Location: The Physics of Physiology - Example 5: A biochemical reaction with mixed stoichiometry @ 385e62f15780 / FAIRDO BG example 3.5.cellml
- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-11 17:21:14+13:00
- Desc:
- Initial documentation to use in making an exposure
- Permanent Source URI:
- https://models.cellml.org/workspace/af1/rawfile/385e62f157807ba847934cef89d8289f9bb01671/FAIRDO BG example 3.5.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG4" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- A biochemical reaction with mixed stoichiometry-->
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="2578.73058" name="RT" units="J_per_mol"/>
<!-- R=8.31446262 J/mol/K, T=310.15 K, F=9.64853321e4 C/mol-->
<!-- State variables-->
<variable initial_value="1" name="q_1" units="mole"/>
<variable initial_value="1" name="q_2" units="mole"/>
<variable initial_value="0" name="q_3" units="mole"/>
<variable initial_value="0" name="q_4" units="mole"/>
<variable name="v_r" units="mol_per_s"/>
<variable name="u_1" units="J_per_mol"/>
<variable name="u_2" units="J_per_mol"/>
<variable name="u_3" units="J_per_mol"/>
<variable name="u_4" units="J_per_mol"/>
<variable name="u_f" units="J_per_mol"/>
<variable name="u_r" units="J_per_mol"/>
<!-- Constitutive parameters-->
<variable initial_value="2" name="K_q_1" units="per_mol"/>
<variable initial_value="2" name="K_q_2" units="per_mol"/>
<variable initial_value="2" name="K_q_3" units="per_mol"/>
<variable initial_value="2" name="K_q_4" units="per_mol"/>
<variable initial_value="0.1" name="kappa_r" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_1</ci>
</apply>
<apply>
<minus/>
<ci>v_r</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_2</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dim">2</cn>
</apply>
<ci>v_r</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_3</ci>
</apply>
<ci>v_r</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_4</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>v_r</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_f</ci>
<apply>
<plus/>
<ci>u_1</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>u_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_r</ci>
<apply>
<plus/>
<ci>u_3</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>u_4</ci>
</apply>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>u_1</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_1</ci>
<ci>q_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_2</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_2</ci>
<ci>q_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_3</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_3</ci>
<ci>q_3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_4</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_4</ci>
<ci>q_4</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_r</ci>
<apply>
<times/>
<ci>kappa_r</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_f</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_r</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>