/*
 * Limit cycle models for circadian rhythms based on transcriptional
 * regulation in Drosophila and Neurospora
 * 
 * Model Status
 * 
 * This CellML model runs in COR and OpenCell to reproduce the
 * published results (figure 2c). The units are consistent. This
 * particular version of the model has been translated from equations
 * 4a-4c (Neurospora).
 * 
 * Model Structure
 * 
 * ABSTRACT: We examine theoretical models for circadian oscillations
 * based on transcriptional regulation in Drosophila and Neurospora.
 * For Drosophila, the molecular model is based on the negative
 * feedback exerted on the expression of the per and tim genes
 * by the complex formed between the PER and TIM proteins. For
 * Neurospora, similarly, the model relies on the feedback exerted
 * on the expression of the frq gene by its protein product FRQ.
 * In both models, sustained rhythmic variations in protein and
 * mRNA levels occur in continuous darkness, in the form of limit
 * cycle oscillations. The effect of light on circadian rhythms
 * is taken into account in the models by considering that it triggers
 * degradation of the TIM protein in Drosophila, and frq transcription
 * in Neurospora. When incorporating the control exerted by light
 * at the molecular level, we show that the models can account
 * for the entrainment of circadian rhythms by light-dark cycles
 * and for the damping of the oscillations in constant light, though
 * such damping occurs more readily in the Drosophila model. The
 * models account for the phase shifts induced by light pulses
 * and allow the construction of phase response curves. These compare
 * well with experimental results obtained in Drosophila. The model
 * for Drosophila shows that when applied at the appropriate phase,
 * light pulses of appropriate duration and magnitude can permanently
 * or transiently suppress circadian rhythmicity. We investigate
 * the effects of the magnitude of light-induced changes on oscillatory
 * behavior. Finally, we discuss the common and distinctive features
 * of circadian oscillations in the two organisms.
 * 
 * The original paper reference is cited below:
 * 
 * Limit Cycle Models for Circadian Rhythms Based on Transcriptional
 * Regulation in Drosophila and Neurospora, Jean-Christophe Leloup,
 * Didier Gonze, and Albert Goldbeter, 1999, Journal of Biological
 * Rhythms, 14, 433-448. PubMed ID: 10643740
 * 
 * reaction diagram1
 * 
 * [[Image file: leloup_1999.png]]
 * 
 * Scheme for the model for circadian oscillations in Drosophila
 * involving negative regulation of gene expression by the PER-TIM
 * protein complex. And beneath this is the scheme for the model
 * for circadian rhythms in Neurospora. This model is based on
 * negative feedback exerted by the protein FRQ on the transcription
 * of the frq gene.
 */

import nsrunit;
unit conversion on;
// unit nanomolar predefined
unit hour=3600 second^1;
unit flux=2.7777778E-10 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 M(time) nanomolar;
	when(time=time.min) M=0.1;
	real vs flux;
	vs=1.6;
	real vm flux;
	vm=0.505;
	real Km nanomolar;
	Km=0.5;
	real KI nanomolar;
	KI=1.0;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real n dimensionless;
//	n=4.0;
	real FN(time) nanomolar;
	when(time=time.min) FN=0.1;
	real FC(time) nanomolar;
	when(time=time.min) FC=0.1;
	real Ft(time) nanomolar;
	real ks first_order_rate_constant;
	ks=0.5;
	real vd flux;
	vd=1.4;
	real Kd nanomolar;
	Kd=0.13;
	real k1 first_order_rate_constant;
	k1=0.5;
	real k2 first_order_rate_constant;
	k2=0.6;

	// <component name="environment">

	// <component name="M">
	M:time=(vs*(KI^4/(KI^4+FN^4))-vm*(M/(Km+M)));

	// <component name="FC">
	FC:time=(ks*M+k2*FN-(vd*(FC/(Kd+FC))+k1*FC));
	Ft=(FC+FN);

	// <component name="FN">
	FN:time=(k1*FC-k2*FN);

	// <component name="parameters">
}