The product formation kinetic is taken into account in conjunction with the growth kinetic. Nowadays, the Gaden [3] classification is still useful. Based on this categorizing, four kinetic types can be defined:

Type 0: This production type occurs even in resting cells that use only a little substrate for their own metabolism. The microbial cells function only as enzyme carriers. Some examples are provided by steroid transformation and vitamin E synthesis by Saccharomyces cerevisiae.

Type 1: Type-1 situations include processes in which product accumulation is directly associated with growth; in this case the product formation is linked to the energy metabolism. Examples include fermentation to produce alcohol and gluconic acid and situations in biological wastewater treatment.

Type 2: Type-2 bioprocesses include fermentations in which there is no direct connection between growth and product formation (for example, penicillin and streptomycin synthesis).

Type 3: This production type includes those having a partial association with growth and thus, an indirect link to energy metabolism (e. g. citric acid and amino acid production)

Afterward there are now more advanced models, the structured and the segregated models.

2. In case of the structured models [12, 13] the biotic phase is not any more viewed as a homogenous component, but they provide information about the physiological state of the cells, their composition and regulatory adaptation to the environment. Conforming to this concept the cell mass is structured in several intracellular compounds and functional groups, which are connected to each other and to the environment by fluxes of material and information. The structured models can be: multi compartment models, genetically structured models, and biochemical structured models.

A case study of the biochemical structured model is the modeling of Penicillin V biosynthesis: The model of Penicillin V biosynthesis [2] is a tool for both: the understanding of the kinetic function of the precursors, the dissolved oxygen, enzymes activities, formation of metabolic intermediates and by-products (the determination of the metabolic step responsible for the global rate limitation can be a basis for the genetic engineering modification of the enzyme expression involved in this metabolic reaction); the bioprocess computer control.

First it is the metabolic pathway with the L-Cysteine, L-Valine and a-Aminoadipic Acid (AAA) as the initial substrates, which can form together Tripeptide ACV (a-a-aminoadipyl- L-cysteinyl-D valine). The further cyclisation reaction of Tripeptide ACV to Isopenicillin N (IPN) is oxygen dependent. The following reactions can be done directly in one step or in two steps. In this second case the intermediate is the 6-Aminopenicillanic Acid (6-APA), with the precursors Phenylacetic Acid (PAA) for Penicillin G or Phenoxyacetic Acid (POA) for Penicillin V, to be incorporated into the Penicillin molecule during the last step. It is also possible in parallel with Penicillin G and Penicillin V formation that 6-APA is alternatively carboxylated with CO2 to form 8-HPA (8-hydroxy-Penicillinic Acid).The model for Penicillin V biosynthesis is presented in Table 5.

The parameters values from the above model were determined in a fed-batch bioprocess; it was found that the IPNS enzyme is metabolic flux limiting and further on the ACVS enzyme. As the IPN formation from Tripeptide ACV is dependent on the O2 concentration, the dissolved oxygen concentration superior to 45% from the saturation can increase productivity.

3. The segregated models [12, 13] can describe more complex phenomena like: alterations or disturbances in the physiology and cell metabolism; cells ‘morphological differentiation; genome mutations; spatial segregations of growth regions; cells aggregation; mixed cultures (including the competition between two or more species for the same substrate). On the contrary the unstructured and structured models have the limit to consider a homogenous population of cells and only one species in the bioreactor. The segregated models can be built by using ordinary differential equations to describe the behavior of several classes of independent/correlated cells. Each cell class behavior can be described by both unstructured and structured models.