Location: Smith, Abdala, Koizumi, Rybak and Paton 2007 @ 8018c7dc4da8 / smith_2007_post_I.cellml

Author:
Hanne Nielsen <hnie010@aucklanduni.ac.nz>
Date:
2011-03-29 14:01:34+13:00
Desc:
Addedi mages in ai svg and png format
Permanent Source URI:
https://models.fieldml.org/workspace/smith_abdala_koizumi_rybak_paton_2007/rawfile/8018c7dc4da8bf52ca790a5b9369c23614da6a97/smith_2007_post_I.cellml

<?xml version='1.0' encoding='utf-8'?>

<model
    name="smith_2007_post_I"
    cmeta:id="smith_2007_post_I"
    xmlns="http://www.cellml.org/cellml/1.1#"
    xmlns:cellml="http://www.cellml.org/cellml/1.1#"
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    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">

	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms</title>
				<author>
					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
					<affiliation>
						<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>
            This CellML model represents a postinspiratory (post-I) neuron.  It forms part of the brain stem respiratory network computational model described by Smith et al. 2007, and modified by Dr Carlo Laing.
          </para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
Abstract: Mammalian central pattern generators (CPGs) producing rhythmic movements exhibit extremely robust and flexible behavior. Network architectures that enable these features are not well understood. Here we studied organization of the brain stem respiratory CPG. By sequential rostral to caudal transections through the pontine-medullary respiratory network within an in situ perfused rat brain stem-spinal cord preparation, we showed that network dynamics reorganized and new rhythmogenic mechanisms emerged. The normal three-phase respiratory rhythm transformed to a two-phase and then to a one-phase rhythm as the network was reduced. Expression of the three-phase rhythm required the presence of the pons, generation of the two-phase rhythm depended on the integrity of Botzinger and pre-Botzinger complexes and interactions between them, and the one-phase rhythm was generated within the pre-Botzinger complex. Transformation from the three-phase to a two-phase pattern also occurred in intact preparations when chloride-mediated synaptic inhibition was reduced. In contrast to the three-phase and two-phase rhythms, the one-phase rhythm was abolished by blockade of persistent sodium current (I(NaP)). A model of the respiratory network was developed to reproduce and explain these observations. The model incorporated interacting populations of respiratory neurons within spatially organized brain stem compartments. Our simulations reproduced the respiratory patterns recorded from intact and sequentially reduced preparations. Our results suggest that the three-phase and two-phase rhythms involve inhibitory network interactions, whereas the one-phase rhythm depends on I(NaP). We conclude that the respiratory network has rhythmogenic capabilities at multiple levels of network organization, allowing expression of motor patterns specific for various physiological and pathophysiological respiratory behaviors.</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="smith_2007.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic of the computational model of the brain stem respiratory network. Model includes interacting neuronal populations within major brain stem respiratory compartments (Pons, BotC, pre-BotC, and rVRG). Spheres represent neuronal populations (excitatory, red; inhibitory, blue; motoneuronal, brown); green triangles represent sources of tonic excitatory drives (in pons, RTN/BotC, and pre-BotC compartments) to different neural populations. Excitatory and inhibitory synaptic connections are indicated by arrows and small circles, respectively. Simulated 
'transections' (dashed lines) mimic those performed in situ.</caption>
</informalfigure>

				<para>
The original paper reference is cited below:
</para>
				<para>
Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms, Smith JC, Abdala AP, Koizumi H, Rybak IA, Paton JF, 2007, <emphasis>Journal of Neurophysiology</emphasis>, 98, 3370-3387. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17913982">PubMed ID: 17913982.</ulink>
				</para>
			
			</sect1>
		</article>
	</documentation>   
	
	
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          In order to facilitate the import of this cell model by the synaptic coupling model the current model is encapsulated in a top component called "post_I".
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        <dc:creator rdf:parseType="Resource">
          <vCard:FN>Catherine Lloyd</vCard:FN>
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               <ci>m</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
					 <cn type="e-notation" cellml:units="dimensionless">1.25<sep/>8</cn>
                     <apply>
                        <power/>
						<ci>Ca</ci>
						<cn cellml:units="dimensionless">2</cn>
					 </apply>
				  </apply>
				  <apply>
                     <times/>
					 <apply>
                        <plus/>
						<apply>
                           <times/>
					       <cn type="e-notation" cellml:units="dimensionless">1.25<sep/>8</cn>
                           <apply>
                              <power/>
						      <ci>Ca</ci>
						      <cn cellml:units="dimensionless">2</cn>
					       </apply>
				        </apply>
						<cn cellml:units="millimolar2">2.5</cn>
					 </apply>
					 <ci>m</ci>
				  </apply>
			   </apply>
			   <apply>
                  <times/>
                  <cn cellml:units="millisecond_millimolar2">1000.0</cn>
                  <ci>kappa</ci>
               </apply>
			</apply>
         </apply>
      </math>
   </component>
   
   <component name="i_L">
      <variable units="nanoA" public_interface="out" name="i_L"/>
      
	  <variable units="nanoS" public_interface="in" name="g_L"/>
      <variable units="millivolt" public_interface="in" name="E_L"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_L</ci>
            <apply>
               <times/>
               <ci>g_L</ci>
               <apply>
                  <divide/>
                  <cn cellml:units="volt">1</cn>
                  <cn cellml:units="millivolt">1000</cn>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_L</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
  
   <component name="i_synE">
      <variable units="nanoA" public_interface="out" name="i_synE"/>
      
	  <variable units="nanoS" public_interface="in" name="g_synE"/>
      <variable units="millivolt" public_interface="in" name="E_synE"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_synE</ci>
            <apply>
               <times/>
               <ci>g_synE</ci>
               <apply>
                  <divide/>
                  <cn cellml:units="volt">1</cn>
                  <cn cellml:units="millivolt">1000</cn>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_synE</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component name="i_synI">
      <variable units="nanoA" public_interface="out" name="i_synI"/>
      
	  <variable units="nanoS" public_interface="in" name="g_synI"/>
      <variable units="millivolt" public_interface="in" name="E_synI"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_synI</ci>
            <apply>
               <times/>
               <ci>g_synI</ci>
               <apply>
                  <divide/>
                  <cn cellml:units="volt">1</cn>
                  <cn cellml:units="millivolt">1000</cn>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_synI</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component name="Ca">
      <variable units="millimolar" public_interface="out" name="Ca" initial_value="5e-5"/>
     
	  <variable units="millisecond" public_interface="in" name="time"/>
	  <variable units="nanoA" public_interface="in" name="i_Ca"/>
	  
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <times/>
			      <cn type="e-notation" cellml:units="millimolar_per_nanoA_millisecond">-2.072<sep/>-5</cn>
				  <apply>
                     <divide/>
                     <apply>
                        <plus/>
						<ci>Ca</ci>
						<cn cellml:units="millimolar">0.001</cn>
					 </apply>
					 <apply>
                        <plus/>
						<ci>Ca</ci>
						<cn cellml:units="millimolar">0.031</cn>
					 </apply>
				  </apply>
				  <ci>i_Ca</ci>
			   </apply>
			   <apply>
                  <divide/>
                  <apply>
                     <minus/>
					 <cn type="e-notation" cellml:units="millimolar">5<sep/>-5</cn>
					 <ci>Ca</ci>
				  </apply>
				  <cn cellml:units="millisecond">500.00</cn>
			   </apply>
			</apply>
         </apply>
      </math>
   </component>
   
   <component name="s_i">
      <variable units="dimensionless" public_interface="out" name="s_i" initial_value="1.00000"/>
     
	  <variable units="millisecond" name="tau_I" initial_value="15.0"/>
	 
	  <variable units="millisecond" public_interface="in" name="time"/>
	  
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s_i</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
			      <ci>s_i</ci>
			   </apply>
			   <ci>tau_I</ci>
			</apply>
         </apply>
      </math>
   </component>
   
   <component name="model_parameters">
      <variable units="nanoF" public_interface="out" name="C" initial_value="36000.0"/>
	  <variable units="millivolt" public_interface="out" name="E_Na" initial_value="55.0"/>
	  <variable units="millivolt" public_interface="out" name="E_K" initial_value="-94.0"/>
	  <variable units="millivolt" public_interface="out" name="E_L" initial_value="1.00000"/>
	  <variable units="millivolt" public_interface="out" name="E_Ca"/>
	  <variable units="millivolt" public_interface="out" name="E_synE" initial_value="-10.0"/>
	  <variable units="millivolt" public_interface="out" name="E_synI" initial_value="-75.0"/>
	  <variable units="nanoS" public_interface="out" name="g_K" initial_value="250.0"/>
	  <variable units="nanoS" public_interface="out" name="g_Na" initial_value="400.0"/>
	  <variable units="nanoS" public_interface="out" name="g_Ca" initial_value="0.05"/>
	  <variable units="nanoS" public_interface="out" name="g_KCa" initial_value="6.0"/>
	  <variable units="nanoS" public_interface="out" name="g_L" initial_value="6.0"/>
	  <variable units="nanoS" public_interface="out" name="g_synE" initial_value="0.1"/>
	  <variable units="nanoS" public_interface="out" name="g_synI"/>
	    
	  <variable units="millimolar" public_interface="in" name="Ca"/>
	  <variable units="dimensionless" public_interface="in" name="S2"/>
	  <variable units="dimensionless" public_interface="in" name="S3"/>
	  
	  <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_Ca</ci>
            <apply>
               <times/>
               <cn cellml:units="millivolt">13.27</cn>
               <apply>
                  <log/>
                  <apply>
                     <divide/>
					 <cn cellml:units="millimolar">4.0</cn>
                     <ci>Ca</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
		 
		 <apply>
            <eq/>
            <ci>g_synI</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="nanoS">0.04</cn>
                  <ci>S2</ci>
               </apply>
			   <apply>
                  <times/>
                  <cn cellml:units="nanoS">0.01</cn>
                  <ci>S3</ci>
               </apply>
            </apply>
         </apply>
	  </math>
   </component>
	 
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="post_I">
	     <component_ref component="V"/>
		 <component_ref component="i_Na">
            <component_ref component="i_Na_m_gate"/>
		    <component_ref component="i_Na_h_gate"/>
         </component_ref>
	     <component_ref component="i_K">
            <component_ref component="i_K_m_gate"/>
	     </component_ref>
	     <component_ref component="i_Ca">
            <component_ref component="i_Ca_m_gate"/>
		    <component_ref component="i_Ca_h_gate"/>
         </component_ref>
	     <component_ref component="i_KCa">
            <component_ref component="i_KCa_m_gate"/>
	     </component_ref>
		 <component_ref component="i_L"/>
		 <component_ref component="i_synE"/>
		 <component_ref component="i_synI"/>
		 <component_ref component="Ca"/>
		 <component_ref component="s_i"/>
		 <component_ref component="model_parameters"/>
	  </component_ref>
   </group>
   
  
   
   <connection>
      <map_components component_2="V" component_1="i_Na"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Na" variable_1="i_Na"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_Ca"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_KCa"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_KCa" variable_1="i_KCa"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_K"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_K" variable_1="i_K"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_L"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_L" variable_1="i_L"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_synE"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_synE" variable_1="i_synE"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="i_synI"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_synI" variable_1="i_synI"/>
   </connection>
   
   <connection>
      <map_components component_2="V" component_1="model_parameters"/>
      <map_variables variable_2="C" variable_1="C"/>
   </connection>
  
   <connection>
      <map_components component_2="i_Na" component_1="model_parameters"/>
      <map_variables variable_2="E_Na" variable_1="E_Na"/>
      <map_variables variable_2="g_Na" variable_1="g_Na"/>
   </connection>
   
   <connection>
      <map_components component_2="i_Ca" component_1="model_parameters"/>
      <map_variables variable_2="E_Ca" variable_1="E_Ca"/>
      <map_variables variable_2="g_Ca" variable_1="g_Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="i_KCa" component_1="model_parameters"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
      <map_variables variable_2="g_KCa" variable_1="g_KCa"/>
   </connection>
   
   <connection>
      <map_components component_2="i_K" component_1="model_parameters"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
      <map_variables variable_2="g_K" variable_1="g_K"/>
   </connection>
   
   <connection>
      <map_components component_2="i_L" component_1="model_parameters"/>
      <map_variables variable_2="E_L" variable_1="E_L"/>
      <map_variables variable_2="g_L" variable_1="g_L"/>
   </connection>
   
   <connection>
      <map_components component_2="i_synE" component_1="model_parameters"/>
      <map_variables variable_2="E_synE" variable_1="E_synE"/>
      <map_variables variable_2="g_synE" variable_1="g_synE"/>
   </connection>
   
   <connection>
      <map_components component_2="i_synI" component_1="model_parameters"/>
      <map_variables variable_2="E_synI" variable_1="E_synI"/>
      <map_variables variable_2="g_synI" variable_1="g_synI"/>
   </connection>
   
   <connection>
      <map_components component_2="Ca" component_1="model_parameters"/>
      <map_variables variable_2="Ca" variable_1="Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="Ca" component_1="i_KCa"/>
      <map_variables variable_2="Ca" variable_1="Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="Ca" component_1="i_Ca"/>
      <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="i_Na_m_gate" component_1="i_Na"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="i_Na_h_gate" component_1="i_Na"/>
      <map_variables variable_2="h" variable_1="h"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="i_Ca_m_gate" component_1="i_Ca"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="i_Ca_h_gate" component_1="i_Ca"/>
      <map_variables variable_2="h" variable_1="h"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="i_KCa_m_gate" component_1="i_KCa"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
	  <map_variables variable_2="Ca" variable_1="Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="i_K_m_gate" component_1="i_K"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="V" variable_1="V"/>
	  <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   
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	<rdf:Description rdf:about="">
      <dc:title>Postinspiratory neuron</dc:title>
	  
	  <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
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          <vCard:Given>Catherine</vCard:Given>
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        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
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    </rdf:Description>
    
    <rdf:Description rdf:about="#smith_2007_post_I">
      
	  <bqs:reference rdf:parseType="Resource">
        <dc:subject rdf:parseType="Resource">
          <bqs:subject_type>keyword</bqs:subject_type>
          <rdf:value>
            <rdf:Bag>
              <rdf:li>neuron</rdf:li>
		      <rdf:li>neurobiology</rdf:li>
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      <bqs:reference rdf:parseType="Resource">
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                  <vCard:N rdf:parseType="Resource">
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          <dc:title>
            Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms
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            <dc:title>Journal of Neurophysiology</dc:title>
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