Location: SLC transporters @ cc67d4f5117e / Facilitated transporter / CellMLV2 / GLUT1_ss_io.cellml

Author:
Weiwei Ai <wai484@aucklanduni.ac.nz>
Date:
2024-04-06 11:32:22+13:00
Desc:
correct the units; Add the model with the parameters converted from kinetic models
Permanent Source URI:
https://models.physiomeproject.org/workspace/b65/rawfile/cc67d4f5117e49e550b0fed51e40854609d05eae/Facilitated transporter/CellMLV2/GLUT1_ss_io.cellml

<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/2.0#" name="GLUT1_BG">
  <import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="params_BG_fit_ss_io.cellml">
    <component component_ref="params_BG" name="params_BG"/>
  </import>
  <import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="./units.cellml">
    <units units_ref="fmol" name="fmol"/>
    <units units_ref="J_per_K_mol" name="J_per_K_mol"/>
    <units units_ref="fmol_per_s" name="fmol_per_s"/>
    <units units_ref="J_per_mol" name="J_per_mol"/>
    <units units_ref="per_fmol" name="per_fmol"/>
  </import>
  <component name="GLUT1_BG">
    <variable name="t" units="second" interface="public"/>
    <variable name="K_Ai" units="per_fmol" interface="public"/>
    <variable name="K_Ao" units="per_fmol" interface="public"/>
    <variable name="K_1" units="per_fmol" interface="public"/>
    <variable name="K_2" units="per_fmol" interface="public"/>
    <variable name="K_3" units="per_fmol" interface="public"/>
    <variable name="K_4" units="per_fmol" interface="public"/>
    <variable name="kappa_r1" units="fmol_per_s" interface="public"/>
    <variable name="kappa_r2" units="fmol_per_s" interface="public"/>
    <variable name="kappa_r3" units="fmol_per_s" interface="public"/>
    <variable name="kappa_r4" units="fmol_per_s" interface="public"/>
    <variable name="q_Ai" units="fmol" interface="public"/>
    <variable name="q_Ao" units="fmol" interface="public"/>
    <variable name="lambda" units="dimensionless"/>
    <variable name="q_tot" units="fmol" interface="public"/>
    <variable name="v_max" units="fmol_per_s"/>
    <variable name="k_m_1" units="dimensionless"/>
    <variable name="k_m_2" units="dimensionless"/>
    <variable name="k_m_3" units="dimensionless"/>
    <variable name="v" units="fmol_per_s"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:cellml="http://www.cellml.org/cellml/2.0#">
      <apply>
        <eq/>
        <ci>lambda</ci>
        <apply>
          <divide/>
          <ci>kappa_r2</ci>
          <ci>kappa_r1</ci>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>v_max</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>q_tot</ci>
            <ci>kappa_r2</ci>
            <ci>K_3</ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_1</ci>
            </apply>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_4</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>k_m_1</ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_1</ci>
            </apply>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_4</ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_2</ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>lambda</ci>
                <ci>K_3</ci>
              </apply>
              <ci>K_4</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>k_m_2</ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_1</ci>
            </apply>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_4</ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless">1</cn>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>lambda</ci>
                <ci>K_3</ci>
              </apply>
              <ci>K_1</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>k_m_3</ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_1</ci>
            </apply>
            <apply>
              <divide/>
              <ci>K_3</ci>
              <ci>K_4</ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci>lambda</ci>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless">1</cn>
              <apply>
                <divide/>
                <ci>K_3</ci>
                <ci>K_2</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>v</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>v_max</ci>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci>K_Ao</ci>
                <ci>q_Ao</ci>
              </apply>
              <apply>
                <times/>
                <ci>K_Ai</ci>
                <ci>q_Ai</ci>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless">1</cn>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>K_Ao</ci>
                <ci>q_Ao</ci>
              </apply>
              <ci>k_m_1</ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>K_Ai</ci>
                <ci>q_Ai</ci>
              </apply>
              <ci>k_m_2</ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>K_Ao</ci>
                <ci>q_Ao</ci>
                <ci>K_Ai</ci>
                <ci>q_Ai</ci>
              </apply>
              <ci>k_m_3</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <connection component_1="params_BG" component_2="GLUT1_BG">
    <map_variables variable_1="t" variable_2="t"/>
    <map_variables variable_1="K_Ai" variable_2="K_Ai"/>
    <map_variables variable_1="K_Ao" variable_2="K_Ao"/>
    <map_variables variable_1="K_1" variable_2="K_1"/>
    <map_variables variable_1="K_2" variable_2="K_2"/>
    <map_variables variable_1="K_3" variable_2="K_3"/>
    <map_variables variable_1="q_init_Ai" variable_2="q_Ai"/>
    <map_variables variable_1="q_init_Ao" variable_2="q_Ao"/>
    <map_variables variable_1="K_4" variable_2="K_4"/>
    <map_variables variable_1="E" variable_2="q_tot"/>
    <map_variables variable_1="kappa_r1" variable_2="kappa_r1"/>
    <map_variables variable_1="kappa_r2" variable_2="kappa_r2"/>
    <map_variables variable_1="kappa_r3" variable_2="kappa_r3"/>
    <map_variables variable_1="kappa_r4" variable_2="kappa_r4"/>
  </connection>
</model>