Location: Terkildsen, Niederer, Crampin, Hunter, Smith, 2008 @ a471aae70edb / Niederer_et_al_2006.cellml

Author:
AnandR <a.rampadarath@auckland.ac.nz>
Date:
2018-12-14 16:04:47+13:00
Desc:
Annotated models using Semgen
Permanent Source URI:
https://models.physiomeproject.org/workspace/55c/rawfile/a471aae70edb5e9f955c60046d52c99d87e69b44/Niederer_et_al_2006.cellml

<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="file:///H:/terkildsen_niederer_crampin_hunter_smith_2008/Niederer_et_al_2006.cellml" cmeta:id="Niederer_et_al_2006" name="Niederer_et_al_2006">


   <units name="per_ms">
      <unit exponent="-1" prefix="milli" units="second"/>
   </units>
   <units name="ms">
      <unit prefix="milli" units="second"/>
   </units>
   <units name="mM">
      <unit prefix="milli" units="mole"/>
      <unit exponent="-1" units="litre"/>
   </units>
   <units name="N_per_mm2">
      <unit units="newton"/>
      <unit exponent="-2" prefix="milli" units="metre"/>
   </units>
   <units name="per_mM_per_ms">
      <unit exponent="-1" units="mM"/>
      <unit exponent="-1" prefix="milli" units="second"/>
   </units>
   <units name="mM_per_ms">
      <unit units="mM"/>
      <unit exponent="-1" prefix="milli" units="second"/>
   </units>


   <component name="environment">
      <variable name="time" public_interface="out" units="ms"/>
   </component>


   <component cmeta:id="id_00003" name="intracellular_ion_concentrations">
      <variable name="time" public_interface="in" units="ms"/>
      <variable cmeta:id="id_00001" name="Ca_i" public_interface="out" units="mM"/>
      <variable cmeta:id="id_00002" name="Ca_b" public_interface="out" units="mM"/>
      <variable cmeta:id="id_00004" initial_value="0.067593139865" name="TRPN" public_interface="out" units="mM"/>
      <variable cmeta:id="id_00005" name="Ca_TRPN_Max" public_interface="in" units="mM"/>
      <variable cmeta:id="id_00006" name="J_TRPN" public_interface="in" units="mM_per_ms"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Ca_b</ci>
            <apply>
               <minus/>
               <ci>Ca_TRPN_Max</ci>
               <ci>TRPN</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>TRPN</ci>
            </apply>
            <ci>J_TRPN</ci>
         </apply>
         <apply>
            <eq/>
            <ci>Ca_i</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <cn type="e-notation" cellml:units="mM">1.8433<sep/>-7</cn>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>time</ci>
                     <cn cellml:units="ms">1</cn>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <apply>
                              <minus/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">1.055</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">3</cn>
                                 </apply>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.03507</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.0003992</cn>
                                 <ci>time</ci>
                              </apply>
                              <cn cellml:units="ms">1000</cn>
                           </apply>
                        </apply>
                        <cn type="e-notation" cellml:units="mM">1.356<sep/>-6</cn>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <geq/>
                        <ci>time</ci>
                        <cn cellml:units="ms">10</cn>
                     </apply>
                     <apply>
                        <lt/>
                        <ci>time</ci>
                        <cn cellml:units="ms">15</cn>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <apply>
                              <minus/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.014</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">3</cn>
                                 </apply>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.002555</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.0001494</cn>
                                 <ci>time</ci>
                              </apply>
                              <cn cellml:units="ms">1000</cn>
                           </apply>
                        </apply>
                        <cn type="e-notation" cellml:units="mM">1.428<sep/>-6</cn>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <geq/>
                        <ci>time</ci>
                        <cn cellml:units="ms">15</cn>
                     </apply>
                     <apply>
                        <lt/>
                        <ci>time</ci>
                        <cn cellml:units="ms">55</cn>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <apply>
                        <plus/>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <apply>
                                 <times/>
                                 <cn type="e-notation" cellml:units="mM">1.739<sep/>-5</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">3</cn>
                                 </apply>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn type="e-notation" cellml:units="mM">3.209<sep/>-6</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn type="e-notation" cellml:units="mM">5.689<sep/>-6</cn>
                                 <ci>time</ci>
                              </apply>
                              <cn cellml:units="ms">1000</cn>
                           </apply>
                        </apply>
                        <cn type="e-notation" cellml:units="mM">1.719<sep/>-6</cn>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <geq/>
                        <ci>time</ci>
                        <cn cellml:units="ms">55</cn>
                     </apply>
                     <apply>
                        <lt/>
                        <ci>time</ci>
                        <cn cellml:units="ms">250</cn>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <apply>
                        <plus/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <apply>
                                 <minus/>
                                 <apply>
                                    <times/>
                                    <cn cellml:units="mM">0.0001321</cn>
                                    <apply>
                                       <power/>
                                       <apply>
                                          <divide/>
                                          <ci>time</ci>
                                          <cn cellml:units="ms">1000</cn>
                                       </apply>
                                       <cn cellml:units="dimensionless">4</cn>
                                    </apply>
                                 </apply>
                                 <apply>
                                    <times/>
                                    <cn cellml:units="mM">0.0002197</cn>
                                    <apply>
                                       <power/>
                                       <apply>
                                          <divide/>
                                          <ci>time</ci>
                                          <cn cellml:units="ms">1000</cn>
                                       </apply>
                                       <cn cellml:units="dimensionless">3</cn>
                                    </apply>
                                 </apply>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn cellml:units="mM">0.0001374</cn>
                                 <apply>
                                    <power/>
                                    <apply>
                                       <divide/>
                                       <ci>time</ci>
                                       <cn cellml:units="ms">1000</cn>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn type="e-notation" cellml:units="mM">3.895<sep/>-5</cn>
                                 <ci>time</ci>
                              </apply>
                              <cn cellml:units="ms">1000</cn>
                           </apply>
                        </apply>
                        <cn type="e-notation" cellml:units="mM">4.441<sep/>-6</cn>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <geq/>
                        <ci>time</ci>
                        <cn cellml:units="ms">250</cn>
                     </apply>
                     <apply>
                        <lt/>
                        <ci>time</ci>
                        <cn cellml:units="ms">490</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1000</cn>
                     <cn type="e-notation" cellml:units="mM">1.2148<sep/>-7</cn>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00007" name="thinfilaments"/>
   <component cmeta:id="id_00008" name="tropomyosin">
      <variable initial_value="0.014417937837" name="z" public_interface="out" units="dimensionless"/>
      <variable name="z_max" public_interface="out" units="dimensionless"/>
      <variable name="time" public_interface="in" units="ms"/>
      <variable name="k_on" public_interface="in" units="per_mM_per_ms"/>
      <variable name="k_Ref_off" public_interface="in" units="per_ms"/>
      <variable cmeta:id="id_00009" name="gamma_trpn" public_interface="in" units="dimensionless"/>
      <variable cmeta:id="id_00011" name="Ca_TRPN_Max" public_interface="in" units="mM"/>
      <variable initial_value="8e-3" name="alpha_0" units="per_ms"/>
      <variable initial_value="2e-3" name="alpha_r1" units="per_ms"/>
      <variable initial_value="1.75e-3" name="alpha_r2" units="per_ms"/>
      <variable initial_value="3" name="n_Rel" units="dimensionless"/>
      <variable initial_value="0.15" name="K_z" units="dimensionless"/>
      <variable initial_value="3" name="n_Hill" units="dimensionless"/>
      <variable initial_value="1.05e-3" name="Ca_50ref" units="mM"/>
      <variable initial_value="0.85" name="z_p" units="dimensionless"/>
      <variable initial_value="-4" name="beta_1" units="dimensionless"/>
      <variable name="Ca_50" units="mM"/>
      <variable cmeta:id="id_00010" name="Ca_TRPN_50" units="mM"/>
      <variable name="K_2" units="per_ms"/>
      <variable name="K_1" units="per_ms"/>
      <variable name="alpha_Tm" units="per_ms"/>
      <variable name="beta_Tm" units="per_ms"/>
      <variable name="beta_0" public_interface="in" units="dimensionless"/>
      <variable name="Ca_b" public_interface="in" units="mM"/>
      <variable name="lambda" public_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>K_2</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>alpha_r2</ci>
                     <apply>
                        <power/>
                        <ci>z_p</ci>
                        <ci>n_Rel</ci>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>z_p</ci>
                        <ci>n_Rel</ci>
                     </apply>
                     <apply>
                        <power/>
                        <ci>K_z</ci>
                        <ci>n_Rel</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>n_Rel</ci>
                        <apply>
                           <power/>
                           <ci>K_z</ci>
                           <ci>n_Rel</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <power/>
                           <ci>z_p</ci>
                           <ci>n_Rel</ci>
                        </apply>
                        <apply>
                           <power/>
                           <ci>K_z</ci>
                           <ci>n_Rel</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>K_1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>alpha_r2</ci>
                  <apply>
                     <power/>
                     <ci>z_p</ci>
                     <apply>
                        <minus/>
                        <ci>n_Rel</ci>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
                  <ci>n_Rel</ci>
                  <apply>
                     <power/>
                     <ci>K_z</ci>
                     <ci>n_Rel</ci>
                  </apply>
               </apply>
               <apply>
                  <power/>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>z_p</ci>
                        <ci>n_Rel</ci>
                     </apply>
                     <apply>
                        <power/>
                        <ci>K_z</ci>
                        <ci>n_Rel</ci>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>z_max</ci>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <divide/>
                     <ci>alpha_0</ci>
                     <apply>
                        <power/>
                        <apply>
                           <divide/>
                           <ci>Ca_TRPN_50</ci>
                           <ci>Ca_TRPN_Max</ci>
                        </apply>
                        <ci>n_Hill</ci>
                     </apply>
                  </apply>
                  <ci>K_2</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>alpha_r1</ci>
                  <ci>K_1</ci>
                  <apply>
                     <divide/>
                     <ci>alpha_0</ci>
                     <apply>
                        <power/>
                        <apply>
                           <divide/>
                           <ci>Ca_TRPN_50</ci>
                           <ci>Ca_TRPN_Max</ci>
                        </apply>
                        <ci>n_Hill</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Ca_50</ci>
            <apply>
               <times/>
               <ci>Ca_50ref</ci>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <ci>beta_1</ci>
                     <apply>
                        <minus/>
                        <ci>lambda</ci>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Ca_TRPN_50</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>Ca_50</ci>
                  <ci>Ca_TRPN_Max</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>Ca_50</ci>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <ci>k_Ref_off</ci>
                        <ci>k_on</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <cn cellml:units="dimensionless">1</cn>
                                 <apply>
                                    <times/>
                                    <ci>beta_0</ci>
                                    <apply>
                                       <minus/>
                                       <ci>lambda</ci>
                                       <cn cellml:units="dimensionless">1</cn>
                                    </apply>
                                 </apply>
                              </apply>
                              <cn cellml:units="dimensionless">0.5</cn>
                           </apply>
                           <ci>gamma_trpn</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_Tm</ci>
            <apply>
               <times/>
               <ci>alpha_0</ci>
               <apply>
                  <power/>
                  <apply>
                     <divide/>
                     <ci>Ca_b</ci>
                     <ci>Ca_TRPN_50</ci>
                  </apply>
                  <ci>n_Hill</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_Tm</ci>
            <apply>
               <plus/>
               <ci>alpha_r1</ci>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>alpha_r2</ci>
                     <apply>
                        <power/>
                        <ci>z</ci>
                        <apply>
                           <minus/>
                           <ci>n_Rel</ci>
                           <cn cellml:units="dimensionless">1</cn>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>z</ci>
                        <ci>n_Rel</ci>
                     </apply>
                     <apply>
                        <power/>
                        <ci>K_z</ci>
                        <ci>n_Rel</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>z</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_Tm</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>z</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_Tm</ci>
                  <ci>z</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00012" name="troponin">
      <variable cmeta:id="id_00013" name="J_TRPN" public_interface="out" units="mM_per_ms"/>
      <variable cmeta:id="id_00014" initial_value="70e-3" name="Ca_TRPN_Max" public_interface="out" units="mM"/>
      <variable cmeta:id="id_00015" name="TRPN" public_interface="in" units="mM"/>
      <variable name="Ca_i" public_interface="in" units="mM"/>
      <variable name="k_off" units="per_ms"/>
      <variable initial_value="100" name="k_on" public_interface="out" units="per_mM_per_ms"/>
      <variable initial_value="0.2" name="k_Ref_off" public_interface="out" units="per_ms"/>
      <variable initial_value="2" name="gamma_trpn" public_interface="out" units="dimensionless"/>
      <variable name="Tension" public_interface="in" units="N_per_mm2"/>
      <variable name="T_ref" public_interface="in" units="N_per_mm2"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>k_off</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <ci>k_Ref_off</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <ci>Tension</ci>
                           <apply>
                              <times/>
                              <ci>gamma_trpn</ci>
                              <ci>T_ref</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <gt/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <ci>Tension</ci>
                           <apply>
                              <times/>
                              <ci>gamma_trpn</ci>
                              <ci>T_ref</ci>
                           </apply>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">0.1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <times/>
                     <ci>k_Ref_off</ci>
                     <cn cellml:units="dimensionless">0.1</cn>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>J_TRPN</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <ci>Ca_TRPN_Max</ci>
                     <ci>TRPN</ci>
                  </apply>
                  <ci>k_off</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>Ca_i</ci>
                  <ci>TRPN</ci>
                  <ci>k_on</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00016" name="Myofilaments">
      <variable name="time" public_interface="in" units="ms"/>
      <variable name="lambda" public_interface="out" units="dimensionless"/>
      <variable name="ExtensionRatio" public_interface="out" units="dimensionless"/>
      <variable name="dExtensionRatiodt" public_interface="out" units="per_ms"/>
      <variable name="lambda_prev" public_interface="out" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>ExtensionRatio</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <gt/>
                     <ci>time</ci>
                     <cn type="e-notation" cellml:units="ms">3<sep/>5</cn>
                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="dimensionless">1</cn>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>lambda_prev</ci>
            <ci>ExtensionRatio</ci>
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