Computational Procedures for Model Identification

Chapter
Part of the Systems Biology book series (SYSTBIOL)

Abstract

Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model’s response. These parameters can be usually estimated by fitting the model to experimental data. This chapter covers the parameter identification problem, its formulation and solution, and two closely related topics: identifiability and optimal experimental design.

Keywords

Parameter estimation Identifiability Optimal experimental design Global optimization 

Notes

Acknowledgments

The authors acknowledge financial support from Spanish MICINN project “MultiSysBio,” ref. DPI2008-06880-C03-02.

References

  1. Balsa-Canto E, Alonso AA, Banga JR (2008a) Computational procedures for optimal experimental design in biological systems. IET Syst Biol 2(4):163–172PubMedCrossRefGoogle Scholar
  2. Balsa-Canto E, Peifer M, Banga JR et al (2008b) Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst Biol 2:26PubMedCentralPubMedCrossRefGoogle Scholar
  3. Banga JR, Versyck KJ, Van Impe JF (2002) Computation of optimal identification experiments for nonlinear dynamic process models: an stochastic global optimization approach. Ind Eng Chem Res 41, 2425–2430CrossRefGoogle Scholar
  4. Bock H (1981) Numerical treatment of inverse problems in chemical reaction kinetics. In: K E, P D, W J (eds) Modelling of chemical reaction systems. Springer, New YorkGoogle Scholar
  5. Bock H (1983) Recent advances in parameter identification techniques for ordinary differential equations. In: P D, E H (ed) Numerical treatment of inverse problems in Differential and Integral BirkhäuserGoogle Scholar
  6. Cho KH, Wolkenhauer O (2003) Analysis and modelling of signal transduction pathways in systems biology. Biochem Soc Trans 31:1503–1509PubMedCrossRefGoogle Scholar
  7. Dennis JE, Gay DM and Welsch RE (1981) An adaptive nonlinear least-squares algorithm. ACM Trans Math Software 7(3)Google Scholar
  8. Dréo J, Petrowski A, Taillard E, Siarry P (2006) Metaheuristics for hard optimization. Methods and case studies. Springer, New YorkGoogle Scholar
  9. Egea JA, Rodriguez-Fernandez M, Banga JR, Martí R (2007). Scatter search for chemical and bioprocess optimization. J Glob Opt 37(3):481–503CrossRefGoogle Scholar
  10. Esposito WR, Floudas C (2000) Global optimization for the parameter estimation of differential-algebraic systems. Ind Eng Chem Res 39:1291–1310CrossRefGoogle Scholar
  11. Fletcher R. (1987) Practical methods of optimization. Wiley, UKGoogle Scholar
  12. Floudas CA (2000) Deterministic global optimization: theory, methods and applications. Kluwer Academics, NetherlandsCrossRefGoogle Scholar
  13. Gau CY, Stadtherr MA (2000) Reliable nonlinear parameter estimation using interval analysis: error in variable approach. Comp Chem Eng 24:631–637CrossRefGoogle Scholar
  14. Goodwin BC (1965) Oscillatory behavior in enzymatic control processes. Adv Enz Regul 3:425–428CrossRefGoogle Scholar
  15. Hairer E, Nørsett SP, Wanner G (1993) Solving ordinary differential equations I: Nonstiff problems, 2nd edn, Springer, BerlinGoogle Scholar
  16. Hairer E, Wanner G (1996) Solving ordinary differential equations II: Stiff and differential-algebraic problems, 2nd edn, Springer, BerlinCrossRefGoogle Scholar
  17. Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005). Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw 31(3):363–396CrossRefGoogle Scholar
  18. Hoffmann A, Levchenko A, Scott ML, Baltimore D (2002) The IkB-NF-kB signaling module: temporal control and selective gene activation. Science 298:1241–1245PubMedCrossRefGoogle Scholar
  19. Janes KA, Lauffenburger DA (2006) A biological approach to computational models of proteomic networks. Curr Op Chem Biol 10:73–80CrossRefGoogle Scholar
  20. Klipp E, Liebermeister W (2006) Mathematical modelling of intracellular signaling pathways. BMC Neurosci 7, doi:10.1186/1471-2202-7-S1-S10Google Scholar
  21. Lee EG, Boone DL, Chai S, Libby SL, Chien M, Lodolce JP, Ma A (2000) Failure to regulate TNF-induced NF-·B and cell death responses in A20-deficient mice. Science 289:2350–2354PubMedCentralPubMedCrossRefGoogle Scholar
  22. Leis JR, Kramer MA (1988) Odessa- an ordinary differential-equation solver with explicit simultaneous sensitivity analysis. ACM Trans Math Soft 14:61–67CrossRefGoogle Scholar
  23. Lin Y, Stadtherr MA (2006) Deterministic global optimization for parameter estimation of dynamic systems. Ind Eng Chem Res 45:8438–8448CrossRefGoogle Scholar
  24. Lipniacki T, Paszek P, Brasier AR et al (2004) Mathematical model of NFκB regulatory module. J Theor Biol 228:195–215PubMedCrossRefGoogle Scholar
  25. Ljung L (1999) System identification: theory for the user. Prentice Hall, NJGoogle Scholar
  26. Mendes P, Kell DB (1998) Nonlinear optimization of biochemical pathways: Applications to metabolic engineering and parameter estimation. Bioinformatics 14:869–883PubMedCrossRefGoogle Scholar
  27. Moles C, Mendes P, Banga J (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res 13:2467–2474PubMedCrossRefGoogle Scholar
  28. Nash SG, Sofer A (1996) Linear and nonlinear programming. McGraw-Hill, New York, NYGoogle Scholar
  29. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313CrossRefGoogle Scholar
  30. Pardalos P, Romeijna H, Tuyb H (2000) Recent developments and trends in global optimization. J Comp App Math 124:209–228CrossRefGoogle Scholar
  31. Peifer M, Timmer J (2007) Parameter estimation in ordinary differential equations for biochemical processes using the method of multiple shooting. IET Syst Biol 1(2):78–88PubMedCrossRefGoogle Scholar
  32. Pinter J (1996) Global optimization in action. Continuous and Lipschitz optimization: Algorithms, implementations and applications. Kluwer, NetherlandsCrossRefGoogle Scholar
  33. Polisetty P, Voit E, Gatzke E (2006) Identification of metabolic system parameters using global optimization methods. Theor Biol Med Mod 3:4CrossRefGoogle Scholar
  34. Rodriguez-Fernandez M, Egea JA, Banga JR (2006a) Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinform 7:483CrossRefGoogle Scholar
  35. Rodriguez-Fernandez M, Mendes P, Banga JR (2006b) A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Bio Syst 83(2–3):248–265Google Scholar
  36. Runarsson T, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comp 564:284–294CrossRefGoogle Scholar
  37. Schittkowski K (2002) Numerical data fitting in dynamical systems. Kluwer, NetherlandsCrossRefGoogle Scholar
  38. Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley series in probability and mathematical statistics. Wiley, New YorkGoogle Scholar
  39. Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359CrossRefGoogle Scholar
  40. Sugimoto M, Kikuchi S, Tomita M (2005) Reverse engineering of biochemical equations from time-course data by means of genetic programming. BioSystems 80:155–164PubMedCrossRefGoogle Scholar
  41. Swameye I, Müller T, Timmer J et al (2003) Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by data-based modeling. Proc Natl Acad Sci 100(3):1028–1033PubMedCrossRefGoogle Scholar
  42. Vera J, Balsa-Canto E, Wellstead P et al (2007) Power-law models of signal transduction pathways. Cell Signal 19:1531–1541PubMedCrossRefGoogle Scholar
  43. Walter E, Pronzato L (1997) Identification of parametric models from experimental data. Springer, New YorkGoogle Scholar
  44. Wolkenhauer O, Ullah M, Kolch W et al (2004) Modeling and simulation of intracellular dynamics: Choosing an appropriate framework. IEEE Trans. Nanobiosci 3(3):200–207CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.(Bio)Process Engineering GroupIIM-CSIC (Spanish National Research Council)VigoSpain

Personalised recommendations