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Partial inhibition and bilevel optimization in flux balance analysis.

Facchetti G, Altafini C - BMC Bioinformatics (2013)

Bottom Line: In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used.The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism.This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

View Article: PubMed Central - HTML - PubMed

Affiliation: SISSA (International School for Advanced Studies) Functional Analysis Dept, - Via Bonomea 265 - 34136, Trieste, Italy. altafini@sissa.it.

ABSTRACT

Motivation: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.

Results: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.

Conclusions: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

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Constructing the inhibition h from the experimental dose-response curve: an example. The points of the curve are hypothetical experimental measurements of the effect of the drug on the activity of the enzyme. The discretization of the curve can be used as basis for the discretization of the interval [0,1]: therefore, referring to (10), we may define hk = 0.10xk,0 + 0.15xk,1 + 0.50xk,2 + 0.15xk,3 + 0.10xk,4.
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Figure 1: Constructing the inhibition h from the experimental dose-response curve: an example. The points of the curve are hypothetical experimental measurements of the effect of the drug on the activity of the enzyme. The discretization of the curve can be used as basis for the discretization of the interval [0,1]: therefore, referring to (10), we may define hk = 0.10xk,0 + 0.15xk,1 + 0.50xk,2 + 0.15xk,3 + 0.10xk,4.

Mentions: Notice that any "representation" of partial inhibition values can be used in place of (9). Let us imagine, for instance, that we would like hk to have the same values obtained in the dose-response experiments for the determination of the half maximal inhibitory concentration (IC50) of drug k (see Figure1):


Partial inhibition and bilevel optimization in flux balance analysis.

Facchetti G, Altafini C - BMC Bioinformatics (2013)

Constructing the inhibition h from the experimental dose-response curve: an example. The points of the curve are hypothetical experimental measurements of the effect of the drug on the activity of the enzyme. The discretization of the curve can be used as basis for the discretization of the interval [0,1]: therefore, referring to (10), we may define hk = 0.10xk,0 + 0.15xk,1 + 0.50xk,2 + 0.15xk,3 + 0.10xk,4.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4219332&req=5

Figure 1: Constructing the inhibition h from the experimental dose-response curve: an example. The points of the curve are hypothetical experimental measurements of the effect of the drug on the activity of the enzyme. The discretization of the curve can be used as basis for the discretization of the interval [0,1]: therefore, referring to (10), we may define hk = 0.10xk,0 + 0.15xk,1 + 0.50xk,2 + 0.15xk,3 + 0.10xk,4.
Mentions: Notice that any "representation" of partial inhibition values can be used in place of (9). Let us imagine, for instance, that we would like hk to have the same values obtained in the dose-response experiments for the determination of the half maximal inhibitory concentration (IC50) of drug k (see Figure1):

Bottom Line: In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used.The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism.This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

View Article: PubMed Central - HTML - PubMed

Affiliation: SISSA (International School for Advanced Studies) Functional Analysis Dept, - Via Bonomea 265 - 34136, Trieste, Italy. altafini@sissa.it.

ABSTRACT

Motivation: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.

Results: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.

Conclusions: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

Show MeSH
Related in: MedlinePlus