Predetermined Conformations in Bends of Polypeptide Chains: A Geometric Analysis

Abstract

β-Bends are typical local structures of the polypeptide chain, are widespread in proteins, and play an important structural and functional role. It is possible to expect a priori with a good degree of certainty that β-bending structures are quite predictable; i.e., there are only a small number of β-bending conformations. Because a pseudo-cycle is closed through hydrogen bonding at the base of a β-bend, the number of independent parameters can be decreased to the extent such that a geometric analysis can be employed instead of a conformational analysis. As an example, a β-bending conformational set can be determined with high accuracy and reliability without using force fields. A conformational analysis of β-bends of the main types (I, I', II, and II') was performed using two independent methods, the original distance geometry procedure and the conformation enumeration procedure with subsequent optimization. A geometric analysis in the developed form was found to be sufficient for a conformational analysis of β-bends; i.e., the number of geometrically consistent β-bending conformations was reduced to two. The first solution found coincided with experimental data from X-ray structural analyses. The second solution was correct based on the geometric analysis, but was improbable in terms of energy because the corresponding values of the dihedral angles fell into strictly forbidden areas of the Ramachandran map as a result of disallowed convergence of atoms; the solution has not been observed experimentally. The results clarified the formation of the main β-bend conformation types, including those containing the so-called forbidden conformations.