- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-04-14 12:19:26+12:00
- Desc:
- Added images in ai and svg format, added clickable SVG to session file
- Permanent Source URI:
- https://models.cellml.org/workspace/mears_sheppard_atwater_rojas_bertram_sherman_1997/rawfile/27df2ef6b23052ad1c0659a2b70432829e7fd742/mears_sheppard_atwater_rojas_bertram_sherman_1997.cellml
<?xml version="1.0"?>
<!--
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/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="" cmeta:id="mears_1997" name="mears_1997">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Evidence That Calcium Release-activated Current Mediates the Biphasic Electrical Activity of Mouse Pancreatic </title>
<author>
<firstname>Tessa</firstname>
<surname>Paris</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<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 </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 <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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<title>Diagram</title>
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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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<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5</cn>
</apply>
<apply>
<power/>
<ci>kdkca</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CRAC_current">
<variable cmeta:id="CRAC_current_i_CRAC" name="i_CRAC" public_interface="out" units="picoA"/>
<variable initial_value="75" name="g_CRAC" units="picoS"/>
<variable initial_value="0" name="V_CRAC" public_interface="out" units="millivolt"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="Ca_er" private_interface="out" public_interface="in" units="micromolar"/>
<variable name="r_infinity" private_interface="in" units="dimensionless"/>
<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 name="CRAC_r_gate">
<variable name="r_infinity" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="Ca_er" public_interface="in" units="micromolar"/>
<variable initial_value="40" name="Ca_er_bar" units="micromolar"/>
<variable initial_value="3" name="sloper" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_infinity</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 name="leak_current">
<variable name="i_leak" public_interface="out" units="picoA"/>
<variable initial_value="0" name="g_leak" units="picoS"/>
<variable name="V_CRAC" public_interface="in" units="millivolt"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<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 name="ER_parameters">
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable cmeta:id="ER_parameters_J_er_p" name="J_er_p" public_interface="out" units="micromolar_per_millisecond"/>
<variable initial_value="0" name="IP3" units="micromolar"/>
<variable initial_value="0.09" name="kerp" units="micromolar"/>
<variable initial_value="0.24" name="verp" units="micromolar_per_millisecond"/>
<variable initial_value="0.35" name="dact" units="micromolar"/>
<variable initial_value="0.4" name="dinh" units="micromolar"/>
<variable initial_value="0.2" name="dip3" units="micromolar"/>
<variable name="a_infinity" units="dimensionless"/>
<variable name="b_infinity" units="dimensionless"/>
<variable name="h_infinity" units="dimensionless"/>
<variable name="O" public_interface="out" units="per_millisecond"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>kerp</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a_infinity</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>b_infinity</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>h_infinity</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">1</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_equations">
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable initial_value="60" name="Ca_er" public_interface="out" units="micromolar"/>
<variable initial_value="0.11" name="Ca_i" private_interface="out" public_interface="out" units="micromolar"/>
<variable name="J_er_tot" public_interface="out" units="micromolar_per_millisecond"/>
<variable name="J_er_p" private_interface="in" units="micromolar_per_millisecond"/>
<variable name="J_er_IP3" units="micromolar_per_millisecond"/>
<variable name="J_er_leak" units="micromolar_per_millisecond"/>
<variable name="J_mem_tot" public_interface="in" units="micromolar_per_millisecond"/>
<variable name="O" private_interface="in" units="per_millisecond"/>
<variable initial_value="0.003" name="perl" units="per_millisecond"/>
<variable initial_value="250" name="lambda_er" units="dimensionless"/>
<variable initial_value="1" name="sigma_er" units="dimensionless"/>
<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 name="Ca_membrane_flux">
<variable name="time" public_interface="in" units="millisecond"/>
<variable initial_value="0.35" name="kmp" units="micromolar"/>
<variable initial_value="0.08" name="vmp" units="micromolar"/>
<variable initial_value="0.000003607" name="gamma" units="micromolar_per_picoA"/>
<variable name="i_Ca" public_interface="in" units="picoA"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable name="J_mem_tot" public_interface="out" units="micromolar_per_millisecond"/>
<variable name="Jmp" units="micromolar"/>
<variable initial_value="0.01" name="f" units="per_millisecond"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>kmp</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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>
<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>
<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>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K_ATP_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="fast_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="slow_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="CRAC_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_equations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_membrane_flux" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="leak_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<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>
<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>
<map_components component_1="fast_Ca_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="slow_Ca_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<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>
<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>
<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>
<map_components component_1="K_current" component_2="K_ATP_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection>
<map_components component_1="K_current" component_2="K_Ca_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection>
<map_components component_1="fast_Ca_current" component_2="slow_Ca_current"/>
<map_variables variable_1="V_Ca" variable_2="V_Ca"/>
</connection>
<connection>
<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>
<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>
<map_components component_1="Ca_current_total" component_2="membrane"/>
<map_variables variable_1="i_Ca" variable_2="i_Ca"/>
</connection>
<connection>
<map_components component_1="Ca_current_total" component_2="Ca_membrane_flux"/>
<map_variables variable_1="i_Ca" variable_2="i_Ca"/>
</connection>
<connection>
<map_components component_1="CRAC_current" component_2="Ca_equations"/>
<map_variables variable_1="Ca_er" variable_2="Ca_er"/>
</connection>
<connection>
<map_components component_1="K_Ca_current" component_2="Ca_equations"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="CRAC_current" component_2="leak_current"/>
<map_variables variable_1="V_CRAC" variable_2="V_CRAC"/>
</connection>
<connection>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
