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This CellML file was generated on 17/12/2009 at 8:45:41 at a.m. using:
COR (0.9.31.1351)
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>A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells</title>
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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>
</para>
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<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="9" 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="0.02"/>
<variable name="lambda_er" units="dimensionless" initial_value="250"/>
<variable name="sigma_er" units="dimensionless" initial_value="5"/>
<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="k_Ca" units="per_millisecond" initial_value="0.07"/>
<variable name="gamma" units="micromolar_per_millisecond_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="f" units="dimensionless" initial_value="0.01"/>
<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 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="m_f_infinity" variable_2="m_f_infinity"/>
<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="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 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="Ca_er" variable_2="Ca_er"/>
</connection>
</model>
