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Flux-Variability Analysis for Optimization


What is Metabolic Flux Analysis?

Metabolic Flux balance analysis (FBA) is an application of linear programming to metabolic network that uses the stoichiometric coefficients for each reaction in the system as the set of constraints for the optimization. Simply, it is a mathematical method for analyzing metabolism. This analysis requires the Steady State Assumption, which is, in chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. In addition, Flux Variability Analysis (FVA) is an extension of Flux balance analysis. FVA determines the ranges of fluxes that correspond to an optimal solution determined through FBA. Hence, FBA is able to calculate the full range of numerical values for each reaction flux within the network.

What are the constraints in model?

Networks can be encoded as stoichiometric matrices (S), in which each row represents a unique metabolite and each column represents a biochemical reaction. The entries in each column of this matrix are the stoichiometric coefficients of the metabolites in the reaction. Metabolites are consumed have a negative coefficient and metabolites that are produced have a positive coefficient. Since most reactions involve only a few metabolites, S is a sparse matrix. The size of S is m*n for a network with m metabolites and n reactions.

Why use Flux Variability Analysis?

Biological systems often contain redundancies that contribute to their robustness. However, flux balance analysis only returns a single flux distribution that corresponds to maximal growth under given growth conditions regardless alternate optimal solutions may exist. FVA is capable to exanimate these redundancies by calculating the full range of numerical values for each reaction flux in a network. Consequently, FVA can be employed to study the entire range of achievable cellular functions as well as the redundancy in optimal phenotypes.


What is it modeling?

It models flux rate of metabolic pathways responding to different growth media conditions. The model is expected to generate an optimal set of metabolites that should be added to growth media in order to improve production rate.

Why needs this kind of model?

Same as chemical reactions need optimal environmental conditions to achieve maximum production rate, microbes also require optimized growth conditions to accomplish their tasks in maximum speed. In industrial scale, the optimal conditions for chemical reactions could increase the production rate in hundreds times which means millions of money. This principle also works even if taking biology pathways over chemical reactions. The difference is that in chemical way, the conditions of enzyme, pH, temperature and pressure are more important; however, in microbiological method, the conditions of growth media is more crucial. Further, the selection of media compounds is one of the most significant conditions for growth media. If a model can predict an optimal set of metabolites that need to be added into media, there will be tons of time and lots of money got saved.

How dose the program work?

This program is built upon constraint-based reconstruction analysis and flux variability analysis. It uses published E.coli (iAF1260) and E.coli core models as base chassis. Upon those models, we reconstruct new models of interests. Specifically, new reactions corresponding to the genes we try to engineer into E.coli from other organisms will be added into base chassis. By running flux variability analysis, program will give different sets of flux rates based on distinct constraints. Finally, the program will analysis those data with designed algorithm to generate a set of media compounds that is expected to accelerate production rate.



Generally, biomass rate reflects the growth condition and production rate is the goal. Cell must be well alive to yield products. However, cellular system may involve trade-offs between growth and production. This implies among all possible set of fluxes, the optimal flux set should locate a place where growth rate multiplies production rate is maximum.

By doing above, the optimal flux rate of biomass is determined and set this biomass rate be the biological objective. Then flux variability analysis will find out full range (from min to max) of numerical values for each reaction flux within the network that satisfy the optimal biomass. Obviously, the set of fluxes with maximum and minimum production rate are generated. Now, the question is how to drive the minimum product flux rate to maximum. As all the values are numerical, one of the possible solutions could be comparing two sets of fluxes, determining differences of each reaction between two sets and changing constraints of reactions. Though turning constraints, cell may choose alternative pathways so that possibly could improve the output of products.


Precondition: The original model is built with glucose minimum media.

1. Determine the relationship between growth rate and production rate

2. Find out the optimal growth rate that can maximize the production rate

3. Examine differences between max fluxes and mix fluxes for each reaction.

4. Collect all reactions that have differences exceed a certain threshold.

5. Score each compound in all reactions. Compound with positive values means extra amount needed and vice verse.

6. For each compounds with positive score:

If a compound can be up-taken by cell and the original media has no such compound or insufficient

Add this compound to list as candidates

Change constrains of this reaction

7. Test each candidate. If the novel model improves the output (growth rate * production rate) compared to original model, label as effector and display




Source Code