Bacterial defense systems protect bacterial cells against foreign DNA invasion. They include toxin-antitoxin (TA), and restriction-modification (R-M) systems, with the latter two forming a generalized TA group. These systems regulate horizontal gene transfer (HGT) and play a critical role in controlling the spread of antibiotic resistance (ABR) and virulence genes, through mechanisms that currently remain unclear. TA systems also contribute to bacterial persistence by enabling phenotypic switching into a dormant state, a key survival strategy under antibiotic stress. Given the nonlinear and inherently quantitative nature of these processes, mathematical modeling provides a critical tool for understanding their regulatory dynamics. This talk will present mathematical models describing the dynamics of both R-M and TA systems. First, we will introduce a mechanistic model of Type-II R-M systems, which incorporates the dynamic regulation of restriction (R) and methylation (M) enzymes by a regulatory protein (C). Through analytically derived stability diagrams and stochastic simulations, we reveal the conditions under which C-regulated R-M systems exhibit monostability or bistability [1]. The results indicate that M-to-R ratio shifts are influenced by factors such as plasmid replication rates and cell division timing, ultimately affecting bacterial permissiveness to foreign DNA. Importantly, our findings suggest that bacterial populations can tune R-M activity to create heterogeneous HGT barriers, which may impact the acquisition of ABR and other pathogenic genes over evolutionary timescales. Second, we will present a mathematical framework for Type-I TA systems [2], which are implicated in bacterial persistence through toxin-antitoxin regulation. In these systems, an antisense RNA inhibits toxin expression, thereby controlling the transition between active and dormant states. Our mathematical model captures the bistability and hysteresis inherent in TA-mediated persister formation, demonstrating how distinct inhibitory mechanisms govern toxin dynamics. Stability analysis confirms the existence of physiological parameter ranges that allow for the stable co-existence of persister and non-persister states. Additionally, stochastic simulations provide insight into the emergence of phenotypic heterogeneity, highlighting the role of noise in state-switching dynamics. By integrating these models, this work provides a quantitative framework for understanding bacterial defense and persistence strategies, offering useful insights into the regulatory principles governing these systems.
[1] Djordjevic, M., Zivkovic, L., Ou, H. Y., & Djordjevic, M. (2025). Nonlinear regulatory dynamics of bacterial restriction-modification systems modulates horizontal gene transfer susceptibility. Nucleic Acids Research, 53(2), gkae1322.
[2] Markovic, S., Djordjevic, M., OU, H., & Djordjevic, M. (2025). Bistability in type I toxin-antitoxin systems may lead to stress-induced persister formation, submitted.
Acknowledgement: This work was funded by the Science Fund of the Republic of Serbia, grant 650 no.7750294, qbio-BDS, and by the National Natural Science Foundation of China, grant no. 32370186.