Circadian clock model based on protein sequestration (simple version) (Kim & Forger 2012)

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Accession:145800
"… To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. …"
Reference:
1 . Kim JK, Forger DB (2012) A mechanism for robust circadian timekeeping via stoichiometric balance. Mol Syst Biol 8:630 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Molecular Network;
Brain Region(s)/Organism:
Cell Type(s): Suprachiasmatic nucleus (SCN) neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program; XPP; MATLAB; Mathematica; SBML;
Model Concept(s): Oscillations; Simplified Models; Circadian Rhythms;
Implementer(s): Kim, Jae Kyoung [kimjack0 at kaist.ac.kr]; 
##########################################################################
# Simple model of circadian clock with NNF structure
# Generated: 12-Sep-2012 00:40:09
# Generated by Jae Kyoung Kim and Daniel Forger by using SBtoolbox2
# This file can be used by XPPAUT for simulation and
# bifurcation analysis.
##########################################################################

########################################################
# DIFFERENTIAL EQUATIONS
########################################################
M'=ao*(A-P-Kd+((A-P-Kd)^2+4*A*Kd)^0.5)/(2*A)-bo*M
Pc'=at*M-bt*Pc
P'=ah*Pc-bh*P
R'=ro*(A-P-Kd+((A-P-Kd)^2+4*A*Kd)^0.5)/(2*A)-do*R
A'=rt/R-dt*A

########################################################
# PARAMETERS
########################################################
param ao=1
param at=1
param ah=1
param bo=1
param bt=1
param bh=1
param ro=1
param rt=0.0043
param do=0.2
param dt=0.2
param Kd=1e-05

########################################################
# FUNCTIONS
########################################################
power(x,y)=x^y

########################################################
# INITIAL CONDITIONS
########################################################
M(0)=0.1
Pc(0)=0.1
P(0)=0.1
R(0)=0.1
A(0)=0.1

########################################################
# INTEGRATOR SETTINGS AND DONE
########################################################
@ method=stiff
@ bounds=100000
@ maxstor=20000
done

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