Chirality and handedness: the Ruch "shoe-potato" dichotomy in the right-left classification problem

Chirality and handedness are concepts that apply to the structure of molecules. Chirality is defined by the lack of certain features of symmetry, which lead to an object not being superimposable on its mirror image. Handedness is a different phenomenon relating to the ability to classify chiral objects into right-handed and left-handed objects. All handed objects are chiral, but not all chiral objects are handed. In 1968 through 1970, Ruch and coworkers developed a theory of chirality that provided a mathematical basis for the handedness of chiral objects. Handed chiral objects are considered to be analogous to shoes, which are readily classified into right and left shoes regardless of the size, material, style, or other attributes of the shoes in question. Nonhanded chiral objects are considered to be analogous to potatoes, which have no symmetry because of their irregular patterns of "bumps" and "eyes," thereby meeting the lack of symmetry requirements for chirality. There is, however, no unambiguous way to classify a set of potatoes into "left" and "right" potatoes. In the case of molecules, a tetrahedron with four different substituents such as an asymmetric carbon atom in organic chemistry can readily be classified into right and left tetrahedra, as is typical for organic molecules in biological systems. An octahedral molecule with six different substituents, however, exhibits nonhanded chirality. For this reason, the fact that the key building block of natural products is a tetrahedral carbon atom rather than an octahedral atom of some type may be a critical factor in the handedness of many molecules found in biological structures.