Twisting nanotubes: from torsion to chirality.

An intriguing aspect of torsion, especially for chemists, is the fact that, unlike stretching, bending, shear, uniaxial, radial or isotropic compression, expansion etc, torsion is the only mode of deformation that is intrinsically chiral. Hence, torsion can turn achiral objects into chiral ones, and it can discriminate between chiral enantiomorphs turning them diastereomorphous. Beside this uniqueness, it might be surprising and inspiring to realize that torsion at different scales plays crucial roles in the Universe (Figure 1). Our Sun, for instance, is a large torsional oscillator with a period of 11 years, which governs solar weather (Figure 1a), causing cyclic disruptions in our communications. A huge torsional wave has just been proposed to propagate vertically away from the center of our Galaxy, inhibiting star formation in that region. Twisting different parts of the human body was probably one of the most ancient forms of torture, as suggested by the common etymological root of the words torsion, torture and extortion. When voluntary, however, twisting the body can increase the sex appeal, so the Twist became the furor of the early 60s (Figure 1d). Torsional penduli have been used from the 1860s to build the classical Anniversary clocks (Figure 1c). A torsion balance was used by Cavendish in 1798 to accurately measure the universal gravitational constant (Figure 1b). Torsional strain in DNA plays such a critical role in gene regulation that special enzymes called topoiso-