Location: Perelson, Neumann, Markowitz, Leonard, Ho, 1996 @ 969e0fd78645 / perelson_neumann_markowitz_leonard_ho_1996.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2010-01-07 13:19:20+13:00
Desc:
Removed redundant (duplicate) .png image and corrected the name of the .svg and .ai files. Model curation: fixed documentation, metadata and corrected units and initial conditions (together with Ethan Choi).
Permanent Source URI:
http://models.cellml.org/workspace/perelson_neumann_markowitz_leonard_ho_1996/rawfile/969e0fd78645025a63ad666ffe792084f3cf632a/perelson_neumann_markowitz_leonard_ho_1996.cellml

<?xml version="1.0"?>
<!--  FILE :  perelson_neumann_markowitz_leonard_ho_1996.cellml
CREATED :  3rd December 2003
LAST MODIFIED : 6th January 2010
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 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Perelson et al.'s 1996 mathematical model of HIV-1 dynamics in vivo.
CHANGES:

-->

<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="perelson_neumann_markowitz_leonard_ho_1996" name="perelson_neumann_markowitz_leonard_ho_1996">
	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time</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 the second model in the published paper (which includes the effects of treatment with ritonavir). The model runs in both COR and PCEnv, the units have been checked and they are consistent. The simulation output from the CellML model looks reasonable, however we were unable to check it against the original model results as the paper does not contain any simulation graphs. Please note that the value of the initial condition of T_star and the parameters k and N were not definied in the paper so these have been set to 0, 2.4e-5, and 774 respectively, according to the values which were defined in Perelson et al. 1993.</para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>ABSTRACT: A new mathematical model was used to analyze a detailed set of human immunodeficiency virus-type 1 (HIV-1) viral load data collected from five infected individuals after the administration of a potent inhibitor of HIV-1 protease. Productively infected cells were estimated to have, on average, a life-span of 2.2 days (half-life t 1/2 = 1.6 days), and plasma virions were estimated to have a mean life-span of 0.3 days (t 1/2 = 0.24 days). The estimated average total HIV-1 production was 10.3 x 10(9) virions per day, which is substantially greater than previous minimum estimates. The results also suggest that the minimum duration of the HIV-1 life cycle in vivo is 1.2 days on average, and that the average HIV-1 generation time--defined as the time from release of a virion until it infects another cell and causes the release of a new generation of viral particles--is 2.6 days. These findings on viral dynamics provide not only a kinetic picture of HIV-1 pathogenesis, but also theoretical principles to guide the development of treatment strategies.</para>
				
				<para>The original paper reference is cited below:</para>
				
				<para>HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Alan S. Perelson, Avidan U. Neumann, Martin Markowitz, John M. Leonard, and David D. Ho, 1996, <emphasis>Science</emphasis>, 271, 1582-1586. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/8599114">PubMed ID: 8599114</ulink>
				</para>
				
				<informalfigure float="0" id="fig_cell_diagram">
					<mediaobject>
						<imageobject>
							<objectinfo>
								<title>cell diagram</title>
							</objectinfo>
							<imagedata fileref="perelson_1996.png"/>
						</imageobject>
					</mediaobject>
					<caption>Schematic diagram summarising the dynamics of an HIV-1 infection <emphasis>in vivo</emphasis>.</caption>
				</informalfigure>
			</sect1>
		</article>
	</documentation>


	<!-- units -->
	<units base_units="yes" name="cell"/>
	
	<units name="per_ml">
	    <unit exponent="-1" prefix="milli" units="litre"/>
	</units>
	
	<units name="per_cell">
	    <unit exponent="-1" units="cell"/>
	</units>
	
	<units name="per_day">
	    <unit exponent="-1" units="day"/>
	</units>
	
	<units name="day">
		<unit multiplier="86400.0" units="second"/>
	</units>
	
	<units name="first_order_rate_constant">
		<unit exponent="-1" units="day"/>
	</units>
	
	<units name="second_order_rate_constant">
	    <unit prefix="milli" units="litre"/>
		<unit exponent="-1" units="day"/>
	</units>
	
	<!-- components -->
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		<variable name="time" public_interface="out" units="day"/>
	</component>
	
	<component cmeta:id="T" name="T">
		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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				<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">T</dc:title>
				<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">uninfected target CD4 cells</dcterms:alternative>
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	<component cmeta:id="T_star" name="T_star">
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				<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">T_star</dc:title>
				<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">infected CD4 cells</dcterms:alternative>
			</rdf:Description>
		</rdf:RDF>
		<variable initial_value="0" name="T_star" public_interface="out" units="per_ml"/>
		<variable initial_value="2.4e-5" name="k" units="second_order_rate_constant"/>
		<variable name="T" public_interface="in" units="per_ml"/>
		<variable name="VI" public_interface="in" units="per_ml"/>
		<variable name="delta" public_interface="in" units="per_day"/>
		<variable name="time" public_interface="in" units="day"/>
		
		<math xmlns="http://www.w3.org/1998/Math/MathML">
			<apply>
				<eq/>
				<apply>
					<diff/>
					<bvar>
						<ci>time</ci>
					</bvar>
					<ci>T_star</ci>
				</apply>
				<apply>
					<minus/>
					<apply>
						<times/>
						<ci>k</ci>
						<ci>VI</ci>
						<ci>T</ci>
					</apply>
					<apply>
						<times/>
						<ci>delta</ci>
						<ci>T_star</ci>
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			<rdf:Description rdf:about="VI">
				<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">VI</dc:title>
				<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">plasma concentration of virions in the infectious pool</dcterms:alternative>
			</rdf:Description>
		</rdf:RDF>
		<variable name="VI" initial_value="216000.0" public_interface="out" units="per_ml"/>
		<variable name="c" public_interface="in" units="first_order_rate_constant"/>
		<variable name="time" public_interface="in" units="day"/>
		<math xmlns="http://www.w3.org/1998/Math/MathML">
			<apply>
				<eq/>
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						<ci>time</ci>
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					<ci>VI</ci>
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						<ci> c </ci>
						<ci> VI </ci>
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				<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">VNI</dc:title>
				<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">plasma concentration of virions in the noninfectious pool</dcterms:alternative>
			</rdf:Description>
		</rdf:RDF>
		<variable initial_value="0" name="VNI" public_interface="out" units="per_ml"/>
		<variable initial_value="774" name="N" units="dimensionless"/>
		<variable name="T_star" public_interface="in" units="per_ml"/>
		<variable name="delta" public_interface="in" units="first_order_rate_constant"/>
		<variable name="c" public_interface="in" units="first_order_rate_constant"/>
		<variable name="time" public_interface="in" units="day"/>
		<math xmlns="http://www.w3.org/1998/Math/MathML">
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				<eq/>
				<apply>
					<diff/>
					<bvar>
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					</bvar>
					<ci>VNI</ci>
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				<apply>
					<minus/>
					<apply>
						<times/>
						<ci>N</ci>
						<ci>delta</ci>
						<ci>T_star</ci>
					</apply>
					<apply>
						<times/>
						<ci>c</ci>
						<ci>VNI</ci>
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				</apply>
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		</math>
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	<component cmeta:id="V" name="V">
		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="V">
				<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">V</dc:title>
				<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">total concentration of plasma virions</dcterms:alternative>
			</rdf:Description>
		</rdf:RDF>
		<variable name="V" public_interface="out" units="per_ml"/>
		<variable name="VI" public_interface="in" units="per_ml"/>
		<variable name="VNI" public_interface="in" units="per_ml"/>
		
		<!-- <variable name="V0" initial_value="216000.0" units="per_ml"/>
		<variable name="Vt" units="per_ml"/>
		<variable name="delta" public_interface="in" units="first_order_rate_constant"/>
		<variable name="c" public_interface="in" units="first_order_rate_constant"/>
		<variable name="time" public_interface="in" units="day"/> -->
		<math xmlns="http://www.w3.org/1998/Math/MathML">
			<apply>
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				<ci>V</ci>
				<apply>
					<plus/>
					<ci> VI </ci>
					<ci> VNI </ci>
				</apply>
			</apply>
			
			<!--
			<apply>
				<eq/>
				<ci>Vt</ci>
				<apply>
					<plus/>
					<apply>
						<times/>
						<ci> V0 </ci>
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							<exp/>
							<apply>
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								<apply>
									<minus/>
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												<ci> delta </ci>
												<ci> time </ci>
											</apply>
										</apply>
									</apply>
									<apply>
										<exp/>
										<apply>
											<minus/>
											<apply>
												<times/>
												<ci> c </ci>
												<ci> time </ci>
											</apply>
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							</apply>
							<apply>
								<times/>
								<ci> delta </ci>
								<ci> time </ci>
								<apply>
									<exp/>
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											<ci> c </ci>
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										</apply>
									</apply>
								</apply>
							</apply>
						</apply>
					</apply>
				</apply>
			</apply> -->
		</math>
	</component>
	
	<component name="kinetic_parameters">
		<variable name="c" initial_value="3.07" public_interface="out" units="first_order_rate_constant"/>
		<variable name="delta" initial_value="0.49" public_interface="out" units="first_order_rate_constant"/>
	</component>


	<!-- connections -->
	<connection>
		<map_components component_1="T_star" component_2="environment"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>
	<connection>
		<map_components component_1="VI" component_2="environment"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>
	<connection>
		<map_components component_1="VNI" component_2="environment"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>
	<!-- <connection>
		<map_components component_1="V" component_2="environment"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection> -->
	<connection>
		<map_components component_1="T" component_2="T_star"/>
		<map_variables variable_1="T" variable_2="T"/>
	</connection>
	<connection>
		<map_components component_1="T_star" component_2="VI"/>
		<map_variables variable_1="VI" variable_2="VI"/>
	</connection>
	<connection>
		<map_components component_1="T_star" component_2="kinetic_parameters"/>
		<map_variables variable_1="delta" variable_2="delta"/>
	</connection>
	<connection>
		<map_components component_1="VI" component_2="kinetic_parameters"/>
		<map_variables variable_1="c" variable_2="c"/>
	</connection>
	<connection>
		<map_components component_1="VNI" component_2="T_star"/>
		<map_variables variable_1="T_star" variable_2="T_star"/>
	</connection>
	<connection>
		<map_components component_1="VNI" component_2="kinetic_parameters"/>
		<map_variables variable_1="c" variable_2="c"/>
		<map_variables variable_1="delta" variable_2="delta"/>
	</connection>
	<connection>
		<map_components component_1="V" component_2="VI"/>
		<map_variables variable_1="VI" variable_2="VI"/>
	</connection>
	<connection>
		<map_components component_1="V" component_2="VNI"/>
		<map_variables variable_1="VNI" variable_2="VNI"/>
	</connection>
	<!-- <connection>
		<map_components component_1="V" component_2="kinetic_parameters"/>
		<map_variables variable_1="c" variable_2="c"/>
		<map_variables variable_1="delta" variable_2="delta"/>
	</connection> -->


	<!-- metadata -->
	<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" 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#">
    
    <rdf:Description rdf:about="">
      <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Lloyd</vCard:Family>
          <vCard:Given>Catherine</vCard:Given>
		  <vCard:Other>May</vCard:Other>
		</vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
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          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
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        <dcterms:W3CDTF>2003-12-03</dcterms:W3CDTF>
      </dcterms:created>
    </rdf:Description>
    
    <rdf:Description rdf:about="#perelson_neumann_markowitz_leonard_ho_1996">
         
      <bqs:reference rdf:parseType="Resource">
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          <rdf:value>
            <rdf:Bag rdf:about="rdf:#cb35a012-2d3e-4cdf-9c80-901f38489d6b">
			  <rdf:li>immunology</rdf:li>
			  <rdf:li>viral dynamics</rdf:li>
			  <rdf:li>CD4 cells</rdf:li>
			  <rdf:li>T cells</rdf:li>
			  <rdf:li>HIV-1</rdf:li>
		    </rdf:Bag>
	      </rdf:value>
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        <bqs:Pubmed_id>8599114</bqs:Pubmed_id>
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                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Perelson</vCard:Family>
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					<vCard:Other>U</vCard:Other>
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                    <vCard:Family>Leonard</vCard:Family>
                    <vCard:Given>J</vCard:Given>
					<vCard:Other>M</vCard:Other>
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			  <rdf:li rdf:parseType="Resource">
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                    <vCard:Family>Ho</vCard:Family>
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					<vCard:Other>D</vCard:Other>
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          </dc:creator>
          <dc:title>
            HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time
          </dc:title>
          <dcterms:issued rdf:parseType="Resource">
            <dcterms:W3CDTF>1996-03-15</dcterms:W3CDTF>
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            <dc:title>Science</dc:title>
          </bqs:Journal>
		  <bqs:volume>15</bqs:volume>
          <bqs:first_page>1582</bqs:first_page>
          <bqs:last_page>1586</bqs:last_page>
        </bqs:JournalArticle>
      </bqs:reference>
    </rdf:Description>
  </rdf:RDF>

</model>