A deterministic model for monophasic growth of batch cultures of bacteria.

Experimental observations of bacterial numbers employing high resolution electrical conductance measurements of the culture provide the basis for a proposed deterministic model of monophasic growth of populations in batch culture. The model postulates that the production and growth of each bacterium is accompanied by the generation of a constant mass of toxic end-products and that specific growth rate declines in proportion to the ratio of the accumulated mass of these substances to the dry mass of the nutrient medium when the substrate is non-limiting. The theoretical relationship is found to fit extensive data for Escherichia coli (NCIB 9132) very closely and offers an analytical basis for the logistic curve frequently observed to represent the time-dependence of growth. These data incidentally provide substantial evidence that lag time and generation time are each independent of both inoculum number and concentration of the medium.