Background for the modelling of mammalian cell cultures

A kinetic model consists of a set of mathematical expressions that relate the rates of cellular growth and metabolism to the composition of the medium. With 

Cell and Tissue Culture Laboratory Procedures in Biotechnology, edited by A. Doyle and J.B. Griffiths. 

An example of a kinetic model that takes into account the effect of these four components - glucose, glutamine, lactate and ammonia - is presented below. The different rate expressions it contains have been found correctly to simulate batch or continuous cultures of several mammalian cell lines. 

The specific rate of cellular growth, x, is defined as the number of new cells produced per unit (e.g. billion) of living cells present in the culture medium per unit time (e.g. hour). 

For a given medium a cell line can be characterized by a maximum specific growth rate, which is the observed growth rate in the absence of any limitations by nutrients or any inhibition by metabolites. This maximal growth rate is related to the doubling time (t ) of the cell by the relationship  

---