Summary: The dynamics of microbial growth is a problem of fundamental interest in microbiology, microbial ecology, and biotechnology. The pioneering work of Jacob Monod served as a starting point for developing a wealth of mathematical models that address different aspects of microbial growth in batch and continuous cultures. A number of phenomenological models have appeared in the literature over the last half century. These models can capture the steady-state behavior of pure and mixed cultures, but fall short of explaining most of the complex dynamic phenomena. This is because the onset of these complex dynamics is invariably driven by one or more intracellular variables not accounted for by phenomenological models.
We provide an overview of the experimental data, and introduce a different class of mathematical models that can be used to understand microbial growth dynamics. In addition to the standard variables such as the cell and substrate concentrations, these models explicitly include the dynamics of the physiological variables responsible for adaptation of the cells to environmental variations. We present these physiological models in the order of increasing complexity. Thus, we begin with models of single-species growth in environments containing a single growth-limiting substrate, then advance to models of single-species growth in mixed-substrate media, and conclude with models of multiple-species growth in mixed-substrate environments.
Throughout the paper, we discuss both the analytical and simulation techniques to illustrate how these models capture and explain various experimental phenomena. Finally, we also present open questions and possible directions for future research that would integrate these models into a global physiological theory of microbial growth.