- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-12-17 10:57:14+13:00
- Desc:
- Fixed RDF.
- Permanent Source URI:
- https://models.cellml.org/workspace/mears_sheppard_atwater_rojas_bertram_sherman_1997/rawfile/86f2435f5605936ca1f6e0da103dd6cb9b3c3793/mears_sheppard_atwater_rojas_bertram_sherman_1997.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 17/12/2009 at 9:56:26 at a.m. using:
COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<title>Evidence That Calcium Release-activated Current Mediates the Biphasic Electrical Activity of Mouse Pancreatic β-Cells</title>
<author>
<firstname>Tessa</firstname>
<surname>Paris</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
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<section id="sec_status">
<title>Model Status</title>
<para>This CellML model runs in both PCEnv and COR to produce simulation graphs which are similar to those in the original published paper, namely figures 2 and 6.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRAct: The electrical response of pancreatic β-cells to step increases in glucose concentration is biphasic, consisting of a prolonged depolarization with action potentials (Phase 1) followed by membrane potential oscillations known as bursts. We have proposed that the Phase 1 response results from the combined depolarizing influences of potassium channel closure and an inward, nonselective cation current (I CRAN) that activates as intracellular calcium stores empty during exposure to basal glucose (Bertram et al., 1995). The stores refill during Phase 1, deactivating I CRAN and allowing steady-state bursting to commence. We support this hypothesis with additional simulations and experimental results indicating that Phase 1 duration is sensitive to the filling state of intracellular calcium stores. First, the duration of the Phase 1 transient increases with duration of prior exposure to basal (2.8 mm) glucose, reflecting the increased time required to fill calcium stores that have been emptying for longer periods. Second, Phase 1 duration is reduced when islets are exposed to elevated K+ to refill calcium stores in the presence of basal glucose. Third, when extracellular calcium is removed during the basal glucose exposure to reduce calcium influx into the stores, Phase 1 duration increases. Finally, no Phase 1 is observed following hyperpolarization of the β-cell membrane with diazoxide in the continued presence of 11 mm glucose, a condition in which intracellular calcium stores remain full. Application of carbachol to empty calcium stores during basal glucose exposure did not increase Phase 1 duration as the model predicts. Despite this discrepancy, the good agreement between most of the experimental results and the model predictions provides evidence that a calcium release-activated current mediates the Phase 1 electrical response of the pancreatic β-cel.</para>
<para>
The original paper reference is cited below:
</para>
<para>Evidence That Calcium Release-activated Current Mediates the Biphasic Electrical Activity of Mouse Pancreatic β-Cells, Authors, year, <emphasis>Journal name</emphasis>, edition, firstpage-lastpage. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/9002424">PubMed ID: 9002424</ulink></para>
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<caption>Schematic diagram of the model.</caption>
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Evidence That Calcium Release-activated Current Mediates the Biphasic Electrical Activity of Mouse Pancreatic Beta-Cells
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<variable name="V" units="millivolt" public_interface="in"/>
<variable name="V_K" units="millivolt" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<variable name="kdkca" units="micromolar" initial_value="0.55"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K_Ca</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">5</cn>
</apply>
<apply>
<power/>
<ci>kdkca</ci>
<cn cellml:units="dimensionless">5</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="CRAC_current">
<variable name="i_CRAC" units="picoA" public_interface="out"/>
<variable name="g_CRAC" units="picoS" initial_value="75"/>
<variable name="V_CRAC" units="millivolt" initial_value="0" public_interface="out"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="Ca_er" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="r_infinity" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CRAC</ci>
<apply>
<times/>
<ci>g_CRAC</ci>
<ci>r_infinity</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_CRAC</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="CRAC_r_gate">
<variable name="r_infinity" units="dimensionless" public_interface="out"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="Ca_er" units="micromolar" public_interface="in"/>
<variable name="Ca_er_bar" units="micromolar" initial_value="40"/>
<variable name="sloper" units="micromolar" initial_value="3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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/>
<ci>Ca_er</ci>
<ci>Ca_er_bar</ci>
</apply>
<ci>sloper</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="leak_current">
<variable name="i_leak" units="picoA" public_interface="out"/>
<variable name="g_leak" units="picoS" initial_value="0"/>
<variable name="V_CRAC" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_leak</ci>
<apply>
<times/>
<ci>g_leak</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_CRAC</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ER_parameters">
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<variable name="J_er_p" units="micromolar_per_millisecond" public_interface="out"/>
<variable name="IP3" units="micromolar" initial_value="0"/>
<variable name="kerp" units="micromolar" initial_value="0.09"/>
<variable name="verp" units="micromolar_per_millisecond" initial_value="0.24"/>
<variable name="dact" units="micromolar" initial_value="0.35"/>
<variable name="dinh" units="micromolar" initial_value="0.4"/>
<variable name="dip3" units="micromolar" initial_value="0.2"/>
<variable name="a_infinity" units="dimensionless"/>
<variable name="b_infinity" units="dimensionless"/>
<variable name="h_infinity" units="dimensionless"/>
<variable name="O" units="per_millisecond" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_er_p</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>verp</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>kerp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>dact</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>b_infinity</ci>
<apply>
<divide/>
<ci>IP3</ci>
<apply>
<plus/>
<ci>IP3</ci>
<ci>dip3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>h_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>dinh</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>O</ci>
<apply>
<times/>
<apply>
<power/>
<ci>a_infinity</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>b_infinity</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>h_infinity</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="per_millisecond">1</cn>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Ca_equations">
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="Ca_er" units="micromolar" initial_value="60" public_interface="out"/>
<variable name="Ca_i" units="micromolar" initial_value="0.11" public_interface="out" private_interface="out"/>
<variable name="J_er_tot" units="micromolar_per_millisecond" public_interface="out"/>
<variable name="J_er_p" units="micromolar_per_millisecond" private_interface="in"/>
<variable name="J_er_IP3" units="micromolar_per_millisecond"/>
<variable name="J_er_leak" units="micromolar_per_millisecond"/>
<variable name="J_mem_tot" units="micromolar_per_millisecond" public_interface="in"/>
<variable name="O" units="per_millisecond" private_interface="in"/>
<variable name="perl" units="per_millisecond" initial_value="0.003"/>
<variable name="lambda_er" units="dimensionless" initial_value="250"/>
<variable name="sigma_er" units="dimensionless" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_er_tot</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>J_er_leak</ci>
<ci>J_er_IP3</ci>
</apply>
<ci>J_er_p</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_er_leak</ci>
<apply>
<times/>
<ci>perl</ci>
<apply>
<minus/>
<ci>Ca_er</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_er_IP3</ci>
<apply>
<times/>
<ci>O</ci>
<apply>
<minus/>
<ci>Ca_er</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_er</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>J_er_tot</ci>
</apply>
<apply>
<times/>
<ci>lambda_er</ci>
<ci>sigma_er</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<ci>J_er_tot</ci>
<ci>lambda_er</ci>
</apply>
<ci>J_mem_tot</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Ca_membrane_flux">
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="kmp" units="micromolar" initial_value="0.35"/>
<variable name="vmp" units="micromolar" initial_value="0.08"/>
<variable name="gamma" units="micromolar_per_picoA" initial_value="0.000003607"/>
<variable name="i_Ca" units="picoA" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<variable name="J_mem_tot" units="micromolar_per_millisecond" public_interface="out"/>
<variable name="Jmp" units="micromolar"/>
<variable name="f" units="per_millisecond" initial_value="0.01"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Jmp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>vmp</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>kmp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_mem_tot</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>f</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>gamma</ci>
<ci>i_Ca</ci>
</apply>
<ci>Jmp</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="K_current">
<component_ref component="K_channel_n_gate"/>
</component_ref>
<component_ref component="K_ATP_current"/>
<component_ref component="fast_Ca_current">
<component_ref component="fast_Ca_channel_m_gate"/>
</component_ref>
<component_ref component="slow_Ca_current">
<component_ref component="slow_Ca_channel_m_gate"/>
<component_ref component="slow_Ca_channel_j_gate"/>
</component_ref>
<component_ref component="K_Ca_current"/>
<component_ref component="CRAC_current">
<component_ref component="CRAC_r_gate"/>
</component_ref>
<component_ref component="ER_parameters"/>
<component_ref component="Ca_equations"/>
<component_ref component="Ca_membrane_flux"/>
</component_ref>
</group>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="encapsulation"/>
<component_ref component="K_current">
<component_ref component="K_channel_n_gate"/>
</component_ref>
<component_ref component="fast_Ca_current">
<component_ref component="fast_Ca_channel_m_gate"/>
</component_ref>
<component_ref component="slow_Ca_current">
<component_ref component="slow_Ca_channel_m_gate"/>
<component_ref component="slow_Ca_channel_j_gate"/>
</component_ref>
<component_ref component="CRAC_current">
<component_ref component="CRAC_r_gate"/>
</component_ref>
<component_ref component="Ca_equations">
<component_ref component="ER_parameters"/>
</component_ref>
</group>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_ATP_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="fast_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="slow_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRAC_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca_equations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca_membrane_flux" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="leak_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K" variable_2="i_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_ATP_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K_ATP" variable_2="i_K_ATP"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="fast_Ca_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="slow_Ca_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_Ca_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K_Ca" variable_2="i_K_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRAC_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_CRAC" variable_2="i_CRAC"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="leak_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_leak" variable_2="i_leak"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_current" component_2="K_ATP_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_current" component_2="K_Ca_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="fast_Ca_current" component_2="slow_Ca_current"/>
<map_variables variable_1="V_Ca" variable_2="V_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="slow_Ca_current" component_2="Ca_current_total"/>
<map_variables variable_1="i_Ca_s" variable_2="i_Ca_s"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="fast_Ca_current" component_2="Ca_current_total"/>
<map_variables variable_1="i_Ca_f" variable_2="i_Ca_f"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca_current_total" component_2="membrane"/>
<map_variables variable_1="i_Ca" variable_2="i_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca_current_total" component_2="Ca_membrane_flux"/>
<map_variables variable_1="i_Ca" variable_2="i_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRAC_current" component_2="Ca_equations"/>
<map_variables variable_1="Ca_er" variable_2="Ca_er"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_Ca_current" component_2="Ca_equations"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRAC_current" component_2="leak_current"/>
<map_variables variable_1="V_CRAC" variable_2="V_CRAC"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca_equations" component_2="Ca_membrane_flux"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="J_mem_tot" variable_2="J_mem_tot"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ER_parameters" component_2="Ca_equations"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="J_er_p" variable_2="J_er_p"/>
<map_variables variable_1="O" variable_2="O"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="K_current" component_2="K_channel_n_gate"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="fast_Ca_current" component_2="fast_Ca_channel_m_gate"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="m_f_infinity" variable_2="m_f_infinity"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="slow_Ca_current" component_2="slow_Ca_channel_m_gate"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="m_s_infinity" variable_2="m_s_infinity"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="slow_Ca_current" component_2="slow_Ca_channel_j_gate"/>
<map_variables variable_1="jm" variable_2="jm"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRAC_current" component_2="CRAC_r_gate"/>
<map_variables variable_1="r_infinity" variable_2="r_infinity"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Ca_er" variable_2="Ca_er"/>
</connection>
</model>
