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Global Optimization in Systems Biology: Stochastic Methods and Their Applications

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Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 736))

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Abstract

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.

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References

  1. Balsa-Canto E, Alonso AA, Banga JR (2008) Computational procedures for optimal experimental design in biological systems. IET Syst Biol 2(4):163–172

    CAS  PubMed  Google Scholar 

  2. Balsa-Canto E, Alonso AA, Banga JR (2010) An iterative identification procedure for dynamic modeling of biochemical networks. BMC Syst Biol 4:11

    PubMed  PubMed Central  Google Scholar 

  3. Balsa-Canto E, Peifer M, Banga JR, Timmer J, Fleck C (2008) Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst Biol 2:26

    PubMed  PubMed Central  Google Scholar 

  4. Balsa-Canto E, Vassiliadis VS, Banga JR (2005) Dynamic optimization of single- and multi-stage systems using a hybrid stochastic–deterministic method. Ind Eng Chem Res 44(5): 1514–1523

    CAS  Google Scholar 

  5. Bandara S, Sclöder J, Eils R, Bock H, Meyer T (2009) Optimal experimental design for parameter estimation of a cell signaling model. Plos Comput Biol 5(11):1–12

    Google Scholar 

  6. Banga JR (2008) Optimization in computational systems biology. BMC Syst Biol 2:47–53

    PubMed  PubMed Central  Google Scholar 

  7. Banga JR, Balsa-Canto E (2008) Parameter estimation and optimal experimental design. Essays Biochem 45:195–210

    CAS  PubMed  Google Scholar 

  8. Bartl M, Li P, Schuster S (2010) Modelling the optimal timing in metabolic pathway activation-use of pontryagin’s maximum principle and role of the golden section. Biosystems 101(1): 67–77

    CAS  PubMed  Google Scholar 

  9. Biegler LT, Cervantes A, Wätcher A (2002) Advances in simulaneous strategies for dynamic process optimization. Chem Eng Sci 57(4):575–593

    CAS  Google Scholar 

  10. Bock H, Plitt K (1984) A multiple shooting algorithm for direct solution of optimal control problems. In: Proc 9th IFAC World Congress, Pergamon Press, New York, pp 242–247

    Google Scholar 

  11. Bryson AE, Ho YC (1975) Applied optimal control. Hemisphere Pub. Corp, New York

    Google Scholar 

  12. Castiglione F, Piccoli B (2007) Cancer immunotherapy, mathematical modeling, and optimal control. J Theor Biol 247(4):723–732

    CAS  PubMed  Google Scholar 

  13. Egea JA, Balsa-Canto E, Garcia MSG, Banga JR (2009) Dynamic optimization of nonlinear processes with an enhanced scatter search method. Ind Eng Chem Res 48(9):4388–4401

    CAS  Google Scholar 

  14. Egea JA, Martí R, Banga JR (2010) An evolutionary method for complex-process optimization. Comp Oper Res 37(2):315–324

    Google Scholar 

  15. Egea JA, Rodriguez-Fernandez M, Banga JR, Marti R (2007) Scatter search for chemical and bio-process optimization. J Global Optim 37(3):481–503

    Google Scholar 

  16. Floudas C (2000) Deterministic global optimization: theory, methods and applications. Kluwer Academics, The Netherlands

    Google Scholar 

  17. Hirmajer T, Balsa-Canto E, Banga JR (2009) DOTcvpSB, a software toolbox for dynamic optimization in systems biology. BMC Bioinformatics 10:199–213

    PubMed  PubMed Central  Google Scholar 

  18. 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(24):3067–3074

    CAS  PubMed  Google Scholar 

  19. Jaqaman K, Danuser G (2006) Linking data to models: data regression. Nat Rev Mol Cell Bio 7(11):813–819

    CAS  Google Scholar 

  20. Joly M, Pinto J (2006) Role of mathematical modeling on the optimal control of hiv-1 pathogenesis. AiChe J 52(3):856–884

    CAS  Google Scholar 

  21. Kauffman K, Prakash P, Edwards J (2003) Advances in flux balance analysis. Curr Opin Biotechnol 14(5):491–496

    CAS  PubMed  Google Scholar 

  22. Klipp E, Heinrich R, Holzhtte H (2002) Prediction of temporal gene expression. metabolic opimization by re-distribution of enzyme activities. Eur J Biochem 269:5406–5413

    CAS  PubMed  Google Scholar 

  23. Kotte O, Zaugg J, Heinemann M (2010) Bacterial adaptation through distributed sensing of metabolic fluxes. Mol Sys Biol 6:355

    Google Scholar 

  24. Lebiedz D (2005) Exploiting optimal control for target-oriented manipulation of (bio)chemical systems: A model-based approach to specific modification of self-organized dynamics. Int J Mod Phys B 19 3763–3798

    CAS  Google Scholar 

  25. Lebiedz D, Maurer H (2004) External optimal control of self-organisation dynamics in a chemotaxis reaction diffusion system. IEE Syst Biol 2:222–229

    Google Scholar 

  26. Maiwald T, Timmer J (2008) Dynamical modeling and multi-experiment fitting with PottersWheel. Bioinformatics 24(18):2037–2043

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Mendes P, Kell D (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14(10):869–883

    CAS  PubMed  Google Scholar 

  28. Moles CG, Mendes P, Banga JR (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res 13:2467–2474

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Oyarzun DA, Ingalls B, Middleton R, Kalamatianos D (2009) Sequential activation of metabolic pathways: a dynamic optimization approach. Bull Math Biol 71:1851–1872

    PubMed  Google Scholar 

  30. Pardalos P, Romeijn HE, Tuyb H (2000) Recent developments and trends in global optimization. J Comp App Math 124:209–228

    Google Scholar 

  31. Pinter J (1996) Global optimization in action. Continuous and Lipschitz optimization: algorithms, implementations and applications. Kluwer Academics, Netherlands

    Google Scholar 

  32. Rateitschak K, Karger A, Fitzner B, Lange F, Wolkenhauer O, Jaster R (2010) Mathematical modelling of interferon-gamma signalling in pancreatic stellate cells reflects and predicts the dynamics of stat1 pathway activity. Cell Signal 22:97–105

    CAS  PubMed  Google Scholar 

  33. Rodriguez-Fernandez M, Egea JA, Banga JR (2006) Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics 7:483

    PubMed  PubMed Central  Google Scholar 

  34. Rodriguez-Fernandez M, Mendes P, Banga JR (2006) A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems 83(2–3):24

    Google Scholar 

  35. Salby O, Sager S, Shaik O, Kummer U, Lebiedz D (2007) Optimal control of self-organized dynamics in cellular signal transduction. Math Comp Model Dyn 13:487–502

    Google Scholar 

  36. Schiesser WE (1994) Computational mathematics in engineering and applied science: ODEs, DAEs, and PDEs. CRC Press, Inc., Florida, USA

    Google Scholar 

  37. Schmidt H, Jirstrand M (2006) Systems biology toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4):514–515

    CAS  PubMed  Google Scholar 

  38. Sendin JOH, Exler O, Banga JR (2010) Multi-objective mixed integer strategy for the optimisation of biological networks. IET Syst Biol 4(3):236–248

    CAS  PubMed  Google Scholar 

  39. Sendin JOH, Vera J, Torres N, Banga JR (2006) Model based optimization of biochemical systems using multiple objectives: A comparison of several solution strategies. Math Comp Mod Dyn Syst 12(5):469–487

    Google Scholar 

  40. Sugimoto M, Kikuchi S, Tomita M (2005) Reverse engineering of biochemical equations from time-course data by means of genetic programming. BioSystems 80:155–164

    CAS  PubMed  Google Scholar 

  41. Sutherland W (2005) The best solution. Nature 435:569

    CAS  PubMed  Google Scholar 

  42. Talbi EG (2009) Metaheuristics: from design to implementation. Wiley Publishing, New Jersey, USA

    Google Scholar 

  43. Toulouse M, Crainic T, Sansó B (2004) Systemic behavior of cooperative search algorithms. Parallel Comput 30:57–79

    Google Scholar 

  44. Vassiliadis VS, Pantelides CC, Sargent RWH (1994) Solution of a class of multistage dynamic optimization problems. 1. problems without path constraints. Ind Eng Chem Res 33(9): 2111–2122

    CAS  Google Scholar 

  45. Vera J, de Atauri P, Torres N, Banga JR (2003) Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by Saccharomyces cerevisiae. Biotechnol Bioeng 83(3):335–343

    CAS  PubMed  Google Scholar 

  46. Vera J, Balsa-Canto E, Wellstead P, Banga JR, Wolkenhauer O (2007) Power-law models of signal transduction pathways. Cell Signal 19:1531–1541

    CAS  PubMed  Google Scholar 

  47. Zaslaver A, Mayo A, Rosenberg R, Bashkin P, Sberro H, Tsalyuk M, Surette M, Alon U (2004) Just-in-time transcription program in metabolic pathways. Nat Genet 36:486–491

    CAS  PubMed  Google Scholar 

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Acknowledgments

This work was supported by the Spanish MICINN project “MultiSysBio” (ref. DPI2008-06880-C03-02), and by CSIC intramural project “BioREDES” (ref. PIE-201170E018).

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Correspondence to Eva Balsa-Canto .

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Balsa-Canto, E., Banga, J.R., Egea, J.A., Fernandez-Villaverde, A., de Hijas-Liste, G.M. (2012). Global Optimization in Systems Biology: Stochastic Methods and Their Applications. In: Goryanin, I.I., Goryachev, A.B. (eds) Advances in Systems Biology. Advances in Experimental Medicine and Biology, vol 736. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7210-1_24

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