Symmetry and dynamics of molecular rotors in amphidynamic molecular crystals

Rotary biomolecular machines rely on highly symmetric supramolecular structures with rotating units that operate within a densely packed frame of reference, stator, embedded within relatively rigid membranes. The most notable examples are the enzyme FoF1 ATP synthase and the bacterial flagellum, which undergo rotation in steps determined by the symmetries of their rotators and rotating units. Speculating that a precise control of rotational dynamics in rigid environments will be essential for the development of artificial molecular machines, we analyzed the relation between rotational symmetry order and equilibrium rotational dynamics in a set of crystalline molecular gyroscopes with rotators having axial symmetry that ranges from two- to fivefold. The site exchange frequency for these molecules in their closely related crystals at ambient temperature varies by several orders of magnitude, up to ca. 4.46 × 10⁸ s^-1.