Population balances, modeling, protein

In this contribution a population balance model of influenza A vims replication during vaccine production in Madin-Darby canine kidney (MDCK) cell cultures is developed. Differentiation on the population level is described by a degree of infection, which is proportional to the amount of intracellular viral proteins. This can be measured directly using flow cytometry. It is shown that the model shows reasonable agreement with experimental data, although not all details of the inner dynamics can be fully reproduced. 

Quantitative analysis of these measurements has been tmder-taken by two different strategies based upon the governing population balance equations which describe the system (25). One method employed the Colllns-Richmond equation (26), the Integrated form of the population balance equation, with results which are summarized In detail elsewhere (25). In the second approach, a simple functional form was chosen for the fission frequency function which contained two adjustable parameters (the results of Harvey, Marr and Painter (27) Indicate that the results of population balance model solutions are not highly sensitive to the functional form of this function In the model). Then, four different function forms for the single-cell rate of protein synthesis fimctlon r were examined. For the following four functional forms. 

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