Mathematical modelling of genetic segregation kinetics obtained with chemostat cultures of procaryotic microorganisms

Abstract

Dedicated to Prof. Ur. F. BERGTER on the occasion of his 60t1' birthday (Eingegangen nrn 4.1. 1984)The total genetic information of procaryotic microorganisms is not absolutely stable and leads to alterations of components of populations with respect to the ratio of genotypes present. An excellent method for investigating such population genetic segregation kinetics is the chemostat allowing the continuous cultivation of microbial population under constant and1 reproducible conditions.I n order to quantitatively describe experimentally elaborated segregation kinetics a mathematical model is presented. The main parameters of this model are the segregation rate 6 describing the transition between the original genotype and a segregated (mutated) genotype and the selection pressure u describing the difference of the specific growth rates of the original genotype and the segregated one. B simple procedure is described for estimating both parameters mentioned above. This method is applied to the quantitative description of four sets of experimental segregation kinetics obtained with both unicellular and mycelial procaryotes with respect to chromosomal and extrachromosomal genetic information.The phenomenon of genetic alteration and segregation in procaryotic microorganisms has been investigated quantitatively preferentially since the method of continuous cultivation by means of the chemostat (NOVICK and SZILARD 1950) was introduced into related research. Summaries concerning various aspects of continuous cultivation have been published by KUBITSCIIEK (1970) and BERGTER (1983). Reviews focusing on population genetics and dynamics are given by NOACK (1968), HARDER and KUENEN (1977) and DYKIIGIZEN and HARTL (1983). The last authors presented mathematical models for the dynamics of competition of two genetically different strains for a limiting substrate in a cheniostat. I n the following paper we propose a mathematical niodel upon population genetic processes in chemostat cultures of procaryotic niicroorganisms. This niodel is characterized by two parameters. The first one is a segregation rate 6 describing the transition of the strain originally inoculated into the chemostat to a segregated strain which is genetically different from the original one. The second one is the selection pressure 0, which is the difference between the specific growth rate of the segregated strain and that of the original strain. A simple mathematical procedure is presented allowing the calculation of both parameters from segregation kinetics. This is demonstrated with experimental data already published. The ModelGenetic segregation within a population of procaryotic rriicroorganisnis continuously cultivated in a chemostat is described by the following system of differential equations

Coevolution in Bacterial-Plasmid Populations

“…Estimates of the rate ofsegregationalloss of the plasmid determined in this way are confounded with selective differences between plasmid-containing and plasmid-free strains (but see Noack et al, 1984;and Lenski and Bouma, 1987). However, this procedure allows relative changes in the rate of segregationalloss to be identified, provided that the differences in the deleterious effects of the plasmids are not large.…”

Mathematical analysis of catabolic function loss in a population of Pseudomonas putida mt-2 during non-limited growth on benzoate

“…For a number of strains harbouring a TOL plasmid, it has been shown that growth on benzoate results rapidly in a population that has lost the ability to grow on toluene and xylene (Nakazawa & Yokota, 1973;Williams & Murray, 1974;Keshavarz et al, 1985;Stephens & Dalton, 1987). Genetic analysis demonstrated that these mutants contain either a partially deleted plasmid or no plasmid at all (Bayley et al, 1977;Osborne et al, 1988).…”

“…In a number of modelling studies of plasmid instability in other host-vector systems, it has been shown that it is possible to distinguish between the two means of loss of plasmid-encoded functions by analysing the kinetics of disappearance of the organisms bearing the original plasmid (Noack et al, 1984;Cooper et al, 1987;Davidson et al, 1990). By means of a similar model, adapted for growth at maximum rate, we quantified in this study both the growth-rate difference and the segregation rate for P .…”

Study of stability of recombinant plasmids during the continuous culture ofBacillus stearothermophilus NUB3621 in nonselective medium

“…The kinetic behavior of such a system with unstable recombinant microorganisms has been described using models for growth competition. In a chemostat culture system, it can be mathematically demonstrated (Cooper et al, 1987;Noak et al, 1984) that, assuming R and ␦ are constant, at time t the fraction of plasmidfree cells, y − , is:…”

“…Because of the nonlinearity involved, it is not a trivial task to solve the equation to obtain an estimate for these two parameters. A model developed by Noak et al (1984), and used by other investigators (Nancib and Boudrant, 1992;Park et al, 1991;San and Weber, 1988), considered only the relationship between R and ␦ when the specific growth rate difference was the dominant effect. A preliminary analysis of the data obtained in the present study showed that Noak's model did not match them.…”