Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network. This primer covers the theoretical basis of the approach, several practical examples and a software toolbox for performing the calculations. Flux balance analysis FBA is a widely used approach for studying biochemical networks, in particular the genome-scale metabolic network reconstructions that have been built in the past decade 1 , 2 , 3 , 4.
These network reconstructions contain all of the known metabolic reactions in an organism and the genes that encode each enzyme. FBA calculates the flow of metabolites through this metabolic network, thereby making it possible to predict the growth rate of an organism or the rate of production of a biotechnologically important metabolite.
Duarte, N. USA , — Feist, A. Article Google Scholar. Oberhardt, M. Thiele, I. Durot, M. FEMS Microbiol. Covert, M. Trends Biochem. Edwards, J. Price, N. Becker, S. Orth, J. Karp, P. Google Scholar. Varma, A. Mahadevan, R. Lee, S. Reed, J. Kumar, V. PLoS Comput. Satish Kumar, V. BMC Bioinformatics 8 , Once all the internal and transport reactions are identified, dynamic mass balance equations for all This is a preview of subscription content, log in to check access.
J Biol Chem 31 — M PubMed Google Scholar. Nature — PubMed Google Scholar. Raman K, Chandra N Flux balance analysis of biological systems: applications and challenges. Brief Bioinform 10 4 — Flux balance models of metabolic pathways enable the simulation of systems under varying experimental conditions.
Such models have value in a variety of applications, such as optimization of bio-processes in industries, identification of drug targets and an improved annotation of genomes. GSMNs have been constructed and analysed using FBA, for various organisms in the past, including bacteria, archaea and eukaryotes. Reconstructions of human metabolism have also been reported [ 43 , 44 ]. Table 2 summarizes some examples of the available studies on GSMNs, indicating the organism studied as well as the major insights obtained.
GSMNs can also be readily subjected to a wide array of analyses. Large-scale gene deletion studies for organisms such as S. GSMNs thus have a wide range of applications, from improving the understanding of microbial metabolism and the capabilities of a metabolic network for metabolic engineering applications , to insights obtained from gene deletion analyses, which can be applied for the identification of potential drug targets, in case of pathogenic organisms [ 32 , 46 ].
With the availability of high-throughput transcriptomics data, which can be integrated with GSMNs and analysed using techniques such as rFBA, better predictions of metabolic capabilities and phenotypes will be possible. It is possible to derive further insights from reconstructed networks, by an examination of their structure and topology based on convex analysis.
Methods such as elementary flux mode analysis [ 47 ] and extreme pathway analysis [ 48 ] have been in vogue for analysing large metabolic networks and have been reviewed elsewhere [ 49 ]. It is easy to envisage applications for flux coupling analyses in metabolic reconstruction refinement , as well as for detailed analyses of reconstructed networks.
In silico gene deletion studies help in identifying those enzymes in a metabolic network, which when deleted, adversely affects the fluxes across the entire network. Joyce and Palsson have given a good overview of using genome-scale in silico models to evaluate gene essentiality [ 51 ]. Gene deletions that are lethal can serve as a first list of putative drug targets, which can be further characterized by sequence analyses and structural studies. We have earlier constructed a model of mycolic acid biosynthesis in M.
Desaturases illustrate examples of such potential drug targets, whose prediction is strengthened by different types of computational target identification approaches [ 52 , 53 ] and by an experimental study that revealed potent anti-mycobacterial activity by two lead compounds NAS and NAS, owing in part to their ability to inhibit mycolic acid biosynthesis [ 54 ].
In a separate study, hard-coupled reaction sets in the genome-scale reconstruction of M. The hard-coupled reaction sets mapped to several known drug targets, as well as potential targets from processes such as mycolic acid biosynthesis, mycothiol synthesis and menaquinone synthesis. Beste et al. Papin and co-workers have reported a reconstruction of Pseudomonas putida [ 55 ], an organism that has a proven potential in environmental and industrial biotechnological applications due to its metabolic versatility, stress resistance and amenability to genetic modifications.
They have used FBA and flux variability analysis to analyse the potential of the metabolic network of the organism, as well as identifying key parameters such as growth yield, network robustness and gene essentiality. By validating the model with data from experimental cell cultures, the authors have provided a valuable framework for biotechnological applications using P.
An excellent application of systems biology in metabolic engineering, with commercial potential, has been illustrated by Stephanopoulos and co-workers, for improving lysine production in a strain of Corynebacterium glutamicum , by the coordinated over expression of two genes, encoding pyruvate carboxylase and aspartate kinase [ 9 , 56 ].
Stephanopoulos and co-workers have also reported a genome-wide FBA of E. Targets identified using this model improve product synthesis on the basis of increased availability of metabolic precursors and cofactor balancing. The study of metabolic networks through FBA also finds application in the refinement of the knowledge on metabolism of an organism, as well as the reconciliation of conflicting knowledge in the literature. Palsson and co-workers have proposed an optimization-based algorithm to predict the missing reactions required to reconcile disagreements between reconstructed metabolic networks and experiment [ 57 ].
A systematic network analysis has a potential to identify and potentially resolve gaps in the knowledge of metabolic networks.
Palsson and co-workers have described the analysis of an integrated model of metabolism and transcriptional regulation in S. By identifying the discrepancies between predicted growth phenotypes and experimentally observed phenotypes, which arise from missing regulatory effects in the model, they have shown that it is possible to investigate novel regulatory mechanisms. This study also highlights how modelling can direct experimentation.
In general, the solution obtained by FBA is only as good as the constraints used to build the model [ 13 ]. Therefore, it is very important to invest a lot of time and effort in a quality reconstruction of metabolic networks, including the selection of constraints. It has been shown, for the genome-scale metabolic reconstruction of P.
FBA suffers from incomplete annotation of the proteins in a genome, although it can provide clues to enhance the current knowledge. Furthermore, FBA focuses only on part of the entire genome of an organism, involving mostly enzymes, which catalyse the various metabolic reactions in the cell.
Due to the incomplete nature of annotation, several reactions may appear to have zero fluxes from FBA, since the reactions involving metabolites, downstream or upstream from these reactions may not have been characterized metabolic gaps. Most reconstructions rely fundamentally on the availability of genome sequences and annotations.
For organisms with low sequence homology to other organisms, such as Plasmodium falciparum , automated reconstructions generally result in highly incomplete GSMNs [ 5 ]. Furthermore, many organisms have unique pathways, for example, the mycolic acid pathway in M. A detailed account of the challenges in the reconstruction of parasitic metabolic networks has been discussed in [ 59 ].
One of the major challenges for FBA is the definition of a biologically relevant objective function. While the maximization of biomass production has been commonly used as an objective function in the genome-scale reconstructions of several prokaryotes, phenotypes may be more accurately predicted with more biologically relevant functions, particularly in case of higher organisms. A recent approach towards resolving the problem of selecting a suitable objective function is a framework proposed by Papin and co-workers, known as the Biological Objective Solution Search BOSS [ 60 ].
In this framework, the biological objective is a new stoichiometric reaction added to the stoichiometric matrix, which is not confined to be a subset of the existing reactions. This reaction is added to the existing constraints and optimized, also minimizing the difference between the resulting flux distribution and available experimental data. While the method provides a useful approach to discriminate between objective functions, it also emphasizes the need for experimental flux data, which is required to compare predictions using different objective functions.
It must be emphasized here, that a synergy between in silico simulations and biochemical experiments can indeed help in multiple ways to synthesize better models of metabolic networks. The choice of objective function cannot be made independent of the conditions of simulation; for instance, it would not be reasonable to use a biomass maximization function to accurately predict the fluxes for an organism that is grown under starvation of nutrients.
Sauer and co-workers have illustrated for E. Thus, the choice of objective function is quite important in the context of FBA, and it is important to choose a biologically relevant objective function. Improvement in methodology is required in two ways: first, the identification of an appropriate objective function and second, the description the chosen function at high resolution, which may require detailed large-scale quantitative experimentation under various conditions.
The importance of integration with experimental data has already been emphasized in previous sections. With the advance in high-throughput techniques for estimating metabolomic data, it is possible to generate large amounts of data for use in FBA models; FBA can benefit from metabolomic measurements, which could aid in identifying more constraints. Furthermore, FBA can also cope with the uncertainty and incompleteness in metabolomic data, since it allows for the incorporation of partial metabolic information [ 62 ].
With the advances in high-throughput 13 C flux analysis [ 63 , 64 ], which can be applied at a genome-scale to estimate intracellular fluxes [ 65 , 66 ], it is possible to generate more data for hypothesis validation, improving constraints in FBA models, as well as to aid in the choice of objective functions. The availability of genome-scale transcriptomics data can be advantageous in the integrated reconstruction of metabolic and regulatory networks. The complexity of biological function arises from the concerted interplay between metabolism, regulation and signal transduction.
However, till recently, most models of biological networks have focussed only on one of these networks, rather than analysing the complexity in its entirety. Papin and co-workers have proposed an FBA—based strategy, referred to as integrated dynamic FBA idFBA , that dynamically simulates cellular phenotypes arising from integrated networks [ 68 ].
The idFBA framework requires an integrated stoichiometric reconstruction of signalling, metabolic, and regulatory processes. A major challenge for such an integration is the fact that the various processes operate on vastly different time-scales. Time is discretized into small steps; at each step, an FBA is performed.
An incidence matrix is computed, which keeps track of which of the R s reactions are to be included at a particular time-step t of t N , thereby accounting for the difference in time scales for the reactions.
Based on the computed flux, the constraints and the incidence matrix for the next time-step are updated. The choice of objective function for such an integrated system is also important; idFBA utilizes BOSS [ 60 ] described earlier to identify objectives for the integrated system. The authors have shown the utility of idFBA for analysing a portion of the high-osmolarity glycerol response pathway in S. It appears that idFBA might serve to improve the accuracy and versatility of constraint-based analyses, at the same time avoiding the stringent requirements of kinetic parameters and detailed mechanisms, imposed by kinetic models.
Covert and co-workers have proposed another method to simultaneously model the metabolic, regulatory and signal transduction networks, by integrating FBA with regulatory Boolean logic and ordinary differential equations for describing signal transduction [ 69 ].
This approach is an improvement over rFBA in that the kinetic description is much more detailed; a dynamic picture of the system is obtained, rather than just the final steady state that would be obtained using rFBA.
Furthermore, certain enzymes, which would never be part of a strictly optimal growth scenario, are expressed and active since they are utilized for important functions such as signal transduction, though not for their metabolic contribution to growth. Such methods provide interesting extensions to the well-established FBA paradigm, giving a greater impetus towards accurate prediction of phenotypes from models of biological networks.
More accurate predictions from biological networks can be obtained only by an integration of models of metabolism, regulation and signal transduction. Although it may be very desirable to have genome-scale mechanistic models of microbial systems, the lack of available metabolomic data and thermodynamic quantities has rendered the probability of achieving cell-scale kinetic models quite low [ 71 ].
Constraint-based models, particularly those using FBA, have filled in the void admirably, enabling analysis of several large systems, including entire GSMNs for prokaryotes [ 32 , 55 , 72—75 ], eukaryotes [ 10 , 76 , 76 ] and even the human [ 43 , 44 ], with wide-ranging applications from metabolic engineering [ 8 , 55 , 56 ] to drug discovery [ 11 ].
The potential of FBA for addressing several biological problems is now well-established, as evident from the number of reports in literature Table 2. The stage seems all set to realize the promise in obtaining biological insights of chosen sets of proteins, in a systematic manner.
However, several challenges remain in the construction and analysis of constraint-based models, particularly in terms of the accurate definition of the metabolic network, the various constraints, as well as the definition of biologically relevant objective functions. It is very likely that constraint-based models will continue to grow in popularity and a wide spectrum of objective functions for analysis, with increasing biological relevance, will be used to enable various types of predictions on the capabilities of metabolic networks.
There have already been interesting advances in the area of FBA, with the integration of regulatory information as well as signalling networks into the metabolic models. The integration of various types of models—kinetic, constraint-based and topological—to draw conclusions at various levels is another exciting challenge ahead of modelling in systems biology, which holds the key to many of the varied applications of systems biology.
Flux balance analysis FBA is a powerful tool for the constraint-based analyses of genome-scale metabolic networks, to identify steady state flux distributions and metabolic capabilities of biochemical networks. The critical steps in FBA are the reconstruction of a metabolic network, followed by mass balance, imposition of constraints, choice of a suitable biologically relevant objective function and linear optimization.
FBA is highly versatile and various recent extensions to FBA such as the rFBA, iFBA and idFBA, to account for the interdependence of metabolic networks on transcriptional regulatory networks and signal transduction networks, have empowered FBA to make better in silico predictions on the phenotypes of biological systems. Google Scholar. Google Preview. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.
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