Knockout Prediction for Reaction Networks with Partial Kinetic Information

  • Mathias John
  • Mirabelle Nebut
  • Joachim Niehren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7737)


In synthetic biology, a common application field for computational methods is the prediction of knockout strategies for reaction networks. Thereby, the major challenge is the lack of information on reaction kinetics. In this paper, we propose an approach, based on abstract interpretation, to predict candidates for reaction knockouts, relying only on partial kinetic information. We consider the usual deterministic steady state semantics of reaction networks and a few general properties of reaction kinetics. We introduce a novel abstract domain over pairs of real domain values to compute the differences between steady states that are reached before and after applying some knockout. We show that this abstract domain allows us to predict correct knockout strategy candidates independent of any particular choice of reaction kinetics. Our predictions remain candidates, since our abstract interpretation over-approximates the solution space. We provide an operational semantics for our abstraction in terms of constraint satisfaction problems and illustrate our approach on a realistic network.


Abstract interpretation deterministic semantics steady state constraint satisfaction synthetic biology 


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  1. 1.
    Andrianantoandro, E., Basu, S., Karig, D.K., Weiss, R.: Synthetic biology: new engineering rules for an emerging discipline.. Molecular Systems Biology 2(1), msb4100073–E1–msb4100073–E14 (2006)Google Scholar
  2. 2.
    Benner, S.A., Michael Sismour, A.: Synthetic biology. Nature Reviews Genetics 6(7), 533–543 (2005)CrossRefGoogle Scholar
  3. 3.
    Bonarius, H.P.J., Schmid, G., Tramper, J.: Flux analysis of underdetermined metabolic networks: the quest for the missing constraints. Trends in Biotechnology 15(8), 308–314 (1997)CrossRefGoogle Scholar
  4. 4.
    Brinsmade, S.R., Kleijn, R.J., Sauer, U., Sonenshein, A.L.: Regulation of CodY Activity through Modulation of Intracellular Branched-Chain Amino Acid Pools. J. Bacteriol. 192(24), 6357–6368 (2010)CrossRefGoogle Scholar
  5. 5.
    Burgard, A.P., Pharkya, P., Maranas, C.D.: Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnology and Bioengineering 84(6), 647–657 (2003)CrossRefGoogle Scholar
  6. 6.
    Camporesi, F., Feret, J.: Formal reduction for rule-based models. In: Mislove, M., Ouaknine, J. (eds.) The 27th Conference on the Mathematical Foundations of Programming Semantics - MFPS 2011, Pittsburgh, États-Unis. Electronic Notes in Theoretical Computer Science, vol. 276, pp. 29–59. Elsevier (September 2011)Google Scholar
  7. 7.
    Cousot, P.: The calculational design of a generic abstract interpreter. In: Broy, M., Steinbrüggen, R. (eds.) Calculational System Design. NATO ASI Series F. IOS Press, Amsterdam (1999)Google Scholar
  8. 8.
    Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL, pp. 269–282 (1979)Google Scholar
  9. 9.
    Covert, M.W., Schilling, C.H., Palsson, B.: Regulation of gene expression in flux balance models of metabolism. Journal of Theoretical Biology 213(1), 73–88 (2001)CrossRefGoogle Scholar
  10. 10.
    Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Abstracting the differential semantics of rule-based models: Exact and automated model reduction. In: LICS, pp. 362–381. IEEE Computer Society (2010)Google Scholar
  11. 11.
    Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403(6767), 335–338 (2000)CrossRefGoogle Scholar
  12. 12.
    Fages, F., Soliman, S.: Abstract interpretation and types for systems biology. Theor. Comput. Sci. 403(1), 52–70 (2008)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Feret, J., Henzinger, T., Koeppl, H., Petrov, T.: Lumpability abstractions of rule-based systems. In: Theoretical Computer Science (2012)Google Scholar
  14. 14.
    Ferrell, J.E.: Feedback regulation of opposing enzymes generates robust, all-or-none bistable responses. Current biology: CB, 18(6) (March 2008)Google Scholar
  15. 15.
    Florez, L., Gunka, K., Polania, R., Tholen, S., Stulke, J.: SPABBATS: A pathway-discovery method based on Boolean satisfiability that facilitates the characterization of suppressor mutants. BMC Systems Biology 5(1), 5+ (2011)Google Scholar
  16. 16.
    Förster, J., Famili, I., Fu, P., Palsson, B.Ø., Nielsen, J.: Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Research 13(2), 244–253 (2003)CrossRefGoogle Scholar
  17. 17.
    Gillespie, C.S.: Moment-closure approximations for mass-action models. IET Systems Biology 3(1), 52–58 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 2340–2361 (1977)CrossRefGoogle Scholar
  19. 19.
    Goelzer, A., Brikci, F.B., Verstraete, I.M., Noirot, P., Bessieres, P., Aymerich, S., Fromion, V.: Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis. BMC Systems Biology, 2(1), 20+ (2008)Google Scholar
  20. 20.
    Henry, C.S., Zinner, J.F., Cohoon, M.P., Stevens, R.L.: iBsu1103: a new genome-scale metabolic model of Bacillus subtilis based on SEED annotations. Genome Biology 10(6), R69+ (2009)Google Scholar
  21. 21.
    Keasling, J.D.: Synthetic biology for synthetic chemistry. ACS Chemical Biology 3(1), 64–76 (2008)CrossRefGoogle Scholar
  22. 22.
    Kholodenko, B.N.: Cell-signalling dynamics in time and space. Nature Reviews Molecular Cell Biology 7, 165–176 (2006)CrossRefGoogle Scholar
  23. 23.
    Kim, J., Reed, J.: OptORF: Optimal metabolic and regulatory perturbations for metabolic engineering of microbial strains. BMC Systems Biology 4(1), 53+ (2010)Google Scholar
  24. 24.
    Koide, T., Pang, W.L.L., Baliga, N.S.: The role of predictive modelling in rationally re-engineering biological systems. Nature Reviews. Microbiology 7(4), 297–305 (2009)Google Scholar
  25. 25.
    Oh, Y.-K., Palsson, B.O., Park, S.M., Schilling, C.H., Mahadevan, R.: Genome-scale Reconstruction of Metabolic Network in Bacillus subtilis Based on High-throughput Phenotyping and Gene Essentiality Data. Journal of Biological Chemistry 282(39), 28791–28799 (2007)CrossRefGoogle Scholar
  26. 26.
    Patil, K.R.R., Rocha, I., Förster, J., Nielsen, J.: Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics 6(1), 308+ (2005)Google Scholar
  27. 27.
    Pharkya, P., Burgard, A.P., Maranas, C.D.: OptStrain: A computational framework for redesign of microbial production systems. Genome Research 14(11), 2367–2376 (2004)CrossRefGoogle Scholar
  28. 28.
    Pharkya, P., Maranas, C.D.: An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems. Metabolic Engineering 8(1), 1–13 (2006)CrossRefGoogle Scholar
  29. 29.
    Price, N.D., Reed, J.L., Palsson, B.Ø.: Genome-scale models of microbial cells: evaluating the consequences of constraints. Nature Reviews. Microbiology 2(11), 886–897 (2004)CrossRefGoogle Scholar
  30. 30.
    Ramakrishna, R., Edwards, J.S., McCulloch, A., Palsson, B.O.: Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. American Journal of Physiology. Regulatory, Integrative and Comparative Physiology 280(3), R695–R704 (2001)Google Scholar
  31. 31.
    Ranganathan, S., Suthers, P.F., Maranas, C.D.: OptForce: An Optimization Procedure for Identifying All Genetic Manipulations Leading to Targeted Overproductions. PLoS Comput. Biol. 6(4), e1000744+ (April 2010)Google Scholar
  32. 32.
    Rodrigo, G., Carrera, J., Landrain, T.E., Jaramillo, A.: Perspectives on the automatic design of regulatory systems for synthetic biology. FEBS Letters 586(15), 2037–2042 (2012)CrossRefGoogle Scholar
  33. 33.
    Rossi, F., van Beek, P., Walsh, T.: Handbook of Constraint Programming. Elsevier (2006)Google Scholar
  34. 34.
    Sauer, U.: Metabolic networks in motion: 13C-based flux analysis. Molecular Systems Biology, 2(1) (November 2006)Google Scholar
  35. 35.
    Segrè, D., Vitkup, D., Church, G.M.: Analysis of optimality in natural and perturbed metabolic networks. Proceedings of the National Academy of Sciences 99(23), 15112–15117 (2002)CrossRefGoogle Scholar
  36. 36.
    Tepper, N., Shlomi, T.: Predicting metabolic engineering knockout strategies for chemical production: accounting for competing pathways. Bioinformatics 26(4), 536–543 (2010)CrossRefGoogle Scholar
  37. 37.
    Thomas, R.: Boolean formalization of genetic control circuits. Journal of Theoretical Biology 42(3), 563–585 (1973)CrossRefGoogle Scholar
  38. 38.
    Varma, A., Palsson, B.O.: Metabolic Capabilities of Escherichia coli II. Optimal Growth Patterns. Journal of Theoretical Biology 165(4), 503–522 (1993)CrossRefGoogle Scholar
  39. 39.
    Varma, A., Palsson, B.O.: Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use. Nature Biotechnology 12(10), 994–998 (1994)CrossRefGoogle Scholar
  40. 40.
    Wolkenhauer, O., Ullah, M., Kolch, W., Cho, K.-H.H.: Modeling and simulation of intracellular dynamics: choosing an appropriate framework. IEEE Transactions on Nanobioscience 3(3), 200–207 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mathias John
    • 1
    • 2
  • Mirabelle Nebut
    • 1
    • 2
  • Joachim Niehren
    • 1
    • 3
  1. 1.BioComputing, LIFL (CNRS UMR8022)France
  2. 2.University of LilleFrance
  3. 3.INRIA LilleFrance

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