- Author:
- Geoff Nunns <gnunns1@jhu.edu>
- Date:
- 2009-12-23 10:48:04+13:00
- Desc:
- Removed and corrected MAX function, changed N_A value to correct unit inconsistencies.
- Permanent Source URI:
- http://models.cellml.org/workspace/fallon_lauffenburger_2000/rawfile/6a368603de83e23e90562d7c7140d66e45b22703/fallon_lauffenburger_2000.cellml
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This CellML file was generated on 18/12/2009 at 12:33:00 at p.m. using:
COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
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<title>Binding, Internalisation and Postendocytotic Sorting of Interleukin-2 and Its Receptor</title>
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The model is known to run in PCEnv, OpenCell and COR and the results replicate the published paper (Figure 5), as generated by the original model. The units have been checked and are consistent.
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Interleukin-2 (IL-2) is a growth factor which is secreted by activated T-cells and which is responsible for stimulating T-cell proliferation. Following the binding of the cell surface IL-2 receptor to its ligand, the entire receptor-ligand complex is internalised into sorting endosomes by endocytosis. Within these endosomes, the receptor-ligand complex may dissociate, and also, internal receptors and ligands may associate to form a new complex. Receptor associated ligand is then subject to lysosomal degradation, while free intracellular ligand is recycled back to extracellular ligand. In the absence of any ligand, cell surface receptors are maintained at a steady level by constitutive internalisation and biosynthesis rates. In the presence of ligand, there are positive feedback effects. Cell surface receptor-ligand complexes stimulate the synthesis of new receptors, and they also enhance cell proliferation.
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Eric M. Fallon and Douglas A. Lauffenburger capture these IL-2 trafficking dynamics in their computational model (see the figure below). The model uses kinetic equations to describe receptor-ligand binding, internalisation and postendocytotic sorting of IL-2 and the IL-2-receptor complex. Model simulations are able to predict T-cell proliferation responses to IL-2.
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The complete original paper reference is cited below:
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Computational Model for Effects of Ligand/Receptor Binding Properties on Interleukin-2 Trafficking Dynamics and T Cell Proliferation Response, Eric M. Fallon and Douglas A. Lauffenburger, 2000, <emphasis>Biotechnology Progress</emphasis>, 16, 905-916. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11027188&dopt=Abstract">PubMed ID: 11027188</ulink>
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<caption>A schematic diagram of Fallon and Lauffenburger's 2000 computational model of IL-2-receptor binding and trafficking. The model follows the path of an extracellular ligand as it is bound to a cell surface receptor, internalised, degraded or recycled.</caption>
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<times/>
<ci>kfe</ci>
<ci>Li</ci>
<ci>Ri</ci>
</apply>
<apply>
<times/>
<ci>kh</ci>
<ci>Ri</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Ci">
<variable name="Ci" units="number_per_cell" initial_value="1" public_interface="out"/>
<variable name="Li" units="picomolar" public_interface="in"/>
<variable name="Ri" units="number_per_cell" public_interface="in"/>
<variable name="Cs" units="number_per_cell" public_interface="in"/>
<variable name="kfe" units="second_order_rate_constant" public_interface="in"/>
<variable name="kre" units="first_order_rate_constant" public_interface="in"/>
<variable name="ke" units="first_order_rate_constant" public_interface="in"/>
<variable name="kh" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ci</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>kfe</ci>
<ci>Li</ci>
<ci>Ri</ci>
</apply>
<apply>
<times/>
<ci>ke</ci>
<ci>Cs</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>kre</ci>
<ci>kh</ci>
</apply>
<ci>Ci</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Li">
<variable name="Li" units="picomolar" initial_value="0.01" public_interface="out"/>
<variable name="Ci" units="number_per_cell" public_interface="in"/>
<variable name="Ri" units="number_per_cell" public_interface="in"/>
<variable name="kfe" units="second_order_rate_constant" public_interface="in"/>
<variable name="kre" units="first_order_rate_constant" public_interface="in"/>
<variable name="kx" units="first_order_rate_constant" public_interface="in"/>
<variable name="Ve" units="L_per_cell" public_interface="in"/>
<variable name="NA" units="number_per_picomole" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Li</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>kre</ci>
<ci>Ci</ci>
</apply>
<apply>
<times/>
<ci>kfe</ci>
<ci>Li</ci>
<ci>Ri</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Ve</ci>
<ci>NA</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kx</ci>
<ci>Li</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Ld">
<variable name="Ld" units="number_per_cell" initial_value="1" public_interface="out"/>
<variable name="Ci" units="number_per_cell" public_interface="in"/>
<variable name="kh" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ld</ci>
</apply>
<apply>
<times/>
<ci>kh</ci>
<ci>Ci</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="L">
<variable name="L" units="picomolar" initial_value="10" public_interface="out"/>
<variable name="Rs" units="number_per_cell" public_interface="in"/>
<variable name="Cs" units="number_per_cell" public_interface="in"/>
<variable name="Li" units="picomolar" public_interface="in"/>
<variable name="Y" units="cell_per_L" public_interface="in"/>
<variable name="kf" units="second_order_rate_constant" public_interface="in"/>
<variable name="kr" units="first_order_rate_constant" public_interface="in"/>
<variable name="kx" units="first_order_rate_constant" public_interface="in"/>
<variable name="Ve" units="L_per_cell" public_interface="in"/>
<variable name="NA" units="number_per_picomole" public_interface="in"/>
<variable name="time" units="minute" 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>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>kr</ci>
<ci>Cs</ci>
</apply>
<apply>
<times/>
<ci>kx</ci>
<ci>Li</ci>
<ci>Ve</ci>
<ci>NA</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kf</ci>
<ci>L</ci>
<ci>Rs</ci>
</apply>
</apply>
<ci>Y</ci>
</apply>
<ci>NA</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Y">
<variable name="Y" units="cell_per_L" initial_value="2.5e8" public_interface="out"/>
<variable name="Cs" units="number_per_cell" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Y</ci>
</apply>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">600</cn>
<ci>Cs</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="number_per_cell">250</cn>
<ci>Cs</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">200</cn>
</apply>
<cn type="e-notation" cellml:units="cell_per_L_minute">1 <sep/>
3</cn>
</apply>
<apply>
<gt/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">600</cn>
<ci>Cs</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="number_per_cell">250</cn>
<ci>Cs</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">200</cn>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="cell_per_L_minute">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="model_parameters">
<variable name="kr" units="first_order_rate_constant" initial_value="0.0138" public_interface="out"/>
<variable name="kf" units="second_order_rate_constant" public_interface="out"/>
<variable name="kre" units="first_order_rate_constant" public_interface="out"/>
<variable name="kfe" units="second_order_rate_constant" public_interface="out"/>
<variable name="kt" units="first_order_rate_constant" initial_value="0.007" public_interface="out"/>
<variable name="Vs" units="number_per_cell_minute" initial_value="11" public_interface="out"/>
<variable name="ksyn" units="first_order_rate_constant" initial_value="0.0011" public_interface="out"/>
<variable name="ke" units="first_order_rate_constant" initial_value="0.04" public_interface="out"/>
<variable name="kx" units="first_order_rate_constant" initial_value="0.15" public_interface="out"/>
<variable name="kh" units="first_order_rate_constant" initial_value="0.035" public_interface="out"/>
<variable name="Ve" units="L_per_cell" initial_value="1e-14" public_interface="out"/>
<variable name="NA" units="number_per_picomole" initial_value="6.022e11" public_interface="out"/>
<variable name="IL2" units="dimensionless" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>kf</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>kr</ci>
<cn cellml:units="picomolar">11.1</cn>
</apply>
<apply>
<eq/>
<ci>IL2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<ci>kr</ci>
<cn cellml:units="picomolar">8.2</cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>kre</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kr</ci>
<cn cellml:units="dimensionless">8</cn>
</apply>
<apply>
<eq/>
<ci>IL2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>kr</ci>
<cn cellml:units="dimensionless">5</cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>kfe</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>kre</ci>
<cn cellml:units="picomolar">1000</cn>
</apply>
<apply>
<eq/>
<ci>IL2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<ci>kre</ci>
<cn cellml:units="picomolar">3000</cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Rs" 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="Cs" 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="Ri" 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="Ci" 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="Li" 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="Ld" 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="Y" 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="Rs" component_2="Cs"/>
<map_variables variable_1="Rs" variable_2="Rs"/>
<map_variables variable_1="Cs" variable_2="Cs"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Rs" component_2="L"/>
<map_variables variable_1="Rs" variable_2="Rs"/>
<map_variables variable_1="L" variable_2="L"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Rs" component_2="model_parameters"/>
<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="kr" variable_2="kr"/>
<map_variables variable_1="ksyn" variable_2="ksyn"/>
<map_variables variable_1="kt" variable_2="kt"/>
<map_variables variable_1="Vs" variable_2="Vs"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cs" component_2="L"/>
<map_variables variable_1="Cs" variable_2="Cs"/>
<map_variables variable_1="L" variable_2="L"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cs" component_2="model_parameters"/>
<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="kr" variable_2="kr"/>
<map_variables variable_1="ke" variable_2="ke"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ri" component_2="Rs"/>
<map_variables variable_1="Rs" variable_2="Rs"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ri" component_2="Li"/>
<map_variables variable_1="Ri" variable_2="Ri"/>
<map_variables variable_1="Li" variable_2="Li"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ri" component_2="Ci"/>
<map_variables variable_1="Ri" variable_2="Ri"/>
<map_variables variable_1="Ci" variable_2="Ci"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ri" component_2="model_parameters"/>
<map_variables variable_1="kfe" variable_2="kfe"/>
<map_variables variable_1="kre" variable_2="kre"/>
<map_variables variable_1="kh" variable_2="kh"/>
<map_variables variable_1="kt" variable_2="kt"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ci" component_2="Li"/>
<map_variables variable_1="Ci" variable_2="Ci"/>
<map_variables variable_1="Li" variable_2="Li"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ci" component_2="Cs"/>
<map_variables variable_1="Cs" variable_2="Cs"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ci" component_2="model_parameters"/>
<map_variables variable_1="kfe" variable_2="kfe"/>
<map_variables variable_1="kre" variable_2="kre"/>
<map_variables variable_1="kh" variable_2="kh"/>
<map_variables variable_1="ke" variable_2="ke"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Li" component_2="model_parameters"/>
<map_variables variable_1="kfe" variable_2="kfe"/>
<map_variables variable_1="kre" variable_2="kre"/>
<map_variables variable_1="kx" variable_2="kx"/>
<map_variables variable_1="Ve" variable_2="Ve"/>
<map_variables variable_1="NA" variable_2="NA"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ld" component_2="Ci"/>
<map_variables variable_1="Ci" variable_2="Ci"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ld" component_2="model_parameters"/>
<map_variables variable_1="kh" variable_2="kh"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="Li"/>
<map_variables variable_1="Li" variable_2="Li"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="Y"/>
<map_variables variable_1="Y" variable_2="Y"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L" component_2="model_parameters"/>
<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="kr" variable_2="kr"/>
<map_variables variable_1="kx" variable_2="kx"/>
<map_variables variable_1="Ve" variable_2="Ve"/>
<map_variables variable_1="NA" variable_2="NA"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Y" component_2="Cs"/>
<map_variables variable_1="Cs" variable_2="Cs"/>
</connection>
</model>
