Influenza virus is an enveloped, negative-stranded RNA virus. It belongs to the Orthomyxoviridae family. There are 3 types of influenza viruses - influenza A, B, and C. The genome of influenza A virus consists of eight negative-strand RNA segments of different size. Encoded by the genes are 11 viral proteins: envelope proteins - hemagglutinin (HA) and neuraminidase (NA), matrix protein (M1), nucleoprotein (NP), polymerase complex consisting of three subunits (PB1, PB2 and PA), ion channel protein (M2), nonstructural proteins (NS1 and NS2) and PB1-F2 protein participating in the induction of apoptosis.

Binding of virus particles with cell surface sialic acid receptors is mediated by hemagglutinin. Cell-bound virions are internalized via clathrin-dependent endocytotic pathway. The low pH in endosomes causes the fusion of viral and endosomal membranes. As a result, viral ribonucleoprotein (vRNP) complexes are released into the cytoplasm and imported to the nucleus, where transcription and replication of the vRNA molecules occur. Translation of viral mRNA molecules takes place in the cytoplasm. In the nucleus the newly synthesized polymerase complexes, NP, NS2, and M1 proteins bind to the recently replicated vRNA molecules to form new M1-vRNP complexes. Envelope proteins and M1-vRNP complexes are finally assembled at the plasma membrane, where budding of mature virions takes place. An overview is given in Fig. 1.

Figure 1: Scheme of influenza virus replication

A thorough investigation of virus replication dynamics would be useful in treating viral-mediated diseases, developing protocols for viral gene therapy, and optimizing vaccine production. For a quantitative understanding of its complex dynamics mathematical modeling plays a crucial role. Based on a mathematical model and a set of initial conditions, it is possible to predict the behavior of the system at any moment of time, to analyze its sensitivity with respect to parameter changes, or to identify possible targets for molecular engineering.

Aim of our Work

For a quantitative description of the infection cycle different methods can be applied. The most widespread of them are unstructured and structured approaches. Unstructured models Unstructured models imply that intracellular processes are not taken into account. Cells are considered as black boxes. For example, uninfected cells, infected cells, and free virus particles are taken into account. Such models enable us to optimize and control vaccine production processes.

In the structured approach every internal event of the cell is represented by one or several functions. For example, different state variables are used to model virus replication at different cellular compartments (free, attached, endosomal, cytosolic, and nuclear). Structured models help us to better understand the complex mechanisms underlying cell growth and virus replication and to analyze virus growth dynamics in animal cells for the optimization of virus yields in vaccine production processes.

The objective of this project is to develop a detailed structured model of influenza A virus replication in Madin Darby canine kidney (MDCK) cells. This model is supposed to consider the individual steps of the process such as attachment, internalization, genome replication and translation, and progeny virion assembly.

Work Strategy

The model involved is represented by a system of nonlinear ordinary differential equations (ODEs). Numerical algorithms to solve the given system of ODEs are provided by MATLAB and DIVA. Kinetic parameters required can be deduced from experiments (a, b) or taken from literature.

Outlook

In the future metabolic flux analysis will be carried out for animal cells infected by influenza virus. Also, structured population balance models of virus infection will be developed.

Literature

1. Sidorenko Y, Reichl U. 2004. Structured model of influenza virus replication in MDCK cells. Biotechnology and Bioengineering 88(1): 1-14.
2. Moehler L, Sidorenko Y, Reichl U. Virus dynamics: Modeling of influenza A virus replication. 5th International Conference on System Biology (October 9-13, 2004, Heidelberg, Germany). Abstracts, p. 62.
3. Reichl. U, Genzel Y, Moehler L, Sidorenko Y. Concepts for vaccine production: Mathematical modeling of cell growth and virus replication. Cell Culture Engineering IX (March 7-12, 2004, Cancun, Mexico). Abstracts, p. 30.
4. Sidorenko Y, Sann H, Reichl. U. Structured model of influenza virus replication in MDCK cells. 11th European Congress on Biotechnology (August 24-29, 2003, Basel, Switzerland). Abstracts, p. 184.
5. Reichl. U, Genzel Y, Moehler L, Sidorenko Y, Sann H. Viral vaccine production in anumal cell culture: Analysis of cell growth, metabolism, and virus replication. Annual DECHEMA Congress on Biotechnology (April 2-4, 2003, Munich, Germany). Abstracts, p. V46.
6. Moehler L, Sidorenko Y, Reichl U.: Mathematical modeling of virus replication in mammalian cell cultures. 2nd International Symposium on Particulate Processes, November 17-19, 2004, Magdeburg, Germany.
7. Sidorenko Y, Reichl U.: Mathematical modeling of influenza virus replication: Limiting factors and control of viral mRNA synthesis. Bioperspectives 2005, Dechema, May 10-12, 2005, Wiesbaden, Germany, pp. 64
8. Flint JS, Racaniello VR, Krug R. 2000. Principles of virology: molecular biology, pathogenesis, and control. American Society for Microbiology.
9. Nicholson KG, Webster RG, Hay AJ. Textbook of influenza. 1998. Blackwell Science Ltd.

Interconnections with other projects of Bioprocess Engineering

Population Balance Systems

Dynamics of Virus-Host Cell Populations in Bioreactors

Coupled Processes

Influenza Vaccine Production in Microcarrier Systems
Design, Scale Up and Process Optimization for Recombinant Hantavirus Nucleocapsid Protein Expression in Saccharomyces cerevisiae for Vaccines and Diagnostics
Cell Growth and Virus Replication in Perfusion Systems
Microscopial Analysis
Physiological Status of Mammalian Cells during Growth and Viral Infection

Network Theory

A systems biology approach to mammalian cell metabolism

Interconnections with other research groups

Process Synthesis and Process Dynamics (Prof. Dr.-Ing. Achim Kienle)

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