Numerical Techniques and Mathematical Modeling for CI857-Controlled Gene Expression and Cell Growth in Recombinant E. coli IMA Journal of Mathematics Applied in Medicine & Biolgy (1998) 15, 257-278. R. Cubarsi a , J. L. Corchero b , P. Vila b,c and A. Villaverde b a Dept. Matem` atica Aplicada i Telem` atica Universitat Polit` ecnica de Catalunya, Barcelona, Spain b Institut de Biologia Fonamental and Departament de Gen` etica i Microbiologia Universitat Aut` onoma de Barcelona, Bellaterra, Spain c Present address: Departament d’Enginyeria Qumica, UAB, Bellaterra, Spain CORRESPONDING AUTHOR: Rafael Cubarsi Dept. Matem` atica Aplicada i Telem` atica Campus Nord, Universitat Polit` ecnica de Catalunya Jordi Girona, 1-3 E08034-Barcelona; Spain Phone: 34-3-401-6030 Fax: 34-3-401-5981 E-mail: rcubarsi@mat.upc.es KEY WORDS: Recombinant proteins, gene expression, E. coli, mathematical modeling, con- strained least esquares Abstract Recombinant gene expression, monitored by β-galactosidase activity, is studied in a p L , p R -CI857 plasmid expression system in temperature-induced E. coli batch cultures. The ex- perimental procedure has been mathematically modeled, and the corresponding parameters are estimated from specific statistical or numerical methods, basically by using a global least squares procedure under some constraints induced by the model. The numerical techniques proposed in this work act by accumulation of data coming from several runs of the modeled experiment, so that more accuracy is obtained in the parameter estimation. In particular, for the production process, an extra-model parameter depending on an indicator vector is intro- duced for each run of the experiment in order to globalize the data. The analysis of obtained data leads to an integrated model for both cell growth and gene expression, which describes an asymmetric dynamics between culture growth and recombinant protein yield, and can serve to predict the maximal value of accumulated gene expression and the time required for it to be achieved at any stage of the preinducing cell growth. 1