  We have modelled stress concentration around small gaps in anisotropic
elastic sheets, corresponding to the peptidoglycan sacculus of bacterial cells,
under loading corresponding to the effects of turgor pressure in rod-shaped
bacteria. We find that under normal conditions the stress concentration is
insufficient to mechanically rupture bacteria, even for gaps up to a micron in
length. We then explored the effects of stress-dependent smart-autolysins, as
hypothesised by Arthur L Koch [Advances in Microbial Physiology 24, 301 (1983);
Research in Microbiology 141, 529 (1990)]. We show that the measured
anisotropic elasticity of the PG sacculus can lead to stable circumferential
propagation of small gaps in the sacculus. This is consistent with the recent
observation of circumferential propagation of PG-associated MreB patches in
rod-shaped bacteria. We also find a bistable regime of both circumferential and
axial gap propagation, which agrees with behavior reported in cytoskeletal
mutants of B. subtilis. We conclude that the elastic anisotropies of a
bacterial sacculus, as characterised experimentally, may be relevant for
maintaining rod-shaped bacterial growth.
