The meaning of sensitivity functions in signaling pathways analysis

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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

Abstract
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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 and Continuous Dynamical Systems - B, 2014, 19 (8) : 2697-2707. doi: 10.3934/dcdsb.2014.19.2697

References:

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[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), 93-103.
[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), 202 pp. doi: 10.1186/1471-2105-11-202.
[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), 512-528.
[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), 8645-8650. doi: 10.1073/pnas.1015814108.
[11]	J. Leis and M. Kramer, Sensitivity analysis of systems of differential and algebraic equations, Computers & Chemical Engineering, 9 (1985), 93-96. doi: 10.1016/0098-1354(85)87008-3.
[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), 178-196. doi: 10.1016/j.jtbi.2008.04.011.
[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), 319-369. doi: 10.1016/B978-0-12-381270-4.00011-1.
[14]	D. A. Rand, Mapping the global sensitivity of cellular network dynamics, J. R. Soc Interface, 5 (2008), S59-S69.
[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), 034103. doi: 10.1063/1.3280166.
[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), 364-374.
[17]	A. Saltelli, M. Ratto, S. Tarantola and F. Campolongo, Sensitivity analysis for chemical models, Chem. Rev., 105 (2005), 2811-2828. doi: 10.1021/cr040659d.
[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), 1109-1125. doi: 10.1016/j.ress.2005.11.014.
[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), 25-45.
[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), 405-408.
[21]	M. Thattai and A. van Oudenaarden, Intrinsic noise in gene regulatory networks, Proc. Natl Acad. Sci., 98 (2001), 8614-8619. doi: 10.1073/pnas.151588598.
[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), 640-649.

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), 839-851. doi: 10.1083/jcb.200404158.
[2]	J. J. Cruz, Feedback Systems, McGraw-Hill, New York, 1972.
[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), 389-395. doi: 10.1016/j.copbio.2008.06.008.
[4]	A. F. Emery and A. V. Nenarokomov, Optimal experiment design, Meas. Sci. Technol., 9 (1998), 864-876. doi: 10.1088/0957-0233/9/6/003.
[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), 342-355. doi: 10.1049/iet-syb.2008.0156.
[6]	P. Iglesias and B. Ingalls, eds., Control Theory and Systems Biology, MIT Press, Cambridge, Mass., 2010.
[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), 93-103.
[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), 202 pp. doi: 10.1186/1471-2105-11-202.
[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), 512-528.
[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), 8645-8650. doi: 10.1073/pnas.1015814108.
[11]	J. Leis and M. Kramer, Sensitivity analysis of systems of differential and algebraic equations, Computers & Chemical Engineering, 9 (1985), 93-96. doi: 10.1016/0098-1354(85)87008-3.
[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), 178-196. doi: 10.1016/j.jtbi.2008.04.011.
[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), 319-369. doi: 10.1016/B978-0-12-381270-4.00011-1.
[14]	D. A. Rand, Mapping the global sensitivity of cellular network dynamics, J. R. Soc Interface, 5 (2008), S59-S69.
[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), 034103. doi: 10.1063/1.3280166.
[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), 364-374.
[17]	A. Saltelli, M. Ratto, S. Tarantola and F. Campolongo, Sensitivity analysis for chemical models, Chem. Rev., 105 (2005), 2811-2828. doi: 10.1021/cr040659d.
[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), 1109-1125. doi: 10.1016/j.ress.2005.11.014.
[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), 25-45.
[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), 405-408.
[21]	M. Thattai and A. van Oudenaarden, Intrinsic noise in gene regulatory networks, Proc. Natl Acad. Sci., 98 (2001), 8614-8619. doi: 10.1073/pnas.151588598.
[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), 640-649.

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