/*
 * Cross-bridge phosphorylation and regulation of latch state in
 * smooth muscle
 * 
 * Model Status
 * 
 * This CellML model runs in both OpenCell and COR to replicate
 * the published results (figure 6a). The units have been checked
 * and they are consistent.
 * 
 * Model Structure
 * 
 * ABSTRACT: We have developed a minimum kinetic model for cross-bridge
 * interactions with the thin filament in smooth muscle. The model
 * hypothesizes two types of cross-bridge interactions: 1) cycling
 * phosphorylated cross bridges and 2) noncycling dephosphorylated
 * cross bridges ("latch bridges"). The major assumptions are that
 * 1) Ca2+-dependent myosin phosphorylation is the only postulated
 * regulatory mechanism, 2) each myosin head acts independently,
 * and 3) latch bridges are formed by dephosphorylation of an attached
 * cross bridge. Rate constants were resolved by fitting data on
 * the time courses of myosin phosphorylation and stress development.
 * Comparison of the rate constants indicates that latch-bridge
 * detachment is the rate-limiting step. Model simulations predicted
 * a hyperbolic dependence of steady-state stress on myosin phosphorylation,
 * which corresponded with the experimental observation of high
 * values of stress with low levels of phosphorylation in intact
 * tissues. Model simulations also predicted the experimental observation
 * that an initial phosphorylation transient only accelerates stress
 * development, with no effect on the final steady-state levels
 * of stress. Because the only Ca2+-dependent regulatory mechanism
 * in this model was activation of myosin light chain kinase, these
 * results are consistent with the hypothesis that myosin phosphorylation
 * is both necessary and sufficient for the development of the
 * latch state.
 * 
 * The original paper reference is cited below:
 * 
 * Cross-bridge phosphorylation and regulation of latch state in
 * smooth muscle, Hai CM, Murphy RA, 1988, American Journal of
 * Physiology, 254, C99-C106. PubMed ID: 3337223
 * 
 * reaction diagram
 * 
 * [[Image file: hai_1988.png]]
 * 
 * Hai and Murphy's four-state model: the latch regulatory scheme
 * for Ca2+-dependent smooth muscle activation and Huxley's slidin
 * filament model. A represents the actin filament, M represents
 * detached myosin, Mp is detached, phosphorylated myosin, AM is
 * the actin-myosin complex, and AMp is the phosphorylated actin-myosin
 * complex.
 */

import nsrunit;
unit conversion on;
// unit nanometre predefined
unit first_order_rate_constant=1 second^(-1);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real M(time) dimensionless;
	when(time=time.min) M=1.0;
	real AM(time) dimensionless;
	when(time=time.min) AM=0.0;
	real Mp(time) dimensionless;
	when(time=time.min) Mp=0.0;
	real k1(time) first_order_rate_constant;
	real k2 first_order_rate_constant;
	k2=0.5;
	real k7 first_order_rate_constant;
	k7=0.01;
	real AMp(time) dimensionless;
	when(time=time.min) AMp=0.0;
	real k3 first_order_rate_constant;
	k3=0.4;
	real k4 first_order_rate_constant;
	k4=0.1;
	real k5 first_order_rate_constant;
	k5=0.5;
	real k6(time) first_order_rate_constant;
	real phosphorylation(time) dimensionless;
	real stress(time) dimensionless;

	// <component name="environment">

	// <component name="M">
	M:time=((-1)*(k1*M)+k2*Mp+k7*AM);

	// <component name="Mp">
	Mp:time=(k4*AMp+k1*M-(k2+k3)*Mp);

	// <component name="AMp">
	AMp:time=(k3*Mp+k6*AM-(k5+k4)*AMp);

	// <component name="AM">
	AM:time=(k5*AMp-(k6+k7)*AM);

	// <component name="phosphorylation">
	phosphorylation=(AMp+Mp);

	// <component name="stress">
	stress=(AMp+AM);

	// <component name="model_parameters">
	k1=(if ((time>=(0 second)) and (time<(5 second))) (.55 first_order_rate_constant) else (.3 first_order_rate_constant));
	k6=k1;
}