Stochastic Population Balance Modeling of Influenza Virus replication in a Vaccine Production Process

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 , and a basic model where the interaction of the virus with a population of cells is described . Here we present a stochastic segregated population balance model, where the dynamics is simulated by a kinetic Monte Carlo approach. Unlike the deterministic models, the 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 intracellular virions carried by individual cells could provide additional information, which can be used to study virus-mediated cellular events, e.g. apoptosis (programmed cell death) and help to interpret experimental results obtained from flow cytometry. The model reproduces the dynamics of virus production, quantifies the number of uninfected, infected, and producing cells, allows to simulate the distribution of infectious virions within a population of individual cells. Furthermore, strategies for the design and optimization of vaccine production processes can be tested. The stochastic model describes a population of cells surrounded by medium containing free virus particles (virions). During the process the cell status progresses over 4 states: uninfected, infected, virus producing and 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 a producing or a dead state. A parameter estimation (10 parameters) for these 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