On the effects of phenotype prediction methods

over strain design algorithms. A Multi-objective approach.

Paulo Maiaa,b, Miguel Rochaa and Isabel Rochaa

a Centre of Biological Engineering, Department of Biological Engineering

University of Minho, 4710-057 Campus de Gualtar, Braga, Portugal. b SilicoLife - Computational Biology Solutions for the Life Sciences Rua do Canastreiro, 15, 4715-387 Braga, Portugal.

Abstract

The past two decades have witnessed great advances in the computational mod- eling and systems biology fields. Soon after the first models of metabolism were developed, several methods for the prediction of phenotypes were also put forward. With the ever-growing information provided by such methods, new questions arose. Metabolic Engineering in particular posed some interesting questions. Recently, Schuetz and co-workers proposed that the metabolism of bacteria operates close to the Pareto-optimal surface of a three-dimensional space defined by competing objectives and demonstrated the validity of their claims for various environmental perturbations [1].
However, phenotype prediction methods have all been developed to operate based on the assumption of a given single-objective, as an example Flux Balance Analysis (FBA) often assumes that the organisms are evolutionarily optimized towards opti- mal growth. On the other hand, Minimization of Metabolic Adjustment (MOMA) proposes that after a perturbation, the goal of the organisms shifts from optimal growth to the minimization of the global metabolic adjustment relative to the wild- type. Albeit multi-objective approaches focused on the bio-engineering objectives have been proposed [2, 3], none tackles the multi-objective nature of the cellular objectives.
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In this work we analyze the influence of sev- eral phenotype prediction methods on the strains designed by metaheuristic algorithms and sug- gest a multi-objective approach capable of find- ing designs compliant with the cellular objec- tives assumed by the various phenotype predic- tion methods.
Using a recent model of Escherichia coli K12 [4], we observed the effect of different phenotype prediction methods in the convergence of meta-
heuristic algorithms performing strain optimiza-

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generator LMOMA pFBA

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tion, evolving growth-coupled production mu- tants in aerobic and anaerobic conditions. A crit- ical analysis of the different mutant flux distri- butions was performed, and we concluded that, for a selected phenotype prediction method, the strain designs proposed by the optimization al- gorithms were generally not robust when another method was used to predict their phenotypes.

The example in Figure 1 shows the variation in the Biomass-product cK=o3 upled yield (BPCY)
of aerobically s0u.6 ccinate producing mutants with

pFBA LMOMA

Figure 1: Box-and-whiskers plot for the succinate productive strains using glucose as carbon source.

K=4

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glucose as carbon source, when solutionpFsBA;gLMeOnMAer- ated with eithe0r.4 pFBA (a variation of FBA that minimizes the overall use of enzyme-a1ssociated

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generator

pFBA; LMOMA

cluster

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2

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flux [5]) or LMOMA (a linear implemen3tation of
MOMA [6]) (box colors) are simulated with the other (x-axis). Be0.s0 ide0s.2 the0.4gre0a.6t va0.r8 iation in fit-

BPCY â?? pFBA(m m o l â?? g D W â??1 â?? h â??1)

ness for the different phenotype simulation meth-

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BPCY â?? pFBA(m m o l â?? g D W â??1 â?? h â??1)

ods, we verified that in soKm=5e cases less than 10%

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Figure 2:

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K=S6 catter plot of the

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of the solutions generated by pFBA agerneratvoralid in

Assumptions regarding the cellular o1bjectives of an organism when subjected to distinct condi-

designs generated usingtphFBeA; LMdOeM-A

y-axis represent the BP1CY of the solutions calculated fro3 m the

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tions (environmental, genetic, etc.)
are4 still the

pFBA and LMOMA flux di5stribu-

object of active discussion. This fact motivated
us to develop a m0e.0tho0d.2 cap0.4able0.6 of s0.u8 ggesting de-

tion respectively. 6

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BPCY â?? pFBA(m m o l â?? g D W â??1 â?? h â??1)

signs compliant with more than one phenotype prediction method. In Figure 2

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K=7

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BPCY â?? pFBA(m m o l â?? g D W â??1 â?? h â??1)

generator pFBA; LMOMA cluster 2

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K=8

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BPCY â?? pFBA(m m o l â?? g D W â??1 â?? h â??1)

generator

pFBA; LMOMA

cluster

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solutions generated by our method are simulated using pFBA and LMOMA and plotted by BPCY for both phenotype simulation methods. The ad-hoc clusters re- veal a group of interesting solutions (cluster 2). An analysis on the flux distribution of the solutions presented in these clusters is also provided and a rational for robust solution design is derived.

References

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