Parameter estimation of dynamic biological network models using integrated fluxes

BMC Systems Biology

Rudiyanto Gunawan¹  Yang Liu¹ 

[1] Institute for Chemical and Bioengineering, ETH Zurich, Vladimir-Perlog-Weg 1, Zurich 8093, Switzerland

关键词: Lin-log model;    Power-law model;    ODE model;    Parameter estimation;   

Others  :  1091659
DOI  :  10.1186/s12918-014-0127-x

 received in 2014-08-07, accepted in 2014-10-29,  发布年份 2014

【 摘 要 】

Background

Parameter estimation is often the bottlenecking step in biological system modeling. For ordinary differential equation (ODE) models, the challenge in this estimation has been attributed to not only the lack of parameter identifiability, but also computational issues such as finding globally optimal parameter estimates over highly multidimensional search space. Recent methods using incremental estimation approach could alleviate the computational difficulty by performing the parameter estimation one-reaction-at-a-time. However, incremental estimation strategies usually require data smoothing and are known to produce biased parameter estimates.

Results

In this article, we presented a new parameter estimation method called integrated flux parameter estimation (IFPE). We employed the integral form of the ODE such that we could compute the integral of reaction fluxes from time-series concentration data without data smoothing. Here, we formulated the parameter estimation as a nested optimization problem. In the outer optimization, we performed a minimization of model prediction errors over parameters associated with a subset of reactions labeled as independent. The dimension of the independent reaction subset was equal to the degrees of freedom in the calculation of integrated fluxes (IF) from concentration data. We selected the independent reactions such that given their IF values, the IFs of the remaining (dependent) reactions could be uniquely determined. Meanwhile, in the inner optimization, we estimated the model parameters associated with the dependent reactions, one-reaction-at-a-time, by minimizing the dependent IF prediction errors. We demonstrated the performance of the IFPE method using two case studies: a generalized mass action model of a branched pathway and a lin-log ODE model of Lactococcus lactis glycolytic pathway.

Conclusions

The IFPE significantly outperformed standard simultaneous parameter estimation in terms of computational efficiency and scaling. In comparison to incremental parameter estimation (IPE) method, the IFPE produced parameter estimates with significantly lower bias and did not require time-series data smoothing. The advantages of IFPE over the IPE however came at the cost of a small increase in the computational time.

【 授权许可】

   
2014 Liu and Gunawan; licensee BioMed Central Ltd.

【 图 表 】

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【 参考文献 】

• [1]Chou IC, Voit EO: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math Biosci 2009, 219(2):57-83.
• [2]Bardow A, Marquardt W: Incremental and simultaneous identification of reaction kinetics: methods and comparison. Chem Eng Sci 2004, 59(13):2673-2684.
• [3]Srinath S, Gunawan R: Parameter identifiability of power-law biochemical system models. J Biotechnol 2010, 149(3):132-140.
• [4]Szederkenyi G, Banga J, Alonso A: Inference of complex biological networks: distinguishability issues and optimization-based solutions. BMC Syst Biol 2011, 5(1):177. BioMed Central Full Text
• [5]Voit EO, Almeida J, Marino S, Lall R, Goel G, Neves AR, Santos H: Regulation of glycolysis in lactococcus lactis: an unfinished systems biological case study. Syst Biol 2006, 153(4):286-298.
• [6]Voit EO, Almeida J: Decoupling dynamical systems for pathway identification from metabolic profiles. Bioinformatics 2004, 20(11):1670-1681.
• [7]Goel G, Chou IC, Voit EO: System estimation from metabolic time-series data. Bioinformatics 2008, 24(21):2505-2511.
• [8]Jia G, Stephanopoulos GN, Gunawan R: Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method. Bioinformatics 2011, 27(14):1964-1970.
• [9]Nim TH, Luo L, Clément M-V, White JK, Tucker-Kellogg L: Systematic parameter estimation in data-rich environments for cell signalling dynamics. Bioinformatics 2013, 29(8):1044-1051.
• [10]Jia G, Stephanopoulos G, Gunawan R: Incremental parameter estimation of kinetic metabolic network models. BMC Syst Biol 2012, 6:142. BioMed Central Full Text
• [11]Amrhein M, Bhatt N, Srinivasan B, Bonvin D: Extents of reaction and flow for homogeneous reaction systems with inlet and outlet streams. AIChE J 2010, 56(11):2873-2886.
• [12]Bhatt N, Amrhein M, Bonvin D: Incremental identification of reaction and mass-transfer kinetics using the concept of extents. Ind Eng Chem Res 2011, 50(23):12960-12974.
• [13]Bhatt N, Kerimoglu N, Amrhein M, Marquardt W, Bonvin D: Incremental identification of reaction systems-a comparison between rate-based and extent-based approaches. Chem Eng Sci 2012, 83:24-38.
• [14]del Rosario RC, Mendoza E, Voit EO: Challenges in lin-log modelling of glycolysis in lactococcus lactis. IET Syst Biol 2008, 2(3):136-149.
• [15]Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS: Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Software 2005, 31(3):363-396.
• [16]Egea JA, Rodríguez-Fernández M, Banga JR: Scatter search for chemical and bio-process optimization. J Global Optim 2007, 37(3):481-503.
• [17]Rodríguez-Fernández M, Egea JA, Banga JR: Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics 2006, 7:483. BioMed Central Full Text
• [18]Egea JA, Martí R, Banga JR: An evolutionary method for complex-process optimization. Comput Oper Res 2010, 37(2):315-324.
• [19]Leander J, Lundh T, Jirstrand M: Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements. Math Biosci 2014, 251(0):54-62.
• [20]Visser D, Heijnen JJ: Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics. Metab Eng 2003, 5(3):164-176.
• [21]Neves AR, Ramos A, Nunes MC, Kleerebezem M, Hugenholtz J, de Vos WM, Almeida J: In vivo nuclear magnetic resonance studies of glycolytic kinetics in lactococcus lactis. Biotechnol Bioeng 1999, 64(2):200-212.
• [22]Pintér JD: Global optimization: software, test problems, and applications. In Handbook of Global Optimization. Volume 2 . Edited by Pardalos PM, Romeijn HE. Kluwer Academic Publishers, Dordrecht; 2002:515-569.