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Team:Freiburg Bioware/Modeling/Virus Infection
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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
To simplify the mathematical description of the reaction scheme we
divide the cell into four compartments: the extracellular matrix
(all quantities with the index ext), the space in endosomes
(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 and endosomes are formed. 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 and
the enzyme for therapeutic approach (E) is produced.
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Reduced Reaction Scheme
The modeling approach only neglects linear transport processes and
describes the receptor binding and dimerization in terms of the law
of mass action (LMA).
Differential Equations
The ODE model consists of 7 equations containing 9 rate constants. To
the equation for the extracellular virus concentration a degradation
term is added corresponding to the immune response of the target
system. The temporal behavior of ssDNA is completed by a linear
degradation term.
Model Extensions
The model is extended by a non-linear dependency of the internalization
rate constant of the degree of modification (m) and the
production efficiency of functional virus particles reduces the amount
of available ssDNA in the nucleus.
The assumed functional dependency is shown in the two figures below.
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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)!
Results and Discussion
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