Simultaneous model discrimination and parameter estimation in dynamic models of cellular systems

BMC Systems Biology

Julio R Banga³  Andreas Kremling²  Markus Rehberg¹  Maria Rodriguez-Fernandez³ 

[1] Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany;Faculty of Mechanical Engineering Specialty Division for Systems Biotechnology, Technische Universitat München, Boltzmannstr. 15, 85748 Garching, Germany;(Bio) Process Engineering Group, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain

关键词: Global optimization;    Model discrimination;    Parameter estimation;    Dynamic modelling;   

Others  :  1142455
DOI  :  10.1186/1752-0509-7-76

 received in 2012-05-08, accepted in 2013-08-08,  发布年份 2013

【 摘 要 】

Background

Model development is a key task in systems biology, which typically starts from an initial model candidate and, involving an iterative cycle of hypotheses-driven model modifications, leads to new experimentation and subsequent model identification steps. The final product of this cycle is a satisfactory refined model of the biological phenomena under study. During such iterative model development, researchers frequently propose a set of model candidates from which the best alternative must be selected. Here we consider this problem of model selection and formulate it as a simultaneous model selection and parameter identification problem. More precisely, we consider a general mixed-integer nonlinear programming (MINLP) formulation for model selection and identification, with emphasis on dynamic models consisting of sets of either ODEs (ordinary differential equations) or DAEs (differential algebraic equations).

Results

We solved the MINLP formulation for model selection and identification using an algorithm based on Scatter Search (SS). We illustrate the capabilities and efficiency of the proposed strategy with a case study considering the KdpD/KdpE system regulating potassium homeostasis in Escherichia coli. The proposed approach resulted in a final model that presents a better fit to the in silico generated experimental data.

Conclusions

The presented MINLP-based optimization approach for nested-model selection and identification is a powerful methodology for model development in systems biology. This strategy can be used to perform model selection and parameter estimation in one single step, thus greatly reducing the number of experiments and computations of traditional modeling approaches.

【 授权许可】

   
2013 Rodriguez-Fernandez et al.; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

【 参考文献 】

• [1]van Riel NAW: Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments. Brief Bioinform 2006, 7(4):364.
• [2]Stelling J: Mathematical models in microbial systems biology. Curr Opin Microbiol 2004, 7(5):513-518.
• [3]Banga JR, Balsa-Canto E: Parameter estimation and optimal experimental design. Essays Biochem 2008, 45:195.
• [4]Jaqaman K, Danuser G: Linking data to models: data regression. Nat Rev Mol Cell Biol 2006, 7(11):813-819.
• [5]Ashyraliyev M, Fomekong-Nanfack Y, Kaandorp JA, Blom JG: Systems biology: parameter estimation for biochemical models. FEBS J 2008, 276(4):886-902.
• [6]Kitano H: Computational systems biology. Nature 2002, 420(6912):206-210.
• [7]Aderem A: Systems biology: its practice and challenges. Cell 2005, 121(4):511-513.
• [8]Arita M, Robert M, Tomita M: All systems go: launching cell simulation fueled by integrated experimental biology data. Curr Opin Biotechnol 2005, 16(3):344-349.
• [9]Feng X, Rabitz H: Optimal identification of biochemical reaction networks. Biophys J 2004, 86(3):1270-1281.
• [10]Kremling A, Fischer S, Gadkar K, Doyle III FJ, Sauter T, Bullinger E, Gilles ED, Allgower F: A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. Genome Res 2004, 14(9):1773.
• [11]Gadkar KG, Gunawan R, Doyle III FJ: Iterative approach to model identification of biological networks. BMC Bioinform 2005, 6:155. BioMed Central Full Text
• [12]Balsa-Canto E, Alonso A, Banga JR: An iterative identification procedure for dynamic modeling of biochemical networks. BMC Syst Biol 2010, 4:11. BioMed Central Full Text
• [13]Bandara S, Schloeder JP, Eils R, Bock HG, Meyer T: Optimal experimental design for parameter estimation of a cell signaling model. PLoS Comput Biol 2009, 5(11):e1000558.
• [14]Apgar JF, Toettcher JE, Endy D, White FM, Tidor B: Stimulus design for model selection and validation in cell signaling. PLoS Comput Biol 2008, 4(2):e30.
• [15]Melykuti B, August E, Papachristodoulou A, El-Samad H: Discriminating between rival biochemical network models: three approaches to optimal experiment design. BMC Syst Biol 2010, 4:38. BioMed Central Full Text
• [16]Skanda D, Lebiedz D: An optimal experimental design approach to model discrimination in dynamic biochemical systems. Bioinform 2010, 26(7):939-945.
• [17]Lillacci G, Khammash M: Parameter estimation and model selection in computational biology. PLoS Comput Biol 2010, 6(3):e1000696.
• [18]Verheijen PJT: Model selection: an overview of practices in chemical engineering. Comput Aided Chem Eng 2003, 16:85-104.
• [19]Petzold L, Zhu W: Model reduction for chemical kinetics: An optimization approach. AIChE J 1999, 45(4):869-886.
• [20]Edwards K, Edgar TF, Manousiouthakis VI: Reaction mechanism simplification using mixed-integer nonlinear programming. Comput Chem Eng 2000, 24:67-79.
• [21]Maurya MR, Bornheimer SJ, Venkatasubramanian V, Subramaniam S: Mixed-integer nonlinear optimisation approach to coarse-graining biochemical networks. IET Syst Biol 2009, 3:24.
• [22]Nikolaev EV: The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems. Metab Eng 2010, 12(1):26-38.
• [23]Banga JR: Optimization in computational systems biology. BMC Syst Biol 2008, 2:47. BioMed Central Full Text
• [24]Aldrich J: R. A. Fisher and the making of maximum likelihood 1912-1922. Stat Sci 1997, 12(3):162-176.
• [25]Akaike H: A new look at the statistical model identification. IEEE Trans Automatic Control 1974, 19(6):716-723.
• [26]Cedersund G, Roll J: Systems biology: model based evaluation and comparison of potential explanations for given biological data. FEBS J 2009, 276(4):903-922.
• [27]McDonald CP, Urban NR: Using a model selection criterion to identify appropriate complexity in aquatic biogeochemical models. Ecol Model 2010, 221(3):428-432.
• [28]Rodriguez-Fernandez M, Mendes P, Banga JR: A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosyst 2006, 83(2-3):248-265.
• [29]Egea JA, Rodriguez-Fernandez M, Banga JR, Martí R: Scatter Search for Chemical and Bio-Process Optimization. J Glob Optimization 2007, 37:481-503.
• [30]Schlüter M, Egea JA, Banga JR: Extended ant colony optimization for non-convex mixed integer nonlinear programming. Comput Oper Res 2009, 36(7):2217-2229.
• [31]Egea JA, Banga JR, Martí R: An evolutionary method for complex-process optimization. Comput Oper Res 2010, 37(2):315-324.
• [32]Exler O, Schittkowski K: A trust region SQP algorithm for mixed-integer nonlinear programming. Optimization Lett 2007, 1(3):269-280.
• [33]Schittkowski K: A collection of 186 test problems for nonlinear mixed-integer programming. 2012. Tech. rep., Department of Computer Science; University of Bayreuth
• [34]Exler O, Lehmann T, Schittkowski K: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization. Math Program Comput 2012, 4(4):383-412.
• [35]Diehl M, Walther A, Bock HG, Kostina E: An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization. Optimization Methods Softw 2010, 25(4):531-552.
• [36]Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmueller U, Timmer J: Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinform 2009, 25(15):1923-1929.
• [37]Vanlier J, Tiemann CA, Hilbers PAJ, van Riel NAW: An integrated strategy for prediction uncertainty analysis. Bioinform 2012, 28(8):1130-1135.
• [38]Brannmark C, Palmer R, Glad ST, Cedersund G, Stralfors P: Mass and information feedbacks through receptor endocytosis govern insulin signaling as revealed using a parameter-free modeling framework. J Biol Chem 2010, 285(26):20171-20179.
• [39]Rodriguez-Fernandez M, Banga JR, Doyle III FJ: Novel global sensitivity analysis methodology accounting for the crucial role of the distribution of input parameters: application to systems biology models. Int J Robust Nonlinear Control 2012, 22(10):1082-1102.
• [40]Jacquez JA, Greif P: Numerical Parameter Identifiability and estimability: integrating identifiability, estimability, and optimal sampling desing. Math Biosci 1985, 77:201-227.
• [41]Audoly S, Bellu G, D’Angio L, Saccomani MP, Cobelli C: Global identifiability of nonlinear models of biological systems. IEEE Trans Biomed Eng 2001, 48(1):55-65.
• [42]Fisher F: Econometrica. 1959, 27(3):431-447.
• [43]Brun R, Reichert P, Kunsch HR: Practical identifiability analysis of large environmental simulation models. Water Resour Res 2001, 37:1015-1030.
• [44]Karnavas WJ, Sanchez P, Bahill AT: Sensitivity analyses of continuous and discrete systems in the time and frequency domains. IEEE Trans Syst, Man, Cybern 1993, 23(2):488-501.
• [45]Kucherenko S, Rodriguez-Fernandez M, Pantelides C, Shah N: Monte Carlo evaluation of derivative based global sensitivity measures. Reliability Eng Syst Saf 2009, 94:1135-1148.
• [46]Rodriguez-Fernandez M, Banga JR: SensSB: A software toolbox for the development and sensitivity analysis of systems biology models. Bioinform 2010, 26(13):1675-1676.
• [47]Kremling A, Heermann R, Centler F, Jung K, Gilles ED: Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli. Biosyst 2004, 78(1-3):23-37.
• [48]Alon U: An Introduction to Systems Biology - Design Principles of Biological Circuits. London: Chapman & Hall/CRC; 2007.
• [49]Widder S, Schicho J, Schuster P: Dynamic patterns of gene regulation I: Simple two-gene systems. J Theor Biol 2007, 246(3):395-419.
• [50]Konkoli Z: A danger of low copy numbers for inferring incorrect cooperativity degree. Theor Biol Med Model 2010, 7:40. BioMed Central Full Text
• [51]Prill R, Marbach D, Saez-Rodriguez J, Sorger P, Alexopoulos L, Xue X, Clarke N, Altan-Bonnet G, Stolovitzky G: Towards a rigorous assessment of systems biology models: the DREAM3 challenges. PloS one 2010, 5(2):e9202.
• [52]Szederkenyi G, Banga JR, Alonso AA: Inference of complex biological networks: distinguishability issues and optimization-based solutions. BMC Syst Biol 2011, 5:177. BioMed Central Full Text