Principles of Protein Structure - G. Schulz 1982

Mechanisms of polypeptide chain folding and association
Supersecondary structures
β-Zigzags and other features of β-structures

The ß-zigzag contains the same number of Hydrogen Bonds per residue as an a-helix of average length. In certain Proteins, such as T4 Lysozyme [241], staphylococcal nuclease [242], Ser proteases [18, 243–246], and the catalytic domain of Lactate dehydrogenase [232], the ß-Structure adopts the conformation of three closely spaced antiparallel peptide chains connected by short segments. This structural motif is referred to as a ß-zigzag and is illustrated schematically in Fig. 5.12, c. Frequently observed in proteins, the ß-zigzag can be classified as a supersecondary structure; it has been found in half of all known three-stranded antiparallel ß-structures [247]. This prevalence stems from the high cooperativity of interactions between antiparallel chains (Section 5.3, see also Fig. 5.15, a). Furthermore, because the ß-zigzag incorporates chain turns at both ends, it provides approximately two-thirds of all possible backbone hydrogen bonds within that region of the chain. This corresponds to the number of hydrogen bonds in a three-turn a-helix of average length (Fig. 5.5). Thus, in terms of Free energy and nearest-neighbor residue interactions, the ß-zigzag is comparable to the a-helix, which presumably explains its widespread occurrence.

Specific chain arrangements are strongly preferred in ß-structures. The strong correlation among residue interactions (Fig. 5.15, a) in ß-structures reflects a distinct preference for certain chain configurations within ß-sheets. The characteristics of ß-structures have been thoroughly examined by Richardson [247], who analyzed the frequency of all structural elements composed of two and three consecutive ß-strands found within ß-sheets comprising four or more strands. The resulting distribution is non-uniform, with ß-zigzags emerging as the most prevalent structural motif in three-stranded peptide arrangements.

Of greater interest, however, is the distribution of ß-sheets by topology*. A sufficiently reliable empirical distribution has not yet been obtained due to the scarcity of experimental data. Therefore, for all five known ß-structure topologies, this distribution was calculated by constructing them from all possible combinations of two or three consecutive ß-strands, followed by an analysis of their occurrence frequency. Based on the resulting non-uniform distribution, it can be predicted that certain ß-sheet topological variants should occur much more frequently than others. This result is important for the identification of supersecondary structures or structural preferences, as well as for assessing The Significance of structural similarities (Section 9.6).

* The topology of a ß-structure is determined by the order of strand alternation along the Amino Acid Sequence, the direction of these strands within the sheet, and the chirality of the ßξß-units.