- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-01-20 12:22:13+13:00
- Desc:
- Extensively curated the maths of the model based on a) the curated 1999 Winslow et al. CellML model and also using COR to fix old problems in the CellML which had previously been overlooked without the support of tools to validate the model. Needs further curation. Waiting for original model code from the author.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/michailova_mcculloch_2001/rawfile/f5267ff69b41fccbe8607437c673fb8c6505fcec/michailova_mcculloch_2001.cellml
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<article>
<articleinfo>
<title>Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both COR and PCEnv. The units have been checked and they are consistent. Unfortunately the CellML model is still not quite reproducing the published results. We will continue to curate the model and hope to get it fully working.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating equations for Ca(2+) and Mg(2+) buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps). The results indicate that, under normal conditions, Ca(2+) binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca(2+) signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers systolic Ca(2+), increases Ca(2+) influx through L-type channels, and decreases the efficiency of the Na(+)/Ca(2+) exchanger in extruding Ca(2+) during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP levels. High Ca(2+) concentrations developed near the membrane might have a greater influence on Mg(2+), ATP, and ADP concentrations than that of the lower Ca(2+) concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte, Anushka Michailova and Andrew McCulloch, 2001, <emphasis>Biophysical Journal</emphasis>, 81, 614-629. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/11463611">PubMed ID: 11463611</ulink>
</para>
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<imageobject>
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<title>cell diagram</title>
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<caption>Schematic diagram of the mechanisms involved in the model.</caption>
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</sect1>
</article>
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<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="X_kr"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_K</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>K_o</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_K_o</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>K_o</ci>
<cn cellml:units="millimolar">4</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_V</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">1.4945</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0446</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Kr</ci>
<apply>
<times/>
<ci>g_Kr</ci>
<ci>f_K_o</ci>
<ci>R_V</ci>
<ci>X_kr</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate">
<variable units="dimensionless" public_interface="out" name="X_kr" initial_value="0.51"/>
<variable units="dimensionless" name="K12"/>
<variable units="dimensionless" name="K21"/>
<variable units="dimensionless" name="X_kr_inf"/>
<variable units="second" name="tau_X_kr"/>
<variable units="dimensionless" name="tau_factor" initial_value="1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K12</ci>
<apply>
<exp/>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">5.495</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.1691</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K21</ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">7.677</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0128</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>X_kr_inf</ci>
<apply>
<divide/>
<ci>K12</ci>
<apply>
<plus/>
<ci>K12</ci>
<ci>K21</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_X_kr</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">0.001</cn>
<apply>
<plus/>
<ci>K12</ci>
<ci>K21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>tau_factor</ci>
<cn cellml:units="second">0.027</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_kr</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>X_kr_inf</ci>
<ci>X_kr</ci>
</apply>
<ci>tau_X_kr</ci>
</apply>
</apply>
</math>
</component>
<component name="slow_activating_delayed_rectifiyer_K_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ks"/>
<variable units="milliS_per_microF" name="g_Ks" initial_value="0.0027134"/>
<variable units="millivolt" name="E_Ks"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="X_ks"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ks</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci>K_o</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01833</cn>
<ci>Na_o</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>K_i</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01833</cn>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<apply>
<power/>
<ci>X_ks</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ks</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_activating_delayed_rectifiyer_K_current_X_ks_gate">
<variable units="dimensionless" public_interface="out" name="X_ks" initial_value="0.264"/>
<variable units="second" name="tau_X_ks"/>
<variable units="dimensionless" name="X_ks_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>X_ks_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">24.7</cn>
</apply>
</apply>
<cn cellml:units="millivolt">13.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_X_ks</ci>
<apply>
<divide/>
<cn cellml:units="second">0.001</cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0000719</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.148</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.000131</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0687</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_ks</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>X_ks_infinity</ci>
<ci>X_ks</ci>
</apply>
<ci>tau_X_ks</ci>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_to1"/>
<variable units="milliS_per_microF" name="g_to1" initial_value="0.23815"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="X_to1"/>
<variable units="dimensionless" private_interface="in" name="Y_to1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to1</ci>
<apply>
<times/>
<ci>g_to1</ci>
<ci>X_to1</ci>
<ci>Y_to1</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_X_to1_gate">
<variable units="dimensionless" public_interface="out" name="X_to1" initial_value="2.63"/>
<variable units="per_second" name="alpha_X_to1"/>
<variable units="per_second" name="beta_X_to1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_X_to1</ci>
<apply>
<times/>
<cn cellml:units="per_second">45.16</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03577</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_X_to1</ci>
<apply>
<times/>
<cn cellml:units="per_second">98.9</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.06237</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_to1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_X_to1</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>X_to1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_X_to1</ci>
<ci>X_to1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_Y_to1_gate">
<variable units="dimensionless" public_interface="out" name="Y_to1" initial_value="0.99"/>
<variable units="per_second" name="alpha_Y_to1"/>
<variable units="per_second" name="beta_Y_to1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_Y_to1</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second">5.415</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.051335</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_Y_to1</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second">5.415</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.051335</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Y_to1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_Y_to1</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Y_to1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_Y_to1</ci>
<ci>Y_to1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="milliS_per_microF" name="g_K1" initial_value="2.8"/>
<variable units="millimolar" name="K_mK1" initial_value="13"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" private_interface="out" name="R"/>
<variable units="kelvin" public_interface="in" private_interface="out" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" private_interface="out" name="F"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E_K"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="dimensionless" private_interface="in" name="K1_infinity_V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<ci>K1_infinity_V</ci>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mK1</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current_K1_gate">
<variable units="dimensionless" public_interface="out" name="K1_infinity_V"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K1_infinity_V</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.5</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.002216"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="Kp_V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kp</ci>
<apply>
<times/>
<ci>g_Kp</ci>
<ci>Kp_V</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current_Kp_gate">
<variable units="dimensionless" public_interface="out" name="Kp_V"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Kp_V</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">7.488</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_exchanger">
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="microA_per_microF" name="K_NaCa" initial_value="0.3"/>
<variable units="dimensionless" name="K_sat" initial_value="0.2"/>
<variable units="dimensionless" name="eta" initial_value="0.35"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_NaCa</ci>
<cn cellml:units="dimensionless">5000</cn>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>K_mNa</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>K_mCa</ci>
<ci>Ca_o</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_sat</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>eta</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>eta</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>eta</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<variable units="microA_per_microF" name="i_NaK_winslow"/>
<variable units="microA_per_microF" name="I_NaK" initial_value="0.693"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="millimolar" name="K_mNa_i" initial_value="10"/>
<variable units="millimolar" name="K_mK_o" initial_value="1.5"/>
<variable units="dimensionless" name="sigma"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="MgATP_i"/>
<variable units="millimolar" public_interface="in" name="MgATP_i0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_NaK</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1245</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0365</cn>
<ci>sigma</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<cn cellml:units="dimensionless">7</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Na_o</ci>
<cn cellml:units="millimolar">67.3</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>MgATP_i</ci>
<ci>MgATP_i0</ci>
</apply>
<ci>i_NaK_winslow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaK_winslow</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>I_NaK</ci>
<ci>f_NaK</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_mNa_i</ci>
<ci>Na_i</ci>
</apply>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mK_o</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<variable units="microA_per_microF" name="i_p_Ca_winslow"/>
<variable units="millimolar" name="K_mpCa" initial_value="0.00005"/>
<variable units="microA_per_microF" name="I_pCa" initial_value="0.05"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="MgATP_i"/>
<variable units="millimolar" public_interface="in" name="MgATP_i0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>MgATP_i</ci>
<ci>MgATP_i0</ci>
</apply>
<ci>i_p_Ca_winslow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_p_Ca_winslow</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>I_pCa</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>K_mpCa</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.0003842"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_o</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_b</ci>
<apply>
<times/>
<ci>g_Cab</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.0031"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na_b</ci>
<apply>
<times/>
<ci>g_Nab</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_Ca_K"/>
<variable units="cm_per_second" name="P_Ca" initial_value="3.125e-4"/>
<variable units="cm_per_second" name="P_K" initial_value="5.79e-7"/>
<variable units="cm_per_second" name="p_prime_k"/>
<variable units="microA_per_microF" name="i_Ca_half" initial_value="-0.265"/>
<variable units="microA_per_microF" name="i_Ca_max"/>
<variable units="dimensionless" name="O" initial_value="9.84546e-21"/>
<variable units="dimensionless" name="O_Ca" initial_value="0"/>
<variable units="per_second" name="alpha"/>
<variable units="per_second" name="beta"/>
<variable units="per_second" name="gamma"/>
<variable units="per_second" name="alpha_a"/>
<variable units="per_second" name="beta_b"/>
<variable units="dimensionless" name="a" initial_value="2"/>
<variable units="dimensionless" name="b" initial_value="2"/>
<variable units="per_second" name="g" initial_value="2000"/>
<variable units="per_second" name="f" initial_value="300"/>
<variable units="per_second" name="gprime" initial_value="7000"/>
<variable units="per_second" name="fprime" initial_value="7"/>
<variable units="per_second" name="omega" initial_value="10"/>
<variable units="dimensionless" name="C0" initial_value="0.997208"/>
<variable units="dimensionless" name="C1" initial_value="6.38897e-5"/>
<variable units="dimensionless" name="C2" initial_value="1.535e-9"/>
<variable units="dimensionless" name="C3" initial_value="1.63909e-14"/>
<variable units="dimensionless" name="C4" initial_value="6.56337e-20"/>
<variable units="dimensionless" name="C_Ca0" initial_value="0.00272826"/>
<variable units="dimensionless" name="C_Ca1" initial_value="6.99215e-7"/>
<variable units="dimensionless" name="C_Ca2" initial_value="6.71989e-11"/>
<variable units="dimensionless" name="C_Ca3" initial_value="2.87031e-15"/>
<variable units="dimensionless" name="C_Ca4" initial_value="4.59752e-20"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="microF_per_cm2" public_interface="in" name="C_sc"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca</ci>
<apply>
<times/>
<ci>i_Ca_max</ci>
<ci>y</ci>
<apply>
<plus/>
<ci>O</ci>
<ci>O_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_K</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>p_prime_k</ci>
<apply>
<times/>
<cn cellml:units="microF_per_cm2">1</cn>
<cn cellml:units="second_per_millisecond">1</cn>
</apply>
</apply>
<ci>y</ci>
<apply>
<plus/>
<ci>O</ci>
<ci>O_Ca</ci>
</apply>
<ci>V</ci>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>K_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>K_o</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p_prime_k</ci>
<apply>
<divide/>
<ci>P_K</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>i_Ca_max</ci>
<ci>i_Ca_half</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_max</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>P_Ca</ci>
<apply>
<times/>
<cn cellml:units="microF_per_cm2">1</cn>
<cn cellml:units="second_per_millisecond">1</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
<ci>V</ci>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dimensionless">1000</cn>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millimolar">0.001</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.341</cn>
<ci>Ca_o</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<times/>
<cn cellml:units="per_second">400</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">2</cn>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<times/>
<cn cellml:units="per_second">50</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_a</ci>
<apply>
<times/>
<ci>alpha</ci>
<ci>a</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_b</ci>
<apply>
<divide/>
<ci>beta</ci>
<ci>b</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second">103.75</cn>
<ci>Ca_ss</ci>
</apply>
<cn cellml:units="millimolar">1</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C0</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta</ci>
<ci>C1</ci>
</apply>
<apply>
<times/>
<ci>omega</ci>
<ci>C_Ca0</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha</ci>
</apply>
<ci>gamma</ci>
</apply>
<ci>C0</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha</ci>
<ci>C0</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
<ci>C2</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>omega</ci>
<ci>b</ci>
</apply>
<ci>C_Ca1</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>beta</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>a</ci>
</apply>
</apply>
<ci>C1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C2</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha</ci>
<ci>C1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>beta</ci>
<ci>C3</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>C_Ca2</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>C2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha</ci>
<ci>C2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>beta</ci>
<ci>C4</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>C_Ca3</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>alpha</ci>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<ci>C3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C4</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>C3</ci>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>O</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<ci>C_Ca4</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>f</ci>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
<ci>C4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>f</ci>
<ci>C4</ci>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>O</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_Ca0</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_b</ci>
<ci>C_Ca1</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>C0</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha_a</ci>
</apply>
<ci>omega</ci>
</apply>
<ci>C_Ca0</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_Ca1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha_a</ci>
<ci>C_Ca0</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta_b</ci>
<ci>C_Ca2</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>a</ci>
<ci>C1</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>beta_b</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha_a</ci>
</apply>
<apply>
<divide/>
<ci>omega</ci>
<ci>b</ci>
</apply>
</apply>
<ci>C_Ca1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_Ca2</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha_a</ci>
<ci>C_Ca1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>beta_b</ci>
<ci>C_Ca3</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>C2</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_b</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha_a</ci>
</apply>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>C_Ca2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_Ca3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha_a</ci>
<ci>C_Ca2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>beta_b</ci>
<ci>C_Ca4</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>C3</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_b</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>alpha_a</ci>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<ci>C_Ca3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_Ca4</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_a</ci>
<ci>C_Ca3</ci>
</apply>
<apply>
<times/>
<ci>gprime</ci>
<ci>O_Ca</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<power/>
<ci>a</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>C4</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_b</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>fprime</ci>
<apply>
<divide/>
<ci>omega</ci>
<apply>
<power/>
<ci>b</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
<ci>C_Ca4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Ca</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>fprime</ci>
<ci>C_Ca4</ci>
</apply>
<apply>
<times/>
<ci>gprime</ci>
<ci>O_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.798"/>
<variable units="dimensionless" name="y_infinity"/>
<variable units="second" name="tau_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>y_infinity</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.8</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">12.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_y</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="second">20</cn>
<apply>
<divide/>
<cn cellml:units="second">600</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">9.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1000</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>y_infinity</ci>
<ci>y</ci>
</apply>
<ci>tau_y</ci>
</apply>
</apply>
</math>
</component>
<component name="RyR_channel">
<variable units="millimolar_per_second" public_interface="out" name="J_rel"/>
<variable units="per_second" name="v1" initial_value="1800"/>
<variable units="millimolar4_per_second" name="k_a_plus" initial_value="1.215e13"/>
<variable units="per_second" name="k_a_minus" initial_value="576"/>
<variable units="millimolar3_per_second" name="k_b_plus" initial_value="4.05e9"/>
<variable units="per_second" name="k_b_minus" initial_value="1930"/>
<variable units="per_second" name="k_c_plus" initial_value="100"/>
<variable units="per_second" name="k_c_minus" initial_value="0.8"/>
<variable units="dimensionless" name="P_O1" initial_value="0"/>
<variable units="dimensionless" name="P_O2" initial_value="0"/>
<variable units="dimensionless" name="P_C1" initial_value="0.47"/>
<variable units="dimensionless" name="P_C2" initial_value="0.53"/>
<variable units="dimensionless" name="n" initial_value="4"/>
<variable units="dimensionless" name="m" initial_value="3"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_C1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k_a_plus</ci>
</apply>
<apply>
<power/>
<ci>Ca_ss</ci>
<ci>n</ci>
</apply>
<ci>P_C1</ci>
</apply>
<apply>
<times/>
<ci>k_a_minus</ci>
<ci>P_O1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_O1</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_a_plus</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<ci>n</ci>
</apply>
<ci>P_C1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k_a_minus</ci>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_b_plus</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<ci>m</ci>
</apply>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_c_plus</ci>
<ci>P_O1</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k_b_minus</ci>
<ci>P_O2</ci>
</apply>
<apply>
<times/>
<ci>k_c_minus</ci>
<ci>P_C2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_O2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_b_plus</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<ci>m</ci>
</apply>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_b_minus</ci>
<ci>P_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_C2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_c_plus</ci>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_c_minus</ci>
<ci>P_C2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_rel</ci>
<apply>
<times/>
<ci>v1</ci>
<apply>
<plus/>
<ci>P_O1</ci>
<ci>P_O2</ci>
</apply>
<apply>
<minus/>
<ci>Ca_JSR</ci>
<ci>Ca_ss</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SERCA2a_pump">
<variable units="millimolar_per_second" public_interface="out" name="J_up"/>
<variable units="millimolar_per_second" name="J_up_winslow"/>
<variable units="millimolar" name="K_fb" initial_value="0.000168"/>
<variable units="millimolar" name="K_rb" initial_value="3.29"/>
<variable units="dimensionless" name="fb"/>
<variable units="dimensionless" name="rb"/>
<variable units="millimolar_per_second" name="Vmaxf" initial_value="0.0813"/>
<variable units="millimolar_per_second" name="Vmaxr" initial_value="0.318"/>
<variable units="dimensionless" name="K_SR" initial_value="1"/>
<variable units="dimensionless" name="N_fb" initial_value="1.2"/>
<variable units="dimensionless" name="N_rb" initial_value="1"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<variable units="millimolar" public_interface="in" name="MgATP_i"/>
<variable units="millimolar" public_interface="in" name="MgATP_i0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fb</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>K_fb</ci>
</apply>
<ci>N_fb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rb</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_NSR</ci>
<ci>K_rb</ci>
</apply>
<ci>N_rb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_up</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>MgATP_i</ci>
<ci>MgATP_i0</ci>
</apply>
<ci>J_up_winslow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_up_winslow</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_SR</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>Vmaxf</ci>
<ci>fb</ci>
</apply>
<apply>
<times/>
<ci>Vmaxr</ci>
<ci>rb</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>fb</ci>
<ci>rb</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_Ca_fluxes">
<variable units="millimolar_per_second" public_interface="out" name="J_tr"/>
<variable units="millimolar_per_second" public_interface="out" name="J_xfer"/>
<variable units="millimolar_per_second" public_interface="out" name="J_trpn"/>
<variable units="second" name="tau_tr" initial_value="0.0005747"/>
<variable units="second" name="tau_xfer" initial_value="0.0267"/>
<variable units="millimolar" name="HTRPNCa" initial_value="0.98"/>
<variable units="millimolar" name="LTRPNCa" initial_value="0.078"/>
<variable units="millimolar_per_second" name="J_HTRPNCa"/>
<variable units="millimolar_per_second" name="J_LTRPNCa"/>
<variable units="dimensionless" name="HTRPN_tot" initial_value="0.14"/>
<variable units="dimensionless" name="LTRPN_tot" initial_value="0.07"/>
<variable units="per_millimolar_second" name="k_htrpn_plus" initial_value="20000"/>
<variable units="per_second" name="k_htrpn_minus" initial_value="0.066"/>
<variable units="per_millimolar_second" name="k_ltrpn_plus" initial_value="40000"/>
<variable units="per_second" name="k_ltrpn_minus" initial_value="40"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_tr</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_NSR</ci>
<ci>Ca_JSR</ci>
</apply>
<ci>tau_tr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_xfer</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
<ci>tau_xfer</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_trpn</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>HTRPN_tot</ci>
<ci>J_HTRPNCa</ci>
</apply>
<apply>
<times/>
<ci>LTRPN_tot</ci>
<ci>J_LTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_HTRPNCa</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HTRPNCa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HTRPNCa</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_htrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>HTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_htrpn_minus</ci>
<ci>HTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_LTRPNCa</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>LTRPNCa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>LTRPNCa</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_ltrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>LTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_ltrpn_minus</ci>
<ci>LTRPNCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="10"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="8.464E-5"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="159.48"/>
<variable units="millimolar" public_interface="out" name="Ca_ss" initial_value="1.315E-4"/>
<variable units="millimolar" public_interface="out" name="Ca_JSR" initial_value="0.2616"/>
<variable units="millimolar" public_interface="out" name="Ca_NSR" initial_value="0.2620"/>
<variable units="cm2" name="A_cap" initial_value="0.0001534"/>
<variable units="microlitre" name="V_myo" initial_value="0.00002584"/>
<variable units="microlitre" name="V_JSR" initial_value="0.00000016"/>
<variable units="microlitre" name="V_NSR" initial_value="0.0000021"/>
<variable units="microlitre" name="V_ss" initial_value="0.0000000012"/>
<variable units="millimolar" name="K_mCMDN" initial_value="0.00238"/>
<variable units="millimolar" name="K_mEGTA" initial_value="0.00015"/>
<variable units="millimolar" name="K_mCSQN" initial_value="0.8"/>
<variable units="millimolar" name="CMDN_tot" initial_value="0.05"/>
<variable units="millimolar" name="EGTA_tot" initial_value="0"/>
<variable units="millimolar" name="CSQN_tot" initial_value="15"/>
<variable units="dimensionless" name="beta_i"/>
<variable units="dimensionless" name="beta_SS"/>
<variable units="dimensionless" name="beta_JSR"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF_per_cm2" public_interface="in" name="C_sc"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_to1"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="millimolar_per_second" public_interface="in" name="J_up"/>
<variable units="millimolar_per_second" public_interface="in" name="J_rel"/>
<variable units="millimolar_per_second" public_interface="in" name="J_xfer"/>
<variable units="millimolar_per_second" public_interface="in" name="J_trpn"/>
<variable units="millimolar_per_second" public_interface="in" name="J_tr"/>
<variable units="per_millimolar_second" public_interface="in" name="k_plus_CaATP"/>
<variable units="per_second" public_interface="in" name="k_minus_CaATP"/>
<variable units="per_millimolar_second" public_interface="in" name="k_plus_CaADP"/>
<variable units="per_second" public_interface="in" name="k_minus_CaADP"/>
<variable units="millimolar" public_interface="in" name="CaADP_i"/>
<variable units="millimolar" public_interface="in" name="CaADP_ss"/>
<variable units="millimolar" public_interface="in" name="CaATP_ss"/>
<variable units="millimolar" public_interface="in" name="ATP_i"/>
<variable units="millimolar" public_interface="in" name="ADP_i"/>
<variable units="millimolar" public_interface="in" name="ADP_ss"/>
<variable units="millimolar" public_interface="in" name="ATP_ss"/>
<variable units="millimolar" public_interface="in" name="CaATP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_i</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_xfer</ci>
<apply>
<plus/>
<ci>J_up</ci>
<ci>J_trpn</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_p_Ca</ci>
<ci>i_Ca_b</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>A_cap</ci>
<ci>C_sc</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_i </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_i </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_Na_b</ci>
<apply>
<times/>
<ci>i_NaCa</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaK</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>A_cap</ci>
<cn cellml:units="microF_per_cm2">1</cn>
</apply>
<apply>
<times/>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<plus/>
<ci>i_Ca_K</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_K1</ci>
<ci>i_Kp</ci>
<ci>i_to1</ci>
<apply>
<times/>
<ci>i_NaK</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>A_cap</ci>
<cn cellml:units="microF_per_cm2">1</cn>
</apply>
<apply>
<times/>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_i</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CMDN_tot</ci>
<ci>K_mCMDN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCMDN</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>EGTA_tot</ci>
<ci>K_mEGTA</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mEGTA</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_SS</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CMDN_tot</ci>
<ci>K_mCMDN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCMDN</ci>
<ci>Ca_ss</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>EGTA_tot</ci>
<ci>K_mEGTA</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mEGTA</ci>
<ci>Ca_ss</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_JSR</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CSQN_tot</ci>
<ci>K_mCSQN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCSQN</ci>
<ci>Ca_JSR</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_ss</ci>
</apply>
<apply>
<times/>
<ci>beta_SS</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_rel</ci>
<ci>V_JSR</ci>
</apply>
<ci>V_ss</ci>
</apply>
<apply>
<times/>
<ci>k_minus_CaATP</ci>
<ci>CaATP_ss</ci>
</apply>
<apply>
<times/>
<ci>k_minus_CaADP</ci>
<ci>CaADP_ss</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_xfer</ci>
<ci>V_myo</ci>
</apply>
<ci>V_ss</ci>
</apply>
<apply>
<times/>
<ci>i_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>A_cap</ci>
<cn cellml:units="microF_per_cm2">1</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_ss</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k_plus_CaATP</ci>
<ci>Ca_ss</ci>
<ci>ATP_ss</ci>
</apply>
<apply>
<times/>
<ci>k_plus_CaADP</ci>
<ci>Ca_ss</ci>
<ci>ADP_ss</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_JSR</ci>
</apply>
<apply>
<times/>
<ci>beta_JSR</ci>
<apply>
<minus/>
<ci>J_tr</ci>
<ci>J_rel</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_NSR</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_up</ci>
<ci>V_myo</ci>
</apply>
<ci>V_NSR</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>J_tr</ci>
<ci>V_JSR</ci>
</apply>
<ci>V_NSR</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_and_Mg_buffering_by_ATP">
<variable units="millimolar" public_interface="out" name="CaATP_ss" initial_value="0.25E-3"/>
<variable units="millimolar" public_interface="out" name="ATP_ss"/>
<variable units="millimolar" public_interface="out" name="MgATP_i" initial_value="6.4395"/>
<variable units="millimolar" public_interface="out" name="MgATP_i0" initial_value="2.888"/>
<variable units="per_millimolar_second" public_interface="out" name="k_plus_CaATP" initial_value="225000.0"/>
<variable units="per_second" public_interface="out" name="k_minus_CaATP" initial_value="45000.0"/>
<variable units="per_millimolar_second" public_interface="out" name="k_plus_CaADP" initial_value="125000.0"/>
<variable units="per_second" public_interface="out" name="k_minus_CaADP" initial_value="193500"/>
<variable units="millimolar" public_interface="out" name="CaADP_i" initial_value="0.11E-6"/>
<variable units="millimolar" public_interface="out" name="CaADP_ss" initial_value="0.13E-6"/>
<variable units="millimolar" public_interface="out" name="ATP_i"/>
<variable units="millimolar" public_interface="out" name="ADP_i"/>
<variable units="millimolar" public_interface="out" name="ADP_ss"/>
<variable units="millimolar" public_interface="out" name="CaATP_i" initial_value="0.237E-3"/>
<variable units="millimolar" name="Mg_ss" initial_value="1.0"/>
<variable units="millimolar" name="Mg_i" initial_value="1.0"/>
<variable units="millimolar" name="MgADP_i" initial_value="0.298E-2"/>
<variable units="millimolar" name="MgADP_ss" initial_value="0.298E-2"/>
<variable units="millimolar" name="MgATP_ss" initial_value="6.4395"/>
<variable units="millimolar" name="ATP_tot" initial_value="7.0"/>
<variable units="per_millimolar_second" name="k_plus_MgATP" initial_value="125000.0"/>
<variable units="per_second" name="k_minus_MgATP" initial_value="10875.0"/>
<variable units="millimolar_per_second" name="Jxfer_CaATP"/>
<variable units="millimolar_per_second" name="Jxfer_MgATP"/>
<variable units="millimolar_per_second" name="Jxfer_Mg"/>
<variable units="second" name="tau_xfer_CaATP" initial_value="0.0534"/>
<variable units="second" name="tau_xfer_MgATP" initial_value="0.0534"/>
<variable units="second" name="tau_xfer_Mg" initial_value="0.0267"/>
<variable units="millimolar" name="ADP_tot" initial_value="0.005"/>
<variable units="per_millimolar_second" name="k_plus_MgADP" initial_value="125000.0"/>
<variable units="per_second" name="k_minus_MgADP" initial_value="84500.0"/>
<variable units="millimolar_per_second" name="Jxfer_CaADP"/>
<variable units="millimolar_per_second" name="Jxfer_MgADP"/>
<variable units="second" name="tau_xfer_CaADP" initial_value="0.0534"/>
<variable units="second" name="tau_xfer_MgADP" initial_value="0.0534"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="microlitre" public_interface="in" name="V_myo"/>
<variable units="microlitre" public_interface="in" name="V_ss"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_ss_calculation">
<eq/>
<ci> ATP_ss </ci>
<apply>
<minus/>
<ci> ATP_tot </ci>
<apply>
<plus/>
<ci> CaATP_ss </ci>
<ci> MgATP_ss </ci>
</apply>
</apply>
</apply>
<apply id="CaATP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaATP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_CaATP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="MgATP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgATP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_MgATP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ATP_i_calculation">
<eq/>
<ci> ATP_i </ci>
<apply>
<minus/>
<ci> ATP_tot </ci>
<apply>
<plus/>
<ci> CaATP_i </ci>
<ci> MgATP_i </ci>
</apply>
</apply>
</apply>
<apply id="CaATP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaATP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_CaATP </ci>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_i </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_i </ci>
</apply>
</apply>
</apply>
<apply id="MgATP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgATP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_MgATP </ci>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_i </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_i </ci>
</apply>
</apply>
</apply>
<apply id="Jxfer_CaATP_calculation">
<eq/>
<ci> Jxfer_CaATP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> CaATP_ss </ci>
<ci> CaATP_i </ci>
</apply>
<ci> tau_xfer_CaATP </ci>
</apply>
</apply>
<apply id="Jxfer_MgATP_calculation">
<eq/>
<ci> Jxfer_MgATP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> MgATP_ss </ci>
<ci> MgATP_i </ci>
</apply>
<ci> tau_xfer_MgATP </ci>
</apply>
</apply>
<apply id="ADP_ss_calculation">
<eq/>
<ci> ADP_ss </ci>
<apply>
<minus/>
<ci> ADP_tot </ci>
<apply>
<plus/>
<ci> CaADP_ss </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
</apply>
<apply id="CaADP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaADP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_CaADP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="MgADP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgADP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_MgADP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ADP_i_calculation">
<eq/>
<ci> ADP_i </ci>
<apply>
<minus/>
<ci> ADP_tot </ci>
<apply>
<plus/>
<ci> CaADP_i </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
</apply>
<apply id="CaADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaADP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_CaADP </ci>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_i </ci>
</apply>
</apply>
</apply>
<apply id="MgADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgADP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_MgADP </ci>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
</apply>
<apply id="Jxfer_CaADP_calculation">
<eq/>
<ci> Jxfer_CaADP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> CaADP_ss </ci>
<ci> CaADP_i </ci>
</apply>
<ci> tau_xfer_CaADP </ci>
</apply>
</apply>
<apply id="Jxfer_MgADP_calculation">
<eq/>
<ci> Jxfer_MgADP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> MgADP_ss </ci>
<ci> MgADP_i </ci>
</apply>
<ci> tau_xfer_MgADP </ci>
</apply>
</apply>
<apply id="Mg_ss_calculation">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Mg_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_ss </ci>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<times/>
<ci> Jxfer_Mg </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Mg_i_calculation">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Mg_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_Mg </ci>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_i </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Jxfer_Mg_calculation">
<eq/>
<ci> Jxfer_Mg </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Mg_ss </ci>
<ci> Mg_i </ci>
</apply>
<ci> tau_xfer_Mg </ci>
</apply>
</apply>
</math>
</component>
<component name="extracellular_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="138"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="4"/>
</component>
<component name="model_parameters">
<variable units="microlitre" public_interface="out" name="V_myo" initial_value="0.00002584"/>
<variable units="microlitre" public_interface="out" name="V_ss" initial_value="0.0000000012"/>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="rapid_activating_delayed_rectifiyer_K_current">
<component_ref component="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate"/>
</component_ref>
<component_ref component="slow_activating_delayed_rectifiyer_K_current">
<component_ref component="slow_activating_delayed_rectifiyer_K_current_X_ks_gate"/>
</component_ref>
<component_ref component="transient_outward_potassium_current">
<component_ref component="transient_outward_potassium_current_X_to1_gate"/>
<component_ref component="transient_outward_potassium_current_Y_to1_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current">
<component_ref component="plateau_potassium_current_Kp_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_y_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_activating_delayed_rectifiyer_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_activating_delayed_rectifiyer_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
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<rdf:RDF>
<rdf:Bag rdf:about="rdf:#6981282f-6933-4b11-8930-6ffdfafbd2fa">
<rdf:li>ventricular myocyte</rdf:li>
<rdf:li>ion pumps</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>energy buffering</rdf:li>
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<bqs:subject_type>keyword</bqs:subject_type>
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<vCard:Given>Anushka</vCard:Given>
<vCard:Family>Michailova</vCard:Family>
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<dc:creator rdf:resource="rdf:#2084fac1-fc3a-43ae-af04-872082d7362d"/>
<dc:title>
Model study of ATP and ADP buffering, transport of Ca2+ and Mg2+, and regulation of ion pumps in ventricular myocyte
</dc:title>
<bqs:volume>81</bqs:volume>
<bqs:first_page>614</bqs:first_page>
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<bqs:last_page>629</bqs:last_page>
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<rdf:Description rdf:about="rdf:#ab97c4d5-3feb-4acc-81ca-0df3754f35b9">
<dcterms:W3CDTF>2001-08</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#b4c02fdb-6f46-4151-a326-a17570778703">
<dcterms:W3CDTF>2004-05-30</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#b725903d-f76b-4c0d-9b0c-94d1627c342c">
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<rdf:Description rdf:about="rdf:#3c704b7c-f80d-41d6-9320-ab878dde6f6a">
<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:Description rdf:about="rdf:#6cc55125-b07b-471c-9583-11da22cea54a">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1ecb4ea7-8799-4a2b-8780-a4da84b07e61">
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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This is the CellML description of Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.
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<rdf:Description rdf:about="rdf:#250f3853-8685-4aa9-8cf4-9bebdaecc17c">
<dc:title>Biophysical Journal</dc:title>
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<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Auckland Bioengineering Institute
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Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.
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