- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:40:29+12:00
- Desc:
- committing version01 of nagerl_novo_mody_vergara_2000
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/nagerl_novo_mody_vergara_2000/rawfile/ab31d00621a5a17c0ee3e02a1bd37aa25c6d0c05/nagerl_novo_mody_vergara_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE :nagerl_model_2000.xml
CREATED : 31st October 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 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Nagerl et al's 2000 study of the binding kinetics of calbindin-D28k.
CHANGES:
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="nagerl_novo_mody_vergara_2000_version01" name="nagerl_novo_mody_vergara_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Ca2+ Binding Kinetics of Calbindin-D28k</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>
Rapid changes in intracellular calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) are characteristic of Ca<superscript>2+</superscript> signalling. Following a stimulus, Ca<superscript>2+</superscript> flows into the cytoplasm through channels in the cell membrane, and it's released from intracellular stores such as the endoplasmic reticulum. Normal [Ca<superscript>2+</superscript>] is resumed by the actions of Ca<superscript>2+</superscript> pumps, exchangers, binding proteins (CBPs) and other buffers. Calbindin-D<subscript>28k</subscript> is a CBP which is present at high cytosolic concentrations in neurons such as cerebellar Purkinje cells and hippocampal granule cells. Together with its high cytosolic concentration, the ability of calbindin-D<subscript>28k</subscript> to bind up to four Ca<superscript>2+</superscript> ions at any one time suggests that it plays an important role in Ca<superscript>2+</superscript> buffering.
</para>
<para>
Little is known about the Ca<superscript>2+</superscript> binding kinetics of calbindin-D<subscript>28k</subscript>, or of CBPs in general. In their 2000 paper, Nagerl <emphasis>et al.</emphasis> describe a new method to measure the binding kinetics of calbindin-D<subscript>28k</subscript>, which involves flash photolysis of DM-nitrophen (DM-n), a caged Ca<superscript>2+</superscript> compound. A mathematical model, which included the Ca<superscript>2+</superscript> binding reactions of all the species in the solution (see <xref linkend="fig_reaction_diagram"/> below), was fitted to the experimental data in order to determine realistic kinetic parameters. The results of their experiments suggested that calbindin-D<subscript>28k</subscript> has two kinetically distinct types of Ca<superscript>2+</superscript> binding sites, one high- and one low-affinity. This heterogeneity was captured by their mathematical model.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/6/3009">Binding Kinetics of Calbindin-D<subscript>28k</subscript> Determined by Flash Photolysis of Caged Ca<superscript>2+</superscript>
</ulink>, U. Valentin Nagerl, David Novo, Istvan Mody and Julio L. Vergara, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 79, 3009-3018. (<ulink url="http://www.biophysj.org/cgi/content/full/79/6/3009">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/6/3009.pdf">PDF versions</ulink> of the article are available to subscribers on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11106608&dopt=Abstract">PubMed ID: 11106608</ulink>
</para>
<para>
The raw CellML descriptions of the model 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>reaction_diagram</title>
</objectinfo>
<imagedata fileref="nagerl_2000.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the mathematical model used to simulate the dynamic redistribution of Ca<superscript>2+</superscript> generated by flash photolysis of DM-n. CaDM1, CaDM2, CaD and CaB represent the concentration of Ca<superscript>2+</superscript> bound to DM-n, dye and buffer, respectively. Alpha models the fraction of Ca<superscript>2+</superscript>-bound DM-n1 that is photolysed by the UV laser flash.</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="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="flux">
<unit units="micromolar" exponent="1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="millisecond" 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="millisecond" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in the reactions.
-->
<component cmeta:id="Ca" name="Ca">
<variable units="micromolar" public_interface="out" name="Ca" initial_value="1.5"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn0"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn1"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn2"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn3"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca</ci>
</apply>
<apply>
<plus/>
<ci>delta_Ca_rxn0</ci>
<ci>delta_Ca_rxn1</ci>
<ci>delta_Ca_rxn2</ci>
<ci>delta_Ca_rxn3</ci>
<ci>delta_Ca_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="D" name="D">
<variable units="micromolar" public_interface="out" name="D" initial_value="100.0"/>
<variable units="flux" public_interface="in" name="delta_D_rxn1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>D</ci>
</apply>
<ci>delta_D_rxn1</ci>
</apply>
</math>
</component>
<component cmeta:id="B" name="B">
<variable units="micromolar" public_interface="out" name="B" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_B_rxn0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B</ci>
</apply>
<ci>delta_B_rxn0</ci>
</apply>
</math>
</component>
<component cmeta:id="CaB" name="CaB">
<variable units="micromolar" public_interface="out" name="CaB" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_CaB_rxn0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CaB</ci>
</apply>
<ci>delta_CaB_rxn0</ci>
</apply>
</math>
</component>
<component cmeta:id="CaD" name="CaD">
<variable units="micromolar" public_interface="out" name="CaD" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_CaD_rxn1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CaD</ci>
</apply>
<ci>delta_CaD_rxn1</ci>
</apply>
</math>
</component>
<component cmeta:id="DM1" name="DM1">
<variable units="micromolar" public_interface="out" name="DM1"/>
<variable units="micromolar" name="DM1_init"/>
<variable units="millimolar" name="DM_tot" initial_value="5.0"/>
<variable units="dimensionless" name="alpha" initial_value="2.1E-3"/>
<variable units="flux" public_interface="in" name="delta_DM1_rxn2"/>
<variable units="flux" public_interface="in" name="delta_DM1_rxn4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="DM2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>DM1</ci>
</apply>
<apply>
<plus/>
<ci>delta_DM1_rxn2</ci>
<ci>delta_DM1_rxn4</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>DM1_init</ci>
<apply>
<times/>
<ci>alpha</ci>
<ci>DM_tot</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>DM_tot</ci>
<apply>
<plus/>
<ci>DM1</ci>
<ci>DM2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="CaDM1" name="CaDM1">
<variable units="micromolar" public_interface="out" name="CaDM1" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_CaDM1_rxn2"/>
<variable units="flux" public_interface="in" name="delta_CaDM1_rxn4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CaDM1</ci>
</apply>
<apply>
<plus/>
<ci>delta_CaDM1_rxn2</ci>
<ci>delta_CaDM1_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="DM2" name="DM2">
<variable units="micromolar" public_interface="out" name="DM2" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_DM2_rxn3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>DM2</ci>
</apply>
<ci>delta_DM2_rxn3</ci>
</apply>
</math>
</component>
<component cmeta:id="CaDM2" name="CaDM2">
<variable units="micromolar" public_interface="out" name="CaDM2" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_CaDM2_rxn3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CaDM2</ci>
</apply>
<ci>delta_CaDM2_rxn3</ci>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction0">
<variable units="micromolar" public_interface="in" name="CaB"/>
<variable units="micromolar" public_interface="in" name="B"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="flux" public_interface="out" name="delta_CaB_rxn0"/>
<variable units="flux" public_interface="out" name="delta_B_rxn0"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn0"/>
<variable units="first_order_rate_constant" name="k0" initial_value="1.0"/>
<variable units="second_order_rate_constant" name="k0_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="CaB">
<role stoichiometry="1" direction="forward" delta_variable="delta_CaB_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="B">
<role stoichiometry="1" direction="forward" delta_variable="delta_B_rxn0" role="product"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn0" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k0</ci>
<ci>CaB</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k0_</ci>
<ci>B</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="CaD"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="micromolar" public_interface="in" name="D"/>
<variable units="flux" public_interface="out" name="delta_CaD_rxn1"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn1"/>
<variable units="flux" public_interface="out" name="delta_D_rxn1"/>
<variable units="first_order_rate_constant" name="k1" initial_value="5.6"/>
<variable units="second_order_rate_constant" name="k1_" initial_value="0.124"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="CaD">
<role stoichiometry="1" direction="forward" delta_variable="delta_CaD_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn1" role="product"/>
</variable_ref>
<variable_ref variable="D">
<role stoichiometry="1" direction="forward" delta_variable="delta_D_rxn1" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k1</ci>
<ci>CaD</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k1_</ci>
<ci>Ca</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="CaDM1"/>
<variable units="micromolar" public_interface="in" name="DM1"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="flux" public_interface="out" name="delta_CaDM1_rxn2"/>
<variable units="flux" public_interface="out" name="delta_DM1_rxn2"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn2"/>
<variable units="first_order_rate_constant" name="k2" initial_value="6.0E-5"/>
<variable units="second_order_rate_constant" name="k2_" initial_value="0.03"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="CaDM1">
<role stoichiometry="1" direction="forward" delta_variable="delta_CaDM1_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="DM1">
<role stoichiometry="1" direction="forward" delta_variable="delta_DM1_rxn2" role="product"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn2" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k2</ci>
<ci>CaDM1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k2_</ci>
<ci>DM1</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="CaDM2"/>
<variable units="micromolar" public_interface="in" name="DM2"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="flux" public_interface="out" name="delta_CaDM2_rxn3"/>
<variable units="flux" public_interface="out" name="delta_DM2_rxn3"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn3"/>
<variable units="first_order_rate_constant" name="k3" initial_value="6.0E-5"/>
<variable units="second_order_rate_constant" name="k3_" initial_value="0.03"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="CaDM2">
<role stoichiometry="1" direction="forward" delta_variable="delta_CaDM2_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="DM2">
<role stoichiometry="1" direction="forward" delta_variable="delta_DM2_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k3</ci>
<ci>CaDM2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k3_</ci>
<ci>DM2</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction4">
<variable units="micromolar" public_interface="in" name="CaDM1"/>
<variable units="micromolar" public_interface="in" name="DM1"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="flux" public_interface="out" name="delta_CaDM1_rxn4"/>
<variable units="flux" public_interface="out" name="delta_DM1_rxn4"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn4"/>
<variable units="first_order_rate_constant" name="k4" initial_value="75.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="no">
<variable_ref variable="CaDM1">
<role stoichiometry="1" delta_variable="delta_CaDM1_rxn4" role="reactant"/>
</variable_ref>
<variable_ref variable="DM1">
<role stoichiometry="1" delta_variable="delta_DM1_rxn4" role="product"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" delta_variable="delta_Ca_rxn4" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<times/>
<ci>k4</ci>
<ci>CaDM1</ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<connection>
<map_components component_2="reaction0" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn0" variable_1="delta_Ca_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn1" variable_1="delta_Ca_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn2" variable_1="delta_Ca_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn3" variable_1="delta_Ca_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction4" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn4" variable_1="delta_Ca_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="D"/>
<map_variables variable_2="D" variable_1="D"/>
<map_variables variable_2="delta_D_rxn1" variable_1="delta_D_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="B"/>
<map_variables variable_2="B" variable_1="B"/>
<map_variables variable_2="delta_B_rxn0" variable_1="delta_B_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="CaB"/>
<map_variables variable_2="CaB" variable_1="CaB"/>
<map_variables variable_2="delta_CaB_rxn0" variable_1="delta_CaB_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="CaD"/>
<map_variables variable_2="CaD" variable_1="CaD"/>
<map_variables variable_2="delta_CaD_rxn1" variable_1="delta_CaD_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="DM1"/>
<map_variables variable_2="DM1" variable_1="DM1"/>
<map_variables variable_2="delta_DM1_rxn2" variable_1="delta_DM1_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction4" component_1="DM1"/>
<map_variables variable_2="DM1" variable_1="DM1"/>
<map_variables variable_2="delta_DM1_rxn4" variable_1="delta_DM1_rxn4"/>
</connection>
<connection>
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Binding Kinetics of Calbindin-D28k Determined by Flash Photolysis of
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