Location: semantic-annotation @ 92367a08b2bb / mackenzie_1996.cellml

Author:
Dewan Sarwar <dsar941@UoA.auckland.ac.nz>
Date:
2020-06-25 21:17:52+12:00
Desc:
annotations changed for mackenzie model
Permanent Source URI:
https://models.cellml.org/workspace/267/rawfile/92367a08b2bb9612257ef3f32b6823adf5e0d53b/mackenzie_1996.cellml

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    <article>
      <articleinfo>
        <title>Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2</title>
        <author>
          <firstname>Jonna</firstname>
          <surname>Terkildsen</surname>
          <affiliation>
            <shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
          </affiliation>
        </author>
      </articleinfo>
      <sect1 id="sec_status">
        <title>Model Status</title>
        <para>This CellML model has been curated, the units are consistent and the model runs in COR and PCEnv. This model recreates the published results.</para>
      </sect1>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>Abstract: The Na-dependent, low affinity glucose transporter SGLT2 cloned from pig kidney is 76% identical (at the amino acid level) to its high affinity homologue SGLT1. Using two-microelectrode voltage clamp, we have characterized the presteady-state and steady-state kinetics of SGLT2 expressed in Xenopus oocytes. The kinetic properties of the steady-state sugar-evoked currents as a function of external Na and a-methyl-D-glucopyranoside (aMG) concentrations were consistent with an ordered, simultaneous transport model in which Na binds first. Na binding was voltage-dependent and saturated with hyperpolarizing voltages. Phlorizin was a potent inhibitor of the sugar-evoked currents (Ki ~10 mM) and blocked an inward Na current in the absence of sugar. SGLT2 exhibited Na-dependent presteadystate currents with time constants 3-7 ms. Charge movements were described by Boltzmann relations with apparent valence ~1 and maximal charge transfer ~11 nC, and were reduced by the addition of sugar or phlorizin. The differences between SGLT1 and SGLT2 were that (i) the apparent affinity constant (K0.5) for aMG (~3 mM) was an order of magnitude higher for SGLT2; (ii) SGLT2 excluded galactose, suggesting discrete sugar binding; (iii) K0.5 for Na was lower in SGLT2; and (iv) the Hill coefficient for Na was 1 for SGLT2 but 2 for SGLT1. Simulations of the six-state kinetic model previously proposed for SGLT1 indicated that many of the kinetic properties observed in SGLT2 are expected by simply reducing the Na/glucose coupling from 2 to 1.</para>
        <para>The original paper reference is cited below:</para>
        <para>
          Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2, M. Mackenzie, D.D.F. Loo, M. Panayotova-Heiermann, and E. M. Wright, 1996,
          <emphasis>Journal of Biological Chemistry</emphasis>
          , 271, 32678-32683.
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=8955098&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 8955098</ulink>
        </para>
        <informalfigure float="0" id="fig_reaction_diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>model diagram</title>
              </objectinfo>
              <imagedata fileref="mackenzie_1996.png" />
            </imageobject>
          </mediaobject>
          <caption>Schematic diagram of the Mackenzie et al 1996 SGLT2 model. C' represents the external-facing carrier. C'' represents the internal-facing carrier.</caption>
        </informalfigure>
      </sect1>
    </article>
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          <times />
          <ci>k0_65</ci>
          <apply>
            <power />
            <ci>Na_i</ci>
            <ci>n</ci>
          </apply>
          <apply>
            <exp />
            <apply>
              <divide />
              <apply>
                <times />
                <ci>n</ci>
                <ci>z_Na</ci>
                <ci>alpha_pp</ci>
                <ci>mu</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>k_61</ci>
        <apply>
          <times />
          <ci>k0_61</ci>
          <apply>
            <exp />
            <apply>
              <divide />
              <apply>
                <times />
                <ci>z_c</ci>
                <ci>delta</ci>
                <ci>mu</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>k_16</ci>
        <apply>
          <times />
          <ci>k0_16</ci>
          <apply>
            <exp />
            <apply>
              <divide />
              <apply>
                <times />
                <apply>
                  <minus />
                  <ci>z_c</ci>
                </apply>
                <ci>delta</ci>
                <ci>mu</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>k_52</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>k0_12</ci>
            <ci>k_25</ci>
            <ci>k0_56</ci>
            <ci>k0_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k0_21</ci>
            <ci>k0_16</ci>
            <ci>k0_65</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>k0_54_temp</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
          </apply>
          <apply>
            <times />
            <ci>k_43</ci>
            <ci>k_32</ci>
            <ci>k_25</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="kinetic_equations">
    <variable cmeta:id="kinetic_equations.k_12" name="k_12" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_21" name="k_21" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_23" name="k_23" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_32" name="k_32" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_34" name="k_34" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_43" name="k_43" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_45" name="k_45" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_54" name="k_54" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_25" name="k_25" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_52" name="k_52" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_56" name="k_56" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_65" name="k_65" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_61" name="k_61" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.k_16" name="k_16" public_interface="in" units="per_second" />
    <variable cmeta:id="kinetic_equations.C_1" initial_value="3.923e-9" name="C_1" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_2" initial_value="1.016e-7" name="C_2" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_3" initial_value="1.515e-8" name="C_3" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_4" initial_value="8.912e-10" name="C_4" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_5" initial_value="1.485e-8" name="C_5" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_6" name="C_6" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_6_temp" initial_value="3.06798e-9" name="C_6_temp" public_interface="out" units="umol" />
    <variable cmeta:id="kinetic_equations.C_T" name="C_T" public_interface="in" units="umol" />
    <variable cmeta:id="kinetic_equations.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_1</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>C_2</ci>
            </apply>
            <apply>
              <times />
              <ci>k_61</ci>
              <ci>C_6</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_12</ci>
              <ci>k_16</ci>
            </apply>
            <ci>C_1</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_2</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_12</ci>
              <ci>C_1</ci>
            </apply>
            <apply>
              <times />
              <ci>k_32</ci>
              <ci>C_3</ci>
            </apply>
            <apply>
              <times />
              <ci>k_52</ci>
              <ci>C_5</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_21</ci>
              <ci>k_23</ci>
              <ci>k_25</ci>
            </apply>
            <ci>C_2</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_3</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_23</ci>
              <ci>C_2</ci>
            </apply>
            <apply>
              <times />
              <ci>k_43</ci>
              <ci>C_4</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_32</ci>
              <ci>k_34</ci>
            </apply>
            <ci>C_3</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_4</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_34</ci>
              <ci>C_3</ci>
            </apply>
            <apply>
              <times />
              <ci>k_54</ci>
              <ci>C_5</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_45</ci>
              <ci>k_43</ci>
            </apply>
            <ci>C_4</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_5</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_45</ci>
              <ci>C_4</ci>
            </apply>
            <apply>
              <times />
              <ci>k_65</ci>
              <ci>C_6</ci>
            </apply>
            <apply>
              <times />
              <ci>k_25</ci>
              <ci>C_2</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_54</ci>
              <ci>k_52</ci>
              <ci>k_56</ci>
            </apply>
            <ci>C_5</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C_6_temp</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>C_1</ci>
            </apply>
            <apply>
              <times />
              <ci>k_56</ci>
              <ci>C_5</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k_61</ci>
              <ci>k_65</ci>
            </apply>
            <ci>C_6_temp</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C_6</ci>
        <apply>
          <minus />
          <ci>C_T</ci>
          <apply>
            <plus />
            <ci>C_1</ci>
            <ci>C_2</ci>
            <ci>C_3</ci>
            <ci>C_4</ci>
            <ci>C_5</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="king_altman_states">
    <variable cmeta:id="king_altman_states.k_12" name="k_12" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_21" name="k_21" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_23" name="k_23" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_32" name="k_32" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_34" name="k_34" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_43" name="k_43" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_45" name="k_45" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_54" name="k_54" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_25" name="k_25" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_52" name="k_52" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_56" name="k_56" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_65" name="k_65" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_61" name="k_61" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.k_16" name="k_16" public_interface="in" units="per_second" />
    <variable cmeta:id="king_altman_states.C1_sum" name="C1_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C2_sum" name="C2_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C3_sum" name="C3_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C4_sum" name="C4_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C5_sum" name="C5_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C6_sum" name="C6_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C_sum" name="C_sum" units="per_second5" />
    <variable cmeta:id="king_altman_states.C_T" name="C_T" public_interface="in" units="umol" />
    <variable cmeta:id="king_altman_states.C1" name="C1" public_interface="out" units="umol" />
    <variable cmeta:id="king_altman_states.C2" name="C2" public_interface="out" units="umol" />
    <variable cmeta:id="king_altman_states.C3" name="C3" public_interface="out" units="umol" />
    <variable cmeta:id="king_altman_states.C4" name="C4" public_interface="out" units="umol" />
    <variable cmeta:id="king_altman_states.C5" name="C5" public_interface="out" units="umol" />
    <variable cmeta:id="king_altman_states.C6" name="C6" public_interface="out" units="umol" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>C1_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C2_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C3_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C4_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C5_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_61</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C6_sum</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_12</ci>
            <ci>k_25</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
          </apply>
          <apply>
            <times />
            <ci>k_16</ci>
            <ci>k_21</ci>
            <ci>k_32</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C_sum</ci>
        <apply>
          <plus />
          <ci>C1_sum</ci>
          <ci>C2_sum</ci>
          <ci>C3_sum</ci>
          <ci>C4_sum</ci>
          <ci>C5_sum</ci>
          <ci>C6_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C1</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C1_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C2</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C2_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C3</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C3_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C4</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C4_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C5</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C5_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>C6</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>C_T</ci>
            <ci>C6_sum</ci>
          </apply>
          <ci>C_sum</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="NBC_current">
    <variable cmeta:id="NBC_current.k_12" name="k_12" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_21" name="k_21" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_56" name="k_56" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_65" name="k_65" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_34" name="k_34" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_43" name="k_43" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_25" name="k_25" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_52" name="k_52" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_61" name="k_61" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.k_16" name="k_16" public_interface="in" units="per_second" />
    <variable cmeta:id="NBC_current.C_1" name="C_1" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C_2" name="C_2" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C_3" name="C_3" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C_4" name="C_4" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C_5" name="C_5" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C_6" name="C_6" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C1" name="C1" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C2" name="C2" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C3" name="C3" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C4" name="C4" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C5" name="C5" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.C6" name="C6" public_interface="in" units="umol" />
    <variable cmeta:id="NBC_current.delta" name="delta" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.alpha_p" name="alpha_p" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.alpha_pp" name="alpha_pp" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.n" name="n" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.z_c" name="z_c" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.z_Na" name="z_Na" public_interface="in" units="dimensionless" />
    <variable cmeta:id="NBC_current.F" name="F" public_interface="in" units="C_per_mol" />
    <variable cmeta:id="NBC_current.I_NaGl_pSS" name="I_NaGl_pSS" public_interface="out" units="uA" />
    <variable cmeta:id="NBC_current.I_NaGl_SS" name="I_NaGl_SS" public_interface="out" units="uA" />
    <variable cmeta:id="NBC_current.J_Na" name="J_Na" public_interface="out" units="umol_per_second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>I_NaGl_pSS</ci>
        <apply>
          <times />
          <apply>
            <minus />
            <ci>F</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>n</ci>
              <ci>z_Na</ci>
              <ci>alpha_p</ci>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_12</ci>
                  <ci>C_1</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_21</ci>
                  <ci>C_2</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times />
              <ci>z_c</ci>
              <ci>delta</ci>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_16</ci>
                  <ci>C_1</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_61</ci>
                  <ci>C_6</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times />
              <ci>n</ci>
              <ci>z_Na</ci>
              <ci>alpha_pp</ci>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_56</ci>
                  <ci>C_5</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_65</ci>
                  <ci>C_6</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>I_NaGl_SS</ci>
        <apply>
          <times />
          <apply>
            <minus />
            <ci>F</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>z_c</ci>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_16</ci>
                  <ci>C1</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_61</ci>
                  <ci>C6</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times />
              <apply>
                <plus />
                <ci>z_c</ci>
                <apply>
                  <times />
                  <ci>z_Na</ci>
                  <ci>n</ci>
                </apply>
              </apply>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_25</ci>
                  <ci>C2</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_52</ci>
                  <ci>C5</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times />
              <apply>
                <plus />
                <ci>z_c</ci>
                <apply>
                  <times />
                  <ci>z_Na</ci>
                  <ci>n</ci>
                </apply>
              </apply>
              <apply>
                <minus />
                <apply>
                  <times />
                  <ci>k_34</ci>
                  <ci>C3</ci>
                </apply>
                <apply>
                  <times />
                  <ci>k_43</ci>
                  <ci>C4</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>J_Na</ci>
        <apply>
          <plus />
          <apply>
            <minus />
            <apply>
              <times />
              <ci>k_25</ci>
              <ci>C2</ci>
            </apply>
            <apply>
              <times />
              <ci>k_52</ci>
              <ci>C5</ci>
            </apply>
          </apply>
          <apply>
            <minus />
            <apply>
              <times />
              <ci>k_34</ci>
              <ci>C3</ci>
            </apply>
            <apply>
              <times />
              <ci>k_43</ci>
              <ci>C4</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="phenomonological_constants">
    <variable cmeta:id="phenomonological_constants.epsilon" name="epsilon" public_interface="out" units="per_second" />
    <variable cmeta:id="phenomonological_constants.lambda" name="lambda" public_interface="out" units="per_M2_per_second5" />
    <variable cmeta:id="phenomonological_constants.chi" name="chi" public_interface="out" units="M" />
    <variable cmeta:id="phenomonological_constants.alpha" name="alpha" public_interface="out" units="M2" />
    <variable cmeta:id="phenomonological_constants.beta" name="beta" public_interface="out" units="M" />
    <variable cmeta:id="phenomonological_constants.gamma" name="gamma" public_interface="out" units="M2_per_second" />
    <variable cmeta:id="phenomonological_constants.phi" name="phi" public_interface="out" units="M_per_second" />
    <variable cmeta:id="phenomonological_constants.k_12" name="k_12" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_21" name="k_21" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_23" name="k_23" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_32" name="k_32" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_34" name="k_34" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_43" name="k_43" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_45" name="k_45" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_54" name="k_54" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_25" name="k_25" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_52" name="k_52" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_56" name="k_56" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_65" name="k_65" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_61" name="k_61" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.k_16" name="k_16" public_interface="in" units="per_second" />
    <variable cmeta:id="phenomonological_constants.ks_12" name="ks_12" public_interface="in" units="per_M_per_second" />
    <variable cmeta:id="phenomonological_constants.k0_23" name="k0_23" public_interface="in" units="per_M_per_second" />
    <variable cmeta:id="phenomonological_constants.C_T" name="C_T" public_interface="in" units="umol" />
    <variable cmeta:id="phenomonological_constants.F" name="F" public_interface="in" units="C_per_mol" />
    <variable cmeta:id="phenomonological_constants.Na_o" name="Na_o" public_interface="in" units="M" />
    <variable cmeta:id="phenomonological_constants.glucose_o" name="glucose_o" public_interface="in" units="M" />
    <variable cmeta:id="phenomonological_constants.Imax_Na" name="Imax_Na" public_interface="out" units="uA" />
    <variable cmeta:id="phenomonological_constants.Imax_gluc" name="Imax_gluc" public_interface="out" units="uA" />
    <variable cmeta:id="phenomonological_constants.Khalf_Na" name="Khalf_Na" public_interface="out" units="M" />
    <variable cmeta:id="phenomonological_constants.Khalf_gluc" name="Khalf_gluc" public_interface="out" units="M" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>lambda</ci>
        <apply>
          <plus />
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_52</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_65</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_43</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_56</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_43</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_54</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_45</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_43</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_52</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_61</ci>
          </apply>
          <apply>
            <times />
            <ci>ks_12</ci>
            <ci>k0_23</ci>
            <ci>k_34</ci>
            <ci>k_45</ci>
            <ci>k_56</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>chi</ci>
        <apply>
          <times />
          <apply>
            <divide />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <ci>lambda</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_54</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_54</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
            </apply>
            <apply>
              <times />
              <ci>ks_12</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>beta</ci>
        <apply>
          <times />
          <apply>
            <divide />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <ci>lambda</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_34</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_34</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k0_23</ci>
              <ci>k_16</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>alpha</ci>
        <apply>
          <times />
          <apply>
            <divide />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <ci>lambda</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_54</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_65</ci>
            </apply>
            <apply>
              <times />
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
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              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
              <ci>k_61</ci>
            </apply>
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              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
              <ci>k_61</ci>
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              <times />
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
            </apply>
            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
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            <apply>
              <times />
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
              <ci>k_61</ci>
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            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
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            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
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              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
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            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_56</ci>
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              <times />
              <ci>k_16</ci>
              <ci>k_25</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
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              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_56</ci>
            </apply>
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              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_54</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_34</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_45</ci>
              <ci>k_52</ci>
            </apply>
            <apply>
              <times />
              <ci>k_16</ci>
              <ci>k_21</ci>
              <ci>k_32</ci>
              <ci>k_43</ci>
              <ci>k_52</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>gamma</ci>
        <apply>
          <times />
          <apply>
            <divide />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <ci>lambda</ci>
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