Location: Kobro-Flatmoen & Omholt 2024 @ c387870ec316 / fig3.cellml
- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-09-30 16:11:53+13:00
- Desc:
- Creating a common model and parameter sets that are reused to produce outputs for figures 1-4 in a single model
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/be4/rawfile/c387870ec31681cb45c3dd50249ef7179da91e50/fig3.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- (4 eqn model for Alzheimer calculation) -->
<units name="molecules">
<unit units="dimensionless"/>
</units>
<units name="hour">
<unit multiplier="3600" units="second"/>
</units>
<units name="per_hour">
<unit exponent="-1" units="hour"/>
</units>
<units name="molecules_per_hour">
<unit units="molecules"/>
<unit units="per_hour"/>
</units>
<units name="per_molecules_per_hour">
<unit exponent="-1" units="molecules"/>
<unit units="per_hour"/>
</units>
<units name="per_hour2">
<unit exponent="-2" units="hour"/>
</units>
<units name="per_hour4">
<unit exponent="-4" units="hour"/>
</units>
<units name="micrometer">
<unit prefix="micro" units="meter"/>
</units>
<units name="micrometer_cubed">
<unit exponent="3" units="micrometer"/>
</units>
<units name="nM">
<unit exponent="-1" units="micrometer_cubed"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="hour"/>
<variable initial_value="0.1" name="beta" units="per_hour"/>
<variable initial_value="0.0000001" name="gamma" units="per_molecules_per_hour"/>
<variable initial_value="79000" name="tau" units="molecules_per_hour"/>
<variable initial_value="0.05" name="rho" units="per_hour"/>
<variable initial_value="0.02" name="delta" units="per_hour"/>
<variable initial_value="12" name="eta" units="per_hour"/>
<variable initial_value="0.65" name="kappa" units="per_hour"/>
<variable initial_value="250000" name="G_tot" units="molecules"/>
<variable name="Q" units="per_hour2"/>
<variable name="QQ" units="per_hour4"/>
<variable initial_value="AB_SS" name="AB" units="molecules"/>
<variable name="AB_SS" units="molecules"/>
<variable initial_value="Reelin_SS" name="Reelin" units="molecules"/>
<variable name="Reelin_SS" units="molecules"/>
<variable initial_value="ABR_SS" name="ABR" units="molecules"/>
<variable name="ABR_SS" units="molecules"/>
<variable initial_value="GSK3Bp_SS" name="GSK3Bp" units="molecules"/>
<variable name="GSK3Bp_SS" units="molecules"/>
<variable initial_value="50" name="period_1" units="hour"/>
<variable initial_value="170" name="period_2" units="hour"/>
<variable name="alpha" units="molecules_per_hour"/>
<variable initial_value="109000" name="alpha_infection" units="molecules_per_hour"/>
<variable initial_value="4680" name="alpha_initial" units="molecules_per_hour"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha</ci>
<piecewise>
<piece>
<ci>alpha_initial</ci>
<apply>
<lt/>
<ci>t</ci>
<ci>period_1</ci>
</apply>
</piece>
<piece>
<ci>alpha_infection</ci>
<apply>
<lt/>
<ci>t</ci>
<ci>period_2</ci>
</apply>
</piece>
<otherwise>
<ci>alpha_initial</ci>
</otherwise>
</piecewise>
</apply>
<!--Steady state-->
<apply>
<eq/>
<ci>Q</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>gamma</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<times/>
<ci>beta</ci>
<ci>rho</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<times/>
<ci>gamma</ci>
<ci>tau</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>beta</ci>
<ci>gamma</ci>
<ci>rho</ci>
</apply>
<apply>
<times/>
<ci>alpha_initial</ci>
<apply>
<power/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>tau</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>gamma</ci>
<ci>rho</ci>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>QQ</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>G_tot</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>gamma</ci>
<apply>
<power/>
<ci>kappa</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>rho</ci>
</apply>
<apply>
<times/>
<ci>G_tot</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>eta</ci>
<ci>gamma</ci>
<ci>kappa</ci>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>eta</ci>
<ci>kappa</ci>
<ci>rho</ci>
</apply>
</apply>
<apply>
<times/>
<ci>eta</ci>
<ci>gamma</ci>
<ci>kappa</ci>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>beta</ci>
<apply>
<power/>
<ci>eta</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>AB_SS</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>rho</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>tau</ci>
</apply>
</apply>
<ci>Q</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
<ci>gamma</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Reelin_SS</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>alpha_initial</ci>
</apply>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>rho</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>tau</ci>
</apply>
<ci>Q</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>gamma</ci>
<ci>rho</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ABR_SS</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>rho</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>tau</ci>
</apply>
</apply>
<ci>Q</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>delta</ci>
<ci>gamma</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>GSK3Bp_SS</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>G_tot</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>eta</ci>
<ci>kappa</ci>
<ci>Q</ci>
</apply>
<apply>
<times/>
<ci>G_tot</ci>
<ci>eta</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>G_tot</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_initial</ci>
<ci>gamma</ci>
<ci>kappa</ci>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>kappa</ci>
<ci>rho</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>kappa</ci>
<ci>tau</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
<ci>eta</ci>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
<ci>QQ</ci>
</apply>
</apply>
<!--Transients-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AB</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>alpha</ci>
<apply>
<times/>
<ci>beta</ci>
<ci>AB</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>AB</ci>
<ci>Reelin</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Reelin</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>tau</ci>
<apply>
<times/>
<ci>rho</ci>
<ci>Reelin</ci>
</apply>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>AB</ci>
<ci>Reelin</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ABR</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>gamma</ci>
<ci>AB</ci>
<ci>Reelin</ci>
</apply>
<apply>
<times/>
<ci>delta</ci>
<ci>ABR</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>GSK3Bp</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>eta</ci>
<ci>Reelin</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>GSK3Bp</ci>
<ci>G_tot</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kappa</ci>
<ci>GSK3Bp</ci>
</apply>
</apply>
</apply>
</math>
<!--Putting eqns 2 & 3 to equilibrium-->
<variable name="Reelin_equil" units="molecules_per_hour"/>
<variable name="ABR_equil" units="molecules_per_hour"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Reelin_equil</ci>
<apply>
<divide/>
<ci>tau</ci>
<apply>
<plus/>
<ci>rho</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>AB</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ABR_equil</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>tau</ci>
<ci>delta</ci>
</apply>
<ci>AB</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<ci>rho</ci>
<ci>gamma</ci>
</apply>
<ci>AB</ci>
</apply>
</apply>
</apply>
</math>
<!--Express AB, Reelin & ABR as concentrations and normalise GSK3Bp-->
<variable initial_value="4846" name="volume" units="micrometer_cubed"/>
<variable name="AB_conc" units="nM"/>
<variable name="Reelin_conc" units="nM"/>
<variable name="ABR_conc" units="nM"/>
<variable name="GSK3Bp_norm" units="molecules"/>
<variable initial_value="0.6023" name="A_N" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>AB_conc</ci>
<apply>
<divide/>
<ci>AB</ci>
<apply>
<times/>
<ci>volume</ci>
<ci>A_N</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Reelin_conc</ci>
<apply>
<divide/>
<ci>Reelin</ci>
<apply>
<times/>
<ci>volume</ci>
<ci>A_N</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ABR_conc</ci>
<apply>
<divide/>
<ci>ABR</ci>
<apply>
<times/>
<ci>volume</ci>
<ci>A_N</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>GSK3Bp_norm</ci>
<apply>
<divide/>
<ci>GSK3Bp</ci>
<ci>G_tot</ci>
</apply>
</apply>
</math>
</component>
</model>