Mathematical Model of Plasmid Transfer between Strains of Streptomycetes in Soil Microcosms

Abstract

A mathematical model was developed and used to simulate the long-term dynamics of growth and plasmid transfer in nutrient-limited soil microcosms of Streptomyces lividans TK24 carrying chromosomal resistance to streptomycin, S. lividans 1326; and S. violaceolatus ISP5438. Donor, recipient, and transconjugant survival was modelled by an extension to the Verhulst logistic equation which takes account of nutrient limitation, and plasmid transfer was modelled by a mass action model. Rate parameters were derived from experimental data on the early stages of the development of sterile systems. The model predicted donor, recipient, and transconjugant populations in 2.4-h (0.1-day) steps and was tested against the long-term behavior of the experimental sterile systems and independent experimental data on nonsterile systems. Bacteria were periodically enumerated onto selective media over a 20-day period. The effects of long-term nutrient-moisture depletion were correctly predicted.