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Filamentous viruses like influenza and torovirus often display systematicbends and arcs of mysterious physical origin. We propose that such virusesundergo an instability from a cylindrically symmetric to a toroidally curvedstate. This "toro-elastic" state emerges via a spontaneous symmetry breakingunder prestress, induced via short range spike protein interactions andmagnified by the filament's surface topography. Once surface stresses becomesufficiently large, the filament buckles and the toroidal, curved stateconstitutes a soft mode that can propagate through the filament's materialframe around a "mexican-hat" potential. In the mucus of our airways, glycanchains are omnipresent that influenza's spike proteins can bind to and cut. Weshow that when coupled to such a non-equilibrium chemical reaction, the curvedtoro-elastic state can attain a spontaneous rotation for sufficiently strongenzymatic activity, leading to a whole body reshaping propulsion similar to --but different from -- eukaryotic flagella and spirochetes.

Reshaping and Enzymatic Activity allow Viruses to move through the Mucus