×

Novel global sensitivity analysis methodology accounting for the crucial role of the distribution of input parameters: application to systems biology models. (English) Zbl 1258.93112

Summary: The reliability of model predictions is affected by multiple sources of uncertainty; therefore, most of the efforts for modeling biological systems include a sensitivity analysis step aiming to identify the key contributors to uncertainty. This generates insight about the robustness of the model to variations in environmental conditions, kinetic parameters, initial concentration of the species, or any other source of uncertainty. Local sensitivities measure the robustness of the model to small perturbations on the inputs around their nominal value. There are several numerical methods for the calculation of local sensitivities, but the calculated values should be identical within the numerical accuracy of the method used. In contrast, as will be shown in this contribution, the results of different global sensitivity analysis methods can be very different and highly dependent on the distribution considered for the inputs under evaluation. In this work, derivative-based global sensitivities are extended to be able to consider an accurate probability density function for the parameters based on the likelihood function. This strategy enforces the areas of the parameter space most likely to reproduce the desired behavior, minimizing the importance of parameter sets with low probability of being optimal to dominate the sensitivity ranking. A model of a biochemical pathway with three enzymatic steps is used here to illustrate the performance of several relevant global sensitivity analysis methods considering different probability density functions for the parameters and revealing important hints about which method and distribution to choose for each type of model and purpose of the analysis.

MSC:

93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
92C42 Systems biology, networks
93C15 Control/observation systems governed by ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Saltelli, Global Sensitivity Analysis: The Primer (2008) · Zbl 1161.00304
[2] Saltelli, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models (2004) · Zbl 1049.62112
[3] Riel, Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments, Briefings in Bioinformatics 7 (4) pp 364– (2006)
[4] Schmidt, Systems biology toolbox for MATLAB: a computational platform for research in systems biology, Bioinformatics 22 (4) pp 514– (2006)
[5] Hoops, COPASI-a COmplex PAthway SImulator, Bioinformatics 22 (24) pp 3067– (2006)
[6] Zi, SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool, BMC Bioinformatics 9 pp 342– (2008)
[7] Maiwald, Dynamical modeling and multi-experiment fitting with PottersWheel, Bioinformatics 24 (18) pp 2037– (2008)
[8] Rodriguez-Fernandez, SensSB: a software toolbox for the development and sensitivity analysis of systems biology models, Bioinformatics 26 (13) pp 1675– (2010)
[9] Zheng, Comparative study of parameter sensitivity analyses of the TCR-activated erk-MAPK signalling pathway, IEE Proceedings Systems Biology 153 (4) pp 201– (2006)
[10] Bagheri, Quantitative performance metrics for robustness in circadian rhythms, Bioinformatics 23 (3) pp 358– (2007)
[11] Kiparissides, Global sensitivity analysis challenges in biological systems modeling, Industrial & Engineering Chemistry Research 48 (15) pp 7168– (2009)
[12] Helton, Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, Reliability Engineering & System Safety 42 (2-3) pp 327– (1993)
[13] Egea, Scatter search for chemical and bio-process optimization, Journal of Global Optimization 37 pp 481– (2007) · Zbl 1108.92001
[14] Morris, Factorial sampling plans for preliminary computational experiments, Technometrics 33 (2) pp 161– (1991)
[15] Sobol’, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation 55 pp 271– (2001) · Zbl 1005.65004
[16] Kucherenko, Monte Carlo evaluation of derivative based global sensitivity measures, Reliability Engineering & System Safety 94 pp 1135– (2009)
[17] Versyck K Dynamic input design for optimal estimation of kinetic parameters in bioprocess models PhD Thesis 2000
[18] Saltelli, Sensitivity analysis (2000)
[19] Maly, Numerical methods and software for sensitivity analysis of differential-algebraic systems, Applied Numerical Mathematics 20 pp 57– (1996) · Zbl 0854.65056
[20] Leis, ODESSA - an ordinary differential-equation solver with explicit simultaneous sensitivity analysis, ACM Transactions on Mathematical Software 14 (1) pp 61– (1988) · Zbl 0639.65043
[21] Campolongo, An effective screening design for sensitivity analysis of large models, Environmental Modelling & Software 22 (10) pp 1509– (2007)
[22] Saltelli, A quantitative model-independent method for global sensitivity analysis of model output, Technometrics 41 (1) pp 39– (1999)
[23] Saltelli, Making best use of model evaluations to compute sensitivity indices, Computer Physics Communications 145 (2) pp 280– (2002) · Zbl 0998.65065
[24] Sobol, Derivative based global sensitivity measures and their link with global sensitivity indices, Mathematics and Computers in Simulation 79 pp 3009– (2009) · Zbl 1167.62005
[25] Cho, Experimental design in systems biology, based on parameter sensitivity analysis using a Monte Carlo method: a case study for the TNF {\(\alpha\)}-mediated NF- {\(\kappa\)}B signal transduction pathway, Simulation 79 pp 726– (2003)
[26] Bentele, Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis, Journal of Cell Biology 166 (6) pp 839– (2004)
[27] Aldrich, Fisher and the making of maximum likelihood 1912-1922, Statistical Science 12 (3) pp 162– (1997) · Zbl 0955.62525
[28] Walter, Identification of Parametric Models from Experimental Data (1997)
[29] Sobol, On quasi Monte Carlo integrations, Mathematics and Computers in Simulation 47 pp 103– (1998)
[30] Zhang, Probabilistic sensitivity analysis of biochemical reaction systems, Journal of Chemical Physics 131 (9) pp 094– (2009)
[31] Feng, Optimizing genetic circuits by global sensitivity analysis, Biophysical Journal 87 (4) pp 2195– (2004)
[32] Kontoravdi, Application of global sensitivity analysis to determine goals for design of experiments: an example study on antibody-producing cell cultures, Biotechnology Progress 21 (4) pp 1128– (2005)
[33] Sahle, A new strategy for assessing sensitivities in biochemical models, Philosophical Transactions of the Royal Society A 366 pp 3619– (2008)
[34] Yue, Sensitivity analysis and robust experimental design of a signal transduction pathway system, International Journal of Chemical Kinetics 40 (11) pp 730– (2008)
[35] Yuraszeck, Vulnerabilities in the tau network and the role of ultrasensitive points in tau pathophysiology, PLoS Computational Biology 6 (11) pp e1000997– (2010)
[36] Gunawardena, Models in Systems Biology: The Parameter Problem and the Meanings of Robustness pp 19– (2009)
[37] Mendes, Modeling Large Biological Systems from Funcational Genomic Data: Parameter Estimation pp 163– (2001)
[38] Moles, Parameter estimation in biochemical pathways: a comparison of global optimization methods, Genome Research 13 pp 2467– (2003)
[39] Rodriguez-Fernandez, A hybrid approach for efficient and robust parameter estimation in biochemical pathways, BioSystems 83 pp 248– (2006)
[40] Liu, Hybrid differential evolution with geometric mean mutation in parameter estimation of bioreaction systems with large parameter search space, Computers & Chemical Engineering 33 (11) pp 1851– (2009)
[41] Gutenkunst, Universally sloppy parameter sensitivities in systems biology models, PLOS Computational Biology 3 (10) pp 1871– (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.