- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 15:17:33+12:00
- Desc:
- committing version02 of niederer_hunter_smith_2006
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/niederer_hunter_smith_2006/rawfile/48953e7294d549e85e3217a118e63b465a5510ba/niederer_hunter_smith_2006.cellml
<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" 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:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="Niederer_Hunter_Smith_2006" name="Niederer_Hunter_Smith_2006">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is known to run in PCEnv and COR to reproduce the output shown in the publication. A PCEnv session file is also associated with this model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
This CellML model was based on the March 2007 paper:
</para>
<para>
"A Quantitative Analysis of Cardiac Myocyte Relaxation: A Simulation Study" by S.A. Niederer, P.J. Hunter and N.P. Smith.
</para>
<para>
The following is the abstract of this paper:
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 [Ca++]i transient magnitude, the unbinding of Ca++ from troponin C (TnC), and the lengthdependence
of tension and Ca++ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively
reviewed experimental literature, to quantitatively characterize the binding of Ca++ 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 Ca++, isometric twitches, and the half-time to relaxation with increasing
sarcomere length experiments. A factorial analysis found that the [Ca++]i transient and the unbinding of Ca++ 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 Ca++ to TnC and length-dependent Ca++ sensitivity. The affects of the [Ca++]i transient
and the unbinding rate of Ca++ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference
[Ca++]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 [Ca21]i. Inputs are in bold,
algebraic length dependencies are in italics, processes
described by differential equations are standard font.</caption>
</informalfigure>
<para>
The complete original publication reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/reprint/90/5/1697">A Quantitative Analysis of Cardiac Myocyte Relaxation: A Simulation Study</ulink>, Steven Niederer, Peter Hunter, Nicholas Smith, 2006 <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 90 1697-1722 <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16339881?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum">PubMed ID: 16339881</ulink>
</para>
</sect1>
</article>
</documentation>
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<units name="mM">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
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<variable units="mM" public_interface="out" cmeta:id="intracellular_ion_concentrations_Ca_i" name="Ca_i"/>
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<variable units="mM" public_interface="out" name="TRPN" initial_value="0.067593139865"/>
<variable units="mM" public_interface="in" name="Ca_TRPN_Max"/>
<variable units="mM_per_ms" public_interface="in" name="J_TRPN"/>
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</apply>
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</math>
</component>
<component name="thinfilaments"/>
<component name="tropomyosin">
<variable units="dimensionless" public_interface="out" name="z" initial_value="0.014417937837"/>
<variable units="dimensionless" public_interface="out" name="z_max"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="per_mM_per_ms" public_interface="in" name="k_on"/>
<variable units="per_ms" public_interface="in" name="k_Ref_off"/>
<variable units="dimensionless" public_interface="in" name="gamma_trpn"/>
<variable units="mM" public_interface="in" name="Ca_TRPN_Max"/>
<variable units="per_ms" name="alpha_0" initial_value="8e-3"/>
<variable units="per_ms" name="alpha_r1" initial_value="2e-3"/>
<variable units="per_ms" name="alpha_r2" initial_value="1.75e-3"/>
<variable units="dimensionless" name="n_Rel" initial_value="3"/>
<variable units="dimensionless" name="K_z" initial_value="0.15"/>
<variable units="dimensionless" name="n_Hill" initial_value="3"/>
<variable units="mM" name="Ca_50ref" initial_value="1.05e-3"/>
<variable units="dimensionless" name="z_p" initial_value="0.85"/>
<variable units="dimensionless" name="beta_1" initial_value="-4"/>
<variable units="mM" name="Ca_50"/>
<variable units="mM" name="Ca_TRPN_50"/>
<variable units="per_ms" name="K_2"/>
<variable units="per_ms" name="K_1"/>
<variable units="per_ms" name="alpha_Tm"/>
<variable units="per_ms" name="beta_Tm"/>
<variable units="dimensionless" public_interface="in" name="beta_0"/>
<variable units="mM" public_interface="in" name="Ca_b"/>
<variable units="dimensionless" public_interface="in" name="lambda"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<power/>
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<divide/>
<ci>Ca_TRPN_50</ci>
<ci>Ca_TRPN_Max</ci>
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<ci>n_Hill</ci>
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<divide/>
<ci>Ca_TRPN_50</ci>
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<ci>Ca_TRPN_50</ci>
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<plus/>
<ci>alpha_r1</ci>
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<times/>
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<power/>
<ci>z</ci>
<ci>n_Rel</ci>
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<ci>n_Rel</ci>
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<eq/>
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<diff/>
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<ci>time</ci>
</bvar>
<ci>z</ci>
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<minus/>
<apply>
<times/>
<ci>alpha_Tm</ci>
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<minus/>
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<ci>z</ci>
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<times/>
<ci>beta_Tm</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</math>
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<variable units="mM_per_ms" public_interface="out" name="J_TRPN"/>
<variable units="mM" public_interface="out" name="Ca_TRPN_Max" initial_value="70e-3"/>
<variable units="mM" public_interface="in" name="TRPN"/>
<variable units="mM" public_interface="in" name="Ca_i"/>
<variable units="per_ms" name="k_off"/>
<variable units="per_mM_per_ms" public_interface="out" name="k_on" initial_value="100"/>
<variable units="per_ms" public_interface="out" name="k_Ref_off" initial_value="0.2"/>
<variable units="dimensionless" public_interface="out" name="gamma_trpn" initial_value="2"/>
<variable units="N_per_mm2" public_interface="in" name="Tension"/>
<variable units="N_per_mm2" public_interface="in" name="T_ref"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k_off</ci>
<piecewise>
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<apply>
<times/>
<ci>k_Ref_off</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tension</ci>
<apply>
<times/>
<ci>gamma_trpn</ci>
<ci>T_ref</ci>
</apply>
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</apply>
</apply>
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<gt/>
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<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tension</ci>
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<times/>
<ci>gamma_trpn</ci>
<ci>T_ref</ci>
</apply>
</apply>
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<times/>
<ci>k_Ref_off</ci>
<cn 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>
</component>
<component name="Myofilaments">
<variable units="ms" public_interface="in" name="time"/>
<variable units="dimensionless" public_interface="out" name="lambda"/>
<variable units="dimensionless" public_interface="out" name="ExtensionRatio"/>
<variable units="per_ms" public_interface="out" name="dExtensionRatiodt"/>
<variable units="dimensionless" public_interface="out" name="lambda_prev"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ExtensionRatio</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<gt/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">1</cn>
</otherwise>
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<apply>
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<ci>lambda_prev</ci>
<ci>ExtensionRatio</ci>
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<apply>
<eq/>
<ci>dExtensionRatiodt</ci>
<cn 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 cellml:units="dimensionless">0.8</cn>
</apply>
<apply>
<leq/>
<ci>ExtensionRatio</ci>
<cn cellml:units="dimensionless">1.15</cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">1.15</cn>
<apply>
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