Nonlinear regulatory dynamics of bacterial restriction-modification systems modulates horizontal gene transfer susceptibility

Type II restriction-modification (R-M) systems play a pivotal role in bacterial defense against invading DNA, influencing the spread of pathogenic traits. These systems often involve coordinated expression of a regulatory protein (C) with restriction (R) enzymes, employing complex feedback loops for regulation. Recent studies highlight the crucial balance between R and M enzymes in controlling horizontal gene transfer (HGT). This manuscript introduces a mathematical model reflecting R-M system dynamics, informed by biophysical evidence, to minimize reliance on arbitrary parameters. Our analysis clarifies the observed variations in M-to-R ratios, emphasizing the regulatory role of the C protein. We analytically derived a stability diagram for C-regulated R-M systems, offering a more straightforward analysis method over traditional numerical approaches. Our findings reveal conditions leading to both monostability and bistability, linking changes in the M-to-R ratio to factors like cell division timing and plasmid replication rates. These variations may link adjusting defense against phage infection, or the acquisition of new genes such as antibiotic resistance determinants, to changing physiological conditions. We also performed stochastic simulations to show that system regulation may significantly increase M-to-R ratio variability, providing an additional mechanism to generate heterogeneity in bacterial population.