Bacterial cell mechanics: bending instabilities, wrinkling and helix formation

Abstract

Bacterial cells are thin-walled, pressurized structures that robustly maintain characteristic morphologies such as straight rods and helices while continuously remodeling their cell walls during growth. This thesis develops a unified continuum-mechanics description of how internal pressure, curvature, and material organization govern the stability and nonlinear deformation of pressurized shells, with bacterial cell envelopes as the primary motivation. By treating the wall as a pressurized elastic shell, we identify the mechanical principles that set instability thresholds, enable pressure-driven shape changes, and determine post-buckling patterns under bending. The thesis is organized around three closely connected studies. First, we analyze the bending of rod-shaped bacteria modeled as pressurized cylindrical shells and characterize the onset of Brazier-type bending localization. We show that, in the parameter regime relevant to bacterial cell walls, turgor pressure is the dominant stabilizing factor: pressure-induced membrane tension substantially increases the critical curvature for instability, while the wall’s bending stiffness plays a comparatively minor role in setting the threshold. Second, we investigate pressure-induced shape transformations in helical bacteria by introducing helical elastic heterogeneity in the shell (e.g., a helical reinforcement or stiffness modulation). In this setting, uniform pressurization couples to patterned elasticity to generate a three-dimensional helical centerline, providing a mechanical route to tunable helical morphologies and delineating regimes with strong, and in some cases counterintuitive, pressure--shape responses. Third, we characterize the post-instability mechanics of bent, pressurized tubes, where bending-induced compression is relieved through wrinkling and stress redistribution. Using numerical simulations together with an analytical description inspired by tension-field concepts, we connect wrinkle emergence and morphology to the nonlinear torque--curvature relation and to the progression toward localized deformation. Together, these results establish a thin-shell framework that links stability, shape selection, and pattern formation in pressurized tubular structures. Beyond bacterial mechanics, the analysis provides general insights into the structure of pressurized shells relevant to soft materials, bio-inspired design, and slender structural systems.