Location: BG_cAMP @ 3b4e9b848bf3 / BG_cAMP.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-08-25 09:46:43+12:00
- Desc:
- Adding volume arguments and changing dimensions of input kinetic parameters to uM (source literature)
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/674/rawfile/3b4e9b848bf30fcd926aacbdcf226d68ad15e0de/BG_cAMP.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
21 Jul 21: constraint of cAMP to 5AMP using gibbs free energy from literature-->
<model name="BG_cAMP" 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="cAMP">
<variable name="time" public_interface="in" units="second"/>
<!-- Physical parameters-->
<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<!-- 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>time</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-->
<!-- 21ju121 with fastKineticConstant = 1e6 and FSK andf dGibbs for rxn 4-->
<variable initial_value="1.44613e+06" name="kappa_1a" units="fmol_per_sec"/>
<variable initial_value="0.000301939" name="kappa_1b" units="fmol_per_sec"/>
<variable initial_value="94062" name="kappa_2a" units="fmol_per_sec"/>
<variable initial_value="0.0253818" name="kappa_2b" units="fmol_per_sec"/>
<variable initial_value="2.7132e+08" name="kappa_3a" units="fmol_per_sec"/>
<variable initial_value="3.15488e-17" name="kappa_3b" units="fmol_per_sec"/>
<variable initial_value="316229" name="kappa_4a" units="fmol_per_sec"/>
<variable initial_value="1.21627" name="kappa_4b" units="fmol_per_sec"/>
<variable initial_value="204.342" name="kappa_5" units="fmol_per_sec"/>
<variable initial_value="761.387" name="kappa_6" units="fmol_per_sec"/>
<variable initial_value="219620" name="kappa_7" units="fmol_per_sec"/>
<variable initial_value="2.35306e-05" name="K_ATP" units="per_fmol"/>
<variable initial_value="2.35306e-05" name="K_cAMP" units="per_fmol"/>
<variable initial_value="23.0954" name="K_AC" units="per_fmol"/>
<variable initial_value="19.2554" name="K_AC_ATP" units="per_fmol"/>
<variable initial_value="38.18" name="K_GsT_AC" units="per_fmol"/>
<variable initial_value="9.73504" name="K_GsT_AC_ATP" units="per_fmol"/>
<variable initial_value="0.132364" name="K_FSK_AC" units="per_fmol"/>
<variable initial_value="0.0921422" name="K_FSK_AC_ATP" units="per_fmol"/>
<variable initial_value="113.566" name="K_PDE" units="per_fmol"/>
<variable initial_value="0.119504" name="K_PDE_cAMP" units="per_fmol"/>
<variable initial_value="2.35306e-05" name="K_five_AMP" units="per_fmol"/>
<variable initial_value="0.00121382" name="K_IBMX" units="per_fmol"/>
<variable initial_value="142.26" name="K_PDEinh" units="per_fmol"/>
<variable initial_value="0.120142" name="K_GsT" units="per_fmol"/>
<variable initial_value="3.78646e-06" name="K_FSK" units="per_fmol"/>
<!-- States (and initial conditions)-->
<!-- 29jun21 WORKS. original concs, but complexes = 1e-13 . -->
<!-- var q_ATP: fmol {init: 1.90E-02};
var q_AC: fmol {init: 1.89E-3};
var q_cAMP: fmol {init: 3.21E-02};
var q_cAMP_noPDE: fmol {init: 3.21E-02};
var q_AC_ATP: fmol {init: 1e-13};
var q_FSK: fmol {init: 1e-9};
var q_FSK_AC: fmol {init: 1e-13};
var q_FSK_AC_ATP: fmol {init: 1e-13};
var q_GsT: fmol {init: 9.52E-04};
var q_GsT_AC: fmol {init: 1e-13};
var q_GsT_AC_ATP: fmol {init: 1e-13};
var q_PDE: fmol {init: 1.48E-03};
var q_PDEinh: fmol {init: 1e-13};
var q_PDE_cAMP: fmol {init: 1e-18};
var q_IBMX: fmol {init: 3.80E-06};
var q_five_AMP: fmol {init: 1e-13};-->
<!-- 8 Jul conserving all species and enzyme states - e.g. all AC-containing species sum to AC_tot (saucerman)-->
<variable initial_value="189.99905570" name="q_ATP" units="fmol"/>
<variable initial_value="0.0006143333" name="q_AC" units="fmol"/>
<variable initial_value="0.0314042742" name="q_cAMP" units="fmol"/>
<variable initial_value="0.0314042742" name="q_cAMP_noPDE" units="fmol"/>
<variable initial_value="0.000614333" name="q_AC_ATP" units="fmol"/>
<variable initial_value="0.0000126667" name="q_FSK" units="fmol"/>
<variable initial_value="0.0000126667" name="q_FSK_AC" units="fmol"/>
<variable initial_value="0.0000126667" name="q_FSK_AC_ATP" units="fmol"/>
<variable initial_value="0.00031730" name="q_GsT" units="fmol"/>
<variable initial_value="0.00031730" name="q_GsT_AC" units="fmol"/>
<variable initial_value="0.00031730" name="q_GsT_AC_ATP" units="fmol"/>
<variable initial_value="0.0007171258" name="q_PDE" units="fmol"/>
<variable initial_value="1e-13" name="q_PDEinh" units="fmol"/>
<variable initial_value="0.0007171258" name="q_PDE_cAMP" units="fmol"/>
<variable initial_value="3.80E-06" name="q_IBMX" units="fmol"/>
<variable initial_value="1e-18" name="q_five_AMP" units="fmol"/>
<!-- Bond variables-->
<variable name="v1a" units="fmol_per_sec"/>
<variable name="v1b" units="fmol_per_sec"/>
<variable name="v2a" units="fmol_per_sec"/>
<variable name="v2b" units="fmol_per_sec"/>
<variable name="v3a" units="fmol_per_sec"/>
<variable name="v3b" units="fmol_per_sec"/>
<variable name="v4a" units="fmol_per_sec"/>
<variable name="v4b" units="fmol_per_sec"/>
<variable name="v5" units="fmol_per_sec"/>
<variable name="v6" units="fmol_per_sec"/>
<variable name="v7" units="fmol_per_sec"/>
<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"/>
<variable name="mu_FSK" units="J_per_mol"/>
<variable name="mu_FSK_AC" units="J_per_mol"/>
<variable name="mu_FSK_AC_ATP" units="J_per_mol"/>
<variable name="mu_GsT" units="J_per_mol"/>
<variable name="mu_GsT_AC" units="J_per_mol"/>
<variable name="mu_GsT_AC_ATP" units="J_per_mol"/>
<variable name="mu_PDE" units="J_per_mol"/>
<variable name="mu_PDEinh" units="J_per_mol"/>
<variable name="mu_PDE_cAMP" units="J_per_mol"/>
<variable name="mu_IBMX" units="J_per_mol"/>
<variable name="mu_five_AMP" units="J_per_mol"/>
<!-- Concentrations - for plotting-->
<variable name="c_ATP" units="uM"/>
<variable name="c_cAMP" units="uM"/>
<variable name="c_cAMP_noPDE" units="uM"/>
<variable name="c_FSK" units="uM"/>
<variable name="c_GsT" units="uM"/>
<variable name="c_PDE" units="uM"/>
<variable name="c_IBMX" units="uM"/>
<variable name="c_five_AMP" units="uM"/>
<variable name="c_AC" units="uM"/>
<variable name="c_AC_ATP" units="uM"/>
<variable name="c_GsT_AC_ATP" units="uM"/>
<variable name="c_GsT_AC" units="uM"/>
<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/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_ATP</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_cAMP</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_cAMP</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_cAMP_noPDE</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_cAMP_noPDE</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_FSK</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_FSK</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_IBMX</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_IBMX</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_GsT</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_GsT</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_PDE</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_PDE</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_five_AMP</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_five_AMP</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_AC</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_AC</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_AC_ATP</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_AC_ATP</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_GsT_AC_ATP</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_GsT_AC_ATP</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_GsT_AC</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_GsT_AC</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<!-- Constitutive equations-->
<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_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>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_FSK_AC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_FSK_AC</ci>
<ci>q_FSK_AC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_FSK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_FSK</ci>
<ci>q_FSK</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_FSK_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_FSK_AC_ATP</ci>
<ci>q_FSK_AC_ATP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_GsT_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_GsT_AC_ATP</ci>
<ci>q_GsT_AC_ATP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_GsT_AC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_GsT_AC</ci>
<ci>q_GsT_AC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_GsT</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_GsT</ci>
<ci>q_GsT</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PDE_cAMP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PDE_cAMP</ci>
<ci>q_PDE_cAMP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PDE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PDE</ci>
<ci>q_PDE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_IBMX</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_IBMX</ci>
<ci>q_IBMX</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PDEinh</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PDEinh</ci>
<ci>q_PDEinh</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_five_AMP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_five_AMP</ci>
<ci>q_five_AMP</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/>
<ci>v2a</ci>
<apply>
<times/>
<ci>kappa_2a</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_GsT_AC</ci>
<ci>mu_ATP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_GsT_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v2b</ci>
<apply>
<times/>
<ci>kappa_2b</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_GsT_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_GsT_AC</ci>
<ci>mu_cAMP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v3a</ci>
<apply>
<times/>
<ci>kappa_3a</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_FSK_AC</ci>
<ci>mu_ATP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_FSK_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v3b</ci>
<apply>
<times/>
<ci>kappa_3b</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_FSK_AC_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_FSK_AC</ci>
<ci>mu_cAMP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v4a</ci>
<apply>
<times/>
<ci>kappa_4a</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PDE</ci>
<ci>mu_cAMP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PDE_cAMP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v4b</ci>
<apply>
<times/>
<ci>kappa_4b</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PDE_cAMP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PDE</ci>
<ci>mu_five_AMP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v5</ci>
<apply>
<times/>
<ci>kappa_5</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PDE</ci>
<ci>mu_IBMX</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PDEinh</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v6</ci>
<apply>
<times/>
<ci>kappa_6</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_AC</ci>
<ci>mu_GsT</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_GsT_AC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v7</ci>
<apply>
<times/>
<ci>kappa_7</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_FSK</ci>
<ci>mu_AC</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_FSK_AC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- velocity in uM_per_sec-->
<variable name="v1b_kinetic" units="uM_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v1b_kinetic</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v1b</ci>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v1a</ci>
</apply>
<ci>v3a</ci>
</apply>
<ci>v2a</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_AC</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v1b</ci>
<ci>v1a</ci>
</apply>
<ci>v6</ci>
</apply>
<ci>v7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_AC_ATP</ci>
</apply>
<apply>
<minus/>
<ci>v1a</ci>
<ci>v1b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_cAMP</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v1b</ci>
<ci>v3b</ci>
<ci>v2b</ci>
</apply>
<ci>v4a</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_FSK</ci>
</apply>
<apply>
<minus/>
<ci>v7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_FSK_AC</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v7</ci>
<ci>v3b</ci>
</apply>
<ci>v3a</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_FSK_AC_ATP</ci>
</apply>
<apply>
<minus/>
<ci>v3a</ci>
<ci>v3b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_GsT</ci>
</apply>
<apply>
<minus/>
<ci>v6</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_GsT_AC</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>v6</ci>
<ci>v2a</ci>
</apply>
<ci>v2b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_GsT_AC_ATP</ci>
</apply>
<apply>
<minus/>
<ci>v2a</ci>
<ci>v2b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PDE_cAMP</ci>
</apply>
<apply>
<minus/>
<ci>v4a</ci>
<ci>v4b</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PDE</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v4b</ci>
<ci>v4a</ci>
</apply>
<ci>v5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_IBMX</ci>
</apply>
<apply>
<minus/>
<ci>v5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_PDEinh</ci>
</apply>
<ci>v5</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_five_AMP</ci>
</apply>
<ci>v4b</ci>
</apply>
</math>
<!-- calculate velocity wrt changing concentration rate-->
<variable name="PDE_ACT_4a" units="mM_per_sec"/>
<variable name="PDE_ACT_4ab" units="mM_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>PDE_ACT_4a</ci>
<apply>
<divide/>
<ci>v4a</ci>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PDE_ACT_4ab</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>v4a</ci>
<ci>v4b</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="cAMP"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="constants" component_2="cAMP"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>