/Users/max_neal/_UW/SemGenGrant/Presentations/AucklandDemo/PHNmerge/origCellMLmodels/niederer_hunter_smith_2006.cellml.xml 0.2 <documentation xmlns="http://cellml.org/tmp-documentation"> <article> <section id="sec_status"> <title>Model Status</title> <para>This model is known to run in OpenCell and COR to reproduce the output shown in the publication. The units have been checked and they are consistent.</para> </section> <sect1 id="sec_structure"> <title>Model Structure</title> <para>Abstract: The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate.</para> <informalfigure float="0" id="fig_reaction_diagram"> <mediaobject> <imageobject> <objectinfo> <title>model diagram</title> </objectinfo> <imagedata fileref="niederer_2006.png" /> </imageobject> </mediaobject> <caption>Schematic diagram depicting the relationships of the active contraction framework proposed by Hunter et al. (11). The model is driven by SL and sarcomere velocity, and intracellular [Ca2+]i. Inputs are in bold, algebraic length dependencies are in italics, processes described by differential equations are standard font.</caption> </informalfigure> <para>The original publication reference is cited below:</para> <para> A Quantitative Analysis of Cardiac Myocyte Relaxation: A Simulation Study, Steven Niederer, Peter Hunter, Nicholas Smith, 2006 <emphasis>Biophysical Journal</emphasis> , 90 1697-1722 <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16339881?ordinalpos=1&amp;itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum">PubMed ID: 16339881</ulink> </para> </sect1> </article> </documentation> <rdf:RDF xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" 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in Niederer et al.'s 2006 paper.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#314dbed2-8642-4da9-80fd-945b5d1ec7ea"> <vCard:FN>James Lawson</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:publisher>Auckland Bioengineering Institute</dc:publisher> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#niederer_2006"> <cmeta:comment> <rdf:Description rdf:about="rdf:#64bb668b-6f2c-493f-ae16-e2071198e2dd"> <rdf:value>This is a CellML description of Niederer et al.'s computational model of cardiac myocyte relaxation as described in the 2006 paper "A quantitative analysis of cardiac myocyte relaxation: a simulation study"</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#982f649b-9600-4031-b4c1-3d8308448733"> <vCard:FN>James Lawson</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <bqs:reference rdf:parseType="Resource"> <dc:subject rdf:parseType="Resource"> <rdf:value> <rdf:Bag> <rdf:li>cardiac myocyte</rdf:li> <rdf:li>endocrine</rdf:li> <rdf:li>electrophysiology</rdf:li> <rdf:li>relaxation</rdf:li> <rdf:li>excitation-contraction coupling</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </dc:subject> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#4f08decc-3fc3-49f4-9dba-6cfaa15a3c57"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#52c457d5-26a5-4a89-89a2-aec7970789e1"> <bqs:last_page>1722</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#ad018539-ea8c-4542-954e-02753e2863fc"> <dcterms:W3CDTF>2006-03-01 00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <bqs:Journal> <rdf:Description rdf:about="rdf:#4be66846-659c-4208-a256-233bf4cfad34"> <dc:title>Biophysical Journal</dc:title> </rdf:Description> </bqs:Journal> <bqs:first_page>1697</bqs:first_page> <bqs:volume>90(5)</bqs:volume> <dc:title>A quantitative analysis of cardiac myocyte relaxation: a simulation study</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#887c750e-c9a6-4af3-bf5c-e07638d57973"> <rdf:li> <bqs:Person rdf:about="rdf:#cd4567e9-796d-415f-8463-bfcc4af7136a"> <vCard:N> <rdf:Description rdf:about="rdf:#4749a01a-3930-41a0-b116-99b69afa57f2"> <vCard:Other>A</vCard:Other> <vCard:Family>Niederer</vCard:Family> <vCard:Given>S</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#f475ac2a-312b-4d06-9917-68437cf6c8da"> <vCard:N> <rdf:Description rdf:about="rdf:#5b2dd97e-1afe-4815-8e78-2542050b7b7d"> <vCard:Other>J</vCard:Other> <vCard:Family>Hunter</vCard:Family> <vCard:Given>P</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#8fbfc9a4-eb83-48fe-8882-d7ca7e25046b"> <vCard:N> <rdf:Description rdf:about="rdf:#dc21789e-b06b-41ab-af35-2d6feb9c5dbd"> <vCard:Other>P</vCard:Other> <vCard:Family>Smith</vCard:Family> <vCard:Given>N</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id>16339881</bqs:Pubmed_id> </rdf:Description> </bqs:reference> <ns7:simulation> <rdf:Description rdf:about="rdf:#$+WTRo2"> <ns7:boundIntervals> <rdf:Description rdf:about="rdf:#$0XTRo2"> <rdf:first> <rdf:Description rdf:about="rdf:#$1XTRo2"> <ns7:maximumStepSize>0.1</ns7:maximumStepSize> <ns7:nonstandard-pointDensity>10000</ns7:nonstandard-pointDensity> <ns7:endingValue>1000</ns7:endingValue> </rdf:Description> </rdf:first> <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/> </rdf:Description> </ns7:boundIntervals> </rdf:Description> </ns7:simulation> </rdf:Description> </rdf:RDF> niederer_2006 niederer_2006 Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Chemical concentration flow rate http://bhi.washington.edu/OPB#OPB_00593 Surface normal tensile stress http://bhi.washington.edu/OPB#OPB_01097 Troponin C, slow skeletal and cardiac muscles (TN-C) http://identifiers.org/uniprot/P02591 calcium(2+) http://purl.obolibrary.org/obo/CHEBI_29108 Cardiac myocyte http://purl.org/sig/ont/fma/fma14067 Portion of cytosol http://purl.org/sig/ont/fma/fma66836 A physical entity that is defined by linking multiple physical entity terms with structural relations. A mathematical and/or logical expression that determines the value of a data structure. An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities. A physical dependency defined in a specific SemSim model. A physical entity defined in a specific SemSim model. A physical process defined in a specific SemSim model. A physical property defined in a specific SemSim model. A computational element that stores numerical and/or logical information related to the model. A data structure whose value is limited to decimals. A data structure whose value is limited to the whole numbers. A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime. A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process. A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants. A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element. A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process. A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values. A data structure whose value is limited to the real numbers. A physical dependency that is defined using a term in an external knowledge resource. A physical entity that is defined using a term from an external knowledge resource. A physical process that is defined using a term in an external knowledge resource. A physical property that is defined using a term in an external knowledge resource. A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0. A computational or physical element of a SemSim model. A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel. A physical quantity chosen as a standard in terms of which other physical quantities may be expressed. calcium(2+) http://purl.obolibrary.org/obo/CHEBI_29108 Calcium (2+) bound to troponin C Calcium (2+) ion bound to site II of troponin C Cross_Bridges -29 false false true Weighting coefficient for process 1 of the crossbridge kinetics fading memory model 138 false false true Weighting coefficient for process 2 of the crossbridge kinetics fading memory model 129 false false true Weighting coefficient for process 3 of the crossbridge kinetics fading memory model false false true Sum of the three exponential processes in the crossbridge dynamics fading memory model 0 false false true Exponential process 1 of the crossbridge kinetics fading memory model 0 false false true Exponential process 2 of the crossbridge kinetics fading memory model 0 false false true Exponential process 3 of the crossbridge kinetics fading memory model false false in true The isometric tension at a given intracellular calcium ion concentration and sarcomere length Cross_Bridges_Tension false false out true Active tension of cardiac myocyte Surface normal tensile stress http://bhi.washington.edu/OPB#OPB_01097 0.35 false false true Curve-shaping constant for relationship between relative sarcomere velocity and relative tension 0.03 false false true Exponential rate constant for process 1 of the crossbridge kinetics fading memory model 0.13 false false true Exponential rate constant for process 2 of the crossbridge kinetics fading memory model 0.625 false false true Exponential rate constant for process 3 of the crossbridge kinetics fading memory model false false in true Change in ExtensionRatio with respect to time Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Temporal solution domain <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>Q</ci> <apply> <plus /> <ci>Q_1</ci> <ci>Q_2</ci> <ci>Q_3</ci> </apply> </apply> <apply> <eq /> <ci>Tension</ci> <piecewise> <piece> <apply> <divide /> <apply> <times /> <ci>T_0</ci> <apply> <plus /> <apply> <times /> <ci>a</ci> <ci>Q</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>Q</ci> </apply> </apply> <apply> <lt /> <ci>Q</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <ci>T_0</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <apply> <plus /> <ci>a</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>Q</ci> </apply> </apply> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>Q</ci> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Q_1</ci> </apply> <apply> <minus /> <apply> <times /> <ci>A_1</ci> <ci>dExtensionRatiodt</ci> </apply> <apply> <times /> <ci>alpha_1</ci> <ci>Q_1</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Q_2</ci> </apply> <apply> <minus /> <apply> <times /> <ci>A_2</ci> <ci>dExtensionRatiodt</ci> </apply> <apply> <times /> <ci>alpha_2</ci> <ci>Q_2</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Q_3</ci> </apply> <apply> <minus /> <apply> <times /> <ci>A_3</ci> <ci>dExtensionRatiodt</ci> </apply> <apply> <times /> <ci>alpha_3</ci> <ci>Q_3</ci> </apply> </apply> </apply> </math> Dissociation of troponin C bound to calcium In this model, the formation of troponin C comes from the dissociation of the calcium (2+) / troponin C complex 1.0 1.0 1.0 Myofilaments false false out true Sarcomere strain false false out true Change in ExtensionRatio with respect to time false false out true Sarcomere strain, constrained to values between 0.8 and 1.15 false false out true Mystery variable mathematically equal to sarcomere strain Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Temporal solution domain <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>ExtensionRatio</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <gt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>lambda_prev</ci> <ci>ExtensionRatio</ci> </apply> <apply> <eq /> <ci>dExtensionRatiodt</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">0</cn> </apply> <apply> <eq /> <ci>lambda</ci> <piecewise> <piece> <ci>ExtensionRatio</ci> <apply> <and /> <apply> <gt /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn> </apply> <apply> <leq /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> </apply> </apply> </piece> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> <apply> <gt /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn> </otherwise> </piecewise> </apply> </math> Troponin C, slow skeletal and cardiac muscles (TN-C) http://identifiers.org/uniprot/P02591 N_per_mm2 -2.0 milli litre true mM milli -1.0 mM_per_ms -1.0 milli metre true mole true ms milli newton true per_mM_per_ms -1.0 -1.0 milli per_ms -1.0 milli second true environment Time environment_time false false http://bhi.washington.edu/OPB#OPB_01023 out true Temporal solution domain filament_overlap 4.9 false false out true Scaling factor (slope) for the relationship between lambda and T_0 false false in true Sarcomere strain? false false out true Sarcomere overlap? <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>overlap</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <ci>beta_0</ci> <apply> <minus /> <ci>lambda</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> </apply> </math> Cardiac myocyte http://purl.org/sig/ont/fma/fma14067 Portion of cytosol http://purl.org/sig/ont/fma/fma66836 intracellular_ion_concentrations false false in true The maximum concentration of calcium ions that can bind to site II on troponin C Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false out true Concentration of calcium (2+) bound to troponin C Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false intracellular_ion_concentrations_Ca_i out true Intracellular calcium (2+) concentration Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Intracellular troponin flux Chemical concentration flow rate http://bhi.washington.edu/OPB#OPB_00593 0.067593139865 false false out true Intracellular troponin concentration Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Temporal solution domain <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>Ca_b</ci> <apply> <minus /> <ci>Ca_TRPN_Max</ci> <ci>TRPN</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>TRPN</ci> </apply> <ci>J_TRPN</ci> </apply> <apply> <eq /> <ci>Ca_i</ci> <piecewise> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.8433 <sep /> -7 </cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1</cn> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <minus /> <apply> <plus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">1.055</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.03507</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0003992</cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.356 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">10</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">15</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <minus /> <apply> <plus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.014</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.002555</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001494</cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.428 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">15</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">55</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <plus /> <apply> <minus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.739 <sep /> -5 </cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 3.209 <sep /> -6 </cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 5.689 <sep /> -6 </cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.719 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">55</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">250</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <plus /> <apply> <minus /> <apply> <plus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001321</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0002197</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001374</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 3.895 <sep /> -5 </cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 4.441 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">250</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">490</cn> </apply> </apply> </piece> <otherwise> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.2148 <sep /> -7 </cn> </apply> </otherwise> </piecewise> </apply> </math> isometric_tension false false isometric_tension_T0 out true The isometric tension at a given intracellular calcium ion concentration and sarcomere length false false in true Isometric tension of cell false false in true <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>T_0</ci> <apply> <times /> <ci>T_Base</ci> <ci>overlap</ci> </apply> </apply> </math> length_independent_tension false false out true Isometric tension of cell 56.2 false false out true Maximum tension at resting sarcomere length false false in true The fraction of actin sites available for crossbridge binding false false in true The fraction of actin sites available at full activation <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>T_Base</ci> <apply> <divide /> <apply> <times /> <ci>T_ref</ci> <ci>z</ci> </apply> <ci>z_max</ci> </apply> </apply> </math> thinfilaments tropomyosin false false true Concentration of free calcium (2+) at half-activation of maximum tension Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 1.05e-3 false false true Offset parameter for Ca_50 vs. lambda dependency Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false true Calcium (2+) bound to TnC at half-activation of maximum tension Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true The maximum concentration of calcium ions that can bind to site II on troponin C Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Concentration of calcium (2+) bound to troponin C Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false true Linearization term for computing z_max false false true Linearization term for computing z_max 0.15 false false true Fast relaxation rate parameter for computing z 8e-3 false false true The monoexponential activation rate seen in caged calcium (2+) experiments. Used to compute z. false false true Intermediate term for first component of varaible z's ODE (equation 9 in reference paper) 2e-3 false false true Slow relaxation rate parameter for computing z 1.75e-3 false false true Fast relaxation rate parameter for computing z false false in true Scaling factor (slope) for the relationship between lambda and T_0 -4 false false true Scaling parameter for Ca_50 vs. lambda dependency false false true Intermediate term for second component of variable z's ODE (equation 9 in reference paper) false false in true A measure of the effect of tension on the unbinding rate of calcium (2+) from troponin C false false in true Rate of calcium (2+) unbinding from Troponin C in the absence of tension false false in true The binding rate of calcium (2+) to troponin C site II false false in true Sarcomere strain? 3 false false true Analogous to the Hill coefficient in the steady-state force-calcium (2+) curve (F-pCa) and provides a phenomenological rep- resentation of the high cooperativity, due to nearest-neighbor interactions between tropomyosin and/or crossbridges, seen in the activation of tension in cardiac muscle 3 false false true Fast relaxation rate parameter for computing z Time false false http://bhi.washington.edu/OPB#OPB_01023 in true Temporal solution domain 0.014417937837 false false out true The fraction of actin sites available for crossbridge binding as determined by thin filament kinetics false false out true the maximum fraction of available actin sites at a given sarcomere length 0.85 false false true Point around which the non-linear component of equation 9 in the paper (solving for dz/dt) is linearized to maintain an explicit formulation for the model <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>K_2</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <apply> <times /> <ci>n_Rel</ci> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>K_1</ci> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z_p</ci> <apply> <minus /> <ci>n_Rel</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> <ci>n_Rel</ci> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <eq /> <ci>z_max</ci> <apply> <divide /> <apply> <minus /> <apply> <divide /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_TRPN_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <ci>n_Hill</ci> </apply> </apply> <ci>K_2</ci> </apply> <apply> <plus /> <ci>alpha_r1</ci> <ci>K_1</ci> <apply> <divide /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_TRPN_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <ci>n_Hill</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>Ca_50</ci> <apply> <times /> <ci>Ca_50ref</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <ci>beta_1</ci> <apply> <minus /> <ci>lambda</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>Ca_TRPN_50</ci> <apply> <divide /> <apply> <times /> <ci>Ca_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <apply> <plus /> <ci>Ca_50</ci> <apply> <times /> <apply> <divide /> <ci>k_Ref_off</ci> <ci>k_on</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <apply> <times /> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <ci>beta_0</ci> <apply> <minus /> <ci>lambda</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn> </apply> <ci>gamma_trpn</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>alpha_Tm</ci> <apply> <times /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_b</ci> <ci>Ca_TRPN_50</ci> </apply> <ci>n_Hill</ci> </apply> </apply> </apply> <apply> <eq /> <ci>beta_Tm</ci> <apply> <plus /> <ci>alpha_r1</ci> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z</ci> <apply> <minus /> <ci>n_Rel</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>z</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_Tm</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>z</ci> </apply> </apply> <apply> <times /> <ci>beta_Tm</ci> <ci>z</ci> </apply> </apply> </apply> </math> troponin 70e-3 false false out true The maximum concentration of calcium ions that can bind to site II on troponin C Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Intracellular calcium (2+) concentration Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false out true Intracellular troponin flux Chemical concentration flow rate http://bhi.washington.edu/OPB#OPB_00593 false false in true Intracellular troponin concentration Chemical concentration http://bhi.washington.edu/OPB#OPB_00340 false false in true Maximum tension at resting sarcomere length false false in true Active tension of cardiac myocyte Surface normal tensile stress http://bhi.washington.edu/OPB#OPB_01097 2 false false out true A measure of the effect of tension on the unbinding rate of calcium (2+) from troponin C 0.2 false false out true Rate of calcium (2+) unbinding from Troponin C in the absence of tension false false true The unbinding rate of calcium (2+) from troponin C site II 100 false false out true The binding rate of calcium (2+) to troponin C site II <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <eq /> <ci>k_off</ci> <piecewise> <piece> <apply> <times /> <ci>k_Ref_off</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <ci>Tension</ci> <apply> <times /> <ci>gamma_trpn</ci> <ci>T_ref</ci> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <ci>Tension</ci> <apply> <times /> <ci>gamma_trpn</ci> <ci>T_ref</ci> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.1</cn> </apply> </piece> <otherwise> <apply> <times /> <ci>k_Ref_off</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.1</cn> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>J_TRPN</ci> <apply> <minus /> <apply> <times /> <apply> <minus /> <ci>Ca_TRPN_Max</ci> <ci>TRPN</ci> </apply> <ci>k_off</ci> </apply> <apply> <times /> <ci>Ca_i</ci> <ci>TRPN</ci> <ci>k_on</ci> </apply> </apply> </apply> </math>