Non-linear stress-softening of peptidoglycan mediates bacterial cell shape homeostasis.

The bacillus-or rod-is a pervasive cellular morphology among bacteria. Rod-shaped bacteria elongate without widening by reinforcing their cell wall anisotropically, along the cell's circumference, but it is unknown how cells prescribe the specific degree of anisotropy that ensures growth at a constant, target width. Through super-resolution measurements of cell wall mechanical properties, we discovered that the Bacillus subtilis cell wall exhibits non-linear stress-stiffening and stress-softening exclusively in the circumferential direction. Furthermore, during steady-state growth, the cell wall is inflated precisely to the acute non-linearity corresponding to softening. Elasticity-based theory explains why this results in cell growth at a constant width. Finally, dynamic measurements of the non-linear mechanical properties during cell-width adaptation identified a negative-feedback system that regulates width homeostatically through tuning of both intracellular pressure and the critical pressure of the non-linearity. In other words, the cell wall is an "adaptive material" whose exotic mechanical properties are exquisitely engineered to execute cellular morphogenesis.