Location: Oyehaug, Ostby, Lloyd, Omholt, Einevoll, 2011 @ 40ea308afe0a / oyehaug_2009_version1.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2011-03-29 20:58:06+13:00
Desc:
Updated both models in line with the revisions made to the Matlab code to satisfy the manuscript reviewers. One equation change (dN_Ko/dt) and 3 parameter changes.
Permanent Source URI:
http://models.cellml.org/workspace/oyehaug_ostby_lloyd_omholt_einevoll_2011/rawfile/40ea308afe0a7dd0728f1cf97fa096a0b43242af/oyehaug_2009_version1.cellml

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<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#"  cmeta:id="oyehaug_2009_1" name="oyehaug_2009">
	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Dependence of spontaneous neuronal firing and depolarization block on astroglial membrane processes</title>
				<author>
					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
					<affiliation>
						<shortaffil>Auckland Bioengineering Institute</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>
				This CellML model is a tranlsation based on the orignal paper and Matlab code.  The model runs in both COR and OpenCell to recreate the published results.  This particular version of the model recreates Figure 2A, with a stimulus duration of 0.6s.
				</para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
ABSTRACT: The chain of events where a neural activity-induced elevation of the extracellular space (ECS) potassium concentration ([K+]o) is followed by a decreased neuronal firing threshold which in turn causes increased neural activity, represents a positive feedback loop. Here we combine a relatively detailed model of glial membrane transport of water and ions and a Hodgkin-Huxley type neuron model to examine the effectof perturbing the magnitudes of transport rates in the glial membrane that may influence this feedback. The perturbations reflect pathological conditions and/or heterogeneity in glial membrane transporter density. When exposed to elevated [K+]o, the combined model responds either (i) by a brief period of neuronal firing followed by a rapid drop in [K+]o or (ii) by a much longer period where the neuron experiences depolarization block during which [K+]o first increases and later slowly returns to baseline levels. By solving the model equations repeatedly for a large number of empirically valid parameter sets, we find that both the high [K+]o-induced duration of neuronal firing and the prevalence of depolarization block show high sensitivities to variation in the time scale of the glial membrane dynamics and to the magnitudes of the sodium-potassium pump rate and the potassium ion channel conductance. In contrast, firing duration is much less sensitive to perturbations of the magnitude of Na+/K+/2Cl- (NKCC1) cotransporter permeability and Na+/2HCO-3 (NBC) cotransporter conductance. An analysis focusing on the model's ability to fire spontaneously discloses the feedback mechanism and allows us to predict which combinations of ion concentrations that give rise to spontaneous firing of action potentials. The results suggest that when [K+]o becomes elevated, spatiotemporal heterogenity of ion and water transport across the astroglialmembrane in the brainmay cause very different potassium clearance profiles that are possibly of biomedical importance. The above insights point to the importance of combining neuronal and astroglial models of some sophistication in order to disclose phenomena associated with the astroglia-neuron interaction.
</para>
				<informalfigure float="0" id="fig_cell_diagram">
					<mediaobject>
						<imageobject>
							<imagedata fileref="oyehaug_2009.png"/>
						</imageobject>
					</mediaobject>
					<caption>Schematic diagram of the model displaying the channels, pumps and exchangers allowing ion transfer between the neuron, the extracellular matrix and the glia.</caption>
				</informalfigure>
			</sect1>
		</article>
	</documentation>
	
	
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			<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">glial transmembrane sodium potassium and chloride ion flux via the NKCC1 cotransporter</dcterms:alternative>
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		<rdf:Description rdf:about="N_Nag">
			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Nag</dc:title>
			<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of sodium ions per unit glial area</dcterms:alternative>
		</rdf:Description>
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	<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-syntax-ns#">
		<rdf:Description rdf:about="wg">
			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">wg</dc:title>
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			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Nao</dc:title>
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                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">51.9</cn>
                 </apply>
              </apply>
              <apply>
                 <minus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.25</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">12.975</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_m</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond_millivolt">0.28</cn>
                 <apply>
                    <plus/>
                    <ci>Vm_n</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">24.89</cn>
                 </apply>
              </apply>
              <apply>
                 <minus/>
                 <apply>
                    <exp/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4.978</cn>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>m</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_m</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>m</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_m</ci>
                 <ci>m</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_NaT_h_gate">
     <variable initial_value="0.9961" name="h" public_interface="out" units="dimensionless"/>
     <variable name="alpha_h" units="per_millisecond"/>
     <variable name="beta_h" units="per_millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_h</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.128</cn>
              <apply>
                 <exp/>
                 <apply>
                    <minus/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.94</cn>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_h</ci>
           <apply>
              <divide/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">4</cn>
              <apply>
                 <plus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">6</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>h</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_h</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>h</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_h</ci>
                 <ci>h</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_NaP">
     <variable name="i_NaP" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_NaP" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="150" name="gNaP" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="ENa_n" public_interface="in" units="millivolt"/>
     <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
     <variable name="Vm_n" private_interface="out" public_interface="in" units="millivolt"/>
     <variable name="m" private_interface="in" units="dimensionless"/>
     <variable name="h" private_interface="in" units="dimensionless"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_NaP</ci>
           <apply>
              <times/>
              <ci>gNaP</ci>
              <apply>
                 <power/>
                 <ci>m</ci>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              </apply>
              <ci>h</ci>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>ENa_n</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_NaP</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gNaP</ci>
                 <apply>
                    <power/>
                    <ci>m</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                 </apply>
                 <ci>h</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_n</ci>
                    <ci>ENa_n</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_NaP_m_gate">
     <variable initial_value="0.0129" name="m" public_interface="out" units="dimensionless"/>
     <variable name="alpha_m" units="per_millisecond"/>
     <variable name="beta_m" units="per_millisecond"/>
     <variable initial_value="6" name="tau_activation" units="millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_m</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <apply>
                    <divide/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>tau_activation</ci>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <apply>
                 <plus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.143</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5.67</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_m</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <apply>
                    <divide/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>tau_activation</ci>
                 </apply>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.143</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5.67</cn>
                       </apply>
                    </apply>
                 </apply>
              </apply>
              <apply>
                 <plus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.143</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5.67</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>m</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_m</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>m</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_m</ci>
                 <ci>m</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_NaP_h_gate">
     <variable initial_value="0.9718" name="h" public_interface="out" units="dimensionless"/>
     <variable name="alpha_h" units="per_millisecond"/>
     <variable name="beta_h" units="per_millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_h</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millisecond">5.12<sep/>-8</cn>
              <apply>
                 <exp/>
                 <apply>
                    <minus/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.94</cn>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_h</ci>
           <apply>
              <divide/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millisecond">1.6<sep/>-6</cn>
              <apply>
                 <plus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">8</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>h</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_h</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>h</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_h</ci>
                 <ci>h</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_KDR">
     <variable name="i_KDR" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_KDR" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="5000" name="gKDR" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="EK_n" public_interface="in" units="millivolt"/>
     <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
     <variable name="Vm_n" private_interface="out" public_interface="in" units="millivolt"/>
     <variable name="n" private_interface="in" units="dimensionless"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_KDR</ci>
           <apply>
              <times/>
              <ci>gKDR</ci>
              <apply>
                 <power/>
                 <ci>n</ci>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              </apply>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>EK_n</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_KDR</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gKDR</ci>
                 <apply>
                    <power/>
                    <ci>n</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                 </apply>
                 <apply>
                    <minus/>
                    <ci>Vm_n</ci>
                    <ci>EK_n</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_KDR_n_gate">
     <variable initial_value="0.0012" name="n" public_interface="out" units="dimensionless"/>
     <variable name="alpha_n" units="per_millisecond"/>
     <variable name="beta_n" units="per_millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_n</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond_millivolt">0.016</cn>
                 <apply>
                    <minus/>
                    <apply>
                       <minus/>
                       <ci>Vm_n</ci>
                    </apply>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34.9</cn>
                 </apply>
              </apply>
              <apply>
                 <minus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">6.98</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_n</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.25</cn>
              <apply>
                 <exp/>
                 <apply>
                    <minus/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.025</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.25</cn>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>n</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_n</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>n</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_n</ci>
                 <ci>n</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_KA">
     <variable name="i_KA" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_KA" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="1000" name="gKA" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="EK_n" public_interface="in" units="millivolt"/>
     <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
     <variable name="Vm_n" private_interface="out" public_interface="in" units="millivolt"/>
     <variable name="m" private_interface="in" units="dimensionless"/>
     <variable name="h" private_interface="in" units="dimensionless"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_KA</ci>
           <apply>
              <times/>
              <ci>gKA</ci>
              <apply>
                 <power/>
                 <ci>m</ci>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              </apply>
              <ci>h</ci>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>EK_n</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_KA</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gKA</ci>
                 <apply>
                    <power/>
                    <ci>m</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                 </apply>
                 <ci>h</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_n</ci>
                    <ci>EK_n</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_KA_m_gate">
     <variable initial_value="0.1193" name="m" public_interface="out" units="dimensionless"/>
     <variable name="alpha_m" units="per_millisecond"/>
     <variable name="beta_m" units="per_millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_m</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond_millivolt">0.02</cn>
                 <apply>
                    <minus/>
                    <apply>
                       <minus/>
                       <ci>Vm_n</ci>
                    </apply>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">56.9</cn>
                 </apply>
              </apply>
              <apply>
                 <minus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5.69</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_m</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond_millivolt">0.0175</cn>
                 <apply>
                    <plus/>
                    <ci>Vm_n</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">29.9</cn>
                 </apply>
              </apply>
              <apply>
                 <minus/>
                 <apply>
                    <exp/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.99</cn>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>m</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_m</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>m</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_m</ci>
                 <ci>m</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_KA_h_gate">
     <variable initial_value="0.1205" name="h" public_interface="out" units="dimensionless"/>
     <variable name="alpha_h" units="per_millisecond"/>
     <variable name="beta_h" units="per_millisecond"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>alpha_h</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.016</cn>
              <apply>
                 <exp/>
                 <apply>
                    <minus/>
                    <apply>
                       <plus/>
                       <apply>
                          <times/>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn>
                          <ci>Vm_n</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4.61</cn>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>beta_h</ci>
           <apply>
              <divide/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.5</cn>
              <apply>
                 <plus/>
                 <apply>
                    <exp/>
                    <apply>
                       <minus/>
                       <apply>
                          <plus/>
                          <apply>
                             <times/>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
                             <ci>Vm_n</ci>
                          </apply>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">11.98</cn>
                       </apply>
                    </apply>
                 </apply>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>h</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <ci>alpha_h</ci>
                 <apply>
                    <minus/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                    <ci>h</ci>
                 </apply>
              </apply>
              <apply>
                 <times/>
                 <ci>beta_h</ci>
                 <ci>h</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_NaKATPase_n">
     <variable name="i_NaKATPase_n" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_NaKATPase_n" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="0.0289" name="I_NaKATPase_n_max" units="picomole_per_cm2_millisecond"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="KmNa" public_interface="in" units="millimolar"/>
     <variable name="KmK" public_interface="in" units="millimolar"/>
     <variable name="Nan" public_interface="in" units="millimolar"/>
     <variable name="Ko" public_interface="in" units="millimolar"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_NaKATPase_n</ci>
           <apply>
              <times/>
              <ci>J_NaKATPase_n</ci>
              <ci>F</ci>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_NaKATPase_n</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <apply>
                    <divide/>
                    <apply>
                       <times/>
                       <ci>I_NaKATPase_n_max</ci>
                       <apply>
                          <power/>
                          <ci>Nan</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                    </apply>
                    <apply>
                       <plus/>
                       <apply>
                          <power/>
                          <ci>Nan</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                       <apply>
                          <power/>
                          <ci>KmNa</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                    </apply>
                 </apply>
                 <ci>Ko</ci>
              </apply>
              <apply>
                 <plus/>
                 <ci>Ko</ci>
                 <ci>KmK</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_leakNa">
     <variable name="i_leakNa" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_leakNa" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="20" name="gleakNa" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="ENa_n" public_interface="in" units="millivolt"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_leakNa</ci>
           <apply>
              <times/>
              <ci>gleakNa</ci>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>ENa_n</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_leakNa</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gleakNa</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_n</ci>
                    <ci>ENa_n</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_leakK">
     <variable name="i_leakK" public_interface="out" units="nanoA_per_cm2"/>
     <variable name="J_leakK" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="66.06" name="gleakK" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="EK_n" public_interface="in" units="millivolt"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_leakK</ci>
           <apply>
              <times/>
              <ci>gleakK</ci>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>EK_n</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>J_leakK</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gleakK</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_n</ci>
                    <ci>EK_n</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="i_leakf">
     <variable name="i_leakf" public_interface="out" units="nanoA_per_cm2"/>
     <variable initial_value="10" name="gleakf" units="microS_per_cm2"/>
     <variable name="Ef_n" public_interface="in" units="millivolt"/>
     <variable name="Vm_n" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>i_leakf</ci>
           <apply>
              <times/>
              <ci>gleakf</ci>
              <apply>
                 <minus/>
                 <ci>Vm_n</ci>
                 <ci>Ef_n</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="Vm_g">
     <variable name="Vm_g" public_interface="out" units="millivolt"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="ENa_g" public_interface="in" units="millivolt"/>
     <variable name="EK_g" public_interface="in" units="millivolt"/>
     <variable name="ECl_g" public_interface="in" units="millivolt"/>
     <variable name="ENBC_g" public_interface="in" units="millivolt"/>
     <variable name="gNa" public_interface="in" units="microS_per_cm2"/>
     <variable name="gK" public_interface="in" units="microS_per_cm2"/>
     <variable name="gCl" public_interface="in" units="microS_per_cm2"/>
     <variable name="gNBC" public_interface="in" units="microS_per_cm2"/>
     <variable name="J_NaKATPase_g" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>Vm_g</ci>
           <apply>
              <minus/>
              <apply>
                 <divide/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>gNa</ci>
                       <ci>ENa_g</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>gK</ci>
                       <ci>EK_g</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>gCl</ci>
                       <ci>ECl_g</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>gNBC</ci>
                       <ci>ENBC_g</ci>
                    </apply>
                 </apply>
                 <apply>
                    <plus/>
                    <ci>gNa</ci>
                    <ci>gK</ci>
                    <ci>gCl</ci>
                    <ci>gNBC</ci>
                 </apply>
              </apply>
              <apply>
                 <divide/>
                 <apply>
                    <times/>
                    <ci>F</ci>
                    <ci>J_NaKATPase_g</ci>
                 </apply>
                 <apply>
                    <plus/>
                    <ci>gNa</ci>
                    <ci>gK</ci>
                    <ci>gCl</ci>
                    <ci>gNBC</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="J_Na">
     <variable name="J_Na" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="100.0" name="gNa" public_interface="out" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="ENa_g" public_interface="in" units="millivolt"/>
     <variable name="Vm_g" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>J_Na</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gNa</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_g</ci>
                    <ci>ENa_g</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="J_K">
     <variable name="J_K" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="1696.0" name="gK" public_interface="out" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="EK_g" public_interface="in" units="millivolt"/>
     <variable name="Vm_g" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>J_K</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gK</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_g</ci>
                    <ci>EK_g</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="J_NaKATPase_g">
     <variable name="J_NaKATPase_g" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="0.1151" name="I_NaKATPase_g_max" units="picomole_per_cm2_millisecond"/>
     <variable name="KmNa" public_interface="in" units="millimolar"/>
     <variable name="KmK" public_interface="in" units="millimolar"/>
     <variable name="Nag" public_interface="in" units="millimolar"/>
     <variable name="Ko" public_interface="in" units="millimolar"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>J_NaKATPase_g</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <apply>
                    <divide/>
                    <apply>
                       <times/>
                       <ci>I_NaKATPase_g_max</ci>
                       <apply>
                          <power/>
                          <ci>Nag</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                    </apply>
                    <apply>
                       <plus/>
                       <apply>
                          <power/>
                          <ci>Nag</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                       <apply>
                          <power/>
                          <ci>KmNa</ci>
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
                       </apply>
                    </apply>
                 </apply>
                 <ci>Ko</ci>
              </apply>
              <apply>
                 <plus/>
                 <ci>Ko</ci>
                 <ci>KmK</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="J_NBC">
     <variable name="J_NBC" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="80" name="gNBC" public_interface="out" units="microS_per_cm2"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="ENBC_g" public_interface="in" units="millivolt"/>
     <variable name="Vm_g" public_interface="in" units="millivolt"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>J_NBC</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <ci>gNBC</ci>
                 <apply>
                    <minus/>
                    <ci>Vm_g</ci>
                    <ci>ENBC_g</ci>
                 </apply>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="J_NKCC1">
     <variable name="J_NKCC1" public_interface="out" units="picomole_per_cm2_millisecond"/>
     <variable initial_value="2" name="gNKCC1" units="microS_per_cm2"/>
     <variable name="Psi" public_interface="in" units="millivolt"/>
     <variable name="F" public_interface="in" units="coulomb_per_mole"/>
     <variable name="Nao" public_interface="in" units="millimolar"/>
     <variable name="Nag" public_interface="in" units="millimolar"/>
     <variable name="Ko" public_interface="in" units="millimolar"/>
     <variable name="P_Ko" public_interface="in" units="millimolar"/>
     <variable name="Kg" public_interface="in" units="millimolar"/>
     <variable name="Clo" public_interface="in" units="millimolar"/>
     <variable name="Clg" public_interface="in" units="millimolar"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>J_NKCC1</ci>
           <piecewise>
              <piece>
                 <apply>
                    <divide/>
                    <apply>
                       <times/>
                       <apply>
                          <divide/>
                          <apply>
                             <power/>
                             <apply>
                                <minus/>
                                <ci>Ko</ci>
                                <ci>P_Ko</ci>
                             </apply>
                             <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10</cn>
                          </apply>
                          <apply>
                             <plus/>
                             <apply>
                                <power/>
                                <apply>
                                   <minus/>
                                   <ci>Ko</ci>
                                   <ci>P_Ko</ci>
                                </apply>
                                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10</cn>
                             </apply>
                             <apply>
                                <power/>
                                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.03</cn>
                                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10</cn>
                             </apply>
                          </apply>
                       </apply>
                       <ci>Psi</ci>
                       <ci>gNKCC1</ci>
                       <apply>
                          <ln/>
                          <apply>
                             <times/>
                             <apply>
                                <divide/>
                                <apply>
                                   <times/>
                                   <apply>
                                      <divide/>
                                      <ci>Ko</ci>
                                      <ci>Kg</ci>
                                   </apply>
                                   <ci>Nao</ci>
                                </apply>
                                <ci>Nag</ci>
                             </apply>
                             <apply>
                                <power/>
                                <apply>
                                   <divide/>
                                   <ci>Clo</ci>
                                   <ci>Clg</ci>
                                </apply>
                                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                             </apply>
                          </apply>
                       </apply>
                    </apply>
                    <ci>F</ci>
                 </apply>
                 <apply>
                    <gt/>
                    <ci>Ko</ci>
                    <ci>P_Ko</ci>
                 </apply>
              </piece>
              <otherwise>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="picomole_per_cm2_millisecond">0</cn>
              </otherwise>
           </piecewise>
        </apply>
     </math>
  </component>
  <component name="N_Nag">
     <variable initial_value="0.75" name="N_Nag" public_interface="out" units="nanomole_per_cm2"/>
     <variable name="dN_Nag_dt" public_interface="out" units="nanomole_per_cm2_millisecond"/>
     <variable name="J_Na" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaKATPase_g" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NKCC1" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NBC" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>N_Nag</ci>
           </apply>
           <ci>dN_Nag_dt</ci>
        </apply>
        <apply>
           <eq/>
           <ci>dN_Nag_dt</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
              <apply>
                 <plus/>
                 <apply>
                    <minus/>
                    <apply>
                       <minus/>
                       <ci>J_Na</ci>
                    </apply>
                    <apply>
                       <times/>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                       <ci>J_NaKATPase_g</ci>
                    </apply>
                 </apply>
                 <ci>J_NKCC1</ci>
                 <ci>J_NBC</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="N_Kg">
     <variable initial_value="5" name="N_Kg" public_interface="out" units="nanomole_per_cm2"/>
     <variable name="dN_Kg_dt" public_interface="out" units="nanomole_per_cm2_millisecond"/>
     <variable name="J_K" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaKATPase_g" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NKCC1" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>N_Kg</ci>
           </apply>
           <ci>dN_Kg_dt</ci>
        </apply>
        <apply>
           <eq/>
           <ci>dN_Kg_dt</ci>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
              <apply>
                 <plus/>
                 <apply>
                    <minus/>
                    <ci>J_K</ci>
                 </apply>
                 <apply>
                    <times/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                    <ci>J_NaKATPase_g</ci>
                 </apply>
                 <ci>J_NKCC1</ci>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="wg">
     <variable initial_value="0.05" name="wg" public_interface="out" units="micrometre"/>
     <variable name="Lp" public_interface="in" units="cm_per_second_millimolar"/>
     <variable name="Xg" public_interface="in" units="millimolar_micrometre"/>
     <variable name="Nao" public_interface="in" units="millimolar"/>
     <variable name="Ko" public_interface="in" units="millimolar"/>
     <variable name="Clo" public_interface="in" units="millimolar"/>
     <variable name="HCO3o" public_interface="in" units="millimolar"/>
     <variable name="Nag" public_interface="in" units="millimolar"/>
     <variable name="Kg" public_interface="in" units="millimolar"/>
     <variable name="Clg" public_interface="in" units="millimolar"/>
     <variable name="HCO3g" public_interface="in" units="millimolar"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>wg</ci>
           </apply>
           <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10</cn>
              <ci>Lp</ci>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <ci>Nag</ci>
                    <ci>Kg</ci>
                    <ci>Clg</ci>
                    <ci>HCO3g</ci>
                    <apply>
                       <divide/>
                       <ci>Xg</ci>
                       <ci>wg</ci>
                    </apply>
                 </apply>
                 <apply>
                    <plus/>
                    <ci>Nao</ci>
                    <ci>Ko</ci>
                    <ci>Clo</ci>
                    <ci>HCO3o</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="wo">
     <variable name="wo" public_interface="out" units="micrometre"/>
     <variable name="P_wo" public_interface="in" units="micrometre"/>
     <variable name="P_wg" public_interface="in" units="micrometre"/>
     <variable name="wg" public_interface="in" units="micrometre"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>wo</ci>
           <apply>
              <minus/>
              <apply>
                 <plus/>
                 <ci>P_wg</ci>
                 <ci>P_wo</ci>
              </apply>
              <ci>wg</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="N_Nao">
     <variable initial_value="3.65" name="N_Nao" public_interface="out" units="nanomole_per_cm2"/>
	 <variable name="J_NaT" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaKATPase_n" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaP" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_leakNa" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="dN_Nag_dt" public_interface="in" units="nanomole_per_cm2_millisecond"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>N_Nao</ci>
           </apply>
		   <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                       <ci>J_NaKATPase_n</ci>
                    </apply>
                    <ci>J_NaT</ci>
                    <ci>J_NaP</ci>
                    <ci>J_leakNa</ci>
                 </apply>
                 <apply>
                    <times/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">100</cn>
                    <ci>dN_Nag_dt</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="N_Ko">
     <variable initial_value="0.075" name="N_Ko" public_interface="out" units="nanomole_per_cm2"/>
	 <variable name="J_NaT" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaKATPase_n" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_NaP" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="J_leakNa" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="dN_Kg_dt" public_interface="in" units="nanomole_per_cm2_millisecond"/>>
	 <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>N_Ko</ci>
           </apply>
           <apply>
              <minus/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-0.01</cn>
                 <apply>
                    <plus/>
                    <ci>J_NaT</ci>
                    <ci>J_NaP</ci>
                    <ci>J_leakNa</ci>
					<apply>
                       <times/>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                       <ci>J_NaKATPase_n</ci>
                    </apply>
                 </apply>
			  </apply>
              <ci>dN_Kg_dt</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="N_HCO3o">
     <variable initial_value="0.375" name="N_HCO3o" public_interface="out" units="nanomole_per_cm2"/>
     <variable name="J_NBC" public_interface="in" units="picomole_per_cm2_millisecond"/>
     <variable name="time" public_interface="in" units="millisecond"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <apply>
              <diff/>
              <bvar>
                 <ci>time</ci>
              </bvar>
              <ci>N_HCO3o</ci>
           </apply>
           <apply>
              <times/>
              <apply>
                 <minus/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              <ci>J_NBC</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="electric_potentials">
     <variable name="ENa_n" public_interface="out" units="millivolt"/>
     <variable name="EK_n" public_interface="out" units="millivolt"/>
     <variable initial_value="-70" name="Ef_n" public_interface="out" units="millivolt"/>
     <variable name="ENa_g" public_interface="out" units="millivolt"/>
     <variable name="EK_g" public_interface="out" units="millivolt"/>
     <variable name="ECl_g" public_interface="out" units="millivolt"/>
     <variable name="ENBC_g" public_interface="out" units="millivolt"/>
     <variable name="Psi" public_interface="in" units="millivolt"/>
     <variable name="Nan" public_interface="in" units="millimolar"/>
     <variable name="Nag" public_interface="in" units="millimolar"/>
     <variable name="Nao" public_interface="in" units="millimolar"/>
     <variable name="Kn" public_interface="in" units="millimolar"/>
     <variable name="Kg" public_interface="in" units="millimolar"/>
     <variable name="Ko" public_interface="in" units="millimolar"/>
     <variable name="HCO3g" public_interface="in" units="millimolar"/>
     <variable name="HCO3o" public_interface="in" units="millimolar"/>
     <variable name="Clg" public_interface="in" units="millimolar"/>
     <variable name="Clo" public_interface="in" units="millimolar"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>ENa_n</ci>
           <apply>
              <times/>
              <ci>Psi</ci>
              <apply>
                 <ln/>
                 <apply>
                    <divide/>
                    <ci>Nao</ci>
                    <ci>Nan</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>EK_n</ci>
           <apply>
              <times/>
              <ci>Psi</ci>
              <apply>
                 <ln/>
                 <apply>
                    <divide/>
                    <ci>Ko</ci>
                    <ci>Kn</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>ENa_g</ci>
           <apply>
              <times/>
              <ci>Psi</ci>
              <apply>
                 <ln/>
                 <apply>
                    <divide/>
                    <ci>Nao</ci>
                    <ci>Nag</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>EK_g</ci>
           <apply>
              <times/>
              <ci>Psi</ci>
              <apply>
                 <ln/>
                 <apply>
                    <divide/>
                    <ci>Ko</ci>
                    <ci>Kg</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>ECl_g</ci>
           <apply>
              <times/>
              <apply>
                 <minus/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>Psi</ci>
              <apply>
                 <ln/>
                 <apply>
                    <divide/>
                    <ci>Clo</ci>
                    <ci>Clg</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>ENBC_g</ci>
           <apply>
              <times/>
              <apply>
                 <minus/>
                 <ci>Psi</ci>
              </apply>
              <apply>
                 <ln/>
                 <apply>
                    <times/>
                    <apply>
                       <divide/>
                       <ci>Nao</ci>
                       <ci>Nag</ci>
                    </apply>
                    <apply>
                       <power/>
                       <apply>
                          <divide/>
                          <ci>HCO3o</ci>
                          <ci>HCO3g</ci>
                       </apply>
                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
     </math>
  </component>
  <component name="ion_concentrations">
     <variable name="Clo" public_interface="out" units="millimolar"/>
     <variable name="Cln" public_interface="out" units="millimolar"/>
     <variable name="Clg" public_interface="out" units="millimolar"/>
     <variable name="Nan" public_interface="out" units="millimolar"/>
     <variable name="Nao" public_interface="out" units="millimolar"/>
     <variable name="Nag" public_interface="out" units="millimolar"/>
     <variable name="Kn" public_interface="out" units="millimolar"/>
     <variable cmeta:id="ion_concentrations_Ko" name="Ko" public_interface="out" units="millimolar"/>
     <variable name="Kg" public_interface="out" units="millimolar"/>
     <variable name="HCO3g" public_interface="out" units="millimolar"/>
     <variable name="HCO3o" public_interface="out" units="millimolar"/>
     <variable initial_value="3" name="P_Ko" public_interface="out" units="millimolar"/>
     <variable initial_value="-85" name="P_Vm_g" units="millivolt"/>
     <variable name="P_Clo" units="millimolar"/>
     <variable initial_value="50" name="P_Cln" units="millimolar"/>
     <variable name="P_Clg" units="millimolar"/>
     <variable initial_value="10" name="P_Nan" units="millimolar"/>
     <variable initial_value="146" name="P_Nao" units="millimolar"/>
     <variable initial_value="15" name="P_Nag" units="millimolar"/>
     <variable initial_value="130" name="P_Kn" units="millimolar"/>
     <variable initial_value="100" name="P_Kg" units="millimolar"/>
     <variable name="P_HCO3g" units="millimolar"/>
     <variable initial_value="15" name="P_HCO3o" units="millimolar"/>
     <variable initial_value="0.05" name="P_wn" units="micrometre"/>
     <variable name="Psi" public_interface="in" units="millivolt"/>
     <variable name="P_wo" public_interface="in" units="micrometre"/>
     <variable name="P_wg" public_interface="in" units="micrometre"/>
     <variable name="Vm_g" public_interface="in" units="millivolt"/>
     <variable name="wo" public_interface="in" units="micrometre"/>
     <variable name="wg" public_interface="in" units="micrometre"/>
     <variable name="Xg" public_interface="in" units="millimolar_micrometre"/>
     <variable name="rho" public_interface="in" units="dimensionless"/>
     <variable name="N_Kg" public_interface="in" units="nanomole_per_cm2"/>
     <variable name="N_Ko" public_interface="in" units="nanomole_per_cm2"/>
     <variable name="N_Nag" public_interface="in" units="nanomole_per_cm2"/>
     <variable name="N_Nao" public_interface="in" units="nanomole_per_cm2"/>
     <variable name="N_HCO3o" public_interface="in" units="nanomole_per_cm2"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>P_Clo</ci>
           <apply>
              <minus/>
              <apply>
                 <plus/>
                 <ci>P_Nao</ci>
                 <ci>P_Ko</ci>
              </apply>
              <ci>P_HCO3o</ci>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>P_HCO3g</ci>
           <apply>
              <times/>
              <ci>P_HCO3o</ci>
              <apply>
                 <root/>
                 <apply>
                    <times/>
                    <apply>
                       <divide/>
                       <ci>P_Nao</ci>
                       <ci>P_Nag</ci>
                    </apply>
                    <apply>
                       <exp/>
                       <apply>
                          <divide/>
                          <ci>P_Vm_g</ci>
                          <ci>Psi</ci>
                       </apply>
                    </apply>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>P_Clg</ci>
           <apply>
              <times/>
              <ci>P_Clo</ci>
              <apply>
                 <exp/>
                 <apply>
                    <divide/>
                    <ci>P_Vm_g</ci>
                    <ci>Psi</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
            <eq/>
            <ci>Kg</ci>
            <apply>
               <divide/>
               <ci>N_Kg</ci>
               <ci>wg</ci>
            </apply>
         </apply>
		 
		 <apply>
            <eq/>
            <ci>Ko</ci>
            <apply>
               <divide/>
               <ci>N_Ko</ci>
               <ci>wo</ci>
            </apply>
         </apply>
		 
        <apply>
           <eq/>
           <ci>Kn</ci>
           <apply>
              <divide/>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>P_wn</ci>
                       <ci>P_Kn</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wg</ci>
                       <ci>P_Kg</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wo</ci>
                       <ci>P_Ko</ci>
                    </apply>
                 </apply>
                 <apply>
                    <plus/>
                    <ci>N_Ko</ci>
                    <ci>N_Kg</ci>
                 </apply>
              </apply>
              <ci>P_wn</ci>
           </apply>
        </apply>
        <apply>
            <eq/>
            <ci>Nag</ci>
            <apply>
               <divide/>
               <ci>N_Nag</ci>
               <ci>wg</ci>
            </apply>
         </apply>
		 
		 <apply>
            <eq/>
            <ci>Nao</ci>
            <apply>
               <divide/>
               <ci>N_Nao</ci>
               <ci>wo</ci>
            </apply>
         </apply>
        <apply>
           <eq/>
           <ci>Nan</ci>
           <apply>
              <divide/>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>P_wn</ci>
                       <ci>P_Nan</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wg</ci>
                       <ci>P_Nag</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wo</ci>
                       <ci>P_Nao</ci>
                    </apply>
                 </apply>
                 <apply>
                    <plus/>
                    <ci>N_Nao</ci>
                    <ci>N_Nag</ci>
                 </apply>
              </apply>
              <ci>P_wn</ci>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>Clg</ci>
           <apply>
              <minus/>
              <apply>
                 <plus/>
                 <ci>Nag</ci>
                 <ci>Kg</ci>
              </apply>
              <apply>
                 <plus/>
                 <ci>HCO3g</ci>
                 <apply>
                    <divide/>
                    <apply>
                       <times/>
                       <ci>rho</ci>
                       <ci>Xg</ci>
                    </apply>
                    <ci>wg</ci>
                 </apply>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>Cln</ci>
           <apply>
              <plus/>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <ci>P_Cln</ci>
                    <ci>Nan</ci>
                 </apply>
                 <ci>P_Nan</ci>
              </apply>
              <apply>
                 <minus/>
                 <ci>Kn</ci>
                 <ci>P_Kn</ci>
              </apply>
           </apply>
        </apply>
        <apply>
           <eq/>
           <ci>Clo</ci>
           <apply>
              <divide/>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>P_wg</ci>
                       <ci>P_Clg</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wo</ci>
                       <ci>P_Clo</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wn</ci>
                       <ci>P_Cln</ci>
                    </apply>
                 </apply>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>wg</ci>
                       <ci>Clg</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wn</ci>
                       <ci>Cln</ci>
                    </apply>
                 </apply>
              </apply>
              <ci>wo</ci>
           </apply>
        </apply>
        <apply>
            <eq/>
            <ci>HCO3o</ci>
            <apply>
               <divide/>
               <ci>N_HCO3o</ci>
               <ci>wo</ci>
            </apply>
        </apply>
        <apply>
           <eq/>
           <ci>HCO3g</ci>
           <apply>
              <divide/>
              <apply>
                 <minus/>
                 <apply>
                    <plus/>
                    <apply>
                       <times/>
                       <ci>P_wg</ci>
                       <ci>P_HCO3g</ci>
                    </apply>
                    <apply>
                       <times/>
                       <ci>P_wo</ci>
                       <ci>P_HCO3o</ci>
                    </apply>
                 </apply>
                 <ci>N_HCO3o</ci>
              </apply>
              <ci>wg</ci>
           </apply>
        </apply>
     </math>
  </component>
  <component name="model_parameters">
     <variable name="Psi" public_interface="out" units="millivolt"/>
     <variable initial_value="9.649e4" name="F" public_interface="out" units="coulomb_per_mole"/>
     <variable initial_value="10" name="KmNa" public_interface="out" units="millimolar"/>
     <variable initial_value="1.5" name="KmK" public_interface="out" units="millimolar"/>
     <variable initial_value="50" name="gCl" public_interface="out" units="microS_per_cm2"/>
     <variable initial_value="2e-8" name="Lp" public_interface="out" units="cm_per_second_millimolar"/>
     <variable initial_value="8.45" name="Xg" public_interface="out" units="millimolar_micrometre"/>
     <variable initial_value="0.5975" name="rho" public_interface="out" units="dimensionless"/>
     <variable initial_value="0.025" name="P_wo" public_interface="out" units="micrometre"/>
     <variable initial_value="0.05" name="P_wg" public_interface="out" units="micrometre"/>
     <variable initial_value="8.315" name="R" units="joule_per_mole_kelvin"/>
     <variable initial_value="300" name="T" units="kelvin"/>
     <math xmlns="http://www.w3.org/1998/Math/MathML">
        <apply>
           <eq/>
           <ci>Psi</ci>
           <apply>
              <divide/>
              <apply>
                 <times/>
                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn>
                 <ci>R</ci>
                 <ci>T</ci>
              </apply>
              <ci>F</ci>
           </apply>
        </apply>
     </math>
  </component>
  <group>
     <relationship_ref relationship="encapsulation"/>
     <component_ref component="i_NaT">
        <component_ref component="i_NaT_m_gate"/>
        <component_ref component="i_NaT_h_gate"/>
     </component_ref>
     <component_ref component="i_NaP">
        <component_ref component="i_NaP_m_gate"/>
        <component_ref component="i_NaP_h_gate"/>
     </component_ref>
     <component_ref component="i_KDR">
        <component_ref component="i_KDR_n_gate"/>
     </component_ref>
     <component_ref component="i_KA">
        <component_ref component="i_KA_m_gate"/>
        <component_ref component="i_KA_h_gate"/>
     </component_ref>
  </group>
  <connection>
     <map_components component_1="Vm_n" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="i_NaT" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="i_NaP" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="i_KDR" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="i_KA" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="N_Nag" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="N_Kg" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="wg" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="N_Nao" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="N_Ko" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
     <map_components component_1="N_HCO3o" component_2="environment"/>
     <map_variables variable_1="time" variable_2="time"/>
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