Location: Sneyd, Tsanevaatanasova, Bruce, Straub, Giovannucci, Yule, 2003 @ 65194c7798de / sneyd_tsanevaatanasova_bruce_straub_giovannucci_yule_2003.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2009-12-14 16:22:53+13:00
Desc:
Added images in ai and svg format
Permanent Source URI:
https://models.cellml.org/workspace/sneyd_tsanevaatanasova_bruce_straub_giovannucci_yule_2003/rawfile/65194c7798dee4179e194739a2ea3e4176c8ce46/sneyd_tsanevaatanasova_bruce_straub_giovannucci_yule_2003.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  sneyd_model_2003.xml

CREATED :  20th October 2003

LAST MODIFIED : 20th October 2003

AUTHOR :  Catherine Lloyd
          The Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Sneyd et al.'s 2003 model of calcium waves in pancreatic and parotid acinar cells. 

CHANGES:  
    
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="sneyd_tsaneva-atanasova_bruce_straub_giovannucci_yule_2003_version01" name="sneyd_tsaneva-atanasova_bruce_straub_giovannucci_yule_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This model contains partial differentials and as such can not currently be solved by existing CellML tools.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Exocrine cells display morphological and functional polarity, which allows distinct physiological processes to occur in specific regions of the cell.  Many of these processes are triggered by an increase in the concentration of cytosolic calcium ([Ca<superscript>2+</superscript>]<subscript>i</subscript>).  Calcium waves can spread across the whole cell, or remain isolated in the apical region, and calcium oscillations can take on several different shapes.  Underlying the wide variety of observed responses, acinar cells possess a wide variety of calcium handling mechanisms, including inositol trisphosphate receptors (IPR), ryanodine receptors (RyR), and mitochondria.  In addition, these mechanisms have well defined spatial distributions which correlate with the spatial characteristics of the observed calcium waves and oscillations.
</para>

<para>
Although there is a vast amount of experimental data, the exact mechanisms underlying Ca<superscript>2+</superscript> wave propagation in an acinar cell remain unknown.  In their 2003 paper described here, Sneyd <emphasis>et al.</emphasis> develop a mathematical model of Ca<superscript>2+</superscript> wave propagation in pancreatic and parotid acinar cells.  Their aim is to better understand the variety of Ca<superscript>2+</superscript> waves and their underlying mechanisms.
</para>

<para>
Due to the complexity of acinar cells, their model is broken down into five detailed sub-models:
</para>
<itemizedlist>
  <listitem>
            <para>The IPR model which is based on <ulink url="${HTML_EXMPL_SNEYD_MODEL}">Sneyd and Dufour, A Dynamic Model of the Type-2 Inositol Triphosphate Receptor, 2002</ulink> (see <xref linkend="fig_diagram1"/> below);</para>
          </listitem>
  <listitem>
            <para>The RyR model which is based on <ulink url="${HTML_EXMPL_KEIZER_MODEL}">Keizer and Levine, RyR Adaptation and Ca<superscript>2+</superscript> Oscillations, 1996</ulink> (see <xref linkend="fig_diagram2"/> below);</para>
          </listitem>
  <listitem>
            <para>The two models combined in a whole-cell model (see <xref linkend="fig_diagram3"/> below);</para>
          </listitem>
  <listitem>
            <para>The spatial model;</para>
          </listitem> and 
  <listitem>
            <para>Mitochondrial transport which is based on <ulink url="${HTML_EXMPL_COLEGROVE_MODEL}">Colegrove <emphasis>et al.</emphasis>, Quantitative Analysis of Mitochondrial Ca<superscript>2+</superscript> Uptake and Release Pathways in Sympathetic Neurons, 2000</ulink>.</para>
          </listitem>
</itemizedlist>

<para>
The principal prediction from the model is that there are two different ways in which calcium waves propagate in acinar cells: at low agonist concentration the wave is propagated by the diffusion of Ca<superscript>2+</superscript> between release sites;  at higher agonist concentrations the basal region of the cell responds later than the apical region, creating a wave which is independent of Ca<superscript>2+</superscript> diffusion.
</para>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/85/3/1392">A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells</ulink>, J. Sneyd, K. Tsaneva-Atanasova, J. I. E. Bruce, S. V. Straub, D. R. Giovannucci, and D. I. Yule, 2003, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophysical Journal</emphasis>
          </ulink>, 85, 1392-1405.  (<ulink url="http://www.biophysj.org/cgi/content/full/85/3/1392">Full text (HTML)</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/85/3/1392.pdf">PDF</ulink> versions of the article are available on the <emphasis>Biophysical Journal</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=12944257&amp;dopt=Abstract">PubMed ID: 12944257</ulink>
</para>

<informalfigure float="0" id="fig_diagram1">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>A diagram of the IPR model</title>
    </objectinfo>
    <imagedata fileref="sneyd_2003a.png"/>
  </imageobject>
</mediaobject>
<caption>A simplified diagram of the IPR model, where R represents the free receptor, O is the open state of the channel, A is the activated state of the channel and I<subscript>1</subscript>, I<subscript>2</subscript>, and S are three inactive states.</caption>
</informalfigure>

<informalfigure float="0" id="fig_diagram2">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>A diagram of the RyR model</title>
    </objectinfo>
    <imagedata fileref="sneyd_2003b.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of transitions among the four states of the RyR used to describe adaptation.  States C1 and C2 are closed states and O1 and O2 represent open states, assumed to have the same single-channel conductance.  The <emphasis>k</emphasis> are rate constants: only steps <emphasis>a</emphasis> and <emphasis>b</emphasis> are Ca<superscript>2+</superscript> dependent.</caption>
</informalfigure>

<informalfigure float="0" id="fig_diagram3">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>A diagram of the whole cell model</title>
    </objectinfo>
    <imagedata fileref="sneyd_2003c.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic of the model indicating Ca<superscript>2+</superscript> compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca<superscript>2+</superscript> ion movement between the compartments.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  
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              <apply>
                <times/>
                <ci> k_4 </ci>
                <ci> L_5 </ci>
              </apply>
              <ci> l_6 </ci>
            </apply>
            <ci> c </ci>
          </apply>
          <apply>
            <plus/>
            <ci> c </ci>
            <ci> L_5 </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="phi_4__calculation">
        <eq/>
        <ci> phi_4_ </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <apply>
              <plus/>
              <apply>
                <times/>
                <ci> k_1 </ci>
                <ci> L_1 </ci>
              </apply>
              <ci> l_2 </ci>
            </apply>
            <ci> c </ci>
          </apply>
          <apply>
            <plus/>
            <ci> c </ci>
            <ci> L_1 </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="phi_5_calculation">
        <eq/>
        <ci> phi_5 </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> L_1 </ci>
            <apply>
              <plus/>
              <ci> k_4_ </ci>
              <ci> l_6_ </ci>
            </apply>
            <ci> c </ci>
          </apply>
          <apply>
            <plus/>
            <ci> c </ci>
            <ci> L_1 </ci>
          </apply>
        </apply>
      </apply>
    </math>     
  </component>
  
  <component cmeta:id="P_RyR" name="P_RyR">
     
    <variable units="dimensionless" public_interface="out" name="P_RyR"/>    
    
    <variable units="micromolar" name="w"/>
    <variable units="dimensionless" name="w_infinity_c"/>
    <variable units="micromolar_4" name="Ka"/>
    <variable units="micromolar_3" name="Kb"/>
    <variable units="dimensionless" name="Kc"/> 
    <variable units="micromolar5_per_second" name="ka_plus" initial_value="1500.0"/>
    <variable units="micromolar4_per_second" name="kb_plus" initial_value="1500.0"/>
    <variable units="first_order_rate_constant" name="ka_minus" initial_value="28.8"/>
    <variable units="first_order_rate_constant" name="kb_minus" initial_value="385.9"/>
    <variable units="first_order_rate_constant" name="kc_plus" initial_value="1.75"/>
    <variable units="first_order_rate_constant" name="kc_minus" initial_value="0.1"/>
    
    <variable units="micromolar" public_interface="in" name="c"/>
    <variable units="second" public_interface="in" name="time"/> 
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="P_RyR_calculation">
        <eq/>
        <ci> P_RyR </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> w </ci>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> c </ci>
                  <ci> Kb </ci>
                </apply>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn> 
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> Ka </ci>
                <ci> c </ci>
              </apply>
              <cn cellml:units="dimensionless"> 4.0 </cn>
            </apply>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> c </ci>
                <ci> Kb </ci>
              </apply>
              <cn cellml:units="dimensionless"> 3.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply> 
      
      <apply id="w_infinity_c_calculation">
        <eq/>
        <ci> w_infinity_c </ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> Ka </ci>
                <ci> c </ci>
              </apply>
              <cn cellml:units="dimensionless"> 4.0 </cn>
            </apply>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> c </ci>
                <ci> Kb </ci>
              </apply>
              <cn cellml:units="dimensionless"> 3.0 </cn>
            </apply>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <divide/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <ci> Kc </ci>
            </apply> 
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> Ka </ci>
                <ci> c </ci>
              </apply>
              <cn cellml:units="dimensionless"> 4.0 </cn>
            </apply>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> c </ci>
                <ci> Kb </ci>
              </apply>
              <cn cellml:units="dimensionless"> 3.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
       
      <apply id="Ka_calculation">
        <eq/>
        <ci> Ka </ci>
        <apply>
          <divide/>
          <ci> ka_minus </ci>
          <ci> ka_plus </ci> 
        </apply>
      </apply>
      
      <apply id="Kb_calculation">
        <eq/>
        <ci> Kb </ci>
        <apply>
          <divide/>
          <ci> kb_minus </ci>
          <ci> kb_plus </ci> 
        </apply>
      </apply> 
      
      <apply id="Kc_calculation">
        <eq/>
        <ci> Kc </ci>
        <apply>
          <divide/>
          <ci> kc_minus </ci>
          <ci> kc_plus </ci> 
        </apply>
      </apply> 
      
      <apply id="w_diff_eq">
        <eq/>
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> w </ci> 
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> kc_minus </ci>
            <apply>
              <minus/>
              <ci> w_infinity_c </ci>
              <ci> w </ci>
            </apply>
          </apply>
          <ci> w_infinity_c </ci>
        </apply>
      </apply>
    </math> 
  </component>
  
  <component name="calcium">
    <variable units="micromolar" public_interface="out" name="c"/>
    <variable units="micromolar" public_interface="out" name="c_e"/>
    
    <variable units="dimensionless" name="c_x2"/>
    <variable units="dimensionless" name="x"/>
    <variable units="micromolar2_per_second" name="Dc" initial_value="20.0"/>
    <variable units="first_order_rate_constant" name="k_f" initial_value="0.71"/>
    <variable units="first_order_rate_constant" name="v_1" initial_value="0.098"/>
    <variable units="dimensionless" name="gamma" initial_value="5.405"/>
    <variable units="dimensionless" name="delta" initial_value="0.1"/>
    <variable units="first_order_rate_constant" name="J_er" initial_value="0.002"/>
    
    <variable units="dimensionless" public_interface="in" name="P_IPR"/>
    <variable units="dimensionless" public_interface="in" name="P_RyR"/>
    <variable units="flux" public_interface="in" name="J_pm"/>
    <variable units="flux" public_interface="in" name="J_in"/>
    <variable units="flux" public_interface="in" name="J_serca"/>
    <variable units="flux" public_interface="in" name="J_mito"/>
    <variable units="micromolar" public_interface="in" name="p"/>
    <variable units="second" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="c_partialdiff_eq">
        <eq/>
        <apply>
          <partialdiff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> c </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> Dc </ci>
              <ci> c_x2 </ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> k_f </ci>
                  <ci> P_IPR </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> v_1 </ci>
                  <ci> P_RyR </ci>
                </apply>
                <ci> J_er </ci>
              </apply>
              <apply>
                <minus/>
                <ci> c_e </ci>
                <ci> c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> delta </ci>
              <apply>
                <minus/>
                <apply>
                  <times/>
                  <ci> J_in </ci>
                  <ci> p </ci>
                </apply>
                <ci> J_pm </ci>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <ci> J_serca </ci>
            <ci> J_mito </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="c_x2_partialdiff_eq">
        <eq/>
        <apply>
          <partialdiff/>
          <bvar>
            <ci> x </ci>
            <degree>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </degree>
          </bvar>
          <degree>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </degree>
          <ci> c </ci>
        </apply>
        <ci> c_x2 </ci>
      </apply>
      
      <apply id="c_e_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> c_e </ci>
        </apply>
        <apply>
          <times/>
          <ci> gamma </ci>
          <apply>
            <minus/>
            <ci> J_serca </ci>
            <apply>
              <times/>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> k_f </ci>
                  <ci> P_IPR </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> v_1 </ci>
                  <ci> P_RyR </ci>
                </apply>
                <ci> J_er </ci>
              </apply>
              <apply>
                <minus/>
                <ci> c_e </ci>
                <ci> c </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="plasma_membrane_calcium_pump">
    <variable units="flux" public_interface="out" name="J_pm"/>
  
    <variable units="micromolar" name="K_pm" initial_value="0.425"/>
    <variable units="flux" name="V_pm" initial_value="28.0"/>
    
    <variable units="micromolar" public_interface="in" name="c"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_pm_calculation">
        <eq/>
        <ci> J_pm </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> V_pm </ci>
            <apply>
              <power/>
              <ci> c </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <power/>
              <ci> K_pm </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <power/>
              <ci> c </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="SERCA_pump">
    <variable units="flux" public_interface="out" name="J_serca"/>
  
    <variable units="micromolar" name="K_serca" initial_value="0.18"/>
    <variable units="micromolar2_per_second" name="V_serca" initial_value="120.0"/>
    
    <variable units="micromolar" public_interface="in" name="c"/>
    <variable units="micromolar" public_interface="in" name="c_e"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_serca_calculation">
        <eq/>
        <ci> J_serca </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> V_serca </ci>
              <ci> c </ci>
            </apply>
            <apply>
              <plus/>
              <ci> K_serca </ci>
              <ci> c </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <ci> c_e </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="mitochondrial_uptake">
    <variable units="flux" public_interface="out" name="J_mito"/>
  
    <variable units="flux" name="V_mito" initial_value="0.0"/>
    
    <variable units="micromolar" public_interface="in" name="c"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_mito_calculation">
        <eq/>
        <ci> J_mito </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> V_mito </ci>
            <ci> c </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <power/>
              <apply>
                <divide/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <ci> c </ci>
              </apply>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="influx_from_outside_the_cell">
    <variable units="flux" public_interface="out" name="J_in"/>
  
    <variable units="micromolar" public_interface="in" name="p"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_in_calculation">
        <eq/>
        <ci> J_in </ci>
        <apply>
          <plus/>
          <cn cellml:units="flux"> 0.2 </cn>
          <apply>
            <times/>
            <cn cellml:units="first_order_rate_constant"> 0.05 </cn>
            <ci> p </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="IP3_dynamics">
    <variable units="micromolar" public_interface="out" name="p"/>
  
    <variable units="micromolar" name="p0"/>
  
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="p_calculation">
        <eq/>
        <ci> p </ci>
        <apply>
          <times/>
          <ci> p0 </ci>
          <apply>
            <exp/>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> -0.8 </cn>
              <ci> time </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
    
  
  <connection>
    <map_components component_2="environment" component_1="R"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="O"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="S"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I_1"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I_2"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection> 
  
  <connection>
    <map_components component_2="environment" component_1="P_RyR"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="calcium"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="plasma_membrane_calcium_pump"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="SERCA_pump"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="mitochondrial_uptake"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="influx_from_outside_the_cell"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="IP3_dynamics"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="R"/>
    <map_variables variable_2="phi_1" variable_1="phi_1"/>
    <map_variables variable_2="phi_2" variable_1="phi_2"/>
    <map_variables variable_2="phi_2_" variable_1="phi_2_"/>
    <map_variables variable_2="k_1_" variable_1="k_1_"/>
    <map_variables variable_2="l_2_" variable_1="l_2_"/>
  </connection>  
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="O"/>
    <map_variables variable_2="phi_4" variable_1="phi_4"/>
    <map_variables variable_2="phi_4_" variable_1="phi_4_"/>
    <map_variables variable_2="phi_2" variable_1="phi_2"/>
    <map_variables variable_2="phi_2_" variable_1="phi_2_"/>
    <map_variables variable_2="phi_3" variable_1="phi_3"/>
    <map_variables variable_2="k_3_" variable_1="k_3_"/>
  </connection> 
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="A"/>
    <map_variables variable_2="phi_4" variable_1="phi_4"/>
    <map_variables variable_2="phi_5" variable_1="phi_5"/>
    <map_variables variable_2="phi_4_" variable_1="phi_4_"/>
    <map_variables variable_2="k_1_" variable_1="k_1_"/>
    <map_variables variable_2="l_2_" variable_1="l_2_"/>
  </connection> 
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="I_1"/>
    <map_variables variable_2="phi_1" variable_1="phi_1"/>
    <map_variables variable_2="k_1_" variable_1="k_1_"/>
    <map_variables variable_2="l_2_" variable_1="l_2_"/>
  </connection>
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="I_2"/>
    <map_variables variable_2="phi_5" variable_1="phi_5"/>
    <map_variables variable_2="k_1_" variable_1="k_1_"/>
    <map_variables variable_2="l_2_" variable_1="l_2_"/>
  </connection>
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="S"/>
    <map_variables variable_2="phi_3" variable_1="phi_3"/>
    <map_variables variable_2="k_3_" variable_1="k_3_"/>
  </connection>  
  
  <connection>
    <map_components component_2="O" component_1="R"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="O" variable_1="O"/>
  </connection> 
  
  <connection>
    <map_components component_2="I_1" component_1="R"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="I_1" variable_1="I_1"/>
  </connection> 
  
  <connection>
    <map_components component_2="A" component_1="O"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="O" variable_1="O"/>
  </connection>
  
  <connection>
    <map_components component_2="A" component_1="P_IPR"/>
    <map_variables variable_2="A" variable_1="A"/>
  </connection>
  
  <connection>
    <map_components component_2="O" component_1="P_IPR"/>
    <map_variables variable_2="O" variable_1="O"/>
  </connection>
  
  <connection>
    <map_components component_2="S" component_1="O"/>
    <map_variables variable_2="S" variable_1="S"/>
    <map_variables variable_2="O" variable_1="O"/>
  </connection> 
  
  <connection>
    <map_components component_2="I_2" component_1="A"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="I_2" variable_1="I_2"/>
  </connection> 
  
  <connection>
    <map_components component_2="R" component_1="IP3_dynamics"/>
    <map_variables variable_2="p" variable_1="p"/>
  </connection>
  
  <connection>
    <map_components component_2="O" component_1="IP3_dynamics"/>
    <map_variables variable_2="p" variable_1="p"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium" component_1="IP3_dynamics"/>
    <map_variables variable_2="p" variable_1="p"/>
  </connection>
  
  <connection>
    <map_components component_2="influx_from_outside_the_cell" component_1="IP3_dynamics"/>
    <map_variables variable_2="p" variable_1="p"/>
  </connection>
  
  <connection>
    <map_components component_2="plasma_membrane_calcium_pump" component_1="calcium"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="J_pm" variable_1="J_pm"/>
  </connection>
  
  <connection>
    <map_components component_2="influx_from_outside_the_cell" component_1="calcium"/>
    <map_variables variable_2="J_in" variable_1="J_in"/>
  </connection>
  
  <connection>
    <map_components component_2="SERCA_pump" component_1="calcium"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="c_e" variable_1="c_e"/>
    <map_variables variable_2="J_serca" variable_1="J_serca"/>
  </connection>
  
  <connection>
    <map_components component_2="mitochondrial_uptake" component_1="calcium"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="J_mito" variable_1="J_mito"/>
  </connection>
  
  <connection>
    <map_components component_2="P_RyR" component_1="calcium"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="P_RyR" variable_1="P_RyR"/>
  </connection>
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="calcium"/>
    <map_variables variable_2="c" variable_1="c"/>
  </connection>
  
  <connection>
    <map_components component_2="IPR_parameters" component_1="IP3_dynamics"/>
    <map_variables variable_2="p" variable_1="p"/>
  </connection>
  
  <connection>
    <map_components component_2="P_IPR" component_1="calcium"/>
    <map_variables variable_2="P_IPR" variable_1="P_IPR"/>
  </connection>


<rdf:RDF>
  <rdf:Bag rdf:about="rdf:#3047ae6b-8b7b-4045-9402-08af39a70fe9">
    <rdf:li>pancreatic acinar cell</rdf:li>
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            A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells
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