The kinetics of conjugative plasmid transmission: fit of a simple mass action model.

A mass action model for the infectious transmission of conjugative plasmids and procedures to estimate its parameters are presented. The suitability of this model as an analog of the kinetics of conjugative plasmid transmission is examined with batch and chemostat populations of Escherichia coli K-12 and three of its plasmids, F-lac-pro, R1 (Km-Cm-Ap), and R1-drd-19 (Km-Cm-Ap). Evidence is presented that this mass action model, with a unique and constant rate parameter, represents a reasonable analog of the kinetics of plasmid transfer for bacterial populations dividing at a constant rate in either exponentially growing cultures or at equilibrium in chemostats. As anticipated from this model magnitudes of the transfer rate constant for these plasmids appear to be relatively insensitive to both total cell density and the donor-recipient ratio. For all plasmids, the value of the transfer rate constant in rapidly dividing (exponentially growing) cultures is considerably greater than its corresponding value in slowly dividing, chemostat equilibrium cultures and the values of the transfer rate constant of the permanently derepressed plasmids F-lac-pro and R1-drd-19 are considerably greater than that of the wild-type, repressed transfer plasmid R1. The implications of this apparent fit to a mass action model are discussed and a recommendation is made to use the transfer rate constant as the measure of the fertility of conjugative plasmids.