/*
 * Rhythmic secretion of prolactin in rats: action of oxytocin
 * coordinated by vasoactive intestinal polypeptide of suprachiasmatic
 * nucleus origin
 * 
 * Model Status
 * 
 * This model has been curated and is known to run in OpenCell
 * and COR to produce the results (figure 6) described in the publication.
 * The units have been checked and they are consistent.
 * 
 * Model Structure
 * 
 * ABSTRACT: Prolactin (PRL) is secreted from lactotrophs of the
 * anterior pituitary gland of rats in a unique pattern in response
 * to uterine cervical stimulation (CS) during mating. Surges of
 * PRL secretion occur in response to relief from hypothalamic
 * dopaminergic inhibition and stimulation by hypothalamic releasing
 * neurohormones. In this study, we characterized the role of oxytocin
 * (OT) in this system and the involvement of vasoactive intestinal
 * polypeptide (VIP) from the suprachiasmatic nucleus (SCN) in
 * controlling OT and PRL secretion of CS rats. The effect of OT
 * on PRL secretion was demonstrated in cultured lactotrophs showing
 * simultaneous enhanced secretion rate and increased intracellular
 * Ca(2+). Neurosecretory OT cells of the hypothalamic paraventricular
 * nucleus that express VIP receptors were identified by using
 * immunocytochemical techniques in combination with the retrogradely
 * transported neuronal tracer Fluoro-Gold (iv injected). OT measurements
 * of serial blood samples obtained from ovariectomized (OVX) CS
 * rats displayed a prominent increase at the time of the afternoon
 * PRL peak. The injection of VIP antisense oligonucleotides into
 * the SCN abolished the afternoon increase of OT and PRL in CS-OVX
 * animals. These findings suggest that VIP from the SCN contributes
 * to the regulation of OT and PRL secretion in CS rats. We propose
 * that in CS rats the regulatory mechanism(s) for PRL secretion
 * comprise coordinated action of neuroendocrine dopaminergic and
 * OT cells, both governed by the daily rhythm of VIP-ergic output
 * from the SCN. This hypothesis is illustrated with a mathematical
 * model.
 * 
 * In the paper described here, Egli et al. present a mathematical
 * model of the mechanisms regulating the rhythmic secretion of
 * prolactin in rats (see figure below). In this model the SCN
 * acts as a pacemaker, controlling the activity of the hypothalamic
 * DA and OT neurons via its rhythmic VIP secretion. In turn, the
 * activity of these DA and OT neurons combine to determine the
 * PRL secretory pattern.
 * 
 * model diagram
 * 
 * [[Image file: egli_2004.png]]
 * 
 * Schematic diagram of the network proposed to be involved in
 * the regulation of prolactin (PRL) secretion in response to uterine
 * cervical stimulation (CS). Vasoactive intestinal polypeptide
 * (VIP) is secreted from the suprachiasmatic nucleus and relays
 * the time of day to DAergic and OTergic neurosecretory cells
 * via inhibition. x represents an additional stimulatory input
 * which feeds into the OT neurons. DA neurons provide an inhibitory
 * input while OT neurons provide a stimulatory input to the lactotrophs
 * to regulate the synthesis and secretion of PRL.
 * 
 * The original paper reference is cited below:
 * 
 * Rhythmic secretion of prolactin in rats: action of oxytocin
 * coordinated by vasoactive intestinal polypeptide of suprachiasmatic
 * nucleus origin, Marcel Egli, Richard Bertram, Michael T. Sellix,
 * and Marc E. Freeman, 2004. Endocrinology , 145, 3386-3394. PubMed
 * ID: 15033917
 * 
 * The authors highlight that the original code they wrote for
 * this model can be downloaded here.
 */

import nsrunit;
unit conversion on;
unit hour=3600 second^1;
unit first_order_rate_constant=2.7777778E-4 second^(-1);
unit nanog_ml=1E-6 kilogram^1*meter^(-3);
unit picog_ml=1E-9 kilogram^1*meter^(-3);
unit nanog_ml_hr=2.7777778E-10 kilogram^1*meter^(-3)*second^(-1);
unit picog_ml_hr=2.7777778E-13 kilogram^1*meter^(-3)*second^(-1);

math main {
	realDomain time hour;
	time.min=0;
	extern time.max;
	extern time.delta;
	real PRL(time) nanog_ml;
	when(time=time.min) PRL=20.0;
	real kD nanog_ml;
	kD=300.0;
	real kO picog_ml;
	kO=9.0;
	real rP nanog_ml_hr;
	rP=300000.0;
	real qP first_order_rate_constant;
	qP=0.5;
	real OT(time) picog_ml;
	when(time=time.min) OT=25.0;
	real DA(time) nanog_ml;
	when(time=time.min) DA=20000.0;
	real vD(time) nanog_ml_hr;
	real vDbar nanog_ml_hr;
	vDbar=10000.0;
	real DA_infinity nanog_ml;
	DA_infinity=20000.0;
	real qD first_order_rate_constant;
	qD=0.2;
	real kx picog_ml;
	kx=50.0;
	real vO(time) picog_ml_hr;
	real vObar picog_ml_hr;
	vObar=500.0;
	real rO picog_ml_hr;
	rO=1100.0;
	real qO first_order_rate_constant;
	qO=1.0;
	real x(time) picog_ml;

	// <component name="environment">

	// <component name="PRL">
	PRL:time=(rP*((1 nanog_ml)/(kD+DA))*(OT/(kO+OT))^2-qP*PRL);

	// <component name="DA">
	DA:time=(qD*(DA_infinity-DA)-vD);
	vD=(if ((time>=(2 hour)) and (time<=(4 hour))) vDbar else (0 nanog_ml_hr));

	// <component name="OT">
	OT:time=(rO*(x/(kx+x))-(qO*OT+vO));
	vO=(if ((time>=(2 hour)) and (time<=(4 hour))) vObar else (0 picog_ml_hr));

	// <component name="x">
	x=(if ((time>=(2 hour)) and (time<=(4 hour))) (51 picog_ml) else if ((time>=(16 hour)) and (time<=(18 hour))) (51 picog_ml) else (1 picog_ml));
}