Location: 12 L Platform 1 model codes @ 4c1ab73f48d7 / skeletal_muscle / myscle_ftu.cellml
- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/skeletal_muscle/myscle_ftu.cellml
<?xml version='1.0'?>
<model name="muscle_ftu" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="uM">
<unit prefix="micro" units="mole"/>
</units>
<units name="ms1">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="uM_per_ms1">
<unit units="uM"/>
<unit exponent="-1" units="ms1"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<component name="Environment">
<variable name="t" public_interface="out" units="ms"/>
</component>
<component name="muscle">
<variable initial_value="1" name="D" units="dimensionless"/>
<variable initial_value="0" name="A1" units="dimensionless"/>
<variable initial_value="0" name="A2" units="dimensionless"/>
<variable name="Roff" units="dimensionless"/>
<variable initial_value="0.05" name="f" units="ms1"/>
<variable initial_value="0.4" name="g" units="ms1"/>
<variable initial_value="0.004" name="gs" units="ms1"/>
<variable initial_value="0.008" name="h1" units="ms1"/>
<variable initial_value="0.006" name="h2" units="ms1"/>
<variable initial_value="0" name="kon0" units="ms1"/>
<variable initial_value="0.1" name="koff0" units="ms1"/>
<variable initial_value="0.12" name="konCa" units="ms1"/>
<variable initial_value="0.05" name="koffCa" units="ms1"/>
<variable initial_value="1" name="RT" units="dimensionless"/>
<variable name="kon" units="ms1"/>
<variable name="koff" units="ms1"/>
<variable name="Ca_ms" public_interface="in" units="uM"/>
<variable name="Ca50" units="uM"/>
<variable name="F" units="dimensionless"/>
<variable name="t" public_interface="in" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca50</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>Ca_ms</ci>
</apply>
</apply>
<!--Assumption-->
<apply>
<eq/>
<ci>kon</ci>
<apply>
<plus/>
<ci>kon0</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>konCa</ci>
<ci>kon0</ci>
</apply>
<ci>Ca_ms</ci>
</apply>
<apply>
<plus/>
<ci>Ca50</ci>
<ci>Ca_ms</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>koff</ci>
<apply>
<plus/>
<ci>koff0</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>koffCa</ci>
<ci>koff0</ci>
</apply>
<ci>Ca_ms</ci>
</apply>
<apply>
<plus/>
<ci>Ca50</ci>
<ci>Ca_ms</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>D</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kon</ci>
<ci>Roff</ci>
</apply>
<apply>
<times/>
<ci>koff</ci>
<ci>D</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gs</ci>
<ci>A2</ci>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>A1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>f</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>f</ci>
<ci>D</ci>
</apply>
<apply>
<times/>
<ci>h2</ci>
<ci>A2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>A1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>h1</ci>
<ci>A1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>h1</ci>
<ci>A1</ci>
</apply>
<apply>
<times/>
<ci>h2</ci>
<ci>A2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gs</ci>
<ci>A2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Roff</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>RT</ci>
<ci>A1</ci>
</apply>
<ci>A2</ci>
</apply>
<ci>D</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>F</ci>
<apply>
<plus/>
<ci>A1</ci>
<ci>A2</ci>
</apply>
</apply>
</math>
</component>
<!-- def comp calcium as
var Ca: dimensionless {init: 0.5, pub: out};
var Caf: dimensionless {init: 0.5};
var C: dimensionless {init: 2};
var S: dimensionless {init: 6};
var k1: dimensionless;
var k2: dimensionless;
var k10: dimensionless {init: 9.6};
var k20: dimensionless {init: 5.9};
var k3: dimensionless {init: 65};
var k4: dimensionless {init: 45};
var t: second {pub: in};
var tp: second {init: 1};
var tau: dimensionless {init: 0.01};
var tol: dimensionless {init: 5};
var dk1dt: dimensionless;
var ton: second {init: 2};
var toff: second {init: 3};-->
<!-- dk1dt = -k10/tau*exp((-t-tp)/tau);-->
<!-- // k1 = k10*exp((-t-tp)/tau);-->
<!-- // k2 = sel
// case abs(dk1dt)<tol:
// k20;
// otherwise:
// 0{dimensionless};
// endsel;-->
<!-- k1 = sel
case (ton < t) and (t < toff):
k10;
otherwise:
0{dimensionless};
endsel;-->
<!-- k2 = sel
case k1 == 0{dimensionless}:
k20;
otherwise:
0{dimensionless};
endsel;-->
<!-- ode(Ca, t) = (k4*Caf-k3*Ca)*(1{dimensionless}-Caf)+k1*(C-Ca-Caf)+k2*Ca*(C-S-Ca-Caf);
ode(Caf, t) = -1{dimensionless}*(k4*Caf-k3*Ca)*(1{dimensionless}-Caf);
enddef;-->
<component name="calcium2">
<variable initial_value="1500" name="Ca_sr" units="uM"/>
<variable name="t" public_interface="in" units="ms"/>
<variable name="Rv" units="uM_per_ms1"/>
<variable initial_value="1" name="V_max" units="mV"/>
<variable initial_value="0.006" name="Ca_ms" public_interface="out" units="uM"/>
<variable initial_value="0.01" name="Lp" units="ms1"/>
<variable initial_value="0.12" name="kt2" units="ms1"/>
<variable initial_value="7.9" name="TC" units="uM"/>
<variable initial_value="140" name="T" units="uM"/>
<variable initial_value="0.12" name="kt1" units="uM_per_ms1"/>
<variable initial_value="506.8" name="PC" units="uM"/>
<variable initial_value="940" name="P" units="uM"/>
<variable initial_value="1" name="K_ms" units="uM"/>
<variable initial_value="0.0195" name="kp1" units="uM_per_ms1"/>
<variable initial_value="0.001" name="kp2" units="ms1"/>
<variable initial_value="0" name="CaR" units="uM"/>
<variable initial_value="0.2" name="kf" units="ms1"/>
<variable initial_value="3" name="K" units="uM"/>
<variable initial_value="0.03" name="kr" units="ms1"/>
<variable name="e1" units="dimensionless"/>
<variable name="e2" units="dimensionless"/>
<variable initial_value="-48.7" name="Ve1_bar" units="mV"/>
<variable initial_value="-4.1" name="Ve2_bar" units="mV"/>
<variable initial_value="12.3" name="ke1" units="mV"/>
<variable initial_value="12.9" name="ke2" units="mV"/>
<variable initial_value="6.58" name="R_max" units="uM_per_ms1"/>
<variable name="V" units="mV"/>
<variable initial_value="20" name="ton" units="ms"/>
<variable initial_value="30" name="toff" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V</ci>
<piecewise>
<piece>
<cn cellml:units="mV">25</cn>
<apply>
<and/>
<apply>
<lt/>
<ci>ton</ci>
<ci>t</ci>
</apply>
<apply>
<lt/>
<ci>t</ci>
<ci>toff</ci>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<cn cellml:units="mV">100</cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Ca_sr</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>Rv</ci>
</apply>
<apply>
<times/>
<ci>V_max</ci>
<apply>
<divide/>
<ci>Ca_ms</ci>
<apply>
<plus/>
<ci>Ca_ms</ci>
<ci>K_ms</ci>
</apply>
</apply>
</apply>
</apply>
<ci>Lp</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Ca_ms</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>Rv</ci>
<apply>
<times/>
<ci>kt2</ci>
<ci>TC</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kt1</ci>
<ci>Ca_ms</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kp2</ci>
<ci>PC</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kp1</ci>
<ci>Ca_ms</ci>
<ci>P</ci>
</apply>
</apply>
<apply>
<times/>
<ci>V_max</ci>
<apply>
<divide/>
<ci>Ca_ms</ci>
<apply>
<plus/>
<ci>Ca_ms</ci>
<ci>K_ms</ci>
</apply>
</apply>
</apply>
</apply>
<ci>Lp</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>TC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kt1</ci>
<ci>Ca_ms</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>kt2</ci>
<ci>TC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>PC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kp1</ci>
<ci>Ca_ms</ci>
<ci>P</ci>
</apply>
<apply>
<times/>
<ci>kp2</ci>
<ci>PC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>CaR</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<ci>kf</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K</ci>
<ci>Ca_ms</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>CaR</ci>
<ci>kr</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>CaR</ci>
<ci>kf</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K</ci>
<ci>Ca_ms</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Rv</ci>
<apply>
<times/>
<ci>R_max</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>e2</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>e1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e1</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ve1_bar</ci>
<ci>V</ci>
</apply>
<ci>ke1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ve2_bar</ci>
<ci>V</ci>
</apply>
<ci>ke2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="Environment" component_2="muscle"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<!-- def map between Environment and calcium for
vars t and t;
enddef;-->
<!-- def map between calcium and muscle for
vars Ca and Ca;
enddef;-->
<connection>
<map_components component_1="Environment" component_2="calcium2"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="calcium2" component_2="muscle"/>
<map_variables variable_1="Ca_ms" variable_2="Ca_ms"/>
</connection>
</model>