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Parameter identification, experimental design and model falsification for biological network models using semidefinite programming

Parameter identification, experimental design and model falsification for biological network models using semidefinite programming

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One of the most challenging tasks in systems biology is parameter identification from experimental data. In particular, if the available data are noisy, the resulting parameter uncertainty can be huge and should be quantified. In this work, a set-based approach for parameter identification in discrete time models of biochemical reaction networks from time series data is developed. The basic idea is to determine an outer approximation to the set of parameters for which trajectories are consistent with the available data. In order to approximate the set of consistent parameters (SCP) a feasibility problem is derived. This feasibility problem is used to verify that complete parameter sets cannot contain consistent parameters. This method is very appealing because instead of checking a finite number of distinct points, complete sets are analysed. With this approach, model falsification simply corresponds to showing that the SCP is empty. Besides parameter identification, a novel set-based method for experimental design is presented. This method yields reliable predictions on the information content of future measurements also for the case of very limited a priori knowledge and uncertain inputs. The properties of the method are presented using a discrete time model of the MAP kinase cascade.

References

    1. 1)
      • M. Joshi , A. Seidel-Morgenstern , A. Kremling . Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems. Metabolic Eng. , 5 , 447 - 455
    2. 2)
      • E. Balsa-Canto , M. Peifer , J.R. Banga , J. Timmer , C. Fleck . Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst. Biol.
    3. 3)
      • J.F. Sturm . Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. , 625 - 653
    4. 4)
      • M. Rodriguez-Fernandez , J.A. Egea , J.R. Banga . Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinf.
    5. 5)
      • B.H. Chen , S.P. Asprey . On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations. Ind. Eng. Chem. Res. , 1379 - 1390
    6. 6)
      • S. Boyd , L. Vandenberghe . (2004) Convex optimization.
    7. 7)
      • C.G. Moles , P. Mendes , J.R. Banga . Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res. , 11 , 2467 - 2474
    8. 8)
      • E.O. Voit . (2000) Computational analysis of biochemical systems.
    9. 9)
      • R.J. Orton , O.E. Sturm , V. Vyshemirsky , M. Calder , D.R. Gilbert , W. Kolch . Computational modelling of the receptor-tyrosine-kinase-activated mapk pathway. Biochem. J. , 249 - 261
    10. 10)
      • Waldherr, S., Findeisen, R., Allgöwer, F.: `Global sensitivity analysis of biochemical reaction networks via semidefinite programming', Proc. 17th IFAC World Congress, 2008, p. 9701–9706.
    11. 11)
      • T. Johnson , W. Tucker . Rigorous parameter reconstruction for differential equations with noisy data. Automatica , 2422 - 2426
    12. 12)
      • L. Jaulin , M. Kieffer , O. Didrit , E. Walter . (2001) Applied interval analysis.
    13. 13)
      • M. Kieffer , E. Walter . Interval analysis for guaranteed nonlinear parameter and state estimation. Math. Comput. Model. Dyn. Syst. , 2 , 171 - 181
    14. 14)
      • W. Tucker , Z. Kutalik , V. Moulton . Estimating parameters for generalized mass action models using constraint propagation. Math. Biosci. , 607 - 620
    15. 15)
      • E. Balsa-Canto , A.A. Alonso , J.R. Banga . Computational procedures for optimal experimental design in biological systems. IET Syst. Biol. , 4 , 163 - 172
    16. 16)
      • Z. Szallasi , Z. Szallasi , J. Stelling , V. Periwal . (2006) Biological data acquisition or system level modeling – an exercise in the art of compromise, System modeling in cellular biology.
    17. 17)
      • S.P. Asprey , S. Macchietto . Designing robust optimal dynamic experiments. J. Process Control , 545 - 556
    18. 18)
      • T. Fujie , M. Kojima . Semidefinite programming relaxation for non-convex quadratic programs. J. Global Optim. , 367 - 380
    19. 19)
      • P.A. Parrilo . Semidefinite programming relaxations for semialgebraic problems. Math. Program. B , 293 - 320
    20. 20)
      • A. Kremling , S. Fischer , K. Gadkar . A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. Genome Res. , 1773 - 1785
    21. 21)
      • Borchers, S., Rumschinski, P., Bosio, S., Weismantel, R., Findeisen, R.: `Model discrimination and parameter estimation via infeasibility certificates for dynamical biochemical reaction networks', 15thIFAC Symp. on System Identification, 2009, p. 245–250.
    22. 22)
      • E. Walter , M. Kieffer . Guaranteed nonlinear parameter estimation in knowledge-based model. J. Comput. Appl. Math. , 2 , 277 - 285
    23. 23)
      • L. Kuepfer , U. Sauer , P.A. Parrilo . Efficient classification of complete parameter regions based on semidefinite programming. BMC Bioinf.
    24. 24)
      • Faisal, S., Lichtenberg, G., Werner, H.: `A polynomial approach to structural gene dynamics modelling', Proc. 16th IFAC World Congress, 2005, Prague.
    25. 25)
      • Hasenauer, J., Rumschinski, P., Waldherr, S., Borchers, S., Allgöwer, F., Findeisen, R.: `Guaranteed steady-state bounds for uncertain chemical processes', Proc. Int. Symp. on Advanced Control of Chemical Processes, Adchem, 2009, p. 674–679.
    26. 26)
      • C.P. Robert , G. Casella . (2004) Monte Carlo statistical methods.
    27. 27)
      • P. Deuflhard , F. Bornemann . (2002) Scientific computing with ordinary differential equations.
    28. 28)
      • L. Ljung . (1999) System identification: theory for the user.
    29. 29)
      • L. Vandenberghe , S. Boyd . Semidefinite programming. SIAM Rev. , 49 - 95
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