<?xml version="1.0" encoding="utf-8"?>
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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 2B, with a stimulus duration of 0.8s.
</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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<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"/>
</connection>
<connection>
<map_components component_1="i_NaT" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_NaT" variable_2="i_NaT"/>
</connection>
<connection>
<map_components component_1="i_NaP" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_NaP" variable_2="i_NaP"/>
</connection>
<connection>
<map_components component_1="i_KDR" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_KDR" variable_2="i_KDR"/>
</connection>
<connection>
<map_components component_1="i_KA" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_KA" variable_2="i_KA"/>
</connection>
<connection>
<map_components component_1="i_leakNa" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_leakNa" variable_2="i_leakNa"/>
</connection>
<connection>
<map_components component_1="i_leakK" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_leakK" variable_2="i_leakK"/>
</connection>
<connection>
<map_components component_1="i_leakf" component_2="Vm_n"/>
<map_variables variable_1="Vm_n" variable_2="Vm_n"/>
<map_variables variable_1="i_leakf" variable_2="i_leakf"/>
</connection>
<connection>
<map_components component_1="i_NaKATPase_n" component_2="Vm_n"/>
<map_variables variable_1="i_NaKATPase_n" variable_2="i_NaKATPase_n"/>
</connection>
<connection>
<map_components component_1="J_Na" component_2="Vm_g"/>
<map_variables variable_1="Vm_g" variable_2="Vm_g"/>
<map_variables variable_1="gNa" variable_2="gNa"/>
</connection>
<connection>
<map_components component_1="J_K" component_2="Vm_g"/>
<map_variables variable_1="Vm_g" variable_2="Vm_g"/>
<map_variables variable_1="gK" variable_2="gK"/>
</connection>
<connection>
<map_components component_1="J_NBC" component_2="Vm_g"/>
<map_variables variable_1="Vm_g" variable_2="Vm_g"/>
<map_variables variable_1="gNBC" variable_2="gNBC"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Vm_g"/>
<map_variables variable_1="gCl" variable_2="gCl"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="J_NaKATPase_g" component_2="Vm_g"/>
<map_variables variable_1="J_NaKATPase_g" variable_2="J_NaKATPase_g"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_NaT"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_NaP"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_KDR"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_KA"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_leakK"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_leakNa"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_Na"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_K"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_NaT"/>
<map_variables variable_1="ENa_n" variable_2="ENa_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_NaP"/>
<map_variables variable_1="ENa_n" variable_2="ENa_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_KDR"/>
<map_variables variable_1="EK_n" variable_2="EK_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_KA"/>
<map_variables variable_1="EK_n" variable_2="EK_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_leakNa"/>
<map_variables variable_1="ENa_n" variable_2="ENa_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_leakK"/>
<map_variables variable_1="EK_n" variable_2="EK_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="i_leakf"/>
<map_variables variable_1="Ef_n" variable_2="Ef_n"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="Vm_g"/>
<map_variables variable_1="EK_g" variable_2="EK_g"/>
<map_variables variable_1="ENa_g" variable_2="ENa_g"/>
<map_variables variable_1="ENBC_g" variable_2="ENBC_g"/>
<map_variables variable_1="ECl_g" variable_2="ECl_g"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="Vm_g"/>
<map_variables variable_1="Vm_g" variable_2="Vm_g"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="J_Na"/>
<map_variables variable_1="ENa_g" variable_2="ENa_g"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="J_K"/>
<map_variables variable_1="EK_g" variable_2="EK_g"/>
</connection>
<connection>
<map_components component_1="electric_potentials" component_2="J_NBC"/>
<map_variables variable_1="ENBC_g" variable_2="ENBC_g"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_NBC"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="i_NaKATPase_n"/>
<map_variables variable_1="KmNa" variable_2="KmNa"/>
<map_variables variable_1="KmK" variable_2="KmK"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="i_NaKATPase_n"/>
<map_variables variable_1="Nan" variable_2="Nan"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_NaKATPase_g"/>
<map_variables variable_1="KmNa" variable_2="KmNa"/>
<map_variables variable_1="KmK" variable_2="KmK"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="J_NaKATPase_g"/>
<map_variables variable_1="Nag" variable_2="Nag"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_NKCC1"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="Psi" variable_2="Psi"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="J_NKCC1"/>
<map_variables variable_1="Nao" variable_2="Nao"/>
<map_variables variable_1="Nag" variable_2="Nag"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
<map_variables variable_1="Kg" variable_2="Kg"/>
<map_variables variable_1="Clo" variable_2="Clo"/>
<map_variables variable_1="Clg" variable_2="Clg"/>
<map_variables variable_1="P_Ko" variable_2="P_Ko"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="wg"/>
<map_variables variable_1="Nao" variable_2="Nao"/>
<map_variables variable_1="Nag" variable_2="Nag"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
<map_variables variable_1="Kg" variable_2="Kg"/>
<map_variables variable_1="Clo" variable_2="Clo"/>
<map_variables variable_1="Clg" variable_2="Clg"/>
<map_variables variable_1="HCO3o" variable_2="HCO3o"/>
<map_variables variable_1="HCO3g" variable_2="HCO3g"/>
<map_variables variable_1="wg" variable_2="wg"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="wg"/>
<map_variables variable_1="Lp" variable_2="Lp"/>
<map_variables variable_1="Xg" variable_2="Xg"/>
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