Location: Butera, Rinzel, Smith, 1999 @ 7b0917439094 / butera_rinzel_smith_1999.cellml

Author:

pmr2.import <nobody@models.cellml.org>

Date:

2008-05-30 02:31:33+12:00

Desc:

committing version03 of butera_rinzel_smith_1999

Permanent Source URI:

https://staging.physiomeproject.org/workspace/butera_rinzel_smith_1999/rawfile/7b0917439094ab0a517f5a56fe6162c5a9227e28/butera_rinzel_smith_1999.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  butera_model_1999.xml

CREATED :  9th May 2002

LAST MODIFIED : 20th April 2005

AUTHOR :  Catherine Lloyd
          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 Butera et al's first 1999 mathematical model of respiratory rhythm generation in the pre-Botzinger complex in bursting pacemaker neurons.

CHANGES:  
  18/07/2002 - CML - Added more metadata.
  09/04/2003 - AAC - Added publication date information.
  20/04/2005 - PJV - Made MathML id's unique  
--><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#" name="butera_rinzel_smith_1999_version01" cmeta:id="butera_rinzel_smith_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Models Of Respiratory Rhythm Generation In The Pre-Botzinger Complex. I. Bursting Pacemaker Neurons</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 is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Inhalation and exhalation movements associated with respiration in mammals are generated by networks of neurons in the lower brain stem that produce a rhythmic pattern of electrical activity.  The principal neuronal kernel for rhythm generation has been located in the pre-Botzinger complex, a subregion of the ventro-lateral medulla.  In order to understand respiratory rhythm generation, it is necessary to consider mechanisms incorporating intrinsic cellular pacemaker properties.  These mechanisms are captured by a hybrid pacemaker model (Smith 1997; Smith <emphasis>et al</emphasis>. 1995), in which a rhythm arises from the dynamic interactions of both intrinsic and synaptic properties within a bilaterally distributed population of coupled bursting pacemaker neurons.  ("Bursting" refers to a complicated pattern of electrical activity.  Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation).
</para>

<para>  
In their 1999 paper, Robert J. Butera, J<subscript>R</subscript>., John Rinzel and Jeffrey C. Smith present two computational versions of this hybrid pacemaker-network model (see <xref linkend="fig_cell_diagram1"/> and <xref linkend="fig_cell_diagram2"/> below).  In the first model, bursting arises via fast activation and slow inactivation of a persistent Na<superscript>+</superscript> current, I<subscript>NaP</subscript>.  In the second model, bursting arises via a fast-activating persistent Na<superscript>+</superscript> current, I<subscript>NaP</subscript>,(the inactivation term "h" has been removed) and slow activation of a K<superscript>+</superscript> current, I<subscript>KS</subscript>.  In both models, action potentials are generated via fast Na<superscript>+</superscript> and K<superscript>+</superscript> currents.  Both models are consistent with experimental data, and the authors suggest several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.
</para>

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

<para>
<ulink url="http://jn.physiology.org/cgi/content/abstract/82/1/382">Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. I. Bursting Pacemaker Neurons</ulink>, Robert J. Butera, Jr., John Rinzel and Jeffrey C. Smith, 1999, <ulink url="http://jn.physiology.org/">
            <emphasis>Journal of Neurophysiology</emphasis>
          </ulink>, 81, 382-397.  (<ulink url="http://jn.physiology.org/cgi/content/full/82/1/382">Full text</ulink> and <ulink url="http://jn.physiology.org/cgi/reprint/82/1/382.pdf">PDF</ulink> versions of the article are available for Journal Members on the JN website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10400966&amp;dopt=Abstract">PubMed ID: 10400966</ulink> 
</para>

<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>
</para>

<informalfigure float="0" id="fig_cell_diagram1">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the first model</title>
    </objectinfo>
    <imagedata fileref="butera_1999a.png"/>
  </imageobject>
</mediaobject>
<caption>The first mathematical model is based on a single-compartment Hodgkin-Huxley type formalism.  It is composed of five ionic currents across the plasma membrane: a fast sodium current, I<subscript>Na</subscript>; a delayed rectifier potassium current, I<subscript>K</subscript>; a persistent sodium current,  I<subscript>NaP</subscript>; a passive leakage current, I<subscript>L</subscript>; and a tonic current, I<subscript>tonic_e</subscript> (although this last current is considered to be inactive in these models).</caption>
</informalfigure>

<informalfigure float="0" id="fig_cell_diagram2">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the first model</title>
    </objectinfo>
    <imagedata fileref="butera_1999b.png"/>
  </imageobject>
</mediaobject>
<caption>The second model appears identical to the first except with the addition of a slow K<superscript>+</superscript> current, I<subscript>KS</subscript>.  (The removal of the inactivation term "h" from I<subscript>NaP</subscript> is not visible in the model diagram.)</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->
  
  <units name="millisecond">
    <unit units="second" prefix="milli"/>
  </units>
  
  <units name="millivolt">
    <unit units="volt" prefix="milli"/>
  </units>
  
  <units name="picoA">
    <unit units="ampere" prefix="nano"/>
  </units>
  
  <units name="nanoS">
    <unit units="siemens" prefix="nano"/>
  </units>
  
  <units name="picoF">
    <unit units="farad" prefix="pico"/>
  </units>
  
  <!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  -->
  <component name="environment">
    <variable units="millisecond" public_interface="out" name="time"/>
  </component>
  
  <component name="membrane">
    <variable units="millivolt" public_interface="out" name="V"/>
    
    <variable units="picoF" name="C" initial_value="21.0"/>
    <variable units="picoA" name="i_app" initial_value="0.0"/>
    
    <variable units="millisecond" public_interface="in" name="time"/>
    <variable units="picoA" public_interface="in" name="i_NaP"/>
    <variable units="picoA" public_interface="in" name="i_Na"/>
    <variable units="picoA" public_interface="in" name="i_K"/>
    <variable units="picoA" public_interface="in" name="i_L"/>
    <variable units="picoA" public_interface="in" name="i_tonic_e"/>
     
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="membrane_voltage_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> V </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <minus/>
              <apply>
                <plus/>
                <ci> i_NaP </ci>
                <ci> i_Na </ci>
                <ci> i_K </ci>
                <ci> i_L </ci>
                <ci> i_tonic_e </ci>
              </apply>
            </apply>
            <ci> i_app </ci>
          </apply>
          <ci> C </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="fast_sodium_current">
    <variable units="picoA" public_interface="out" name="i_Na"/>
    <variable units="millivolt" public_interface="out" name="E_Na" initial_value="50.0"/>
    
    <variable units="nanoS" name="g_Na" initial_value="28.0"/>   
   
    <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="m_infinity"/>
    <variable units="dimensionless" private_interface="in" name="n"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Na_calculation">
        <eq/>
        <ci> i_Na </ci>
        <apply>
          <times/>
          <ci> g_Na </ci>
          <apply>
            <power/>
            <ci> m_infinity </ci>
            <cn cellml:units="dimensionless"> 3.0 </cn>
          </apply>
          <apply>
            <minus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <ci> n </ci>
          </apply>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> E_Na </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="fast_sodium_current_m_gate">
    <variable units="dimensionless" public_interface="out" name="m_infinity"/>
    
    <variable units="millivolt" name="theta_m" initial_value="-34.0"/>
    <variable units="millivolt" name="omega_m" initial_value="-5.0"/>
     
    <variable units="millivolt" public_interface="in" name="V"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="fast_sodium_current_m_gate_m_infinity_calculation">
        <eq/>
        <ci> m_infinity </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> V </ci>
                  <ci> theta_m </ci>
                </apply>
                <ci> omega_m </ci>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="fast_sodium_current_n_gate">
    <variable units="dimensionless" public_interface="out" name="n"/>
    
    <variable units="dimensionless" name="n_infinity"/>
    <variable units="millisecond" name="tau_n"/>
    <variable units="millisecond" name="tau_n_max" initial_value="10.0"/>
    <variable units="millivolt" name="theta_n" initial_value="-29.0"/>
    <variable units="millivolt" name="omega_n" initial_value="-4.0"/>
     
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millisecond" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="fast_sodium_current_n_gate_n_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> n </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> n_infinity </ci>
            <ci> n </ci>
          </apply>
          <ci> tau_n </ci>
        </apply>
      </apply>
      
      <apply id="fast_sodium_current_n_gate_n_infinity_calculation">
        <eq/>
        <ci> n_infinity </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> V </ci>
                  <ci> theta_n </ci>
                </apply>
                <ci> omega_n </ci>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
      
      <apply id="fast_sodium_current_n_gate_tau_n_calculation">
        <eq/>
        <ci> tau_n </ci>
        <apply>
          <divide/>
          <ci> tau_n_max </ci>
          <apply>
            <cosh/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <ci> V </ci>
                <ci> theta_n </ci>
              </apply>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.0 </cn>
                <ci> omega_n </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="potassium_current">
    <variable units="picoA" public_interface="out" name="i_K"/>
    
    <variable units="nanoS" name="g_K" initial_value="11.2"/>   
    <variable units="millivolt" name="E_K" initial_value="-85.0"/>
    
    <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="n"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K_calculation">
        <eq/>
        <ci> i_K </ci>
        <apply>
          <times/>
          <ci> g_K </ci>
          <apply>
            <power/>
            <ci> n </ci>
            <cn cellml:units="dimensionless"> 4.0 </cn>
          </apply>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> E_K </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="potassium_current_n_gate">
    <variable units="dimensionless" public_interface="out" name="n"/>
    
    <variable units="dimensionless" name="n_infinity"/>
    <variable units="millisecond" name="tau_n"/>
    <variable units="millisecond" name="tau_n_max" initial_value="10.0"/>
    <variable units="millivolt" name="theta_n" initial_value="-29.0"/>
    <variable units="millivolt" name="omega_n" initial_value="-4.0"/>
     
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millisecond" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="potassium_current_n_gate_n_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> n </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> n_infinity </ci>
            <ci> n </ci>
          </apply>
          <ci> tau_n </ci>
        </apply>
      </apply>
      
      <apply id="potassium_current_n_gate_n_infinity_calculation">
        <eq/>
        <ci> n_infinity </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> V </ci>
                  <ci> theta_n </ci>
                </apply>
                <ci> omega_n </ci>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
      
      <apply id="potassium_current_n_gate_tau_n_calculation">
        <eq/>
        <ci> tau_n </ci>
        <apply>
          <divide/>
          <ci> tau_n_max </ci>
          <apply>
            <cosh/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <ci> V </ci>
                <ci> theta_n </ci>
              </apply>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.0 </cn>
                <ci> omega_n </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="persistent_sodium_current">
    <variable units="picoA" public_interface="out" name="i_NaP"/>
    
    <variable units="nanoS" name="g_NaP" initial_value="2.8"/>   
   
    <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    <variable units="millivolt" public_interface="in" name="E_Na"/>         
    
    <variable units="dimensionless" private_interface="in" name="m_infinity"/>
    <variable units="dimensionless" private_interface="in" name="h"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_NaP_calculation">
        <eq/>
        <ci> i_NaP </ci>
        <apply>
          <times/>
          <ci> g_NaP </ci>
          <ci> m_infinity </ci>
          <ci> h </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> E_Na </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="persistent_sodium_current_m_gate">
    <variable units="dimensionless" public_interface="out" name="m_infinity"/>
    
    <variable units="millivolt" name="theta_m" initial_value="-40.0"/>
    <variable units="millivolt" name="omega_m" initial_value="-6.0"/>
     
    <variable units="millivolt" public_interface="in" name="V"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="persistent_sodium_current_m_gate_m_infinity_calculation">
        <eq/>
        <ci> m_infinity </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
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            <apply>
              <exp/>
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                  <minus/>
                  <ci> V </ci>
                  <ci> theta_m </ci>
                </apply>
                <ci> omega_m </ci>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="persistent_sodium_current_h_gate">
    <variable units="dimensionless" public_interface="out" name="h"/>
    
    <variable units="dimensionless" name="h_infinity"/>
    <variable units="millisecond" name="tau_h"/>
    <variable units="millisecond" name="tau_h_max" initial_value="10000.0"/>
    <variable units="millivolt" name="theta_h" initial_value="-48.0"/>
    <variable units="millivolt" name="omega_h" initial_value="6.0"/>
     
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millisecond" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="h_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> h </ci>
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        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> h_infinity </ci>
            <ci> h </ci>
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          <ci> tau_h </ci>
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      <apply id="h_infinity_calculation">
        <eq/>
        <ci> h_infinity </ci>
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                  <ci> V </ci>
                  <ci> theta_h </ci>
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                <ci> omega_h </ci>
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            </apply>    
          </apply>
        </apply>
      </apply>
      
      <apply id="tau_h_calculation">
        <eq/>
        <ci> tau_h </ci>
        <apply>
          <divide/>
          <ci> tau_h_max </ci>
          <apply>
            <cosh/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <ci> V </ci>
                <ci> theta_h </ci>
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              <apply>
                <times/>
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                <ci> omega_h </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="leakage_current">
    <variable units="picoA" public_interface="out" name="i_L"/>
     
    <variable units="nanoS" name="g_L" initial_value="2.8"/>
    <variable units="millivolt" name="E_L" initial_value="-65.0"/> 
    
    <variable units="millisecond" public_interface="in" name="time"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_L_calculation">
        <eq/>
        <ci> i_L </ci>
        <apply>
          <times/>
          <ci> g_L </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> E_L </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="tonic_current">
    <variable units="picoA" public_interface="out" name="i_tonic_e"/>
     
    <variable units="nanoS" name="g_tonic_e" initial_value="0.0"/>
    <variable units="millivolt" name="E_syn_e" initial_value="0.0"/> 
    
    <variable units="millisecond" public_interface="in" name="time"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathMtonic_e">
      <apply id="i_tonic_e_calculation">
        <eq/>
        <ci> i_tonic_e </ci>
        <apply>
          <times/>
          <ci> g_tonic_e </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> E_syn_e </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <group>
    <relationship_ref relationship="containment"/>
    <component_ref component="membrane">
      <component_ref component="fast_sodium_current">
        <component_ref component="fast_sodium_current_m_gate"/>
        <component_ref component="fast_sodium_current_n_gate"/>
      </component_ref>
      <component_ref component="potassium_current">
        <component_ref component="potassium_current_n_gate"/>
      </component_ref>
      <component_ref component="persistent_sodium_current">
        <component_ref component="persistent_sodium_current_m_gate"/>
        <component_ref component="persistent_sodium_current_h_gate"/>
      </component_ref>
      <component_ref component="leakage_current"/>
      <component_ref component="tonic_current"/>  
    </component_ref>
  </group>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="fast_sodium_current">
      <component_ref component="fast_sodium_current_m_gate"/>
      <component_ref component="fast_sodium_current_n_gate"/>
    </component_ref>
    <component_ref component="potassium_current">
      <component_ref component="potassium_current_n_gate"/>
    </component_ref>
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