Microbial systems, mathematical models

When a more detailed analysis of microbial systems is undertaken, the limitations of unstructured models become increasingly apparent. The most common area of failure is that where the growth is not exponential as, for example, during the so-called lag phase of a batch culture. Mathematically, the analysis is similar to that of the interaction of predator and prey, involving a material balance for each component being considered. 

The mathematical modeling of animal cell processes has many elements in common with the modeling of microbial systems. In fact, many examples of mathematical modeling discussed in Section 8.3.1 were initially considered for microorganisms and were later adapted to animal cells. 

De Freitas and Fredrickson (28) have analyzed mathematical models of situations of the latter type, and these show that the production of autoinhibitors can allow competitors—partial competitors—to coexist. Finally, Miura t al. (29) have analyzed a mathematical model of a situation where partial competition for a resource is coupled with commensalism again, coexistence is predicted to be possible. Broad as well as deep knowledge of microbial nutrition and physiology are probably necessities for creating successful experimental systems of partial competition, and one hopes that more poeple having such knowledge will attempt to apply it in the direction noted. 

Microorganisms have a complex cell envelope structure. Their surfaces charge and their hydrophobicity cannot be predicted, only experimentally determined [131]. Several microorganisms are not hydrophobic enough to be floated. They need collectors, similar to ore flotation. In cultivation media proteins which adsorb on the cell surface act as collectors. The interrelationship between cell envelope and proteins caimot be predicted, only experimentally evaluated. The accumulation of cells on the bubble surface depends not only on the properties of the interface, proteins and cells, but on the bubble size and velocity as well [132]. On account of this complex interrelationship between several parameters, prediction of flotation performance of microbial cells based on physicochemical fundamentals is not possible. Therefore, only empirical relationships are known which cannot be generalized. Based on the large amount of information collected in recent years, mathematical models have been developed for the calculation of the behavior of protein solutions and particular microbial cells. They hold true only for systems (e.g. BSA solutions and particular yeast strains) which are used for their evaluation. In spite of this, several recommendations for protein and microbial cell flotation can be made. 

By adopting a system approach, the book deals with a wide range of subjects normally covered in a number of separate courses— mass and energy balances, transport phenomena, chemical reaction engineering, mathematical modeling, and process control. Students are thus enabled to address problems concerning physical systems, chemical reactors, and biochemical processes (in which microbial growth and enzymes play key roles). 

---