Derivation of a growth rate equation describing microbial surface colonization

A surface growth rate equation is derived which describes simultaneous growth and attachment during microbial surface colonization. The equation simplifies determination of attachment and growth rate, and does not require a computer program for solution. This rate equation gives the specific growth rate (Μ) as a function of the number of cells on the surface (N), the incubation period (t), and the number of colonies (Ci) containing either one cell, two cells, four cells, etc, as shown below.[Formula: see text] The attachment rate (A) is given by the following relationship:[Formula: see text] The proposed colonization kinetics are compared with exponential growth kinetics using 3-dimensional computer plots. Colonization kinetics diverged most from exponential kinetics when the growth rate was low or the attachment rate was high. Using these kinetics, it is possible to isolate the effects of growth and attachment on microbial surface colonization.