/*
 * Metabolic Control Analysis of Glycerol Synthesis in Saccharomyces
 * cerevisiae
 * 
 * Model Status
 * 
 * This model runs in COR and OpenCell and the units are consistent
 * throughout. The model does not currently reproduce the published
 * results, possibly due to missing parameter values in the paper.
 * 
 * Model Structure
 * 
 * ABSTRACT: Glycerol, a major by-product of ethanol fermentation
 * by Saccharomyces cerevisiae, is of significant importance to
 * the wine, beer, and ethanol production industries. To gain a
 * clearer understanding of and to quantify the extent to which
 * parameters of the pathway affect glycerol flux in S. cerevisiae,
 * a kinetic model of the glycerol synthesis pathway has been constructed.
 * Kinetic parameters were collected from published values. Maximal
 * enzyme activities and intracellular effector concentrations
 * were determined experimentally. The model was validated by comparing
 * experimental results on the rate of glycerol production to the
 * rate calculated by the model. Values calculated by the model
 * agreed well with those measured in independent experiments.
 * The model also mimics the changes in the rate of glycerol synthesis
 * at different phases of growth. Metabolic control analysis values
 * calculated by the model indicate that the NAD(+)-dependent glycerol
 * 3-phosphate dehydrogenase-catalyzed reaction has a flux control
 * coefficient (C(J)v1) of approximately 0.85 and exercises the
 * majority of the control of flux through the pathway. Response
 * coefficients of parameter metabolites indicate that flux through
 * the pathway is most responsive to dihydroxyacetone phosphate
 * concentration (R(J)DHAP= 0.48 to 0.69), followed by ATP concentration
 * (R(J)ATP = -0.21 to -0.50). Interestingly, the pathway responds
 * weakly to NADH concentration (R(J)NADH = 0.03 to 0.08). The
 * model indicates that the best strategy to increase flux through
 * the pathway is not to increase enzyme activity, substrate concentration,
 * or coenzyme concentration alone but to increase all of these
 * parameters in conjunction with each other.
 * 
 * The complete original paper reference is cited below:
 * 
 * Metabolic Control Analysis of Glycerol Synthesis in Saccharomyces
 * cerevisiae , Garth R. Cronwright, Johann M. Rohwer, and Bernard
 * A. Prior, 2002, Applied and Environmental Microbiology , 68,
 * 4448-4456. PubMed ID: 12200299
 * 
 * reaction diagram
 * 
 * [[Image file: cronwright_2002.png]]
 * 
 * Schematic diagram of the glycerol synthesis pathway in Saccharomyces
 * cerevisiae.
 */

import nsrunit;
unit conversion on;
// unit millimolar predefined
unit minute=60 second^1;
unit flux=.01666667 meter^(-3)*second^(-1)*mole^1;
unit first_order_rate_constant=.01666667 second^(-1);

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real F16BP millimolar;
	real G3P(time) millimolar;
	when(time=time.min) G3P=24;
	real V_Gpd_p(time) flux;
	real V_Gpp_p(time) flux;
	real DHAP millimolar;
	real ATP millimolar;
	real ADP millimolar;
	real NADH millimolar;
	real NAD millimolar;
	real Pi_ millimolar;
	real K_F16BP millimolar;
	K_F16BP=4.8;
	real K_ATP millimolar;
	K_ATP=0.73;
	real K_ADP millimolar;
	K_ADP=2;
	real K_NAD millimolar;
	K_NAD=0.93;
	real K_NADH millimolar;
	K_NADH=0.023;
	real V_Gpd_p.K_G3P millimolar;
	V_Gpd_p.K_G3P=1.2;
	real K_DHAP millimolar;
	K_DHAP=0.54;
	real K_eq dimensionless;
	K_eq=1e4;
	real Vf flux;
	Vf=36;
	real V_Gpp_p.K_G3P millimolar;
	V_Gpp_p.K_G3P=3.5;
	real K_Pi millimolar;
	K_Pi=1;
	real V flux;
	V=18;

	// <component name="environment">

	// <component name="F16BP">
	F16BP=(0 millimolar);

	// <component name="G3P">
	G3P:time=((-1)*V_Gpp_p+V_Gpd_p);

	// <component name="DHAP">
	DHAP=(.59 millimolar);

	// <component name="ATP">
	ATP=(2.37 millimolar);

	// <component name="ADP">
	ADP=(2.17 millimolar);

	// <component name="NADH">
	NADH=(1.87 millimolar);

	// <component name="NAD">
	NAD=(1.45 millimolar);

	// <component name="Pi">
	Pi_=(2.17 millimolar);

	// <component name="V_Gpd_p">
	V_Gpd_p=(Vf/(K_NADH*K_DHAP)*(NADH*DHAP-NAD*G3P/K_eq)/((1+F16BP/K_F16BP+ATP/K_ATP+ADP/K_ADP)*(1+NADH/K_NADH+NAD/K_NAD)*(1+DHAP/K_DHAP+G3P/V_Gpd_p.K_G3P)));

	// <component name="V_Gpp_p">
	V_Gpp_p=(V*G3P/V_Gpp_p.K_G3P/((1+G3P/V_Gpp_p.K_G3P)*(1+Pi_/K_Pi)));
}