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A Mathematical Model for Optimal Functional Disruption of Biochemical Networks

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Journal of Mathematical Modelling and Algorithms

Abstract

Biochemical networks are a particular kind of biological networks which describe the cell metabolism and regulate various biological functions, from biochemical pathways to cell growth. The relationship between structure, function and regulation in complex cellular networks is still a largely open question. This complexity calls for proper mathematical models and methods relating network structure and functional properties. In this paper we focus on the problem of drug targets’ identification by detecting network alteration strategies which lead to a cell functionality loss. We propose a mathematical model, based on a bi-level programming formulation, to obtain the minimum cost disruption policy through the identification of specific gene deletions. These deletions represent drug target identification of new drug treatments for hindering bacterial infections.

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References

  1. Alberghina, L., Westerhoff, H.V. (eds.): Systems Biology: Definitions and Perspectives. Springer, New York (2005)

    Google Scholar 

  2. Bard, J.F.: Practical Bilevel Optimization Algorithms and Applications. Kluwer Academic, Dordrecht (1998)

    MATH  Google Scholar 

  3. Becker, S.A., Palsson, B.Ø.: Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation. BMC Microbiol. 5(8) (2005)

  4. Burgard, A.P., Pharkya, P., Maranas, C.D.: OptKnock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol. Bioeng. 84(6), 647–657 (2003)

    Article  Google Scholar 

  5. Chen, B.S., Li, C.W.: Analysing microarray data in drug discovery using systems biology. Expert Opinion Drug Discovery 2, 755–768 (2007)

    Article  Google Scholar 

  6. Chu, L.H., Chen, B.S.: Construction of cancer-perturbed protein-protein interaction network for discovery of apoptosis drug targets. BMC Systems Biology 2-56- (2008)

  7. Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic, Dordrecht (2002)

    MATH  Google Scholar 

  8. Edwards, J.S., Palsson, B.O.: How will bioinformatics influence metabolic engineering? Biotechnol. Bioeng. 58, 162–169 (1998)

    Article  Google Scholar 

  9. Fortuny-Amat, J., McCarl, B.: A representation and ecnomic interpretation of a two-level programming problem. J. Oper. Soc. 32 783–792 (1981)

    MathSciNet  MATH  Google Scholar 

  10. Haus, U., Klamt, S., Stephen, T.: Computing knock-out strategies in metabolic networks. J. Comput. Biol. 15, 259–268 (2008)

    Article  MathSciNet  Google Scholar 

  11. Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Chapman and Hall, New York (1996)

    MATH  Google Scholar 

  12. Kadirkamanathan, V., Yang, J., Billings, S.A., Wright, P.C.: Markov chain Monte Carlo algorithm based metabolic flux distribution analysis on Corynebacterium glutamicum. Bioinformatics 22(21), 2681–2687 (2006)

    Article  Google Scholar 

  13. Kitano, H., et al.: Foundations of Systems Biology. MIT, Cambridge (2001)

    Google Scholar 

  14. Klamt, S., Gilles, E.D.: Minimal cut sets in biochemical reaction networks. Bioinformatics 20, 226–234 (2004)

    Article  Google Scholar 

  15. Kotaka, M., Dhaliwal, B., Ren, J., Nichols, C.E., Angell, R., Lockyer, M., Hawkins, A.R., Stammers, D.K.: Structures of S. aureus thymidylate kinase reveal an atypical active site configuration and an intermediate conformational state upon substrate binding. Protein Sci. 15, 774–784 (2006)

    Article  Google Scholar 

  16. Lanzeni, S., Messina, E., Archetti, F.: Graph models and mathematical programming in biochemical networks analysis and metabolic engineering design. Comput. Math. Appl. 55(5), 970–983 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Moore, J.T., Bard, J.F.: The mixed integer linear bilevel programming problem. Oper. Res. 38(5), 911–921 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Neidhardt, F.C.: Escherichia Coli and Salmonella. American Society for Microbiology Press, Washington DC (1996)

    Google Scholar 

  19. Palsson, B.O.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge (2006)

    Google Scholar 

  20. Paun, G., Sheng, Y.: On synchronization in P systems. Fundam. Inform. 38(4), 397–410 (1999)

    MATH  Google Scholar 

  21. Popova-Zeugmann, L.: Time petri nets for modelling and analysis of biochemical networks. Fundam. Inform. 67, 149–162 (2005)

    MathSciNet  MATH  Google Scholar 

  22. Reed, J.L., Vo, T.D., Schilling, C.H., Palsson, B.Ø.: An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR). Genome Biol. 4(9), R54.1–R54.12 (2003)

    Article  Google Scholar 

  23. Segre, D., Vitkup, D., Mc Church, G.: Analysis of optimality in natural and perturbed metabolic networks. PNAS 99(23) (2002)

  24. Shlomi, T., Berkman, O., Ruppin, E.: Regulatory on/off minimization of metabolic flux changes after gene perturbations. PNAS 102(21), 7696–7700 (2005)

    Article  Google Scholar 

  25. Thiele, I., Vo, T.D., Price, N.D., Palsson, B.Ø.: An expanded metabolic reconstruction of Helicobacter pylori (iIT341 GSM/GPR): an in silico genome-scale characterization of single and double deletion mutants. J. Bacteriol. 187(16), 5818–5830 (2005)

    Article  Google Scholar 

  26. Tomlin, C.D.S.: The Pesticide Manual, 13th edn. The British Crop Protection Council, Croydon (2003)

    Google Scholar 

  27. Treble, D.H., Lamport, D.T.A., Peters, R.A.: The inhibition of plant Aconitate hydratase (aconitase) by fluorocitrate. Biochem. J. 85, 113–115 (1962)

    Google Scholar 

  28. Varma, A., Palsson, B.O.: Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl. Environ. Microbiol. 60, 3724–3731 (1994)

    Google Scholar 

  29. Vincente, L., Savard, G., Judice, J.: The discrete linear bilevel programming problem. J. Optim. Theory Appl. 89, 597–614 (1996)

    Article  MathSciNet  Google Scholar 

  30. Vogel, D.S., Axelrod, R.C.: Predicting the effects of gene deletion. SIGKDD Explorations 4(2), 101–103 (2002)

    Article  Google Scholar 

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Correspondence to Guglielmo Lulli.

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Lulli, G., Messina, E., Archetti, F. et al. A Mathematical Model for Optimal Functional Disruption of Biochemical Networks. J Math Model Algor 9, 19–37 (2010). https://doi.org/10.1007/s10852-009-9118-0

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  • DOI: https://doi.org/10.1007/s10852-009-9118-0

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