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

Recombinant gene expression, monitored by beta-galactosidase activity, is studied in a pL, pR-CI857 plasmid expression system in temperature-induced E. coli batch cultures. The experimental procedure has been mathematically modelled, and the corresponding parameters are estimated from specific statistical and 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 modelled 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 introduced for each run of the experiment in order to globalize the data. The analysis of the data obtained 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 age of the preinducing cell growth.