<?xml version="1.0" encoding="iso-8859-1"?>

<model
    name="TNNP_extended_IK1"
    cmeta:id="TNNP_extended_IK1"
    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#"
    xmlns:xlink="http://www.w3.org/1999/xlink">
  <rdf:RDF
      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
      xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
      xmlns:bqs="http://www.cellml.org/bqs/1.0#"
      xmlns:dc="http://purl.org/dc/elements/1.1/"
      xmlns:dcterms="http://purl.org/dc/terms/"
      xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
    <rdf:Description rdf:about="">
      <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Nickerson</vCard:Family>
          <vCard:Given>David</vCard:Given>
        </vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>david.nickerson@nus.edu.sg</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
        </vCard:EMAIL>
        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>National University of Singapore</vCard:Orgname>
          <vCard:Orgunit>Division of Bioengineering</vCard:Orgunit>
        </vCard:ORG>
      </dc:creator>
      <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2006-11-23</dcterms:W3CDTF>
      </dcterms:created>
      <dc:publisher>
        Division of Bioengineering, National University of Singapore
      </dc:publisher>
    </rdf:Description>
    <rdf:Description rdf:about="#TNNP_extended_IK1">
      <dc:title>
        Various formulations for the pH dependence of the IK1 current.
      </dc:title>
    </rdf:Description>
  </rdf:RDF>
  
  <import xlink:href="../../../../cellml/models/common/units.xml">
    <units name="mV" units_ref="mV"/>
    <units name="mM" units_ref="mM"/>
    <units name="uA_per_mmsq" units_ref="uA_per_mmsq"/>
    <units name="mS_per_mmsq" units_ref="mS_per_mmsq"/>
  </import>
  <import xlink:href="../../../../cellml/models/2004_tenTusscher-version-2/components/IK1.xml">
    <component name="IK1_original" component_ref="IK1"/>
  </import>
  
  <component name="IK1_Ito" cmeta:id="IK1_Ito">
    <rdf:RDF
      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
      xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
      xmlns:bqs="http://www.cellml.org/bqs/1.0#"
      xmlns:dc="http://purl.org/dc/elements/1.1/"
      xmlns:dcterms="http://purl.org/dc/terms/"
      xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
      <rdf:Description rdf:about="#IK1_Ito">
        <dc:title>
          Ito et al. (1992) formulation of pH dependence of IK1.
        </dc:title>
        <cmeta:species>guinea pig</cmeta:species>
        <cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
        <bqs:reference rdf:parseType="Resource">
          <bqs:Pubmed_id>1336853</bqs:Pubmed_id>
          <bqs:JournalArticle rdf:parseType="Resource">
            <dc:creator>
              <rdf:Seq>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Ito</vCard:Family>
                      <vCard:Given>Hiroyuki</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Vereecke</vCard:Family>
                      <vCard:Given>Johan</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Carmeliet</vCard:Family>
                      <vCard:Given>Edward</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
              </rdf:Seq>
            </dc:creator>
            <dc:title>
              Intracellular protons inhibit inward rectifier K+ channel of 
              guinea-pig ventricular cell membrane.
            </dc:title>
            <dcterms:issued rdf:parseType="Resource">
              <dcterms:W3CDTF>1992</dcterms:W3CDTF>
            </dcterms:issued>
            <bqs:Journal rdf:parseType="Resource">
              <dc:title>Pflugers Arch.</dc:title>
            </bqs:Journal>
            <bqs:volume>422</bqs:volume>
            <bqs:first_page>280</bqs:first_page>
            <bqs:last_page>286</bqs:last_page>
          </bqs:JournalArticle>
        </bqs:reference>
      </rdf:Description>
    </rdf:RDF>
    
    <variable cmeta:id="IK1" name="IK1" public_interface="out" units="uA_per_mmsq"/>

    <!-- variables used and defined by the original IK1 formulation -->
    <variable cmeta:id="IK1_original" name="IK1_original" private_interface="in" units="uA_per_mmsq"/>
    <variable name="g_K1" public_interface="in" private_interface="out" units="mS_per_mmsq"/>
    <variable name="Ko" public_interface="in" private_interface="out" units="mM"/>
    <variable name="V" public_interface="in" private_interface="out" units="mV"/>  
    <variable name="E_K" public_interface="in" private_interface="out" units="mV"/>
    
    <!-- variables for the pH dependence -->
    <variable name="H_i" public_interface="in" private_interface="out" units="mM"/>
    <variable name="K_half_NPo" public_interface="in" private_interface="out" units="mM"/>
    <variable name="H_NPo" public_interface="in" private_interface="out" units="dimensionless"/>
    <variable name="K_half_IK1max" public_interface="in" private_interface="out" units="mM"/>
    <variable name="H_IK1max" public_interface="in" private_interface="out" units="dimensionless"/>

    <!-- relative single channel current amplitude scale factor -->    
    <variable cmeta:id="IK1max" name="IK1max" units="dimensionless"/>
    <!-- relative channel open probability -->
    <variable cmeta:id="NPo" name="NPo" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq/>
        <ci>IK1max</ci>
        <apply><divide/>
          <cn cellml:units="dimensionless">1.0</cn>
          <apply><plus/>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply><power/>
              <apply><divide/>
                <ci>H_i</ci>
                <ci>K_half_IK1max</ci>
              </apply>
              <ci>H_IK1max</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply><eq/>
        <ci>NPo</ci>
        <apply><divide/>
          <cn cellml:units="dimensionless">1.0</cn>
          <apply><plus/>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply><power/>
              <apply><divide/>
                <ci>H_i</ci>
                <ci>K_half_NPo</ci>
              </apply>
              <ci>H_NPo</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply><eq/>
        <ci>IK1</ci>
        <apply><times/>
          <ci>IK1max</ci>
          <ci>NPo</ci>
          <ci>IK1_original</ci>
        </apply>
      </apply>
    </math>
  </component>  

  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="IK1_Ito">
      <component_ref component="IK1_original"/>
    </component_ref>
  </group>

  <connection>
    <map_components component_1="IK1_Ito" component_2="IK1_original"/>
    <map_variables variable_1="IK1_original" variable_2="IK1"/>
    <map_variables variable_1="g_K1" variable_2="g_K1"/>
    <map_variables variable_1="Ko" variable_2="Ko"/>
    <map_variables variable_1="V" variable_2="V"/>
    <map_variables variable_1="E_K" variable_2="E_K"/>
  </connection>
  
  <component name="IK1_Ito_new" cmeta:id="IK1_Ito_new">
    <rdf:RDF
            xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
            xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
            xmlns:bqs="http://www.cellml.org/bqs/1.0#"
            xmlns:dc="http://purl.org/dc/elements/1.1/"
            xmlns:dcterms="http://purl.org/dc/terms/"
            xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
      <rdf:Description rdf:about="#IK1_Ito_new">
        <dc:title>
          Ito et al. (1992) formulation of pH dependence of IK1.
        </dc:title>
        <cmeta:species>guinea pig</cmeta:species>
        <cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
        <bqs:reference rdf:parseType="Resource">
          <bqs:Pubmed_id>1336853</bqs:Pubmed_id>
          <bqs:JournalArticle rdf:parseType="Resource">
            <dc:creator>
              <rdf:Seq>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Ito</vCard:Family>
                      <vCard:Given>Hiroyuki</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Vereecke</vCard:Family>
                      <vCard:Given>Johan</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
                <rdf:li rdf:parseType="Resource">
                  <bqs:Person rdf:parseType="Resource">
                    <vCard:N rdf:parseType="Resource">
                      <vCard:Family>Carmeliet</vCard:Family>
                      <vCard:Given>Edward</vCard:Given>
                    </vCard:N>
                  </bqs:Person>
                </rdf:li>
              </rdf:Seq>
            </dc:creator>
            <dc:title>
              Intracellular protons inhibit inward rectifier K+ channel of 
              guinea-pig ventricular cell membrane.
            </dc:title>
            <dcterms:issued rdf:parseType="Resource">
              <dcterms:W3CDTF>1992</dcterms:W3CDTF>
            </dcterms:issued>
            <bqs:Journal rdf:parseType="Resource">
              <dc:title>Pflugers Arch.</dc:title>
            </bqs:Journal>
            <bqs:volume>422</bqs:volume>
            <bqs:first_page>280</bqs:first_page>
            <bqs:last_page>286</bqs:last_page>
          </bqs:JournalArticle>
        </bqs:reference>
      </rdf:Description>
    </rdf:RDF>
    
    <variable cmeta:id="IK1_new" name="IK1" public_interface="out" units="uA_per_mmsq"/>
    <variable cmeta:id="IK1_original_new" name="IK1_original" public_interface="in" private_interface="in" units="uA_per_mmsq"/>
    
    <!-- variables for the pH dependence -->
    <variable name="H_i" public_interface="in" private_interface="out" units="mM"/>
    <variable name="K_half_NPo" public_interface="in" private_interface="out" units="mM"/>
    <variable name="H_NPo" public_interface="in" private_interface="out" units="dimensionless"/>
    <variable name="K_half_IK1max" public_interface="in" private_interface="out" units="mM"/>
    <variable name="H_IK1max" public_interface="in" private_interface="out" units="dimensionless"/>
    
    <!-- relative single channel current amplitude scale factor -->    
    <variable cmeta:id="IK1max_new" name="IK1max" public_interface="out" private_interface="out" units="dimensionless"/>
    <!-- relative channel open probability -->
    <variable cmeta:id="NPo_new" name="NPo" public_interface="out" private_interface="out" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq/>
        <ci>IK1max</ci>
        <apply><divide/>
          <cn cellml:units="dimensionless">1.0</cn>
          <apply><plus/>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply><power/>
              <apply><divide/>
                <ci>H_i</ci>
                <ci>K_half_IK1max</ci>
              </apply>
              <ci>H_IK1max</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply><eq/>
        <ci>NPo</ci>
        <apply><divide/>
          <cn cellml:units="dimensionless">1.0</cn>
          <apply><plus/>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply><power/>
              <apply><divide/>
                <ci>H_i</ci>
                <ci>K_half_NPo</ci>
              </apply>
              <ci>H_NPo</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="IK1_pH_eq"><eq/>
        <ci>IK1</ci>
        <apply><times/>
          <ci>IK1_original</ci>
          <ci>IK1max</ci>
          <ci>NPo</ci>
        </apply>
      </apply>
    </math>
  </component>
  

</model>
