Enumeration and Cartesian Product Decomposition of Alternate Optimal Fluxes in Cellular Metabolism

Published Online:https://doi.org/10.1287/ijoc.2016.0724

References

  • Alam MT, Medema MH, Takano E, Breitling R (2011) Comparative genome-scale metabolic modeling of actinomycetes: The topology of essential core metabolism. FEBS Lett. 585(14):2389–2394.CrossrefGoogle Scholar
  • Almaas E, Kovcs B, Vicsek T, Oltvai ZN, Barabsi A-L (2004) Global organization of metabolic fluxes in the bacterium escherichia coli. Nature 427:839–843.CrossrefGoogle Scholar
  • Appa G (2002) On the uniqueness of solutions to linear programs. J. Oper. Res. Soc. 53(10):1127–1132.CrossrefGoogle Scholar
  • Aurenhammer F, Hagauer J, Imrich W (1992) Cartesian graph factorization at logarithmic cost per edge. Computational Complexity 4:331–349.CrossrefGoogle Scholar
  • Barrett C, Herrgard M, Palsson BØ (2009) Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation. BMC Systems Biol. 3:30.CrossrefGoogle Scholar
  • Bretto A, Silvestre Y, Vallee T (2013) Factorization of products of hypergraphs: Structure and algorithms. Theoret. Comput. Sci. 475:47–58.CrossrefGoogle Scholar
  • Crespelle C, Thierry E, Lambert T (2013) A linear-time algorithm for computing the prime decomposition of a directed graph with regard to the Cartesian product. Proc. 19th Annual Internat. Comput. Combinatorics Conf. (COCOON 2013), Hangzhou, China, 469–480.CrossrefGoogle Scholar
  • de Souza W, de Carvalho TMU, Barrias ES (2010) Review on Trypanosoma cruzi: Host cell interaction. Internat. J. Cell Biol. Article 295394.CrossrefGoogle Scholar
  • Fishburn PC (1976) Utility independence on subsets of product sets. Oper. Res. 24(2):245–255.LinkGoogle Scholar
  • Gringmann L, Hellmuth M, Stadler PF (2012) The Cartesian product of hypergraphs. J. Graph Theory 70(2):180–196.CrossrefGoogle Scholar
  • Halbwachs N, Merchat D, Parent-Vigouroux C (2003) Cartesian factoring of polyhedra in linear relation analysis. Proc. 10th Internat. Conf. Static Anal. (SAS’03), Cousot R, ed. (Springer-Verlag, Berlin), 355–365.CrossrefGoogle Scholar
  • Haus U-U, Klamt S, Stephen T (2008) Computing knock-out strategies in metabolic networks. J. Computational Biol. 15:259–268.CrossrefGoogle Scholar
  • Klamt S, Hauw U-U, Theis F (2009) Hypergraphs and cellular networks. PLOS Computational Biol. 5(5):e10000385.CrossrefGoogle Scholar
  • Lacroix V, Cottret L, Theébault P, Sagot M-F (2011) An introduction to metabolic networks and their structural analysis. IEEE/ACM Trans. Comput. Biol. Bioinformatics 5(4):594–617.CrossrefGoogle Scholar
  • Lambert TJ III, Epelman MA, Smith RL (2005) A fictitious play approach to large-scale optimization. Oper. Res. 53(3):477–489.LinkGoogle Scholar
  • Lee S, Phalakornkule C, Domach MM, Grossmann IE (2000) Recursive MILP model for finding all the alternate optima in LP models for metabolic networks. Comput. Chemical Engrg. 24(2–7):711–716.CrossrefGoogle Scholar
  • Mahadevan R, Schilling CH (2003) The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metabolic Engrg. 5(4):264–276.CrossrefGoogle Scholar
  • Matheiss TH, Rubin DS (1980) A survey and comparison of methods for finding all vertices of convex polyhedral sets. Math. Oper. Res. 5(2):167–185.LinkGoogle Scholar
  • Muharremoglu A, Tsitsiklis JN (2008) A single-unit decomposition approach to multiechelon inventory systems. Oper. Res. 56(5):1089–1103.LinkGoogle Scholar
  • Roberts SB, Robichaux JL, Chavali AK, Manque PA, Lee V, Lara AM, Papin JA, Buck GA (2009) Proteomic and network analysis characterize stage-specific metabolism in Tyrpanosoma cruzi. BMC Systems Biol. 3:52.Google Scholar
  • Rosicki W (1997) On decomposition of polyhedra into a Cartesian product of 1-dimensional and 2-dimensional factors. Colloquium Mathematicum 72(1):103–109.CrossrefGoogle Scholar
  • Rosicki W (2004) On uniqueness of decomposition of 4-polyhedron into Cartesian product of the 2-dimensional factors. Topology and Its Appl. 143(1–3):159–173.CrossrefGoogle Scholar
  • Sabidussi G (1960) Graph multiplication. Mathematische Zeitschrift 72:446–457.CrossrefGoogle Scholar
  • Sainfort F, Deichtmann JM (1996) Decomposition of utility functions on subsets of product sets. Oper. Res. 44(4):609–616.LinkGoogle Scholar
  • Schilling CH, Letscher D, Palsson BØ (2000) Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J. Theor. Biol. 203(3):229–248.CrossrefGoogle Scholar
  • Şeref O, Brooks JP, Fong SS (2013) Decomposition of flux distributions into metabolic pathways. IEEE/ACM Trans. Comput. Biol. Bioinformatics 10(4):984–993.CrossrefGoogle Scholar
  • Vanderbeck F (2000) On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1):111–128.LinkGoogle Scholar
  • Vizing VG (1963) The Cartesian product of graphs (Russian). Vycisl. Sistemy 9:30–43.Google Scholar
  • Wiback SJ, Famili I, Greenberg HJ, Palsson BØ (2004) Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space. J. Theoret. Biol. 228(4):437–447.CrossrefGoogle Scholar
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