- Author:
- Geoff Nunns <gnunns1@jhu.edu>
- Date:
- 2010-05-12 16:33:35+12:00
- Desc:
- Edited model status and simplified structure to include only abstract.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/sobie_dilly_dossantoscruz_lederer_jafri_2002/rawfile/19a4c1b7442f814e91d31410d752d8b5512d2c03/sobie_dilly_dossantoscruz_lederer_jafri_2002.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : sobie_model_2002.xml
CREATED : 26th June 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Sobie et al's
2002 model of calcium-induced calcium release in cardiac muscle.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
--><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#" cmeta:id="sobie_dilly_dossantoscruz_lederer_jafri_2002_version01" name="sobie_dilly_dossantoscruz_lederer_jafri_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mechanism of Cardiac Ca2+ Spark Termination</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is a faithful representation of the published equations, but it is not compatible with any CellML tools. It contains the sum MathML element, which is not supported by PCEnv, OpenCell or COR, rendering further curation useless. Inspection of the model suggests that there are significant errors beyond the presence of the sum operator that would render it unsuitable for description in CellML.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A Ca(2+) spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca(2+) influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca(2+) spark has been shown to be the elementary Ca(2+) signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca(2+) spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca(2+) release that simulates Ca(2+) spark behavior and enables robust Ca(2+) spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca(2+)]. Using a Monte Carlo method, local Ca(2+)-induced Ca(2+) release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca(2+) flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca(2+) indicator fluo-3 to produce the model Ca(2+) spark. Ca(2+) sparks generated by the sticky cluster model resemble those observed experimentally, and Ca(2+) spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca(2+) spark rate in the model increases with elevated cytosolic or SR lumenal [Ca(2+)]. Furthermore, reduction of RyR coupling leads to prolonged model Ca(2+) sparks just as treatment with FK506 lengthens Ca(2+) sparks in heart cells. This new model of Ca(2+) spark behavior provides a "proof of principle" test of a new hypothesis for Ca(2+) spark termination and reproduces critical features of Ca(2+) sparks observed experimentally.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Termination of Cardiac Ca<superscript>2+</superscript> Sparks: An Investigative Mathematical Model of Calcium-Induced Calcium Release, Eric A. Sobie, Keith W. Dilly, Jader dos Santos Cruz, W. Jonathan Lederer, and M. Saleet Jafri, 2002, <emphasis>Biophysical Journal</emphasis>, 83, 59-78. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12080100&dopt=Abstract">PubMed ID: 12080100</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell_diagram</title>
</objectinfo>
<imagedata fileref="sobie_2002.png"/>
</imageobject>
</mediaobject>
<caption>Layout of the model elements.</caption>
</informalfigure>
<para>
The model is separated out into two main components: 1) Mathematical description of SR Ca<superscript>2+</superscript> release through an RyR cluster at the extracellular-sarcolemmal junction. 2) Mathematical description of the Ca<superscript>2+</superscript> spark produced by the Ca<superscript>2+</superscript> efflux. This component of the model is largely based on a previously published model of Ca<superscript>2+</superscript> diffusion, buffering and imaging processes that produce the Ca<superscript>2+</superscript> spark (Smith <emphasis>et al.</emphasis>, 1998).
</para>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="third_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="subspace">
<variable units="millimolar" public_interface="out" name="Ca_SS"/>
<variable units="flux" public_interface="out" name="J_RyR"/>
<variable units="flux" public_interface="out" name="J_buf"/>
<variable units="micro_litre" public_interface="out" name="V_SS" initial_value="1.0E-13"/>
<variable units="micromolar" name="Ca_myo" initial_value="0.1"/>
<variable units="coulomb_per_mole" name="F" initial_value="96480.0"/>
<variable units="flux" name="J_release"/>
<variable units="flux" name="J_DHPR"/>
<variable units="flux" name="J_efflux"/>
<variable units="dimensionless" name="i" initial_value="0.0"/>
<variable units="dimensionless" name="N" initial_value="50.0"/>
<variable units="picoA" name="I_DHPR" initial_value="-0.5"/>
<variable units="first_order_rate_constant" name="D_RyR" initial_value="4000.0"/>
<variable units="micromolar" name="Ca_B_SR_tot" initial_value="47.0"/>
<variable units="micromolar" name="Ca_B_CaM_tot" initial_value="24.0"/>
<variable units="micromolar" name="Ca_B_SL_tot" initial_value="1124.0"/>
<variable units="micromolar" name="Ca_B_trpnC_tot" initial_value="70.0"/>
<variable units="millimolar" name="Ca_B_SR"/>
<variable units="micromolar" name="Ca_B_CaM"/>
<variable units="micromolar" name="Ca_B_SL"/>
<variable units="micromolar" name="Ca_B_trpnC"/>
<variable units="second_order_rate_constant" name="k_on_SR" initial_value="115.0"/>
<variable units="first_order_rate_constant" name="k_off_SR" initial_value="100.0"/>
<variable units="second_order_rate_constant" name="k_on_CaM" initial_value="100.0"/>
<variable units="first_order_rate_constant" name="k_off_CaM" initial_value="38.0"/>
<variable units="second_order_rate_constant" name="k_on_trpnC" initial_value="39.0"/>
<variable units="first_order_rate_constant" name="k_off_trpnC" initial_value="20.0"/>
<variable units="second_order_rate_constant" name="k_on_SL" initial_value="115.0"/>
<variable units="first_order_rate_constant" name="k_off_SL" initial_value="1000.0"/>
<variable units="second" name="tau_efflux" initial_value="7.0E-7"/>
<variable units="dimensionless" name="RyR_open" initial_value="0.0"/>
<variable units="millimolar" public_interface="in" name="Ca_lumen"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="calcium_subspace_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_SS </ci>
</apply>
<apply>
<plus/>
<ci> J_release </ci>
<ci> J_DHPR </ci>
<ci> J_efflux </ci>
<ci> J_buf </ci>
</apply>
</apply>
<apply id="J_DHPR_calculation">
<eq/>
<ci> J_DHPR </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> I_DHPR </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> V_SS </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="J_release_calculation">
<eq/>
<ci> J_release </ci>
<apply>
<sum/>
<bvar>
<ci> i </ci>
</bvar>
<lowlimit>
<cn cellml:units="dimensionless"> 1.0 </cn>
</lowlimit>
<highlimit>
<ci> N </ci>
</highlimit>
<apply>
<times/>
<ci> RyR_open </ci>
<ci> J_RyR </ci>
</apply>
</apply>
</apply>
<apply id="J_RyR_calculation">
<eq/>
<ci> J_RyR </ci>
<apply>
<times/>
<ci> D_RyR </ci>
<apply>
<minus/>
<ci> Ca_lumen </ci>
<ci> Ca_SS </ci>
</apply>
</apply>
</apply>
<apply id="RyR_open_calculation">
<eq/>
<ci> RyR_open </ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless"> 0.0 </cn>
<apply>
<eq/>
<ci> i </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless"> 1.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="Ca_B_SR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_B_SR </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_SR </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_SR </ci>
</apply>
<apply>
<times/>
<ci> k_off_SR </ci>
<apply>
<minus/>
<ci> Ca_B_SR_tot </ci>
<ci> Ca_B_SR </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_B_trpnC_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_B_trpnC </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_trpnC </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_trpnC </ci>
</apply>
<apply>
<times/>
<ci> k_off_trpnC </ci>
<apply>
<minus/>
<ci> Ca_B_trpnC_tot </ci>
<ci> Ca_B_trpnC </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_B_CaM_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_B_CaM </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_CaM </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_CaM </ci>
</apply>
<apply>
<times/>
<ci> k_off_CaM </ci>
<apply>
<minus/>
<ci> Ca_B_CaM_tot </ci>
<ci> Ca_B_CaM </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_B_SL_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_B_SL </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_SL </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_SL </ci>
</apply>
<apply>
<times/>
<ci> k_off_SL </ci>
<apply>
<minus/>
<ci> Ca_B_SL_tot </ci>
<ci> Ca_B_SL </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="J_buf_calculation">
<eq/>
<ci> J_buf </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_CaM </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_CaM </ci>
</apply>
<apply>
<times/>
<ci> k_off_CaM </ci>
<apply>
<minus/>
<ci> Ca_B_CaM_tot </ci>
<ci> Ca_B_CaM </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_trpnC </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_trpnC </ci>
</apply>
<apply>
<times/>
<ci> k_off_trpnC </ci>
<apply>
<minus/>
<ci> Ca_B_trpnC_tot </ci>
<ci> Ca_B_trpnC </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_SR </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_SR </ci>
</apply>
<apply>
<times/>
<ci> k_off_SR </ci>
<apply>
<minus/>
<ci> Ca_B_SR_tot </ci>
<ci> Ca_B_SR </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on_SL </ci>
<ci> Ca_SS </ci>
<ci> Ca_B_SL </ci>
</apply>
<apply>
<times/>
<ci> k_off_SL </ci>
<apply>
<minus/>
<ci> Ca_B_SL_tot </ci>
<ci> Ca_B_SL </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="J_efflux_calculation">
<eq/>
<ci> J_efflux </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> Ca_myo </ci>
<ci> Ca_SS </ci>
</apply>
<ci> tau_efflux </ci>
</apply>
</apply>
</math>
</component>
<component name="lumen">
<variable units="millimolar" public_interface="out" name="Ca_lumen"/>
<variable units="flux" name="J_refill"/>
<variable units="second" name="tau_refill" initial_value="0.01"/>
<variable units="millimolar" name="Ca_NSR" initial_value="1.0"/>
<variable units="micro_litre" name="V_JSR" initial_value="1.0E-11"/>
<variable units="millimolar" name="CSQ_tot" initial_value="10.0"/>
<variable units="millimolar" name="CSQ"/>
<variable units="millimolar" name="K_CSQ" initial_value="0.8"/>
<variable units="dimensionless" name="beta_JSR"/>
<variable units="flux" public_interface="in" name="J_RyR"/>
<variable units="micro_litre" public_interface="in" name="V_SS"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="calcium_lumen_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_lumen </ci>
</apply>
<apply>
<times/>
<ci> beta_JSR </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> J_RyR </ci>
</apply>
<apply>
<divide/>
<ci> V_SS </ci>
<ci> V_JSR </ci>
</apply>
</apply>
<ci> J_refill </ci>
</apply>
</apply>
</apply>
<apply id="J_refill_calculation">
<eq/>
<ci> J_refill </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_lumen </ci>
</apply>
<ci> tau_refill </ci>
</apply>
</apply>
<apply id="beta_JSR_calculation">
<eq/>
<ci> beta_JSR </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CSQ_tot </ci>
<ci> K_CSQ </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> CSQ </ci>
<ci> K_CSQ </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="RyR_receptor_gating">
<variable units="dimensionless" name="k_coop" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k_close"/>
<variable units="first_order_rate_constant" name="k_open"/>
<variable units="dimensionless" name="CF_close"/>
<variable units="dimensionless" name="CF_open"/>
<variable units="dimensionless" name="N_closed"/>
<variable units="dimensionless" name="N_open"/>
<variable units="micromolar" name="K_m"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_lumen"/>
<variable units="millimolar" public_interface="in" name="Ca_SS"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k_close_calculation">
<eq/>
<ci> k_close </ci>
<apply>
<times/>
<ci> CF_close </ci>
<cn cellml:units="first_order_rate_constant"> 480.0 </cn>
</apply>
</apply>
<apply id="k_open_calculation">
<eq/>
<ci> k_open </ci>
<apply>
<times/>
<ci> CF_open </ci>
<cn cellml:units="first_order_rate_constant"> 30000.0 </cn>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_SS </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ca_SS </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<power/>
<ci> K_m </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="K_m_calculation">
<eq/>
<ci> K_m </ci>
<apply>
<minus/>
<cn cellml:units="micromolar"> 6.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0024 </cn>
<ci> Ca_lumen </ci>
</apply>
</apply>
</apply>
<apply id="CF_open_calculation">
<eq/>
<ci> CF_open </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> N_open </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<ci> N_open </ci>
<ci> N_closed </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="CF_close_calculation">
<eq/>
<ci> CF_close </ci>
<apply>
<times/>
<ci> k_coop </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> N_closed </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<ci> N_open </ci>
<ci> N_closed </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="spark_model">
<variable units="millimolar" name="Ca"/>
<variable units="millimolar" name="Ca_F"/>
<variable units="millimolar" name="Ca_trpnC"/>
<variable units="millimolar" name="Ca_CaM"/>
<variable units="third_order_rate_constant" name="DC" initial_value="250.0"/>
<variable units="third_order_rate_constant" name="DF" initial_value="20.0"/>
<variable units="micromolar" name="F_T" initial_value="50.0"/>
<variable units="flux" name="J_pump"/>
<variable units="flux" name="J_leak"/>
<variable units="flux" name="J_n"/>
<variable units="flux" name="J_dye"/>
<variable units="flux" name="Vmax_pump" initial_value="208.0"/>
<variable units="micromolar" name="Km_pump" initial_value="0.184"/>
<variable units="dimensionless" name="m" initial_value="3.9"/>
<variable units="nanomolar" name="C_infinity" initial_value="100.0"/>
<variable units="second_order_rate_constant" name="k_F_plus" initial_value="80.0"/>
<variable units="first_order_rate_constant" name="k_F_minus" initial_value="40.0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="flux" public_interface="in" name="J_RyR"/>
<variable units="flux" public_interface="in" name="J_buf"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="cytosolic_calcium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> DC </ci>
<ci> Ca </ci>
</apply>
<ci> J_dye </ci>
<ci> J_buf </ci>
<ci> J_pump </ci>
<ci> J_leak </ci>
<ci> J_RyR </ci>
</apply>
</apply>
<apply id="calcium_bound_dye_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_F </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> DF </ci>
<ci> Ca_F </ci>
</apply>
<ci> J_dye </ci>
</apply>
</apply>
<apply id="J_dye_calculation">
<eq/>
<ci> J_dye </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> k_F_plus </ci>
</apply>
<ci> Ca </ci>
<apply>
<minus/>
<ci> F_T </ci>
<ci> Ca_F </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_F_minus </ci>
<ci> Ca_F </ci>
</apply>
</apply>
</apply>
<apply id="J_pump_calculation">
<eq/>
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This is the CellML description of Sobie et al's 2002 model of
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Added publication date information.
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Termination of Cardiac Ca2+ Sparks: An Investigative Mathematical Model of Calcium-Induced Calcium Release
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Sobie et al's 2002 model of calcium-induced calcium release in cardiac
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