- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-17 10:25:01+13:00
- Desc:
- Using sympy for rational nullspace
- Permanent Source URI:
- https://models.cellml.org/workspace/6d6/rawfile/f9bdcb85bc92bc1fa231b0b5f12c098624985937/BG_Inhib1.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- PLB Inhib1 module,
5 Aug 21 - not containing PLBphos/PLBdephos reactions (this is a separate module)
Use [Ip] where [Ip] = [Ip(PLB)] + [Ip(inhib1)]
Use [PKACI] where [PKACI] = [PKACI(PLB)] + [PKACI(inhib1)]-->
<model name="BG_Inhib1" 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="units_and_constants/units_BG.cellml">
<units name="per_sec" units_ref="per_sec"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="fmol" units_ref="fmol"/>
<units name="fmol_per_L" units_ref="fmol_per_L"/>
<units name="fmol_per_L_per_sec" units_ref="fmol_per_L_per_sec"/>
<units name="per_sec_per_fmol_per_L" units_ref="per_sec_per_fmol_per_L"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="fmol_per_sec" units_ref="fmol_per_sec"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="mM" units_ref="mM"/>
<units name="uM" units_ref="uM"/>
<units name="mM_per_sec" units_ref="mM_per_sec"/>
<units name="uM_per_sec" units_ref="uM_per_sec"/>
<units name="pL" units_ref="pL"/>
<units name="m_to_u" units_ref="m_to_u"/>
</import>
<import xlink:href="units_and_constants/constants_BG.cellml">
<component component_ref="constants" name="constants"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="1.117E-03" name="q_PKACI_init" units="fmol"/>
<variable initial_value="9.994E-04" name="q_Ip_init" units="fmol"/>
<variable initial_value="1e-13" name="q_Ip_PKACI_init" units="fmol"/>
<variable initial_value="8.512E-03" name="q_PP2a_init" units="fmol"/>
<variable initial_value="1e-13" name="q_Ip_PP2a_init" units="fmol"/>
<variable initial_value="1.140E-02" name="q_I_init" units="fmol"/>
<!-- Global value-->
<variable name="q_PKACI" public_interface="out" units="fmol"/>
<variable name="q_Ip" public_interface="out" units="fmol"/>
<variable name="q_Ip_PKACI" public_interface="out" units="fmol"/>
<variable name="q_PP2a" public_interface="out" units="fmol"/>
<variable name="q_Ip_PP2a" public_interface="out" units="fmol"/>
<variable name="q_I" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="q_PKACI_mInhib1" public_interface="in" units="fmol"/>
<variable name="q_Ip_mInhib1" public_interface="in" units="fmol"/>
<variable name="q_Ip_PKACI_mInhib1" public_interface="in" units="fmol"/>
<variable name="q_PP2a_mInhib1" public_interface="in" units="fmol"/>
<variable name="q_Ip_PP2a_mInhib1" public_interface="in" units="fmol"/>
<variable name="q_I_mInhib1" public_interface="in" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_PKACI</ci>
<apply>
<plus/>
<ci>q_PKACI_mInhib1</ci>
<ci>q_PKACI_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Ip</ci>
<apply>
<plus/>
<ci>q_Ip_mInhib1</ci>
<ci>q_Ip_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Ip_PKACI</ci>
<apply>
<plus/>
<ci>q_Ip_PKACI_mInhib1</ci>
<ci>q_Ip_PKACI_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_PP2a</ci>
<apply>
<plus/>
<ci>q_PP2a_mInhib1</ci>
<ci>q_PP2a_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Ip_PP2a</ci>
<apply>
<plus/>
<ci>q_Ip_PP2a_mInhib1</ci>
<ci>q_Ip_PP2a_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_I</ci>
<apply>
<plus/>
<ci>q_I_mInhib1</ci>
<ci>q_I_init</ci>
</apply>
</apply>
</math>
</component>
<component name="Inhib1_parameters">
<variable initial_value="20.9606" name="kappa_PKAi1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="22.2706" name="kappa_PKAi2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.39341" name="kappa_PP2ai1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.30013" name="kappa_PP2ai2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.284433" name="K_PKACI" public_interface="out" units="per_fmol"/>
<variable initial_value="0.133405" name="K_Ip" public_interface="out" units="per_fmol"/>
<variable initial_value="1.38688" name="K_Ip_PKACI" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0704691" name="K_PP2a" public_interface="out" units="per_fmol"/>
<variable initial_value="0.342795" name="K_Ip_PP2a" public_interface="out" units="per_fmol"/>
<variable initial_value="0.150247" name="K_I" public_interface="out" units="per_fmol"/>
</component>
<component name="Inhib1">
<variable name="time" public_interface="in" units="second"/>
<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<!-- Inhib1 parameters-->
<variable name="kappa_PKAi1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_PKAi2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_PP2ai1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_PP2ai2" public_interface="in" units="fmol_per_sec"/>
<variable name="K_PKACI" public_interface="in" units="per_fmol"/>
<variable name="K_Ip" public_interface="in" units="per_fmol"/>
<variable name="K_Ip_PKACI" public_interface="in" units="per_fmol"/>
<variable name="K_PP2a" public_interface="in" units="per_fmol"/>
<variable name="K_Ip_PP2a" public_interface="in" units="per_fmol"/>
<variable name="K_I" public_interface="in" units="per_fmol"/>
<variable name="vPKAi1" units="fmol_per_sec"/>
<variable name="vPKAi2" units="fmol_per_sec"/>
<variable name="vPP2ai1" units="fmol_per_sec"/>
<variable name="vPP2ai2" units="fmol_per_sec"/>
<variable name="mu_PKACI" units="J_per_mol"/>
<variable name="mu_Ip" units="J_per_mol"/>
<variable name="mu_Ip_PKACI" units="J_per_mol"/>
<variable name="mu_PP2a" units="J_per_mol"/>
<variable name="mu_Ip_PP2a" units="J_per_mol"/>
<variable name="mu_I" units="J_per_mol"/>
<!-- Input from global environment-->
<variable name="q_PKACI_global" public_interface="in" units="fmol"/>
<variable name="q_Ip_global" public_interface="in" units="fmol"/>
<variable name="q_Ip_PKACI_global" public_interface="in" units="fmol"/>
<variable name="q_PP2a_global" public_interface="in" units="fmol"/>
<variable name="q_Ip_PP2a_global" public_interface="in" units="fmol"/>
<variable name="q_I_global" public_interface="in" units="fmol"/>
<!-- Output to global environment-->
<variable initial_value="1e-16" name="q_PKACI" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Ip" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Ip_PKACI" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_PP2a" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Ip_PP2a" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_I" public_interface="out" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PKACI</ci>
<ci>q_PKACI_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ip</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ip</ci>
<ci>q_Ip_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ip_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ip_PKACI</ci>
<ci>q_Ip_PKACI_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PP2a</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PP2a</ci>
<ci>q_PP2a_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ip_PP2a</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ip_PP2a</ci>
<ci>q_Ip_PP2a_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_I</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_I</ci>
<ci>q_I_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPKAi1</ci>
<apply>
<times/>
<ci>kappa_PKAi1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PKACI</ci>
<ci>mu_I</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ip_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPKAi2</ci>
<apply>
<times/>
<ci>kappa_PKAi2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ip_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PKACI</ci>
<ci>mu_Ip</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPP2ai1</ci>
<apply>
<times/>
<ci>kappa_PP2ai1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PP2a</ci>
<ci>mu_Ip</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ip_PP2a</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPP2ai2</ci>
<apply>
<times/>
<ci>kappa_PP2ai2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ip_PP2a</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PP2a</ci>
<ci>mu_I</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PKACI</ci>
</apply>
<apply>
<minus/>
<ci>vPKAi2</ci>
<ci>vPKAi1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ip</ci>
</apply>
<apply>
<minus/>
<ci>vPKAi2</ci>
<ci>vPP2ai1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ip_PKACI</ci>
</apply>
<apply>
<minus/>
<ci>vPKAi1</ci>
<ci>vPKAi2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PP2a</ci>
</apply>
<apply>
<minus/>
<ci>vPP2ai2</ci>
<ci>vPP2ai1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ip_PP2a</ci>
</apply>
<apply>
<minus/>
<ci>vPP2ai1</ci>
<ci>vPP2ai2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_I</ci>
</apply>
<apply>
<minus/>
<ci>vPP2ai2</ci>
<ci>vPKAi1</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="Inhib1"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_PKACI_mInhib1" variable_2="q_PKACI"/>
<map_variables variable_1="q_PKACI" variable_2="q_PKACI_global"/>
<map_variables variable_1="q_Ip_mInhib1" variable_2="q_Ip"/>
<map_variables variable_1="q_Ip" variable_2="q_Ip_global"/>
<map_variables variable_1="q_Ip_PKACI_mInhib1" variable_2="q_Ip_PKACI"/>
<map_variables variable_1="q_Ip_PKACI" variable_2="q_Ip_PKACI_global"/>
<map_variables variable_1="q_PP2a_mInhib1" variable_2="q_PP2a"/>
<map_variables variable_1="q_PP2a" variable_2="q_PP2a_global"/>
<map_variables variable_1="q_Ip_PP2a_mInhib1" variable_2="q_Ip_PP2a"/>
<map_variables variable_1="q_Ip_PP2a" variable_2="q_Ip_PP2a_global"/>
<map_variables variable_1="q_I_mInhib1" variable_2="q_I"/>
<map_variables variable_1="q_I" variable_2="q_I_global"/>
</connection>
<connection>
<map_components component_1="Inhib1_parameters" component_2="Inhib1"/>
<map_variables variable_1="kappa_PKAi1" variable_2="kappa_PKAi1"/>
<map_variables variable_1="kappa_PKAi2" variable_2="kappa_PKAi2"/>
<map_variables variable_1="kappa_PP2ai1" variable_2="kappa_PP2ai1"/>
<map_variables variable_1="kappa_PP2ai2" variable_2="kappa_PP2ai2"/>
<map_variables variable_1="K_PKACI" variable_2="K_PKACI"/>
<map_variables variable_1="K_Ip" variable_2="K_Ip"/>
<map_variables variable_1="K_Ip_PKACI" variable_2="K_Ip_PKACI"/>
<map_variables variable_1="K_PP2a" variable_2="K_PP2a"/>
<map_variables variable_1="K_Ip_PP2a" variable_2="K_Ip_PP2a"/>
<map_variables variable_1="K_I" variable_2="K_I"/>
</connection>
<connection>
<map_components component_1="constants" component_2="Inhib1"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>
