
The simulation results are shown in the
Figure 1. This plot corresponds to Fig 3A from the paper (Becker-Weimann, 2004).
Parameters
| Type | Name | Default | Description |
|---|
| Real | v1b | 9 | |
| Real | c_sbml | 0.01 | |
| Real | k1b | 1 | |
| Real | k1i | 0.56 | |
| Real | hill_coeff | 8 | |
| Real | v4b | 3.6 | |
| Real | r_sbml | 3 | |
| Real | k4b | 2.16 | |
| Real | k1d | 0.12 | |
| Real | k2b | 0.3 | |
| Real | q | 2 | |
| Real | k2d | 0.05 | |
| Real | k2t | 0.24 | |
| Real | k3t | 0.02 | |
| Real | k3d | 0.12 | |
| Real | k4d | 0.75 | |
| Real | k5b | 0.24 | |
| Real | k5d | 0.06 | |
| Real | k5t | 0.45 | |
| Real | k6t | 0.06 | |
| Real | k6d | 0.12 | |
| Real | k6a | 0.09 | |
| Real | k7a | 0.003 | |
| Real | k7d | 0.09 | |
Components
| Type | Name | Default | Description |
|---|
| BioChem.Units.Volume | V (from Compartment) | | Compartment volume |
| BioChem.Examples.CircadianOscillator.Nucleus | nucleus | | |
| Cytoplasm | cytoplasm | | |
| Real | Nucleus_V | nucleus.V | Variable used to make the compartment volume of inner compartments accessible. Do not edit. |
| Real | Cytoplasm_V | cytoplasm.V | Variable used to make the compartment volume of inner compartments accessible. Do not edit. |
| Real | Container_V | V | Variable used to make the compartment volume accessible for inner components. Do not edit. |
| Real | trans_per2_cry | | |
| Real | trans_Bmal1 | | |
| Real | y5_y6_y7 | | |
