Enumeration of minimal stoichiometric precursor sets in metabolic networks.
BACKGROUND
What an organism needs at least from its environment to produce a set of metabolites, e.g. target(s) of interest and/or biomass, has been called a minimal precursor set. Early approaches to enumerate all minimal precursor sets took into account only the topology of the metabolic network (topological precursor sets). Due to cycles and the stoichiometric values of the reactions, it is often not possible to produce the target(s) from a topological precursor set in the sense that there is no feasible flux. Although considering the stoichiometry makes the problem harder, it enables to obtain biologically reasonable precursor sets that we call stoichiometric. Recently a method to enumerate all minimal stoichiometric precursor sets was proposed in the literature. The relationship between topological and stoichiometric precursor sets had however not yet been studied.


RESULTS
Such relationship between topological and stoichiometric precursor sets is highlighted. We also present two algorithms that enumerate all minimal stoichiometric precursor sets. The first one is of theoretical interest only and is based on the above mentioned relationship. The second approach solves a series of mixed integer linear programming problems. We compared the computed minimal precursor sets to experimentally obtained growth media of several Escherichia coli strains using genome-scale metabolic networks.


CONCLUSIONS
The results show that the second approach efficiently enumerates minimal precursor sets taking stoichiometry into account, and allows for broad in silico studies of strains or species interactions that may help to understand e.g. pathotype and niche-specific metabolic capabilities. sasita is written in Java, uses cplex as LP solver and can be downloaded together with all networks and input files used in this paper at http://www.sasita.gforge.inria.fr.
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|UMR CNRS 5558, LBBE, "Biométrie et Biologie évolutive", Université Lyon 1, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France.
Ricardo
R
Andrade
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|UMR CNRS 5558, LBBE, "Biométrie et Biologie évolutive", Université Lyon 1, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France.
Martin
M
Wannagat
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|UMR CNRS 5558, LBBE, "Biométrie et Biologie évolutive", Université Lyon 1, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France.
Cecilia C
CC
Klein
Center for Mathematical Modeling (UMI 2807 CNRS), University of Chile, Beauchef 851, 837 0456 Santiago de Chile, Chile.
Vicente
V
Acuña
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy.
Alberto
A
Marchetti-Spaccamela
Applied Research Department, Tecsinapse, São Paulo, Brazil.
Paulo V
PV
Milreu
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands.|Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands.
Leen
L
Stougie
Erable team, INRIA Grenoble Rhône-Alpes, 655 Avenue de l'Europe, 38330 Montbonnot Saint-Martin, France.|UMR CNRS 5558, LBBE, "Biométrie et Biologie évolutive", Université Lyon 1, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France.
Marie-France
MF
Sagot
Metabolic network; Minimal precursor sets; Mixed integer linear programming
PLoS One. 2013;8(1):e53957
23349773
Infect Immun. 2014 May;82(5):1931-8
24566621
Biophys J. 2006 Apr 15;90(8):2659-72
16461408
Biomed J. 2014 Sep-Oct;37(5):259-68
25179725
PLoS Comput Biol. 2014 Jan;10(1):e1003378
24391481
BMC Bioinformatics. 2013 Mar 27;14:114
23537498
Proc Natl Acad Sci U S A. 2013 Dec 10;110(50):20338-43
24277855
Bioinformatics. 2009 Dec 1;25(23):3158-65
19793869
PLoS Comput Biol. 2014 Jul 17;10(7):e1003726
25033033
J Theor Biol. 2008 Jun 7;252(3):530-7
18086477
Bioinformatics. 2012 Oct 1;28(19):2474-83
22782547
Infect Immun. 2008 Mar;76(3):1143-52
18180286
Pac Symp Biocomput. 2001;:471-82
11262965
Infect Immun. 2009 Jul;77(7):2876-86
19364832