Protein secondary structure consists of recurring local arrangements of the protein backbone, notably the alpha helix and beta sheet. Backbone hydrogen bonds help stabilize these patterns. A beta sheet can bring together stretches far apart in the protein primary structure; local refers to the pattern of backbone geometry, not necessarily neighboring sequence positions. See Alberts et al.: alpha helices, beta sheets and backbone interactions.
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Protein secondary structure refers to the local folding and spatial arrangement of the polypeptide chain into specific structural motifs. It is one of the levels of protein structure, following the primary structure (the sequence of amino acids) and preceding the tertiary structure (the overall three-dimensional shape of a single polypeptide).