STRUCTURAL PROPERTIES OF PROTEIN fi-SHEETS

i. I N T R O D U C T I O N X-ray crystallographic studies of proteins have revealed a rich variety of structural architectures. Despite this diversity, many proteins share common features of structural organization. The extent to which proteins can be described as being structurally similar depends upon their incorporation of regular secondary structures. The observation that many proteins are predominantly composed of ~-helices, antiparallel /#sheet, or a combination of 2-helices and parallel fl-sheet, has provided a basis for the structural classification of proteins (Levitt and Chothia, 1976; Richardson, 1981 ). Such classification schemes have been an important first step in understanding protein structural organization. More importantly, these studies make evident that many structural motifs recur among proteins otherwise bearing little similarity in amino acid sequence or function. The recurrence of similar structural motifs among evolutionarily unrelated proteins presumably reflects underlying physical factors which depend only in a general way on protein sequence, but nevertheless are effective determinants of protein structural organization. The present work examines the structural properties of fl-sheets in proteins. Crystallographically observed fi-sheets in globular proteins exhibit an extraordinary diversity of structural forms. In contrast to the classical flat /#sheet arrangements first described by Pauling and Corey (1951), globular protein fl-sheets conform to a variety of twisted and curved surfaces. A basic objective of this review is to describe the operative forces and constraints which produce different twisted//-sheet geometries. The factors involved are most readily understood by considering the properties of a classical flat structure (Fig. 1 ). A fl-sheet is basically an aligned, planar array of conformationally regular polypeptide chains which are interconnected by hydrogen bonds. The flat sheet can be viewed as a regular, twodimensional lattice stabilized by covalent bonds along the direction of the polypeptide chains, and by hydrogen-bonds (i.e. dipole interactions) between or across the chains. The minimum energy configuration of the lattice will generally reflect the simultaneous