Location: The Glucose-induced Switch Between Glycogen Phosphorylase and Glycogen Synthase in the Liver: Outlines of a Theoretical Approach @ 77d0fefb599a / cardenas_1996_four_equations.cellml

Author:
Hanne Nielsen <hnie010@aucklanduni.ac.nz>
Date:
2011-08-10 13:56:39+12:00
Desc:
Added image to HTML file
Permanent Source URI:
https://staging.physiomeproject.org/w/hnielsen/cardenas_1996/rawfile/77d0fefb599af9836fcebffcd9b5138c2476b2af/cardenas_1996_four_equations.cellml

<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 8/4/2011 at 2:09:09 at PM using:

COR (0.9.31.1409)
Copyright 2002-2011 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk

CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
<model name="cardenas_1996" cmeta:id="cardenas_1996" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
   <units name="millimole">
      <unit units="mole" prefix="milli"/>
   </units>
   <units name="millimolar">
      <unit units="millimole"/>
      <unit units="litre" exponent="-1"/>
   </units>
   <units name="minute">
      <unit units="second" multiplier="60"/>
   </units>
   <units name="per_minute">
      <unit units="minute" exponent="-1"/>
   </units>
   <units name="millimolar_per_minute">
      <unit units="millimolar"/>
      <unit units="minute" exponent="-1"/>
   </units>
   <component name="environment">
      <variable name="time" units="minute" public_interface="out"/>
   </component>
   <component name="Pha">
      <variable name="Pha" units="millimolar" initial_value="0.845" public_interface="out"/>
      <variable name="V_1" units="per_minute" initial_value="1.25"/>
      <variable name="K_1" units="dimensionless" initial_value="0.1" public_interface="out"/>
      <variable name="K_2" units="dimensionless" initial_value="0.2"/>
      <variable name="V_M2" units="per_minute" initial_value="0.22"/>
      <variable name="alpha" units="dimensionless" initial_value="9"/>
      <variable name="GLC" units="millimolar" public_interface="in"/>
      <variable name="K_a1" units="millimolar" initial_value="10"/>
      <variable name="K_a2" units="millimolar" initial_value="10"/>
      <variable name="time" units="minute" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Pha</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>V_1</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>Pha</ci>
                     </apply>
                  </apply>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>K_1</ci>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                     <ci>Pha</ci>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>V_M2</ci>
  <ci>Pha</ci>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <ci>alpha</ci>
                              <ci>GLC</ci>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>K_a1</ci>
                              <ci>GLC</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <divide/>
                        <ci>K_2</ci>
                        <apply>
                           <plus/>
                           <cn cellml:units="dimensionless">1</cn>
                           <apply>
                              <divide/>
                              <ci>GLC</ci>
                              <ci>K_a2</ci>
                           </apply>
                        </apply>
                     </apply>
                     <ci>Pha</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="GSa">
      <variable name="GSa" units="millimolar" initial_value="0.02"/>
      <variable name="Pha" units="millimolar" public_interface="in"/>
      <variable name="V_M3" units="per_minute" initial_value="0.05"/>
      <variable name="beta" units="dimensionless" initial_value="9"/>
      <variable name="G6P" units="millimolar" public_interface="in"/>
      <variable name="K_a3" units="millimolar" initial_value="0.5"/>
      <variable name="K_1" units="dimensionless" public_interface="in"/>
      <variable name="K_3" units="dimensionless" initial_value="0.4"/>
      <variable name="K_4" units="dimensionless" initial_value="0.4"/>
      <variable name="K_a4" units="millimolar" initial_value="0.5"/>
      <variable name="V_4" units="per_minute" initial_value="0.2"/>
      <variable name="time" units="minute" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>GSa</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>V_M3</ci>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <ci>beta</ci>
                              <ci>G6P</ci>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>K_a3</ci>
                              <ci>G6P</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <divide/>
                           <ci>K_1</ci>
                           <apply>
                              <plus/>
                              <ci>K_1</ci>
                              <ci>Pha</ci>
                           </apply>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="dimensionless">1</cn>
                           <ci>GSa</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <apply>
                           <divide/>
                           <ci>K_3</ci>
                           <apply>
                              <plus/>
                              <cn cellml:units="dimensionless">1</cn>
                              <apply>
                                 <divide/>
                                 <ci>G6P</ci>
                                 <ci>K_a4</ci>
                              </apply>
                           </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                     <ci>GSa</ci>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>V_4</ci>
                     <ci>GSa</ci>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>K_4</ci>
                     <apply>
                        <times/>
                        <ci>GSa</ci>
                        <cn cellml:units="per_minute">1</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="GLC">
      <variable name="GLC" units="millimolar" initial_value="5" public_interface="out"/>
      <variable name="k5" units="millimolar_per_minute" initial_value="2.75"/>
      <variable name="time" units="minute" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>GLC</ci>
            </apply>
            <ci>k5</ci>
         </apply>
      </math>
   </component>
   <component name="G6P">
      <variable name="G6P" units="millimolar" initial_value="0.1" public_interface="out"/>
      <variable name="k6" units="millimolar_per_minute" initial_value="0.03"/>
      <variable name="time" units="minute" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>G6P</ci>
            </apply>
            <ci>k6</ci>
         </apply>
      </math>
   </component>
   <connection>
      <map_components component_1="environment" component_2="Pha"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="GSa"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="GLC"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="G6P"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="Pha" component_2="GSa"/>
      <map_variables variable_1="K_1" variable_2="K_1"/>
      <map_variables variable_1="Pha" variable_2="Pha"/>
   </connection>
   <connection>
      <map_components component_1="Pha" component_2="GLC"/>
      <map_variables variable_1="GLC" variable_2="GLC"/>
   </connection>
   <connection>
      <map_components component_1="G6P" component_2="GSa"/>
      <map_variables variable_1="G6P" variable_2="G6P"/>
   </connection>
</model>