Location: Mitochondria regulate the amplitude of simple and complex calcium oscillations @ f78690e2f464 / grubelnik_2001_4b.cellml

Author:
Hanne Nielsen <hnie010@aucklanduni.ac.nz>
Date:
2011-09-26 13:51:05+13:00
Desc:
Added cellML models for 2a, 2b, 3a, 3b, 4a and 4b and clickable sessions.
Permanent Source URI:
https://models.physiomeproject.org/w/hnielsen/grubelnik_2001/rawfile/f78690e2f46454aa4ef277c8a5e8eabda2b8759c/grubelnik_2001_4b.cellml

<?xml version="1.0"?>
<!--
This CellML file was generated on 9/26/2011 at 10:02:50 at AM 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 xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="grubelnik_2001_4b" name="grubelnik_2001_4b">





   <units name="micromole">
      <unit prefix="micro" units="mole"/>
   </units>
   <units name="micromolar">
      <unit units="micromole"/>
      <unit exponent="-1" units="litre"/>
   </units>
   <units name="micromolar_per_minute">
      <unit units="micromolar"/>
      <unit exponent="-1" units="second"/>
   </units>
   <units name="per_micromolar_per_second">
      <unit exponent="-1" units="micromolar"/>
      <unit exponent="-1" units="second"/>
   </units>
   <units name="minute">
      <unit multiplier="60" units="second"/>
   </units>
   <units name="per_minute">
      <unit exponent="-1" units="minute"/>
   </units>
   <units name="per_second">
      <unit exponent="-1" units="second"/>
   </units>
   <component name="environment">
      <variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
   </component>
   <component name="Ca_m">
      <variable cmeta:id="Ca_m_Ca_m" initial_value="0.1" name="Ca_m" public_interface="out" units="micromolar"/>
      <variable name="J_min" public_interface="in" units="micromolar"/>
      <variable name="J_mout" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_m</ci>
            </apply>
            <apply>
               <minus/>
               <ci>J_min</ci>
               <ci>J_mout</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_min">
      <variable cmeta:id="J_min_J_min" name="J_min" public_interface="out" units="micromolar"/>
      <variable initial_value="330" name="k_min" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable initial_value="1.6" name="K_m" units="micromolar"/>
      <variable initial_value="8" name="n" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_min</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>k_min</ci>
                  <apply>
                     <power/>
                     <ci>Ca_cyt</ci>
                     <ci>n</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>K_m</ci>
                     <ci>n</ci>
                  </apply>
                  <apply>
                     <power/>
                     <ci>Ca_cyt</ci>
                     <ci>n</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_mout">
      <variable cmeta:id="J_mout_J_mout" name="J_mout" public_interface="out" units="micromolar"/>
      <variable initial_value="0.5" name="k_mout" units="micromolar"/>
      <variable name="Ca_m" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_mout</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>k_mout</ci>
                  <ci>Ca_m</ci>
               </apply>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micromolar">1</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_cyt">
      <variable cmeta:id="Ca_cyt_Ca_cyt" initial_value="0.01" name="Ca_cyt" public_interface="out" units="micromolar"/>
      <variable name="J_ERch" public_interface="in" units="micromolar"/>
      <variable name="J_ERpump" public_interface="in" units="micromolar"/>
      <variable name="J_ERleak" public_interface="in" units="micromolar"/>
      <variable name="J_CaPr" public_interface="in" units="micromolar"/>
      <variable name="J_Pr" public_interface="in" units="micromolar"/>
      <variable initial_value="0.01" name="rho_m" public_interface="out" units="dimensionless"/>
      <variable initial_value="0.025" name="beta_m" public_interface="out" units="dimensionless"/>
      <variable name="J_mout" public_interface="in" units="micromolar"/>
      <variable name="J_min" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_cyt</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <plus/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <apply>
                           <minus/>
                           <ci>J_ERch</ci>
                           <ci>J_ERpump</ci>
                        </apply>
                        <ci>J_ERleak</ci>
                        <ci>J_CaPr</ci>
                     </apply>
                     <ci>J_Pr</ci>
                  </apply>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <ci>rho_m</ci>
                        <ci>beta_m</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <ci>J_mout</ci>
                        <ci>J_min</ci>
                     </apply>
                  </apply>
               </apply>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_minute">1</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_tot">
      <variable cmeta:id="Ca_tot_Ca_tot" initial_value="0.01" name="Ca_tot" public_interface="out" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable name="Ca_ER" public_interface="in" units="micromolar"/>
      <variable name="rho_m" public_interface="in" units="dimensionless"/>
      <variable name="beta_m" public_interface="in" units="dimensionless"/>
      <variable name="rho_ER" public_interface="in" units="dimensionless"/>
      <variable name="beta_ER" public_interface="in" units="dimensionless"/>
      <variable name="Ca_m" public_interface="in" units="micromolar"/>
      <variable name="CaPr" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_tot</ci>
            </apply>
            <apply>
               <plus/>
               <ci>Ca_cyt</ci>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <ci>rho_ER</ci>
                     <ci>beta_ER</ci>
                  </apply>
                  <ci>Ca_ER</ci>
               </apply>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <ci>rho_m</ci>
                     <ci>beta_m</ci>
                  </apply>
                  <ci>Ca_m</ci>
               </apply>
               <ci>CaPr</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_ER">
      <variable cmeta:id="Ca_ER_Ca_ER" initial_value="20" name="Ca_ER" public_interface="out" units="micromolar"/>
      <variable initial_value="0.0025" name="beta_ER" public_interface="out" units="dimensionless"/>
      <variable initial_value="0.01" name="rho_ER" public_interface="out" units="dimensionless"/>
      <variable name="J_ERpump" public_interface="in" units="micromolar"/>
      <variable name="J_ERleak" public_interface="in" units="micromolar"/>
      <variable name="J_ERch" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_ER</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <ci>beta_ER</ci>
                  <ci>rho_ER</ci>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <minus/>
                     <ci>J_ERpump</ci>
                     <ci>J_ERleak</ci>
                  </apply>
                  <ci>J_ERch</ci>
               </apply>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_minute">1</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_ERch">
      <variable cmeta:id="J_ERch_J_ERch" name="J_ERch" public_interface="out" units="micromolar"/>
      <variable initial_value="0.001" name="k_ERch" units="micromolar"/>
      <variable initial_value="5" name="K_ch" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable name="Ca_ER" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_ERch</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>k_ERch</ci>
                     <apply>
                        <power/>
                        <ci>Ca_cyt</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>K_ch</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                     </apply>
                     <apply>
                        <power/>
                        <ci>Ca_cyt</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <ci>Ca_ER</ci>
                  <ci>Ca_cyt</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_ERpump">
      <variable cmeta:id="J_ERpump_J_ERpump" name="J_ERpump" public_interface="out" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable initial_value="20" name="k_ERpump" units="per_second"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_ERpump</ci>
            <apply>
               <times/>
               <ci>k_ERpump</ci>
               <ci>Ca_cyt</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_ERleak">
      <variable cmeta:id="J_ERleak_J_ERleak" name="J_ERleak" public_interface="out" units="micromolar"/>
      <variable initial_value="0.05" name="k_ERleak" units="per_second"/>
      <variable name="Ca_ER" public_interface="in" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_ERleak</ci>
            <apply>
               <times/>
               <ci>k_ERleak</ci>
               <apply>
                  <minus/>
                  <ci>Ca_ER</ci>
                  <ci>Ca_cyt</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_CaPr">
      <variable cmeta:id="J_CaPr_J_CaPr" name="J_CaPr" public_interface="out" units="micromolar"/>
      <variable initial_value="0.01" name="k_min" units="per_second"/>
      <variable name="CaPr" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_CaPr</ci>
            <apply>
               <times/>
               <ci>k_min</ci>
               <ci>CaPr</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="J_Pr">
      <variable cmeta:id="J_Pr_J_Pr" name="J_Pr" public_interface="out" units="micromolar"/>
      <variable initial_value="0.1" name="k_plus" units="per_micromolar_per_second"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable name="Pr" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_Pr</ci>
            <apply>
               <times/>
               <ci>k_plus</ci>
               <ci>Ca_cyt</ci>
               <ci>Pr</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="CaPr">
      <variable cmeta:id="CaPr_CaPr" name="CaPr" public_interface="out" units="micromolar"/>
      <variable name="Ca_cyt" public_interface="in" units="micromolar"/>
      <variable name="rho_ER" public_interface="in" units="dimensionless"/>
      <variable name="beta_ER" public_interface="in" units="dimensionless"/>
      <variable name="Ca_ER" public_interface="in" units="micromolar"/>
      <variable initial_value="90" name="Ca_tot" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>CaPr</ci>
            <apply>
               <minus/>
               <ci>Ca_tot</ci>
               <apply>
                  <plus/>
                  <ci>Ca_cyt</ci>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <ci>rho_ER</ci>
                        <ci>beta_ER</ci>
                     </apply>
                     <ci>Ca_ER</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Pr">
      <variable cmeta:id="Pr_Pr" name="Pr" public_interface="out" units="micromolar"/>
      <variable initial_value="120" name="Pr_tot" units="micromolar"/>
      <variable name="CaPr" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Pr</ci>
            <apply>
               <minus/>
               <ci>Pr_tot</ci>
               <ci>CaPr</ci>
            </apply>
         </apply>
      </math>
   </component>
   <connection>
      <map_components component_1="environment" component_2="Ca_tot"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="Ca_m"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_min"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_mout"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="Ca_cyt"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="Ca_ER"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_ERch"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_ERpump"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_ERleak"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_CaPr"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="J_Pr"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="CaPr"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="Pr"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_ERch"/>
      <map_variables variable_1="J_ERch" variable_2="J_ERch"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_ERpump"/>
      <map_variables variable_1="J_ERpump" variable_2="J_ERpump"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_ERleak"/>
      <map_variables variable_1="J_ERleak" variable_2="J_ERleak"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_CaPr"/>
      <map_variables variable_1="J_CaPr" variable_2="J_CaPr"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_Pr"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
      <map_variables variable_1="J_Pr" variable_2="J_Pr"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="CaPr"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="Ca_tot"/>
      <map_variables variable_1="rho_m" variable_2="rho_m"/>
      <map_variables variable_1="beta_m" variable_2="beta_m"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_min"/>
      <map_variables variable_1="J_min" variable_2="J_min"/>
      <map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
   </connection>
   <connection>
      <map_components component_1="Ca_cyt" component_2="J_mout"/>
      <map_variables variable_1="J_mout" variable_2="J_mout"/>
   </connection>
   <connection>
      <map_components component_1="CaPr" component_2="Pr"/>
      <map_variables variable_1="CaPr" variable_2="CaPr"/>
   </connection>
   <connection>
      <map_components component_1="Ca_ER" component_2="J_ERpump"/>
      <map_variables variable_1="J_ERpump" variable_2="J_ERpump"/>
   </connection>
   <connection>
      <map_components component_1="Ca_ER" component_2="CaPr"/>
      <map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
      <map_variables variable_1="rho_ER" variable_2="rho_ER"/>
      <map_variables variable_1="beta_ER" variable_2="beta_ER"/>
   </connection>
   <connection>
      <map_components component_1="Ca_ER" component_2="J_ERch"/>
      <map_variables variable_1="J_ERch" variable_2="J_ERch"/>
      <map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
   </connection>
   <connection>
      <map_components component_1="Pr" component_2="J_Pr"/>
      <map_variables variable_1="Pr" variable_2="Pr"/>
   </connection>
   <connection>
      <map_components component_1="CaPr" component_2="J_CaPr"/>
      <map_variables variable_1="CaPr" variable_2="CaPr"/>
   </connection>
   <connection>
      <map_components component_1="CaPr" component_2="Ca_tot"/>
      <map_variables variable_1="CaPr" variable_2="CaPr"/>
   </connection>
   <connection>
      <map_components component_1="Ca_m" component_2="Ca_tot"/>
      <map_variables variable_1="Ca_m" variable_2="Ca_m"/>
   </connection>
   <connection>
      <map_components component_1="Ca_m" component_2="J_mout"/>
      <map_variables variable_1="Ca_m" variable_2="Ca_m"/>
      <map_variables variable_1="J_mout" variable_2="J_mout"/>
   </connection>
   <connection>
      <map_components component_1="Ca_m" component_2="J_min"/>
      <map_variables variable_1="J_min" variable_2="J_min"/>
   </connection>
   <connection>
      <map_components component_1="Ca_ER" component_2="Ca_tot"/>
      <map_variables variable_1="rho_ER" variable_2="rho_ER"/>
      <map_variables variable_1="beta_ER" variable_2="beta_ER"/>
      <map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
   </connection>
   <connection>
      <map_components component_1="J_ERleak" component_2="Ca_ER"/>
      <map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
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