Location: FAIR DOs example 4.2 @ 2b37128464bd / FAIRDO BG example 4.2.cellml
- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-29 23:19:10+13:00
- Desc:
- update from Peter
- Permanent Source URI:
- https://models.cellml.org/workspace/b58/rawfile/2b37128464bd1e58ba66a90deec7ab078bf0fe82/FAIRDO BG example 4.2.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG42" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Facilitated diffusion -->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="per_s3">
<unit exponent="-3" units="second"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="per_mol2">
<unit exponent="-2" units="mole"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mol_per_s">
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mM">
<unit units="mole"/>
<unit exponent="-3" units="meter"/>
</units>
<units name="mM_per_s">
<unit units="mM"/>
<unit exponent="-1" units="second"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="100" name="q_1" units="mole"/>
<variable initial_value="0" 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="0" name="q_5" units="mole"/>
<variable name="q_6" units="mole"/>
<variable initial_value="1" name="q_tot" units="mole"/>
<variable name="v_1" units="mol_per_s"/>
<variable name="v_2" units="mol_per_s"/>
<variable name="v_3" units="mol_per_s"/>
<variable name="v_4" units="mol_per_s"/>
<variable initial_value="100" name="kappa_1" units="mol_per_s"/>
<variable initial_value="100" name="kappa_2" units="mol_per_s"/>
<variable initial_value="1" name="kappa_3" units="mol_per_s"/>
<variable initial_value="0.1" name="kappa_4" units="mol_per_s"/>
<variable initial_value="0.1" name="K_1" units="per_mol"/>
<variable initial_value="0.1" name="K_2" units="per_mol"/>
<variable initial_value="0.1" name="K_s" units="per_mol"/>
<variable initial_value="1" name="K_3" units="per_mol"/>
<variable initial_value="1" name="K_4" units="per_mol"/>
<variable initial_value="1" name="K_5" units="per_mol"/>
<variable initial_value="1" name="K_6" units="per_mol"/>
<variable initial_value="1" name="K_m" units="per_mol"/>
<variable name="k_m" units="mole"/>
<variable name="v_max" units="mol_per_s"/>
<!-- Full bond graph model-->
<variable name="k_f_1" units="per_mol_per_s"/>
<variable name="k_r_1" units="per_s"/>
<variable name="k_f_2" units="per_s"/>
<variable name="k_r_2" units="per_mol_per_s"/>
<variable name="k_f_3" units="per_s"/>
<variable name="k_r_3" units="per_s"/>
<variable name="k_f_4" units="per_s"/>
<variable name="k_r_4" units="per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k_f_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<ci>K_1</ci>
<ci>K_6</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_r_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<ci>K_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_f_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<ci>K_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_r_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<ci>K_2</ci>
<ci>K_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_f_3</ci>
<apply>
<times/>
<ci>kappa_3</ci>
<ci>K_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_r_3</ci>
<apply>
<times/>
<ci>kappa_3</ci>
<ci>K_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_f_4</ci>
<apply>
<times/>
<ci>kappa_4</ci>
<ci>K_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_r_4</ci>
<apply>
<times/>
<ci>kappa_4</ci>
<ci>K_6</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_1</ci>
</apply>
<apply>
<minus/>
<ci>v_1</ci>
</apply>
</apply>
<!-- ode(q_2, t) = v_2;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_2</ci>
</apply>
<apply>
<minus/>
<ci>v_2</ci>
<apply>
<times/>
<cn cellml:units="per_s">1000</cn>
<ci>q_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_3</ci>
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<apply>
<minus/>
<ci>v_1</ci>
<ci>v_3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_4</ci>
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<apply>
<minus/>
<ci>v_3</ci>
<ci>v_2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_5</ci>
</apply>
<apply>
<minus/>
<ci>v_2</ci>
<ci>v_4</ci>
</apply>
</apply>
<!-- ode(q_6, t) = v_4-v_1;-->
<apply>
<eq/>
<ci>q_6</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>q_tot</ci>
<ci>q_3</ci>
</apply>
<ci>q_4</ci>
</apply>
<ci>q_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_1</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_f_1</ci>
<ci>q_1</ci>
<ci>q_6</ci>
</apply>
<apply>
<times/>
<ci>k_r_1</ci>
<ci>q_3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_f_2</ci>
<ci>q_4</ci>
</apply>
<apply>
<times/>
<ci>k_r_2</ci>
<ci>q_2</ci>
<ci>q_5</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_3</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_f_3</ci>
<ci>q_3</ci>
</apply>
<apply>
<times/>
<ci>k_r_3</ci>
<ci>q_4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_4</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_f_4</ci>
<ci>q_5</ci>
</apply>
<apply>
<times/>
<ci>k_r_4</ci>
<ci>q_6</ci>
</apply>
</apply>
</apply>
</math>
<!-- Rapid binding & unbinding & SS flux-->
<variable name="v_SF" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_SF</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_tot</ci>
<ci>kappa_3</ci>
<ci>kappa_4</ci>
<ci>K_m</ci>
<ci>K_s</ci>
<apply>
<minus/>
<ci>q_1</ci>
<ci>q_2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>kappa_4</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>kappa_3</ci>
<ci>kappa_4</ci>
</apply>
<ci>K_s</ci>
<apply>
<plus/>
<ci>q_1</ci>
<ci>q_2</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>kappa_3</ci>
<ci>K_s</ci>
<ci>K_s</ci>
<ci>q_1</ci>
<ci>q_2</ci>
</apply>
</apply>
</apply>
</apply>
<!-- Michaelis-Menten-->
<apply>
<eq/>
<ci>k_m</ci>
<apply>
<divide/>
<cn cellml:units="dim">2</cn>
<apply>
<times/>
<ci>K_s</ci>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>kappa_3</ci>
<ci>kappa_4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_tot</ci>
<ci>kappa_3</ci>
<ci>K_m</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>kappa_3</ci>
<ci>kappa_4</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_MM" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_MM</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max</ci>
<ci>q_1</ci>
</apply>
<apply>
<plus/>
<ci>k_m</ci>
<ci>q_1</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>