/*
 * A kinetic model of the branch-point between the methionine and
 * threonine biosynthesis pathways in Arabidopsis thaliana
 * 
 * Model Status
 * 
 * This model contains no ODEs and as such can not currently be
 * solved by any of the available CellML tools. However the model
 * is known to be valid CellML and the units are consistent. Also
 * the CellML model appears to match the published equations.
 * 
 * Model Structure
 * 
 * ABSTRACT: This work proposes a model of the metabolic branch-point
 * between the methionine and threonine biosynthesis pathways in
 * Arabidopsis thaliana which involves kinetic competition for
 * phosphohomoserine between the allosteric enzyme threonine synthase
 * and the two-substrate enzyme cystathionine gamma-synthase. Threonine
 * synthase is activated by S-adenosylmethionine and inhibited
 * by AMP. Cystathionine gamma-synthase condenses phosphohomoserine
 * to cysteine via a ping-pong mechanism. Reactions are irreversible
 * and inhibited by inorganic phosphate. The modelling procedure
 * included an examination of the kinetic links, the determination
 * of the operating conditions in chloroplasts and the establishment
 * of a computer model using the enzyme rate equations. To test
 * the model, the branch-point was reconstituted with purified
 * enzymes. The computer model showed a partial agreement with
 * the in vitro results. The model was subsequently improved and
 * was then found consistent with flux partition in vitro and in
 * vivo. Under near physiological conditions, S-adenosylmethionine,
 * but not AMP, modulates the partition of a steady-state flux
 * of phosphohomoserine. The computer model indicates a high sensitivity
 * of cystathionine flux to enzyme and S-adenosylmethionine concentrations.
 * Cystathionine flux is sensitive to modulation of threonine flux
 * whereas the reverse is not true. The cystathionine gamma-synthase
 * kinetic mechanism favours a low sensitivity of the fluxes to
 * cysteine. Though sensitivity to inorganic phosphate is low,
 * its concentration conditions the dynamics of the system. Threonine
 * synthase and cystathionine gamma-synthase display similar kinetic
 * efficiencies in the metabolic context considered and are first-order
 * for the phosphohomoserine substrate. Under these conditions
 * outflows are coordinated.
 * 
 * The original paper reference is cited below:
 * 
 * A Kinetic Model of the Branch-Point between the Methionine and
 * Threonine Biosynthesis Pathways in Arabidopsis thaliana , Gilles
 * Curien, Stephane Ravanel and Renaud Dumas, 2003, European Journal
 * of Biochemistry , 270, 4615-4627. PubMed ID: 14622248
 * 
 * reaction diagram
 * 
 * [[Image file: curien_2003.png]]
 * 
 * Schematic diagram of the Phser branch-point in the aspartate-derived
 * amino acid biosynthetic pathway in plants.
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
unit micromolar2=1E-6 meter^(-6)*mole^2;
unit flux=1E-3 meter^(-3)*second^(-1)*mole^1;
unit first_order_rate_constant=1 second^(-1);

math main {
	real v_cystathionine flux;
	real Cys micromolar;
	Cys=15.0;
	real CGS micromolar;
	CGS=0.7;
	real Pi micromolar;
	Pi=10000.0;
	real Phser micromolar;
	Phser=500.0;
	real Km_CGS_app_Cys micromolar;
	real Km_CGS_Cys micromolar;
	Km_CGS_Cys=460.0;
	real kcat_CGS first_order_rate_constant;
	kcat_CGS=30.0;
	real kcat_CGS_app_Cys first_order_rate_constant;
	real Km_CGS_Phser micromolar;
	Km_CGS_Phser=2500.0;
	real Ki_CGS_Pi micromolar;
	Ki_CGS_Pi=2500.0;
	real v_Thr flux;
	real TS micromolar;
	TS=5.0;
	real AdoMet micromolar;
	AdoMet=20.0;
	real Km_TS micromolar;
	real kcat_TS_noAdoMet first_order_rate_constant;
	kcat_TS_noAdoMet=0.42;
	real kcat_TS_AdoMet first_order_rate_constant;
	kcat_TS_AdoMet=3.5;
	real kcat_TS first_order_rate_constant;
	real K1K2 micromolar2;
	K1K2=73.0;
	real Ki_TS_Pi micromolar;
	Ki_TS_Pi=1000.0;
	real J_Phser flux;

	// <component name="v_cystathionine">
	v_cystathionine=(kcat_CGS_app_Cys*CGS*Cys/(Km_CGS_app_Cys+Cys));
	kcat_CGS_app_Cys=(kcat_CGS/(1+Km_CGS_Phser/Phser*(1+Pi/Ki_CGS_Pi)));
	Km_CGS_app_Cys=(Km_CGS_Cys/(1+Km_CGS_Phser/Phser*(1+Pi/Ki_CGS_Pi)));

	// <component name="v_Thr">
	v_Thr=(TS*kcat_TS*Phser/(Km_TS+Phser));
	kcat_TS=((kcat_TS_noAdoMet+kcat_TS_AdoMet*(AdoMet^2/K1K2))/(1+AdoMet^2/K1K2));
	Km_TS=((250 micromolar)*((1+AdoMet/(.5 micromolar))/(1+AdoMet/(1.1 micromolar)))/(1+AdoMet^2/(140 micromolar2))*(1+Pi/Ki_TS_Pi));

	// <component name="J_Phser">
	J_Phser=(v_cystathionine+v_Thr);

	// <component name="CGS">

	// <component name="Phser">

	// <component name="AdoMet">

	// <component name="Cys">

	// <component name="Pi">

	// <component name="TS">
}