Metabolic Flux Analysis (MFA) models are true linear m odels. As such they also have a number of associated limitations as mentioned above. However, they can generally take into account much larger biochem ical systems than any com peting method. Metabolic pathways describing 50 reactions or more can with ease be m odelled using MFA methods. Attempting to model the same large network in a kinetic model would almost certainly be impossible. Not only is it unlikely that so much kinetic information would be available, but it would also require computer power on a level not generally available.
It is recognised that metabolic fluxes are key variables, which must be determined in order to understand metabolic regulation and flux patterns. However, the direct measurement o f internal metabolic fluxes is complicated. Alternatively, the analysis of the stoichiometry o f the metabolic pathways can provide significant information on cellular metabolism and the overall distribution o f carbon flow among various metabolic reactions. Provided the metabolic routes of the pathway are known, and data on the carbon inputs and outputs can be obtained, the internal metabolic fluxes (mmol/g/hr) may be calculated using linear algebra methods.
In MFA studies, a quasi steady state o f the biochemical pathway being investigated is assumed. This quasi steady state assumes that the intermediate metabolite concentrations are constant at all times. The steady state balance equation is given by:
S -v = b
Eq. 4-36
where S is the stoichiometric matrix of the metabolic network, v is the vector o f reaction fluxes and b is the net accumulation rate vector. For all the internal metabolites the value of b will be zero, as no accumulation is taking place. The mathematical methods involved are covered in more detail in chapters 8 to 1 0.
MFA is most commonly used to investigate central metabolic pathways of bacterial metabolism. This is due to the fact that the inputs and outputs o f this system are readily obtainable. The inputs are defined as the substrate fluxes into the system, and the outputs are defined as and metabolic products and biomass precursor monomers leaving the pathway to be incorporated into new cell material.
MFA techniques can be used to investigate metabolic control and flux patterns in a number of ways. The most com m on approach is to measure enough inputs and outputs o f a system to be able to use a fully determined matrix system in order to calculate the internal fluxes. However M FA studies can also be carried out using optimisation criteria where the inputs and outputs o f the system have not been fully defined (Savinell and Palsson, 1992a,b; Varma and Palsson, 1995).
A good example o f a fully determined MFA study is the one carried out by Jdrgensen et al. (1995). The group developed a metabolic MFA model for Penicillium chrysogenum
during fed-batch cultivations. The stoichiometric model considered 61 internal fluxes and 49 intracellular metabolites. In addition, the model considered the uptake o f 21 amino acids. Uptake rates o f various substrates and the synthesis rates of RNA/DNA, protein, lipid, carbohydrate and amino carbohydrate during fed-batch cultivation were measured. From these measurements and the stoichiometric model the metabolic fluxes where calculated. Calculation showed that penicillin formation was accompanied by a
large flux through the pentose phosphate pathway due to a large requirement for NADPH used in the biosynthesis o f cystein, a precursor o f penicillin.
MFA modelling can be optimised subject to certain constraints, to explain certain physiological phenomenon. In constrained optimisation, certain values in the v vector are fixed or maximised. For constrained optimisation calculations a fully determined matrix system is not required. Majewski and Domach (1990) developed a MFA model based on simple constrained optimisation view o f acetate overflow in E. coli. The problem was formulated in terms o f a network flow that has as its objective to maximise ATP synthesis. It was found that switching to acetate overflow could be predicted when loads were imposed and flux constraints existed either at the level o f NADH turnover rate or the activity o f a key TCA cycle enzyme. These results correlated well with experimental results showing that aerobic production o f acetate by E. coli commenced after a critical growth rate had been exceeded. Other M FA models with constraints showed similar results (Ko et al., 1993 and Ko et al.} 1994). This gives credibility to the modelling technique.
MFA studies may aid in the investigation o f metabolic networks, identifying which metabolic pathways are present in the organism under investigation. Lysine production in Corynebacterium glutamicum has been extensively studied using MFA techniques. Vallino and Stephanopoulos (1993, 1996a,b) studied this system using MFA techniques, fermentation studies and intracellular assays. They found that the glyoxylate shunt was inactive and that the only anaplerotic reaction expressed in C. glutamicum cultivated on glucose minimal media was via phosphoenolpyruvate carboxylase (PPC). The pentose phosphate pathway was also found to support significant fluxes.
Finding the limits o f substrate-to-product conversion is a definite goal in metabolic engineering. MFA studies can aid in the identification o f maximum possible product yields. Varma et al. (1993) used a flux balance approach to study the biosynthesis of 20 amino acids and 4 nucleotides as biochemical products in E. coli. Growth was defined as a balanced drain on the metabolite pools corresponding to the cellular composition. Activities such as gradient maintenance, regulatory functions and protein turnover were accounted for by including a maintenance energy loss in the metabolic network. Optimal biomass generation was shown to decrease in a linear manner with increasing product
formation. In som e cases, synergy between biochemical production and growth was observed, leading to an increased overall carbon conversion.
The recognition o f metabolic bottlenecks is also important in metabolic engineering. Again, MFA studies can be used with good results. Goel et a l (1993) investigated the glycolytic and TCA cycle fluxes in Bacillus subtilis. It was found that the TCA flux was significantly lower compared to the glycolytic activity in batch cultures. Hence, a possible metabolic bottleneck was identified.
Quantitative prediction of metabolic by-product secretion can also be obtained from MFA models. Varma and Palsson (1994) determined various strain specific parameters of wild type E. coli, including maximum oxygen utilisation rate, maximum aerobic and anaerobic glucose utilisation rate, non-growth associated maintenance requirements and growth associated maintenance requirements. The flux balance models specified by these parameters were found to quantitatively predict glucose and oxygen uptake rates as well as acetate secretion rates observed in chemostat experiments. The model predictions were further shown to be consistent with stoichiometrically optimal pathway utilisation as verified by experiments.
As can be appreciated from the examples described above, M FA is an extremely useful approach when the system o f investigation is large and kinetic information is unavailable for all or many o f the reactions. It is probably the best available approach to take if attempting to understand key features o f metabolic physiology. An established model can serve as a virtual research tool for investigating feeding strategies, introduction o f new pathways or “deletion” o f existing pathways.