title: A comparison of approximation techniques for variance-based sensitivity analysis of biochemical reaction systems.
abstract: BACKGROUND
  Sensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species.
  
  
  RESULTS
  We present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for analytically approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge.
  
  
  CONCLUSIONS
  Estimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.
authors.affiliation: Whitaker Biomedical Engineering Institute, The Johns Hopkins University, Baltimore, MD 21218, USA.
authors.forename: Hong-Xuan
authors.initials: HX
authors.lastname: Zhang
authors.forename: John
authors.initials: J
authors.lastname: Goutsias
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D001669:Biochemical Phenomena; D009010:Monte Carlo Method; D015398:Signal Transduction
references.citation: Oncogene. 2005 Aug 25;24(36):5533-42
references.pmid: 16007170
references.citation: J Phys Chem A. 2006 Feb 23;110(7):2474-85
references.pmid: 16480307
references.citation: Bioinformatics. 2009 Oct 1;25(19):2466-72
references.pmid: 19648136
references.citation: Chem Rev. 2005 Jul;105(7):2811-28
references.pmid: 16011325
references.citation: J Biopharm Stat. 1995 Nov;5(3):245-71
references.pmid: 8580927
references.citation: Proc Natl Acad Sci U S A. 2004 Sep 7;101(36):13210-5
references.pmid: 15340155
references.citation: Cell. 1995 Jan 27;80(2):179-85
references.pmid: 7834738
references.citation: Clin Pharmacokinet. 2003;42(10):883-908
references.pmid: 12885263
references.citation: PLoS Comput Biol. 2007 Jul;3(7):e130
references.pmid: 17616983
references.citation: J Phys Chem A. 2006 Apr 27;110(16):5361-70
references.pmid: 16623463
references.citation: Biophys J. 2004 Oct;87(4):2195-202
references.pmid: 15454422
references.citation: Nat Cell Biol. 2002 Aug;4(8):556-64
references.pmid: 12134156
references.citation: Neural Comput. 2007 Jan;19(1):231-57
references.pmid: 17134324
references.citation: Biophys J. 2004 Nov;87(5):L01-2
references.pmid: 15454405
references.citation: J Theor Biol. 2004 Oct 21;230(4):541-62
references.pmid: 15363675
references.citation: J Cell Sci. 2000 Dec;113 Pt 24:4499-510
references.pmid: 11082043
references.citation: Biophys J. 2007 Mar 15;92(6):1846-57
references.pmid: 17208985
references.citation: J Cell Sci. 2005 Jul 15;118(Pt 14):2997-3002
references.pmid: 16014377
references.citation: Mol Cell Biol. 2004 Jan;24(1):144-53
references.pmid: 14673150
references.citation: J Chem Phys. 2009 Sep 7;131(9):094101
references.pmid: 19739843
references.citation: Biochem J. 1998 Mar 15;330 ( Pt 3):1451-60
references.pmid: 9494119