## 6 Metabolic Flux Analysis
### Flux Balance Analysis  
FBA is basically a constraint-based optimization method that is used for simulating different kinds of possible rete of reactions [139; 140]. This approach initiates with the creation of a stoichiometric matrix S that has all the existing information related to the  
Figure 6: Different MFA approaches. (**A**) Standard stoichiometric MFA, (**B**) flux balance analysis (FBA), (**C**) \({}^{13}\)C-MFA.  
stoichiometry of the metabolic network. At first, the network is expected to be in a quasi-steady state, i.e., S.v = 0. Here v represents the fluxes over every reaction. By the application of lower and upper limits, the directionality and capacity necessities of the reactions are defined. Generally, in a constraint-based model with various resolutions regarding the distributions of flux, the system is underdetermined. The enhancement of biomass production is defined by an optimized objective function. A standard FBA design is categorized by various equivalents and provides solutions that are optimally non-unique to the problem. It also enhances particular objective functions related to its stoichiometric limitation with required lower and upper limits of the system fluxes. FBA attempts to maximize or minimize the objective function \(Z=c^{\mathrm{T}}\mathrm{v}\), which could be any linear mix of fluxes, where c denotes the vector of weights and recommends the contribution of each reaction to the total objective function. Hence, FBA is the method of elucidating the equation S.v = 0 with the help of linear programming. Here a linear combination of fluxes has been established as the objective function and the lower as well as upper limits of v have been provided. The output of FBA signifies a certain flux distribution (v), which maximizes or minimizes the objective function [141].  
The mass balance limitations as well as the objective function are applied in this approach, and here the biomass maximization or yield of ATP is primarily regarded as the objective function. Meanwhile, it is possible to estimate the interested compound's maximum yield by considering the maximization of the target production rate as the objective function. The FBA method does not analyze any single tiny pathway; rather, it focuses on the total metabolic network across the genome, like central carbon metabolism. This approach has the capability of analyzing the pathway data even in the absence of enzyme kinetics information. FBA is one of the more powerful methods to solve the underdetermined systems, but still there are a few setbacks. One of the major setbacks is the identification of an appropriate objective function, and it is a cautious concern. In the prediction of one gene-deleted mutant, it is uncertain how to choose a single objective function for enhancing the biomass yield. To resolve these issues of designing gene-deletion mutants, advanced FBA methods like Regulatory on/off Minimization [142] as well as Minimization of Metabolic Adjustment [142] are being used. The predictions as well as flux determination are less accurate, as all of the approaches are dependent on assumptions only. Hence, to obtain highly reliable fluxes, 13C labelling approaches have been employed [143].