Estimating the growth pattern of micro-organisms in distinct stages of the cell cycle.

Knowledge of the growth patterns of micro-organisms is required to understand how cell growth and division are controlled and co-ordinated in relation to mechanisms of wall assembly and chromosome duplication. Direct observation, e.g. by time-lapse studies, is usually limited in accuracy by the small size of the cells. Indirect methods have therefore been developed which give estimates of the growth patterns of cells, based on the analysis of distributions of cell size in populations in balanced exponential growth. Previously, we have compared such methods (Burdett & Kirkwood, 1983) and concluded that the most powerful approach is that proposed by Collins & Richmond (1962), in which growth rate is calculated as a function of cell size using size distributions of extant, separating and new-born cells. A limitation of this method has been, however, that it gives only an estimate for the average growth rate of cells at a given size, irrespective of the state of progress of individual cells through the cell cycle. In this paper, we describe an extension to the standard Collins-Richmond procedure which provides separate estimates for the growth pattern of cells in distinct stages of the cell cycle, and we illustrate the method in relation to growth of mononucleate, binucleate and septate cells of Bacillus subtilis. It is demonstrated that this three-stage analysis is clearly superior to the standard method, in that it provides more detailed and probably more realistic information. We also demonstrate how to assess the precision and accuracy of the estimated growth pattern. Generalization of the method to any number of stages and to multiple as well as binary fission is described.