The statistics of colony development by Bact. coli mutabile on lactose agar

Abstract

A quantitative study has been made of the formation of colonies on lactose-agar plates by Bact. coli mutabile, previously unadapted to lactose $(\text{lac}^{-})$. For comparison, observations have also been made on adapted strains $(\text{lac}^{+})$. Observations have been recorded of the following: (a) The number of colonies reaching a standard size as a function of time for different numbers, $N_{0}$, of cells plated. (b) The distribution of colony diameters at a series of given times, and for a series of values of $N_{0}$. (c) The final yield of colonies as a function of $N_{0}$. (d) The maximum diameter of colonies of the $\text{lac}^{+}$ strain as a function of $N_{0}$. (e) The rate of increase with time of the diameter of individual colonies. The results generally can be interpreted by the assumptions (1) The delays preceding the onset of growth for any given cell are distributed about a modal value in an approximately Gaussian manner. (2) The diameter increases steadily until the nutrient on the plate is nearly exhausted, when there is a fairly abrupt cut-off. (3) Maximum numbers of colonies can be related to total numbers of cells plated by imagining the plate divided into small regions within any one of which the occurrence of two inoculated cells can no longer give rise to separate colonies, the distribution of the $N_{0}$ cells among the regions being governed by the laws of probability. The early appearance of a few relatively large colonies when $N_{0}$ is made very great is generally similar to what might be predicted from observations with small values of $N_{0}$ and from the Gaussian distribution. Such observations with massive inocula thus form an uncertain basis for conclusions about the presence of small fractions of special mutants in the original culture.