The stochastic model describes a population of cells surrounded by a medium containing free virus particles (virions). During the process the cell status progresses in 4 states: from uninfected to infected to virus producing to dead (final state). The cells perform a virus replication cycle and produce new virions, which are released to the medium. In the model we define probabilities for the transition from one state to the next, e.g., a cell in the infected state might transit to either the producing or dead state. A parameter estimation (10 parameters) for this transition probabilities leads to quantitative agreement of simulation and experimental data on virus production (HA test, flow cytometry). It could be shown that the number of produced virions effectively increases when virus-induced apoptosis is inhibited. A more detailed analysis of the number of living cells with a certain number of virions carried by those cells could show the dynamical distribution of infectious virions through the cell population. This dynamics indicates that the number of endosomes and cellular receptors to which virions attach is not limiting the virus replication.
In summary, the presented model helps to investigate the dynamics of influenza virus replication at a detailed level. Together with detailed experimental studies it will help to improve the understanding of virus- related diseases, to identify molecular targets for viral therapies and to optimize vaccine production processes.
[1] Sidorenko and Reichl, 2004. Structured model of influenza virus replication in MDCK cells. Biotechnol. Bioeng. 88(1): 1-14.
[2] Moehler L, Flockerzi D, Sann H, Reichl U. 2005. A Mathematical Model of Influenza A Virus Production in Large-Scale Microcarrier Culture. Biotechnol. Bioeng. 90(1): 46-58.