Location: BG_PLB @ aada2114e3bd / BG_PLB.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-08-05 13:53:33+12:00
- Desc:
- Equations, with initial conditions and parameters included
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/6d1/rawfile/aada2114e3bdf81563efbfc6cc942f5dd3bb2dbe/BG_PLB.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- PLB module,
5 Aug 21 - not containing Inhib1 reactions (this is a separate module)
Use [Ip_S1] where [Ip] = [Ip_s1] + [Ip_S2]
Use [PKACI_S1] where [PKACI] = [PKACI_S1] + [PKACI_S2]-->
<model name="BG_PLB" 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"/>
</component>
<component name="PLB">
<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"/>
<!-- PLB parameters-->
<variable initial_value="4.17714e+06" name="kappa_PLBph1" units="fmol_per_sec"/>
<variable initial_value="6.01807e-13" name="kappa_PLBph2" units="fmol_per_sec"/>
<variable initial_value="2.46084e-13" name="kappa_PLBd1" units="fmol_per_sec"/>
<variable initial_value="771769" name="kappa_PLBd2" units="fmol_per_sec"/>
<variable initial_value="8.96752" name="kappa_Inh" units="fmol_per_sec"/>
<variable initial_value="1.14426e-21" name="K_PLB" units="per_fmol"/>
<variable initial_value="0.0105006" name="K_PKACI_S1" units="per_fmol"/>
<variable initial_value="0.000239398" name="K_PLB_PKACI" units="per_fmol"/>
<variable initial_value="0.0013867" name="K_PP1" units="per_fmol"/>
<variable initial_value="1.10137e-05" name="K_PLBp_PP1" units="per_fmol"/>
<variable initial_value="1.58244e+17" name="K_PLBp" units="per_fmol"/>
<variable initial_value="0.0804164" name="K_Ip_S1" units="per_fmol"/>
<variable initial_value="111.514" name="K_Ip_PP1" units="per_fmol"/>
<variable initial_value="4.028E+00" name="q_PLB" units="fmol"/>
<variable initial_value="1.117E-03" name="q_PKACI_S1" units="fmol"/>
<variable initial_value="1e-13" name="q_PLB_PKACI" units="fmol"/>
<variable initial_value="3.382E-02" name="q_PP1" units="fmol"/>
<variable initial_value="1e-13" name="q_PLBp_PP1" units="fmol"/>
<variable initial_value="1.560E-01" name="q_PLBp" units="fmol"/>
<variable initial_value="9.994E-04" name="q_Ip_S1" units="fmol"/>
<variable initial_value="1e-13" name="q_Ip_PP1" units="fmol"/>
<variable name="vPLBph1" units="fmol_per_sec"/>
<variable name="vPLBph2" units="fmol_per_sec"/>
<variable name="vPLBd1" units="fmol_per_sec"/>
<variable name="vPLBd2" units="fmol_per_sec"/>
<variable name="vInh" units="fmol_per_sec"/>
<variable name="mu_PLB" units="J_per_mol"/>
<variable name="mu_PKACI_S1" units="J_per_mol"/>
<variable name="mu_PLB_PKACI" units="J_per_mol"/>
<variable name="mu_PP1" units="J_per_mol"/>
<variable name="mu_PLBp_PP1" units="J_per_mol"/>
<variable name="mu_PLBp" units="J_per_mol"/>
<variable name="mu_Ip_S1" units="J_per_mol"/>
<variable name="mu_Ip_PP1" units="J_per_mol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_PLB</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PLB</ci>
<ci>q_PLB</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PKACI_S1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PKACI_S1</ci>
<ci>q_PKACI_S1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PLB_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PLB_PKACI</ci>
<ci>q_PLB_PKACI</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PP1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PP1</ci>
<ci>q_PP1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PLBp_PP1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PLBp_PP1</ci>
<ci>q_PLBp_PP1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PLBp</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PLBp</ci>
<ci>q_PLBp</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ip_S1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ip_S1</ci>
<ci>q_Ip_S1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ip_PP1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ip_PP1</ci>
<ci>q_Ip_PP1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPLBph1</ci>
<apply>
<times/>
<ci>kappa_PLBph1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PLB</ci>
<ci>mu_PKACI_S1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PLB_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPLBph2</ci>
<apply>
<times/>
<ci>kappa_PLBph2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PLB_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PLBp</ci>
<ci>mu_PKACI_S1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPLBd1</ci>
<apply>
<times/>
<ci>kappa_PLBd1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PLBp</ci>
<ci>mu_PP1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PLBp_PP1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vPLBd2</ci>
<apply>
<times/>
<ci>kappa_PLBd2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PLBp_PP1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PLB</ci>
<ci>mu_PP1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vInh</ci>
<apply>
<times/>
<ci>kappa_Inh</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PP1</ci>
<ci>mu_Ip_S1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ip_PP1</ci>
<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_PLB</ci>
</apply>
<apply>
<minus/>
<ci>vPLBd2</ci>
<ci>vPLBph1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PKACI_S1</ci>
</apply>
<apply>
<minus/>
<ci>vPLBph2</ci>
<ci>vPLBph1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PLB_PKACI</ci>
</apply>
<apply>
<minus/>
<ci>vPLBph1</ci>
<ci>vPLBph2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PP1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vPLBd2</ci>
<ci>vPLBd1</ci>
</apply>
<ci>vInh</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PLBp_PP1</ci>
</apply>
<apply>
<minus/>
<ci>vPLBd1</ci>
<ci>vPLBd2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PLBp</ci>
</apply>
<apply>
<minus/>
<ci>vPLBph2</ci>
<ci>vPLBd1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ip_S1</ci>
</apply>
<apply>
<minus/>
<ci>vInh</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ip_PP1</ci>
</apply>
<ci>vInh</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="PLB"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="constants" component_2="PLB"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>