- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2008-03-19 22:54:50+13:00
- Desc:
- committing version02 of zhang_holden_kodama_honjo_lei_varghese_boyett_2000
- Permanent Source URI:
- http://models.cellml.org/workspace/zhang_holden_kodama_honjo_lei_varghese_boyett_2000/rawfile/709bc6d14b3bde2452497a4e930bd320ad72dfac/zhang_holden_kodama_honjo_lei_varghese_boyett_2000.cellml
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<!--
This CellML file was generated on 20/06/2005 at 13:15:40 using:
COR (0.9.31.71)
Copyright 2002-2005 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
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<article>
<articleinfo>
<title>Mathematical Model Of Action Potentials In The Periphery Of The Sinoatrial Node, 2000</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>Oxford University</shortaffil>
</affiliation>
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</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original published version of this model, which is known to run in PCEnv. Please note that the published version of this model (i.e. the one downloadable from this page) contains some errors which have been addressed in Garny et al. (2003). The CellML model for Garny et al. 2003 can be found <ulink url="http://www.cellml.org/models/garny_kohl_hunter_boyett_noble_varghese_boyett_2003_version04">here</ulink>.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 2000 H. Zhang <emphasis>et al</emphasis> published a mathematical model which describes the action potentials in the periphery and center of the rabbit sinoatrial node (see the figure below). The SA node is functionally, anatomically and electrophysiologically heterogeneous. In their model, Zhang <emphasis>et al</emphasis> accounted for this heterogeneity by defining two distinct models for the peripheral and the central cells of the SA node. These models have the same equations to define the ionic currents, but they vary in their parameters. The CellML description here is of the peripheral SA node cell model. To make it appropriate for the central SA node cells, certain parameters need to be changed (refer to the original paper reference which is cited below).
</para>
<para>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/279/1/H397">Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node</ulink>, H. Zhang, A.V. Holden, I. Honjo, M. Lei, T. Varghese and M.R. Boyett, 2000, <ulink url="http://ajpheart.physiology.org/">
<emphasis>Am. J. Physiol. Heart Circ. Physiol.</emphasis>
</ulink>, 279, H397-H421. (The <ulink url="http://ajpheart.physiology.org/cgi/content/full/279/1/H397">full text</ulink> of the article is available on the American Journal of Physiology website for Journal Members.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10899081&dopt=Abstract">PubMed ID: 10899081</ulink>
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<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Zhang <emphasis>et al</emphasis> 2000 model of the action potentials in the peripheral cells of the SA node.</caption>
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<variable units="dimensionless" public_interface="out" name="d_L" initial_value="0.04804900895"/>
<variable units="per_second" name="alpha_d_L"/>
<variable units="per_second" name="beta_d_L"/>
<variable units="dimensionless" name="d_L_infinity"/>
<variable units="second" name="tau_d_L"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>d_L</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_L_infinity</ci>
<ci>d_L</ci>
</apply>
<ci>tau_d_L</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d_L</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt_second">28.38</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">2.5</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt">84.9</cn>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.208</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">11.42</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.4</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<plus/>
<ci>alpha_d_L</ci>
<ci>beta_d_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_L_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23.1</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="dimensionless" public_interface="out" name="f_L" initial_value="0.48779845203"/>
<variable units="per_second" name="alpha_f_L"/>
<variable units="per_second" name="beta_f_L"/>
<variable units="dimensionless" name="f_L_infinity"/>
<variable units="second" name="tau_f_L"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>f_L</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L</ci>
</apply>
<ci>tau_f_L</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">3.12</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_L</ci>
<apply>
<divide/>
<cn cellml:units="per_second">25</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_L</ci>
<ci>beta_f_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_L_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel">
<variable units="dimensionless" public_interface="in" private_interface="out" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_Ca_T"/>
<variable units="microS" name="g_Ca_T_Centre" initial_value="0.0043"/>
<variable units="microS" name="g_Ca_T_Periphery" initial_value="0.0139"/>
<variable units="microS" name="g_Ca_T"/>
<variable units="millivolt" name="E_Ca_T" initial_value="45"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d_T"/>
<variable units="dimensionless" private_interface="in" name="f_T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_Ca_T</ci>
<apply>
<plus/>
<ci>g_Ca_T_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_Ca_T_Periphery</ci>
<ci>g_Ca_T_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_T</ci>
<apply>
<times/>
<ci>g_Ca_T</ci>
<ci>d_T</ci>
<ci>f_T</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca_T</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d_T" initial_value="0.42074047435"/>
<variable units="per_second" name="alpha_d_T"/>
<variable units="per_second" name="beta_d_T"/>
<variable units="dimensionless" name="d_T_infinity"/>
<variable units="second" name="tau_d_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>d_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_T_infinity</ci>
<ci>d_T</ci>
</apply>
<ci>tau_d_T</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">1068</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">1068</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_d_T</ci>
<ci>beta_d_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_T_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6.8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="dimensionless" public_interface="out" name="f_T" initial_value="0.038968420558"/>
<variable units="per_second" name="alpha_f_T"/>
<variable units="per_second" name="beta_f_T"/>
<variable units="dimensionless" name="f_T_infinity"/>
<variable units="second" name="tau_f_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>f_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_T_infinity</ci>
<ci>f_T</ci>
</apply>
<ci>tau_f_T</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">15.3</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.7</cn>
</apply>
</apply>
<cn cellml:units="millivolt">83.3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">15</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.7</cn>
</apply>
<cn cellml:units="millivolt">15.38</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_T</ci>
<ci>beta_f_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_T_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71</cn>
</apply>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents">
<variable units="dimensionless" public_interface="in" private_interface="out" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_to"/>
<variable units="nanoA" public_interface="out" name="i_sus"/>
<variable units="microS" name="g_to_Centre" initial_value="0.00491"/>
<variable units="microS" name="g_to_Periphery" initial_value="0.03649"/>
<variable units="microS" name="g_to"/>
<variable units="microS" name="g_sus_Centre" initial_value="6.65e-5"/>
<variable units="microS" name="g_sus_Periphery" initial_value="0.0114"/>
<variable units="microS" name="g_sus"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="dimensionless" private_interface="in" name="q"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_to</ci>
<apply>
<plus/>
<ci>g_to_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_to_Periphery</ci>
<ci>g_to_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_sus</ci>
<apply>
<plus/>
<ci>g_sus_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_sus_Periphery</ci>
<ci>g_sus_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>q</ci>
<ci>r</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_sus</ci>
<apply>
<times/>
<ci>g_sus</ci>
<ci>r</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents_q_gate">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="dimensionless" public_interface="out" name="q" initial_value="0.29760539675"/>
<variable units="dimensionless" name="q_infinity"/>
<variable units="second" name="tau_q"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>q</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>q_infinity</ci>
<ci>q</ci>
</apply>
<ci>tau_q</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">59.37</cn>
</apply>
<cn cellml:units="millivolt">13.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_q</ci>
<apply>
<plus/>
<cn cellml:units="second">0.0101</cn>
<apply>
<divide/>
<cn cellml:units="second">0.06517</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.57</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="millivolt">0.08</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">49</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="second">2.4e-5</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt">0.1</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">50.93</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0.064402950262"/>
<variable units="dimensionless" name="r_infinity"/>
<variable units="second" name="tau_r"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_infinity</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10.93</cn>
</apply>
</apply>
<cn cellml:units="millivolt">19.7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.001</cn>
<apply>
<plus/>
<cn cellml:units="second">2.98</cn>
<apply>
<divide/>
<cn cellml:units="second">15.59</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.037</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt">0.09</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30.61</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.369</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="millivolt">0.12</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23.84</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_K_r"/>
<variable units="microS" name="g_K_r_Centre" initial_value="0.000797"/>
<variable units="microS" name="g_K_r_Periphery" initial_value="0.016"/>
<variable units="microS" name="g_K_r"/>
<variable units="dimensionless" name="P_a"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="P_af"/>
<variable units="dimensionless" private_interface="in" name="P_as"/>
<variable units="dimensionless" private_interface="in" name="P_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_K_r</ci>
<apply>
<plus/>
<ci>g_K_r_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_K_r_Periphery</ci>
<ci>g_K_r_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K_r</ci>
<apply>
<times/>
<ci>g_K_r</ci>
<ci>P_a</ci>
<ci>P_i</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_a</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<ci>P_af</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.4</cn>
<ci>P_as</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_af_gate">
<variable units="dimensionless" public_interface="out" name="P_af" initial_value="0.13034201158"/>
<variable units="dimensionless" public_interface="out" name="P_af_infinity"/>
<variable units="second" name="tau_P_af"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>P_af</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>P_af_infinity</ci>
<ci>P_af</ci>
</apply>
<ci>tau_P_af</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_af_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">14.2</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_P_af</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">37.2</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">9</cn>
</apply>
<cn cellml:units="millivolt">15.9</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.96</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
<cn cellml:units="millivolt">22.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_as_gate">
<variable units="dimensionless" public_interface="out" name="P_as" initial_value="0.46960956028"/>
<variable units="dimensionless" name="P_as_infinity"/>
<variable units="second" name="tau_P_as"/>
<variable units="dimensionless" public_interface="in" name="P_af_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>P_as</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>P_as_infinity</ci>
<ci>P_as</ci>
</apply>
<ci>tau_P_as</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_as_infinity</ci>
<ci>P_af_infinity</ci>
</apply>
<apply>
<eq/>
<ci>tau_P_as</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4.2</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">9</cn>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.15</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
<cn cellml:units="millivolt">21.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_i_gate">
<variable units="dimensionless" public_interface="out" name="P_i" initial_value="0.87993375273"/>
<variable units="dimensionless" name="P_i_infinity"/>
<variable units="second" name="tau_P_i" initial_value="0.002"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>P_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>P_i_infinity</ci>
<ci>P_i</ci>
</apply>
<ci>tau_P_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_i_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">18.6</cn>
</apply>
<cn cellml:units="millivolt">10.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifying_potassium_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_K_s"/>
<variable units="microS" name="g_K_s_Centre" initial_value="0.000518"/>
<variable units="microS" name="g_K_s_Periphery" initial_value="0.0104"/>
<variable units="microS" name="g_K_s"/>
<variable units="millivolt" public_interface="in" name="E_K_s"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_K_s</ci>
<apply>
<plus/>
<ci>g_K_s_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_K_s_Periphery</ci>
<ci>g_K_s_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K_s</ci>
<apply>
<times/>
<ci>g_K_s</ci>
<apply>
<power/>
<ci>xs</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K_s</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifying_potassium_current_xs_gate">
<variable units="dimensionless" public_interface="out" name="xs" initial_value="0.082293827208"/>
<variable units="per_second" name="alpha_xs"/>
<variable units="per_second" name="beta_xs"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>xs</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_xs</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>xs</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_xs</ci>
<ci>xs</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xs</ci>
<apply>
<divide/>
<cn cellml:units="per_second">14</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xs</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">45</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_f_Na"/>
<variable units="nanoA" public_interface="out" name="i_f_K"/>
<variable units="microS" name="g_f_Na_Centre" initial_value="0.000548"/>
<variable units="microS" name="g_f_Na_Periphery" initial_value="0.0069"/>
<variable units="microS" name="g_f_Na"/>
<variable units="microS" name="g_f_K_Centre" initial_value="0.000548"/>
<variable units="microS" name="g_f_K_Periphery" initial_value="0.0069"/>
<variable units="microS" name="g_f_K"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_f_Na</ci>
<apply>
<plus/>
<ci>g_f_Na_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_f_Na_Periphery</ci>
<ci>g_f_Na_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f_Na</ci>
<apply>
<times/>
<ci>g_f_Na</ci>
<ci>y</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_f_K</ci>
<apply>
<plus/>
<ci>g_f_K_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_f_K_Periphery</ci>
<ci>g_f_K_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f_K</ci>
<apply>
<times/>
<ci>g_f_K</ci>
<ci>y</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.03889291759"/>
<variable units="per_second" name="alpha_y"/>
<variable units="per_second" name="beta_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<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>y</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_y</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_y</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_y</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">78.91</cn>
</apply>
</apply>
<cn cellml:units="millivolt">26.62</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_y</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75.13</cn>
</apply>
<cn cellml:units="millivolt">21.25</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_b_Na"/>
<variable units="microS" name="g_b_Na_Centre" initial_value="5.8e-5"/>
<variable units="microS" name="g_b_Na_Periphery" initial_value="0.000189"/>
<variable units="microS" name="g_b_Na"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_b_Na</ci>
<apply>
<plus/>
<ci>g_b_Na_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_b_Na_Periphery</ci>
<ci>g_b_Na_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_b_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_background_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_b_K"/>
<variable units="microS" name="g_b_K_Centre" initial_value="2.52e-5"/>
<variable units="microS" name="g_b_K_Periphery" initial_value="8.19e-5"/>
<variable units="microS" name="g_b_K"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_b_K</ci>
<apply>
<plus/>
<ci>g_b_K_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_b_K_Periphery</ci>
<ci>g_b_K_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_b_K</ci>
<apply>
<times/>
<ci>g_b_K</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_b_Ca"/>
<variable units="microS" name="g_b_Ca_Centre" initial_value="1.32e-5"/>
<variable units="microS" name="g_b_Ca_Periphery" initial_value="4.3e-5"/>
<variable units="microS" name="g_b_Ca"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_b_Ca</ci>
<apply>
<plus/>
<ci>g_b_Ca_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>g_b_Ca_Periphery</ci>
<ci>g_b_Ca_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_b_Ca</ci>
<apply>
<times/>
<ci>g_b_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchanger">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_NaCa"/>
<variable units="nanoA" name="k_NaCa_Centre" initial_value="2.7e-6"/>
<variable units="nanoA" name="k_NaCa_Periphery" initial_value="8.8e-6"/>
<variable units="nanoA" name="k_NaCa"/>
<variable units="dimensionless" name="d_NaCa" initial_value="0.0001"/>
<variable units="dimensionless" name="gamma_NaCa" initial_value="0.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k_NaCa</ci>
<apply>
<plus/>
<ci>k_NaCa_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>k_NaCa_Periphery</ci>
<ci>k_NaCa_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.03743</cn>
<ci>V</ci>
<ci>gamma_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0374</cn>
<ci>V</ci>
<apply>
<minus/>
<ci>gamma_NaCa</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_p"/>
<variable units="millimolar" name="K_m_Na" initial_value="5.64"/>
<variable units="millimolar" name="K_m_K" initial_value="0.621"/>
<variable units="nanoA" name="i_p_max_Centre" initial_value="0.0478"/>
<variable units="nanoA" name="i_p_max_Periphery" initial_value="0.16"/>
<variable units="nanoA" name="i_p_max"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_max</ci>
<apply>
<plus/>
<ci>i_p_max_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>i_p_max_Periphery</ci>
<ci>i_p_max_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_p</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_p_max</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Na_i</ci>
<apply>
<plus/>
<ci>K_m_Na</ci>
<ci>Na_i</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_o</ci>
<apply>
<plus/>
<ci>K_m_K</ci>
<ci>K_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dimensionless">1.6</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
</apply>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_calcium_current">
<variable units="dimensionless" public_interface="in" name="FCell"/>
<variable units="nanoA" public_interface="out" name="i_Ca_p"/>
<variable units="nanoA" name="i_Ca_p_max_Centre" initial_value="0"/>
<variable units="nanoA" name="i_Ca_p_max_Periphery" initial_value="0"/>
<variable units="nanoA" name="i_Ca_p_max"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca_p_max</ci>
<apply>
<plus/>
<ci>i_Ca_p_max_Centre</ci>
<apply>
<times/>
<ci>FCell</ci>
<apply>
<minus/>
<ci>i_Ca_p_max_Periphery</ci>
<ci>i_Ca_p_max_Centre</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_p</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_Ca_p_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0004</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="8"/>
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.0001"/>
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<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
</component>
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<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="millivolt" public_interface="out" name="E_K_s"/>
<variable units="millivolt" public_interface="out" name="E_Ca"/>
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<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
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