Revision as of 13:45, 23 October 2010

Model for Virus Infection

As in the previous model for the virus production we established a ODE model based on the law of mass action. The following paragraph explains the reaction scheme and our model assumptions. In the subsequent paragraphs the system of differential equations is specified and the implementation in MathWorks® MATLAB is discussed.
The last section deals with our modeling results.

Reaction Scheme

Like in the previous model we divide the cell into four compartments: the extracellular matrix (all quantities with the index ext), the space in an endosome (end), the cytoplasm (cyt) and the nucleus (nuc). A target cell is transduced by viral particles (V) in the extracellular matrix. Depending on their degree of modification (m) and thus their specificity they can bind to receptors (R) on the cell surface. Once a receptor has formed a complex with a virus particle (VR) receptor dimerization (R₂) occurs and the whole complex (VR₂) is invaginated into cytoplasm. The virus is released from the endosome to the cytoplasm and is transported to the nucleus where uncoating of the capsid is initiated and the single stranded DNA (ssDNA) is released.
Finally viral mRNA is processed and transported into the cytoplasm where the enzyme for therapeutic approach (E) is produced.

Reduced Reaction Scheme

Differential Equations

Methods and Simulation

The ODE model was implemented in MathWorks® MATLAB R2010b. Integration of the differential equations was achieved using the stiff integrator ode15s with automatic integration step size management.
To calibrate the dynamics of the mathematical model to those of biological system we used time lapse data of fluorescence experiments as well as published values for the rate constants.

The parameters used are given in the table below. Also you can download the MATLAB source code.

get the .m-File (MATLAB source code)

@@ Line 11: / Line 11: @@
 <h2>Reaction Scheme</h2>
-Like in the previous model we divide the cell into four compartments: the <b>extracellular matrix</b> (all quantities with the index <i>ext</i>), the space in an <b>endosom</b> (<i>end</i>), the <b>cytoplasm</b> (<i>cyt</i>) and the <b>nucleus</b> (<i>nuc</i>).
+Like in the previous model we divide the cell into four compartments: the <b>extracellular matrix</b> (all quantities with the index <i>ext</i>), the space in an <b>endosome</b> (<i>end</i>), the <b>cytoplasm</b> (<i>cyt</i>) and the <b>nucleus</b> (<i>nuc</i>).
-A target cell is transduced by <b>viral particles</b> (<i>V</i>) in the extracellular matrix. Depending on their <b>degree of modification</b> (<i>m</i>) and thus their specificity they can bind to <b>receptors</b> (<i>R</i>) on the cell surface. Once a receptor has formed a <b>complex with a virus particle</b> (<i>VR</i>) receptor dimerization (<i>R<sub>2</sub></i>) occurs and the whole <b>complex</b> (<i>VR<sub>2</sub></i>) is invaginated into cytoplasm. The virus <br>
+A target cell is transduced by <b>viral particles</b> (<i>V</i>) in the extracellular matrix. Depending on their <b>degree of modification</b> (<i>m</i>) and thus their specificity they can bind to <b>receptors</b> (<i>R</i>) on the cell surface. Once a receptor has formed a <b>complex with a virus particle</b> (<i>VR</i>) receptor dimerization (<i>R<sub>2</sub></i>) occurs and the whole <b>complex</b> (<i>VR<sub>2</sub></i>) is invaginated into cytoplasm. The virus is released from the endosome to the cytoplasm and is transported to the nucleus where uncoating of the capsid is initiated and the <b>single stranded DNA</b> (<i>ssDNA</i>) is released.<br>
+Finally viral mRNA is processed and transported into the cytoplasm where the <b>enzyme for therapeutic approach</b> (<i>E</i>) is produced.
-transported into the nucleus where gene expression is initiated. Processed mRNA is transported into the cytoplasm and <b>proteins</b> (<i>phelper</i>, <i>pcapwt</i>, <i>pcapmod</i>) are produced. Containing a nuclear localization sequence proteins are relocated into the nucleus where capsid assembly occurs. The viral capsid is compose of 60 subunits of viral coat proteins. Titration of the two plasmids coding for the capsid proteins leads to virus surfaces with different ratios of wild type and modified capsid proteins.<br>
-The gene of interest is replicated by cellular polymerases and <b>single stranded DNA</b> (<i>ssDNA</i>) is encapsidated into the preformed <b>capsids</b> (<i>capsid</i>) forming infectious <b>viral particles</b> (<i>V</i>).<br>
-Finally the recombinant viruses are released into the extracellular matrix and can be harvested for transduction.
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Team:Freiburg Bioware/Modeling/Virus Infection

From 2010.igem.org