Location: The Physics of Physiology - Example 6: An enzyme-catalyzed reaction and Michaelis-Menten kinetics @ 8954fb4e0c0a / FAIRDO BG example 3.6.cellml
- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-11 17:26:15+13:00
- Desc:
- Adding initial example CellML model and SED-ML. Example files obtained from Peter Hunter and match the FAIR DOs lecture notes from January 2024.
- Permanent Source URI:
- http://models.cellml.org/workspace/af2/rawfile/8954fb4e0c0aa1676f02db9ebb80a7823a2da86c/FAIRDO BG example 3.6.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG6" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- An enzyme catalyzed reaction-->
<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="per_mol3">
<unit exponent="-3" units="mole"/>
</units>
<units name="per_mol3_per_s">
<unit exponent="-3" units="mole"/>
<unit exponent="-1" units="second"/>
</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="3" 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 initial_value="1" name="q_e0" units="mole"/>
<variable initial_value="1" name="q_e1" units="mole"/>
<variable name="v_1" units="mol_per_s"/>
<variable name="v_2" 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_e0" units="J_per_mol"/>
<variable name="u_e1" units="J_per_mol"/>
<variable name="u_f_1" units="J_per_mol"/>
<variable name="u_r_1" units="J_per_mol"/>
<variable name="u_f_2" units="J_per_mol"/>
<variable name="u_r_2" 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="2" name="K_q_e0" units="per_mol"/>
<variable initial_value="2" name="K_q_e1" units="per_mol"/>
<variable initial_value="0.2" name="kappa_1" units="mol_per_s"/>
<variable initial_value="0.1" name="kappa_2" 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_1</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_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_3</ci>
</apply>
<ci>v_2</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_2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_e0</ci>
</apply>
<apply>
<minus/>
<ci>v_2</ci>
<ci>v_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_e1</ci>
</apply>
<apply>
<minus/>
<ci>v_1</ci>
<ci>v_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_f_1</ci>
<apply>
<plus/>
<ci>u_1</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>u_2</ci>
</apply>
<ci>u_e0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_r_1</ci>
<ci>u_e1</ci>
</apply>
<apply>
<eq/>
<ci>u_f_2</ci>
<ci>u_e1</ci>
</apply>
<apply>
<eq/>
<ci>u_r_2</ci>
<apply>
<plus/>
<ci>u_3</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>u_4</ci>
</apply>
<ci>u_e0</ci>
</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>u_e0</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_e0</ci>
<ci>q_e0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_e1</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q_e1</ci>
<ci>q_e1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_f_1</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_r_1</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_f_2</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u_r_2</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="q_e_tot" units="mole"/>
<variable name="A_f" units="per_mol3_per_s"/>
<variable name="A_r" units="per_mol3_per_s"/>
<variable name="B_f" units="per_mol3"/>
<variable name="B_r" units="per_mol3"/>
<variable name="v_SS" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_e_tot</ci>
<apply>
<plus/>
<ci>q_e0</ci>
<ci>q_e1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>A_f</ci>
<apply>
<times/>
<ci>q_e_tot</ci>
<ci>K_q_e0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
<apply>
<plus/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
</apply>
<ci>K_q_1</ci>
<apply>
<power/>
<ci>K_q_2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>A_r</ci>
<apply>
<times/>
<ci>q_e_tot</ci>
<ci>K_q_e0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
<apply>
<plus/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
</apply>
<ci>K_q_3</ci>
<apply>
<power/>
<ci>K_q_4</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>B_f</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K_q_e0</ci>
<ci>K_q_e1</ci>
</apply>
<apply>
<divide/>
<ci>kappa_1</ci>
<apply>
<plus/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
</apply>
<ci>K_q_1</ci>
<apply>
<power/>
<ci>K_q_2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>B_r</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K_q_e0</ci>
<ci>K_q_e1</ci>
</apply>
<apply>
<divide/>
<ci>kappa_1</ci>
<apply>
<plus/>
<ci>kappa_1</ci>
<ci>kappa_2</ci>
</apply>
</apply>
<ci>K_q_3</ci>
<apply>
<power/>
<ci>K_q_4</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_SS</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>A_f</ci>
<ci>q_1</ci>
<apply>
<power/>
<ci>q_2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>A_r</ci>
<ci>q_3</ci>
<apply>
<power/>
<ci>q_4</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<times/>
<ci>B_f</ci>
<ci>q_1</ci>
<apply>
<power/>
<ci>q_2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>B_r</ci>
<ci>q_3</ci>
<apply>
<power/>
<ci>q_4</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>