Mathematical model of the interactions between Micrococcus spp. and Pseudomonas aeruginosa on agar surface

The interactions between six different Micrococcus species and two strains of Pseudomonas aeruginosa were studied on an agar surface. This type of interaction on solid surface could act as a model of situations occurring either in the environment, in food or in man. The hypothesis of an amensalistic relationship between a Micrococcus spp. and Pseudomonas aeruginosa, due essentially to Ps. aeruginosa bacteriolytic enzymes, is retained as the basis for a mathematical model of the variations of the colony surface of Micrococcus spp. (S) with respect to the distance (d) from Ps. aeruginosa cells. The diffusion of the bacteriolytic substance in agar explains the limitation of the growth of the Micrococcus spp. This model S = Smax (1-e-md2) is shown to be adapted to all the interactions studied.