Characterization of multiple bends in proteins

The concept of bends or chain reversals nonhelical dipeptide sequences in which the distance R₃ (i,i+3) between the C^α atoms of residues i and i+3 is ≦ 7.0 Å] has been extended to define double bends as tripeptide sequences, not in an α-helix, in which two successive distances R₃(i,i+3) and R₃ (i+1, i+4) are both ≦7.0 Å, with analogous definitions for higher-order multiple bends. A sample of 23 proteins, consisting of 4050 residues, contains 235 single, 58 double, and 11 higher-order multiple bends. Multiple bends may occur as combinations of the “standard” type I, II, and III chain reversals (as well as their mirror images), but usually they require distortions from these well-defined conformations. The frequency of occurrence of amino acids often differs significantly between single and multiple bends. The probability distribution of R₃ distances does not differ in single and multiple bends. However, R₄ (the distance between the C^α atoms of residues i and i+4) in multiple bends is generally shorter than in tripeptide sequences containing single bends. The value of R₄ in many multiple bends is near those for α-helices. In some other multiple bends, R₄ is even shorter, indicating that these structures are very compact. The signs of the dihedral angles about the virtual bonds connecting C^α atoms and the values of curvature and torsion, as defined by means of differential geometry, indicate that there is a preference for single and multiple bends to be right-handed (like an α-helical sequence, for example) and that there is a strong tendency to conserve the handedness in both single-bend components of many multiple bends. These often have a strong resemblance to distorted single turns of an α-helix and do not constitute chain reversals. Double bends, in which the signs of two successive virtual-bond dihedral angles differ, have conformations that are very different from an α-helix. They act as chain reversals occuring over three residues. These chain reversals have not been described previously. Multiple bends may play an important role in protein folding because they occur fairly frequently in proteins and cause major changes in the direction of the polypeptide chain.