The Theory of Bacterial Constant Growth Apparatus

Recent work in bacterial genetics has emphasised the usefulness of apparatus whose purpose is to maintain a constant population of bacteria in a state of active growth. Several such devices have been described for example by Monod (1950), Novick and Szilard (1950), and Perret (1954). It seems worthwhile to give a short account of the underlying theory as a guide to the problems of design likely to be encountered with organisms of different growth characteristics; or under various conditions of culture. Mathematically the problem may be stated as follows:-Consider an organism growing freely in a limited, conistant volume of nutrient. After some period of growth factors come into play which depress the power of the organism, to divide and eventually stop it growing altogether. These factors may be of several different kinds: for example, exhaustion of nutrient, insufficiency of oxygen, or production of some toxic metabolite, the general effect however, is that the growth rate of the population at any time is a function of its size (n) so that