/*
 * Modelling The In Vitro Kinetics Of The Anti-Cancer Agent Topotecan
 * 
 * Model Status
 * 
 * This model is valid CellML and has consistent units but is unable
 * to be integrated in OpenCell or COR because it is unsuitably
 * constrained.
 * 
 * Model Structure
 * 
 * The compartmental approach to modelling the kinetics of a drug
 * can be used to provide a mathematical description of the characteristcis
 * of that drug and how it is delivered to a particular target.
 * With this aim in mind, Evans et al. propose a compartmental
 * model for the anti-cancer agent topotecan (TPT). The mathematical
 * equations used to describe the physiological processes are based
 * on biological assumptions, and the model parameters are estimated
 * using high performance liquid chromatograpy data.
 * 
 * TPT is a water soluble anti-cancer drug which has been approved
 * for use against ovarian and small cell lung carcinomas. The
 * drug's molecular target is DNA topoismerase I, an enzyme which
 * resolves topological distortions in DAN by cleavage and re-ligation
 * of one strand of the double stranded helix. TPT administration
 * traps topoismerase I in a covalently bound intermediate complex
 * with DNA. When the DNA replication machinary collides with this
 * complex, the double stranded DNA breaks apart.
 * 
 * The activity of TPT is pH dependent. AT physiological pH the
 * active form of the agent is not stable, and it undergoes reversible
 * hydrolisis to form the more stable, inactive form. The reversible
 * hydrolisis of TPT is first modelled by a linear, two compartment
 * model. This simple model then forms the basis of a cell based
 * model for drug activity in live cell experiments (see below).
 * 
 * The cell based model has been described here in CellML (the
 * raw CellML description of the Evans et al. 2004 model can be
 * downloaded in various formats as described in ).
 * 
 * The complete original paper reference is cited below:
 * 
 * A mathematical model for the in vitro kinetics of the anti-cancer
 * agent topotecan, Neil D. Evans, Rachel J. Errington, Micchael
 * Shelley, Graham P. Feeney, Michael J. Chapman, Keith R. Godfrey,
 * Paul J. Smith, Michael J. Chappell, 2004, Mathematical Biosciences,
 * 189, 185-217. PubMed ID: 15094319
 * 
 * cell diagram
 * 
 * [[Image file: evans_2004.png]]
 * 
 * Schematic diagram of the mathematical model used to investigate
 * the effect of injecting the anticancer drug TPT into a culture
 * of human lymphoma cells.
 */

import nsrunit;
unit conversion on;
unit minute=60 second^1;
unit first_order_rate_constant=.01666667 second^(-1);
// unit micromolar predefined
unit per_micromolar_minute=16.66666667 meter^3*second^(-1)*mole^(-1);
unit picol=1E-15 meter^3;

math main {
	//Warning:  the following variables were set 'extern' or given
	//  an initial value of '0' because the model would otherwise be
	//  underdetermined:  Vm, Vn, Vc
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Lm(time) micromolar;
	when(time=time.min) Lm=10.0;
	real ko_m first_order_rate_constant;
	ko_m=2.89E-2;
	real kc_m first_order_rate_constant;
	kc_m=1.06E-4;
	real ki first_order_rate_constant;
	ki=3.09E-4;
	real ke first_order_rate_constant;
	ke=1.0140;
	real Hm(time) micromolar;
	when(time=time.min) Hm=0.0;
	real Lc(time) micromolar;
	when(time=time.min) Lc=0.0;
	real v1 dimensionless;
	real ko_c first_order_rate_constant;
	ko_c=2.6553E-2;
	real kc_c first_order_rate_constant;
	kc_c=1.8637E-1;
	real kb per_micromolar_minute;
	kb=8.5341E-4;
	real kd first_order_rate_constant;
	kd=4.4489;
	real BT micromolar;
	BT=2.89E1;
	real Hc(time) micromolar;
	when(time=time.min) Hc=0.0;
	real Ln(time) micromolar;
	when(time=time.min) Ln=0.0;
	real v2 dimensionless;
	extern real Vm picol;
	extern real Vn picol;
	extern real Vc picol;

	// <component name="environment">

	// <component name="Lm">
	Lm:time=(kc_m*Hm+ke/v1*Lc-(ko_m+ki)*Lm);

	// <component name="Hm">
	Hm:time=(ko_m*Lm-kc_m*Hm);

	// <component name="Lc">
	Lc:time=(ki*v1*Lm+kc_c*Hc+v2*kd*Ln-((ke+ko_c)*Lc+kb*(BT-Ln)*Lc));

	// <component name="Hc">
	Hc:time=(ko_c*Lc-kc_c*Hc);

	// <component name="Ln">
	Ln:time=(kb/v2*(BT-Ln)*Lc-kd*Ln);

	// <component name="kinetic_parameters">
	v1=(Vm/Vc);
	v2=(Vn/Vc);
}