- Author:
- AnandR <a.rampadarath@auckland.ac.nz>
- Date:
- 2018-12-18 16:37:00+13:00
- Desc:
- Extracted cellML model from the original paper.
Annotated the model using SemGen
- Permanent Source URI:
- http://models.cellml.org/workspace/562/rawfile/d244a015b9a673a14de122e4dcfbe0cf0f7667e2/yang_et_al_2005cd.cellml
<?xml version='1.0'?>
<!--
This CellML file was generated on 17/12/2018 at 11:05:29 at AM using:
COR (0.9.31.1409)
Copyright 2002-2018 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
Author: Anand Rampadarath
The Auckland Bioengineering Institute
University of Auckland
Model Status: This model recreates the time dependent results associated with
Figure 3, in the original model of Yang et al 2005.
-->
<model cmeta:id="yang_et_al_2005" name="yang_et_al_2005" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="nanomolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="nm_per_s">
<unit units="nanomolar"/>
<unit units="per_s"/>
</units>
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_nM_per_s">
<unit exponent="-1" units="nanomolar"/>
<unit units="per_s"/>
</units>
<units name="per_microM_per_s">
<unit exponent="-1" units="micromolar"/>
<unit units="per_s"/>
</units>
<units name="microM_per_s">
<unit units="micromolar"/>
<unit units="per_s"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="sGC_activation">
<variable initial_value="1" name="E_b" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="E_6c" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="E_5c" public_interface="out" units="dimensionless"/>
<variable initial_value="2" name="k_1" units="per_nM_per_s"/>
<variable initial_value="100" name="k_m1" units="per_s"/>
<variable initial_value="0.1" name="k_2" units="per_s"/>
<variable initial_value="0.003" name="k_3" units="per_nM_per_s"/>
<variable name="k_4" units="per_s"/>
<variable initial_value="220" name="NO" units="nanomolar"/>
<variable initial_value="3" name="J_no" units="nm_per_s"/>
<variable initial_value="0.01" name="k_dno" units="per_s"/>
<variable initial_value="0.011" name="K_4" public_interface="out" units="per_s"/>
<!-- K_4 = 0.4 use for Fig 3 a & b-->
<variable initial_value="2" name="m" public_interface="out" units="dimensionless"/>
<!-- m = 0 use for Fig 3 a & b-->
<variable name="cGMP" public_interface="in" units="micromolar"/>
<variable name="E0" units="dimensionless"/>
<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>E_b</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k_1</ci>
</apply>
<ci>E_b</ci>
<ci>NO</ci>
</apply>
<apply>
<times/>
<ci>k_m1</ci>
<ci>E_6c</ci>
</apply>
<apply>
<times/>
<ci>k_4</ci>
<ci>E_5c</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>E_6c</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_1</ci>
<ci>E_b</ci>
<ci>NO</ci>
</apply>
<apply>
<times/>
<ci>k_m1</ci>
<ci>E_6c</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_2</ci>
<ci>E_6c</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_3</ci>
<ci>E_6c</ci>
<ci>NO</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>E_5c</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_3</ci>
<ci>E_6c</ci>
<ci>NO</ci>
</apply>
<apply>
<times/>
<ci>k_2</ci>
<ci>E_6c</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_4</ci>
<ci>E_5c</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_4</ci>
<apply>
<times/>
<ci>K_4</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>cGMP</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
<ci>m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NO</ci>
</apply>
<apply>
<minus/>
<ci>J_no</ci>
<apply>
<times/>
<ci>k_dno</ci>
<ci>NO</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E0</ci>
<apply>
<plus/>
<ci>E_b</ci>
<ci>E_6c</ci>
<ci>E_5c</ci>
</apply>
</apply>
</math>
</component>
<component name="c_GMP">
<variable initial_value="0.8520" name="V_max_sGC" public_interface="out" units="microM_per_s"/>
<!-- V_max_sGC = 1.26 use for Fig 3 a & b-->
<variable name="E_5c" public_interface="in" units="dimensionless"/>
<variable initial_value="0" name="cGMP" public_interface="out" units="micromolar"/>
<variable name="V_max_pde" units="microM_per_s"/>
<variable initial_value="2" name="K_m_pde" units="micromolar"/>
<variable initial_value="0.0195" name="k_pde" public_interface="out" units="per_s"/>
<!-- k_pde = 0.0695 use for Fig 3 a & b-->
<variable name="time" public_interface="in" units="second"/>
<variable name="V_p" public_interface="out" units="microM_per_s"/>
<variable name="V_d" public_interface="out" units="microM_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>cGMP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>V_max_sGC</ci>
<ci>E_5c</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>cGMP</ci>
<ci>V_max_pde</ci>
</apply>
<apply>
<plus/>
<ci>K_m_pde</ci>
<ci>cGMP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_max_pde</ci>
<apply>
<times/>
<ci>k_pde</ci>
<ci>cGMP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_p</ci>
<apply>
<times/>
<ci>V_max_sGC</ci>
<ci>E_5c</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_d</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>cGMP</ci>
<ci>V_max_pde</ci>
</apply>
<apply>
<plus/>
<ci>K_m_pde</ci>
<ci>cGMP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="VSMC_relaxation">
<variable name="R_cGMP" public_interface="out" units="dimensionless"/>
<variable name="R_NO" public_interface="out" units="dimensionless"/>
<variable name="R_mlcp" public_interface="out" units="dimensionless"/>
<variable name="cGMP" public_interface="in" units="micromolar"/>
<variable initial_value="2" name="n_H" units="dimensionless"/>
<variable initial_value="1" name="n_NO" units="dimensionless"/>
<variable initial_value="2" name="n_mlcp" units="dimensionless"/>
<variable initial_value="0.55" name="K_m_nh" units="micromolar"/>
<variable initial_value="200" name="K_m_NO" units="nanomolar"/>
<variable initial_value="5.5" name="K_m_mlcp" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>R_cGMP</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>cGMP</ci>
<ci>n_H</ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>cGMP</ci>
<ci>n_H</ci>
</apply>
<apply>
<power/>
<ci>K_m_nh</ci>
<ci>n_H</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_NO</ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<divide/>
<ci>cGMP</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
<ci>n_NO</ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci>cGMP</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
<ci>n_NO</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_m_NO</ci>
<cn cellml:units="nanomolar">1</cn>
</apply>
<ci>n_NO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_mlcp</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>cGMP</ci>
<ci>n_mlcp</ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>cGMP</ci>
<ci>n_mlcp</ci>
</apply>
<apply>
<power/>
<ci>K_m_mlcp</ci>
<ci>n_mlcp</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca2_entry">
<variable name="P_0" units="dimensionless"/>
<variable initial_value="40" name="V_m" units="millivolt"/>
<variable name="v_half" units="millivolt"/>
<variable initial_value="30.8" name="S_KCa" units="millivolt"/>
<variable initial_value="-53.7" name="V_ca" units="millivolt"/>
<variable initial_value="1" name="Ca_i" public_interface="out" units="micromolar"/>
<variable initial_value="66.9" name="V_cGMP" units="millivolt"/>
<variable name="R_cGMP" public_interface="in" units="dimensionless"/>
<variable initial_value="100" name="V_NO" units="millivolt"/>
<variable name="R_NO" public_interface="in" units="dimensionless"/>
<variable initial_value="283.7" name="V_b" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_0</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V_m</ci>
<ci>v_half</ci>
</apply>
</apply>
<ci>S_KCa</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_half</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>V_ca</ci>
<apply>
<log/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>V_cGMP</ci>
<ci>R_cGMP</ci>
</apply>
</apply>
<apply>
<times/>
<ci>V_NO</ci>
<ci>R_NO</ci>
</apply>
</apply>
<ci>V_b</ci>
</apply>
</apply>
</math>
</component>
<component name="smooth_muscle_contraction">
<variable initial_value="0" name="AM" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="AMp" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="Mp" units="dimensionless"/>
<variable initial_value="1" name="M" units="dimensionless"/>
<variable name="R_mlcp" public_interface="in" units="dimensionless"/>
<variable name="k_mlcp" units="per_s"/>
<variable initial_value="0.0086" name="kb_mlcp" units="per_s"/>
<variable initial_value="0.0327" name="kc_mlcp" units="per_s"/>
<variable name="k_mlck" units="per_s"/>
<variable initial_value="1180" name="k_mlck_bar" units="dimensionless"/>
<variable initial_value="1.8" name="K3" units="per_s"/>
<variable initial_value="0.1" name="K4" units="per_s"/>
<variable initial_value="0.045" name="K7" units="per_s"/>
<variable initial_value="1.66" name="gamma" units="dimensionless"/>
<variable name="theta_ca" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_mlcp</ci>
<ci>Mp</ci>
</apply>
<apply>
<times/>
<ci>K7</ci>
<ci>AM</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_mlck</ci>
<ci>M</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Mp</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_mlck</ci>
<ci>M</ci>
</apply>
<apply>
<times/>
<ci>K4</ci>
<ci>AMp</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>k_mlcp</ci>
<ci>K3</ci>
</apply>
<ci>Mp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AMp</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_mlck</ci>
<ci>AM</ci>
</apply>
<apply>
<times/>
<ci>K3</ci>
<ci>Mp</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>k_mlcp</ci>
<ci>K4</ci>
</apply>
<ci>AMp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AM</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_mlcp</ci>
<ci>AMp</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>K7</ci>
<ci>k_mlck</ci>
</apply>
<ci>AM</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_mlcp</ci>
<apply>
<plus/>
<ci>kb_mlcp</ci>
<apply>
<times/>
<ci>kc_mlcp</ci>
<ci>R_mlcp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>theta_ca</ci>
<apply>
<divide/>
<ci>gamma</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>k_mlck</ci>
<ci>k_mlcp</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_mlck</ci>
<apply>
<times/>
<cn cellml:units="per_s">1</cn>
<ci>k_mlck_bar</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
<ci>gamma</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="smooth_muscle_contraction" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sGC_activation" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="c_GMP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sGC_activation" component_2="c_GMP"/>
<map_variables variable_1="E_5c" variable_2="E_5c"/>
<map_variables variable_1="cGMP" variable_2="cGMP"/>
</connection>
<connection>
<map_components component_1="c_GMP" component_2="VSMC_relaxation"/>
<map_variables variable_1="cGMP" variable_2="cGMP"/>
</connection>
<connection>
<map_components component_1="Ca2_entry" component_2="VSMC_relaxation"/>
<map_variables variable_1="R_cGMP" variable_2="R_cGMP"/>
<map_variables variable_1="R_NO" variable_2="R_NO"/>
</connection>
<connection>
<map_components component_1="smooth_muscle_contraction" component_2="VSMC_relaxation"/>
<map_variables variable_1="R_mlcp" variable_2="R_mlcp"/>
</connection>
<connection>
<map_components component_1="Ca2_entry" component_2="smooth_muscle_contraction"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
</model>
