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An alpha helix is a coiled protein secondary structure with a repeated pattern of backbone hydrogen bonds. In the standard pattern, the backbone group of amino acid residue $i$ bonds to that of residue $i+4$: for example, positions 2 and 6. This is an additional spatial interaction, not a replacement peptide bond between those positions. Pauling, Corey and Branson proposed the helical arrangement in their 1951 paper by reasoning from the geometry of small molecules. See Pauling, Corey and Branson, The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain, PNAS 37, 205–211 (1951).

Protein denaturation is the loss of a protein's native spatial organization, often with loss of biological function. Changes in temperature, pH or surroundings can disrupt protein secondary structure, protein tertiary structure or protein quaternary structure. Protein denaturation ordinarily preserves the peptide bonds and protein primary structure; it is different from cutting the chain. Recovery by protein folding is possible in some cases, but removing the denaturing conditions does not guarantee that every protein recovers. See Clark, Douglas and Choi: denaturation, environmental conditions and loss of function.

In the diagram, unfolding preserves all eleven peptide bonds. Cleaving the connection between positions 6 and 7 leaves two six-residue fragments: each contains five peptide bonds, so there are $5+5=10$ in total. Simply cooling or otherwise restoring suitable conditions cannot recover the original chain by protein folding alone; the missing covalent bond would have to be remade. Conversely, protein aggregation can impede recovery without breaking any peptide bond. These distinctions explain why loss of function does not by itself reveal whether a protein unfolded, associated with other chains, or suffered chemical damage.

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.

Protein structure describes both the chain's chemical organization and its spatial arrangement. Four levels answer different questions: protein primary structure gives the order; protein secondary structure gives recurring local patterns; protein tertiary structure gives one chain's overall arrangement; protein quaternary structure gives the assembly of multiple chains. These are levels of description, not four mandatory stages that every protein must pass through. See Clark, Douglas and Choi: four levels of protein structure.

The protein tertiary structure is the overall spatial arrangement of one polypeptide chain. It includes how its protein secondary structures and intervening regions fit together. For example, the schematic under protein places positions 4 and 9 near each other despite their separation in protein primary structure. Such cooperation can help construct an active site; sequence distance and spatial separation answer different questions. Hydrophobicity, backbone hydrogen bonds and other interactions help stabilize folds, and some proteins additionally contain protein disulfide bonds. See Cooper: tertiary structure and interactions between chain regions.