/*
 * Function of Stretch Activation in Heart Muscle
 * 
 * Model Status
 * 
 * This model runs in PCEnv and COR, but does not recreate the
 * published results. The units are continuous throughout, but
 * since most of the model parameters were not defined in the paper,
 * they were set to 1, which does not generate correct results.
 * All the equations are correct, either taken from the paper or
 * referenced papers (and are listed as such). The model authors
 * have been contacted.
 * 
 * Model Structure
 * 
 * ABSTRACT: Stretch activation is an intrinsic length-sensing
 * mechanism that allows muscle to function with an autonomous
 * regulation that reduces reliance on extrinsic regulatory systems.
 * This autonomous regulation is most dramatic in asynchronous
 * insect flight muscle and gives rise to wing beat frequencies
 * that exceed the frequency capacity of neural motor control systems.
 * Stretch activation in insect flight muscle allows the contractile
 * features of the flight muscle to be matched and tuned to the
 * wing-thorax-aerodynamic load to ensure proper muscle contraction
 * frequency and effort for flight (Pringle, 1977); a role for
 * which intrinsic autonomous regulation is especially suited.
 * In stretch-sensitive insect flight muscles, neurally controlled
 * intracellular calcium plays a permissive role (it needs to be
 * present at adequate levels to allow the intrinsic stretch activation
 * mechanisms to operate) but it is not the dominant player in
 * force generation or in work production. That role belongs to
 * stretch itself, which activates the myofilament system in such
 * a way (i.e., with appropriate phase delay) to generate force
 * and perform rhythmic work.
 * 
 * The original paper reference is cited below:
 * 
 * Function of Stretch Activation in Heart Muscle, Kenneth B. Campbell,
 * Murali Chandra, 2006, Journal of General Physiology , 127, 89-94.
 * PubMed ID: 16446501
 * 
 * reaction diagram
 * 
 * [[Image file: campbell_2006.png]]
 * 
 * Figure 1. Kinetic scheme for model of myofilament activation
 * and myosin cross-bridge cycling. Myofilament activation occurs
 * by steps responsible for the transition between Blocked and
 * Closed states. This scheme allows myofilament activation by
 * both calcium binding and by cooperative cross-bridge mechanisms.
 */

import nsrunit;
unit conversion on;
unit force = fundamental;
unit um=1E-6 meter^1;
unit per_um=1E6 meter^(-1);
unit um_per_second=1E-6 meter^1*second^(-1);
unit per_second=1 second^(-1);
unit force_per_um=1E6 meter^(-1)*force^1;

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real F(time) force;
	real R_on(time) dimensionless;
	when(time=time.min) R_on=1;
	real A(time) dimensionless;
	when(time=time.min) A=0;
	real alpha dimensionless;
	alpha=0.1;
	real D(time) dimensionless;
	real k_XB(time) per_second;
	real k_a per_second;
	k_a=0;
	real x(time) um;
	when(time=time.min) x=1;
	real x_0 um;
	x_0=1;
	real epsilon force_per_um;
	epsilon=1;
	real beta per_um;
	beta=2;
	real g per_second;
	g=1;
	real f per_second;
	f=1;
	real k_off per_second;
	k_off=1;
	real k_on per_second;
	k_on=1;
	real L(time) um;
	when(time=time.min) L=2.12;
	real L_0 um;
	L_0=2.12;
	real dL_dt(time) um_per_second;

	// <component name="environment">

	// <component name="equations">
	D=(1-A);
	F=(A*epsilon*x);
	R_on:time=((-1)*((k_off+k_XB+alpha*k_on)/(1+alpha)+f*D)*R_on+(g-(k_XB+alpha*k_on)/(1+alpha))*A+(k_XB+alpha*k_on/(1+alpha))*beta*(L-L_0));
	A:time=(f*D*R_on-g*A);
	x:time=((-1)*g*(x-x_0)+dL_dt);
	k_XB=(k_a*A);

	// <component name="undefined_parameters">

	// <component name="parameters_stelzer_et_al">
	dL_dt=(if (((.001 second)<time) and (time<=(.003 second))) (10.6 um_per_second) else (0 um_per_second));
	L:time=dL_dt;
}