= Beta sheet
{title2=$\beta$}
{wiki}
A <beta sheet> consists of extended stretches of <protein backbone> lying alongside one another, joined by <backbone hydrogen bonds>. The stretches can belong to different portions of the same <polypeptide chain> or to different chains.
Each extended stretch is a <beta strand>. Neighboring <beta strands> pack side by side, with repeated <backbone hydrogen bonds> between their backbone $\mathrm{C=O}$ and $\mathrm{N-H}$ groups: the <oxygen> is a <hydrogen bond acceptor>, and the backbone <nitrogen> with its attached <hydrogen> provides a <hydrogen bond donor>. These are interactions of the shared <protein backbone>, not merely contacts between <amino acid side chains>. Unlike an <alpha helix>, a <beta sheet> joins adjacent extended stretches rather than coiling one stretch around an axis. See https://openstax.org/books/biology-2e/pages/3-4-proteins[Clark, Douglas and Choi, Biology 2e, 3.4: backbone groups in secondary structure].
Read each <beta strand> in the sequence direction from the <N-terminus> toward the <C-terminus>, even when it is an internal part of a longer <polypeptide chain>. In a <parallel beta sheet>, neighboring <beta strands> run in the same N→C direction; in an <antiparallel beta sheet>, they run in opposite N→C directions. A three-strand example can therefore have arrows right–right–right or right–left–right. A <beta sheet> can also mix the two arrangements. Direction does not identify chain membership: a single <polypeptide chain> can fold back to supply several <beta strands>, and different <polypeptide chains> can contribute to one <beta sheet>. See https://www.ncbi.nlm.nih.gov/books/NBK26830/[Alberts et al., Molecular Biology of the Cell: beta-sheet strand arrangements].
\Image[/beta-sheet-strand-directions.png]
{title=<Parallel beta sheet> and <antiparallel beta sheet>: sequence directions}
{description=Three <beta strands> in each panel, with arrows showing N→C sequence direction. N-side and C-side labels indicate direction toward the <N-terminus> and <C-terminus>, not necessarily free chain ends. Dashed links symbolize interstrand <backbone hydrogen bonds>; they locate no <chemical atoms> and specify neither actual bond angles nor an exact pairing of <amino acid residues>. Chain connections are omitted.}
The pleated appearance comes from the geometry of the <protein backbone>. Successive <amino acid residues> carry <amino acid side chains> on alternating faces of an ideal <beta strand>, conventionally drawn above and below the sheet. The attachment positions are the <amino acid alpha carbons>. Thus a six-position cartoon has groups 1, 3 and 5 on one face and 2, 4 and 6 on the other. This alternation is a spatial pattern, not a rule that alternating positions must contain identical <amino acids>. See https://openstax.org/books/biology-2e/pages/3-4-proteins[Clark, Douglas and Choi: side chains above and below the pleats].
\Image[/beta-strand-pleating-and-side-chains.png]
{title=Pleating and alternating <amino acid side chains> along a <beta strand>}
{description=An original two-dimensional side-view cartoon of six consecutive <amino acid alpha carbons>, numbered in N→C sequence order, with generic R groups alternating above and below. Segments between marked positions summarize the intervening <protein backbone>, not every individual <covalent bond> or literal atomic coordinates. No <backbone hydrogen bonds> are drawn: their <hydrogen bond donor> and <hydrogen bond acceptor> groups would have to be shown separately from the marked <carbon> positions.}
Real <beta sheets> commonly twist and curve; pleating does not make them perfectly flat plates. Which <beta strands> are neighbors, how connecting regions join them, and how their faces pack are features of the three-dimensional <protein structure>. An alternating pattern in the <protein primary structure> alone neither establishes a <beta sheet> nor specifies a unique fold independently of surroundings and interacting <molecules>. See https://www.ncbi.nlm.nih.gov/books/NBK6824/[Breda et al., Protein Structure, Modelling and Applications: extended strands, sheet twist and three-dimensional organization] and <protein folding>.
Why this arrangement is useful: repeated <backbone hydrogen bonds> organize extended chain regions into a framework that can contribute to the interior of a folded <protein>. <Amino acid side chains> and connecting loops give that framework chemical variety and can shape a <protein binding site> for a <ligand>. Its attractive feature is the combination of a reusable backbone pattern with variable exposed groups: similar <beta sheets> can support different recognition surfaces. See https://www.ncbi.nlm.nih.gov/books/NBK26830/[Alberts et al.: beta-sheet cores and loops that form binding sites].
Historically, Linus Pauling and Robert B. Corey published \i[The Pleated Sheet, a New Layer Configuration of Polypeptide Chains] in PNAS 37, 251–256 (1951). They reasoned from <peptide bond> geometry and possible <backbone hydrogen bonds>, proposing an idealized layer rather than measuring every modern <beta sheet>. Their initial model should not be identified with all present-day <beta sheet> geometries; they published further pleated-sheet configurations later in 1951. See https://authors.library.caltech.edu/records/esvfg-ahe09[Pauling and Corey: original 1951 paper and scan], https://williams.chemistry.gatech.edu/course_Information/6572/papers/Pauling_PNAS-1951_sheet.pdf[accessible scan of the original paper]{ref}, and https://authors.library.caltech.edu/records/hq2fj-hqw64[Pauling and Corey, Configurations of Polypeptide Chains With Favored Orientations Around Single Bonds: Two New Pleated Sheets, PNAS 37, 729–740 (1951)].
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