Sensitivity Function-Based Model Reduction A Bacterial Gene Expression Case Study Ilse Smets, 1 Kristel Bernaerts, 1 Jun Sun, 2 Kathleen Marchal, 3 Jos Vanderleyden, 2 Jan Van Impe 1* 1 BioTeC ± Bioprocess Technology and Control, Katholieke Universiteit Leuven, Kasteelpark Arenberg 22 B-3001, Leuven, Belgium; telephone: +32-16-32.14.66; fax: +32-16-32.19.60; e-mail: jan.vanimpe@agr.kuleuven.ac.be 2 Centre of Microbial and Plant Genetics, Katholieke Universiteit Leuven, Kasteelpark Arenberg 20 B-3001, Leuven, Belgium 3 ESAT±Department of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10 B-3001, Leuven, Belgium Received 24 October 2001; accepted 5 April 2002 DOI: 10.1002/bit.10359 Abstract: Mathematical models used to predict the be- havior of genetically modi®ed organisms require 1) a (rather) large number of state variables, and 2) compli- cated kinetic expressions containing a large number of parameters. Since these models are hardly identi®able and of limited use in model-based optimization and control strategies, a generic methodology based on sensitivity function analysis is presented to reduce the model complexity at the level of the kinetics, while maintaining high prediction power. As a case study to illustrate the method and results obtained, the in¯uence of the dissolved oxygen concentration on the cytN gene expression in the bacterium Azospirillum brasilense Sp7 is modeled. As a ®rst modeling approach, available mechanistic knowledge is incorporated into a mass balance equation model with 3 states and 14 parameters. The large differences in order of magnitude of the model parameters identi®ed on the available experimental data indicate 1) possible structural problems in the kinetic model and, associated with this, 2) a possibly too high number of model parameters. A careful sensitivity function analysis reveals that a reduced model with only seven parameters is almost as accurate as the original model. ã 2002 Wiley Periodicals, Inc. Biotechnol Bioeng 80: 195±200, 2002. Keywords: mathematical modeling; model reduction; sensitivity functions; bacterial gene expression; contin- uous systems; reporter gene INTRODUCTION To qualify and quantify the in¯uence of external signals on bacterial gene expression, continuous culture steady- state experiments have been performed throughout the past (Chao et al., 1997; Kasimoglu et al., 1996). These costly, labor-intensive and time-consuming experiments can be reduced to a minimum with the aid of a mathe- matical model that describes the intrinsic properties of the dynamic bioprocess. Although the advantages of model-based optimiza- tion and control of fermentations (e.g., baker's yeast production processes and biological wastewater treat- ment systems) are well established, the introduction of mathematical modeling in the ®eld of genetic engineer- ing is fairly recent. The scarce, knowledge-based models that have been developed are usually characterized by complex kinetic expressions involving a large number of parameters. In this article it is illustrated that sensitivity function analysis is a powerful tool to reduce the complexity of a knowledge-based model. To date, most reported appli- cations of parametric sensitivity analysis are concerned with design and optimal operation of chemical systems (see, e.g., Varma et al., 1999). Also optimal experimental design techniques aimed at obtaining experimental data with a high information content to facilitate parameter identi®cation, rely on sensitivity functions (see, e.g., Bernaerts et al., 2000, in the ®eld of predictive micro- biology). To the authors' knowledge, sensitivity func- tion-based methodologies have, however, not yet found widespread appeal in modeling and analysis of biologi- cal systems. One exception is the article by Pertev et al. (1997) in the context of modeling the (kinetics) of baker's *Correspondence to: J. Van Impe Contract grant sponsors: the Flemish Government (GOA), the Fund for Scienti®c Research Flanders, Project OT/99/24 of the Research Council of the Katholieke Universiteit Leuven and the Belgian Pro- gram on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Oce for Science, Technology and Culture. ã 2002 Wiley Periodicals, Inc.