(622f) Stochastic Population Balance Modeling of Influenza Virus Replication in a Vaccine Production Process

Sidorenko, Y. - Presenter, Max Planck Institute Magdeburg
Schulze-Horsel, J. - Presenter, Max Planck Institute Magdeburg
Voigt, A. - Presenter, University of Magdeburg
Reichl, U. - Presenter, Max Planck Institute for Dynamics of Complex Technical Systems
Kienle, A. - Presenter, Otto von Guericke University Magdeburg

This presentation deals with the mathematical modeling of the influenza virus replication in mammalian cells, such as Madin Darby canine kidney (MDCK) cells, which are used in vaccine production. Influenza viruses are negative-strand RNA viruses, which cause severe human and animal suffering, as well as high economic losses. In order to obtain and improve the quantitative understanding of the virus replication dynamics, mathematical modeling plays a crucial role. Previously two deterministic model approaches were reported: a detailed structured model, which accounts for all major steps of the infection cycle[1], and a basic model where the interaction of virus and cell populations is described[2]. Here we present a stochastic segregated population balance model, where the dynamics is simulated by a kinetic Monte Carlo approach. Unlike deterministic models, a stochastic model takes into account the random nature of the process, and thus might provide a more realistic representation of process dynamics. On the other hand, structuring the population of cells by the number of virions carried could provide additional information, which might be used to study virus-mediated intracellular events, e.g., apoptosis (programmed cell death). The model is aimed to reproduce the dynamics of virus production, to quantify the number of uninfected, infected, and producing cells, to simulate the distribution of infectious virions through the cells, and to test the existing strategies for vaccine production optimization and to propose new ideas.

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.