Predicting the potential cell size limit prior to bacterial cell division

Bacterial cells exhibit a diverse range of shapes and sizes, often regulated by the bacterial cell wall, in conjunction with cytoskeletal proteins and internal turgor pressure. Unlike typical polymeric membranes, bacterial cell walls possess greater thickness and rigidity, allowing them to maintain cell shapes while withstanding significant turgor pressure. Our study introduces a theoretical framework to model the dynamics of growing cell walls, rooted in the principle of minimizing energy dissipation. Within a bacterial cell wall, dissipative forces arise from the incorporation of peptidoglycan (PG) strands, while driving forces stem from changes in mechanochemical energy associated with maintaining wall shape. The interplay between mechanical and chemical energy offers insight into cell wall growth dynamics and provides a means to predict the maximum size of bacterial cells prior to cell division. Remarkably, our analysis, employing linear stability techniques on a typical system, closely matches the phase diagram obtained from numerical analysis of the full nonlinear theory. Nonetheless, the molecular intricacies of cell wall composition are still challenging, and we anticipate that a more precise constitutive model will yield even more accurate quantitative results.