/*
 * Network topology determines dynamics of the mammalian MAPK1,2
 * signaling network: bifan motif regulation of C-Raf and B-Raf
 * isoforms by FGFR and MC1R
 * 
 * Model Status
 * 
 * This cellML model is known to run in both OpenCell and COR to
 * recreate the published results. The units have been checked
 * and they are consistent. Please note that this CellML model
 * corresponds to the reduced 6-node network, not the full 106-node
 * network. Also, we have chosen the parameters such that the model
 * recreates figure 4B in the paper (experiment 3, where there
 * is a stimulus of MSH at 0–5 min followed by a stimulus of FGF
 * at 5–10 min).
 * 
 * Model Structure
 * 
 * ABSTRACT: Activation of the fibroblast growth factor (FGFR)
 * and melanocyte stimulating hormone (MC1R) receptors stimulates
 * B-Raf and C-Raf isoforms that regulate the dynamics of MAPK1,2
 * signaling. Network topology motifs in mammalian cells include
 * feed-forward and feedback loops and bifans where signals from
 * two upstream molecules integrate to modulate the activity of
 * two downstream molecules. We computationally modeled and experimentally
 * tested signal processing in the FGFR/MC1R/B-Raf/C-Raf/MAPK1,2
 * network in human melanoma cells; identifying 7 regulatory loops
 * and a bifan motif. Signaling from FGFR leads to sustained activation
 * of MAPK1,2, whereas signaling from MC1R results in transient
 * activation of MAPK1,2. The dynamics of MAPK activation depends
 * critically on the expression level and connectivity to C-Raf,
 * which is critical for a sustained MAPK1,2 response. A partially
 * incoherent bifan motif with a feedback loop acts as a logic
 * gate to integrate signals and regulate duration of activation
 * of the MAPK signaling cascade. Further reducing a 106-node ordinary
 * differential equations network encompassing the complete network
 * to a 6-node network encompassing rate-limiting processes sustains
 * the feedback loops and the bifan, providing sufficient information
 * to predict biological responses.
 * 
 * model diagram
 * 
 * [[Image file: muller_2008.png]]
 * 
 * Schematic diagram of the model proposed for the activation of
 * MAPK1,2 when initiated due to upstream activation of the FGFR
 * and MC1R.
 * 
 * The original paper reference is cited below:
 * 
 * Network topology determines dynamics of the mammalian MAPK1,2
 * signaling network: bifan motif regulation of C-Raf and B-Raf
 * isoforms by FGFR and MC1R, Melissa Muller, Mandri Obeyesekere,
 * Gordon B. Mills and Prahlad T. Ram, 2008, The FASEB Journal
 * PubMed ID: 18171696
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
unit minute=60 second^1;
unit flux=1.6666667E-5 meter^(-3)*second^(-1)*mole^1;
unit first_order_rate_constant=.01666667 second^(-1);
unit second_order_rate_constant=16.66666667 meter^3*second^(-1)*mole^(-1);

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real y1(time) micromolar;
	when(time=time.min) y1=0.0;
	real a1 flux;
	a1=10.0;
	real g1(time) micromolar;
	real b1 micromolar;
	b1=10.0;
	real d1 first_order_rate_constant;
	d1=0.2;
	real y2(time) micromolar;
	when(time=time.min) y2=0.0;
	real a2 flux;
	a2=10.0;
	real g2(time) micromolar;
	real b2 micromolar;
	b2=10.0;
	real d2 first_order_rate_constant;
	d2=0.1;
	real y3(time) micromolar;
	when(time=time.min) y3=0.0;
	real f53 second_order_rate_constant;
	f53=1.5;
	real f13 second_order_rate_constant;
	f13=0.6;
	real y3.h36 second_order_rate_constant;
	y3.h36=0.1;
	real d3 first_order_rate_constant;
	d3=1.0;
	real E micromolar;
	E=10.0;
	real y5(time) micromolar;
	when(time=time.min) y5=0.0;
	real y6(time) micromolar;
	when(time=time.min) y6=0.0;
	real y4(time) micromolar;
	when(time=time.min) y4=0.0;
	real f14 first_order_rate_constant;
	f14=0.1;
	real f24 first_order_rate_constant;
	f24=0.8;
	real d4 first_order_rate_constant;
	d4=1.1;
	real f35 first_order_rate_constant;
	f35=0.3;
	real f45 first_order_rate_constant;
	f45=0.1;
	real d5 first_order_rate_constant;
	d5=1.0;
	real y6.h36 second_order_rate_constant;
	y6.h36=0.1;
	real d6 first_order_rate_constant;
	d6=0.001;

	// <component name="environment">

	// <component name="y1">
	y1:time=(a1*(g1/(b1+g1))-d1*y1);
	g1=(if ((time>=(0 minute)) and (time<(5 minute))) (0 micromolar) else if ((time>=(5 minute)) and (time<=(10 minute))) (1 micromolar) else (0 micromolar));

	// <component name="y2">
	y2:time=(a2*(g2/(b2+g2))-d2*y2);
	g2=(if ((time>=(0 minute)) and (time<=(5 minute))) (1 micromolar) else (0 micromolar));

	// <component name="y3">
	y3:time=(f13*(E-(y3+y6))*y1+f53*(E-(y3+y6))*y5-(y3.h36*y2*y3+d3*y3));

	// <component name="y4">
	y4:time=(f14*y1+f24*y2-d4*y4);

	// <component name="y5">
	y5:time=(f35*y3+f45*y4-d5*y5);

	// <component name="y6">
	y6:time=(y6.h36*y2*y3-d6*y6);
}