Chirality ("handedness") is an important feature of all biomacromolecules. In proteins the L-stereochemistry of individual amino acids influences the chirality of higher level structural features such as the right-handed helical sense of' cu-helices, the right-handed twist of P-sheets (viewed along the strand axis), and the right-handed sense of the backbone chain connecting two adjacent, packed a-helices.',' Characterization of new chiral features can provide information that may be valuable in elucidating subtle structural relationships a t all levels of protein architecture. These relationships could prove useful, for example, in attempts to predict a three-dimensional (3D ) structure from a knowledge of sequence data.
Recently, Murzin and F i n k e l ~t e i n ~. ~ were able t o describe the packing of helices in the a-helical domains of proteins with a simple model based on regular quasispherical polyhedra. In their approach helices represented as uniform cylinders are aligned along the edges of the polyhedra as depicted in Figure 1 for the case of three, four, and five helices. Note that the helices are nonoriented, that is, the direction of the backbone chain is unspecified. Moreover, Murzin and Finkelstein showed that the packing of three-, four-, five-, and six-helix domains of proteins currently in the Brookhaven Protein Data Bank could be uniquely described respectively by octahedral, dodecahedral, hexadecahedral, and icosahedral packing models. However, all possible allowed helix packings (see Figure 3 of Ref. 3 ) were not realized in this set of proteins: whether this will remain true as the database becomes larger is not, clear a t this time.
The orderliness of polyhedral helix packings suggests the possihility that additional topological chiral properties may be present. Clearly, any pair of oriented helices, regardless of whether or not they are in contact, are chiral unless they lie in the same plane. This type of relationship can also be described by placing the two oriented helices ( represented by cylinders) along the edges of the tetrahedron shown in Figure 2a. If, however, the two helices are nonoriented, chirality is lost. On the other hand, chirality may be regained even in the nonoriented case if one