- Author:
- Tessa Paris <tpar054@aucklanduni.ac.nz>
- Date:
- 2010-01-08 14:14:43+13:00
- Desc:
- Added initial conditions to the models which were estimated from the graphs in the paper
- Permanent Source URI:
- https://models.cellml.org/workspace/wodarz_sierro_klenerman_2007/rawfile/f2f925828e11a2d96021b88e9e713f0d1451ef5f/wodarz_sierro_klenerman_2007_a.cellml
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<title>Dynamics of killer T cell inflation in viral infections</title>
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<firstname>Catherine</firstname>
<surname>Lloyd</surname>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
CD8+ T cell, or cytotoxic T lymphocyte (CTL), responses play an important role in the host immune response against viral infections. Activated antigen-specific CTL kill virus-infected target host cells either by lysing them, or through the secretion of soluble mediators which act to inhibit viral replication. During an acute viral infection, virus-specific CTL respond by dividing. This population expansion is followed by a phase of contraction, during which ~95% of the virus-specific CTL die, and the population then stabilises to form a population of memory CTL. However, during a chronic viral infection, such as cytomegalovirus (CMV), different patterns of the CTL immune response can be observed. While some of the CMV-specific CTL responses display the same kinetics as in the classic memory pattern, others are distinct in that they manifest steady accumulation of CTL during the latent phase of the virus infection. These dynamics have been described as <emphasis>memory inflation</emphasis>
, and it has been suggested the dominance of these immune cell repertoires may compromise the responsiveness against other infections, especially in elderly individuals.</para>
<para>
While <emphasis>memory inflation</emphasis>
has been observed and is well characterised experimentally, the mechanisms underlying these CTL kinetics remain poorly understood. To address this issue Wodarz, Sierro and Klenerman (2007) have developed a simple mathematical model to describe this process (see the figure below). Through the results of model simulations they discovered that memory inflation can be promoted by competition dynamics between CMV-specific CTL and innate natural killer (NK) cell responses. If NK cells can reduce the viral load more quickly than the virus-specific CTL during the initial acute phase of the infection, then CTL inflation is more likely to occur during the latent phase of the viral infection. Weaker NK cell responses can correlate with even more pronounced CTL inflation because a greater chronic virus load is maintained allowing for subsequent CTL activation and further expansion. </para>
<para> The original publication contains three different mathematical models:</para>
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<para>The first represents the core model which describes the basic dynamics of CTL infection.</para>
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<para>The second model builds on this basic core model by including a description of the CTL response to the virus infection.</para>
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<para>Finally, the third model adds further complexity by incorporating an NK cell response.</para>
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<para> The CellML model presented here represents the first model. The other two models have also been coded in CellML and can be downloaded as version 1 variants 1 and 2 of the model.</para>
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<caption>Schematic diagram of the different components and variables included in the mathematical model of the dynamics of killer T cell inflation. The core model comprises five components: susceptible host cells (x), free virus particles (v), early-infected cells (y0), late-infected cells (y1), and latently-infected cells (L). When susceptible host cells become infected with virus, the product cells are either productively infected or are latently infected. Productively infected cells can be divided into two subsets; those which express early-gene products and those which express late-gene products. The latter produce new free virus particles and the replication cycle is completed. Latently infected cells are initially silent but can become activated, giving rise to more productively infected cells.</caption>
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<para>The complete original paper reference is cited below:</para>
<para>
Dynamics of killer T cell inflation in viral infections, Dominik Wodarz, Sophie Sierro and Paul Klenerman, 2007, <emphasis>Journal of the Royal Society, Interface</emphasis>
, volume 4, issue 14, 5330543. (Full text and PDF versions of the article are available to journal subscribers on the <emphasis>Journal of the Royal Society, Interface</emphasis>
website.) <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17251133?dopt=AbstractPlus">PubMed ID: 17251133</ulink>
</para>
</sect1>
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<variable name="v" units="dimensionless" public_interface="in"/>
<variable name="phi" units="first_order_rate_constant" public_interface="in"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="hour" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>L</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>gamma</ci>
<ci>x</ci>
<ci>v</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>phi</ci>
<ci>L</ci>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>L</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="v">
<variable name="v" units="dimensionless" initial_value="1" public_interface="out"/>
<variable name="k" units="first_order_rate_constant" public_interface="in"/>
<variable name="y1" units="dimensionless" public_interface="in"/>
<variable name="u" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="hour" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k</ci>
<ci>y1</ci>
</apply>
<apply>
<times/>
<ci>u</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="R0">
<variable name="R0" units="dimensionless"/>
<variable name="gamma" units="first_order_rate_constant" public_interface="in"/>
<variable name="lambda" units="first_order_rate_constant" public_interface="in"/>
<variable name="eta" units="first_order_rate_constant" public_interface="in"/>
<variable name="a1" units="first_order_rate_constant" public_interface="in"/>
<variable name="a0" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta" units="first_order_rate_constant" public_interface="in"/>
<variable name="phi" units="first_order_rate_constant" public_interface="in"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>R0</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>lambda</ci>
<ci>eta</ci>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>a1</ci>
<apply>
<plus/>
<ci>a0</ci>
<ci>eta</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>beta</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>phi</ci>
</apply>
<apply>
<plus/>
<ci>phi</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="model_parameters">
<variable name="a0" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="a1" units="first_order_rate_constant" initial_value="0.2" public_interface="out"/>
<variable name="k" units="first_order_rate_constant" initial_value="1" public_interface="out"/>
<variable name="u" units="first_order_rate_constant" initial_value="1" public_interface="out"/>
<variable name="lambda" units="first_order_rate_constant" initial_value="10" public_interface="out"/>
<variable name="d" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="beta" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="gamma" units="first_order_rate_constant" initial_value="0.5" public_interface="out"/>
<variable name="phi" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="eta" units="first_order_rate_constant" initial_value="0.01" public_interface="out"/>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="x" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y0" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="v" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="x" component_2="v"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="x" component_2="model_parameters"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
<map_variables variable_1="lambda" variable_2="lambda"/>
<map_variables variable_1="beta" variable_2="beta"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y0" component_2="v"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y0" component_2="x"/>
<map_variables variable_1="x" variable_2="x"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y0" component_2="L"/>
<map_variables variable_1="L" variable_2="L"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y0" component_2="model_parameters"/>
<map_variables variable_1="a0" variable_2="a0"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="eta" variable_2="eta"/>
<map_variables variable_1="phi" variable_2="phi"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y1" component_2="y0"/>
<map_variables variable_1="y0" variable_2="y0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="y1" component_2="model_parameters"/>
<map_variables variable_1="a1" variable_2="a1"/>
<map_variables variable_1="eta" variable_2="eta"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="v"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="x"/>
<map_variables variable_1="x" variable_2="x"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="model_parameters"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
<map_variables variable_1="phi" variable_2="phi"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="v" component_2="y1"/>
<map_variables variable_1="y1" variable_2="y1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="v" component_2="model_parameters"/>
<map_variables variable_1="k" variable_2="k"/>
<map_variables variable_1="u" variable_2="u"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R0" component_2="model_parameters"/>
<map_variables variable_1="a0" variable_2="a0"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
<map_variables variable_1="lambda" variable_2="lambda"/>
<map_variables variable_1="phi" variable_2="phi"/>
<map_variables variable_1="a1" variable_2="a1"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="eta" variable_2="eta"/>
<map_variables variable_1="d" variable_2="d"/>
</connection>
</model>
