Modeling

For the modeling part we considered three main parts:

• the virus production
• the infection of a target cell
• the therapy

For the first two models we assumed reactions according to the law of mass action to create a model of ordinary differential equations (ODE).

Model for Virus Production

Reaction Scheme

Reducing the complexity of virus production we divide the cell into three compartments: the extracellular matrix (all quantities with the index ext), the cytoplasm (cyt) and the nucleus (nuc). Four plasmids are transfected - the plasmid coding for the helper proteins (helper), the gene of interest (goi) and two types of plasmids coding for the capsid proteins (capwt [wild type], capmod [modified]).
The plasmids are transported into the nucleus where gene expression is initiated. Processed mRNA is transported into the cytoplasm and proteins (phelper, pcapwt, pcapmod) 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.
The gene of interest is replicated by cellular polymerases and single stranded DNA (ssDNA) is encapsidated into the preformed capsids (capsid) forming infectious viral particles (V).
Finally the recombinant viruses are released into the extracellular matrix and can be harvested for transduction.

Reduced Reaction Scheme

Even the coarse model for virus production would still consist of 24 ODEs containing 35 parameters i.e. rate constants. Taking into account the linearity of the law of mass action (LMA) we can neglect the fast reactions and for this reason reduce the model to the rate limiting step.

Differential Equations

Model for Virus Infection

Reaction Scheme

Reduced Reaction Scheme

Differential Equations