The most sophisticated modeling tool is that introduced by the metabolic engineering. This approach relies upon the concept of metabolic pathways as sequences of specific enzyme — catalyzed reaction steps converting substrates into cells’ products. The manipulation of metabolic pathways to improve the cellular properties and especially the yield or the productivity of some important metabolites is of interest. So the metabolic engineering is recently developed with the purpose of generating information for the oriented modification of the enzymatic, regulatory or transport activities of the cells. The information will be used to build upgraded cells by the further application of the recombinant DNA technology.

The determination and the correct interpretation of the structure and the control mechanisms of metabolic networks are the first critical tasks of the metabolic engineering in order to fulfill the goal of rational pathway manipulation [14]. The main accent is towards considering the metabolic network as a whole and not the individual reactions. Due to the increased complexity of these networks and of the corresponding regulatory mechanisms the physiological state (metabolic steps characteristics at specific genetic and environmental conditions) of the cells is determined by the in vivo metabolic fluxes and their control.

The flux can be defined as the rate of material processing through a whole metabolic pathway. The value of the flux does not introduce information about the activity of the enzymes from the considered pathway, but it represents only their contribution regarding the substrate conversion into the final metabolite of this pathway.

The quantification of the metabolic fluxes is the principal objective realized by the techniques of Metabolic Flux Analysis (MFA) [15]. Metabolite balancing is the first operation in the determination of fluxes, done with the major hypothesis that the intracellular fluxes can be evaluated by measuring the extracellular fluxes. The metabolite balancing is performed by using a stoichiometric model for the intracellular reactions and by applying a mass balance around each intracellular metabolite, without any enzyme kinetic information. The general defining relationship is of matrix form:

S ■ v = r (29)

where: S=stoichiometric matrix of the metabolic network

v=vector of unknown fluxes

r=vector of measured metabolite extracellular concentrations, whereas the metabolite intracellular concentrations is 0.

The rows number is representing the number of metabolites in the pathway and the number of columns is equal to the unknown number of fluxes at steady state condition. The resulting system is normally underdetermined as the number of reactions is normally greater than the metabolite number. There are also various network structure characteristics (metabolic branch, reversible reactions, and metabolic cycles) that can increase the system degree of freedom.

So beside the metabolic balancing constraints additional constraints are needed to solve the equations system. If finally there are more constraints than the freedom degree, the system becomes over determined and redundant equations are to be used to test the consistency of the overall balances. The supplementary constraints can be obtained by using other information regarding the intracellular biochemistry and/or by applying others techniques

[15].

So, another tool to perform MFA is the Linear Programming (LP) [14, 16]. Conforming to this method the metabolic fluxes are determined by simultaneously accomplishing 2 conditions: to be in line with the metabolic balances constraints and to optimize a certain objective function. So it is to formulate the mathematical problem:

Minimize c ■ v = ^ cjvi

Subject to S ■ v = r (30)

where: c= vector of the weight factors of fluxes in the objective function.

The objective functions can be: maximize the metabolite production rate or cells’ growth rate; minimize the ATP production rate or substrate uptake rate; maximize growth rate for a given metabolite formation rate.

Another source of additional constraints is usually the introduction of certain types of supplementary measurements. The most useful tool of this type is the application of isotopic tracer methods. In isotopic tracer techniques there is a substrate in the cells labeled with an easily detectable isotope of a specific atom, normally 14C, but especially 13C , stable and non radioactive isotopes, to be detected by Nuclear Magnetic Resonance (NMR).

The isotope distribution among the metabolites from a network for a certain labeled substrate and known biochemistry is a function of the in vivo metabolic fluxes. This distribution can be obtained by studying the NMR spectra or by measuring the mass isotopomer (the molecules of the same metabolite, but with different labeling characteristics) distribution by Gas / Liquid Chromatography coupled with Mass Spectrometry (GC / LC-MS).

The general model for the determination of metabolic flux distribution is presented in the Fig. 2. The implementation of such flux quantification methods seems simple, but due to the high integrated networks complexity is rather an intensive computer application. There are now important studies of metabolic modeling used to improve the metabolite production in aerobic bioprocesses [17-22].