Abstract
Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.
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References
Asprey, S. P., & Macchietto, S. (2002). Designing robust optimal dynamic experiments,. J. Process Control, 12, 545–556.
Atkinson, A. C., & Bailey, R. A. (2001). One hundred years of the design of experiments on and off the pages of biometrika. Biometrika, 88, 53–97.
Balsa-Canto, E., Alonso, A. A., & Banga, J. R. (2008). Computational procedures for optimal experimental design in biological systems. IET Syst. Biol., 2, 163–172.
Balsa-Canto, E., Alonso, A. A., & Banga, J. R. (2010). An iterative identification procedure for dynamic modeling of biochemical networks. BMC Syst. Biol., 4.
Bandara, S., Schloder, J. P., Eils, R., Bock, H. G., & Meyer, T. (2009). Optimal experimental design for parameter estimation of a cell signaling model. PLoS Comput. Biol., 5, e1000558.
Bazil, J. N. (2010). An integrated bioenergetics modeling approach to mitochondrial permeability transition. Purdue University, Weldon School of Biomedical Engineering.
Beck, J. V., & Woodbury, K. A. (1998). Inverse problems and parameter estimation: integration of measurements and analysis. Meas. Sci. Technol., 9, 839–847.
Box, J. F. (1980). Fisher, R.A. and the design of experiments, 1922–1926. Am. Stat., 34, 1–7.
Box, G. E. P., & Hill, W. J. (1967). Discrimination among mechanistic models. Technometrics, 9, 57–71.
Buzzard, G. T. (in submission). Efficient basis change for sparse-grid interpolating polynomials.
Buzzard, G. T., & Xiu, D. B. (2011). Variance-based global sensitivity analysis via sparge-grid interpolation and cubature. Commun. Comput. Phys., 9, 542–567.
Casey, F. P., et al. (2006). Optimal experimental design in an egfr signaling and down-regulation model. eprint arXiv:q-bio/0610024.
Chen, B. H., & Asprey, S. P. (2003). On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations. Ind. Eng. Chem. Res., 42, 1379–1390.
Cho, K. H., Shin, S. Y., Kolch, W., & Wolkenhauer, O. (2003). 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, 726–739.
Chu, Y. F., & Hahn, J. (2008). Integrating parameter selection with experimental design under uncertainty for nonlinear dynamic systems. AIChE J., 54, 2310–2320.
Chu, Y. F., & Hahn, J. (2010). Quantitative optimal experimental design using global sensitivity analysis via quasi-linearization. Ind. Eng. Chem. Res., 49, 7782–7794.
Donahue, M. M., Buzzard, G. T., & Rundell, A. E. (2010). Experiment design through dynamical characterisation of non-linear systems biology models utilising sparse grids. IET Syst. Biol., 4, 249–262.
Donckels, B. M. R., De Pauw, D. J. W., De Baets, B., Maertens, J., & Vanrolleghem, P. A. (2009). An anticipatory approach to optimal experimental design for model discrimination. Chemom. Intell. Lab. Syst., 95, 53–63.
Emery, A. F., Nenarokomov, A. V., & Fadale, T. D. (2000). Uncertainties in parameter estimation: the optimal experiment design. Int. J. Heat Mass Transf., 43, 3331–3339.
Espie, D., & Macchietto, S. (1989). The optimal-design of dynamic experiments. AIChE J., 35, 223–229.
Ferraris, G. B., Forzatti, P., Emig, G., & Hofmann, H. (1984). Sequential experimental-design for model discrimination in the case of multiple responses. Chem. Eng. Sci., 39, 81–85.
Franceschini, G., & Macchietto, S. (2005). A numerical experiment design study on a biodiesel production process. In European symposium on computer-aided process engineering-15 (Vols. 20a–20b, pp. 349–354).
Franceschini, G., & Macchietto, S. (2007). Validation of a model for biodiesel production through model-based experiment design. Ind. Eng. Chem. Res., 46, 220–232.
Franceschini, G., & Macchietto, S. (2008a). Model-based design of experiments for parameter precision: state of the art. Chem. Eng. Sci., 63, 4846–4872.
Franceschini, G., & Macchietto, S. (2008b). Anti-correlation approach to model-based experiment design: application to a biodiesel production process. Ind. Eng. Chem. Res., 47, 2331–2348.
Franceschini, G., & Macchietto, S. (2008c). Novel anticorrelation criteria for model-based experiment design: theory and formulations. AIChE J., 54, 1009–1024.
Gadkar, K. G., Gunawan, R., & Doyle, F. J. (2005). Iterative approach to model identification of biological networks. BMC Bioinf., 6.
Galvanin, F., Macchietto, S., & Bezzo, F. (2007). Model-based design of parallel experiments. Ind. Eng. Chem. Res., 46, 871–882.
Gerstner, T., & Griebel, M. (2003). Dimension-adaptive tensor-product quadrature. Computing, 71, 65–87.
Gulpinar, N., Rustem, B., & Settergren, R. (2004). Simulation and optimization approaches to scenario tree generation. J. Econ. Dyn. Control, 28, 1291–1315.
Gutenkunst, R. N., et al. (2007). Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol., 3, 1871–1878.
He, F., Brown, M., & Yue, H. (2010). Maximin and Bayesian robust experimental design for measurement set selection in modelling biochemical regulatory systems. Int. J. Robust Nonlinear Control, 20, 1059–1078.
Hoyland, K., & Wallace, S. W. (2001). Generating scenario trees for multistage decision problems. Manag. Sci., 47, 295–307.
Joshi, M., Seidel-Morgenstern, A., & Kremling, A. (2006). Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems. Metab. Eng., 8, 447–455.
Klimke, A., & Wohlmuth, B. (2005). Algorithm 847: {Spinterp}: piecewise multilinear hierarchical sparse grid interpolation in {Matlab}. ACM Trans. Math. Softw., 31.
Kremling, A., et al. (2004). A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. Genome Res., 14, 1773–1785.
Kreutz, C., & Timmer, J. (2009). Systems biology: experimental design. FEBS J., 276, 923–942.
Kreutz, C., et al. (2007). An error model for protein quantification. Bioinformatics, 23, 2747–2753.
Kutalik, Z., Cho, K. H., & Wolkenhauer, O. (2004). Optimal sampling time selection for parameter estimation in dynamic pathway modeling. Biosystems, 75, 43–55.
Lillacci, G., & Khammash, M. (2010). Parameter estimation and model selection in computational biology. PLoS Comput. Biol., 6, e1000696.
Lipniacki, T., Hat, B., Faeder, J. R., & Hlavacek, W. S. (2008). Stochastic effects and bistability in T cell receptor signaling. J. Theor. Biol., 254, 110–122.
Preece, D. A. (1990). Fisher, R.A. and experimental-design—a review. Biometrics, 46, 925–935.
Pritchard, D. J., & Bacon, D. W. (1974). Potential pitfalls in model discrimination. Can. J. Chem. Eng., 52, 103–109.
Pritchard, D. J., & Bacon, D. W. (1978). Prospects for reducing correlations among parameter estimates in kinetic-models. Chem. Eng. Sci., 33, 1539–1543.
Pronzato, L. (2008). Optimal experimental design and some related control problems. Automatica, 44, 303–325.
Pronzato, L., & Walter, E. (1994). Minimum-volume ellipsoids containing compact-sets—application to parameter bounding. Automatica, 30, 1731–1739.
Rodriguez-Fernandez, M., Mendes, P., & Banga, J. R. (2006). A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems, 83, 248–265.
Van Derlinden, E., Bernaerts, K., & Van Impe, J. F. (2010). Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature. J. Theor. Biol., 264, 347–355.
Vatcheva, I., de Jong, H., Bernard, O., & Mars, N. J. I. (2006). Experiment selection for the discrimination of semi-quantitative models of dynamical systems. Artif. Intell., 170, 472–506.
Wong, W. K. (1999). Recent advances in multiple-objective design strategies. Stat. Neerl., 53, 257–276.
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Bazil, J.N., Buzzard, G.T. & Rundell, A.E. A Global Parallel Model Based Design of Experiments Method to Minimize Model Output Uncertainty. Bull Math Biol 74, 688–716 (2012). https://doi.org/10.1007/s11538-011-9686-9
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DOI: https://doi.org/10.1007/s11538-011-9686-9