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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).

A backbone hydrogen bond is a hydrogen bond involving groups of the protein backbone, typically a backbone oxygen chemical atom and a hydrogen chemical atom already joined by a covalent bond to backbone nitrogen. It can connect positions that are not adjacent along the polypeptide chain. The peptide bonds still determine which amino acid residues are consecutive. See the original structural argument cited under alpha helix.

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 $\mathrm{C}=\mathrm{O}$ and $\mathrm{N}-\mathrm{H}$ 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 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 Alberts et al., Molecular Biology of the Cell: beta-sheet strand arrangements.

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 Clark, Douglas and Choi: side chains above and below the pleats.

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 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 Alberts et al.: beta-sheet cores and loops that form binding sites.

Historically, Linus Pauling and Robert B. Corey published 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 Pauling and Corey: original 1951 paper and scan, ^[ref], and Pauling and Corey, Configurations of Polypeptide Chains With Favored Orientations Around Single Bonds: Two New Pleated Sheets, PNAS 37, 729–740 (1951).

The same base sequence can present different molecular surfaces in different helical conformations. A-DNA, B-DNA and Z-DNA all retain paired antiparallel strands, but differ in handedness, backbone geometry, sugar puckering and groove accessibility. The familiar dimensions are approximate averages: sequence, hydration and bound molecules change the details, so they are structural signatures rather than rigid constants.

B-DNA is a right-handed DNA double helix with about $10.5$ base pairs per turn, a rise near $0.34\mathrm{nm}$ per pair and a diameter near $2\mathrm{nm}$. Its base pairs lie approximately perpendicular to the helical axis; the sugars are predominantly C2′-endo and the glycosidic bonds are anti. A broad accessible major groove and a narrower minor groove expose different edges of the paired nucleobases. Hydrated duplex DNA commonly adopts this family of conformations, although local bends and groove widths depend on sequence.

A-DNA is also right-handed, but is shorter and wider: roughly $11$ base pairs per turn, a rise around $0.26\mathrm{nm}$ per pair, and a diameter near $2.3\mathrm{nm}$. C3′-endo sugar puckering brings successive phosphates closer along each strand. The base pairs are inclined and displaced from the axis, producing a deep narrow major groove and a broad shallow minor groove. Reduced hydration favours A-DNA. Double-stranded RNA and many DNA-RNA hybrids adopt A-like geometry because the ribose 2′-hydroxyl constrains the backbone; this is important when extending a DNA-only comparison to cellular nucleic acids.

Z-DNA is a left-handed duplex with a zigzag backbone and a two-base-pair conformational repeat. It has approximately $12$ base pairs per turn, a rise near $0.37\mathrm{nm}$ per pair and a diameter around $1.8\mathrm{nm}$. Alternating purine–pyrimidine sequences, especially alternating G and C, favour it under suitable conditions. Purines commonly adopt syn glycosidic bonds and C3′-endo sugars, whereas pyrimidines remain anti with C2′-endo sugars. Its minor groove is narrow and deep, while the conventional major groove is flattened and poorly defined. Atomic-resolution analysis of an alternating CG oligomer established that a duplex can adopt this left-handed fold.^[ref] High salt in a crystal experiment is evidence of an accessible conformation, not proof that most cellular DNA is in that state; negative supercoiling and protein binding can instead favour local transitions.

These geometries determine how proteins read sequence. In B-DNA, the pattern of hydrogen bond donors, acceptors and hydrophobic groups in the major groove distinguishes the four oriented base pairs without strand separation. The minor groove carries less direct chemical information: A–T and T–A present similar patterns there, as do G–C and C–G. Specificity can nevertheless arise from DNA shape readout, including groove width, electrostatic potential, deformability and hydration, combined with contacts to the phosphate backbone. The chemical accessibility of base edges underlies the classic analysis of sequence-specific recognition of duplex nucleic acids.^[ref]

An alpha helix from a transcription factor can fit a B-DNA major groove, but the same docking arrangement need not fit the deep narrow groove of A-DNA. Many double-stranded RNA-binding interactions therefore emphasize backbone or shape, although A-form geometry does not make sequence-specific RNA recognition impossible. A Z-DNA-binding domain can recognize the characteristic left-handed backbone, making recognition partly conformation-specific rather than simply recognition of an exposed base code. In cells, nucleosomes, competing proteins, torsional stress and local hydration further determine access. Binding assays should compare sequences and conformations independently, using structural or spectroscopic controls: a sequence mutation can change both the chemical recognition pattern and the probability of adopting the recognized structure.

For a carbonyl oxygen of residue $i$ accepting from the NH of a later residue, the possibilities are:

The alpha helix provides a favourable combination of allowed backbone torsions, reasonably linear hydrogen bonds, and side-chain packing. Its successive side chains advance by about $100^{\circ }$, rather than lining up in the three columns of the narrower 3-10 helix. Smaller repeating rings impose more severe backbone constraints; the wider pi helix gives a different, generally less favourable packing arrangement. Short 3-10 and pi-helical segments can still occur in proteins, so this is a preference for a common extended secondary structure, not a prohibition of the alternatives. Proline and sequence-specific interactions can disrupt the idealized backbone donor pattern.

Protein primary structure is the ordered amino acid sequence of a polypeptide, linked by covalent peptide bonds. The approximately planar peptide bond restricts local geometry, while backbone torsion angles give conformational freedom subject to steric exclusion. Protein secondary structure comprises local backbone arrangements, especially the alpha helix, with backbone hydrogen bonds between residues $i$ and $i+4$, and the beta sheet, whose strands are joined by backbone hydrogen bonds. Turns and loops connect these elements. Protein tertiary structure is the full three-dimensional organization of a single chain, often including several protein domains. Protein quaternary structure is the arrangement of multiple chains in a protein complex.

Protein folding is governed by the Gibbs free energy of the chain together with its solvent, not by the chain's energy alone. Folding reduces the chain's conformational entropy, but can gain solvent entropy through the hydrophobic effect, burying nonpolar side chains away from water. Favorable hydrogen bonds, Van der Waals forces, electrostatic interactions and sometimes covalent disulfide bonds stabilize particular structures. Steric repulsion prevents atomic overlap. At fixed temperature and pressure, the native ensemble is favored when its total $\Delta G=\Delta H-T\Delta S$ is lower than competing ensembles. The balance depends on the solvent, pH, salt and ligands. Molecular chaperones help avoid aggregation or kinetic traps; a stable fold is not a perfectly rigid conformation, and some proteins have disordered regions.

For a soluble globular protein, a typical pattern is a nonpolar core and a polar, hydrated surface. A transmembrane protein instead presents nonpolar side chains to the hydrocarbon interior of the lipid bilayer. Membrane-spanning alpha helices satisfy their polar backbone groups through internal hydrogen bonds; a roughly membrane-thickness helix commonly contains about twenty residues, depending on tilt and bilayer thickness. Multiple helices can enclose polar channels or binding sites. Membrane-spanning beta barrels likewise expose mainly nonpolar groups outward towards lipid while arranging backbone hydrogen bonds between strands and often lining an aqueous pore with polar groups. Exposed loops and domains contacting water can resemble soluble proteins. Not every membrane-associated protein spans the membrane: peripheral attachment and lipid anchoring are distinct possibilities.

The organizing distinction is the environment of each surface: water favors accessible polar groups, while the membrane core favors outward-facing nonpolar groups. Buried polar groups can still be essential to a transport pathway or catalytic site.

The protein primary structure is the ordered protein sequence along a polypeptide, from its N-terminus to its C-terminus. In cells, information in a DNA coding sequence is copied into messenger RNA by transcription. During translation, the ribosome reads successive three-base codons; transfer RNA molecules match these by their anticodons and supply the corresponding amino acids. The genetic code is degenerate: different codons can encode the same amino acid. A start establishes the reading frame and a stop terminates translation. Peptide bonds link the amino acids into the backbone, leaving chemically different side chains. Thus the sequence specifies the order of side-chain interactions, rather than a literal coordinate list for the folded molecule.

Protein secondary structure describes local backbone arrangements. An alpha helix is stabilized by a regular pattern of backbone hydrogen bonds, typically between the carbonyl of residue $i$ and the amide of residue $i+4$. Beta sheets assemble extended strands through inter-strand hydrogen bonding, with parallel or antiparallel strand orientations. Turns and loops connect these elements; not every region belongs to a helix or sheet. The peptide bond is approximately planar, while backbone torsion angles provide conformational freedom subject to steric restrictions.

Protein tertiary structure is the complete three-dimensional organization of one chain, often arranged into protein domains. Protein quaternary structure describes the organization of multiple chains in an assembly. Soluble globular proteins often bury nonpolar side chains and expose polar ones; membrane proteins can instead expose hydrophobic surfaces to the surrounding lipid. Other stabilizing interactions include hydrogen bonds, electrostatic interactions, Van der Waals forces and sometimes covalent disulfide bonds. These competing contributions define active sites, binding pockets and mechanically useful structures; folded proteins are dynamic ensembles, not perfectly rigid objects.

The connection from sequence to structure is thermodynamic and kinetic. Folding usually decreases the chain's conformational entropy, but favorable interactions and changes in solvent entropy, including the hydrophobic effect, can lower the total Gibbs free energy. Under suitable conditions the native ensemble is favored over unfolded alternatives. A change in sequence can therefore change the balance of accessible conformations and alter folding or function. Reversible refolding of a denatured protein in an appropriate environment demonstrates that the sequence can contain the information needed for its native structure.^[ref]

The environment is part of the specification: temperature, pH, ionic conditions, ligands and post-translational modifications matter. Molecular chaperones can prevent aggregation and help chains escape kinetic traps without providing a residue-by-residue structural template. Some sequences are intrinsically disordered proteins or disordered regions, and some require partners for a stable fold. Thus primary structure strongly constrains structure, but does not guarantee one unique rigid shape independent of conditions.

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.