Location: Bertram, Smolen, Sherman, Mears, Atwater, Martin, Soria, 1995 @ 738df7b0ab39 / bertram_smolen_sherman_mears_atwater_martin_soria_1995.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2010-05-27 23:33:07+12:00
Desc:
Fixed my typo in the model name.
Permanent Source URI:
https://models.cellml.org/workspace/bertram_smolen_sherman_mears_atwater_martin_soria_1995/rawfile/738df7b0ab3936ee135c90cf97c54c30c08ce44d/bertram_smolen_sherman_mears_atwater_martin_soria_1995.cellml

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				<title>A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells</title>
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					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
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						<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
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				<para> This model runs in both COR and PCEnv to reproduce the figures shown in the original paper.  The units have been checked and they are consistent.</para>
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				<para>ABSTRACT: S. Bordin and colleagues have proposed that the depolarizing effects of acetylcholine and other muscarinic agonists on pancreatic beta-cells are mediated by a calcium release-activated current (CRAC). We support this hypothesis with additional data, and present a theoretical model which accounts for most known data on muscarinic effects. Additional phenomena, such as the biphasic responses of beta-cells to changes in glucose concentration and the depolarizing effects of the sarco-endoplasmic reticulum calcium ATPase pump poison thapsigargin, are also accounted for by our model. The ability of this single hypothesis, that CRAC is present in beta-cells, to explain so many phenomena motivates a more complete characterization of this current.
                        </para>
				<para>The complete paper reference is cited below:</para>
				<para>A Role for Calcium Release-Activated Current (CRAC) in Cholinergic Modulation of Electrical Activity in Pancreatic Beta-Cells, Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani Atwater, Franz Martin and Bernat Soria, 1995,
                                    <emphasis>Biophysical Journal</emphasis>, 68, 2323-2332. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/7647236">PubMed ID: 7647236</ulink>
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			<publisher xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">The University of Auckland, Auckland Bioengineering Institute</publisher>
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			<Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other>
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			<W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">1995-06</W3CDTF>
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			<Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname>
			<Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit>
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			<rdf:value xml:lang="en">This is the CellML description of Bertram et al's 1995 model for a modulatory role for CRAC in islet electrical activity.</rdf:value>
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			<Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other>
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	</rdf:RDF>   <units name="millisecond">
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      <variable name="time" public_interface="in" units="millisecond"/>
      <variable name="V" 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="Ca_er" public_interface="in" units="micromolar"/>
      <variable initial_value="3" name="Ca_er_bar" 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>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_micromolar">1</cn>
                        <apply>
                           <minus/>
                           <ci>Ca_er</ci>
                           <ci>Ca_er_bar</ci>
                        </apply>
                     </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="0.1" name="kerp" units="micromolar"/>
      <variable initial_value="0.24" name="verp" units="micromolar_per_millisecond"/>
      <variable initial_value="0.1" 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="9" 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="0.02" name="perl" units="per_millisecond"/>
      <variable initial_value="250" name="lambda_er" units="dimensionless"/>
      <variable initial_value="5" 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="0.07" name="k_Ca" units="per_millisecond"/>
      <variable initial_value="0.000003607" name="gamma" units="micromolar_per_millisecond_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 initial_value="0.01" name="f" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <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>
                  <apply>
                     <times/>
                     <ci>k_Ca</ci>
                     <ci>Ca_i</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <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="m_f_infinity" variable_2="m_f_infinity"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="slow_Ca_current" component_2="slow_Ca_channel_m_gate"/>
      <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="Ca_er" variable_2="Ca_er"/>
   </connection>
</model>