Numerical techniques and mathematical modelling for CI857-controlled gene expression and cell growth in recombinant E. coli

Author to whom all correspondence should be addressed. E-mail: rcubarsi{at}mat.upc.es Recombinant gene expression, monitored by ß-galactosidaseactivity, is studied in a PL, PR-C1857 plasmid expression systemin temperature-induced E. coli batch cultures. The experimentalprocedure has been mathematically modelled, and the correspondingparameters are estimated from specific statistical and numericalmethods, basically by using a global least-squares procedureunder some constraints induced by the model. The numerical techniquesproposed in this work act by accumulation of data coming fromseveral runs of the modelled experiment, so that more accuracyis obtained in the parameter estimation. In particular, forthe production process, an extra-model parameter depending onan indicator vector is introduced for each run of the experimentin order to globalize the data. The analysis of the data obtainedleads to an integrated model for both cell growth and gene expression,which describes an asymmetric dynamics between culture growthand recombinant protein yield, and can serve to predict themaximal value of accumulated gene expression and the time requiredfor it to be achieved at any age of the preinducing cell growth.