Location: BondGraph Basic @ 21fce073170d / BG Tutorial Biochemical Systems / Michaelis-Menten-Enzyme.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2017-06-27 15:43:20+12:00
- Desc:
- tidy up the pendulum
- Permanent Source URI:
- https://models.cellml.org/workspace/43b/rawfile/21fce073170d32ce5258c738529ec775fa211a90/BG Tutorial Biochemical Systems/Michaelis-Menten-Enzyme.cellml
<?xml version='1.0'?>
<model name="MichaelisMenten_Enzyme" 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.cellml">
<units name="per_mol" units_ref="per_mol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="J_per_mol_K" units_ref="J_per_mol_K"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
</import>
<component name="state">
<variable initial_value="0.0" name="t" units="second"/>
<!-- Parameters-->
<variable initial_value="8.324" name="R" units="J_per_mol_K"/>
<variable initial_value="300" name="T" units="kelvin"/>
<variable initial_value="19036539.4" name="K_1" units="per_mol"/>
<variable initial_value="0.00725" name="K_2" units="per_mol"/>
<variable initial_value="137.97" name="K_3" units="per_mol"/>
<variable initial_value="0.00000000038" name="K_4" units="per_mol"/>
<variable initial_value="0.00725" name="kappa_1" units="mol_per_s"/>
<variable initial_value="0.00036" name="kappa_2" units="mol_per_s"/>
<variable initial_value="10.0" name="kappa_0" units="mol_per_s"/>
<!-- State variables-->
<variable initial_value="0.001" name="q_1" units="mole"/>
<variable initial_value="0.0005" name="q_2" units="mole"/>
<variable initial_value="1e-9" name="q_3" units="mole"/>
<variable initial_value="1e-9" name="q_4" units="mole"/>
<variable name="upsilon_1" units="mol_per_s"/>
<variable name="upsilon_2" units="mol_per_s"/>
<variable name="upsilon_3" units="mol_per_s"/>
<variable name="upsilon_4" units="mol_per_s"/>
<variable name="upsilon_0" units="mol_per_s"/>
<variable name="mu_1" units="J_per_mol"/>
<variable name="mu_2" units="J_per_mol"/>
<variable name="mu_3" units="J_per_mol"/>
<variable name="mu_4" units="J_per_mol"/>
<variable name="mu_5" units="J_per_mol"/>
<variable name="mu_6" units="J_per_mol"/>
<variable name="mu_0" units="J_per_mol"/>
<!-- Constitutive relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_1</ci>
<ci>q_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_2</ci>
<ci>q_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_3</ci>
<ci>q_3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_4</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_4</ci>
<ci>q_4</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>upsilon_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_5</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>upsilon_4</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_6</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>upsilon_0</ci>
<apply>
<times/>
<ci>kappa_0</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_0</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- Conservation laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_1</ci>
</apply>
<apply>
<minus/>
<ci>upsilon_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_2</ci>
</apply>
<ci>upsilon_2</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_3</ci>
</apply>
<ci>upsilon_3</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_4</ci>
</apply>
<ci>upsilon_4</ci>
</apply>
<apply>
<eq/>
<ci>upsilon_2</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>upsilon_4</ci>
<ci>upsilon_1</ci>
</apply>
<ci>upsilon_0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>upsilon_3</ci>
<apply>
<minus/>
<ci>upsilon_1</ci>
<ci>upsilon_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_5</ci>
<apply>
<plus/>
<ci>mu_1</ci>
<ci>mu_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_6</ci>
<apply>
<plus/>
<ci>mu_2</ci>
<ci>mu_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_0</ci>
<ci>mu_4</ci>
</apply>
</math>
</component>
</model>