Computational Methods to Model Persistence

Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin–antitoxin modules play a significant role in the generation of such persister cells. Toxin–antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin–antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin–antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin–antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin–antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin–antitoxin module expression to the generation of persister cells.