Experimental and Mathematical Models of
Escherichia coli
Plasmid Transfer In Vitro and In Vivo
Authors: Freter Rolf , Freter Rolf R. , Brickner Howard 
Published: January 2020

Little is known about the factors that govern plasmid transfers in natural ecosystems such as the gut. The consistent finding by earlier workers that plasmid transfer in the normal gut can be detected only at very low rates, if at all, has given rise to numerous speculations concerning the presence in vivo of various inhibitors of plasmid transfer. Plasmids R1, R1
drd-19
, and pBR322 were studied in
Escherichia coli
K-12 and wild-type
E. coli
hosts in two experimental systems: (i) gnotobiotic mice carrying a synthetic indigenous microflora (F-strains) which resemble in their function the normal indigenous microflora of the mouse large intestine, and (ii) anaerobic continuous-flow cultures of indigenous large intestinal microflora of the mouse, which can simulate bacterial interactions observed in the mouse gut. Mathematical models were developed to estimate plasmid transfer rates as a measure of the “fertility,” i.e., of the intrinsic ability to transfer the plasmid under the environmental conditions of the gut. The models also evaluate the effects of plasmid segregation, reduction of the growth rates of plasmid-bearing bacterial hosts, repression of transfer functions, competition for nutrients, and bacterial attachment to the wall of the gut or culture vessel. Some confidence in the validity of these mathematical models was gained because they were able to reproduce a number of known phenomena such as the repression of fertility of the R1 plasmid, as well as known differences in the transmission and mobilization of the plasmids studied. Interpretation of the data obtained permitted a number of conclusions, some of which were rather unexpected. (i) Fertility of plasmid-bearing
E. coli
in the normal intestine was not impaired. The observed low rates of plasmid transfer in the normal gut can be explained on quantitative grounds alone and do not require hypothetical inhibitory mechanisms. (ii) Conditions for long-term spread and maintenance throughout human or animal populations of a diversity of conjugative and nonconjugative plasmids may be optimal among
E. coli
strains of low fertility, as are found among wild-type strains. (iii)
E. coli
strains carrying plasmid pBR322 plus R1
drd-19
were impaired in their ability to transfer R1
drd-19
, but strains carrying pBR322 were significantly better recipients of R1
drd-19
than a plasmid-free recipient
E. coli.
(iv) Long-term coexistence of plasmid-bearing and plasmid-free
E. coli
, in spite of undiminished fertility, appeared to be due to a detrimental effect of the plasmid on the growth rate of its host bacterium, rather than due to high rates of plasmid segregation. (v) Mathematical analysis of experimental data published by earlier investigators is consistent with the conclusion that plasmid transfer occurs consistently in the human gut, but that the resulting transconjugant
E. coli
populations are too small to be detected regularly with the culture methods used by earlier investigators. It is concluded that the long-term interactions observed were often the consequences of minor differences in parameters such as growth rates, fertility, rates of segregation, etc., which were too small to be detected except by precise mathematical analysis of long-term experiments, but which were nevertheless decisive determinants of the ultimate fates of the plasmids and their hosts.