Biochemical networks are not only complex but also extremely large. The dynamic biological model of great complexity resulting in a large number of parameters is a main difficulty for optimization and control processes. In practice, it is highly desirable to further simplify the structure of biological models for the sake of reducing computational cost or simplification for the task of system analysis. This paper considers the S-system model used for describing the response of biochemical networks. By introducing the technique of singular value decomposition (SVD), we are able to identify the major state variables and parameters and eliminate unimportant metabolites and the corresponding signal transduction pathways. The model reduction by multiobjective analysis integrates the criteria of reactive weight, sensitivity, and flux analyses to obtain a reduced model in a systematic way. The resultant model is closed to the original model in performance but with a simpler structure. Representative numerical examples are illustrated to prove feasibility of the proposed method. 1. Introduction Metabolic models are usually with extremely high complexity with their system model because those networks are entangled by numerous molecules and reaction pathways [1–3]. The complexity of full-scale metabolic models is commonly cognized as a major obstacle for their effective use in computational systems biology. Direct analysis of that kind of systems based on the mathematical models is usually inefficient from the viewpoint of computational cost. To cope with the difficulty, one appropriate approach is to simplify the model before conducting the analysis that is, configuration of biological systems is simplified to reduce its actual size [4–6]. In the mathematics, the stoichiometric matrix is commonly applied to express the framework of biochemical networks, which is built from the stoichiometric coefficients of the reactions. The -system model is a generalized representation of the dynamic behaviors of genetic networks or metabolic networks. Most results commence from considering the mathematical model of biochemical networks by -system architecture [7, 8]. The model consists of a number of particular features of biochemical systems as well as with observation from their behaviors. The biochemical reactions of the -system models in heterogeneous media show fractal kinetic orders [9]. The technique of SVD has been used in the field of engineering for model simplification and data compression. In biochemical territory, the stoichiometric matrix can be disassembled
References
[1]
B. O. Palsson, Systems Biology: Properties of Reconstructed Networks Systems Biology, Cambridge University Press, New York, NY, USA, 2006.
[2]
J. A. Papin, J. L. Reed, and B. O. Palsson, “Hierarchical thinking in network biology: the unbiased modularization of biochemical networks,” Trends in Biochemical Sciences, vol. 29, no. 12, pp. 641–647, 2004.
[3]
E. O. Voit, Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists, Cambridge University Press, New York, NY, USA, 2000.
[4]
H. Schmidt, M. F. Madsen, S. Dan？, and G. Cedersund, “Complexity reduction of biochemical rate expressions,” Bioinformatics, vol. 24, no. 6, pp. 848–854, 2008.
[5]
H. Conzelmann, J. Saez-Rodriguez, T. Sauter, E. Bullinger, F. Allg？wer, and E. D. Gilles, “Reduction of mathematical models of signal transduction networks: simulation-based approach applied to EGF receptor signalling,” Systems Biology, vol. 1, no. 1, pp. 159–169, 2004.
[6]
A. N. Gorban, N. Kazantzis, I. G. Kevrekidis, H. C. Ottinger, and C. Theodoropoulos, Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena,, Springer, New York, NY, USA, 2006.
[7]
M. A. Savageau and E. O. Voit, “Recasting nonlinear differential equations as S-systems: a canonical nonlinear form,” Mathematical Biosciences, vol. 87, no. 1, pp. 83–115, 1987.
[8]
F. S. Wang, C. L. Ko, and E. O. Voit, “Kinetic modeling using S-systems and lin-log approaches,” Biochemical Engineering Journal, vol. 33, no. 3, pp. 238–247, 2007.
[9]
M. A. Savageau, “Influence of fractal kinetics on molecular recognition,” Journal of Molecular Recognition, vol. 6, no. 4, pp. 149–157, 1993.
[10]
I. Famili and B. O. Palsson, “Systemic metabolic reactions are obtained by singular value decomposition of genome-scale stoichiometric matrices,” Journal of Theoretical Biology, vol. 224, no. 1, pp. 87–96, 2003.
[11]
D. P. Berrar, W. Dubitzky, and M. Granzow, A Practical Approach to Microarray Data Analysis, Kluwer Academic Publishers, Boston, Mass, USA, 2003.
[12]
O. Alter, P. O. Brown, and D. Botstein, “Singular value decomposition for genome-wide expression data processing and modeling,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 18, pp. 10101–10106, 2000.
[13]
N. D. Price, J. L. Reed, J. A. Papin, I. Famili, and B. O. Palsson, “Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices,” Biophysical Journal, vol. 84, no. 2, pp. 794–804, 2003.
[14]
G. Liu, M. T. Swihart, and S. Neelamegham, “Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling,” Bioinformatics, vol. 21, no. 7, pp. 1194–1202, 2005.
[15]
R. Boyer, Concepts in Biochemistry, John Wiley & Sons, New York, NY, USA, 2006.
[16]
J. Kim, D. G. Bates, I. Postlethwaite, L. Ma, and P. A. Iglesias, “Robustness analysis of biochemical network models,” IEE Proceedings on Systems Biology, vol. 153, no. 3, pp. 96–104, 2006.
[17]
M. T. Laub and W. F. Loomis, “A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium,” Molecular Biology of the Cell, vol. 9, no. 12, pp. 3521–3532, 1998.
