Emergence of E. coli Critically Buckled Motile Helices Under Antibiotic Stress*

Bacteria under external stress can reveal unexpected emergent phenotypes. We show that the intensely studied bacterium E. coli can transform into long, highly motile
helical filaments poised at a torsional buckling criticality when exposed to minimum inhibitory concentrations of several antibiotics. While the highly motile helices are
physically either right- or left-handed, the motile helices always rotate with a right-handed angular
velocity $\vec \omega$ which points in the same direction as the translational velocity $\vec v_{T}$ of the helix.
Furthermore, these helical cells do not swim by a ``run and tumble'' but rather rather synchronously flip their spin $\vec \omega$ and thus translational velocity \textemdash{} backing
up rather than tumbling. By increasing the translational persistence length, these dynamics give rise to an effective diffusion coefficient up to 20 times that of a normal E. coli cell. Finally, we propose an evolutionary mechanism for this phenotype's emergence whereby the increased effective diffusivity provides a fitness advantage in allowing filamentous cells to more readily escape regions of high external stress.