- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:52:55+12:00
- Desc:
- committing version01 of keizer_levine_1996
- Permanent Source URI:
- https://models.cellml.org/workspace/keizer_levine_1996/rawfile/55c5605051d7888b1fddfbb21559887a9d34db34/keizer_levine_1996.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : keizer_model_1996.xml
CREATED : 3rd April 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 Kiezer and Levine's
1996 model of ryanodine receptor adaptation and Ca_i2+-induced Ca_i2+ release-dependent Ca_i2+ oscillations.
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="keizer_levine_1996_version01" name="keizer_levine_1996_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>RyR Adaptation and Ca2+ Oscillations</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 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The ryanodine receptor (RyR) from cardiac cells and skeletal muscle undergoes a Ca<superscript>2+</superscript>-dependent process called adaptation. Adaptation occurs during the slow, spontaneous decrease in the open probability of a channel after it has been rapidly activated by a pulse of cytosolic calcium ([Ca<superscript>2+</superscript>]<subscript>i</subscript>). RyR activation occurs within milliseconds, whereas inactivation occurs on a timescale of a few seconds. The RyR is said to have "adapted" during inactivation because a subsequent increase in [Ca<superscript>2+</superscript>]<subscript>i</subscript> produces a nearly identical rise in the open probability.
</para>
<para>
In their 1996 paper, Joel Keizer and Leslie Levine develop a simplified model that mimics the "adaptation" of the RyR, and they investigate its significance for Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> release and Ca<superscript>2+</superscript> oscillations in cardiac cells. The mechanism used to mimic adaptation of the RyR is shown schematically in <xref linkend="fig_reaction_diagram"/> below. States C1 and C2 are closed states and O1 and O2 are open states. Transitions from C1 to O1 and from O1 to O2 are assumed to be Ca<superscript>2+</superscript>-dependent. These steps correspond to the phenomenon of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> release (CICR). To analyse the mechanism in <xref linkend="fig_reaction_diagram"/>, Keizer and Levine translated the schematic diagram into kinetic equations. In addition, they test these equations in a closed-cell kinetic model, and they find that RyR adaptation can cause Ca<superscript>2+</superscript> oscillations. However, in an open-cell, CICR, not RyR adaptation, produces Ca<superscript>2+</superscript> oscillations.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/71/6/3477">Ryanodine Receptor Adaptation and Ca<superscript>2+</superscript>-Induced Ca<superscript>2+</superscript> Release-Dependent Ca<superscript>2+</superscript> Oscillations</ulink>, Joel Keizer and Leslie Levine, 1996, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 71, 3477-3487. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8968617&dopt=Abstract">PubMed ID: 8968617</ulink>
</para>
<para>
The raw CellML description of the kinetic model of cardiac RyR adaptation can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>Schematic diagram of the RyR model</title>
</objectinfo>
<imagedata fileref="keizer_1996.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of transitions among the four states of the RyR used to describe adaptation. States C1 and C2 are closed states and O1 and O2 represent open states, assumed to have the same single-channel conductance. The <emphasis>k</emphasis> are rate constants: only steps <emphasis>a</emphasis> and <emphasis>b</emphasis> are Ca<superscript>2+</superscript> dependent.</caption>
</informalfigure>
</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="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar_3">
<unit units="micromolar" exponent="3"/>
</units>
<units name="micromolar_4">
<unit units="micromolar" exponent="4"/>
</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="forth_order_rate_constant">
<unit units="micromolar" exponent="-3"/>
<unit units="second" exponent="-1"/>
</units>
<units name="fifth_order_rate_constant">
<unit units="micromolar" exponent="-4"/>
<unit units="second" exponent="-1"/>
</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>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="O1" name="O1">
<variable units="micromolar" public_interface="out" name="O1"/>
<variable units="flux" public_interface="in" name="delta_O1_rxn_1"/>
<variable units="flux" public_interface="in" name="delta_O1_rxn_2"/>
<variable units="flux" public_interface="in" name="delta_O1_rxn_3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O1</ci>
</apply>
<apply>
<plus/>
<ci>delta_O1_rxn_1</ci>
<ci>delta_O1_rxn_2</ci>
<ci>delta_O1_rxn_3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="O2" name="O2">
<variable units="micromolar" public_interface="out" name="O2"/>
<variable units="flux" public_interface="in" name="delta_O2_rxn_2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O2</ci>
</apply>
<ci>delta_O2_rxn_2</ci>
</apply>
</math>
</component>
<component cmeta:id="O_slow" name="O_slow">
<variable units="micromolar" public_interface="out" name="O_slow"/>
<variable units="micromolar" name="w"/>
<variable units="micromolar" name="w_init"/>
<variable units="dimensionless" name="w_infinity_Ca_i"/>
<variable units="dimensionless" name="tau_Ca_i"/>
<variable units="micromolar_4" name="Ka"/>
<variable units="micromolar_3" name="Kb"/>
<variable units="dimensionless" name="Kc"/>
<variable units="fifth_order_rate_constant" public_interface="in" name="ka_plus"/>
<variable units="forth_order_rate_constant" public_interface="in" name="kb_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="ka_minus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kb_minus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kc_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kc_minus"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="micromolar" public_interface="in" name="C2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="O_slow_calculation">
<eq/>
<ci> O_slow </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> w </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> Kb </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Ka </ci>
<ci> Ca_i </ci>
</apply>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> Kb </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="w_init_calculation">
<eq/>
<ci> w_init </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> C2 </ci>
</apply>
</apply>
<apply id="w_infinity_Ca_i_calculation">
<eq/>
<ci> w_infinity_Ca_i </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Ka </ci>
<ci> Ca_i </ci>
</apply>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> Kb </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Kc </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> Ka </ci>
<ci> Ca_i </ci>
</apply>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> Kb </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_Ca_i_calculation">
<eq/>
<ci> tau_Ca_i </ci>
<apply>
<divide/>
<ci> w_infinity_Ca_i </ci>
<ci> kc_minus </ci>
</apply>
</apply>
<apply id="Ka_calculation">
<eq/>
<ci> Ka </ci>
<apply>
<divide/>
<ci> ka_minus </ci>
<ci> ka_plus </ci>
</apply>
</apply>
<apply id="Kb_calculation">
<eq/>
<ci> Kb </ci>
<apply>
<divide/>
<ci> kb_minus </ci>
<ci> kb_plus </ci>
</apply>
</apply>
<apply id="Kc_calculation">
<eq/>
<ci> Kc </ci>
<apply>
<divide/>
<ci> kc_minus </ci>
<ci> kc_plus </ci>
</apply>
</apply>
<apply id="w_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> w </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> w </ci>
<apply>
<times/>
<ci> w_infinity_Ca_i </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> tau_Ca_i </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C1" name="C1">
<variable units="micromolar" public_interface="out" name="C1"/>
<variable units="flux" public_interface="in" name="delta_C1_rxn_1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C1</ci>
</apply>
<ci>delta_C1_rxn_1</ci>
</apply>
</math>
</component>
<component cmeta:id="C2" name="C2">
<variable units="micromolar" public_interface="out" name="C2"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn_3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C2</ci>
</apply>
<ci>delta_C2_rxn_3</ci>
</apply>
</math>
</component>
<component cmeta:id="Ca_i" name="Ca_i">
<variable units="micromolar" public_interface="out" name="Ca_i"/>
<variable units="dimensionless" name="fi" initial_value="0.01"/>
<variable units="first_order_rate_constant" name="v1" initial_value="40.0"/>
<variable units="first_order_rate_constant" name="v2" initial_value="0.5"/>
<variable units="second_order_rate_constant" name="v3" initial_value="1000.0"/>
<variable units="micromolar" name="K3" initial_value="0.30"/>
<variable units="micromolar" name="Ca_s"/>
<variable units="micromolar" name="C0" initial_value="9.0"/>
<variable units="dimensionless" name="c1" initial_value="0.15"/>
<variable units="micromolar" public_interface="in" name="O_slow"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci> fi </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> v1 </ci>
<ci> O_slow </ci>
</apply>
<ci> v2 </ci>
</apply>
<apply>
<minus/>
<ci> Ca_s </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> v3 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> K3 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_s_calculation">
<eq/>
<ci> Ca_s </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> C0 </ci>
<ci> Ca_i </ci>
</apply>
<ci> c1 </ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="micromolar" public_interface="in" name="C1"/>
<variable units="micromolar" public_interface="in" name="O1"/>
<variable units="fifth_order_rate_constant" public_interface="out" name="ka_plus" initial_value="1500.0"/>
<variable units="first_order_rate_constant" public_interface="out" name="ka_minus" initial_value="28.8"/>
<variable units="flux" public_interface="out" name="delta_C1_rxn_1"/>
<variable units="flux" public_interface="out" name="delta_O1_rxn_1"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="C1">
<role stoichiometry="1" direction="forward" delta_variable="delta_C1_rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_i">
<role stoichiometry="4" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="O1">
<role stoichiometry="1" direction="forward" delta_variable="delta_O1_rxn_1" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> ka_plus </ci>
<ci> C1 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> ka_minus </ci>
<ci> O1 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="micromolar" public_interface="in" name="O1"/>
<variable units="micromolar" public_interface="in" name="O2"/>
<variable units="forth_order_rate_constant" public_interface="out" name="kb_plus" initial_value="1500.0"/>
<variable units="first_order_rate_constant" public_interface="out" name="kb_minus" initial_value="385.9"/>
<variable units="flux" public_interface="out" name="delta_O1_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_O2_rxn_2"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="O1">
<role stoichiometry="1" direction="forward" delta_variable="delta_O1_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_i">
<role stoichiometry="3" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="O2">
<role stoichiometry="1" direction="forward" delta_variable="delta_O2_rxn_2" role="product"/>
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<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> kb_plus </ci>
<ci> O1 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kb_minus </ci>
<ci> O2 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="O1"/>
<variable units="micromolar" public_interface="in" name="C2"/>
<variable units="first_order_rate_constant" public_interface="out" name="kc_plus" initial_value="1.75"/>
<variable units="first_order_rate_constant" public_interface="out" name="kc_minus" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="delta_O1_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_C2_rxn_3"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="O1">
<role stoichiometry="1" direction="forward" delta_variable="delta_O1_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="C2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C2_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> kc_minus </ci>
<ci> O1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kc_plus </ci>
<ci> C2 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<connection>
<map_components component_2="environment" component_1="O1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="O2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="O_slow"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="O1"/>
<map_variables variable_2="O1" variable_1="O1"/>
<map_variables variable_2="delta_O1_rxn_1" variable_1="delta_O1_rxn_1"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="O1"/>
<map_variables variable_2="O1" variable_1="O1"/>
<map_variables variable_2="delta_O1_rxn_2" variable_1="delta_O1_rxn_2"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="O1"/>
<map_variables variable_2="O1" variable_1="O1"/>
<map_variables variable_2="delta_O1_rxn_3" variable_1="delta_O1_rxn_3"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="O2"/>
<map_variables variable_2="O2" variable_1="O2"/>
<map_variables variable_2="delta_O2_rxn_2" variable_1="delta_O2_rxn_2"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="O_slow"/>
<map_variables variable_2="ka_minus" variable_1="ka_minus"/>
<map_variables variable_2="ka_plus" variable_1="ka_plus"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="O_slow"/>
<map_variables variable_2="kb_minus" variable_1="kb_minus"/>
<map_variables variable_2="kb_plus" variable_1="kb_plus"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="O_slow"/>
<map_variables variable_2="kc_minus" variable_1="kc_minus"/>
<map_variables variable_2="kc_plus" variable_1="kc_plus"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="C1"/>
<map_variables variable_2="C1" variable_1="C1"/>
<map_variables variable_2="delta_C1_rxn_1" variable_1="delta_C1_rxn_1"/>
</connection>
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<connection>
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<connection>
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<connection>
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The University of Auckland, Bioengineering Institute
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Keizer and Levine's 1996 model of a gating scheme for ryanodine
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Ryanodine Receptor Adaptation and Ca2+-Induced Ca2+
Release-Dependent Ca2+ Oscillations
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<dc:title>Biophysical Journal</dc:title>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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Open state on a slow time scale
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Intracellular calcium concentration in a closed cell
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Added more metadata.
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Added publication date information.
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This is the CellML description of Keizer and Levine's 1996 model of a
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