- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-17 10:26:39+13:00
- Desc:
- Using sympy for rational nullspace
- Permanent Source URI:
- https://models.cellml.org/workspace/6cc/rawfile/959a1eab6b859e88de73c065526e3aff5828cd39/saucerman_PKA.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="saucerman_PKA" 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="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_mM4">
<unit exponent="-4" units="mM"/>
</units>
<units name="uM">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="m_to_u">
<unit units="uM"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="per_sec">
<unit exponent="-1" units="second"/>
</units>
<units name="ms">
<unit prefix="3" units="second"/>
</units>
<units name="mM_per_sec">
<unit units="mM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="uM_per_sec">
<unit units="uM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mM_per_sec">
<unit exponent="-1" units="mM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_uM_per_sec">
<unit exponent="-1" units="uM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="uL">
<unit prefix="micro" units="litre"/>
</units>
<units name="pL">
<unit prefix="pico" units="litre"/>
</units>
<units name="cm_per_sec">
<unit prefix="centi" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="cm2">
<unit exponent="2" prefix="centi" units="metre"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="per_mV">
<unit exponent="-1" units="mV"/>
</units>
<units name="per_mV_per_second">
<unit units="per_mV"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mV_per_sec">
<unit prefix="milli" units="volt"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mS_per_uF">
<unit prefix="milli" units="siemens"/>
<unit exponent="-1" prefix="micro" units="farad"/>
</units>
<units name="uA_per_uF">
<unit prefix="micro" units="ampere"/>
<unit exponent="-1" prefix="micro" units="farad"/>
</units>
<units name="joules_per_kmole_kelvin">
<unit units="joule"/>
<unit exponent="-3" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="ng">
<unit prefix="nano" units="gram"/>
</units>
<units name="coulombs_per_mole">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="pmol_per_mg">
<unit prefix="pico" units="mole"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="uM_to_pmol_per_mg">
<unit units="pmol_per_mg"/>
<unit exponent="-1" units="uM"/>
</units>
<units name="nFC_per_sAcm2">
<unit prefix="nano" units="farad"/>
<unit units="coulomb"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="ampere"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="ibar_to_I">
<unit units="ampere"/>
<unit units="second"/>
<unit units="litre"/>
<unit exponent="-1" units="farad"/>
<unit exponent="-1" units="metre"/>
<unit exponent="-1" units="coulomb"/>
</units>
<component name="PKA_module">
<!-- [RC] regulatory subunit-bound PKA (mM)
[ARC] complex of cAMP, PKA and regulatory subunit (mM)
[A2RC] complex of 2 cAMP, PKA and regulatory subunit (mM)
[A2R] complex of 2 cAMP and regulatory subunit (mM)-->
<variable name="time" units="second"/>
<variable initial_value="0.59" name="PKAI_tot" units="uM"/>
<variable initial_value="0.025" name="PKAII_tot" units="uM"/>
<variable initial_value="0.18" name="PKI_tot" units="uM"/>
<variable initial_value="9.14" name="K_a" units="uM"/>
<variable initial_value="1.64" name="K_b" units="uM"/>
<variable initial_value="4.375" name="K_d" units="uM"/>
<variable initial_value="0.2e-3" name="Ki_pki" units="uM"/>
<variable cmeta:id="PKI" name="PKI" units="uM"/>
<variable cmeta:id="A2RC_I" name="A2RC_I" units="uM"/>
<variable cmeta:id="A2R_I" name="A2R_I" units="uM"/>
<variable cmeta:id="A2RC_II" name="A2RC_II" units="uM"/>
<variable cmeta:id="A2R_II" name="A2R_II" units="uM"/>
<variable cmeta:id="ARC_I" name="ARC_I" units="uM"/>
<variable cmeta:id="ARC_II" name="ARC_II" units="uM"/>
<variable cmeta:id="PKA_temp" name="PKA_temp" units="uM"/>
<variable cmeta:id="cAMP" name="cAMP" units="uM"/>
<variable cmeta:id="PKAC_I" name="PKAC_I" units="uM"/>
<variable cmeta:id="PKAC_II" name="PKAC_II" units="uM"/>
<variable initial_value="0.8453" name="cAMP_tot" units="uM"/>
<variable initial_value="0" name="zed" units="dimensionless"/>
<variable initial_value="0" name="zed1" units="dimensionless"/>
<variable name="RC_I" units="uM"/>
<variable name="RC_II" units="uM"/>
<!-- real equations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>PKI</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>PKI_tot</ci>
<ci>Ki_pki</ci>
</apply>
<apply>
<plus/>
<ci>Ki_pki</ci>
<ci>PKAC_I</ci>
<ci>PKAC_II</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>A2RC_I</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>PKAC_I</ci>
<ci>K_d</ci>
</apply>
<ci>PKAC_I</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>A2R_I</ci>
<apply>
<times/>
<ci>PKAC_I</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ARC_I</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K_a</ci>
<ci>cAMP</ci>
</apply>
<ci>A2RC_I</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>A2RC_II</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>PKAC_II</ci>
<ci>K_d</ci>
</apply>
<ci>PKAC_II</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>A2R_II</ci>
<apply>
<times/>
<ci>PKAC_II</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ARC_II</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K_a</ci>
<ci>cAMP</ci>
</apply>
<ci>A2RC_II</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PKA_temp</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_a</ci>
<ci>K_b</ci>
</apply>
<ci>K_d</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K_a</ci>
<ci>cAMP</ci>
</apply>
<ci>K_d</ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>K_d</ci>
</apply>
</apply>
</apply>
<!-- for completion (not part of MATLAB script)-->
<apply>
<eq/>
<ci>RC_I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>A2RC_I</ci>
<ci>K_a</ci>
<ci>K_b</ci>
</apply>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>RC_II</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>A2RC_II</ci>
<ci>K_a</ci>
<ci>K_b</ci>
</apply>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<!-- the guts
1. conservation of cAMP-->
<apply>
<eq/>
<ci>cAMP</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>cAMP_tot</ci>
<apply>
<plus/>
<ci>ARC_I</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>A2RC_I</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>A2R_I</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>ARC_II</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>A2RC_II</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>A2R_II</ci>
</apply>
</apply>
</apply>
</apply>
<!-- 2. conservation of PKAC_I-->
<apply>
<eq/>
<ci>zed</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>PKAI_tot</ci>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>PKAC_I</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>PKA_temp</ci>
<ci>PKAC_I</ci>
</apply>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- 3. conservation of PKAC_II-->
<apply>
<eq/>
<ci>zed1</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>PKAII_tot</ci>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>PKAC_II</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>PKI</ci>
<ci>Ki_pki</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>PKA_temp</ci>
<ci>PKAC_II</ci>
</apply>
<apply>
<power/>
<ci>cAMP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- 0{dimensionless} = 2{dimensionless}*PKAI_tot*sqr(cAMP)-PKAC_I*(1{dimensionless}+PKI/Ki_pki)*(PKA_temp*PKAC_I+sqr(cAMP));
0{dimensionless} = 2{dimensionless}*PKAII_tot*sqr(cAMP)-PKAC_II*(1{dimensionless}+PKI/Ki_pki)*(PKA_temp*PKAC_II+sqr(cAMP));-->
<variable initial_value="0" name="a" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>a</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
</math>
</component>
</model>
