<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2 <author> <firstname>Jonna</firstname> <surname>Terkildsen</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil> </affiliation> </author> </articleinfo> <sect1 id="sec_status"> Model Status This CellML model has been curated, the units are consistent and the model runs in COR and PCEnv. This model recreates the published results. </sect1> <sect1 id="sec_structure"> Model Structure 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. The original paper reference is cited below: 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, Journal of Biological Chemistry , 271, 32678-32683. PubMed ID: 8955098 <informalfigure float="0" id="fig_reaction_diagram"> <mediaobject> <imageobject> <objectinfo> model diagram </objectinfo> <imagedata fileref="mackenzie_1996.png" /> </imageobject> </mediaobject> Schematic diagram of the Mackenzie et al 1996 SGLT2 model. C' represents the external-facing carrier. C'' represents the internal-facing carrier. </informalfigure> </sect1> </documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:j.0="http://www.example.org/foo/bar/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:j.1="http://imc.org/vCard/3.0#"> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <dcterms:created rdf:parseType="Resource"> <dcterms:W3CDTF>2009-10-28</dcterms:W3CDTF> </dcterms:created> <dc:creator rdf:parseType="Resource"> <vCard:ORG rdf:parseType="Resource"> <vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname> </vCard:ORG> <vCard:EMAIL> <j.1:internet> <rdf:value>j.terkildsen@auckland.ac.nz</rdf:value> </j.1:internet> </vCard:EMAIL> <vCard:N rdf:parseType="Resource"> <vCard:Given>Jonna</vCard:Given> <vCard:Family>Terkildsen</vCard:Family> </vCard:N> </dc:creator> </rdf:Description> <j.0:bazfoo/> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#mackenzie_1996"> <bqs:reference rdf:parseType="Resource"> <bqs:JournalArticle rdf:parseType="Resource"> <bqs:last_page>32683</bqs:last_page> <bqs:first_page>32678</bqs:first_page> <bqs:volume>271</bqs:volume> <bqs:Journal rdf:parseType="Resource"> <dc:title>Journal of Biological Chemistry</dc:title> </bqs:Journal> <dc:title>Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2</dc:title> <dc:creator> <rdf:Seq> <rdf:li rdf:parseType="Resource"> <bqs:Person rdf:parseType="Resource"> <vCard:N rdf:parseType="Resource"> <vCard:Given>M</vCard:Given> <vCard:Family>Mackenzie</vCard:Family> </vCard:N> </bqs:Person> </rdf:li> <rdf:li rdf:parseType="Resource"> <bqs:Person rdf:parseType="Resource"> <vCard:N rdf:parseType="Resource"> <vCard:Other>F</vCard:Other> <vCard:Other>D</vCard:Other> <vCard:Given>D</vCard:Given> <vCard:Family>Loo</vCard:Family> </vCard:N> </bqs:Person> </rdf:li> <rdf:li rdf:parseType="Resource"> <bqs:Person rdf:parseType="Resource"> <vCard:N rdf:parseType="Resource"> <vCard:Given>M</vCard:Given> <vCard:Family>Panayotova-Heiermann</vCard:Family> </vCard:N> </bqs:Person> </rdf:li> <rdf:li rdf:parseType="Resource"> <bqs:Person rdf:parseType="Resource"> <vCard:N rdf:parseType="Resource"> <vCard:Other>M</vCard:Other> <vCard:Given>E</vCard:Given> <vCard:Family>Wright</vCard:Family> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </bqs:JournalArticle> <bqs:Pubmed_id>8955098</bqs:Pubmed_id> </bqs:reference> <bqs:reference rdf:parseType="Resource"> <dc:subject rdf:parseType="Resource"> <rdf:value> <rdf:Bag> <rdf:li>Na/glucose cotransport</rdf:li> <rdf:li>ion transport</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </dc:subject> </bqs:reference> <cmeta:comment rdf:parseType="Resource"> <dc:creator rdf:parseType="Resource"> <vCard:FN>Jonna Terkildsen</vCard:FN> </dc:creator> <rdf:value>This is the CellML description of the Mackenzie et al 1996 quantitative model of the Na/glucose cotransporter (SGLT2).</rdf:value> </cmeta:comment> <dc:title>The Mackenzie et al 1996 quantitative model of the Na/glucose cotransporter (SGLT2).</dc:title> </rdf:Description> </rdf:RDF>
C:\Users\Christopher\Dropbox\Work Related\Annotated Models\MacKenzie_1996\mackenzie_1996.cellml
Model of the pig kidney Na1/Glucose cotransporter SGLT2
Area of spatial entity
Charge flow rate
Chemical concentration
Chemical molar amount
Electrical potential
sodium(1+)
methyl alpha-D-glucopyranoside
sodium-glucose transport protein subtype 2 inhibitor
oocyte
Plasma membrane
Portion of cytosol
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
Cell culture medium
External Na Bound SGLT2 Cotransporter
External Na and Substrate Bound SGLT2 Cotransporter
External Unbound SGLT2 Cotransporter
Glucose transport across cell membrane via SGLT2 cotransporters
Internal Na Bound SGLT2 Cotransporter
Internal Na and Substrate Bound SGLT2 Cotransporter
Internal Unbound SGLT2 Cotransporter
Steady state external unbound cotransporter concentration
Steady state external Na bound cotransporter concentration
Steady state external CNaS concentration
Steady state internal CNaS concentration
Steady state internal CNa concentration
Steady state internal unbound cotransporter concentration
Pre-steady state external unbound cotransporter concentration
Pre-steady state external Na bound cotransporter concentration
Pre-steady state external CNaS concentration
Pre-steady state internal CNa concentration
Pre-steady state internal unbound cotransporter concentration
Faraday constant
Na glucose steady state current
Na-glucose pre-steady state current
Sodium ion flow into the cytosol
Fraction of membrane electric field between bulk solution and external face Na binding site.
Fraction of membrane electric field between bulk solution and internal face Na binding site.
Fraction of the membrane field sensed by the empty binding on the carrier durring translocation.
Rate for sodium ion binding to external unbound cotransporter.
Rate for external unbound transport site to internal unbound transport site reaction step
Rate for sodium ion release from external bound cotransporter.
Rate for external CNa to internal CNa reaction step.
Rate for external CNaS to internal CNas reaction step
Rate for internal CNaS to external CNaS reaction step
Rate for internal CNa to external CNa reaction step
Rate for release of Sodium from internal Na bound cotransporter
Rate for internal unbound cotransporter binding site to external unbound cotransporter binding site reaction step
Rate for sodium ion release from internal Na bound cotransporter.
Sodium-glucose coupling coefficent
Na valence
Empty transporter valence
<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>
Sodium ion flow into cytosol via SGLT2 cotransporter
Time - Solution Domain
Intracellular sodium concentration
Sodium concentration in cell culture medium
Electrical potential of the cell membrane
Intracellular glucose concentration
Glucose concentration in experimental medium
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>V</ci> </apply> <cn type="e-notation" xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="volt_per_second"> 100 <sep /> -6 </cn> </apply>
Density of functional SGLT2 carriers in the oocyte membrane
Rate for binding of glucose to external CNa binding site
Rate for release of glucose from external CNaS
Rate constant for release of glucose from internal CNaS
Rate for binding of glucose to internal CNa binding site
<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>
Avogadro's number
Boltzmann constant
Temperature
Rate constant for sodium ion binding to external unbound cotransporter.
Rate constant for external unbound transport site to internal unbound transport site reaction step
Rate constant for sodium ion release from external bound cotransporter.
Rate constant for binding of glucose to external CNa binding site
Rate constant for external CNa to internal CNa reaction step.
Rate constant for release of glucose from external CNaS
Rate constant for external CNaS to internal CNas reaction step
Rate constant for internal CNaS to external CNaS reaction step
Rate constant for internal CNa to external CNa reaction step
Rate constant for binding of glucose to internal CNa binding site
Rate constant for internal unbound cotransporter binding site to external unbound cotransporter binding site reaction step
Rate constant for sodium ion release from internal Na bound cotransporter.
Relationship between membrane voltage and F*R/T.
<apply> <eq /> <ci>alpha_p</ci> <apply> <minus /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>delta</ci> </apply> <ci>alpha_pp</ci> </apply> </apply> <apply> <eq /> <ci>C_T</ci> <apply> <divide /> <apply> <times /> <cn type="e-notation" xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="umol_per_mol"> 1 <sep /> 6 </cn> <ci>N_C</ci> </apply> <ci>N_Avo</ci> </apply> </apply> <apply> <eq /> <ci>mu</ci> <apply> <divide /> <apply> <times /> <ci>F</ci> <ci>V</ci> </apply> <apply> <times /> <ci>R</ci> <ci>T</ci> </apply> </apply> </apply>
Maximum sodium current across cell membrane
Maximum glucose current across cell membrane
Experimental substrate sodium concentration for half maximal current.
Experimental substrate glucose concentration for half maximal current.
Membrane dislocation
Sodium concentration independent rate for sodium ion binding to external unbound cotransporter.
Sum of all enzymes.
Glucose independent rate constant for binding of glucose to internal CNa binding site
Rate constant for release of Sodium from internal Na bound cotransporter
Rate for release of glucose from internal CNaS
Glucose concentration independent rate for internal CNa to external CNa reaction step
<apply> <eq /> <ci>ks_12</ci> <apply> <times /> <ci>k0_12</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <ci>n</ci> </apply> <ci>alpha_p</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_12</ci> <apply> <times /> <ci>ks_12</ci> <apply> <power /> <ci>Na_o</ci> <ci>n</ci> </apply> </apply> </apply> <apply> <eq /> <ci>k_21</ci> <apply> <times /> <ci>k0_21</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <ci>n</ci> <ci>z_Na</ci> <ci>alpha_p</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_23</ci> <apply> <times /> <ci>k0_23</ci> <ci>glucose_o</ci> </apply> </apply> <apply> <eq /> <ci>k_32</ci> <ci>k0_32</ci> </apply> <apply> <eq /> <ci>k_34</ci> <apply> <times /> <ci>k0_34</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <apply> <plus /> <ci>z_c</ci> <ci>n</ci> </apply> </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_43</ci> <apply> <times /> <ci>k0_43</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <plus /> <ci>z_c</ci> <ci>n</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_45</ci> <ci>k0_45</ci> </apply> <apply> <eq /> <ci>k_54</ci> <apply> <times /> <ci>k0_54_temp</ci> <ci>glucose_i</ci> </apply> </apply> <apply> <eq /> <ci>k_25</ci> <apply> <times /> <ci>k0_25</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <apply> <plus /> <ci>z_c</ci> <ci>n</ci> </apply> </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_temp</ci> <apply> <times /> <ci>k0_52</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <plus /> <ci>z_c</ci> <ci>n</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_56</ci> <apply> <times /> <ci>k0_56</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <ci>n</ci> </apply> <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_65</ci> <apply> <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>