A new computational tool for establishing model parameter identifiability

Journal of Computational Biology

Volumn 16, Issue 6, 2009, Pages 875-884

  August, Elias ^a   Papachristodoulou, Antonis ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Parameter identifiability; Sum of squares decomposition; Systems biology

Indexed keywords

ARTICLE; CHEMICAL REACTION; ENZYME SUBSTRATE COMPLEX; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; MICHAELIS CONSTANT; NONLINEAR SYSTEM; PRIORITY JOURNAL; REACTION ANALYSIS; BIOLOGICAL MODEL; BIOLOGY; METHODOLOGY;

COMPUTATIONAL BIOLOGY; MODELS, BIOLOGICAL;

EID: 69249205522     PISSN: 10665277     EISSN: None     Source Type: Journal    
DOI: 10.1089/cmb.2008.0211     Document Type: Article

References (27)

1. Anguelova, M. 2004. Nonlinear observability and identifiability: general theory and a case study of a kinetic model for S. cerevisiae [M.S. thesis]. Göteborg University.
2. Audoly, S., Bellu, G., D'Angio, L., et al. 2001. Global identifiability of nonlinear models of biological systems. IEEE Trans. Biomed. Eng. 48, 55-65.
3. Balsa-Canto, E., Alonso, A.A., and Banga, J.R. 2007. An optimal identification procedure for model development in systems biology. Proc. Found. Syst. Biol. Eng. 46-51.
4. Boyd, S., and Vandenberghe, L. 2004. Convex Optimization. Cambridge University Press, Cambridge, UK.
5. Chaves, M.C.F. 2003. Observer design for a class of nonlinear systems, with applications to biochemical networks [Ph.D. dissertation]. Rutgers, The State University of New Jersey, New Brunswick, NJ.
6. Denis-Vidal, L., Joly-Blanchard, G., and Noiret, C. 2001. Some effective approaches to check the identifiability of uncontrolled nonlinear systems. Math. Comput. Simulation 57, 35-44.
7. El Samad, H., Papachristodoulou, A., Prajna, S., et al. 2006. Advanced methods and algorithms for biological networks analysis. Proc. IEEE 94, 832-853.
8. Farina, M., Findeisen, R., Bullinger, E., et al. 2006. Results towards identifiability properties of biochemical reaction networks. Proc. 45th IEEE Conf. Decision Control 2104-2109.
9. Feinberg, M. 1979. Lectures on chemical reaction networks. Mathematics Research Centre, University of Wisconsin, Madison, WI.
10. Feinberg, M. 1987. Chemical reaction network structure and the stability of complex isothermal reactors-I. The deficiency zero and deficiency one theorems. Chem. Eng. Sci. 42, 2229-2268.
11. Feng, X., and Rabitz, H., 2004. Optimal identification of biochemical reaction networks. Biophys. J. 86, 1270-1281.
12. Fitch, K.R.G.W.R. 1984. The deterministic identifiability of nonlinear pharmacokinetic models. J. Pharmacokinet. Biopharm. 12, 177-191.
13. Geffen, D., Findeisen, R., Schliemann, M., et al. 2007. The question of parameter identifiability for biochemical reaction networks considering the NF-kB signal transduction pathway. Proc. FOSBE 504-509.
14. Guberman, J.M. 2003. Mass action networks and the deficiency zero theorem [B.Sc thesis]. Harvard University, Cambridge, MA.
15. Gunawardena, J. 2003. Chemical reaction network theory for in silico biologists. Bauer Center for Genomics Research, Harvard University, Cambridge, MA.
16. Hermann, R., and Krener, A.J. 1977. Nonlinear controllability and observability. IEEE Trans. Automatic Control AC22, 728-740.
17. Ljung, L., and Glad, T. 1994. On global identifiability for arbitrary model parametrizations. Automatica 30, 265-276.
18. Murty, K.G., and Kabadi, S.N. 1987. Some NP-complete problems in quadratic and nonlinear programming. Math.-Program. 39, 117-129.
19. Parrilo, P. A. 2003. Semidefinite programming relaxations for semialgebraic problems. Math. Program. Ser. B 96, 293-320.
20. Prajna, S., Papachristodoulou, A., and Parrilo, P.A. 2002. SOSTOOLS-Sum of Squares Optimization Toolbox, user's guide. Available at: www.cds.caltech.edu/sostools. Accessed March 15, 2009.
21. Quaiser, T., Marquardt, W., and Mönnigmann, M. 2007. Local identifiability analysis of large signaling pathway models. Proc. FOSBE 460-465.
22. Respondek, W. 2002. Geometry of static and dynamic feedback [Lectures given at the Summer Schools on Mathematical Control Theory, Trieste, Italy, September 2001 and Bedlewo-Warsaw, Poland, September 2002]. Laboratoire de Mathe matiques INSA, Rouen, France.
23. Sedoglavic, A. 2002. A probabilistic algorithm to test local algebraic observability in polynomial time. J.Symbolic Comput. 33, 735-755.
24. Sturm, J.F. 1999. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11-12, 625-653. Available at: http://fewcal.kub.nl/sturm/software/sedumi.html. Accessed March 15, 2009.
25. Vajda, S., and Rabitz, H. 1994. Identifiability and distinguishability of general reaction systems. J. Phys. Chem. 98, 5265-5271.
26. Vandenberghe, L., and Boyd, S. 1996. Semidefinite programming. SIAM Rev. 38, 49-95.
27. Zhou, K., Doyle, J., and Glover, K. 1996. Robust and Optimal Control. Prentice-Hall, Upper Saddle River, NJ.