Elementary mode analysis: A useful metabolic pathway analysis tool for reprograming microbial metabolic pathways

Subcellular Biochemistry

Volumn 64, Issue , 2012, Pages 21-42

  Trinh, Cong T ^a,b   Thompson, R Adam ^a,b  

^a University of Tennessee Knoxville   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Elementary mode analysis; Engineering; Genetic knockout analysis; Metabolic minimal metabolic functionality; Rational strain design

Indexed keywords

ALGORITHM; BACTERIUM; BIOLOGY; COMPUTER PROGRAM; FUNGUS; GENE TARGETING; GENETICS; METABOLIC ENGINEERING; METABOLISM; METHODOLOGY; MOLECULAR CLONING; REVIEW;

ALGORITHMS; BACTERIA; CLONING, MOLECULAR; COMPUTATIONAL BIOLOGY; FUNGI; GENE TARGETING; METABOLIC ENGINEERING; METABOLIC NETWORKS AND PATHWAYS; SOFTWARE;

EID: 84907227559     PISSN: 03060225     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-94-007-5055-5_2     Document Type: Article

References (137)

1. Ay F, Kahveci T (2010) Functional similarities of reaction sets in metabolic pathways. In: Proceedings of thefirst ACM international conference on bioinformatics and computational biology, ACM, Niagara Falls, New York, pp 102-111.
2. Bartek T, Blombach B, Zonnchen E, Makus P, Lang S, Eikmanns BJ, Oldiges M (2010) Importance of NADPH supply for improved L-valine formation in corynebacterium glutamicum. Biotechnol Prog 26: 361-371.
3. Behre J, Wilhelm T, von Kamp A, Ruppin E, Schuster S (2008) Structural robustness of metabolic networks with respect to multiple knockouts. J Theor Biol 252: 433-441.
4. Bell SL, Palsson BO (2005) Expa: a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21: 1739-1740.
5. Beurton-Aimar M, Beauvoit B, Monier A, Vallee F, Dieuaide-Noubhani M, Colombie S (2011) Comparison between elementaryflux modes analysis and 13c-metabolicfluxes measured in bacterial and plant cells. BMC Syst Biol 5: 95.
6. Beuster G, Zarse K, Kaleta C, Thierbach R, Kiehntopf M, Steinberg P, Schuster S, Ristow M (2011) Inhibition of alanine aminotransferase in silico and in vivo promotes mitochondrial metabolism to impair malignant growth. J Biol Chem 286: 22323-22330.
7. Burgard AP, Pharkya P, Maranas CD (2003) Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol Bioeng 84: 647-657.
8. Cakir T, Kirdar B, Ulgen KO (2004) Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks. Biotechnol Bioeng 86: 251-260.
9. Cakir T, Kirdar B, Onsan ZI, Ulgen KO, Nielsen J (2007) Effect of carbon source perturbations on transcriptional regulation of metabolicfluxes in saccharomyces cerevisiae. BMC Syst Biol 1: 18.
10. Carlson RP (2007) Metabolic systems cost-benefit analysis for interpreting network structure and regulation. Bioinformatics 23: 1258-1264.
11. Carlson R, Srienc F (2004a) Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions. Biotech Bioeng 85: 1-18.
12. Carlson R, Srienc F (2004b) Fundamental Escherichia coli biochemical pathways for biomass and energy production: creation of overallflux states. Biotech Bioeng 86: 149-162.
13. Carlson R, Fell D, Srienc F (2002) Metabolic pathway analysis of a recombinant yeast for rational strain development. Biotech Bioeng 79: 121-134.
14. Centler F, Kaleta C, di Speroni Fenizio P, Dittrich P (2010) A parallel algorithm to compute chemical organizations in biological networks. Bioinformatics 26: 1788-1789.
15. Chandrasekaran S, Price ND (2010) Probabilistic integrative modeling of genome-scale metabolic and regulatory networks in Escherichia coli and mycobacterium tuberculosis. Proc Natl Acad Sci U S A 107: 17845-17850.
16. Chen N, Du J, Liu H, Xu QY (2009) Elementary mode analysis and metabolicflux analysis of L-glutamate biosynthesis by corynebacterium glutamicum. Ann Microbiol 59: 317-322.
17. Chen Z, Zhang JA, Liu DH (2010) Elementary mode analysis for the rational design of efficient succinate conversion from glycerol by Escherichia coli. J Biomed Biotechnol 518743.
18. Chen Z, Liu H, Liu D (2011) Metabolic pathway analysis of 1, 3-propanediol production with a genetically modified klebsiella pneumoniae by overexpressing an endogenous NADPHdependent alcohol dehydrogenase. Biochem Eng J 54: 151-157.
19. Christensen B, Karoly Gombert A, Nielsen J (2002) Analysis offlux estimates based on 13c-labelling experiments. Eur J Biochem 269: 2795-2800.
20. de Figueiredo LF, Podhorski A, Rubio A, Kaleta C, Beasley JE, Schuster S, Planes FJ (2009) Computing the shortest elementaryflux modes in genome-scale metabolic networks. Bioinformatics 25: 3158-3165.
21. Diniz SC, Voss I, Steinbuchel A (2006) Optimization of cyanophycin production in recombinant strains of pseudomonas putida and ralstonia eutropha employing elementary mode analysis and statistical experimental design. Biotechnol Bioeng 93: 698-717.
22. Driouch H, Melzer G, Wittmann C (2012) Integration of in vivo and in silico metabolicfluxes for improvement of recombinant protein production. Metab Eng 14: 47-58.
23. Durot M, Bourguignon P-Y, Schachter V (2009) Genome-scale models of bacterial metabolism: reconstruction and applications. FEMS Microbiol Rev 33: 164-190.
24. Feist A, Palsson B (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli. Nat Biotech 26: 659-667.
25. Feist AM, Palsson BO (2010) The biomass objective function. Curr Opin Microbiol 1(3): 344-349.
26. Fell DA (1992) Metabolic control analysis: a survey of its theoretical and experimental development. Biochem J 286(Pt 2): 313-330.
27. Flynn CM, Hunt KA, Gralnick JA, Srienc F (2012) Construction and elementary mode analysis of a metabolic model for shewanella oneidensis Mr-1. Biosystems 107: 120-128.
28. Fong SS, Burgard AP, Herring CD, Knight EM, Blattner FR, Maranas CD, Palsson BO (2005) In silico design and adaptive evolution of Escherichia coli for production of lactic acid. Biotechnol Bioeng 91: 643-648.
29. Fowler ZL, Gikandi WW, Koffas MAG (2009) Increased malonyl coenzyme a biosynthesis by tuning the Escherichia coli metabolic network and its application toflavanone production. Appl Environ Microbiol 75: 5831-5839.
30. Hädicke O, Klamt S (2010) Casop: a computational approach for strain optimization aiming at high productivity. J Biotechnol 147: 88-101.
31. Henry CS, DeJongh M, Best AA, Frybarger PM, Linsay B, Stevens RL (2010) High-throughput generation, optimization and analysis of genome-scale metabolic models. Nat Biotech 28: 977-982.
32. Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) Copasi-a complex pathway simulator. Bioinformatics 22: 3067-3074.
33. Jamshidi N, Palsson BO (2008) Formulating genome-scale kinetic models in the post-genome era. Mol Syst Biol 4: 171.
34. Jensen P, Lutz K, Papin J (2011) Tiger: toolbox for integrating genome-scale metabolic models, expression data, and transcriptional regulatory networks. BMC Syst Biol 5: 147.
35. Jevremovic D, Trinh CT, Srienc F, Boley D (2010) On algebraic properties of extreme pathways in metabolic networks. J Comput Biol 17: 107-119.
36. Jevremovic D, Trinh CT, Srienc F, Sosa CP, Boley D (2011) Parallelization of nullspace algorithm for the computation of metabolic pathways. Parallel Comput 37: 261-278.
37. Kaleta C, de Figueiredo LF, Schuster S (2009) Can the whole be less than the sum of its parts? Pathway analysis in genome-scale metabolic networks using elementaryflux patterns. Genome Res 19: 1872-1883.
38. Kaleta C, de Figueiredo LF, Werner S, Guthke R, Ristow M, Schuster S (2011) In Silico Evidence for gluconeogenesis from fatty acids in humans. PLoS Comput Biol 7: e1002116.
39. Kauffman KJ, Prakash P, Edwards JS (2003) Advances influx balance analysis. Curr Opin Biotechnol 14: 491-496.
40. Kenanov D, Kaleta C, Petzold A, Hoischen C, Diekmann S, Siddiqui RA, Schuster S (2010) Theoretical study of lipid biosynthesis in wild-type Escherichia coli and in a protoplast-type L-form using elementaryflux mode analysis. FEBS J 277: 1023-1034.
41. Kim J, Reed J (2010) Optorf: optimal metabolic and regulatory perturbations for metabolic engineering of microbial strains. BMC Syst Biol 4: 53.
42. Kim J, Reed JL, Maravelias CT (2011) Large-scale Bi-level strain design approaches and mixedinteger programming solution techniques. PLoS One 6: e24162.
43. Kind S, Wittmann C (2011) Bio-based production of the platform chemical 1, 5-diaminopentane. Appl Microbiol Biotechnol 91: 1287-1296.
44. Klamt S (2006) Generalized concept of minimal Cut sets in biochemical networks. Bio Syst 83: 233-247.
45. Klamt S, Gilles ED (2004) Minimal cut sets in biochemical reaction networks. Bioinformatics 20: 226-234.
46. Klamt S, Stelling J (2003) Two approaches for metabolic pathway analysis? Trends Biotechnol 21: 64-69.
47. Klamt S, Saez-Rodriguez J, Gilles ED (2007) Structural and functional analysis of cellular networks with cellnetanalyzer. BMC Syst Biol 1: 2.
48. Kromer JO, Wittmann C, Schroder H, Heinzle E (2006) Metabolic pathway analysis for rational design of L-methionine production by Escherichia coli and corynebacterium glutamicum. Metab Eng 8: 353-369.
49. Kurata H, Zhao Q, Okuda R, Shimizu K (2007) Integration of enzyme activities into metabolicflux distributions by elementary mode analysis. BMC Syst Biol 1: 31.
50. Larhlimi A, Bockmayr A (2009) A New constraint-based description of the steady-stateflux cone of metabolic networks. Discret Appl Math 157: 2257-2266.
51. Larhlimi A, Blachon S, Selbig J, Nikoloski Z (2011) Robustness of metabolic networks: a review of existing definitions. Biosystems 106: 1-8.
52. Lee S, Phalakornkule C, Domach MM, Grossmann IE (2000) Recursive milp model forfinding all the alternate optima in Lp models for metabolic networks. Comput Chem Eng 24: 711-716.
53. Lewis NE, Nagarajan H, Palsson BO (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods. Nat Rev Micro 10: 291-305.
54. Liao JC, Hou SY, Chao YP (1996) Pathway analysis, engineering, and physiological considerations for redirecting central metabolism. Biotechnol Bioeng 52: 129-140.
55. Machado D, Costa RS, Ferreira EC, Rocha I, Tidor B (2012) Exploring the gap between dynamic and constraint-based models of metabolism. Metab Eng 14: 112-119.
56. Mahadevan R, Schilling CH (2003) The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng 5: 264-276.
57. Martínez I, Bennett GN, San K-Y (2010) Metabolic impact of the level of aeration during cell growth on anaerobic succinate production by an engineered Escherichia coli strain. Metab Eng 12: 499-509.
58. Matsuda F, Furusawa C, Kondo T, Ishii J, Shimizu H, Kondo A (2011) Engineering strategy of yeast metabolism for higher alcohol production. Microb Cell Fact 10: 70.
59. Medema MH, van Raaphorst R, Takano E, Breitling R (2012) Computational tools for the synthetic design of biochemical pathways. Nat Rev Micro 10: 191-202.
60. Melzer G, Esfandabadi M, Franco-Lara E, Wittmann C (2009) Flux design: in silico design of cell factories based on correlation of pathwayfluxes to desired properties. BMC Syst Biol 3: 120.
61. Min Y, Jin X, Chen M, Pan Z, Ge Y, Chang J (2011) Pathway knockout and redundancy in metabolic networks. J Theor Biol 270: 63-69.
62. Neuner A, Heinzle E (2011) Mixed glucose and lactate uptake by corynebacterium glutamicum through metabolic engineering. Biotechnol J 6: 318-329.
63. Nookaew I, Meechai A, Thammarongtham C, Laoteng K, Ruanglek V, Cheevadhanarak S, Nielsen J, Bhumiratana S (2007) Identification offlux regulation coefficients from elementaryflux modes: a systems biology tool for analysis of metabolic networks. Biotechnol Bioeng 97: 1535-1549.
64. Pagani I, Liolios K, Jansson J, Chen I-MA, Smirnova T, Nosrat B, Markowitz VM, Kyrpides NC (2012) The genomes online database (gold) V. 4: status of genomic and metagenomic projects and their associated metadata. Nucleic Acids Res 40: D571-D579.
65. Papin JA, Price ND, Edwards JS, Palsson BBO (2002a) The genome-scale metabolic extreme pathway structure in haemophilus influenzae shows significant network redundancy. J Theor Biol 215: 67-82.
66. Papin JA, Price ND, Palsson BO (2002b) Extreme pathway lengths and reaction participation in genome-scale metabolic networks. Genome Res 12: 1889-1900.
67. Papin JA, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO (2004) Comparison of networkbased pathway analysis methods. Trends Biotechnol 22: 400-405.
68. Park JH, Lee KH, Kim TY, Lee SY (2007) Metabolic engineering of Escherichia coli for the production of L-valine based on transcriptome analysis and in silico gene knockout simulation. Proc Natl Acad Sci U S A 104: 7797-7802.
69. Patil K, Rocha I, Forster J, Nielsen J (2005) Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinform 6: 308.
70. Peres S, Vallee F, Beurton-Aimar M, Mazat JP (2011) Acom: a classi fication method for elementaryflux modes based on motiffinding. Biosystems 103: 410-419.
71. Pfeiffer T, Sanchez-Valdenebro I, Nuno JC, Montero F, Schuster S (1999) Metatool: for studying metabolic networks. Bioinformatics 15: 251-257.
72. Pharkya P, Maranas CD (2006) An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems. Metab Eng 8: 1-13.
73. Pharkya P, Burgard A, Maranas C (2004) Optstrain: a computational framework for redesign of microbial production systems. Genome Res 14: 2367-2376.
74. Poolman MG (2006) Scrumpy: metabolic modelling with python. IEE Proc Syst Biol 153: 375-378.
75. Poolman MG, Fell DA, Raines CA (2003) Elementary modes analysis of photosynthate metabolism in the chloroplast stroma. Eur J Biochem 270: 430-439.
76. Poolman MG, Venkatesh KV, Pidcock MK, Fell DA (2004) A method for the determination offlux in elementary modes, and its application to lactobacillus rhamnosus. Biotechnol Bioeng 88: 601-612.
77. Poolman MG, Sebu C, Pidcock MK, Fell DA (2007) Modular decomposition of metabolic systems via null-space analysis. J Theor Biol 249: 691-705.
78. Price ND, Reed JL, Papin JA, Famili I, Palsson BO (2003) Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices. Biophys J 84: 794-804.
79. Price ND, Reed JL, Palsson BO (2004) Genome-scale models of microbial cells: evaluating the consequences of constraints. Nat Rev Microbiol 2: 886-897.
80. Rajvanshi M, Venkatesh K (2011) Phenotypic characterization of corynebacterium glutamicum under osmotic stress conditions using elementary mode analysis. J Ind J Ind Microbiol Biotechnol 38: 1345-1357.
81. Reder C (1988) Metabolic control theory: a structural approach. J Theor Biol 135: 175-201.
82. Reed JL, Palsson BØ (2004) Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states. Genome Res 14: 1797-1805.
83. Rockafellar RT (1970) Convex analysis, 28th edn. Princeton University Press, Princeton.
84. Rügen M, Bockmayr A, Legrand J, Cogne G (2012) Network reduction in metabolic pathway analysis: elucidation of the key pathways involved in the photoautotrophic growth of the green alga Chlamydomonas reinhardtii. Metab Eng 14(4): 458-467.
85. 13 C-basedflux analysis. Mol Syst Biol 2: 62.
86. Schaeuble S, Schuster S, Kaleta C (2011) Hands-on metabolism: analysis of complex biochemical networks using elementaryflux modes. In: Jameson D, Verma, M, Westerhoff, HV (eds) Methods in enzymology, vol 500. Elsevier/Academic, San Diego, pp 437-456.
87. Schauble S, Heiland I, Voytsekh O, Mittag M, Schuster S (2011) Predicting the physiological role of circadian metabolic regulation in the green alga Chlamydomonas reinhardtii. PLoS One 6: e23026.
88. Schellenberger J, Park J, Conrad T, Palsson B (2010) Bigg: a biochemical genetic and genomic knowledgebase of large scale metabolic reconstructions. BMC Bioinform 11: 213.
89. Schilling CH, Edwards JS, Letscher D, Palsson BO (2000a) Combining pathway analysis withflux balance analysis for the comprehensive study of metabolic systems. Biotechnol Bioeng 71: 286-306.
90. Schilling CH, Letscher D, Palsson BO (2000b) Theory for the systemic definition of metabolic pathways and their Use in interpreting metabolic function from a pathway-oriented perspective. J Theor Biol 203: 229-248.
91. Schuetz R, Kuepfer L, Sauer U (2007) Systematic evaluation of objective functions for predicting intracellularfluxes in Escherichia coli. Mol Syst Biol 3: 119.
92. Schuster S, Hilgetag S (1994) On elementaryflux modes in biochemical reaction systems at steady state. J Biol Syst 2: 165-182.
93. Schuster R, Schuster S (1993) Refined algorithm and computer program calculating All Nonnegativefluxes admissible in steady states of biochemical reaction systems with and without somefluxes ratesfixed. CABIOS 9: 79-85.
94. Schuster S, Hilgetag C, Woods JH, Fell DA (1994) Elementary modes of functioning in biochemical networks. In: Cuthbertson R, Holcombe M, Paton R (eds) Computation in cellular and molecular biological systems. World Scientific, Singapore, pp 151-165.
95. Schuster S, Dandekar T, Fell DA (1999) Detection of elementaryflux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol 17: 53-60.
96. Schuster S, Hilgetag C, Woods JH, Fell DA (2002) Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J Math Biol 45: 153-181.
97. Schuster S, Kamp A, Pachkov M (2006) Understanding the roadmap of metabolism by pathway analysis. Method Mol Biol 358: 199-226.
98. Schuster S, Pfeiffer T, Fell DA (2008) Is maximization of molar yield in metabolic networks favoured by evolution? J Theor Biol 252: 497-504.
99. Schwartz J-M, Kanehisa M (2005) A quadratic programming approach for decomposing steadystate metabolicflux distributions onto elementary modes. Bioinformatics 21: ii204-205.
100. Schwartz J-M, Kanehisa M (2006) Quantitative elementary mode analysis of metabolic pathways: the example of yeast glycolysis. BMC Bioinform 7: 186.
101. Schwarz R, Liang C, Kaleta C, Kuehnel M, Hoffmann E, Kuznetsov S, Hecker M, Griffiths G, Schuster S, Dandekar T (2007) Integrated network reconstruction, visualization and analysis using Yanasquare. BMC Bioinform 8: 313.
102. Song H-S, Ramkrishna D (2012) Prediction of dynamic behavior of mutant strains from limited wild-type data. Metab Eng 14: 69-80.
103. Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED (2002) Metabolic network structure determines key aspects of functionality and regulation. Nature 420: 190-193.
104. Stelling J, Sauer U, Szallasi Z, Doyle FJ 3rd, Doyle J (2004) Robustness of cellular functions. Cell 118: 675-685.
105. Stephanopoulos G, Aristidou AA, Nielsen JH (1998) Metabolic engineering: principles and methodologies. Academic, San Diego.
106. Tepper N, Shlomi T (2010) Predicting metabolic engineering knockout strategies for chemical production: accounting for competing pathways. Bioinformatics 26: 536-543.
107. Terzer M, Stelling J (2008) Large scale computation of elementaryflux modes with Bit pattern trees. Bioinformatics 24(19): 2229-2235.
108. Thiele I, Palsson BO (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat Protoc 5: 93-121.
109. Tran LM, Rizk ML, Liao JC (2008) Ensemble modeling of metabolic networks. Biophys J 95: 5606-5617.
110. Trinh C (2012) Elucidating and optimizing E. coli metabolisms for obligate anaerobic butanol and isobutanol production. Appl Microbiol Biotechnol 95(4): 1083-1094.
111. Trinh CT, Srienc F (2009) Metabolic engineering of Escherichia coli for efficient conversion of glycerol to ethanol. Appl Environ Microbiol 75: 6696-6705.
112. Trinh CT, Carlson R, Wlaschin A, Srienc F (2006) Design, construction and performance of the most efficient biomass producing E. coli bacterium. Metab Eng 8: 628-638.
113. Trinh CT, Unrean P, Srienc F (2008) Minimal Escherichia coli cell for the most efficient production of ethanol from hexoses and pentoses. Appl Environ Microbiol 74: 3634-3643.
114. Trinh CT, Wlaschin A, Srienc F (2009) Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism. Appl Microbiol Biotechnol 81: 813-826.
115. Trinh CT, Li J, Blanch HW, Clark DS (2011) Redesigning Escherichia coli metabolism for anaerobic production of isobutanol. Appl Environ Microbiol 77: 4894-4904.
116. Unrean P, Srienc F (2011) Metabolic networks evolve towards states of maximum entropy production. Metab Eng 13: 666-673.
117. Unrean P, Srienc F (2012) Predicting the adaptive evolution of thermoanaerobacterium saccharolyticum. J Biotechnol 158: 259-266.
118. Unrean P, Trinh CT, Srienc F (2010) Rational design and construction of an efficient E. coli for production of diapolycopendioic acid. Metab Eng 12: 112-122.
119. Vijayasankaran N, Carlson R, Srienc F (2005) Metabolic pathway structures for recombinant protein synthesis in Escherichia coli. Appl Microbiol Biotechnol 68: 737-746.
120. von Kamp A, Schuster S (2006) Metatool 5. 0: fast andflexible elementary modes analysis. Bioinformatics 22: 1930-1931.
121. Wang L, Birol I, Hatzimanikatis V (2004) Metabolic control analysis under uncertainty: framework development and case studies. Biophys J 87: 3750-3763.
122. Wessely F, Bartl M, Guthke R, Li P, Schuster S, Kaleta C (2011) Optimal regulatory strategies for metabolic pathways in Escherichia coli depending on protein costs. Mol Syst Biol 7: 515.
123. Wiback SJ, Mahadevan R, Palsson BO (2003) Reconstructing metabolicflux vectors from extreme pathways: defining the alpha-spectrum. J Theor Biol 224: 313-324.
124. Wiback SJ, Mahadevan R, Palsson BO (2004) Using metabolicflux data to further constrain the metabolic solution space and predict internalflux patterns: the Escherichia coli spectrum. Biotechnol Bioeng 86: 317-331.
125. Wiechert W, Möllney M, Petersen S, de Graaf AA (2001) A universal framework for 13c metabolicflux analysis. Metab Eng 3: 265-283.
126. Wilhelm T, Behre J, Schuster S (2004) Analysis of structural robustness of metabolic networks. Syst Biol 1: 114-120.
127. Wlaschin AP, Trinh CT, Carlson R, Srienc F (2006) The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies. Metab Eng 8: 338-352.
128. Yang L, Cluett WR, Mahadevan R (2011) Emilio: a fast algorithm for genome-scale strain design. Metab Eng 13: 272-281.
129. Yim H, Haselbeck R, Niu W, Pujol-Baxley C, Burgard A, Boldt J, Khandurina J, Trawick JD, Osterhout RE, Stephen R, Estadilla J, Teisan S, Schreyer HB, Andrae S, Yang TH, Lee SY, Burk MJ, Van Dien S (2011) Metabolic engineering of Escherichia coli for direct production of 1, 4-butanediol. Nat Chem Biol 7: 445-452.
130. Young JD, Henne KL, Morgan JA, Konopka AE, Ramkrishna D (2008) Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control. Biotechnol Bioeng 100: 542-559.
131. Yuan J, Fowler WU, Kimball E, Lu W, Rabinowitz JD (2006) Kineticflux profiling of nitrogen assimilation in Escherichia coli. Nat Chem Biol 2: 529-530.
132. Yuan J, Bennett BD, Rabinowitz JD (2008) Kineticflux profiling for quantitation of cellular metabolicfluxes. Nat Protoc 3: 1328-1340.
133. 13 C metabolicflux analysis for larger scale cultivation using Gas chromatography-combustion-isotope ratio mass spectrometry. Metab Eng 12: 392-400.
134. 13 C-glucose experiments. BMC Bioinform 6: 209.
135. 13 C-based metabolicflux analysis. Nat Protoc 4: 878-892.
136. Zhang Q, Xiu Z (2009) Metabolic pathway analysis of glycerol metabolism in Klebsiella pneumoniae incorporating oxygen regulatory system. Biotechnol Prog 25: 103-115.
137. Zhao Q, Kurata H (2010) Use of maximum entropy principle with Lagrange multipliers extends the feasibility of elementary mode analysis. J Biosci Bioeng 110: 254-261.