  Viruses are right at the interface of inanimate matter and life. However,
recent experiments [T. Sakai, et al., J.~Virol.~{\bf 92}, e01522-17 (2018)]
have shown that some influenza strains can actively roll on glycan-covered
surfaces. In a previous letter [F. Ziebert and I. M. Kuli\'{c}, Phys. Rev.
Lett. {\bf 126}, 218101 (2021)] we suggested this to be a form of viral surface
metabolism: a collection of spike proteins that attach to and cut the glycans
act as a self-organized mechano-chemical motor. Here we study in more depth the
physics of the emergent self-rolling states. We give scaling arguments how the
motion arises, substantiated by a detailed analytical theory that yields the
full torque-angular velocity relation of the self-organized motor. Stochastic
Gillespie simulations are used to validate the theory and to quantify
stochastic effects like virus detachment and reversals of its direction.
Finally, we also cross-check several approximations made previously and show
that the proposed mechanism is very robust. All these results point together to
the statistical inevitability of viral rolling in presence of enzymatic
activity.
