Figure 7.15 Cybernetic modeling of diauxic growth of
on glucose and xylose (inocolum
precultured on glucose). The data points are measurements, and the line is model simulations. [Reprinted by
permission from D. S. Kompala, D. Ramkrishna, and G. T. Tsao (1986), "Investigation of bacterial growth
on mixed substrates: Experimental evaluation of cybernetic models,"
concept was a substantial step forward in the 1980’s but future efforts in model building must be
spent on truly mechanistic models such as those described in the following section.
7.5 Mechanistic Models
With the many complex regulatory structures that operate in the living cell (see Fig. 2.2) it may
be desirable to evaluate the relative importance of different cell processes. This can only be done
through quantitative analysis, and here mathematical models are well suited as they allow
integration of information from different experiments into an overall description of the system.
As yet it is impossible to describe all the individual processes involved in cell growth - not all
processes are identified and even the most powerful computers could not handle the large and
complex models involved. Still there is a move towards construction of complete cellular models
in modem biology. As mentioned in Chapter 1 this is referred to as
Section 7.5.2 we are going to consider some of the first attempts to describe cell growth using
very detailed models. In many casés it is, however, interesting to study specific processes in the
cell separately, and here models where mechanistic information is included must be used. These
models are normally set up at the molecular level just as the models for enzyme kinetics in
Chapter 6. They include a certain amount of information about the prevailing mechanisms - and
they are therefore referred to as
Among the best studied processes in the cell
at the molecular level is regulation of gene transcription, which clearly plays a very important
role in overall control of cell function (but as discussed in Section 2.1.1 not necessarily a
dominant role). Before we discuss single cell models we will therefore consider genetically
structured models as an example of detailed mechanistic models.