Choujun Zhan
ABSTRACT
Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and still one of the most challenging tasks. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints. Parameter estimation method of combining spline theory with Nonlinear Programming (NLP) is developed. The method removes the need for ODE solver during the identification process. Our analysis shows that the augmented cost function surface used in the proposed method is smoother than the original one; which can ease the optima searching process and hence enhance the robustness and speed. Moreover, the core of our algorithms is NLP based, which is very flexible and consequently additional constraints can be added/removed easily. Our results confirm that the proposed method is both efficient and robust.
- D. Boor. A practical guide to splines. Springer, New York, 1987.Google Scholar
- W. C. Chang, C. W. Li, and B. S. Chen. Quantitative inference of dynamic regulatory pathways via microarray data. BMC Bioinformatics, 6:1--19, 2005.Google ScholarCross Ref
- I. C. Chou, H. Martens, and E. O. Voit. Parameter estimation in biochemical systems models with alternating regression. Theor Biol Med Model., 19:3--25, 2006.Google Scholar
- G. Goel, I. C. Chou, and E. O. Voit. System estimation from metabolic time-series data. Bioinformatics, 24(21):2505--2511, 2008. Google ScholarDigital Library
- O. R. Gonzalez, C. Küer, K. Jung, P. C. J. Naval, and E. Mendoza. Parameter estimation using simulated annealing for s-system models of biochemical networks. Bioinformatics, 23(4):480--486, 2007. Google ScholarDigital Library
- R. N. Gutenkunst, J. J. Waterfall, F. P. Casey, K. S. Brown, C. R. Myers, and J. P. Sethna. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol., 3(10):1871--1878, 2007.Google ScholarCross Ref
- S. Kikuchi, D. Tominaga, M. Arita, K. Takahashi, and M. Tomita. Dynamic modeling of genetic networks using genetic algorithm and s-system. Bioinformatics, 19(5):643--650, 2003.Google ScholarCross Ref
- G. Koh, H. F. Teong, M. V. Cléent, D. Hsu, and P. S. Thiagarajan. A decompositional approach to parameter estimation in pathway modeling: a case study of the akt and mapk pathways and their crosstalk. Bioinformatics, 22(24):271--280, 2006. Google ScholarDigital Library
- R. Lall and E. O. Voit. Parameter estimation in modulated, unbranched reaction chains within biochemical systems. Comput Biol Chem., 29(5):309--318, 2005. Google ScholarDigital Library
- P. Mendes and D. Kell. Non-linear optimization of biochemical pathways: application to metabolic engineering and parameter estimation. Bioinformatics, 14(10):869--883, 1998.Google ScholarCross Ref
- C. G. Moles, P. Mendes, and J. R. Banga. Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res., 13(11):2467--2474, 2003.Google ScholarCross Ref
- T. P. Runarsson and X. Yao. Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput., 4:284--294, 2000. Google ScholarDigital Library
- M. A. Savageau. Biochemical Systems Analysis: a study of Function and Design in Molecular Biology. Reading, MA: Addison-Wesley, Reading, 1976.Google Scholar
- M. Swat, A. Kel, and H. Herzel. Bifurcation analysis of the regulatory modules of the mammalian g1/s transition. Bioinformatics, 20(10):1506--1511, 2004. Google ScholarDigital Library
- I. V. Tetko, D. J. Livingstone, and A. I. Luik. Neural network studies. 1. comparison of overfitting and overtraining. J. Chem. Inf. Comput. Sci., 35:826--833, 1995.Google ScholarCross Ref
- K. Y. Tsai and F. S. Wang. Evolutionary optimization with data, collocation for reverse engineering of biological networks. Bioinformatics, 21(7):1180--1188, 2005. Google ScholarDigital Library
- S. R. Veflingstad, J. Almeida, and E. O. Voit. Priming nonlinear searches for pathway identification. Theor Biol Med Model., page 1:8, 2004.Google Scholar
- E. O. Voit. Computational analysis of biochemical systems, a practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge, 2000.Google Scholar
- E. O. Voit and J. Almeida. Decoupling dynamical systems for pathway identification from metabolic profiles. Bioinformatics, 20(11):1670--1681, 2004. Google ScholarDigital Library
- J. J. Waterfall, F. P. Casey, R. N. Gutenkunst, K. S. Brown, C. R. Myers, P. W. Brouwer, V. Elser, and J. P. Sethna. Sloppy-model universality class and the vandermonde matrix. Phys Rev Lett., 97(15):150601, 2006.Google ScholarCross Ref
- H. Yue, M. Brown, J. Knowles, H. Wang, D. S. Broomhead, and D. B. Kell. Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an nf-kb signalling pathway. Mol Biosyst., 2(12):640--649, 2006.Google ScholarCross Ref
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