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Experimental and mathematical analysis of productivity of cultures containing recombinant plasmids is based in this work on the following paradigm: molecular controls leads to single cell kinetics leads to cell population dynamics leads to reactor productivity. Mathematical models have been developed for replication control of the lambda dv plasmid and for efficiency of the lac promoter-operator based on the molecular control mechanisms of these systems in Escherichia coli. A special and important attribute of these models is their ability to describe quantitatively a wide range of genetic effects as well as environmental influences on molecular control function. Equations describing plasmid maintenance and distribution in growing cell cultures have been determined based on the population-balance equations applicable to a segregated culture model. The washout dilution rate for continuous cultivation of plasmid-containing Saccharomyces cerevisiae in selective medium is given in terms of single-cell division-cycle parameters and plasmid copy number for one single-cell model of plasmid replication and segregation. A new experimental method based on flow cytometry for rapid characterization of heterogeneity of single-cell accumulation of a plasmid gene product is also described. Generalization of these methods and of the overall strategy should provide a useful framework for synthesis of biological and engineering principles and methods to optimize organisms and processes based on recombinant DNA technology.
Bailey et al. (1983) studied this question.