- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-06-21 16:30:43+12:00
- Desc:
- Codes to reproduce Saucerman Figs 2 and 3a
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/674/rawfile/348913e60cebcf090b62de195a8a13165b1512f7/BG_cAMP_basalAC.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- BG model of cAMP, based on saucerman2003, v1
20may21 initialising file
24may21: basal reaction with AC.
given Km and kcat for kinetic versions of enzyme reaction, recreate BG parameters by setting k1+ = 1, k2+ = 0, K_E = 1 to be able to solve for K_S, K_C, kappa1 and kappa2
See Pan thesis section 4.2 -->
<model name="BG_cAMP" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<units name="per_sec">
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_K_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="fmol">
<unit prefix="femto" units="mole"/>
</units>
<units name="fmol_per_L">
<unit prefix="femto" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_sec_per_fmol_per_L">
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="fmol_per_L"/>
</units>
<units name="per_fmol">
<unit exponent="-1" units="fmol"/>
</units>
<units name="fmol_per_sec">
<unit units="fmol"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="pL">
<unit prefix="pico" units="litre"/>
</units>
<component name="environment">
<variable initial_value="0" name="t" units="second"/>
<!-- Physical parameters-->
<variable initial_value="8.31" name="R" units="J_per_K_per_mol"/>
<variable initial_value="310" name="T" units="kelvin"/>
<variable initial_value="96485" name="F" units="C_per_mol"/>
<!-- kinetic parameters - for comparing. (basal reaction)-->
<variable initial_value="1.03e0" name="Km_basal_mM" units="mM"/>
<variable initial_value="1.03e12" name="Km_basal" units="fmol_per_L"/>
<variable initial_value="1e-12" name="k1p_basal" units="per_sec_per_fmol_per_L"/>
<variable initial_value="0.83" name="k1m_basal" units="per_sec"/>
<variable initial_value="0.2" name="k2p_basal" units="per_sec"/>
<variable initial_value="2.41e-13" name="k2m_basal" units="per_sec_per_fmol_per_L"/>
<variable initial_value="49.7e-6" name="AC_tot" units="mM"/>
<variable initial_value="0.00263157894736842" name="ATP_kinetic" units="mM"/>
<!-- kinetic states-->
<variable initial_value="0.002631579" name="cAMP_kinetic" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>cAMP_kinetic</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k2p_basal</ci>
<ci>AC_tot</ci>
<ci>ATP_kinetic</ci>
</apply>
<apply>
<plus/>
<ci>Km_basal_mM</ci>
<ci>ATP_kinetic</ci>
</apply>
</apply>
</apply>
</math>
<!-- Bond graph parameters, found using pinv of kinetic parameters-->
<variable initial_value="1.82E-03" name="K_ATP" units="per_fmol"/>
<variable initial_value="1.82E-03" name="K_cAMP" units="per_fmol"/>
<variable initial_value="3.32E-06" name="K_AC" units="per_fmol"/>
<variable initial_value="1897.961663" name="K_AC_ATP" units="per_fmol"/>
<variable initial_value="1.406245475" name="kappa_1a" units="fmol_per_sec"/>
<variable initial_value="0.004478489" name="kappa_1b" units="fmol_per_sec"/>
<!-- var K_ATP: per_fmol {init: 4.77E-04};
var K_AC: per_fmol {init: 2.27E-07};
var K_cAMP: per_fmol {init: 4.77E-04};
var K_AC_ATP: per_fmol {init: 90.03415927};
var kappa_1a: fmol_per_sec {init: 0.009218723};
var kappa_1b: fmol_per_sec {init: 0.002221379};-->
<!-- States (and initial conditions)-->
<variable initial_value="0.1" name="q_ATP" units="fmol"/>
<variable initial_value="0.0018886" name="q_AC" units="fmol"/>
<!--q_AC: consistent with AC_tot (kinetic)-->
<variable initial_value="0.1" name="q_cAMP" units="fmol"/>
<variable initial_value="0.0" name="q_AC_ATP" units="fmol"/>
<!-- Concentrations - for plotting-->
<variable name="c_ATP" units="mM"/>
<variable name="c_cAMP" units="mM"/>
<variable name="c_AC" units="mM"/>
<variable name="c_AC_ATP" units="mM"/>
<variable initial_value="38.0" name="vol" units="pL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_ATP</ci>
<apply>
<divide/>
<ci>q_ATP</ci>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_cAMP</ci>
<apply>
<divide/>
<ci>q_cAMP</ci>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_AC</ci>
<apply>
<divide/>
<ci>q_AC</ci>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_AC_ATP</ci>
<apply>
<divide/>
<ci>q_AC_ATP</ci>
<ci>vol</ci>
</apply>
</apply>
</math>
<!-- Bond variables-->
<variable name="v1a" units="fmol_per_sec"/>
<variable name="v1b" units="fmol_per_sec"/>
<!-- Constitutive equations-->
<variable name="mu_ATP" units="J_per_mol"/>
<variable name="mu_AC" units="J_per_mol"/>
<variable name="mu_cAMP" units="J_per_mol"/>
<variable name="mu_AC_ATP" units="J_per_mol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ATP</ci>
<ci>q_ATP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_AC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_AC</ci>
<ci>q_AC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_AC_ATP</ci>
<ci>q_AC_ATP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_cAMP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_cAMP</ci>
<ci>q_cAMP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v1a</ci>
<apply>
<times/>
<ci>kappa_1a</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_AC</ci>
<ci>mu_ATP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v1b</ci>
<apply>
<times/>
<ci>kappa_1b</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_AC</ci>
<ci>mu_cAMP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ATP</ci>
</apply>
<cn cellml:units="fmol_per_sec">0</cn>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AC</ci>
</apply>
<cn cellml:units="fmol_per_sec">0</cn>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AC_ATP</ci>
</apply>
<apply>
<minus/>
<ci>v1a</ci>
<ci>v1b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_cAMP</ci>
</apply>
<ci>v1b</ci>
</apply>
</math>
</component>
</model>
