Microtubule

A microtubule of undefined length can be extended through a polimerization reaction.

Within the context of the example detailed below, where only microtubules and tubulin dimers can bind, the figure above is effectively equivalent to the figure below, both representing the same reactions.

<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level3/version1/core" 
             level="3" version="1"
             xmlns:multi="http://www.sbml.org/sbml/level3/version1/multi/version1"
             multi:required="true">

  <model name="microtubule_elongation">
    <listOfCompartments>
      <compartment id="cell" constant="true" size="1" />
    </listOfCompartments>
  
    <multi:listOfSpeciesTypes>
      <multi:speciesType 
                   multi:id="st_tubulin" 
                   multi:name="tubulin" 
                   multi:bindingSite="false">
      <multi:speciesType 
                   multi:id="st_tbs" 
                   multi:name="tbs" 
                   multi:bindingSite="true" />
    </multi:listOfSpeciesTypes>

<!-- -------------------------------------------------------------------------------- -->
<!-- Description of a free dimer of tubulin                                           -->
<!-- -------------------------------------------------------------------------------- -->

    <multi:selector multi:id="sel_tubulin_free">
        <multi:listOfSpeciesTypeStates>
          <multi:speciesTypeState multi:id="sts_tbs1" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tbs2" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tubulin" multi:speciesType="st_tubulin" 
                                   multi:minOccur="1" multi:maxOccur="1" />
            <multi:listOfContainedSpeciesTypes>
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs1" /> 
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs2" />
            </multi:listOfContainedSpeciesTypes>
          </multi:speciesTypeState>
        </multi:listOfSpeciesTypeStates>
        <multi:listOfUnboundBindingSites>
          <multi:bindingSiteReference multi:speciesTypeState="sts_tbs1" />
          <multi:bindingSiteReference multi:speciesTypeState="sts_tbs2" />
        </multi:listOfUnboundBindingSites>
      </multi:selector>

<!-- -------------------------------------------------------------------------------- -->
<!-- To signify a microtubule, we describe a tubulin with one binding site free, the  -->
<!-- other being bound                                                                -->
<!-- -------------------------------------------------------------------------------- -->
      <multi:selector multi:id="sel_microtubule">
        <multi:listOfSpeciesTypeStates>
          <multi:speciesTypeState multi:id="sts_tbs1" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tbs2" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tubulin" multi:speciesType="st_tubulin" 
                                   multi:minOccur="1" multi:maxOccur="1" />
            <multi:listOfContainedSpeciesTypes>
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs1" /> 
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs2" />
            </multi:listOfContainedSpeciesTypes>
          </multi:speciesTypeState>
        </multi:listOfSpeciesTypeStates>
        <multi:listOfUnboundBindingSites>
          <multi:bindingSiteReference multi:speciesTypeState="sts_tbs1" />
        </multi:listOfUnboundBindingSites>
        <multi:listOfBonds>
          <multi:bond multi:occurrence="required" >
            <multi:bindingSiteReference multi:speciesTypeState="sts_tbs2" />
          </multi:bond>
        </multi:listOfBonds>
      </multi:selector>

<!-- -------------------------------------------------------------------------------- -->
<!-- This is a microtubule with at least three monomers                               -->
<!-- -------------------------------------------------------------------------------- -->
      <multi:selector multi:id="sel_microtubuleExtended">
        <multi:listOfSpeciesTypeStates>
          <multi:speciesTypeState multi:id="sts_tbs1" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tbs2" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tbs3" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tbs4" multi:speciesType="st_tbs" 
                                   multi:minOccur="1" multi:maxOccur="1" />
          <multi:speciesTypeState multi:id="sts_tubulin1" multi:speciesType="st_tubulin" 
                                   multi:minOccur="1" multi:maxOccur="1">
            <multi:listOfContainedSpeciesTypes>
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs1" /> 
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs2" />
            </multi:listOfContainedSpeciesTypes>
          </multi:speciesTypeState>
          <multi:speciesTypeStates multi:id="sts_tubulin2" multi:speciesType="st_tubulin" 
                                   multi:minOccur="1" multi:maxOccur="1">
            <multi:listOfContainedSpeciesTypes>
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs3" /> 
              <multi:containedSpeciesType multi:speciesTypeState="sts_tbs4" />
            </multi:listOfContainedSpeciesTypes>
          </multi:speciesTypeState>
        </multi:listOfSpeciesTypeStates>
        <multi:listOfBonds>
          <multi:bond multi:occurrence="required" >
            <multi:bindingSiteReference multi:speciesTypeState="sts_tbs2" />
            <multi:bindingSiteReference multi:speciesTypeState="sts_tbs3" />
          </multi:bond>
        </multi:listOfBonds>
        <multi:listOfUnboundBindingSites>
          <multi:bindingSiteReference multi:speciesTypeState="sts_tbs1" />
        </multi:listOfUnboundBindingSites>
      </multi:selector>
    </multi:listOfSelectors>

    <listOfSpecies>
      <species id="tubulin" compartment="cell" multi:speciesType="st_tubulin"
               boundaryCondition="false" hasOnlySubstanceUnit="false" 
               constant="false" initialAmount="500" >
        <multi:listOfSpeciesTypeInstances>
          <multi:SpeciesTypeInstance multi:id="free_tubulin" multi:initialAmount="100">
            <multi:listOfSelectorReferences>
              <multi:selectorReference multi:selector="sel_tubulin_free" />
            </multi:listOfSelectorReferences>
          </multi:speciesTypeInstance>
          <multi:SpeciesTypeInstance multi:id="microtubule" multi:initialAmount="400">
            <multi:listOfSelectorReferences>
              <multi:selectorReference multi:selector="sel_microtubule" />
            </multi:listOfSelectorReferences>
          </multi:speciesTypeInstance>
          <multi:SpeciesTypeInstance multi:id="microtubuleExtended" multi:initialAmount="0">
            <multi:listOfSelectorReferences>
              <multi:selectorReference multi:selector="sel_microtubuleExtended">
            </multi:listOfSelectorReferences>
          </multi:speciesTypeInstance>
        </multi:listOfSpeciesTypeInstances>
      </species>
    </listOfSpecies>

    <listOfReactions>
      <reaction id="tubulin_binding" reversible="false" fast="false"> 
        <listOfReactants>
          <speciesReference species="tubulin" stoichiometry="1">
            <multi:listOfSpeciesRestriction>
              <multi:speciesRestriction multi:id="free_tubul"
                                        multi:speciesTypeInstance="free_tubulin"/>
              <multi:speciesRestriction multi:id="micro" 
                                        multi:speciesTypeInstance="microtubule"/>
            </multi:listOfSpeciesRestriction>
          </speciesReference>
        </listOfReactants>
        <listOfProducts>
          <multi:productSpeciesReference species="tubulin" stoichiometry="1">
            <multi:listOfSpeciesRestriction>
              <multi:speciesRestriction multi:id="micro_extended"
                                   multi:speciesTypeInstance="microtubule_extended"/>
            </multi:listOfSpeciesRestriction>
          </multi:productSpeciesReference>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML" />
        </kineticLaw>
        <multi:listOfReactionRules>
          <multi:reactionRule multi:id="bindingNonPhospho">
            <multi:listOfConditions>
              <multi:speciesTypeRestrictionReference multi:speciesTypeRestriction="free_tubul"/>
              <multi:speciesTypeRestrictionReference multi:speciesTypeRestriction="micro"/>
            </multi:listOfConditions>
            <multi:listOfResults>
              <multi:speciesTypeRestrictionReference
                                      multi:speciesTypeRestriction="micro_extended"/>
            </multi:listOfResults>
            <kineticLaw>
              <math xmlns="http://www.w3.org/1998/Math/MathML" >
                <apply>
                  <times />
                  <ci> cell </ci>
                  <ci> kon </ci>
                  <ci> tubulin </ci>
                </apply>
              </math>
              <listOfLocalParameters>
                <localParameter id="kon" value="1">
              </listOfLocalParameters>
            </kineticLaw>
          </multi:reactionRule>
        </multi:listOfReactionRules>
      </reaction>
    </listOfReactions>
  </model>
</sbml>

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