The kinetics of chromosome transfer in Escherichia coli: a mathematical treatment

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Abstract
A mathematical treatment has been presented of the ideas of de Haan & Gross concerning transfer delay and chromosomal withdrawal during conjugation In Escherichia coli. The calculations involve three parameters: (i) the maximum delay, λ, which can occur between the formation of effective contact in mating pairs and the initiation of chromosomal transfer, (ii) the probability, b, that mating pairs separate with the withdrawal of that segment of the Hfr chromosome which has entered the female cell, and (iii) the probability, c, that mating pairs separate with the breakage of the Hfr chromosome at the point where it enters the female cell, leaving the injected fragment in the female.A comparison of the theory with the experimental results of de Haan & Gross obtained when chromosomal transfer occurs either in minimal medium or in broth shows good agreement under the following conditions:(i) the value of λ is the same under both growth conditions,(ii) the value of b is the same under both growth conditions,(iii) the value of c is much greater during transfer in broth than it is in minimal medium.

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