/*
 * A Substrate Switch: A New Mode of Regulation in the Methionine
 * Metabolic Pathway
 * 
 * Model Status
 * 
 * This model runs in COR and OpenCell, and the units are consistent
 * throughout. It is a faithful reproduction of the paper equations,
 * and the output is similar (but not identical) to the published
 * results (Fig 5).
 * 
 * Model Structure
 * 
 * ABSTRACT: We propose a simple mathematical model of liver S-adenosylmethionine
 * (AdoMet) metabolism. Analysis of the model has shown that AdoMet
 * metabolism can operate under two different modes. The first,
 * with low metabolic rate and low AdoMet concentration, serves
 * predominantly to supply the cell with AdoMet, the substrate
 * for various cellular methylation reactions. The second, with
 * high metabolic rate and high AdoMet concentration, provides
 * an avenue for cleavage of excess methionine and can serve as
 * a source of cysteine when its increased synthesis is necessary.
 * The switch that triggers interconversion between the "low" and
 * "high" modes is methionine concentration. Under a certain set
 * of parameters both modes may coexist. This behavior results
 * from the kinetic properties of (i) the two isoenzymes of AdoMet
 * synthetase, MATI and MATIII, that catalyse AdoMet production;
 * one is inhibited by AdoMet, whereas the other is activated by
 * it, and (ii) glycine-N-methyltransferase that displays highly
 * cooperative kinetics that is different from that of other AdoMet-dependent
 * methyltransferases. Thus, the model provides an explanation
 * for how different cellular needs are met by regulation of this
 * pathway. The model also correctly identifies a critical role
 * for glycine N-methyltransferase in depleting excess methionine
 * in the high mode, thus avoiding the toxicity associated with
 * elevated levels of this essential amino acid.
 * 
 * The original paper reference is cited below:
 * 
 * A Substrate Switch: A New Mode of Regulation in the Methionine
 * Metabolic Pathway, Michael V. Martinov, Victor M. Vitvitsky,
 * Eugene V. Mosharov, Ruma Banerjee, and Fazoil I. Ataullakhanov,
 * 2000, Journal of Theoretical Biology, 204, 521-532. PubMed ID:
 * 10833353
 * 
 * reaction diagram
 * 
 * [[Image file: martinov_2000.png]]
 * 
 * Simplified pathway of methionine metabolism in liver cells employed
 * for modelling in the study described here. The main metabolites
 * are shown in blue boxes and the enzymes in red boxes.
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
unit hour=3600 second^1;
unit flux=2.7777778E-7 meter^(-3)*second^(-1)*mole^1;
unit first_order_rate_constant=2.7777778E-4 second^(-1);

math main {
	realDomain time hour;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Ado micromolar;
	Ado=1;
	real Met(time) micromolar;
	real Hcy(time) micromolar;
	real AdoHcy(time) micromolar;
	when(time=time.min) AdoHcy=3;
	real K_AHC micromolar;
	K_AHC=0.1;
	real AdoMet(time) micromolar;
	when(time=time.min) AdoMet=60;
	real V_MET(time) flux;
	real V_GNMT(time) flux;
	real V_MATI(time) flux;
	real V_MATIII(time) flux;
	real V_D(time) flux;
	real V_MATImax flux;
	V_MATImax=561;
	real Km_MATI micromolar;
	Km_MATI=41;
	real Ki_MATI micromolar;
	Ki_MATI=50;
	real V_MATIIImax flux;
	V_MATIIImax=22870;
	real Km1_MATIII(time) micromolar;
	real Km2_MATIII micromolar;
	Km2_MATIII=21.1;
	real V_METmax flux;
	V_METmax=4544;
	real Km1_MET(time) micromolar;
	real Km2_MET_A dimensionless;
	Km2_MET_A=10;
	real V_GNMTmax flux;
	V_GNMTmax=10600;
	real Km_GNMT micromolar;
	Km_GNMT=4500;
	real Ki_GNMT micromolar;
	Ki_GNMT=20;
	real alpha_d first_order_rate_constant;
	alpha_d=1333;

	// <component name="environment">

	// <component name="Ado">

	// <component name="Met">
	Met=(if ((time>=(0 hour)) and (time<(5 hour))) (45 micromolar) else if ((time>=(5 hour)) and (time<(15 hour))) (52 micromolar) else if ((time>=(15 hour)) and (time<(60 hour))) (55 micromolar) else if ((time>=(60 hour)) and (time<(75 hour))) (52 micromolar) else if (time>=(75 hour)) (45 micromolar) else 0);

	// <component name="Hcy">
	Hcy=(AdoHcy*K_AHC/Ado);

	// <component name="K_AHC">

	// <component name="AdoMet">
	AdoMet:time=(V_MATI+V_MATIII-(V_MET+V_GNMT));

	// <component name="AdoHcy">
	AdoHcy:time=((V_MET+V_GNMT-V_D)/(1+K_AHC/Ado));

	// <component name="V_MATI">
	V_MATI=(V_MATImax/(1+Km_MATI/Met*(1+AdoMet/Ki_MATI)));

	// <component name="V_MATIII">
	V_MATIII=(V_MATIIImax/(1+Km1_MATIII*Km2_MATIII/(Met^2+Met*Km2_MATIII)));
	Km1_MATIII=((2E4 micromolar)/(1+5.7*(AdoMet/(AdoMet+(600 micromolar)))^2));

	// <component name="V_MET">
	V_MET=(V_METmax/(1+Km1_MET/AdoMet+Km2_MET_A+Km2_MET_A*Km1_MET/AdoMet));
	Km1_MET=((10 micromolar)*(1+AdoHcy/(4 micromolar)));

	// <component name="V_GNMT">
	V_GNMT=(V_GNMTmax/(1+(Km_GNMT/AdoMet)^2.3)*1/(1+AdoHcy/Ki_GNMT));

	// <component name="V_D">
	V_D=(alpha_d*Hcy);
}