Maximizing output and recognizing autocatalysis in chemical reaction networks is NP-complete

Journal of Systems Chemistry

Volumn 3, Issue 1, 2012, Pages

  Andersen, Jakob L ^a   Flamm, Christoph ^b   Merkle, Daniel ^a   Stadler, Peter F ^b,c,d,e,f,g  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b UNIVERSITY OF VIENNA   (Austria)

^c Interdisciplinary Center for Bioinformatics   (Germany)

^d MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^e FRAUNHOFER INSTITUTE FOR CELL THERAPY AND IMMUNOLOGY   (Germany)

^f UNIVERSITY OF COPENHAGEN   (Denmark)

^g SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84873338125     PISSN: None     EISSN: 17592208     Source Type: Journal    
DOI: 10.1186/1759-2208-3-1     Document Type: Article

References (32)

1. Bernal A, Daza E: Metabolic networks: beyond the graph. Curr Comput Aided Drug Des 2011, 7:122-132.
2. Zeigarnik AV: On Hypercycles and Hypercircuits in Hypergraphs. In Discrete Mathematical Chemistry, Volume 51 of DIMACS series in discrete mathematics and theoretical computer science. Edited by: Hansen P, Fowler PW, Zheng M. Providence, RI: American Mathematical Society; 2000:377-383.
3. Gallo G, Scutellà M: Directed hypergraphs as a modelling paradigm. Decisions in Economics and Finance 1998, 21:97-123.
4. Ausiello G, Franciosa PG, Frigioni D: Directed hypergraphs: problems, algorithmic results, and a novel decremental approach. In ICTCS, Volume 2202 of Lecture Notes in Computer Science. Edited by: Restivo A, Rocca SRD, Roversi L. Springer; 2001:312327.
5. Kauffman KJ, Prakash P, Edwards JS: Advances influx balance analysis. Curr Opin Biotechnol 2003, 14:491-496.
6. Hatzimanikatis V, Emmerling M, Sauer U, Bailey JE: Application of mathematical tools for metabolic design of microbial ethanol production. Biotech Bioeng 1998, 58:154-161.
7. Schuster S, Hilgetag C: On elementary flux modes in biochemical reaction systems at steady state. J Biol Syst 1994, 2:165-182.
8. Schuster S, Fell DA, Dandekar T: A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat Biotechnol 2000, 18:326-332.
9. Klamt S, Stelling J: Two approaches for metabolic pathway analysis? Trends Biotechnol 2003, 21:64-69.
10. Klamt S, Stelling J: Combinatorial complexity of pathway analysis in metabolic networks. Mol Biol Rep 2002, 29:233-236.
11. Ip K, Colijn C, Lun DS: Analysis of Complex Metabolic Behavior through Pathway Decomposition. BMC Systems Biology 2011, 5:91.
12. Acuña V, Chierichetti F, Lacroix V, Marchetti-Spaccamela A, Sagot MF, Stougie L: Modes and cuts in metabolic networks: Complexity and algorithms. BioSystems 2009, 95:51-60.
13. Özturan C: On finding hypercycles in chemical reaction networks. Appl Math Letters 2008, 21:881-884.
14. Acuña V, Marchetti-Spaccamela A, Sagot MF, Stougie L: A note on the complexity of finding and enumerating elementary modes. Biosystems 2010, 99:210-214.
15. Klamt S, Gilles ED: Minimal cut sets in biochemical reaction networks. Bioinformatics 2004, 20:226-234.
16. Klamt S: Generalized concept of minimal cut sets in biochemical networks. Biosystems 2006, 83:233-247.
17. Pitkänen E, Rantanen A, Rousu J, Ukkonen E: Finding Feasible Pathways in Metabolic Networks. In Panhellenic Conference on Informatics, Volume 3746. Edited by: Bozanis P, Houstis EN. Heidelberg: Springer; 2005:123-133.
18. Kaleta C, Centler F, Dittrich P: Analyzing molecular reaction networks: from pathways to chemical organizations. Mol Biotechnol 2006, 34:117-123.
19. Centler F, Kaleta C, Speroni Di Fenizio P, Dittrich P: Computing chemical organizations in biological networks. Bioinformatics 2008, 24:1611-1618.
20. Kaleta C, Richter S, Dittrich P: Using chemical organization theory for model checking. Bioinformatics 2009, 25:1915-1922.
21. Benkö G, Centler F, Dittrich P, Flamm C, Stadler B M R, Stadler PF: A Topological Approach to Chemical Organizations. Alife 2009, 15:71-88.
22. Domach MM: Introduction to biomedical engineering Upper Saddle River: Pearson Prentice Hall; 2004.
23. Ahuja RK, Magnanti TL, Orlin J: Network Flows: Theory, Algorithms, and Applications Englewood Cliffs, NJ: Prentice Hall; 1993.
24. Kun Á, Papp B, Szathmáry E: Computational identification of obligatorily autocatalytic replicators embedded in metabolic networks. Genome Biol 2008, 9:R51.
25. Hordijk W, Steel M: Detecting autocatalytic, self-sustaining sets in chemical reaction systems. J Theor Biol 2004, 227:451-461.
26. Cambini R, Gallo G, Scutellà MG: Flows on hypergraphs. Mathematical Programming 1997, 78:195-217.
27. Garey MR, Johnson DS: Computers and Intractability: A Guide to the Theory of NP-Completeness New York, NY: W. H. Freeman & Co; 1979.
28. Garey MR, Johnson DS: Complexity results for multiprocessor scheduling under resource constraints. SIAM J Comput 1975, 4:397-411.
29. Hulett H, Will TG, Woeginger GJ: Multigraph realizations of degree sequences: Maximization is easy, minimization is hard. Operations Res Let 2008, 36:594-596.
30. Fortnow L: The Status of the P versus NP problem. Comm ACM 2009, 52(9):78-86.
31. Karp RM: Reducibility among combinatorial problems. In Complexity of Computer Computations. Edited by: Miller RE, Thatcher JW. NY: Plenum Press; 1972:.
32. Coleman TF, Pothen A: The null space problem I: Complexity. SIAM J Alg Disc Meth 1986, 7:527-537.