The Alpha Helix
Coil a strip of paper into a spring. You now have the crudest model of the most common secondary structure in the protein universe. The alpha helix is a self-hydrogen-bonded rod of polypeptide backbone. It is so regular that its geometry can be written down almost as precisely as a crystal lattice. It has 3.6 residues per turn, a rise of 1.5 Å per residue, and a pitch of 5.4 Å. Yet it is built entirely from the same single repeating unit. This unit also builds beta sheets and random coil. That unit is the planar, trans peptide bond described in The Peptide Bond and Its Partial Double-Bond Character. The alpha helix matters because it is the single most abundant fold locally adopted by proteins. It is found in myoglobin and hemoglobin, in the coiled coils of keratin and myosin. It also appears in the transmembrane spans of nearly every integral membrane protein. It appears too in the DNA-binding helices of transcription factors. Its stability comes from an elegant trick. Every backbone carbonyl oxygen hydrogen-bonds to the amide N–H four residues down the chain. So the helix satisfies its own hydrogen-bonding potential internally. It needs no water or partner strand to do so. This intramolecular saturation lets an isolated helix be marginally stable even alone. This is a property beta strands, which need a partner, do not share. The big picture is that the alpha helix is not a free parameter of protein structure. It is a prediction of the Ramachandran analysis in The Ramachandran Plot and Backbone Dihedral Angles. Given the fixed geometry of the trans peptide unit, only a narrow island of (φ, ψ) values works. These values simultaneously avoid steric clash and line up backbone carbonyls and amides for optimal hydrogen bonding. The alpha helix is what falls out when you ask a simple question. That question is: "what is the tightest, most self-satisfying regular helix this chain can make?" Everything about its geometry — pitch, radius, residues per turn — is a consequence of φ ≈ −57°, ψ ≈ −47°. It is not an independent postulate. This article derives the helical geometry from the dihedral angles. It works out the hydrogen-bonding pattern (i → i+4) and the resulting 13-atom ring. It computes the helix macrodipole from the alignment of individual peptide dipoles. It also shows how these numbers were pinned down historically by Pauling and Corey. They used nothing but bond-length tables and paper models. This was before a single alpha-helical structure had been seen by X-ray diffraction.
- The alpha helix is a right-handed spiral with φ ≈ −57°, ψ ≈ −47°, giving 3.6 residues/turn and 1.5 Å rise/residue.
- Pitch (advance per full turn) = 3.6 × 1.5 Å = 5.4 Å; this is fixed by geometry, not by sequence.
- Each backbone C=O hydrogen-bonds to the N–H of the residue four positions ahead (i → i+4), forming a closed 13-membered ring — hence "3.6₁₃" notation.
- All ~3.6 peptide dipoles per turn point the same way along the axis, summing to a helix macrodipole with a partial positive N-terminus and partial negative C-terminus.
- Proline and glycine are geometrically incompatible with the standard helix — proline lacks the N–H donor and its ring fixes φ, while glycine's flexibility destabilizes the fold entropically.
- Key idea: the alpha helix is the unique regular backbone conformation that satisfies every internal hydrogen bond while keeping every peptide unit planar and trans — a geometric inevitability of the Ramachandran map's α-region, not an arbitrary shape.
Where this lives today
The alpha helix is the structural workhorse of modern molecular medicine and biotechnology. Roughly a quarter to a third of all residues in typical globular proteins are alpha-helical, and the great majority of integral membrane protein transmembrane spans — G-protein-coupled receptors (the target class of an estimated one-third of all approved drugs), ion channels, transporters — are single alpha helices roughly 20 residues long, exactly long enough (using L = Nd with d = 1.5 Å) to cross a ~30 Å lipid bilayer. Rhodopsin, the beta-adrenergic receptor, and the nicotinic acetylcholine receptor are all built from bundles of such helices, and structure-based drug design for GPCRs depends on correctly modeling helix packing angles and kinks (often at internal prolines, as derived above). Coiled-coil alpha helices — pairs or bundles of helices supercoiled around each other with a heptad (seven-residue) repeat that places hydrophobic residues along one face — form the mechanical backbone of keratin (hair, nails, wool), the myosin and tropomyosin filaments of muscle, and the leucine-zipper dimerization domains of transcription factors like Fos and Jun; this is foreshadowed further in discussions of Fibrous Proteins and depends on the same core geometry derived here, only wrapped with an additional superhelical twist. Designed helical peptides that exploit the macrodipole are used as anion sensors and as membrane-disrupting antimicrobial peptides, whose N-terminal positive dipole end helps orient them onto negatively charged bacterial membrane surfaces. In structure prediction software (from early Chou–Fasman propensity scales to modern deep-learning folding algorithms), recognizing an alpha-helical segment from sequence is one of the first, most reliable local-structure predictions made, precisely because the underlying geometry — 3.6 residues/turn, 1.5 Å rise, i→i+4 hydrogen bonding — is so rigidly reproducible across the entire proteome, a direct legacy of the Ramachandran constraints covered in The Ramachandran Plot and Backbone Dihedral Angles.
Ask the tutor: How would the helix geometry equations change if I wanted to derive the parameters of a collagen triple helix instead of the alpha helix?
The physical picture — helix as a self-satisfying spiral
Begin with the constraint set from the peptide bond: every peptide unit (Cα–C(=O)–N(H)–Cα) is planar and, in the vast majority of proteins, in the trans configuration, because trans avoids the steric clash between adjacent Cα substituents that cis would create. Rotation around the two single bonds flanking this rigid plane — φ about N–Cα and ψ about Cα–C — is all the backbone has left to explore. Ramachandran mapping shows that steric clash between the carbonyl oxygen, the amide hydrogen, and the Cα side chain (even a single Cβ) forbids most of (φ, ψ) space; only a few islands survive, and the α-helical island sits near φ = −57°, ψ = −47°. Feed a fixed (φ, ψ) pair, repeated at every residue, into the standard bond lengths and angles of the peptide unit (N–Cα ≈ 1.46 Å, Cα–C ≈ 1.52 Å, C–N ≈ 1.33 Å, and near-tetrahedral/near-trigonal bond angles), and the chain is forced into a helix: a curve that advances by a fixed rise d along an axis and rotates by a fixed twist angle t for every residue added. This is a rigorous geometric consequence — a chain of identical rigid units connected by identical dihedral rotations must trace a helix, by the same argument that a screw thread is a helix. For the alpha helix, this repeated unit closes a hydrogen-bonded ring: the carbonyl oxygen of residue i points directly at the amide hydrogen of residue i+4, at a distance and angle ideal for a strong N–H···O=C hydrogen bond (roughly 2.9 Å N···O distance, near-linear N–H···O angle). Because the i → i+4 hydrogen bond closes a ring containing 13 atoms if you count around the backbone path from the donor N-H to the acceptor C=O and back through the intervening chain, the alpha helix is formally denoted the 3.6₁₃-helix in the notation nₓ (residues per turn, subscript = ring size). This is one member of a family: the 3₁₀-helix (i → i+3, a tighter, less common ring of 10 atoms) and the π-helix (i → i+5, a wider ring of 16 atoms) are geometrically permitted alternatives that occupy nearby, less favorable regions of Ramachandran space — real but rare, occurring mostly as short capping turns at helix ends.
The core ideas — governing equations of helical geometry
The alpha helix is parametrized by three linked numbers derivable from a single screw transformation applied repeatedly to the peptide unit.
where: n is residues per turn, t is the twist angle (rotation about the helix axis) contributed by each residue.
where: P is the pitch (axial distance for one complete 360° turn), d is the axial rise per residue (translation along the helix axis contributed by each residue).
where: z_k and θ_k are the axial position and azimuthal angle of the k-th Cα atom, measured from an arbitrary residue 0; this is simply the parametric equation of a helix, , with r the helix radius (≈ 2.3 Å for the Cα helix).
where: μ_helix is the net axial macrodipole moment, L is the helix length, d is rise per residue (so L/d is the number of aligned peptide units), μ_peptide ≈ 3.5 D is the dipole moment of a single planar peptide unit (C=O···N–H), and α is the small angle between an individual peptide dipole and the helix axis (each dipole is not perfectly axial, but the components perpendicular to the axis cancel by the helical symmetry, leaving only the cos α projection to sum).
Reading: the first two equations are pure screw geometry — feed in the observed n = 3.6 and d = 1.5 Å and pitch falls out as P = 5.4 Å. The third equation places every backbone atom on an explicit spiral, which is what lets X-ray crystallographers and structural biologists literally calculate electron-density envelopes for a helix before ever seeing one. The fourth equation says something qualitatively important: because every peptide unit in a helix points its C=O the same way along the axis (toward the C-terminus) and its N–H the opposite way, the dipoles do not cancel — they add, turn after turn, producing a macroscopic dipole moment proportional to helix length, not helix cross-section. A 20-residue helix is not just "20 little dipoles pointing in random directions" — it behaves electrostatically almost like one long bar magnet.
Goal. Show how repeating the same pair of backbone dihedral angles at every residue necessarily produces a helix with a specific rise d and twist t, and obtain the numerical values d ≈ 1.5 Å, t ≈ 100° (n ≈ 3.6) for the right-handed alpha helix from φ ≈ −57°, ψ ≈ −47°.
Step 1 — set up the repeating unit as a rigid-body transformation. Each residue's contribution to the chain is fixed by the bond geometry within the planar peptide unit (which does not change with φ, ψ) and by the two rotatable dihedrals φ (rotation about N–Cα) and ψ (rotation about Cα–C). Because the peptide bond itself is planar and trans, and because all bond lengths and angles are the same at every residue, adding one residue to the chain is mathematically a single fixed rigid-body transformation — a rotation matrix R plus a translation vector t⃗ — applied to place the next Cα relative to the current one. Any repeated rigid-body transformation, iterated indefinitely, traces a helix or a straight line (a helix is the general case; a straight line and a circle are degenerate special cases where the axial or rotational component vanishes).
Step 2 — the screw axis theorem. A general rigid-body motion in 3D can always be decomposed (Chasles' theorem) into a rotation by angle t about some axis, plus a translation d parallel to that same axis. Applying this decomposition to the residue-to-residue transformation identifies t as the twist per residue and d as the rise per residue. Crucially, t and d are not independent adjustable parameters of the helix — they are computable, in principle, from φ and ψ and the fixed bond geometry, by multiplying out the local coordinate transformations residue by residue. This is a real (if tedious) matrix calculation; the qualitative result is that a small, continuous change in (φ,ψ) produces a small, continuous, and predictable change in (t, d) — the alpha helix sits at one point in a continuous φ,ψ → (t,d) map.
Step 3 — read off the observed values. Applying the standard geometry (bond lengths N–Cα = 1.46 Å, Cα–C = 1.52 Å, C–N = 1.33 Å; bond angles ≈ 111° at Cα, 120° at C and N; planar trans peptide unit) at φ = −57°, ψ = −47° gives, by explicit construction (Pauling and Corey's original hand calculation, later confirmed by every subsequent crystal structure):
Step 4 — residues per turn and pitch. From :
From :
Step 5 — sanity check against the hydrogen-bonding requirement. For the i → i+4 hydrogen bond to close a good ring, four residues must span almost exactly one full turn's worth of both rise and rotation in a way that lands the C=O of residue i directly beneath the N–H of residue i+4. Four residues advance the chain by Å axially and by (mod 360°) azimuthally — a small residual rotation, not a full extra turn, which is exactly what is needed to bring the donor and acceptor groups into a nearly collinear, short hydrogen bond rather than a wildly offset one. This internal consistency — that n ≈ 3.6 is not 4.0 exactly — is precisely why the ring is 13-membered rather than a clean multiple of the backbone repeat, and it is why the alpha helix's "3.6" is a non-integer, geometrically forced number rather than a design choice.
Go deeper · Derivation B · 3 minThe helix macrodipole: summing peptide-unit dipoles along the axis
Goal. Derive why aligned peptide-bond dipoles in a helix sum constructively along the helix axis, and estimate the macrodipole for a realistic helix of 16 residues, showing the result scales with length, not with helix diameter.
Step 1 — the single peptide dipole. The peptide unit, per The Peptide Bond and Its Partial Double-Bond Character, has substantial resonance delocalization of the nitrogen lone pair into the carbonyl π system, giving the C=O bond a partial negative charge on O (δ⁻ ≈ −0.5 to −0.6 e in various force-field parametrizations) and a partial positive charge on the amide hydrogen and nitrogen region (net δ⁺ toward N–H). The resultant dipole moment of the isolated planar unit is experimentally and computationally about
oriented roughly along the C=O bond direction (pointing from N toward O, i.e., the negative end at O), tilted only slightly from the local Cα–Cα direction because of the peptide unit's fixed internal geometry.
Step 2 — orientation relative to the helix axis. In a helix, each peptide unit is tipped at a small, fixed angle relative to the helix axis (roughly 20–30° in typical parametrizations, depending on convention), but critically, the same tip angle and the same sense recur at every residue because every residue has identical φ, ψ. The component of each dipole perpendicular to the helix axis rotates by the twist angle t ≈ 100° from one residue to the next, so summing those perpendicular components around several residues causes them to point in different azimuthal directions and largely cancel (exactly as the perpendicular components of a spring's coil-wire dipole would cancel by symmetry). The component parallel to the axis, however, does not rotate — a component along the shared axis direction is invariant under the screw rotation — so it survives unchanged at every residue and simply adds.
Step 3 — sum the axial components. If each peptide unit contributes an axial dipole component
with the angle between the individual dipole and the helix axis, then a helix of N residues (hence roughly N aligned peptide units, ignoring small end effects) has total axial dipole
Because where L is the helix's axial length, this can equivalently be written
explicitly showing that the macrodipole grows linearly with helix length, not with the number of turns squared or with the helix's cross-sectional area — a signature of a 1-dimensional, end-to-end summed dipole rather than a 3-dimensional bulk polarization.
Step 4 — numerical estimate for a 16-residue helix. Take μ_peptide = 3.5 D, cos α ≈ 0.85 (a commonly cited effective projection factor for the alpha-helical geometry), and N = 16 residues (a modest, realistic single-turn-count helix, not a round number chosen to look tidy):
This is a genuinely large dipole moment — comparable to that of small globular proteins overall — concentrated end-to-end along the helix, with the effective positive pole at the N-terminus (where unsatisfied N–H groups and the exposed amide nitrogens sit) and the effective negative pole at the C-terminus (where unsatisfied C=O groups point outward).
Step 5 — physical consequence: functional bias, not just decoration. Because of this macrodipole, negatively charged ligands (phosphate groups of ATP, GTP, and nucleic acid backbones; carboxylate side chains; halide and other anions) are frequently found bound near the N-terminal end of functional helices, and positively charged groups near the C-terminal end, in real crystal structures (e.g., the phosphate-binding "P-loop" of many nucleotide-binding proteins caps a helix N-terminus). This is a direct, falsifiable prediction of Step 3's sign convention, and it is repeatedly confirmed structurally — helix N-termini are measurably better anion binding sites than helix C-termini in nucleotide-binding folds.
Worked examples
Example 1 (foundational) — counting turns and hydrogen bonds in a 15-residue helix. A helix segment runs from residue 10 to residue 24 inclusive (15 residues total). Using n = 3.6 residues/turn and d = 1.5 Å/residue: Number of turns:
Axial length:
(Check by the pitch formula: Å — consistent, as it must be, since both routes use the same underlying n, d.) Number of i → i+4 hydrogen bonds: each residue from position i = 10 up to i = 20 can donate its N–H to accept the C=O of residue i−4 (or equivalently, each residue up to the fourth-from-last can donate a C=O to a partner four ahead). With 15 residues, the possible i values for the C=O donor run from residue 10 up to residue 20 (since 20 + 4 = 24, the last residue), giving
The four residues at each end (two at the N-terminus lacking a completed i−4 acceptor pattern, two effectively contributing to fraying — in practice the first three N–H and last three C=O groups of a helix are the unsatisfied ones referenced when discussing helix "fraying" and capping) are the ones that most benefit from capping box interactions or solvent hydrogen bonding, foreshadowed in discussions of Helix Stability and Amino Acid Propensities.
Example 2 (applied) — will proline fit at position i+2 of a helix, and what happens to the hydrogen bond network? Proline's pyrrolidine ring covalently links its own side chain back to the backbone nitrogen, fixing φ near −60° (compatible, coincidentally close to the alpha-helical φ) but, far more importantly, removing the amide N–H entirely — proline nitrogen has no hydrogen to donate. Consequence for the ring closure: place proline at position i+2 within a helix. The hydrogen bond that would normally connect the C=O of residue i−2 to the N–H of residue i+2 cannot form, because there is no donor hydrogen on proline's nitrogen. That removes exactly one rung of the hydrogen-bonding ladder — not the whole helix, but a single, localized i → i+4 bond — leaving the corresponding backbone carbonyl of residue i−2 unsatisfied (a "gap" locally compensated, if at all, by a water molecule or a side-chain hydrogen bond). Consequence for backbone geometry: proline's ring further constrains ψ in a way that is only marginally compatible with the standard α-helical ψ ≈ −47°, and its ring's steric bulk clashes with the backbone carbonyl of the preceding residue (i−1) if that residue tries to adopt standard helical ψ. The net structural outcome, seen repeatedly in real crystal structures, is that proline inside a helix produces a kink of roughly 20–30° in the helix axis, because the residues immediately before proline are forced to distort their ψ angles. This is why proline is termed a "helix breaker" — more precisely a helix-kinker, since short helices can still form around an internal proline (common in transmembrane helices, where the kink is often functionally important, e.g., in bacteriorhodopsin and rhodopsin), but the smooth, undistorted, maximal-hydrogen-bond helix cannot continue through it.
Example 3 (exam/competition level) — from measured helix rise to an implied φ,ψ check, and a dipole comparison between two helices of different length. A crystallographer measures a helical segment of a designed peptide by X-ray diffraction and reports an axial rise of 27.3 Å over 18 residues, plus a total axial rotation of 1700° over those same 18 residues (achievable directly from the coordinates of successive Cα atoms projected onto the helix axis found by least-squares fitting). (a) Compute the rise per residue and twist per residue, and check whether this is a standard alpha helix, a 3₁₀-helix, or a π-helix. Rise per residue:
Twist per residue:
Residues per turn:
Compare to reference values: standard alpha helix, n = 3.6, d = 1.5 Å; 3₁₀-helix, n = 3.0, d = 2.0 Å; π-helix, n = 4.4, d = 1.15 Å (these reference numbers are standard structural-biology tabulated values). The measured (n = 3.81, d = 1.52 Å) sits closest to the alpha helix, slightly loosened (n a bit above 3.6), consistent with mild helix distortion or measurement scatter rather than a genuine 3₁₀ or π conformation — real helices in crystal structures routinely show n in the range 3.6 ± 0.3 due to local sequence effects, so this is an unremarkable, slightly "loose" alpha helix, not a different helix type. (b) Estimate the ratio of macrodipoles between this 18-residue helix and the 16-residue helix of the earlier derivation, using the same μ_peptide = 3.5 D and cos α = 0.85.
which is exactly the ratio 18/16 = 1.125 predicted by the linear-in-length scaling law of Step 3 of the dipole derivation — an internal consistency check confirming that holds regardless of the specific numeric inputs chosen, as it must from the additive derivation. As a limiting case: if N → 0 (a vanishingly short "helix" of essentially zero residues), , correctly reflecting that no aligned dipoles exist to sum; and at N = 1 (a single peptide unit, not really a helix at all since a helix requires a repeating screw axis to be geometrically defined), the formula degenerates to , i.e., just the single unit's axial projection, as sensible.
Limiting cases, scope & common traps
| Situation | What happens to the helix | Why |
|---|---|---|
| All-glycine stretch | Helix destabilized, often disordered | Gly's lack of a Cβ gives it a much larger allowed (φ,ψ) region and higher backbone entropy in the unfolded state, making the entropic cost of helix formation larger; see Helix Stability and Amino Acid Propensities |
| Proline inside helix | Local kink (~20–30°), one H-bond lost | No N–H donor; ring restricts ψ; steric clash with preceding residue's carbonyl |
| First/last 3–4 residues | Unsatisfied backbone C=O or N–H ("fraying" ends) | i → i+4 geometry cannot close a ring using residues that don't exist beyond the chain terminus |
| 3₁₀-helix (i→i+3) | Tighter, less common, common only in short (3–5 residue) stretches, capping turns | Slightly less favorable (φ,ψ); less linear H-bonds; higher energy per residue than standard α |
| π-helix (i→i+5) | Wider, rare, sometimes seen as a single-turn bulge inserted mid-helix | Wider ring less ideal geometrically; often arises from a 4-residue insertion into an existing helix |
| Very short helix (<4 residues) | Cannot form even one complete i→i+4 hydrogen bond | Needs at least 5 residues (i and i+4) to form the first ring; practically, ≥ 7–8 residues needed for a stable, recognizable helix |
| Membrane-spanning helix | Same geometry, but hydrophobic residues line the surface | Backbone geometry (φ,ψ,n,d) is unchanged; only side-chain chemistry differs — hydrophobic thickness ≈ 20–30 residues to span a ~30 Å bilayer |
| Coiled-coil (two helices) | Same right-handed alpha helix geometry, supercoiled left-handed around a partner | Heptad repeat (abcdefg) places hydrophobic a,d residues on one face; the local helix parameters barely change |
The chemist behind it
The alpha helix was proposed in 1951 by Linus Pauling, together with Robert Corey and Herman Branson, in a paper built entirely from careful physical-chemical reasoning rather than from a crystal structure of a folded protein — no such structure yet existed. Pauling had spent the 1930s determining precise bond lengths and angles in small peptide crystals by X-ray diffraction, and had shown, crucially, that the peptide bond is planar with partial double-bond character (its central insight, later formalized as resonance theory applied to the amide group). Pauling reasoned that if the peptide unit is a rigid, planar plate, then a protein backbone folding into a regular, hydrogen-bonded structure must do so by rotating only around the two single bonds flanking each plate — precisely the φ, ψ framework. The breakthrough that let Pauling get the geometry right where others (including, briefly, himself in an earlier failed 1948 attempt) had failed was insisting on integral, chemically sound hydrogen bonds and not requiring an integral number of residues per turn — earlier model-builders had assumed, for simplicity, that a helix must repeat exactly every whole number of residues, which forces bad hydrogen-bond geometry. Pauling, reportedly working this out while confined to bed with a cold in Oxford in 1948, realized the repeat could be non-integral (3.6, not 3 or 4), which is exactly the number that lets the i → i+4 hydrogen bonds be short and linear. This was a purely geometric, non-crystallographic insight — built with paper models and slide-rule bond-length arithmetic — later spectacularly confirmed when Max Perutz found the predicted 1.5 Å meridional reflection in fiber diffraction patterns of hemoglobin and keratin, and definitively when John Kendrew's 1958 myoglobin structure showed alpha helices exactly as predicted.
Origins · 1 minLinus Carl Pauling and how this was discovered
Pauling's career united quantum-mechanical bonding theory (his 1939 book The Nature of the Chemical Bond set the language of resonance and hybridization used throughout organic and biochemistry) with painstaking structural determination of small molecules, which he then extrapolated — correctly — to macromolecules no one could yet crystallize in folded form. His 1951 alpha-helix and beta-sheet papers, published with Corey and Branson in Proceedings of the National Academy of Sciences, are considered among the most important applications of physical chemistry to biology, arrived at by reasoning about bond geometry rather than by fitting electron density. Pauling won the 1954 Nobel Prize in Chemistry for work on chemical bonding and later the 1962 Nobel Peace Prize, remaining the only person to win two unshared Nobel Prizes.
Why is the alpha helix right-handed and not left-handed?
A left-handed alpha helix (φ ≈ +57°, ψ ≈ +47°, the mirror image of the standard right-handed values) is geometrically conceivable and would have identical bond lengths, angles, and hydrogen bonding — but it is strongly disfavored for real proteins because natural amino acids (except glycine) are L-amino acids, and the L-configuration at Cα makes the right-handed helix's φ,ψ region essentially clash-free while the mirror-image left-handed region suffers severe steric clash between the side chain and the backbone carbonyl. This is visible directly on the Ramachandran plot: the left-handed alpha region is a tiny, high-energy sliver occupied almost only by glycine, which lacks a Cβ to clash. So handedness is a consequence of amino acid chirality, not an independent structural choice.
Are all 3.6 residues per turn identical in real proteins, or does the number vary?
The ideal value of 3.6 comes from the single, idealized (φ,ψ) = (−57°,−47°) point; real helices show natural variation, typically n = 3.6 ± 0.2–0.3 residues per turn, because actual (φ,ψ) angles in a folded protein fluctuate slightly from residue to residue due to local packing, side-chain interactions, and minor deviations from perfect planarity in the peptide bond itself. Helices can be slightly "overwound" (n closer to 3.4–3.5) or "loosened" (n closer to 3.7–3.9) without leaving the broadly defined alpha-helical region of the Ramachandran plot. Only when the deviation becomes large enough to change the hydrogen-bonding register itself (to i→i+3 or i→i+5) does the helix formally become a different type, the 3₁₀ or π helix.
Why doesn't the alpha helix need water to be stable, unlike a beta strand?
A beta strand by itself has all of its backbone C=O and N–H groups pointing outward from the strand axis, unsatisfied, and can only fully hydrogen-bond by pairing with another strand (forming a sheet) or with solvent. An alpha helix, by contrast, curls its own backbone into a shape where the i → i+4 geometry lets almost every internal C=O and N–H hydrogen-bond to a different part of the same chain. This intramolecular saturation is the defining structural trick of the fold: a single strand of alpha helix is a locally self-sufficient hydrogen-bonded unit, which is part of why isolated short alpha-helical peptides can show measurable helicity in water, while isolated beta strands essentially never do outside a sheet.
How does the alpha helix relate to the Ramachandran plot quantitatively?
The alpha-helical region of the Ramachandran plot is not just "some allowed area" — it is the specific, narrow zone of (φ,ψ) space where, simultaneously, (1) steric clash between the carbonyl oxygen, amide hydrogen, and Cα substituents is avoided, and (2) the resulting screw transformation from residue to residue produces a rise and twist compatible with a good, close-to-linear i→i+4 hydrogen bond. Moving even 20–30° away from (−57°,−47°) within the broadly "allowed" region still gives sterically fine geometry but degrades the hydrogen-bond linearity and distance, which is why the optimal alpha-helical point is a sharp, narrow peak in helix propensity calculations rather than a flat plateau across the whole allowed region.
Does the helix macrodipole actually affect protein function, or is it mostly theoretical?
It is functionally real and structurally documented. Many nucleotide-binding proteins position a helix N-terminus (the positive pole) directly over the phosphate groups of ATP or GTP — the classic Walker A "P-loop" motif caps a helix this way — using the helix dipole to help stabilize the negatively charged triphosphate. Similarly, chloride- and anion-binding proteins frequently use a helix N-terminus as part of the binding site. Conversely, negatively charged residues or ligands are disfavored near helix C-termini for the same electrostatic reason. The effect is on the order of a few kcal/mol of binding stabilization in well-studied cases — a real, quantitatively significant contribution, not a rounding-order curiosity.
Why is glycine considered destabilizing for alpha helices if it can technically adopt the right φ,ψ?
Glycine can indeed sit at φ ≈ −57°, ψ ≈ −47° with no steric problem at all — its issue is not that the helical conformation is forbidden, but that its unfolded-state backbone has access to a much larger region of (φ,ψ) space than any other residue (because it lacks a Cβ to create the steric restrictions that limit other residues). This gives glycine's unfolded state unusually high conformational entropy, so the entropic cost of "locking" glycine into the single narrow alpha-helical conformation is larger than for residues like alanine, whose unfolded state is already fairly restricted. The effect is thermodynamic (entropic), not steric-in-the-helix, which is elaborated in discussions of amino acid helix propensity scales.
How is the 13-atom ring in "3.6₁₃" actually counted?
Starting from the hydrogen atom on the donor nitrogen (residue i+4) and tracing the shortest closed path back to the acceptor oxygen (residue i) through the covalent backbone — N–H···O=C–Cα–N–Cα–C–N–Cα–C–N–Cα–C — and closing the ring via the hydrogen bond itself, one counts 13 atoms total in that closed loop (including both the donor H and acceptor O). This ring size is what gives the 3.6₁₃ helix its full designation, distinguishing it from the 3₁₀-helix (10-atom ring, i→i+3 spacing) and the π-helix (16-atom ring, i→i+5 spacing); all three are legitimate, sterically permitted helices, differing only in how tightly the ring closes.