Abstract
Computer simulation is an important technique to capture the dynamics of biochemical networks. Since few quantitative values are measured in vivo, the values for unmeasured parameters should be estimated so that the simulation agrees with the experimental data. Considering the sparsity and error rates of experimentally measured data, the first thing is not to find a numerically exact and global solution but to explore a variety of the plausible parameter solutions. To find many plausible parameter solutions without any biases, we developed the two-phase search (TPS) method. However, calculation complexity makes it hard for TPS to optimize a large-scale dynamic model. In this study divide-and-conquer methods are used to solve this problem. The flux module decomposition (FMD) is first proposed that separates a complex, large-scale dynamic model into multiple flux modules without deteriorating its basic control architectures. FMD is combined with TPS, named FMD-TPS, to find many plausible parameter solutions for a dynamic model. To demonstrate the feasibility of FMD-TPS, it is applied to the E. coli ammonia assimilation system that consists of multiple-feedback loops. The variability of the solutions is verified by measuring the space distribution of the parameter solution vectors and by defining the binary vectors checking the consistency with biological behaviors. Compared with non-decomposition methods, FMD-TPS efficiently explored a variety of plausible parameter solutions that reproduce the dynamic behaviors in vivo.
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References
Jaqaman K, Danuser G (2006) Linking data to models: data regression. Nat Rev Mol Cell Biol 7:813–819
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
Banga JR (2008) Optimization in computational systems biology. BMC Syst Biol 2:47
Mendes P, Kell D (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14:869–883
Maeda K, Fukano Y, Yamamichi S, Nitta D, Kurata H (2011) An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks. Bioprocess Biosyst Eng 34:433–446
Maeda K, Kurata H (2011) Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks. J Theor Biol 272:174–186
Maeda K, Kurata H (2009) Two-phase search (TPS) method: nonbiased and high-speed parameter search for dynamic models of biochemical networks. IPSJ Trans Bioinforma 2:2–14
Kurata H, Tanaka T, Ohnishi F (2007) Mathematical identification of critical reactions in the interlocked feedback model. PLoS One 2:e1103
Maeda K, Kurata H (2012) A symmetric dual feedback system provides a robust and entrainable oscillator. PLoS One 7:e30489
Kimura S, Ide K, Kashihara A, Kano M, Hatakeyama M, Masui R, Nakagawa N, Yokoyama S, Kuramitsu S, Konagaya A (2005) Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics 21:1154–1163
Koh G, Teong HF, Clement MV, Hsu D, Thiagarajan PS (2006) A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk. Bioinformatics 22:e271–e280
van Riel NA (2006) Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments. Brief Bioinforma 7:364–374
van Riel NA, Sontag ED (2006) Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach. Syst Biol 153:263–274
Voit EO, Almeida J (2004) Decoupling dynamical systems for pathway identification from metabolic profiles. Bioinformatics 20:1670–1681
Kurata H, El-Samad H, Iwasaki R, Ohtake H, Doyle JC, Grigorova I, Gross CA, Khammash M (2006) Module-based analysis of robustness tradeoffs in the heat shock response system. PLoS Comput Biol 2:e59
Masaki K, Maeda K, Kurata H (2012) Biological design principles of complex feedback modules in the E. coli ammonia assimilation system. Artif Life 18:53–90
Nishio Y, Usuda Y, Matsui K, Kurata H (2008) Computer-aided rational design of the phosphotransferase system for enhanced glucose uptake in Escherichia coli. Mol Syst Biol 4:160
Kurata H, Masaki K, Sumida Y, Iwasaki R (2005) CADLIVE dynamic simulator: direct link of biochemical networks to dynamic models. Genome Res 15:590–600
Kurata H, Taira K (2000) Two-phase partition method for simulating a biological system at an extremely high speed. Genome Inform Ser Workshop Genome Inform 11:185–195
Moles CG, Mendes P, Banga JR (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res 13:2467–2474
Sun J, Garibaldi JM, Hodgman C (2012) Parameter estimation using metaheuristics in systems biology: a comprehensive review. IEEE/ACM Trans Comput Biol Bioinforma 9:185–202
Ono I, Kobayashi S (1997) A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: Proceedings of the 7th international conference on genetic algorithms, pp 246–253
Satoh H, Yamamura M, Kobayashi S (1997) Minimal generation gap model for GAs considering both exploration and exploitation. In: Proceedings of the international conference on fuzzy logic, neural networks and soft computing, pp 494–497
Kurata H, Inoue K, Maeda K, Masaki K, Shimokawa Y, Zhao Q (2007) Extended CADLIVE: a novel graphical notation for design of biochemical network maps and computational pathway analysis. Nucleic Acids Res 35:e134
Kurata H, Matoba N, Shimizu N (2003) CADLIVE for constructing a large-scale biochemical network based on a simulation-directed notation and its application to yeast cell cycle. Nucleic Acids Res 31:4071–4084
Ninfa AJ, Jiang P, Atkinson MR, Peliska JA (2000) Integration of antagonistic signals in the regulation of nitrogen assimilation in Escherichia coli. Curr Top Cell Regul 36:31–75
Acknowledgments
This work was supported by Grant-in-Aid for Scientific Research (B) (22300101) from the Japan Society for the Promotion of Science and by Grant-in-Aid for Scientific Research on Innovative Areas (23134506) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. KM was supported by Research Fellowships from the Japan Society for the Promotion of Science for Young Scientists. The super-computing resource was provided by Human Genome Center, Institute of Medical Science, University of Tokyo.
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Maeda, K., Minamida, H., Yoshida, K. et al. Flux module decomposition for parameter estimation in a multiple-feedback loop model of biochemical networks. Bioprocess Biosyst Eng 36, 333–344 (2013). https://doi.org/10.1007/s00449-012-0789-y
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DOI: https://doi.org/10.1007/s00449-012-0789-y