Flux balance analysis

FBA finds applications in bioprocess engineering to systematically identify modifications to the metabolic networks of microbes used in fermentation processes that improve product yields of industrially important chemicals such as ethanol and succinic acid.

[2] It has also been used for the identification of putative drug targets in cancer [3] and pathogens,[4] rational design of culture media,[5] and host–pathogen interactions.

At steady state, metabolite concentrations remain constant as the rates of production and consumption are balanced, resulting in no net change over time.

To obtain a single solution, the flux that maximizes a reaction of interest, such as biomass or ATP production, is selected.

FBA is not computationally intensive, taking on the order of seconds to calculate optimal fluxes for biomass production for a typical network (around 10,000 reactions).

This means that the effect of deleting reactions from the network and/or changing flux constraints can be sensibly modelled on a single computer.

The utility of reaction inhibition and deletion analyses becomes most apparent if a gene-protein-reaction matrix has been assembled for the network being studied with FBA.

PhPP involves applying FBA repeatedly on the model while co-varying the nutrient uptake constraints and observing the value of the objective function (or by-product fluxes).

PhPP makes it possible to find the optimal combination of nutrients that favor a particular phenotype or a mode of metabolism resulting in higher growth rates or secretion of industrially useful by-products.

To understand key factors in this system; a multi-scale, dynamic flux-balance analysis is proposed as FBA is classified as less computationally intensive.

[12] In contrast to the traditionally followed approach of metabolic modeling using coupled ordinary differential equations, flux balance analysis requires very little information in terms of the enzyme kinetic parameters and concentration of metabolites in the system.

The steady-state assumption reduces the system to a set of linear equations, which is then solved to find a flux distribution that satisfies the steady-state condition subject to the stoichiometry constraints while maximizing the value of a pseudo-reaction (the objective function) representing the conversion of biomass precursors into biomass.

The steady-state assumption dates to the ideas of material balance developed to model the growth of microbial cells in fermenters in bioprocess engineering.

During microbial growth, a substrate consisting of a complex mixture of carbon, hydrogen, oxygen and nitrogen sources along with trace elements are consumed to generate biomass.

These rates can be experimentally determined to constrain and improve the predictive accuracy of the model even further or they can be specified to an arbitrarily high value indicating no constraint on the flux through the reaction.

A notable example of the success of FBA is the ability to accurately predict the growth rate of the prokaryote E. coli when cultured in different conditions.

The model itself can be experimentally verified by cultivating organisms using a chemostat or similar tools to ensure that nutrient concentrations are held constant.

This typically means that extensive manual curation is required, making the preparation of a metabolic network for flux-balance analysis a process that can take months or years.

Software packages for creation of FBA models include: Pathway Tools/MetaFlux,[19][20] Simpheny,[21][22] MetNetMaker,[23] COBRApy,[24] CarveMe,[25] MIOM,[26] or COBREXA.jl.

[27] Generally models are created in BioPAX or SBML format so that further analysis or visualization can take place in other software although this is not a requirement.

A key part of FBA is the ability to add constraints to the flux rates of reactions within networks, forcing them to stay within a range of selected values.

This provides a secondary method of making sure that the simulated metabolism has experimentally verified properties rather than just mathematically acceptable ones.

Constrained FBA-ready metabolic models can be analyzed using software such as the COBRA toolbox[28] (available implementations in MATLAB and Python), SurreyFBA,[29] or the web-based FAME.

[32] An open-source alternative is available in the R (programming language) as the packages abcdeFBA or sybil[33] for performing FBA and other constraint based modeling techniques.

that maximises the flux through a biomass function composed of the constituent metabolites of the organism placed into the stoichiometric matrix and denoted

In the more general case any reaction can be defined and added to the biomass function with either the condition that it be maximised or minimised if a single “optimal” solution is desired.

can be introduced, which defines the weighted set of reactions that the linear programming model should aim to maximise or minimise, In the case of there being only a single separate biomass function/reaction within the stoichiometric matrix

The analysis of the null space of matrices is implemented in software packages specialized for matrix operations such as Matlab and Octave.

[35] FBA avoids this impediment by applying the homeostatic assumption, which is a reasonably approximate description of biological systems.

Unlike dynamic metabolic simulation, FBA assumes that the internal concentration of metabolites within a system stays constant over time and thus is unable to provide anything other than steady-state solutions.

The results of FBA on a prepared metabolic network of the top six reactions of glycolysis . The predicted flux through each reaction is proportional to the width of the line. Objective function in red, constraints on alpha-D-glucose and beta-D-glucose import represented as red bars. [ 1 ]
An example of a non lethal gene deletion in a sample metabolic network with fluxes shown by the weight of the reaction lines as calculated by FBA. Here the flux through the objective function is halved but is still present. [ 1 ]
An example of a lethal gene deletion in a sample metabolic network with fluxes shown by the weight of the reaction lines as calculated by FBA. Here there is no flux through the objective function, simulating that the pathway is no longer functional. [ 1 ]
Reaction inhibition: Plot of FBA predicted growth rate (y-axis) to decreasing influx of Oxygen (x-axis) in an E.coli FBA model. [ citation needed ]
A 3-D Phenotypic Phase Plane showing the effect of varying glucose and glycerol input fluxes on the growth rate of Mycobacterium tuberculosis. The X axis represents glycerol influx and the Y axis represents glucose influx, the height of the surface (red) represents the value of the growth flux for each combination of the input fluxes. [ citation needed ]
A levelplot version of the Phenotypic Phase Plane showing the effect of varying glucose and glycerol input fluxes on the growth rate of Mycobacterium tuberculosis. The X axis represents glycerol influx and the Y axis represents glucose influx, the color represents the value of the growth flux. [ citation needed ]
Comparison of correlation plots of lethal Pairwise reaction deletions across different subsystems for E.coli(left) and M.tuberculosis(right). [ citation needed ]
The first six reactions in Glycolysis prepared for FBA through the addition of an objective function (red) and the import and export of nutrients (ATP, ADP, BDG, ADG) across the system boundary (dashed green line). [ 1 ]
Visual and numerical representation of FVA on a complete network. [ 1 ]
Visual and numerical representation of FVA on a network with non-lethal deletion. [ 1 ]