/*
 * A mathematical model for elongation of a peptide chain
 * 
 * Model Status
 * 
 * This CellML model runs in both OpenCell and COR. The units have
 * been checked and they are consistent. We are unsure as to whether
 * or not this CellML model recreates the results of the original
 * model as there are no simple concentration against time simulation
 * figures in the published paper to compare it with.
 * 
 * Model Structure
 * 
 * ABSTRACT: A mathematical model is presented for the steps in
 * the elongation process, and the steady-state elongation rate
 * as a function of the amino acid concentrations is found. In
 * addition, the reset sub-process of the elongation process is
 * modeled. The rate of elongation of peptide chains is found to
 * be a function of the concentration of the amino acid to be bound
 * and the concentration of all other amino acids. In addition,
 * the overall elongation rate depends on the concentrations of
 * elongation factors.
 * 
 * The original paper reference is cited below:
 * 
 * A Mathematical Model for Elongation of a Peptide Chain, Andrew
 * Heyd and Donald A. Drew, 2003, Bulletin of Mathematical Biology,
 * 65, 1095-1109. PubMed ID: 14607290
 * 
 * reaction diagram
 * 
 * [[Image file: heyd_2003.png]]
 * 
 * A schematic diagram displaying the reaction steps described
 * by the mathematical model.
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
unit flux=1E-3 meter^(-3)*second^(-1)*mole^1;
unit first_order_rate_constant=1 second^(-1);
unit second_order_rate_constant=1E3 meter^3*second^(-1)*mole^(-1);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real k11 second_order_rate_constant;
	k11=110.0;
	real k11_ first_order_rate_constant;
	k11_=25.0;
	real k71 first_order_rate_constant;
	k71=0.1;
	real k72 first_order_rate_constant;
	k72=60.0;
	real k12 second_order_rate_constant;
	k12=110.0;
	real k12_ first_order_rate_constant;
	k12_=0.2;
	real k51 first_order_rate_constant;
	k51=7.0;
	real k52 first_order_rate_constant;
	k52=0.0;
	real k41 first_order_rate_constant;
	k41=60.0;
	real k31 first_order_rate_constant;
	k31=500.0;
	real k32 first_order_rate_constant;
	k32=50.0;
	real k42 first_order_rate_constant;
	k42=70.0;
	real k22 first_order_rate_constant;
	k22=100.0;
	real k22_ first_order_rate_constant;
	k22_=17.0;
	real k21 first_order_rate_constant;
	k21=100.0;
	real k21_ first_order_rate_constant;
	k21_=0.2;
	real PB(time) micromolar;
	when(time=time.min) PB=0.1;
	real kreset1 first_order_rate_constant;
	kreset1=35.0;
	real A1(time) micromolar;
	when(time=time.min) A1=0.1;
	real A2(time) micromolar;
	when(time=time.min) A2=0.1;
	real PC1(time) micromolar;
	when(time=time.min) PC1=0.1;
	real PF1(time) micromolar;
	when(time=time.min) PF1=0.1;
	real PG1(time) micromolar;
	when(time=time.min) PG1=0.1;
	real PC2(time) micromolar;
	when(time=time.min) PC2=0.1;
	real PF2(time) micromolar;
	when(time=time.min) PF2=0.1;
	real PD1(time) micromolar;
	when(time=time.min) PD1=0.1;
	real PE1(time) micromolar;
	when(time=time.min) PE1=0.1;
	real PD2(time) micromolar;
	when(time=time.min) PD2=0.1;
	real PE2(time) micromolar;
	when(time=time.min) PE2=0.1;

	// <component name="environment">

	// <component name="kinetic_constants">

	// <component name="PB">
	PB:time=(k11_*PC1+k71*PF1+kreset1*PG1+k12_*PC2+k72*PF2-(k11*A1*PB+k12*A2*PB));

	// <component name="A1">
	A1:time=(k11_*PC1-k11*A1*PB);

	// <component name="A2">
	A2:time=(k12_*PC2-k12*A2*PB);

	// <component name="PC1">
	PC1:time=(k11*A1*PB-(k11_+k21)*PC1+k21_*PD1);

	// <component name="PD1">
	PD1:time=(k21*PC1-(k21_+k31)*PD1);

	// <component name="PE1">
	PE1:time=(k31*PD1-k41*PE1);

	// <component name="PF1">
	PF1:time=(k41*PE1-(k51+k71)*PF1);

	// <component name="PG1">
	PG1:time=(k51*PF1-kreset1*PG1);

	// <component name="PC2">
	PC2:time=(k12*A2*PB-(k12_+k22)*PC2+k22_*PD2);

	// <component name="PD2">
	PD2:time=(k22*PC2-(k22_+k32)*PD2);

	// <component name="PE2">
	PE2:time=(k32*PD2-k42*PE2);

	// <component name="PF2">
	PF2:time=(k42*PE2-(k52+k72)*PF2);

	// <component name="kreset1">
}