III. Geometrical framework for thinking about globular proteins: turns in proteins

We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry. α-helices and β-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the α-helix and non-local along a pair of adjacent strands within a β-sheet. Pairwise poking interactions also govern tertiary structure formation, but they are weaker and there are no special geometrical constraints as in secondary structure formation. Here we demonstrate that protein turns, the most prevalent non-repetitive structural element in proteins, are instances of local (as in α-helices) and isolated (non-repetitive) poking pairwise contacts for which the geometrical constraints are partially relaxed. This simple and purely geometrical definition of protein turns (also sometimes known as reverse turns, β-turns, β-bends, hairpin bends, 3 10 bends, kinks, widgets, …) provides a simple framework for unifying them. We present the results of a systematic analysis and identify their structural classes as well as their respective amino acid preferences. Statement for broader audience Poking interaction along a discrete chain signals the affinity of one part of the chain with another. It has been shown that a simple and purely geometrical model based on poking interactions is able to capture the essential features of complex protein chains, especially their building blocks and their assembly. We demonstrate that poking interactions also provide a simple framework to describe protein turns as isolated (not coordinated) local poking interactions. This framework allows one to comprehend the structural variety of protein turns that have been extensively studied in the past.