Location: Oyehaug, Ostby, Lloyd, Omholt, Einevoll, 2011 @ 218a299de13f / oyehaug_2009_version1.cellml

Author:
Tommy Yu <tommy.yu@auckland.ac.nz>
Date:
2011-03-30 16:32:20+13:00
Desc:
Updated publication dates.
Permanent Source URI:
http://models.cellml.org/workspace/oyehaug_ostby_lloyd_omholt_einevoll_2011/rawfile/218a299de13f0570531c6e6767a7039f5dbe096d/oyehaug_2009_version1.cellml

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	<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: Exposed to a sufficiently high extracellular potassium concentration ([K+ ]o ), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarization ('depolarization block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K+ ]o causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K+]o conditions, we combined a recently developed dynamical model of glial membrane water and ion transport with a Hodgkin-Huxley type neuron model. In this interconnected astroglia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K+]o -induced duration of spontaneous neuronal firing and the prevalence of depolarization block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available. 
</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>
				<para>
The original paper reference is cited below:
</para>
				<para>
Dependence of spontaneous neuronal firing and depolarization block on astroglial membrane processes, Leiv Oyehaug, Ivar Ostby, Catherine M. Lloyd, Stog W. Omholt, and Gaute T. Einevoll, 2011, <emphasis>Journal of Computational Neuroscience</emphasis>.
				</para>
			</sect1>
		</article>
	</documentation>
	
	
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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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  <connection>
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