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     <p>These selections of models are described in the paper:
Cellular interactions constrain tumor growth
by Jeffrey West and Paul K. Newton

Significance:
A mathematical model relating tumor heterogeneity at the cellular level to tumor growth at the macroscopic level is described based on a statistical mechanics framework. The model takes into account the number of accessible states available to each cell as well as their long-range coupling (population cooperation) to other cells. We show that the degree to which cell populations cooperate determines the number of independent cell states, which in turn dictates the macroscopic (volumetric) growth law. It follows that targeting cell-to-cell interactions or functional coupling among cell populations could be a way of mitigating and controlling tumor growth.

Abstract:
A tumor is made up of a heterogeneous collection of cell types, all competing on a fitness landscape mediated by microenvironmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling, cellular cooperation, and the functional constraints that affect cellular behavior, the specifics of how these constraints (and the range over which they act) affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy and show how different assumptions on correlations of these states give rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of states at the cellular level is what determines macroscopic growth characteristics.</p>
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	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C120284"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isPropertyOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000531"/>
	</rdf:Bag>
	</bqbiol:isPropertyOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI5">
                <bqbiol:isPropertyOf rdf:resource="urn:miriam:sbo:SBO:0000531"/>
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:44:15Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C120284"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
      <species boundaryCondition="false" compartment="compartment" constant="false" id="tumor_at_Von_Bert__growth" initialConcentration="1" metaid="COPASI6" name="tumor at Von Bert. growth">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI6">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C120284"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI6">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:44:23Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C120284"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
      <species boundaryCondition="false" compartment="compartment" constant="false" id="tumor_at_Exp_growth" initialConcentration="1" metaid="COPASI7" name="tumor at Exp growth">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI7">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C120284"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI7">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:42:19Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C120284"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
      <species boundaryCondition="false" compartment="compartment" constant="false" id="tumor_at_Logistic_growth" initialConcentration="1" metaid="COPASI8" name="tumor at Logistic growth">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI8">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C120284"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI8">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:44:03Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C120284"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
    </listOfSpecies>
    <listOfParameters>
      <parameter constant="true" id="alpha_0" metaid="COPASI9" name="alpha_0" value="1">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI9">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000382"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI9">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:49:42Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000382"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="alpha_1" name="alpha_1" value="10000"/>
      <parameter constant="true" id="tau" name="tau" value="10"/>
      <parameter constant="false" id="alpha_1_variable" name="alpha_1 variable" value="0"/>
      <parameter constant="false" id="alpha_0_variable" metaid="COPASI10" name="alpha_0 variable" value="1">
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI10">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:11:21Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="alpha" name="alpha" value="1"/>
      <parameter constant="true" id="K" name="K" value="100"/>
      <parameter constant="true" id="nu" name="nu" value="0.3"/>
      <parameter constant="true" id="a" metaid="COPASI11" name="a" value="4">
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI11">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:26:10Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="b" metaid="COPASI12" name="b" value="0.2">
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI12">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:26:15Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="false" id="gamma" metaid="COPASI13" name="gamma" value="0.666666666666667">
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI13">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:26:04Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
    </listOfParameters>
    <listOfRules>
      <assignmentRule variable="gamma">
        <math xmlns="http://www.w3.org/1998/Math/MathML">        
          <apply>
            <divide/>
            <cn> 2 </cn>
            <cn> 3 </cn>
          </apply>
        </math>
            </assignmentRule>
    </listOfRules>
    <listOfReactions>
      <reaction id="exponential_linear_growth" metaid="COPASI15" name="exponential-linear growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI15">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI15">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:00:39Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Exp_Lin_growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_exponential_linear_growth </ci>
                <ci> alpha_0_variable </ci>
                <ci> tumor_at_Exp_Lin_growth </ci>
                <ci> alpha_1_variable </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="generalized_logistic_growth" metaid="COPASI16" name="generalized logistic growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI16">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI16">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:17:12Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Gen__logistic_growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_generalized_logistic_growth </ci>
                <ci> alpha </ci>
                <ci> tumor_at_Gen__logistic_growth </ci>
                <ci> K </ci>
                <ci> nu </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="Gompertz_growth" metaid="COPASI17" name="Gompertz growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI17">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI17">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:22:23Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Gomp__growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_Gompertz_growth </ci>
                <ci> alpha </ci>
                <ci> tumor_at_Gomp__growth </ci>
                <ci> K </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="power_law_model" metaid="COPASI18" name="power law model" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI18">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isPropertyOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000531"/>
	</rdf:Bag>
	</bqbiol:isPropertyOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI18">
                <bqbiol:isPropertyOf rdf:resource="urn:miriam:sbo:SBO:0000531"/>
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:23:26Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Power_growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_power_law_model </ci>
                <ci> a </ci>
                <ci> tumor_at_Power_growth </ci>
                <ci> gamma </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="Von_Bertalanffy_equation" metaid="COPASI19" name="Von Bertalanffy equation" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI19">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI19">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:24:41Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Von_Bert__growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_Von_Bertalanffy_equation </ci>
                <ci> a </ci>
                <ci> tumor_at_Von_Bert__growth </ci>
                <ci> gamma </ci>
                <ci> b </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="exponential_growth" metaid="COPASI20" name="exponential growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI20">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI20">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:37:22Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0040007"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Exp_growth" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_exponential_growth </ci>
                <ci> alpha_0 </ci>
                <ci> tumor_at_Exp_growth </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction id="logistic_growth" metaid="COPASI21" name="logistic growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI21">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0040007"/>
	</rdf:Bag>
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	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI21">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:40:00Z</dcterms:W3CDTF>
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        </annotation>
              <listOfProducts>
          <speciesReference species="tumor_at_Logistic_growth" stoichiometry="1"/>
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        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> compartment </ci>
              <apply>
                <ci> Function_for_logistic_growth </ci>
                <ci> alpha </ci>
                <ci> tumor_at_Logistic_growth </ci>
                <ci> K </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
    </listOfReactions>
    <listOfEvents>
      <event id="exponential_model_switch" metaid="COPASI14" name="exponential model switch">
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI14">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-09-24T10:06:24Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
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            <apply>
              <gt/>
              <csymbol encoding="text" definitionURL="http://www.sbml.org/sbml/symbols/time"> time </csymbol>
              <ci> tau </ci>
            </apply>
          </math>
                </trigger>
        <listOfEventAssignments>
          <eventAssignment variable="alpha_1_variable">
            <math xmlns="http://www.w3.org/1998/Math/MathML">            
              <apply>
                <plus/>
                <ci> alpha_1_variable </ci>
                <ci> alpha_1 </ci>
              </apply>
            </math>
                    </eventAssignment>
          <eventAssignment variable="alpha_0_variable">
            <math xmlns="http://www.w3.org/1998/Math/MathML">            
              <apply>
                <minus/>
                <ci> alpha_0_variable </ci>
                <ci> alpha_0 </ci>
              </apply>
            </math>
                    </eventAssignment>
        </listOfEventAssignments>
      </event>
    </listOfEvents>
  </model>
</sbml>