Inhibition of bacterial growth by antibiotics: a minimal model

Growth in bacterial populations generally depends on the environment (availability and quality of nutrients, presence of a toxic inhibitor, product inhibition..). Here, we build a minimal model to describe the action of a bacteriostatic antibiotic, assuming that this drug inhibits an essential autocatalytic cycle of the cell metabolism. The model recovers known growth laws, can describe various types of antibiotics and confirms the existence of two distinct regimes of growth-dependent susceptibility, previously identified only for ribosome targeting antibiotics. We introduce a proxy for cell risk, which proves useful to compare the effects of various types of antibiotics. We also develop extensions of our model to describe the effect of combining two antibiotics targeting two different autocatalytic cycles or a regime where cell growth is inhibited by a waste product.