- Author:
- rcai987 <devnull@localhost>
- Date:
- 2014-12-19 14:42:28+13:00
- Desc:
- Addded annotations to skouibine_trayavona_moore_1999 model
- Permanent Source URI:
- https://models.cellml.org/workspace/skouibine_trayanova_moore_1999/rawfile/cd47d4e07a6c5b1a9c4943b9ad6db3a2f6f31f96/skouibine_trayanova_moore_1999.cellml
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<title>The Defibrillation Beeler-Reuter Model</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The goal of this simulation study is to examine, in a sheet of myocardium, the contribution of anode and cathode break phenomena in terminating a spiral wave reentry by the defibrillation shock. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. Two case studies are presented in this article: tissue that can electroporate at high levels of transmembrane potential, and model tissue that does not support electroporation. In both cases, the spiral wave is initiated via cross-field stimulation of the bidomain sheet. The extracellular defibrillation shock is delivered via two small electrodes located at opposite tissue boundaries. Modifications in the active membrane kinetics enable the delivery of high-strength defibrillation shocks. Numerical solutions are obtained using an efficient semi-implicit predictor-corrector scheme that allows one to execute the simulations within reasonable time. The simulation results demonstrate that anode and/or cathode break excitations contribute significantly to the activity during and after the shock. For a successful defibrillation shock, the virtual electrodes and the break excitations restrict the spiral wave and render the tissue refractory so it cannot further maintain the reentry. The results also indicate that electroporation alters the anode/cathode break phenomena, the major impact being on the timing of the cathode-break excitations. Thus, electroporation results in different patterns of transmembrane potential distribution after the shock. This difference in patterns may or may not result in change of the outcome of the shock.
</para>
<para>
The original paper reference is cited below:
</para>
<para>Anode/cathode make and break phenomena during defibrillation: Does electroporation make a difference?, Skouibine, K., Trayanova, N., Moore, P. 1999, <emphasis>IEEE Transactions on Biomedical Engineering</emphasis>, 46, 769-777. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10396895&dopt=Abstract">PubMed ID: 10396895</ulink>
</para>
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<ci> g_s </ci>
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<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dCai_dt_eq">
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<piecewise>
<piece>
<cn cellml:units="flux"> 0.0 </cn>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="mV"> 200.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci> i_s </ci>
<cn cellml:units="dimensionless"> -0.01 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.07 </cn>
<apply>
<minus/>
<cn cellml:units="concentration_units"> 0.0001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="slow_inward_current_d_gate" name="slow_inward_current_d_gate">
<variable initial_value="0.0" name="d" public_interface="out" units="dimensionless"/>
<variable name="alpha_d" units="per_ms"/>
<variable name="beta_d" units="per_ms"/>
<variable initial_value="1.0" name="R_d" units="dimensionless"/>
<variable name="V" public_interface="in" units="mV"/>
<variable name="time" public_interface="in" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_d_calculation_eq">
<apply id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.095 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
<cn cellml:units="mV"> 100.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
<cn cellml:units="mV"> 13.89 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_d_calculation_eq">
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.07 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
<cn cellml:units="mV"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dd_dt_eq">
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> alpha_d </ci>
<ci> R_d </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="slow_inward_current_f_gate" name="slow_inward_current_f_gate">
<variable initial_value="1.0" name="f" public_interface="out" units="dimensionless"/>
<variable name="alpha_f" units="per_ms"/>
<variable name="beta_f" units="per_ms"/>
<variable initial_value="1.0" name="R_f" units="dimensionless"/>
<variable name="V" public_interface="in" units="mV"/>
<variable name="time" public_interface="in" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_f_calculation_eq">
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.012 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
<cn cellml:units="mV"> 125.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
<cn cellml:units="mV"> 6.67 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_f_calculation_eq">
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.0065 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="df_dt_eq">
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> alpha_f </ci>
<ci> R_f </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
<component_ref component="time_independent_outward_current"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="time_dependent_outward_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="time_independent_outward_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="fast_sodium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="slow_inward_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_s" variable_2="i_s"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="time_dependent_outward_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_x1" variable_2="i_x1"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="time_independent_outward_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate"/>
<map_variables variable_1="m" variable_2="m"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate"/>
<map_variables variable_1="h" variable_2="h"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="time_dependent_outward_current" component_2="time_dependent_outward_current_x1_gate"/>
<map_variables variable_1="x1" variable_2="x1"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="slow_inward_current_d_gate"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="slow_inward_current_f_gate"/>
<map_variables variable_1="f" variable_2="f"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<rdf:RDF><rdf:Description rdf:about="#beta_h_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#82c4214e-337c-4268-ab27-08aaa1c42c0b"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#82c4214e-337c-4268-ab27-08aaa1c42c0b"><rdf:value xml:lang="en">
The closing rate for the h gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#f540d6dd-eb83-48c7-8ccf-6cc22602a0b6"><rdf:value xml:lang="en">
The kinetics of the f gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#dCai_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#f03eca1c-378a-48f5-a480-13ee2254ad2c"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#f03eca1c-378a-48f5-a480-13ee2254ad2c"><rdf:value xml:lang="en">
The time rate of change of intracellular calcium concentration.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#e7e61ee5-2624-423e-880f-7c58e028e478"><rdf:value xml:lang="en">
The opening rate for the h gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#b12606d9-c6d7-4bad-bd1b-db79dbec301c"><rdf:value xml:lang="en">
The main differential equation for the model, specifing membrane
potential as the summation of all ionic currents and an applied
stimulus current.
</rdf:value></rdf:Description><rdf:Description rdf:about="#beta_d_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#1c537c12-951c-4628-8c44-1da4a250cfdb"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#1c537c12-951c-4628-8c44-1da4a250cfdb"><rdf:value xml:lang="en">
The closing rate of the d gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#dh_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#4797bc9f-9082-442b-b1fc-087514cd737c"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#4797bc9f-9082-442b-b1fc-087514cd737c"><rdf:value xml:lang="en">
The kinetics of the h gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#dx1_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#57593dc1-8f39-4a81-b08b-e273b58bc0fa"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#57593dc1-8f39-4a81-b08b-e273b58bc0fa"><rdf:value xml:lang="en">
The kinetics of the x1 gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#beta_x1_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#b1d6da41-9ac3-49ec-9bf3-2192d2531531"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#b1d6da41-9ac3-49ec-9bf3-2192d2531531"><rdf:value xml:lang="en">
The closing rate of the x1 gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#b3f8b236-413b-4746-9567-721d0eff69d1"><rdf:value xml:lang="en">
The kinetics of the m gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#b12532fb-cc21-4165-9a6e-795dc98017ef"><rdf:value xml:lang="en">
The opening rate of the d gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#236a0d67-26ed-42ee-a6e5-b894ea982af2"><rdf:value xml:lang="en">
The opening rate of the f gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#dm_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#b3f8b236-413b-4746-9567-721d0eff69d1"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#5bd403fa-c258-45f7-acfd-98a29d9a5055"><rdf:value xml:lang="en">
The closing rate of the f gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#beta_f_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#5bd403fa-c258-45f7-acfd-98a29d9a5055"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#55dbf119-b6a1-4873-9e00-1c9e95f24f55"><rdf:value xml:lang="en">
The opening rate for the m gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#i_Na_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#4b2a53b7-9820-4e91-b5bd-ceb150ab8ac9"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#4b2a53b7-9820-4e91-b5bd-ceb150ab8ac9"><rdf:value xml:lang="en">
Calculation of the fast sodium current.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#ea56eca4-c289-4941-91f3-885b4c00c310"><rdf:value xml:lang="en">
The closing rate for the m gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#beta_m_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#ea56eca4-c289-4941-91f3-885b4c00c310"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#membrane_voltage_diff_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#b12606d9-c6d7-4bad-bd1b-db79dbec301c"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#c166c403-d0f0-4ff0-833c-0ef9872f464a"><rdf:value xml:lang="en">
Calculation of the slow inward current.
</rdf:value></rdf:Description><rdf:Description rdf:about="#dd_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#a0770d70-cd58-4d72-ada8-80782eef2cf3"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#a0770d70-cd58-4d72-ada8-80782eef2cf3"><rdf:value xml:lang="en">
The kinetics of the d gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#c967adca-bdb9-4ee5-a848-ed8b5f1f7de3"><rdf:value xml:lang="en">
The opening rate of the x1 gate.
</rdf:value></rdf:Description><rdf:Description rdf:about="#alpha_x1_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#c967adca-bdb9-4ee5-a848-ed8b5f1f7de3"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#ae14a4f4-ee6a-4ea2-8457-822eb82f267a"><rdf:value xml:lang="en">
Calculation of the reversal potential for the slow inward current.
</rdf:value></rdf:Description><rdf:Description rdf:about="#alpha_h_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#e7e61ee5-2624-423e-880f-7c58e028e478"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#df_dt_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#f540d6dd-eb83-48c7-8ccf-6cc22602a0b6"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#alpha_f_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#236a0d67-26ed-42ee-a6e5-b894ea982af2"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#i_s_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#c166c403-d0f0-4ff0-833c-0ef9872f464a"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#alpha_m_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#55dbf119-b6a1-4873-9e00-1c9e95f24f55"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#alpha_d_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#b12532fb-cc21-4165-9a6e-795dc98017ef"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#E_s_calculation_eq"><cmeta:comment><rdf:Description rdf:about="rdf:#ae14a4f4-ee6a-4ea2-8457-822eb82f267a"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#membrane"><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0060075"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0030322"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0042391"/></isVersionOf></rdf:Description><rdf:Description rdf:about="#fast_sodium_current"><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0005272"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0034706"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0005248"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0001518"/></isVersionOf></rdf:Description><rdf:Description rdf:about="#fast_sodium_current_m_gate"><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0005272"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0034706"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description rdf:about="http://identifiers.org/go/GO:0005248"/></isVersionOf><isVersionOf xmlns="http://biomodels.net/biology-qualifiers/"><rdf:Description 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