<?xml version="1.0" encoding="UTF-8"?>
<!-- FILE : pasek_model_2006.xml -->
<model
name="pasek_simurda_christe_2006"
cmeta:id="pasek_simurda_christe_2006"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bqs="http://www.cellml.org/bqs/1.0#"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" >
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auclkand Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is a CellML 1.1 model. The units have been checked and are valid, and the model is valid CellML. Unfortunately the model is not able to be integrated in OpenCell at this point.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
"The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes" - Michal Pasek, Jiri Simurda, and Georges Christe, 2006, <emphasis>Philosophical Transactions of The Royal Society A</emphasis>, 81, 3029-3051. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16608703&dopt=Abstract">PubMed ID: 16608703</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<imagedata fileref="pasek_2006.png"/>
</imageobject>
</mediaobject>
<pCation>Schematic of a ventricular myocyte. The description of electrical activity of surface (s) and tubular (t) membrane comprises formulation of ion transporters that are labelled in the scheme. The intracellular space contains the subspace, the Ca2+ uptake and Ca2+ release compartments of sarcoplasmic reticulum (NSR, JSR) and the Ca2+ buffers calmodulin (Bcm), troponin (Bltrpn,Bhtrpn) and calsequestrin (Bcs). The small filled rectangles in JSR membrane represent ryanodine receptors. The small bi-directional arrows denote Ca2+ diffusion. The dashed arrow represents ionic diffusion between the tubular and the bulk space. The currents included in the model were: ICa, calcium inward current; IKto, time-dependent transient outward potassium current; IKst, steady-state outward potassium current; IKf, hyperpolarization-activated current; IK1, time-independent inward rectifier potassium current; INab, background sodium current; ICab, background calcium current; IKb, background potassium current; INaCa, Na+/Ca2+ exchanger current; INaK, electrogenic Na+/K+ ATPase pump current; IpCa, sarcolemmal Ca-pump current.</pCation>
</informalfigure>
<para>
Note that this model is based on a quantitative description of electrical activity of the rat ventricular myocyte proposed by Pandit et al. (2001), which has also been described in CellML and can be found in the CellML Model Respository.
</para>
</sect1>
</article>
</documentation>
<import xlink:href="pasek_model_2006_surface_membrane.cellml">
<component name="surface_membrane" component_ref="surface_membrane" />
</import>
<connection>
<map_components component_1="surface_membrane" component_2="common_current" />
<map_variables variable_1="Vm_s" variable_2="Vm_s" />
<map_variables variable_1="i_circ" variable_2="i_circ" />
</connection>
<connection>
<map_components component_1="surface_membrane" component_2="ion_concentrations" />
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="Ca_ss" variable_1="Ca_ss"/>
<map_variables variable_1="i_Kext" variable_2="i_Kext" />
<map_variables variable_1="i_Na_s" variable_2="i_Na_s" />
<map_variables variable_1="i_Ca_s" variable_2="i_Ca_s" />
<map_variables variable_1="i_BNa_s" variable_2="i_BNa_s" />
<map_variables variable_1="i_BCa_s" variable_2="i_BCa_s" />
<map_variables variable_1="i_BK_s" variable_2="i_BK_s" />
<map_variables variable_1="i_NaCa_s" variable_2="i_NaCa_s" />
<map_variables variable_1="i_NaK_s" variable_2="i_NaK_s" />
<map_variables variable_1="i_K1_s" variable_2="i_K1_s" />
<map_variables variable_1="i_Kto_s" variable_2="i_Kto_s" />
<map_variables variable_1="i_Kss_s" variable_2="i_Kss_s" />
<map_variables variable_1="i_CaP_s" variable_2="i_CaP_s" />
<map_variables variable_1="i_fNa_s" variable_2="i_fNa_s" />
<map_variables variable_1="i_fK_s" variable_2="i_fK_s" />
</connection>
<connection>
<map_components component_1="surface_membrane" component_2="model_parameters" />
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="Ca_e" variable_1="Ca_e"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="Cms" variable_1="Cms"/>
<map_variables variable_2="Sms" variable_1="Sms"/>
<map_variables variable_2="Smt" variable_1="Smt"/>
</connection>
<connection>
<map_components component_1="surface_membrane" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<import xlink:href="pasek_model_2006_tubular_membrane.cellml">
<component name="tubular_membrane" component_ref="tubular_membrane" />
</import>
<connection>
<map_components component_1="tubular_membrane" component_2="common_current" />
<map_variables variable_1="Vm_t" variable_2="Vm_t" />
<map_variables variable_1="i_circ" variable_2="i_circ" />
</connection>
<connection>
<map_components component_1="tubular_membrane" component_2="ion_concentrations" />
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="Na_t" variable_1="Na_t"/>
<map_variables variable_2="Ca_t" variable_1="Ca_t"/>
<map_variables variable_2="K_t" variable_1="K_t"/>
<map_variables variable_2="Ca_ss" variable_1="Ca_ss"/>
<map_variables variable_1="i_Na_t" variable_2="i_Na_t" />
<map_variables variable_1="i_Ca_t" variable_2="i_Ca_t" />
<map_variables variable_1="i_BNa_t" variable_2="i_BNa_t" />
<map_variables variable_1="i_BCa_t" variable_2="i_BCa_t" />
<map_variables variable_1="i_BK_t" variable_2="i_BK_t" />
<map_variables variable_1="i_NaCa_t" variable_2="i_NaCa_t" />
<map_variables variable_1="i_NaK_t" variable_2="i_NaK_t" />
<map_variables variable_1="i_K1_t" variable_2="i_K1_t" />
<map_variables variable_1="i_Kto_t" variable_2="i_Kto_t" />
<map_variables variable_1="i_Kss_t" variable_2="i_Kss_t" />
<map_variables variable_1="i_CaP_t" variable_2="i_CaP_t" />
<map_variables variable_1="i_fNa_t" variable_2="i_fNa_t" />
<map_variables variable_1="i_fK_t" variable_2="i_fK_t" />
</connection>
<connection>
<map_components component_1="tubular_membrane" component_2="model_parameters" />
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="Cmt" variable_1="Cmt"/>
<map_variables variable_2="Sms" variable_1="Sms"/>
<map_variables variable_2="Smt" variable_1="Smt"/>
</connection>
<connection>
<map_components component_1="tubular_membrane" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<units name="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_second">
<unit units="millivolt" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="per_millivolt2">
<unit units="volt" prefix="milli" exponent="-2"/>
</units>
<units name="cm">
<unit units="metre" prefix="centi" />
</units>
<units name="per_cm">
<unit units="metre" prefix="centi" exponent="-1"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="microS">
<unit units="siemens" prefix="micro"/>
</units>
<units name="microF">
<unit units="farad" prefix="micro"/>
</units>
<units name="microA">
<unit units="ampere" prefix="micro"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="millimolar2">
<unit units="millimolar" exponent="2"/>
</units>
<units name="millimolar_per_second">
<unit units="millimolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="millimolar2_per_cm3">
<unit units="millimolar" exponent="2"/>
<unit units="metre" prefix="centi" exponent="-3"/>
</units>
<units name="per_millimolar_per_second">
<unit units="millimolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="per_millimolar3_per_second">
<unit units="millimolar" exponent="-3"/>
<unit units="second" exponent="-1"/>
</units>
<units name="per_millimolar4">
<unit units="millimolar" exponent="-4"/>
</units>
<units name="per_millimolar4_per_second">
<unit units="per_millimolar4"/>
<unit units="second" exponent="-1"/>
</units>
<units name="microA_per_millimolar">
<unit units="microA"/>
<unit units="millimolar" exponent="-1"/>
</units>
<units name="microA_per_cm2">
<unit units="microA"/>
<unit units="cm2" exponent="-1"/>
</units>
<units name="microF_per_cm2">
<unit units="microF"/>
<unit units="cm2" exponent="-1"/>
</units>
<units name="kilo_ohm">
<unit units="ohm" prefix="kilo" />
</units>
<units name="ohm_per_cm2">
<unit units="ohm"/>
<unit units="cm2" exponent="-1"/>
</units>
<units name="microA_per_millimolar4">
<unit units="microA"/>
<unit units="per_millimolar4"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="kelvin" exponent="-1"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="mole_per_coulomb">
<unit units="coulomb_per_mole" exponent="-1"/>
</units>
<units name="cm3">
<unit units="metre" prefix="centi" exponent="3"/>
</units>
<!-- global variables -->
<component name="environment">
<variable name="time" units="second" public_interface="out"/>
</component>
<component name="model_parameters">
<variable name="R" units="joule_per_kilomole_kelvin" initial_value="8310" public_interface="out"/>
<variable name="T" units="kelvin" initial_value="295" public_interface="out"/>
<variable name="F" units="coulomb_per_mole" initial_value="96500" public_interface="out"/>
<variable name="Na_e" units="millimolar" initial_value="140" public_interface="out"/>
<variable name="Ca_e" units="millimolar" initial_value="1.2" public_interface="out"/>
<variable name="K_e" units="millimolar" initial_value="5.4" public_interface="out"/>
<variable name="Vt" units="cm3" public_interface="out"/>
<variable name="Vd" units="cm3" public_interface="out"/>
<variable name="Vmyo" units="cm3" public_interface="out"/>
<variable name="Sms" units="cm2" public_interface="out"/>
<variable name="Smt" units="cm2" public_interface="out"/>
<variable name="Cms" units="microF" public_interface="out"/>
<variable name="Cmt" units="microF" public_interface="out"/>
<variable name="Vc" units="cm3" />
<variable name="VSRup" units="cm3" />
<variable name="VSRrel" units="cm3" />
<variable name="pt" units="dimensionless" />
<variable name="Lt" units="cm" />
<variable name="Rst" units="ohm" />
<variable name="Rot" units="ohm_per_cm2" initial_value="83.33" />
<variable name="radiust" units="cm" initial_value="150e-7" />
<variable name="ptcm" units="per_cm" initial_value="30000000" />
<variable name="Smtot" units="cm2" initial_value="0.0001" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<ci>Vc</ci>
<apply><divide/>
<ci>Smtot</ci>
<cn cellml:units="per_cm">7850</cn>
</apply>
</apply>
<apply><eq/>
<ci>Vmyo</ci>
<apply><times/>
<ci>Vc</ci>
<cn cellml:units="dimensionless">0.585</cn>
</apply>
</apply>
<apply><eq/>
<ci>VSRup</ci>
<apply><times/>
<ci>Vc</ci>
<cn cellml:units="dimensionless">0.0315</cn>
</apply>
</apply>
<apply><eq/>
<ci>VSRrel</ci>
<apply><times/>
<ci>Vc</ci>
<cn cellml:units="dimensionless">0.0035</cn>
</apply>
</apply>
<apply><eq/>
<ci>Vd</ci>
<apply><times/>
<ci>Vc</ci>
<cn cellml:units="dimensionless">0.000075</cn>
</apply>
</apply>
<apply><eq/>
<ci>Sms</ci>
<apply><minus/>
<ci>Smtot</ci>
<apply><times/>
<cn cellml:units="per_cm">0.44e4</cn>
<ci>Vc</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci>Smt</ci>
<apply><minus/>
<ci>Smtot</ci>
<ci>Sms</ci>
</apply>
</apply>
<apply><eq/>
<ci>pt</ci>
<apply><times/>
<ci>ptcm</ci>
<ci>Sms</ci>
</apply>
</apply>
<apply><eq/>
<ci>Lt</ci>
<apply><divide/>
<ci>Smt</ci>
<apply><times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="dimensionless">3.14159</cn>
<ci>radiust</ci>
<ci>pt</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci>Vt</ci>
<apply><times/>
<cn cellml:units="dimensionless">3.14159</cn>
<apply><power/>
<ci>radiust</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Lt</ci>
<ci>pt</ci>
</apply>
</apply>
<apply><eq/>
<ci>Cmt</ci>
<apply><times/>
<ci>Smt</ci>
<cn cellml:units="microF_per_cm2">1</cn>
</apply>
</apply>
<apply><eq/>
<ci>Cms</ci>
<apply><times/>
<ci>Sms</ci>
<cn cellml:units="microF_per_cm2">1</cn>
</apply>
</apply>
<apply><eq/>
<ci>Rst</ci>
<apply><divide/>
<apply><times/>
<ci>Rot</ci>
<apply><divide/>
<ci>Lt</ci>
<cn cellml:units="cm">2</cn>
</apply>
</apply>
<apply><times/>
<cn cellml:units="dimensionless">3.14159</cn>
<apply><power/>
<ci>radiust</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>pt</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Electrical interaction -->
<component name="common_current">
<variable name="i_circ" public_interface="out" units="microA" />
<variable name="R_st" units="kilo_ohm" initial_value="20.0"/>
<variable name="Vm_s" units="millivolt" public_interface="in"/>
<variable name="Vm_t" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<ci>i_circ</ci>
<apply><times/>
<cn cellml:units="dimensionless">1000</cn>
<apply><divide/>
<apply><minus/>
<ci>Vm_s</ci>
<ci>Vm_t</ci>
</apply>
<ci>R_st</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- intracellular calcium handling -->
<component name="SR_Ca_release_channel">
<variable name="J_CaSRrel" units="millimolar_per_second" public_interface="out"/>
<variable name="kap" units="per_millimolar4_per_second" initial_value="12.15e12"/>
<variable name="kam" units="per_second" initial_value="576"/>
<variable name="kbp" units="per_millimolar3_per_second" initial_value="4.05e9"/>
<variable name="kbm" units="per_second" initial_value="1930"/>
<variable name="kcp" units="per_second" initial_value="100"/>
<variable name="kcm" units="per_second" initial_value="0.8"/>
<variable name="F2" units="dimensionless" initial_value="3.8333331e-4"/>
<variable name="F3" units="dimensionless" initial_value="6.4516879e-11"/>
<variable name="F1" units="dimensionless" initial_value="6.7606483e-1"/>
<variable name="F4" units="dimensionless" initial_value="3.2355462e-1"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_ss" units="millimolar" public_interface="in"/>
<variable name="CaSRrel" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>kap</ci>
</apply>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>F1</ci>
</apply>
<apply>
<times/>
<ci>kam</ci>
<ci>F2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F2</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kap</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>F1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>kam</ci>
<ci>F2</ci>
</apply>
<apply>
<times/>
<ci>kbp</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>F2</ci>
</apply>
<apply>
<times/>
<ci>kcp</ci>
<ci>F2</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kbm</ci>
<ci>F3</ci>
</apply>
<apply>
<times/>
<ci>kcm</ci>
<ci>F4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kbp</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>F2</ci>
</apply>
<apply>
<times/>
<ci>kbm</ci>
<ci>F3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F4</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kcp</ci>
<ci>F2</ci>
</apply>
<apply>
<times/>
<ci>kcm</ci>
<ci>F4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_CaSRrel</ci>
<apply>
<times/>
<cn cellml:units="per_second">1800</cn>
<apply>
<plus/>
<ci>F2</ci>
<ci>F3</ci>
</apply>
<apply>
<minus/>
<ci>CaSRrel</ci>
<ci>Ca_ss</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SERCA2a_pump">
<variable name="J_CaSRup" units="millimolar_per_second" public_interface="out"/>
<variable name="K_fb" units="millimolar" initial_value="0.000168"/>
<variable name="K_rb" units="millimolar" initial_value="3.29"/>
<variable name="fb" units="dimensionless"/>
<variable name="rb" units="dimensionless"/>
<variable name="Vmaxf" units="millimolar_per_second" initial_value="0.4"/>
<variable name="Vmaxr" units="millimolar_per_second" initial_value="0.9"/>
<variable name="K_SR" units="dimensionless" initial_value="1"/>
<variable name="N_fb" units="dimensionless" initial_value="1.2"/>
<variable name="N_rb" units="dimensionless" initial_value="1"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="CaSRup" units="millimolar" public_interface="in"/>
<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>CaSRup</ci>
<ci>K_rb</ci>
</apply>
<ci>N_rb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_CaSRup</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_and_SR_Ca_fluxes">
<variable name="J_tr" units="millimolar_per_second" public_interface="out"/>
<variable name="J_xfer" units="millimolar_per_second" public_interface="out"/>
<variable name="J_trpn" units="millimolar_per_second" public_interface="out"/>
<variable name="J_BTRH" units="millimolar_per_second" public_interface="out"/>
<variable name="J_BTRL" units="millimolar_per_second" public_interface="out"/>
<variable name="BTRHmax" units="millimolar" initial_value="0.14" public_interface="out"/>
<variable name="BTRLmax" units="millimolar" initial_value="0.07" public_interface="out"/>
<variable name="tau_tr" units="second" initial_value="0.02"/>
<variable name="tau_xfer" units="second" initial_value="0.008"/>
<variable name="BTRH" units="millimolar" initial_value="9.2804169e-1"/>
<variable name="BTRL" units="millimolar" initial_value="3.4317829e-2"/>
<variable name="k_htrpn_plus" units="per_millimolar_per_second" initial_value="20000"/>
<variable name="k_htrpn_minus" units="per_second" initial_value="0.07"/>
<variable name="k_ltrpn_plus" units="per_millimolar_per_second" initial_value="40000"/>
<variable name="k_ltrpn_minus" units="per_second" initial_value="40"/>
<variable name="Ca_ss" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="CaSRup" units="millimolar" public_interface="in"/>
<variable name="CaSRrel" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<ci>J_tr</ci>
<apply><divide/>
<apply><minus/>
<ci>CaSRup</ci>
<ci>CaSRrel</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_BTRH</ci>
<apply><minus/>
<apply><times/>
<ci>k_htrpn_plus</ci>
<ci>Ca_i</ci>
<apply><minus/>
<cn cellml:units="millimolar">1</cn>
<ci>BTRH</ci>
</apply>
</apply>
<apply><times/>
<ci>k_htrpn_minus</ci>
<ci>BTRH</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>BTRH</ci>
</apply>
<ci>J_BTRH</ci>
</apply>
<apply><eq/>
<ci>J_BTRL</ci>
<apply><minus/>
<apply><times/>
<ci>k_ltrpn_plus</ci>
<ci>Ca_i</ci>
<apply><minus/>
<cn cellml:units="millimolar">1</cn>
<ci>BTRL</ci>
</apply>
</apply>
<apply><times/>
<ci>k_ltrpn_minus</ci>
<ci>BTRL</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>BTRL</ci>
</apply>
<ci>J_BTRL</ci>
</apply>
<apply>
<eq/>
<ci>J_trpn</ci>
<apply>
<plus/>
<ci>J_BTRH</ci>
<ci>J_BTRL</ci>
</apply>
</apply>
</math>
</component>
<component name="ion_concentrations">
<variable name="Na_i" units="millimolar" initial_value="6.9435814e0" public_interface="out"/>
<variable name="Ca_i" units="millimolar" initial_value="3.5486498e-5" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="1.3753311e2" public_interface="out"/>
<variable name="Na_t" units="millimolar" initial_value="1.4001386e2" public_interface="out"/>
<variable name="Ca_t" units="millimolar" initial_value="1.2271399e0" public_interface="out"/>
<variable name="K_t" units="millimolar" initial_value="5.3627676e0" public_interface="out"/>
<variable name="Ca_ss" units="millimolar" initial_value="4.3112114e-5" public_interface="out"/>
<variable name="CaSRrel" units="millimolar" initial_value="2.2638169e-1" public_interface="out"/>
<variable name="CaSRup" units="millimolar" initial_value="2.2755058e-1" public_interface="out"/>
<variable name="i_Kext" units="microA" public_interface="out"/>
<variable name="K_mCMDN" units="millimolar" initial_value="0.00238"/>
<variable name="K_mCSQN" units="millimolar" initial_value="0.8"/>
<variable name="K_mEGTA" units="millimolar" initial_value="0.00015"/>
<variable name="CMDN_tot" units="millimolar" initial_value="0.05"/>
<variable name="CSQN_tot" units="millimolar" initial_value="15"/>
<variable name="EGTA_tot" units="millimolar" initial_value="10"/>
<variable name="tau_d" units="second" initial_value="0.008"/>
<variable name="STIMULATION" units="dimensionless" initial_value="1"/>
<variable name="time0" units="second" initial_value="0"/>
<variable name="J_BTRH" units="millimolar_per_second" public_interface="in"/>
<variable name="J_BTRL" units="millimolar_per_second" public_interface="in"/>
<variable name="BTRHmax" units="millimolar" public_interface="in"/>
<variable name="BTRLmax" units="millimolar" public_interface="in"/>
<variable name="Vd" units="cm3" public_interface="in"/>
<variable name="Vt" units="cm3" public_interface="in"/>
<variable name="Vmyo" units="cm3" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="i_Na_s" units="microA" public_interface="in"/>
<variable name="i_Ca_s" units="microA" public_interface="in"/>
<variable name="i_BNa_s" units="microA" public_interface="in"/>
<variable name="i_NaCa_s" units="microA" public_interface="in"/>
<variable name="i_NaK_s" units="microA" public_interface="in"/>
<variable name="i_fNa_s" units="microA" public_interface="in"/>
<variable name="i_fK_s" units="microA" public_interface="in"/>
<variable name="i_BK_s" units="microA" public_interface="in"/>
<variable name="i_K1_s" units="microA" public_interface="in"/>
<variable name="i_Kto_s" units="microA" public_interface="in"/>
<variable name="i_Kss_s" units="microA" public_interface="in"/>
<variable name="i_CaP_s" units="microA" public_interface="in"/>
<variable name="i_BCa_s" units="microA" public_interface="in"/>
<variable name="i_Na_t" units="microA" public_interface="in"/>
<variable name="i_Ca_t" units="microA" public_interface="in"/>
<variable name="i_BNa_t" units="microA" public_interface="in"/>
<variable name="i_NaCa_t" units="microA" public_interface="in"/>
<variable name="i_NaK_t" units="microA" public_interface="in"/>
<variable name="i_fNa_t" units="microA" public_interface="in"/>
<variable name="i_fK_t" units="microA" public_interface="in"/>
<variable name="i_BK_t" units="microA" public_interface="in"/>
<variable name="i_K1_t" units="microA" public_interface="in"/>
<variable name="i_Kto_t" units="microA" public_interface="in"/>
<variable name="i_Kss_t" units="microA" public_interface="in"/>
<variable name="i_CaP_t" units="microA" public_interface="in"/>
<variable name="i_BCa_t" units="microA" public_interface="in"/>
<variable name="J_CaSRup" units="millimolar_per_second" public_interface="in"/>
<variable name="J_CaSRrel" units="millimolar_per_second" public_interface="in"/>
<variable name="J_xfer" units="millimolar_per_second" public_interface="in"/>
<variable name="J_trpn" units="millimolar_per_second" public_interface="in"/>
<variable name="J_tr" units="millimolar_per_second" public_interface="in"/>
<variable name="Jte_Na" units="millimolar_per_second" public_interface="in"/>
<variable name="Jte_Ca" units="millimolar_per_second" public_interface="in"/>
<variable name="Jte_K" units="millimolar_per_second" public_interface="in"/>
<variable name="Sms" units="cm2" public_interface="in"/>
<variable name="Smt" units="cm2" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Na_i</ci>
</apply>
<apply><divide/>
<apply><minus/>
<apply><plus/>
<ci>i_Na_s</ci>
<ci>i_Na_t</ci>
<ci>i_BNa_s</ci>
<ci>i_BNa_t</ci>
<apply>
<times/>
<ci>i_NaCa_s</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaCa_t</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaK_s</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaK_t</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Vmyo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Na_t</ci>
</apply>
<apply><divide/>
<apply><divide/>
<apply><plus/>
<ci>i_Na_t</ci>
<ci>i_BNa_t</ci>
<apply>
<times/>
<ci>i_NaCa_t</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaK_t</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply><minus/>
<ci>F</ci>
<ci>Jte_Na</ci>
</apply>
</apply>
<ci>Vt</ci>
</apply>
</apply>
<apply><eq/>
<ci>i_Kext</ci>
<piecewise>
<piece>
<apply><times/>
<cn cellml:units="microA_per_cm2">52</cn>
<apply><plus/>
<ci>Sms</ci>
<ci>Smt</ci>
</apply>
</apply>
<apply><and/>
<apply><eq/>
<ci>STIMULATION</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply><lt/>
<apply><minus/>
<ci>time</ci>
<ci>time0</ci>
</apply>
<cn cellml:units="second">0.001</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="microA">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply><divide/>
<apply><minus/>
<apply><plus/>
<apply><minus/>
<ci>i_Kext</ci>
</apply>
<ci>i_fK_s</ci>
<ci>i_fK_t</ci>
<ci>i_Kss_s</ci>
<ci>i_Kss_t</ci>
<ci>i_K1_s</ci>
<ci>i_K1_t</ci>
<ci>i_BK_s</ci>
<ci>i_BK_t</ci>
<apply>
<times/>
<ci>i_NaK_s</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>i_NaK_t</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>i_Kto_s</ci>
<ci>i_Kto_t</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Vmyo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>K_t</ci>
</apply>
<apply><divide/>
<apply><divide/>
<apply><plus/>
<ci>i_fK_t</ci>
<ci>i_Kss_t</ci>
<ci>i_K1_t</ci>
<ci>i_BK_t</ci>
<apply>
<times/>
<ci>i_NaK_t</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>i_Kto_t</ci>
</apply>
<apply><minus/>
<ci>F</ci>
<ci>Jte_K</ci>
</apply>
</apply>
<ci>Vt</ci>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Ca_i</ci>
</apply>
<apply><times/>
<apply><divide/>
<cn cellml:units="millimolar_per_second">1</cn>
<apply><plus/>
<cn cellml:units="millimolar2">1</cn>
<apply><times/>
<ci>CMDN_tot</ci>
<apply><divide/>
<ci>K_mCMDN</ci>
<apply><power/>
<apply><plus/>
<ci>K_mCMDN</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus/>
<apply><plus/>
<apply><divide/>
<apply><plus/>
<apply><times/>
<cn cellml:units="dimensionless">-2</cn>
<apply><plus/>
<ci>i_NaCa_s</ci>
<ci>i_NaCa_t</ci>
</apply>
</apply>
<apply><plus/>
<ci>i_BCa_s</ci>
<ci>i_BCa_t</ci>
<ci>i_CaP_s</ci>
<ci>i_CaP_t</ci>
</apply>
</apply>
<apply><times/>
<cn cellml:units="dimensionless">-2</cn>
<ci>Vmyo</ci>
<ci>F</ci>
</apply>
</apply>
<apply><divide/>
<apply><minus/>
<apply><plus/>
<apply><divide/>
<apply><times/>
<apply><minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
<ci>Vmyo</ci>
</apply>
<ci>tau_d</ci>
</apply>
<ci>J_CaSRrel</ci>
</apply>
<ci>J_CaSRup</ci>
</apply>
<ci>Vmyo</ci>
</apply>
</apply>
<apply><plus/>
<apply><times/>
<ci>J_BTRH</ci>
<ci>BTRHmax</ci>
</apply>
<apply><times/>
<ci>J_BTRL</ci>
<ci>BTRLmax</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Ca_t</ci>
</apply>
<apply><divide/>
<apply><divide/>
<apply><plus/>
<ci>i_Ca_t</ci>
<ci>i_CaP_t</ci>
<ci>i_BCa_t</ci>
<apply><times/>
<ci>i_NaCa_t</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply><minus/>
<apply><times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
<ci>Jte_Ca</ci>
</apply>
</apply>
<ci>Vt</ci>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Ca_ss</ci>
</apply>
<apply><times/>
<apply><divide/>
<cn cellml:units="millimolar_per_second">1</cn>
<apply><plus/>
<cn cellml:units="millimolar2">1</cn>
<apply><times/>
<ci>CMDN_tot</ci>
<apply><divide/>
<ci>K_mCMDN</ci>
<apply><power/>
<apply><plus/>
<ci>K_mCMDN</ci>
<ci>Ca_ss</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><divide/>
<apply><minus/>
<apply><plus/>
<ci>i_Ca_s</ci>
<ci>i_Ca_t</ci>
</apply>
</apply>
<apply><minus/>
<apply><plus/>
<apply><times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vd</ci>
<ci>F</ci>
</apply>
<apply><divide/>
<ci>J_CaSRrel</ci>
<ci>Vd</ci>
</apply>
</apply>
<apply><divide/>
<apply><divide/>
<apply><times/>
<apply><minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
<ci>Vmyo</ci>
</apply>
<ci>tau_d</ci>
</apply>
<ci>Vd</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CaSRrel</ci>
</apply>
<apply>
<times/>
<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>CaSRrel</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>J_tr</ci>
<ci>J_CaSRrel</ci>
</apply>
</apply>
</apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>CaSRup</ci>
</apply>
<apply><minus/>
<ci>J_CaSRup</ci>
<ci>J_tr</ci>
</apply>
</apply>
</math>
</component>
<component name="t_tubular_ion_fluxes">
<variable name="Jte_Na" units="millimolar_per_second" public_interface="out"/>
<variable name="Jte_Ca" units="millimolar_per_second" public_interface="out"/>
<variable name="Jte_K" units="millimolar_per_second" public_interface="out"/>
<variable name="tau_Na" units="second" initial_value="0.15"/>
<variable name="tau_Ca" units="second" initial_value="0.5"/>
<variable name="tau_K" units="second" initial_value="0.15"/>
<variable name="Vt" units="cm3" public_interface="in"/>
<variable name="Na_t" units="millimolar" public_interface="in"/>
<variable name="Ca_t" units="millimolar" public_interface="in"/>
<variable name="K_t" units="millimolar" public_interface="in"/>
<variable name="Na_e" units="millimolar" public_interface="in"/>
<variable name="Ca_e" units="millimolar" public_interface="in"/>
<variable name="K_e" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><eq/>
<ci>Jte_Na</ci>
<apply><divide/>
<apply><times/>
<cn cellml:units="millimolar2_per_cm3">1</cn>
<ci>Vt</ci>
</apply>
<apply><times/>
<ci>tau_Na</ci>
<apply><minus/>
<ci>Na_t</ci>
<ci>Na_e</ci>
</apply>
</apply>
</apply>
</apply>
<apply><eq/>
<ci>Jte_Ca</ci>
<apply><divide/>
<apply><times/>
<cn cellml:units="millimolar2_per_cm3">1</cn>
<ci>Vt</ci>
</apply>
<apply><times/>
<ci>tau_Ca</ci>
<apply><minus/>
<ci>Ca_t</ci>
<ci>Ca_e</ci>
</apply>
</apply>
</apply>
</apply>
<apply><eq/>
<ci>Jte_K</ci>
<apply><divide/>
<apply><times/>
<cn cellml:units="millimolar2_per_cm3">1</cn>
<ci>Vt</ci>
</apply>
<apply><times/>
<ci>tau_K</ci>
<apply><minus/>
<ci>K_t</ci>
<ci>K_e</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="SR_Ca_release_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="SERCA2a_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="intracellular_and_SR_Ca_fluxes" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ion_concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="ion_concentrations"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="Vmyo" variable_2="Vmyo"/>
<map_variables variable_1="Vd" variable_2="Vd"/>
<map_variables variable_1="Vt" variable_2="Vt"/>
<map_variables variable_1="Sms" variable_2="Sms"/>
<map_variables variable_1="Smt" variable_2="Smt"/>
</connection>
<connection>
<map_components component_1="SR_Ca_release_channel" component_2="ion_concentrations"/>
<map_variables variable_1="J_CaSRrel" variable_2="J_CaSRrel"/>
<map_variables variable_1="Ca_ss" variable_2="Ca_ss"/>
<map_variables variable_1="CaSRrel" variable_2="CaSRrel"/>
</connection>
<connection>
<map_components component_1="SERCA2a_pump" component_2="ion_concentrations"/>
<map_variables variable_1="J_CaSRup" variable_2="J_CaSRup"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="CaSRup" variable_2="CaSRup"/>
</connection>
<connection>
<map_components component_1="intracellular_and_SR_Ca_fluxes" component_2="ion_concentrations"/>
<map_variables variable_1="J_tr" variable_2="J_tr"/>
<map_variables variable_1="J_xfer" variable_2="J_xfer"/>
<map_variables variable_1="J_trpn" variable_2="J_trpn"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="CaSRup" variable_2="CaSRup"/>
<map_variables variable_1="Ca_ss" variable_2="Ca_ss"/>
<map_variables variable_1="CaSRrel" variable_2="CaSRrel"/>
<map_variables variable_1="J_BTRL" variable_2="J_BTRL"/>
<map_variables variable_1="J_BTRH" variable_2="J_BTRH"/>
<map_variables variable_1="BTRLmax" variable_2="BTRLmax"/>
<map_variables variable_1="BTRHmax" variable_2="BTRHmax"/>
</connection>
<connection>
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<dc:title>Philosophical Transactions of the Royal Society</dc:title>
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Please note that this model is relatively stiff. If you run the model using the default COR settings, you will get a message that reads: "Problem with the CVODE integrator: at t=0.00170178, mxstep steps taken before reaching tout." This basically means that you have to increase the maximum number of steps which is, by default, set to 500. Such a value is sufficient for most ODE problems, but not for ODE problems that have very stiff ODEs, such as the current model. Anyway, you will see that the model runs fine if you increase the value to something like 5000. Note that you also need to set the maximum time step to a sensible value, i.e. the duration of the stimulus which is here 1 ms.
Regarding PCEnv, it uses a higher value than COR for the maximum number of steps, which is why the model will run in PCEnv without having to change this particular setting. Otherwise, like in COR there is a need to set the maximum time step to a sensible value. PCEnv uses a default value of 1 s for the Pasek model, which is clearly not small enough as can be seen when running the model for 10 s. If one uses 0.001 s, then everything is fine.</rdf:value>
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<vCard:Given>Georges</vCard:Given>
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