Abstract
An integral part of any systems biology approach is the modelling and simulation of the respective system under investigation. However, the values of many parameters of the system have often not been determined or are not identifiable due to technical experimental difficulties or other constraints. Sensitivity analysis is often employed to quantify the importance of each of the model's parameters in the behaviour of the system. This approach can also be useful in identifying those parts of the system that are most sensitive with the potential of becoming drug targets. A problem of the commonly used methods of sensitivity analysis is that they constitute local methods meaning that they depend directly on the exact parameter space, which in turn is not known exactly. One way to circumvent this problem is to carry out sensitivity analysis over a wide range of values for all parameters, but this is handicapped by expensive computations when the systems are high dimensional. Another approach is to employ global sensitivity analysis, which in this context is mostly based on random sampling methods. In this paper we present an efficient approach that involves using numerical optimizing methods that search a wide region of parameter space for a given model to determine the maximum and minimum values of its metabolic control coefficients. A relevant example for drug development is presented to demonstrate the strategy using the software COPASI.
References
Bentele M, Lavrik I, Ulrich M, Stösser S, Heermann D.W, Kalthoff H, Krammer P.H& Eils R . 2004Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis. J. Cell Biol. 166, 839–851.doi:10.1083/jcb.200404158. . Crossref, PubMed, ISI, Google ScholarButcher E.C . 2005Can cell systems biology rescue drug discovery?. Nat. Rev. Drug Discov. 4, 461–467.doi:10.1038/nrd1754. . Crossref, PubMed, ISI, Google ScholarCampolongo F, Saltelli A& Tarantola S . 2000Sensitivity analysis as an ingredient of modeling. Stat. Sci. 15, 377–395.doi:10.1214/ss/1009213004. . Crossref, ISI, Google ScholarCascante M, Boros L.G, Comin-Anduix B, de Atauri P, Centelle J.J& Lee P.W.N . 2002Metabolic control analysis in drug discovery and disease. Nat. Biotechnol. 20, 243–249.doi:10.1038/nbt0302-243. . Crossref, PubMed, ISI, Google ScholarCorana A, Marchesi M, Martini C& Ridella S . 1987Minimizing multimodal functions of continuous variables with thesimulated annealin algorithm. ACM Trans. Math. Software. 13, 262–280.doi:10.1145/29380.29864. . Crossref, ISI, Google Scholar- Eberhart, R. C. & Kennedy, J. 1995 A new optimizer using particle swarm theory. In Proc. of the 6th Int. Symp. on Micromachine and Human Science, Nagoya, Japan, pp. 39–43. Google Scholar
Heinrich R& Rapoport T.A . 1974A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur. J. Biochem. 42, 89–95.doi:10.1111/j.1432-1033.1974.tb03318.x. . Crossref, PubMed, Google ScholarHeinrich R& Schuster S The regulation of cellular systems. 1996Berlin, Germany:Springer. Google ScholarHoops S, 2006COPASI—a COmplex PAthway SImulator. Bioinformatics. 22, 3067–3074.doi:10.1093/bioinformatics/btl485. . Crossref, PubMed, ISI, Google ScholarHucka M, 2003The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics. 19, 524–531.doi:10.1093/bioinformatics/btg015. . Crossref, PubMed, ISI, Google ScholarKacser H& Burns J.A . 1973The control of flux. Symp. Soc. Exp. Biol. 27, 65–104. PubMed, Google ScholarKirkpatrick S, Gelatt C.D& Vecchi M.P . 1983Optimization by simulated annealing. Science. 220, 671–680.doi:10.1126/science.220.4598.671. . Crossref, PubMed, ISI, Google ScholarLambeth M.J& Kushmerick M.J . 2002A computational model for glycogenolysis in skeletal muscle. Ann. Biomed. Eng. 30, 808–827.doi:10.1114/1.1492813. . Crossref, PubMed, ISI, Google ScholarLe Novère N, 2006BioModels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res. 34, D689–D691.doi:10.1093/nar/gkj092. . Crossref, PubMed, ISI, Google ScholarLudtke N, Panzeri S, Brown M, Broomhead D.S, Knowles J, Montemurro M.A& Kell D.B . 2008Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks. J. R. Soc. Interface. 5, 223–235.doi:10.1098/rsif.2007.1079. . Link, ISI, Google ScholarMendes P& Kell D.B . 1998Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics. 14, 869–883.doi:10.1093/bioinformatics/14.10.869. . Crossref, PubMed, ISI, Google ScholarMetropolis N, Rosenbluth A.W, Rosenbluth M.N& Teller A.H . 1953Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092.doi:10.1063/1.1699114. . Crossref, ISI, Google ScholarStephanopoulos G& Vallino J.J . 1991Network rigidity and metabolic engineering in metabolite overproduction. Science. 252, 1675–1681.doi:10.1126/science.1904627. . Crossref, PubMed, ISI, Google ScholarVan Riel N.A . 2006Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments. Brief Bioinform. 7, 364–374.doi:10.1093/bib/bbl040. . Crossref, PubMed, ISI, Google ScholarWolpert D.H& Macready W.G . 1997No free lunch theorems for optimization. IEEE Trans. Evol. Comp. 1, 67–82.doi:10.1109/4235.585893. . Crossref, Google Scholar


