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];
function [output] = SNF(varargin)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% simple model with SNF structure
% Generated: 03-Sep-2012 16:57:35
% Generated by Jae Kyoung Kim and Daniel Forger by using SBtoolbox2.  
% 
% [output] = simplemodel() => output = initial conditions in column vector
% [output] = simplemodel('states') => output = state names in cell-array
% [output] = simplemodel('algebraic') => output = algebraic variable names in cell-array
% [output] = simplemodel('parameters') => output = parameter names in cell-array
% [output] = simplemodel('parametervalues') => output = parameter values in column vector
% [output] = simplemodel(time,statevector) => output = time derivatives in column vector
% [t,x]=ode15s(@SNF,[0 20],SNF()); => output = solution
% 
% State names and ordering:
% 
% statevector(1): M
% statevector(2): Pc
% statevector(3): P
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global time
parameterValuesNew = [];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% HANDLE VARIABLE INPUT ARGUMENTS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargin == 0,
	% Return initial conditions of the state variables (and possibly algebraic variables)
	output = [0.1, 0.1, 0.1];
	output = output(:);
	return
elseif nargin == 1,
	if strcmp(varargin{1},'states'),
		% Return state names in cell-array
		output = {'M', 'Pc', 'P'};
	elseif strcmp(varargin{1},'algebraic'),
		% Return algebraic variable names in cell-array
		output = {};
	elseif strcmp(varargin{1},'parameters'),
		% Return parameter names in cell-array
		output = {'ao', 'at', 'ah', 'bo', 'bt', 'bh', 'A', 'Kd'};
	elseif strcmp(varargin{1},'parametervalues'),
		% Return parameter values in column vector
		output = [1, 1, 1, 1, 1, 1, 0.0659, 1e-05];
	else
		error('Wrong input arguments! Please read the help text to the ODE file.');
	end
	output = output(:);
	return
elseif nargin == 2,
	time = varargin{1};
	statevector = varargin{2};
elseif nargin == 3,
	time = varargin{1};
	statevector = varargin{2};
	parameterValuesNew = varargin{3};
	if length(parameterValuesNew) ~= 8,
		parameterValuesNew = [];
	end
elseif nargin == 4,
	time = varargin{1};
	statevector = varargin{2};
	parameterValuesNew = varargin{4};
else
	error('Wrong input arguments! Please read the help text to the ODE file.');
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% STATES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
M = statevector(1);
Pc = statevector(2);
P = statevector(3);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PARAMETERS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if isempty(parameterValuesNew),
	ao = 1;
	at = 1;
	ah = 1;
	bo = 1;
	bt = 1;
	bh = 1;
	A = 0.0659;
	Kd = 1e-05;
else
	ao = parameterValuesNew(1);
	at = parameterValuesNew(2);
	ah = parameterValuesNew(3);
	bo = parameterValuesNew(4);
	bt = parameterValuesNew(5);
	bh = parameterValuesNew(6);
	A = parameterValuesNew(7);
	Kd = parameterValuesNew(8);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DIFFERENTIAL EQUATIONS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
M_dot = ao*(A-P-Kd+((A-P-Kd)^2+4*A*Kd)^0.5)/(2*A)-bo*M;
Pc_dot = at*M-bt*Pc;
P_dot = ah*Pc-bh*P;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% RETURN VALUES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% STATE ODEs
output(1) = M_dot;
output(2) = Pc_dot;
output(3) = P_dot;
% return a column vector 
output = output(:);
return



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