Multi-element probabilistic collocation for sensitivity analysis in cellular signalling networks

IET Systems Biology

Volumn 3, Issue 4, 2009, Pages 239-254

  Foo, J ^a   Sindi, S ^a   Karniadakis, G E ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APOPTOSIS; CELLULAR SIGNALLING; CHEMICAL SPECIES; DIFFERENTIAL EQUATION MODEL; EFFICIENT SAMPLING; FUNCTION OF TIME; MULTI-ELEMENT; MULTI-ELEMENT PROBABILISTIC COLLOCATION METHOD; PARAMETER SPACES; SIGNALLING NETWORK;

CELL DEATH; COMPOSITE MICROMECHANICS; LEARNING ALGORITHMS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PULSE CODE MODULATION;

SENSITIVITY ANALYSIS;

CHEMICAL COMPOUND;

ALGORITHM; APOPTOSIS; ARTICLE; CONTROLLED STUDY; MULTI ELEMENT PROBABILISTIC COLLOCATION; SAMPLING; SENSITIVITY ANALYSIS; SIGNAL TRANSDUCTION; STATISTICAL ANALYSIS; STATISTICAL MODEL;

COMPUTER SIMULATION; MODELS, BIOLOGICAL; PROTEOME; SENSITIVITY AND SPECIFICITY; SIGNAL TRANSDUCTION;

EID: 68349157606     PISSN: 17518849     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-syb.2008.0126     Document Type: Article

References (29)

1. Riel, N.: 'Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments', Brief. Bioinform., 2006, 7, p. 364-374
2. Ihekwaba, A.E.C., Broomhead, D.S., and Grimley, R.L.: Et al. 'Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kB pathway: The roles of IKK and IkBα' IEE Proc. Syst. Biol., 2004, 1, p. 93-103 10.1049/sb:20045009
3. Schoeberl, B., Eichler-Jonsson, C., Gilles, E.D., and Müller, G.: 'Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors', Nat. Biotechnol., 2002, 20, p. 370-375
4. Gutenkunst, R.N., Waterfall, J.J., and Casey, F.P.: Et al. 'Universally sloppy parameter sensitivities in systems biology models', PLoS Comput. Biol., 2007, 3, (10), p. e189
5. Kholodenko, B.N., Demin, O.V., and Westerhoff, H.V.: 'Control analysis of periodic phenomena in biological systems', J. Phys. Chem., 1997, 101, p. 2070-2081 0022-3654
6. van Stiphout, R.G.P.M., Verhoog, P.J., and van Riel, N.A.W.: Et al. 'Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers', IEE Proc. Syst. Biol., 2006, 153, p. 405-408 10.1049/ ip-syb:20060017
7. Wilkins, A.K., Barton, P.I., and Tidor, B.: 'The Per2 negative feedback loop sets the period in the mammalian circadian clock mechanism', PLoS Comput. Biol., 2007, 3, (12), p. e242
8. Ingalls, B., and Sauro, H.: 'Sensitivity analysis of stoichiometric networks: An extension of metabolic control analysis to non-steady state trajectories', J. Theor. Biol., 2003, 222, p. 23-36
9. Aldridge, B.B., Haller, G., Sorger, P.K., and Lauffenburger, D.A.: 'Direct Lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour', IEE Proc. Syst. Biol., 2006, 153, p. 425-432 10.1049/ip-syb:20050065
10. Cho, K.H., Shin, S.Y., Kolch, W., and Wolkenhauer, O.: 'Experimental design in systems biology, based on parameter sensitivity analysis using a Monte Carlo method: A case study for the TNFα-mediated NF-kB signal transduction pathway', Simulation, 2003, 79, p. 726-739 10.1177/ 0037549703040943
11. Zi, Z., Cho, K.H., Sung, M.H., Xia, X., Zheng, J., and Sun, Z.: 'In silico identification of the key components and steps in IFN-γ induced JAK-STAT signaling pathway', FEBS Lett., 2005, 570, p. 1101-1108
12. Cho, K., Shin, S., and Kolch, W.: Et al. 'Experimental design in systems biology, based on parameter sensitivity analysis using a Monte-Carlo method: A case study for the TNKα-mediated NF-kB signal transduction pathway', Simulation, 2003, 79, p. 729-739
13. Foo, J., Wan, X., and Karniadakis, G.: 'The multi-element probabilistic collocation method: Error analysis and applications', J. Comput. Phys., 2008, 227, p. 9572-9595 10.1016/j.jcp.2008.07.009 0021-9991
14. Ghanem, R.G.: 'Ingredients for a general purpose stochastic finite element formulation', Comput. Methods Appl. Mech. Eng., 1999, 168, p. 19-34
15. Ghanem, R.G.: 'Stochastic finite elements for heterogeneous media with multiple random non-Gaussian properties', ASCE J Eng. Mech., 1999, 125, (1), p. 26-40
16. Matthies, H.G., and Bucker, C.G.: 'Finite element for stochastic media problems', Comput. Methods Appl. Mech. Eng., 1999, 168, p. 3-17
17. Foo, J., Yosibash, Z., and Karniadakis, G.: 'Stochastic simulation of riser-sections with uncertain measured-pressure loads and/or uncertain material properties', Comput. Methods Appl. Mech. Eng., 2007, 196, p. 4250-4271 10.1016/j.cma.2007.04.005
18. Kim, D., Debusschere, B.J., and Najm, H.N.: 'Spectral methods for parametric sensitivity in stochastic dynamical systems', Biophys. J., 2007, 92, p. 379-393 10.1529/biophysj.106.085084 0006-3495
19. 'Direct treatment of uncertainty in models of reaction and transport', MIT Technical Reports, 1994
20. Smolyak, S.: 'Quadrature and interpolation formulas for tensor products of certain classes of functions', Sov. Math. Dokl., 1963, 4, p. 240-243
21. Eissing, T., Conzelmann, H., Gilles, E.D., Allgower, F., and Bullinger, E.: 'Bistability analyses of a caspase activation model for receptor-induced apoptosis', J. Biol. Chem., 2004, 279, p. 36892-36897
22. Bagci, E.Z., Vodovotz, Y., Billiar, T., Ermentrout, G., and Bahar, I.: 'Bistability in apoptosis: Roles of Bax, Bcl-2 and mitochondrial permeability transition pores', Biophys. J., 2005, 0006-3495
23. Ghanem, R.G., and SpanoA, P.: 'Stochastic finite elements: a spectral approach', (Springer-Verlag, New York 1991)
24. Xiu, D., and Hesthaven, J.: 'High-order collocation methods for differential equations with random inputs', SIAM J. Sci. Comput., 2005, 27, (3), p. 1118-1139 10.1137/040615201 1064-8275
25. Wan, X., and Karniadakis, G.E.: 'An adaptive multi-element generalized polynomial chaos method for stochastic differential equations', J. Comput. Phys., 2005, 209, (2), p. 617-642 10.1016/j.jcp.2005.03.023 0021-9991
26. Kincaid, D., and Cheney, W.: 'Numerical analysis', (Brooks/Cole Publishing Company, Pacific Grove, CA, USA 1991)
27. Barthelmann, V., Novak, E., and Ritter, K.: 'High dimensional polynomial interpolation on sparse grids', Adv. Comput. Math., 2000, 12, p. 273-288 10.1023/A:1018977404843
28. Novak, E., and Ritter, K.: 'High dimensional integration of smooth functions over cubes', Numer Math., 1996, 75, p. 79-97 10.1007/ s002110050231 0029-599X
29. Novak, E., and Ritter, K.: 'Simple cubature formulas with high polynomial exactness', Constr. Approx., 1999, 15, p. 499-522