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October  2014, 19(8): 2697-2707. doi: 10.3934/dcdsb.2014.19.2697

The meaning of sensitivity functions in signaling pathways analysis

Jaroslaw Smieja 1, , Malgorzata Kardynska 2, and  Arkadiusz Jamroz 2,

1. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice
2. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland, Poland

Received  November 2013 Revised  May 2014 Published  August 2014

The paper deals with local sensitivity analysis of signaling pathway models, based on sensitivity functions. Though the methods are well known, their application to various models is always based on the assumption that the output of the system whose sensitivity is analyzed is given by absolute quantitative data. In signaling pathways models, however, this data is always normalized. In this paper we show what are the implications of the way the signaling pathways models are built for the interpretation of sensitivity functions and parameter rankings based on them. The reasoning is illustrated using simple first- and second order systems as well as an example of a simple regulatory module.
Keywords: Signaling pathways, parameter ranking., frequency-domain analysis, sensitivity analysis, Fano factor.
Mathematics Subject Classification: Primary: 92C40, 92C45, 93B35; Secondary: 65C0.
Citation: Jaroslaw Smieja, Malgorzata Kardynska, Arkadiusz Jamroz. The meaning of sensitivity functions in signaling pathways analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2697-2707. doi: 10.3934/dcdsb.2014.19.2697
References:
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R. G. P. M. van Stiphout, N. A. W. van Riel, P. J. Verhoog, P. A. J. Hilbers, K. Nicolay and J. A. L. Jeneson, Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers,, IEE Syst. Biol., 153 (2006), 405.   Google Scholar

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M. Thattai and A. van Oudenaarden, Intrinsic noise in gene regulatory networks,, Proc. Natl Acad. Sci., 98 (2001), 8614.  doi: 10.1073/pnas.151588598.  Google Scholar

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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-kappab signalling pathway,, Molecular BioSystems, 2 (2006), 640.   Google Scholar

show all references

References:
[1]

M. Bentele, I. Lavrik, M. Ulrich, S. Stosser, D. W. Heermann, H. Kalthoff, P. H. Krammer and R. Eils, Mathematical modeling reveals threshold mechanism in cd95-induced apoptosis,, The Journal of Cell Biology, 166 (2004), 839.  doi: 10.1083/jcb.200404158.  Google Scholar

[2]

J. J. Cruz, Feedback Systems,, McGraw-Hill, (1972).   Google Scholar

[3]

B. C. Daniels, Y. J. Chen, J. P. Sethna, R. N. Gutenkunst and C. R. Myers, Sloppiness, robustness, and evolvability in systems biology,, Curr. Opin. Biotech., 19 (2008), 389.  doi: 10.1016/j.copbio.2008.06.008.  Google Scholar

[4]

A. F. Emery and A. V. Nenarokomov, Optimal experiment design,, Meas. Sci. Technol., 9 (1998), 864.  doi: 10.1088/0957-0233/9/6/003.  Google Scholar

[5]

B. Hat, K. Puszynski and T. Lipniacki, Exploring mechanisms of oscillations in p53 and nuclear factor-$\kappa$B systems,, IET Systems Biology, 3 (2009), 342.  doi: 10.1049/iet-syb.2008.0156.  Google Scholar

[6]

P. Iglesias and B. Ingalls, eds., Control Theory and Systems Biology,, MIT Press, (2010).   Google Scholar

[7]

A. E. C. Ihekwaba, D. S. Broomhead, R. L. Grimley, N. Benson and D. B. Kell, Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kB pathway: the roles of IKK and IkBa,, IEE Syst. Biol., 1 (2004), 93.   Google Scholar

[8]

K. A. Kim, S. L. Spencer, J. G. Albeck, J. M. Burke, P. K. Sorger, S. Gaudet and H. Kim do, Systematic calibration of a cell signaling network model,, BMC Bioinformatics, 11 (2010).  doi: 10.1186/1471-2105-11-202.  Google Scholar

[9]

G. Koh and D-Y. Lee, Mathematical modeling and sensitivity analysis of the integrated TNF -mediated apoptotic pathway for identifying key regulators,, Computers in Biology and Medicine, 41 (2011), 512.   Google Scholar

[10]

M. Komorowski, M. J. Costa, D. A. Rand and M. P. H. Stumpf, Sensitivity, robustness, and identifiability in stochastic chemical kinetics models,, PNAS, 108 (2011), 8645.  doi: 10.1073/pnas.1015814108.  Google Scholar

[11]

J. Leis and M. Kramer, Sensitivity analysis of systems of differential and algebraic equations,, Computers & Chemical Engineering, 9 (1985), 93.  doi: 10.1016/0098-1354(85)87008-3.  Google Scholar

[12]

S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, Journal of Theoretical Biology, 254 (2008), 178.  doi: 10.1016/j.jtbi.2008.04.011.  Google Scholar

[13]

A. Marin-Sanguino, S. K. Gupta, E. O. Voit and J. Vera, Biochemical pathway modeling tools for drug target detection in cancer and other complex diseases,, Methods in Enzymology, 487 (2011), 319.  doi: 10.1016/B978-0-12-381270-4.00011-1.  Google Scholar

[14]

D. A. Rand, Mapping the global sensitivity of cellular network dynamics,, J. R. Soc Interface, 5 (2008).   Google Scholar

[15]

M. Rathinam, P. W. Sheppard and M. Khammash, Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks,, Journal of Chemical Physics, 132 (2010).  doi: 10.1063/1.3280166.  Google Scholar

[16]

N. A. W. van Riel, Dynamic modelling and analysis of biochemical networks: Mechanism-based models and model-based experiments,, Briefings in Bioinformatics, 7 (2006), 364.   Google Scholar

[17]

A. Saltelli, M. Ratto, S. Tarantola and F. Campolongo, Sensitivity analysis for chemical models,, Chem. Rev., 105 (2005), 2811.  doi: 10.1021/cr040659d.  Google Scholar

[18]

A. Saltelli, M. Ratto, S. Tarantola and F. Campolongo, Sensitivity analysis practices: Strategies for model-based inference,, Reliability Engineering and System Safety, 91 (2006), 1109.  doi: 10.1016/j.ress.2005.11.014.  Google Scholar

[19]

S.-Y. Shin, S.-M. Choo, S.-H. Woo and K.-H. Cho, Cardiac systems biology and parameter sensitivity analysis: Intracellular $Ca^{2+}$ regulatory mechanisms in mouse ventricular myocytes,, Adv Biochem Engin/Biotechnol, 110 (2008), 25.   Google Scholar

[20]

R. G. P. M. van Stiphout, N. A. W. van Riel, P. J. Verhoog, P. A. J. Hilbers, K. Nicolay and J. A. L. Jeneson, Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers,, IEE Syst. Biol., 153 (2006), 405.   Google Scholar

[21]

M. Thattai and A. van Oudenaarden, Intrinsic noise in gene regulatory networks,, Proc. Natl Acad. Sci., 98 (2001), 8614.  doi: 10.1073/pnas.151588598.  Google Scholar

[22]

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-kappab signalling pathway,, Molecular BioSystems, 2 (2006), 640.   Google Scholar

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