A Mathematical Model for the Replication of Influenza A Virus

Mathematical methods are widely used in biotechnology to improve process analysis, to support experimental design and as a basis for rational design, control and optimization. While several models describing cell growth and product formation of hybridoma cells have been published, such approaches are not very common to investigate vaccine production processes so far. This is partly due to the inherent complexity of virus-host interaction but also related to problems in monitoring and quantifying virus replication in tissue culture and difficulties in handling human or animal pathogens. We have developed a detailed structured model of influenza A virus replication in Madin Darby canine kidney (MDCK) cells, which considers all major steps of the infection cycle, such as virus attachment, internalization, genome replication, translation, and progeny virions assembly. Our model deals with a single MDCK cell, interacting with a low number of virus particles. The system of nonlinear ordinary differential equations (ODE), underlying the model, is solved numerically by the algorithms provided by DIVA and ProMoT, a software package developed at our institute to build structured dynamic simulation models. Simulations show that the number of released virions per cell increases proportional to the square of time after an initial exponential replication phase. Overall dynamics of the infection cycle and the total number of virus particles produced per cells correspond well experimental results typically obtained for influenza A virus replication in tissue culture. In addition, the model allows us to identify bottlenecks of progeny virus production and release. For example, the formation of viral ribonucleoprotein complexes (vRNP) in the nucleus is limited by the number of newly synthesized virus matrix proteins (M1) while other viral proteins (e.g. nucleoprotein NP) or viral RNAs accumulate. During budding, the number of vRNPs represents a limiting factor while viral envelope proteins (haemagglutinin, neuraminidase) seem to accumulate in the cell membrane. In contrast, other cellular resources such as the number of surface receptors, the number of free amino acids and the number of free nucleotides seem not to limit virus replication for the first 12 to 15 hours after infection. Experimental work is on progress to identify key parameters of our model in tissue culture and to test several hypotheses concerning virus replication mechanisms. Based on the detailed insight of the basic laws that control the replication of viruses in animal cells, we eventually hope not only to optimize vaccine production processes but also to improve our understanding of virus-related diseases and to identify molecular targets for viral therapies