In the previous papers [35,36] the process variables of plasmid-free, one-, two-and three-plasmid harboring E. coli JM109 cells were investigated in batch and continuous cultivation as a function of the medium composition, plasmid content, dilution rate and cultivation (generation) time. In the present paper the growth of the recombinant E. coli JM109 [pEcoR4, pRK248cI, pMTC48] and the production of the fusion protein EcoRI::SPA are simulated by using a four-compartment model, consisting of the active cell components (ribosomes, mRNA, tRNA, and others) (A), the structure forming materials and chromosomal DNA (Z), the plasmid-DNA (G) and the recombinant enzyme protein (E). At the ®rst time, all of the three plasmids: the production plasmid (Gp), the repressor plasmid (Gr) and the protection plasmid (Gs) are taken into account in the plasmid DNA-compartment of the model. The calculated and measured courses of the cell mass, the concentrations of glucose and acetate, and the products as well as the particular plasmids agree well.
List of symbolsA active cell compartment [g (g X) A1 ] Ac acetate concentration [g l A1 ] E enzyme protein compartment; Ep for fusion protein, Er for repressor protein, Es for methylase [g (g X) A1 ] F¯ow rate [l h A1 ] G plasmid-DNA compartment; Gp for production plasmid, Gr for repressor plasmid, Gs for protection plasmidextracellular substrate concentration [g l A1 ] S Ã intracellular substrate concentration [g l A1 ] t cultivation time [h] t f the time ®lled up the second reactor with medium [h] V reactor volume [l] X cell mass [g l A1 ] X i intracellular concentration of the i-th component [g (g X) A1 ] y A,Z stoichiometric coef®cients for the formation of components Z compartment for structure forming material [g (g X) A1 ] l speci®c growth rate [h A1 ] g stoichiometric coef®cients for acetate formation x segregation coef®cient of the production plasmid 1 index for the ®rst reactor 2 index for the second reactor 20 index for the¯ow of induction medium to the second reactor + exponent for the three plasmids harbouring cells A exponent for the two plasmids harbouring cells 1 Introduction Several researcher developed mathematical models for the description of the growth and host plasmid interaction in recombinant E. coli [13, 38]. One can distinguish between small and large structured and population models [2]. In small structured models the cell mass and biological properties of the cells lumped into few compartments. A four-compartment model was presented by Nielsen et al. [24], which was later improved [26] based on the lactobacillus model [25]. An eight-compartment model was formulated by Bentley and Kompala [3]. Large scale computer models containing many variables and parameters represent an attempt to calculate, in systematic and coordinated fashion, the consequences of many simultaneous interactions within the cell, sometimes on the known molecular mechanism [2]. Such models were developed by Lee and Bailey [16±19, 21]. These models make it possible to simulate the cells growth, ...