- Author:
- Fariba <fbir042@aucklanduni.ac.nz>
- Date:
- 2023-10-05 14:13:59+13:00
- Desc:
- Smooth Muscle Cell
- Permanent Source URI:
- https://models.cellml.org/workspace/b36/rawfile/f8db5b8aa3bcbfc716249eb230cabd3cfcaf8907/Main_SMC_Model.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="Hai" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="SMC_Units.cellml">
<units name="per_uM_per_sec" units_ref="per_uM_per_sec"/>
<units name="mV" units_ref="mV"/>
<units name="per_sec" units_ref="per_sec"/>
<units name="uM" units_ref="uM"/>
<units name="nS_per_uM" units_ref="nS_per_uM"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="per_uM" units_ref="per_uM"/>
<units name="uM_per_sec" units_ref="uM_per_sec"/>
<units name="mJ_per_K_per_mol" units_ref="mJ_per_K_per_mol"/>
<units name="uA_per_cmsq" units_ref="uA_per_cmsq"/>
<units name="umetre2" units_ref="umetre2"/>
<units name="umetre" units_ref="umetre"/>
<units name="umetre_per_sec" units_ref="umetre_per_sec"/>
<units name="uN" units_ref="uN"/>
<units name="uN_per_umetre" units_ref="uN_per_umetre"/>
<units name="uN_sec_per_umetre" units_ref="uN_sec_per_umetre"/>
<units name="first_order_rate_constant" units_ref="first_order_rate_constant"/>
<units name="uP" units_ref="uP"/>
<units name="uN_umetre2" units_ref="uN_umetre2"/>
</import>
<import xlink:href="SMC_Wang_2010.cellml">
<component component_ref="asm_ca" name="asm_ca"/>
<component component_ref="ca_parameters" name="ca_parameters"/>
<component component_ref="calcium" name="calcium"/>
</import>
<import xlink:href="SMC_Yang_2005.cellml">
<component component_ref="sGC" name="sGC"/>
</import>
<component name="Environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="NO_sGC">
<variable name="Eb" public_interface="in" units="dimensionless"/>
<variable name="E6c" public_interface="in" units="dimensionless"/>
<variable name="E5c" public_interface="in" units="dimensionless"/>
<variable name="NO" public_interface="in" units="uM"/>
<variable name="cGMP" public_interface="in" units="uM"/>
<variable name="vd" public_interface="in" units="uM_per_sec"/>
<variable name="vp" public_interface="in" units="uM_per_sec"/>
<variable name="vdvp" units="uM_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>vdvp</ci>
<apply>
<minus/>
<ci>vd</ci>
<ci>vp</ci>
</apply>
</apply>
</math>
</component>
<component name="kay2">
<variable name="k2y" public_interface="in" units="per_sec"/>
<variable name="k2h" public_interface="in" units="per_sec"/>
<variable name="k2" public_interface="out" units="per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k2</ci>
<apply>
<plus/>
<ci>k2y</ci>
<ci>k2h</ci>
</apply>
</apply>
</math>
</component>
<component name="M">
<variable initial_value="1" name="M" public_interface="out" units="dimensionless"/>
<variable name="AM" public_interface="in" units="dimensionless"/>
<variable name="Mp" public_interface="in" units="dimensionless"/>
<variable name="k1" public_interface="in" units="first_order_rate_constant"/>
<variable name="k2" public_interface="in" units="first_order_rate_constant"/>
<variable name="k7" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1</ci>
</apply>
<ci>M</ci>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>Mp</ci>
</apply>
<apply>
<times/>
<ci>k7</ci>
<ci>AM</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Mp">
<variable initial_value="0" name="Mp" public_interface="out" units="dimensionless"/>
<variable name="AMp" public_interface="in" units="dimensionless"/>
<variable name="M" public_interface="in" units="dimensionless"/>
<variable name="k1" public_interface="in" units="first_order_rate_constant"/>
<variable name="k2" public_interface="in" units="first_order_rate_constant"/>
<variable name="k3" public_interface="in" units="first_order_rate_constant"/>
<variable name="k4" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Mp</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k4</ci>
<ci>AMp</ci>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>M</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>k2</ci>
<ci>k3</ci>
</apply>
<ci>Mp</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="AMp">
<variable initial_value="0" name="AMp" public_interface="out" units="dimensionless"/>
<variable name="Mp" public_interface="in" units="dimensionless"/>
<variable name="AM" public_interface="in" units="dimensionless"/>
<variable name="k5" public_interface="in" units="first_order_rate_constant"/>
<variable name="k6" public_interface="in" units="first_order_rate_constant"/>
<variable name="k3" public_interface="in" units="first_order_rate_constant"/>
<variable name="k4" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AMp</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k3</ci>
<ci>Mp</ci>
</apply>
<apply>
<times/>
<ci>k6</ci>
<ci>AM</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>k5</ci>
<ci>k4</ci>
</apply>
<ci>AMp</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="AM">
<variable initial_value="0" name="AM" public_interface="out" units="dimensionless"/>
<variable name="AMp" public_interface="in" units="dimensionless"/>
<variable name="k5" public_interface="in" units="first_order_rate_constant"/>
<variable name="k6" public_interface="in" units="first_order_rate_constant"/>
<variable name="k7" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AM</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k5</ci>
<ci>AMp</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>k6</ci>
<ci>k7</ci>
</apply>
<ci>AM</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="phosphorylation">
<variable name="phosphorylation" units="dimensionless"/>
<variable name="AMp" public_interface="in" units="dimensionless"/>
<variable name="Mp" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>phosphorylation</ci>
<apply>
<plus/>
<ci>AMp</ci>
<ci>Mp</ci>
</apply>
</apply>
</math>
</component>
<component name="stress">
<variable name="stress" public_interface="out" units="dimensionless"/>
<variable name="AMp" public_interface="in" units="dimensionless"/>
<variable name="AM" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>stress</ci>
<apply>
<plus/>
<ci>AMp</ci>
<ci>AM</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_ag">
<variable name="Ca_in" public_interface="in" units="uM"/>
<variable name="Ca_SR" public_interface="in" units="uM"/>
<variable name="Ca_t" public_interface="in" units="uM"/>
<variable name="p_agonist" public_interface="in" units="uM"/>
<variable name="J_release" public_interface="in" units="uM_per_sec"/>
<variable name="J_serca" public_interface="in" units="uM_per_sec"/>
<variable name="J_in" public_interface="in" units="uM_per_sec"/>
<variable name="J_pm" public_interface="in" units="uM_per_sec"/>
<variable name="J_in_KCL" public_interface="in" units="uM_per_sec"/>
<variable name="Ca_in_KCL" public_interface="in" units="uM"/>
</component>
<component name="model_parameters1">
<variable name="k1" public_interface="in" units="first_order_rate_constant"/>
<variable name="k2" public_interface="in" units="first_order_rate_constant"/>
<variable name="k5" public_interface="out" units="first_order_rate_constant"/>
<variable name="k6" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.88" name="k3" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.22" name="k4" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.12" name="k7" public_interface="out" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k6</ci>
<ci>k1</ci>
</apply>
<apply>
<eq/>
<ci>k5</ci>
<ci>k2</ci>
</apply>
</math>
</component>
<component name="active_passive_elasticity_and_viscoelastic_forces">
<variable name="r_i" units="umetre"/>
<variable name="r_o" units="umetre"/>
<variable initial_value="7.5" name="beta" units="dimensionless"/>
<variable initial_value="23.35" name="la" units="umetre"/>
<variable initial_value="150" name="lopt" units="umetre"/>
<variable initial_value="12.5" name="kx1" units="uN_per_umetre"/>
<variable initial_value="8.8" name="kx2" units="uN_per_umetre"/>
<variable name="AM" public_interface="in" units="dimensionless"/>
<variable name="AMp" public_interface="in" units="dimensionless"/>
<variable initial_value="37.05" name="ls" units="umetre"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.1" name="k_pp" units="uN"/>
<variable name="A" units="umetre2"/>
<variable initial_value="5000" name="N" units="dimensionless"/>
<variable initial_value="6" name="n" units="dimensionless"/>
<variable initial_value="0.2" name="alpha_pp" units="dimensionless"/>
<variable initial_value="10000" name="L" units="umetre"/>
<variable initial_value="15" name="h" units="umetre"/>
<variable initial_value="2100" name="p_i" units="pascal"/>
<variable initial_value="40" name="l0" units="umetre"/>
<variable name="sigma_a" units="uN_umetre2"/>
<variable name="sigma_p" units="uN_umetre2"/>
<variable name="sigma" units="uN_umetre2"/>
<variable name="Fx" units="uN"/>
<variable name="Fa" units="uN"/>
<variable name="Fs" units="uN"/>
<variable initial_value="0.2" name="ks" units="uN"/>
<variable initial_value="30" name="ls0" units="umetre"/>
<variable initial_value="1e-05" name="mu_s" units="uN_sec_per_umetre"/>
<variable initial_value="4.5" name="alpha_s" units="dimensionless"/>
<variable initial_value="5000" name="vx" units="umetre_per_sec"/>
<variable initial_value="0.0013" name="fAMp" units="uN_sec_per_umetre"/>
<variable initial_value="0.0855" name="fAM" units="uN_sec_per_umetre"/>
<variable name="lc" units="umetre"/>
<variable name="lx" units="umetre"/>
<variable initial_value="0" name="zero" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A</ci>
<apply>
<times/>
<ci>L</ci>
<ci>h</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Fa</ci>
<ci>Fx</ci>
</apply>
<apply>
<eq/>
<ci>Fs</ci>
<ci>Fx</ci>
</apply>
<apply>
<eq/>
<ci>Fx</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>kx1</ci>
<ci>AMp</ci>
</apply>
<apply>
<times/>
<ci>kx2</ci>
<ci>AM</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>lc</ci>
<ci>la</ci>
</apply>
<ci>ls</ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>beta</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>la</ci>
<ci>lopt</ci>
</apply>
<ci>lopt</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- ode(ls, time) = (Fx-ks*(exp(alpha_s*(ls-ls0)/ls0)-1{dimensionless}))/mu_s;
ode(la, time) = (Fx*exp(beta*sqr((la-lopt)/lopt))-fAMp*(AMp)*vx)/(fAM*AM+fAMp*AMp+epsilon);-->
<apply>
<eq/>
<ci>sigma_a</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>N</ci>
<ci>A</ci>
</apply>
<ci>Fx</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_p</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>N</ci>
<ci>k_pp</ci>
</apply>
<ci>A</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_pp</ci>
<apply>
<minus/>
<ci>lc</ci>
<ci>l0</ci>
</apply>
</apply>
<ci>l0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<!-- zero = N/A*(kx1*AMp+kx2*AM)*(lc-la-ls)*exp(-beta*sqr((la-lopt)/lopt))+N*k_pp/A*(exp(alpha_pp*(lc-l0)/l0)-1{dimensionless})-p_i/2{dimensionless}*(n*lc/(pi*h)-1{dimensionless});-->
<apply>
<eq/>
<ci>zero</ci>
<apply>
<minus/>
<ci>sigma</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>p_i</ci>
<cn cellml:units="dimensionless">0.000001</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>n</ci>
<ci>lc</ci>
</apply>
<apply>
<times/>
<pi/>
<ci>h</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>lx</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>lc</ci>
<ci>ls</ci>
</apply>
<ci>la</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma</ci>
<apply>
<plus/>
<ci>sigma_a</ci>
<ci>sigma_p</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_i</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>n</ci>
<ci>lc</ci>
</apply>
<pi/>
</apply>
<ci>h</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>r_o</ci>
<apply>
<plus/>
<ci>h</ci>
<ci>r_i</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="sGC" component_2="NO_sGC"/>
<map_variables variable_1="Eb" variable_2="Eb"/>
<map_variables variable_1="E5c" variable_2="E5c"/>
<map_variables variable_1="E6c" variable_2="E6c"/>
<map_variables variable_1="NO" variable_2="NO"/>
<map_variables variable_1="cGMP" variable_2="cGMP"/>
<map_variables variable_1="vd" variable_2="vd"/>
<map_variables variable_1="vp" variable_2="vp"/>
</connection>
<connection>
<map_components component_1="calcium" component_2="asm_ca"/>
<map_variables variable_1="Ca_in" variable_2="Ca_in"/>
<map_variables variable_1="p_agonist" variable_2="p_agonist"/>
<map_variables variable_1="Ca_in_KCL" variable_2="Ca_in_KCL"/>
</connection>
<connection>
<map_components component_1="asm_ca" component_2="Ca_ag"/>
<map_variables variable_1="Ca_in" variable_2="Ca_in"/>
<map_variables variable_1="Ca_SR" variable_2="Ca_SR"/>
<map_variables variable_1="Ca_t" variable_2="Ca_t"/>
<map_variables variable_1="p_agonist" variable_2="p_agonist"/>
<map_variables variable_1="J_release" variable_2="J_release"/>
<map_variables variable_1="J_serca" variable_2="J_serca"/>
<map_variables variable_1="J_in" variable_2="J_in"/>
<map_variables variable_1="J_pm" variable_2="J_pm"/>
<map_variables variable_1="J_in_KCL" variable_2="J_in_KCL"/>
<map_variables variable_1="Ca_in_KCL" variable_2="Ca_in_KCL"/>
</connection>
<connection>
<map_components component_1="calcium" component_2="model_parameters1"/>
<map_variables variable_1="k1" variable_2="k1"/>
</connection>
<connection>
<map_components component_1="kay2" component_2="model_parameters1"/>
<map_variables variable_1="k2" variable_2="k2"/>
</connection>
<connection>
<map_components component_1="sGC" component_2="kay2"/>
<map_variables variable_1="k2y" variable_2="k2y"/>
</connection>
<connection>
<map_components component_1="calcium" component_2="kay2"/>
<map_variables variable_1="k2h" variable_2="k2h"/>
</connection>
<connection>
<map_components component_1="M" component_2="Environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Mp" component_2="Environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="AMp" component_2="Environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="AM" component_2="Environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="calcium"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="asm_ca"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="sGC"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="active_passive_elasticity_and_viscoelastic_forces"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M" component_2="model_parameters1"/>
<map_variables variable_1="k7" variable_2="k7"/>
</connection>
<connection>
<map_components component_1="M" component_2="calcium"/>
<map_variables variable_1="k1" variable_2="k1"/>
</connection>
<connection>
<map_components component_1="M" component_2="kay2"/>
<map_variables variable_1="k2" variable_2="k2"/>
</connection>
<connection>
<map_components component_1="Mp" component_2="model_parameters1"/>
<map_variables variable_1="k4" variable_2="k4"/>
<map_variables variable_1="k3" variable_2="k3"/>
</connection>
<connection>
<map_components component_1="Mp" component_2="calcium"/>
<map_variables variable_1="k1" variable_2="k1"/>
</connection>
<connection>
<map_components component_1="Mp" component_2="kay2"/>
<map_variables variable_1="k2" variable_2="k2"/>
</connection>
<connection>
<map_components component_1="AMp" component_2="model_parameters1"/>
<map_variables variable_1="k5" variable_2="k5"/>
<map_variables variable_1="k6" variable_2="k6"/>
<map_variables variable_1="k4" variable_2="k4"/>
<map_variables variable_1="k3" variable_2="k3"/>
</connection>
<connection>
<map_components component_1="AM" component_2="model_parameters1"/>
<map_variables variable_1="k5" variable_2="k5"/>
<map_variables variable_1="k6" variable_2="k6"/>
<map_variables variable_1="k7" variable_2="k7"/>
</connection>
<connection>
<map_components component_1="AM" component_2="M"/>
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection>
<map_components component_1="AM" component_2="AMp"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection>
<map_components component_1="M" component_2="Mp"/>
<map_variables variable_1="M" variable_2="M"/>
<map_variables variable_1="Mp" variable_2="Mp"/>
</connection>
<connection>
<map_components component_1="Mp" component_2="AMp"/>
<map_variables variable_1="Mp" variable_2="Mp"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
<connection>
<map_components component_1="phosphorylation" component_2="AMp"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
<connection>
<map_components component_1="phosphorylation" component_2="Mp"/>
<map_variables variable_1="Mp" variable_2="Mp"/>
</connection>
<connection>
<map_components component_1="stress" component_2="AMp"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
<connection>
<map_components component_1="stress" component_2="AM"/>
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection>
<map_components component_1="AM" component_2="active_passive_elasticity_and_viscoelastic_forces"/>
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection>
<map_components component_1="AMp" component_2="active_passive_elasticity_and_viscoelastic_forces"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
</model>
