Accepted_test

This study introduces a novel mathematical model to explore the dynamics of Type II restriction-modification (R-M) systems, essential bacterial defenses against invasive genetic elements. Governed by a regulatory protein C, our model investigates the interactions between restriction enzymes (R) and methyltransferase (M) and aims to predict their behavior under various biological conditions.

We developed a comprehensive model that integrates biophysical evidence and minimizes arbitrary parameters. It includes the transcription dynamics of protein C, incorporating feedback mechanisms that influence R and M levels. Using stability analysis and bifurcation diagrams, we examined conditions that lead to monostability and bistability, key for understanding environmental response mechanisms. Numerical simulations validated the model, accurately predicting M-to-R ratio variations observed in R-M systems like Esp1396I, AhdI, and EcoRV.

Our results show that transitions from monostability to bistability can significantly alter bacterial susceptibility to phage infections and defense effectiveness. The model also highlighted how external factors such as plasmid copy numbers and growth rates influence the M-to-R ratio.

This research offers a robust theoretical framework that enhances our understanding of R-M system dynamics, crucial for bacterial adaptability and evolution. It emphasizes the vital role of the regulatory protein C in balancing restriction and modification enzymes, essential for shaping bacterial defenses against horizontal gene transfer. This study not only deepens our understanding of these systems but also guides future experimental work and therapeutic approaches to counter antibiotic resistance.