Abstract
Constraint-based modeling is largely used in computational studies of metabolism. We propose here a novel approach that aims to identify ensembles of flux distributions that comply with one or more target phenotype(s). The methodology has been tested on a small-scale model of yeast energy metabolism. The target phenotypes describe the differential pattern of ethanol production and O2 consumption observed in “Crabtree-positive” and “Crabtree-negative” yeasts in changing environment (i.e., when the upper limit of glucose uptake is varied). The ensembles were obtained either by selection among sampled flux distributions or by means of a search heuristic (genetic algorithm). The former approach provided indication about the probability to observe a given phenotype, but the resulting ensembles could not be unambiguously partitioned into “Crabtree-positive” and “Crabtree-negative” clusters. On the contrary well-separated clusters were obtained with the latter method. The cluster analysis further allowed identification of distinct groups within each target phenotype. The method may thus prove useful in characterizing the design principles underlying metabolic plasticity arising from evolving physio-pathological or developmental constraints.
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Notes
In the present work we used standard values for the GA parametrization as our focus is on the development of the eeFBA appoach rather than finding the most effective GA tuning.
References
Alberghina L, Gaglio D, Moresco RM, Gilardi MC, Messa C, Vanoni M (2013) A systems biology road map for the discovery of drugs targeting cancer cell metabolism. Curr Pharm Des 20(15):2648–2666
Alberghina L, Westerhoff HV (eds) (2005) Systems biology: definitions and perspectives, volume 13 of topics in current genetics. Springer, Berlin
Almaas E, Kovács B, Vicsek T, Oltvai Z, Barabási A-L (2004) Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature 427(6977):839–843
Barford JP, Hall RJ (1979) An examination of the Crabtree effect in Saccharomyces cerevisiae: the role of respiratory adaptation. J Gen Microbiol 114(2):267–275
Beardmore RE, Gudelj I, Lipson DA, Hurst LD (2011) Metabolic trade-offs and the maintenance of the fittest and the flattest. Nature 472(7343):342–346
Bordel S, Agren R, Nielsen J (2010) Sampling the solution space in genome-scale metabolic networks reveals transcriptional regulation in key enzymes. PLoS Comput Biol 6(7):e1000859
Chang I, Heiske M, Letellier T, Wallace D, Baldi P (2011) Modeling of mitochondria bioenergetics using a composable chemiosmotic energy transduction rate law: theory and experimental validation. PloS One 6(9):e14820
Chiu M, Ottaviani L, Bianchi MG, Franchi-Gazzola R, Bussolati O (2012) Towards a metabolic therapy of cancer? Acta Bio-Med: Atenei Parm 83(3):168–176
Cortassa S, Aon MA, ORourke B, Jacques R, Tseng H-J, Marbán E, Winslow RL (2006) A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte. Biophys J 91(4):1564–1589
Covert MW, Famili I, Palsson BO (2003) Identifying constraints that govern cell behavior: a key to converting conceptual to computational models in biology? Biotechnol Bioeng 84(7):763–772
De Deken RH (1966) The Crabtree effect: a regulatory system in yeast. J Gen Microbiol 44(2):149–156
Diaz-Ruiz R, Rigoulet M, Devin A (2011) The Warburg and Crabtree effects: on the origin of cancer cell energy metabolism and of yeast glucose repression. Biochim Biophys Acta 1807(6):568–576
Feist A, Palsson B (2010) The biomass objective function. Curr Opin Microbiol 13(3):344–349
Gianchandani EP, Chavali AK, Papin JA (2010) The application of flux balance analysis in systems biology. Wiley Interdiscip Rev Syst Biol Med 2(3):372–382
Hagman A, Säll T, Compagno C, Piskur J (2013) Yeast “make-accumulate-consume” life strategy evolved as a multi-step process that predates the whole genome duplication. PloS One 8(7):e68734
Harcombe WR, Delaney NF, Leiby N, Klitgord N, Marx CJ (2013) The ability of flux balance analysis to predict evolution of central metabolism scales with the initial distance to the optimum. PLoS Comput Biol 9(6):e1003091
Johnson SC (1967) Hierarchical clustering schemes. Psychometrika 2:241–254
Kitano H, Oda K, Kimura T, Matsuoka Y, Csete M, Doyle J, Muramatsu M (2004) Metabolic syndrome and robustness tradeoffs. Diabetes 53(suppl 3):S6–S15
Maharjan R, Seeto S, Notley-McRobb L, Ferenci T (2006) Clonal adaptive radiation in a constant environment. Science 313(5786):514–517
Mardinoglu A, Gatto F, Nielsen J (2013) Genome-scale modeling of human metabolism—a systems biology approach. Biotechnol J 8(9):985–996
McCloskey D, Bernhard OP, Feist AM (2013) Basic and applied uses of genome-scale metabolic network reconstructions of Escherichia coli. Mol Syst Biol 9(1):661. doi:10.1038/msb.2013.18
Mitchell M (1996) An introduction to genetic algorithms. The MIT Press, Cambridge
Oliveira JS, Bailey CG, Jones-Oliveira JB, Dixon DA, Gull DW, Chandler ML (2003) A computational model for the identification of biochemical pathways in the Krebs cycle. J Comput Biol 10(1):57–82
Orth JD, Thiele I, Palsson BO (2010) What is flux balance analysis? Nat Biotechnol 28(3):245–248
Papin J, Reed JL, Palsson BO (2004) Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. Trends Biochem Sci 29(12):641–647
Papini M, Nookaew I, Uhlén M, Nielsen J (2012) Scheffersomyces stipitis: a comparative systems biology study with the Crabtree positive yeast Saccharomyces cerevisiae. Microb Cell Fact 11:136
Patil KR, Rocha I, Förster J, Nielsen J (2005) Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics 6:308
Porro D, Brambilla L, Alberghina L (2003) Glucose metabolism and cell size in continuous cultures of Saccharomyces cerevisiae. FEMS Microbiol Lett 229(2):165–171
Raman K, Chandra N (2009) Flux balance analysis of biological systems: applications and challenges. Brief Bioinform 10(4):435–449
Razinkov IA, Baumgartner BL, Bennett MR, Tsimring LS, Hasty J (2013) Measuring competitive fitness in dynamic environments. J Phys Chem B 117(42):13175–13181
Schellenberger J, Palsson BO (2009) Use of randomized sampling for analysis of metabolic networks. J Biol Chem 284(9):5457–5461
Schuetz R, Zamboni N, Zampieri M, Heinemann M, Sauer U (2012) Multidimensional optimality of microbial metabolism. Science 336(6081):601–604
Segre D, DeLuna A, Church GM, Kishony R (2005) Modular epistasis in yeast metabolism. Nat Genet 37(1):77–83
Soga T (2013) Cancer metabolism: key players in metabolic reprogramming. Cancer Sci 104(3):275–281
Supudomchok S, Chaiyaratana N, Phalakomkule C (2008) Co-operative co-evolutionary approach for flux balance in Bacillus subtilis. In: Evolutionary computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on, pp 1226–1231
Terzer M, Maynard ND, Covert MW, Stelling J (2009) Genome-scale metabolic networks. Wiley Interdiscip Rev Syst Biol Med 1(3):285–297
Teusink B, Passarge J, Reijenga CA, Esgalhado E, van der Weijden CC, Schepper M, Walsh MC, Bakker BM, van Dam K, Westerhoff HV et al (2000) Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur J Biochem 267(17):5313–5329
Van Urk H, Voll W, Scheffers W, Van Dijken J (1990) Transient-state analysis of metabolic fluxes in Crabtree-positive and Crabtree-negative yeasts. Appl Environ Microbiol 56(1):281–287
Wu F, Yang F, Vinnakota KC, Beard D (2007) Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology. J Biol Chem 282(34):24525–24537
Acknowledgments
This work has been supported by grants from Regione Lombardia (NEDD) to LA, GM and MV and and FP7 (Unicellsys) to LA and MV and from project SysBioNet, Italian Roadmap Research Infrastructures 2012 to LA. We warmly thank Prof. Hans Westerhoff for constructive discussions and criticism.
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Damiani, C., Pescini, D., Colombo, R. et al. An ensemble evolutionary constraint-based approach to understand the emergence of metabolic phenotypes. Nat Comput 13, 321–331 (2014). https://doi.org/10.1007/s11047-014-9439-4
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DOI: https://doi.org/10.1007/s11047-014-9439-4