In brief, secondary structure refers to the local geometry of the polypeptide backbone and well-defined, often repetitive patterns of stabilising hydrogen bonds. Based on these criteria, different classes of secondary structure elements can be defined. To the left you can see an overview of most of these classes and subclasses described in the literature.

There are many known subclasses, some of which (shown in blue) are not even included in any of the tools available for secondary structure decomposition analysis for far-UV CD data. This is one of the reasons why results obtained with this traditional data analysis approach should be considered estimates rather than accurate, definite answers.

In fact, not even secondary structure content based on 3d models obtained from techniques such as x-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy is definite. Secondary structure assignments based on 3d structures are most often carried out using the DSSP algorithm developed by Kabsch and Sander in 1983. However, other valid algorithms for this purpose exist that make use of different criteria and won't yield the exact same assignments (Martin et al. 2005). Secondary structure assignments based on such algorithms are always employed for the compilation of reference far-UV CD data sets that secondary structure decomposition analysis relies upon. This poses another factor that ultimately affects the accuracy of this kind of analysis.

🖰 Helices in polypetides comprised of L-amino acids are virtually always right-handed, i.e., when looking down the helical axis and tracing the trajectory of the main chain into the distance, the projection of this trace will follow a clockwise direction. The side chains of the amino acid residues are more or less staggered and point away from the helical axis.

🖰 The main chain of a helix is stabilised by intrahelical hydrogen bonds. A helix consisting of n residues will always only have up to n - 4 hydrogen bonds because neither the N-H groups of the four residues at the start (N-terminus) nor the C=O groups of the four residues at the end (C-terminus) of the helix participate in intrahelical hydrogen bonds. The very first and very last residue of a helix is called N-Cap and C-Cap, respectively.

🖰 Due to the relatively high electronegativity of nitrogen and oxygen, the N-H and C=O groups of peptide bonds have partial charges which result in a strong dipole moment. As all peptide groups point more or less into the same direction parallel to the helical axis, the amide dipole moments are in near perfect alignment and cumulatively form a helix macrodipole where the N‑terminus and C‑terminus have unit charges of approximately δ⁺ = +0.5 and δ^- = -0.5, respectively.

Three types of helices can be defined based on the number n of peptide bonds between any two residues that provide the donor (i + n) and acceptor group (i) for a hydrogen bond:

• π-helices (i + 5 → i)
• α-Helices (i + 4 → i)
• 3₁₀-helices (i + 3 → i)

On average, α-helices account for about a third of the secondary structures observed in proteins, whereas 3₁₀-helices and π-helices are less abundant, contributing to about 4% and less than 1% of average protein secondary structure, respectively. Short segments of these rarer types of helices are often found at the ends of α-helices.

In π-helices, hydrogen bonds are formed between the amino group of one residue (i) and the carbonyl group of the residue five residues upstream in the sequence (i - 5).

π-Helices follow certain overall charasteristics:

• Any two consecutive residues are
  • translated by 1.15 Å relative to each other.
  • rotated around the helical axis by 87° relative to each other.
• A single turn in the helix
  • corresponds to 4.4 amino acids.
  • has a pitch (i.e., vertical distance between consecutive turns) of 1.15 Å · 4.4 = 5.1 Å.
• The dihedral angles are typically close to φ ≈ -57° and ψ ≈ -70°.

Hydrogen bonds of α-Helices are formed between the amino group of one residue (i) and the carbonyl group of the residue four residues upstream in the sequence (i - 4).

Regular α-Helices are more or less straight, have an average length of 10 to 12 residues, and follow certain overall charasteristics:

• Any two consecutive residues are
  • translated by 1.5 Å relative to each other.
  • rotated around the helical axis by 100° relative to each other.
• A single turn in the helix
  • corresponds to 3.6 amino acids.
  • has a pitch (i.e., vertical distance between consecutive turns) of 1.5 Å · 3.6 = 5.4 Å.
• The dihedral angles are typically close to φ ≈ -58° and ψ = -47°.

Canonical α-helices hardly exist, as dihedral angles and other characteristics rarely conform to strict textbook definitions. Deviations from ideal conformation often observed include:

• Curvature of the helical axis (~60 Å radius, Barlow et al. 1988)
• Splits, breaks, kinks, or bends
• Distortions located at the helix
  • caps, i.e., first (N-cap) or last (C-cap) residue of the helix
  • termini, i.e., first (N-terminus) or last (C-terminus) few residues at either end of the helix

Such irregularities can involve dihedral angles that are more typical for other secondary structure elements. On average, about one third of residues in α-helices can be considered distorted.

Atypical helix conformations are promoted by certain amino acids because their side chains impose restictions on the torsion angles of the main chain, as otherwise steric clashes would occur. This includes, for example, amino acids with side chains that are branched at the β-carbon atom such as threonine or valine. Due to their inferior capability to stabilise a helical structure, these amino acids have a lower propensity to occur within α-helices.

Breaks or kinks are often introduced by proline because its backbone nitrogen is unavailable for the formation of hydrogen bonds.

In 3₁₀-helices, hydrogen bonds are formed between the amino group of one residue (i) and the carbonyl group of the residue three residues upstream in the sequence (i - 3).

3₁₀-Helices are typically short with an average length of 3 to 5 residues and follow certain overall charasteristics:

• Any two consecutive residues are
  • translated by 2.0 Å relative to each other.
  • rotated around the helical axis by 120° relative to each other.
• A single turn in the helix
  • corresponds to 3 amino acids.
  • has a pitch (i.e., vertical distance between consecutive turns) of 2 Å · 3 = 6 Å.
• The dihedral angles are typically close to φ ≈ -49° and ψ ≈ -26°.

3₁₀-Helices make up about 10 to 15% of all helices. Their name originates from a historical designation based on the number of residues per helical turn (3) and the number of backbone atoms (10) between a hydrogen bond's donor and acceptor groups.

In β-strands, the backbone has an extended conformation with dihedral angles of ideally φ ≈ -120° and ψ ≈ +120°, which might be conceptualised as a stretched-out helix with two residues per turn.

🖰 Within a single β-strand, i.e., a segment of limited length with this conformation, the amide and carbonyl groups are too far apart to form hydrogen bonds with each other. Therefore, β-strands are virtually never found in isolation; instead, multiple strands align alongside each other so that hydrogen bonds can form between them and stabilise a larger structure, the β-sheet.

🖰 Parallel and anti-parallel β-sheets can be distinguished, depending on which direction strands are aligned in relative to each other. However, mixed β-sheets that include both are possible, as shown here for human thioredoxin.

🖰 β-Sheets are sometimes called "pleated" β-sheets because consecutive C_α-atoms and their corresponding side chains are alternatingly located on either side of the sheet's plane.

On average, β-strands span 6 residues, and most β-sheets consist of fewer than 6 strands. About a quarter of the residues in known protein structures have a beta-sheet conformation.

It is possible for more distant parts of an amino acid sequence to form strands and come together with the same direction to form parallel β-sheets. On average, the dihedral angles in untwisted parallel β-sheets are close to φ ≈ -116° and ψ ≈ +118° (Nesloney et al. 1996).

The distances between hydrogen bonds formed between adjacent strands are more or less equivalent in parallel β-sheets. Moreover, the hydrogen bonds in parallel β-sheets are neither perpendicular to the strands nor parallel to each other. Due to this hydrogen bonding geometry, parallel β-sheets are less stable than anti-parallel β-sheets, which might be the reason why parallel β-sheets usually contain at least four strands and don't show the same propensity for twists or bulges.

Left-twisted β-sheets are virtually never observed because right-twisted β-sheets are energetically favoured. This is, in part, due to steric hindrance that would occur in left-twisted β-sheets, but also due to hydrogen bonding (Shamovsky et al. 2000) and electrostatic effects (Maccallum et al. 1995).

The example shows β-strands in pea lectin that are slighty left-twisted at least locally. Left-handed twists usually involve glycine, because it is the only amino acid that lacks a β-carbon and, thus, cannot suppress a left-hand twist (Shamovsky et al. 2000).

A β-sheet often conists of strands that span the amino acid sequence sequentially and are separated only by short turns; this results in anti-parallel β-sheets, because the backbone changes direction as it folds onto itself.

Relaxed, anti-parallel β-sheets form a pattern of alternating shorter and longer distances between consecutive hydrogen bonds. Moreover, the hydrogen bonds are both perpendicular to the strands and more or less parallel to each other. On average, the dihedral angles in untwisted anti-parallel β-sheets are close to φ ≈ -145° and ψ ≈ +140° (Nesloney et al. 1996).

Truly relaxed β-sheets are not that common because most β-sheets are at least slighty right-twisted.

Hardly any anti-parallel β-sheet is actually planar; most anti-parallel β-sheets have a twist which results from a relative right-handed rotation of 30° per residue.

Definition of the twist sense (Weatherford et al. 1979) can sometimes seem a bit confusing, so let's have a look at the example for a right-twisted β-sheet here.

🖰 Firstly, the individual β-strands are right-twisted, i.e., looking down along the polypeptide chain, a clockwise rotation around the axis parallel to the β-strand is apparent.

🖰 Similarly, multiple β-strands make up a right-twisted β-sheet, i.e., looking down along an axis with the same orientation as the β-strands, a clockwise rotation of the hydrogen bonds around this axis is apparent.

🖰 Confusingly, right-twisted β-sheets are sometimes ascribed a left twist; this occurs if a different reference axis is chosen that is orthogonal to the orientation of the β-strands: when looking along the direction of the hydrogen bonds, a left-handed interchain twist, i.e., across the β-strands, is apparent.

On average, the dihedral angles in heavily twisted anti-parallel β-sheets are close to φ ≈ -96° and ψ ≈ +158° (Nesloney et al. 1996).

β-Bulges have been characterised well in the literature, so we shall quote a primary source here. As described in Richardson et al. 1978, "a β bulge is a region between two consecutive β-type hydrogen bonds which includes two residues (positions 1 and 2) on one strand opposite a single residue (position x) on the other strand."

"Compared to regular β structure, a β bulge puts the usual alternation of side-chain direction out of register on one of the strands, introduces a slight bend in the β sheet, and locally accentuates the usual right-handed strand twist. Almost all β bulges are between antiparallel strands, usually between a narrow rather than a wide pair of hydrogen bonds."

And furthermore, "a β bulge is defined as a region between two consecutive β-type hydrogen bonds which includes two residues on one strand opposite a single residue on the other strand. [...] In more than 80% of the cases, β bulges occur between a closely spaced pair of hydrogen bonds rather than a widely spaced pair. β bulges are extremely rare in parallel β structure."

"[...] an additional β strand cannot continue to bond past the bulge on the two-residue side, so that a bulge is always at either an edge or an end of the β sheet. The additional backbone length of the extra residue on the bulged strand is accommodated partly by bulging that strand up and out and partly by putting a slight bend in the β sheet. The distance between α carbons n and n + 3 on either end of the two-residue bulged side averages 8.0 Å."

Turns are structural segments that reverse the overall directionality of the main chain; "Turns comprise n consecutive residues (denoted i to i + n), in which the distance between C_α(s) of residues i and i + n must be smaller than 7 Å [...]. [...] The restrictive distance between C_αs applies a particular geometry to the backbone, thereby causing it to turn back on itself." (de Brevern et al. 2016)

Turns are typically stabilised by intramolecular backbone-backbone hydrogen bonds, and there are turns that are characterised by hydrogen bonds between the amine hydrogen (N-H) of one residue and the carbonyl oxygen (C=O) of a residue upstream in the amino acid sequence, as well as turns with hydrogen bonds between the N-H of a residue and the C=O of a residue downstream in the amino acid sequence.

Turns with C=O···H-N H-bonds:	Turns with N-H···O=C H-bonds:
π-turns (n = 6) α-turns (n = 5) β-turns (n = 4) γ-turns (n = 3)	ɛ-turns (n = 3) δ-turns (n = 2)

For most types of turns, multiple classes and subclasses can be differentiated based on dihedral angles of the peptide bonds, i.e., backbone torsion angles of the amino acids involved.

Turns that are longer, i.e., π-turns and α-turns in particular, may incorporate smaller internal turns. For example, there can be multiple overlapping α- or β-turns embedded in a π-turn, and α-turns can include tighter β-turns or a γ-turn (as is the case for α-turns of the II‑α_LS subclass).

An example for this is shown: this π-turn comprises residues i to i + 5 and includes two overlapping type I β-turns that span residues i to i + 3 and i + 1 to i + 4, respectively.

π-Turns, which are often found at the C-terminus of α-helices, have originally been classified based on the conformation of the amino acid residue in position i + 4 (Rajashankar et al. 1996). However, an alternative classification has been proposed later that takes into account the dihedral angles of all residues that are in the middle of the turn (Dasgupta et al. 2008).

This new classification distinguishes between non-hydrogen-bonded (NHB) and hydrogen-bonded (HB) π-turns (specifically referring to hydrogen bonds between the residues in positions i and i + 5) and further separates the latter into turns that are isolated and those that are part of α-helix termini ('Schellman motif'); a further distinction is made for the latter based on whether a second hydrogen bond is present or not:

• Non-hydrogen-bonded π-turns (π-NHB)
• Hydrogen-bonded π-turns (π-HB)
  • Isolated
  • Schellman (SCH) motif
    • SCH_+β
    • SCH_-β

α-Turns comprise five amino acid residues; they introduce a chain reversal and are stabilised by a hydrogen bond between the first and last residue of the turn just like other turns.

The structural definition of type I‑α_RS α-turns implies an ambiguity in the classification of secondary structure elements: the typical dihedral angles of these α-turns are similar to those of the basic repetitive unit of the right-handed α-helix. Similarly, α-turns of opposite handedness can be observed (type I‑α_LS), with dihedral angles that correspond to the basic repetitive unit of left-handed α-helices (Pavone et al. 1996).

α-Turns are relatively common; on average, two α-turns can be found per protein.

From all types of turns, β-turns have received the most attention in the literature. Multiple types of β-turns have been described, including corresponding mirror images (denoted with an apostrophe, ').

While looking through the types of β-turns, you might wonder why numbering suggests that some types are missing. This is because some types have been defined in the past, but later excluded due to various reasons:

• Type III (and III') has been excluded because it is basically a distortion of type I (I') and corresponds to the basic repetititve unit of 3₁₀-helices.
• Type V (and V') is rare and its definition is inaccurate.
• Type VII, which is associated with a kink, is also rare and poorly defined.

γ-Turns are a tripeptide conformation of which only two types exist, the classic γ-turn and the inverse γ-turn (Milner-White et al. 1988).

Both types of γ-turns are characterised by a seven-membered pseudo-cycle which is formed by the donor and acceptor atoms of an intramolecular hydrogen bond and the main chain atoms between them.

Note that only 6 member atoms of this pseudo-cycle are visible in the 3d model because the hydrogen of the amide group is not shown.

While ɛ-turns are formed by three residues just like γ-turns, they are structurally different as the direction of the stabilising hydrogen bond between the first and last residue is reversed, i.e., the donor amide group is upstream rather than downstream of the carbonyl acceptor group.

The hydrogen bond in ɛ-turns hence forms a pseudo-cycle with eleven member atoms rather than seven. However, a γ-turn may actually be included in an ɛ-turn (Toniolo et al. 2017).

ɛ-Turns have been classified in six different families and can be found in proteins in isolation or as part of hairpin motifs that consist of a pair of anti-parallel β-strands.

The shorter a turn gets the fewer options there are for main-chain reversal due to steric constraints.

However, even a δ-turn, a turn consisting of only two residues, is possible: for example, if the turn begins with a flexible residue such as a glycine (GLY) which is followed by a proline (PRO) in a semi-extended conformation, and the pair assumes the cis-conformation (i.e., the dihedral angle of the peptide bond between the two residues is close to zero, ω ≈ 0°), then sterical hindrance is not too large (Toniolo et al. 2015).

Just like ɛ-turns, δ-turns can be stabilised by a hydrogen bond that has a direction opposite to hydrogen bonds found in longer turns.

'Random coil' usually refers to any local polypeptide structure that lacks a well-defined or periodic pattern of hydrogen bonds and thus cannot be ascribed to any of the other classes of secondary structure. This typically includes loops that connect segments with defined secondary structure. However, the term is somewhat misleading because segments with random coil structure usually are neither coiled nor randomly structured.

It is true that random coil segments are often more flexible and their dihedral angles don't follow canonic definitions but rather populate a distribution of values that give rise to an ensemble of conformations (Smith et al. 1996). This holds usually true for terminal segments at the ends of the polypeptide chain and solvent-exposed loops at the protein surface.

However, even random coil structure can be subjected to a certain level of classification and loops are not always necessarily highly flexible. For example, the omega loop is a non-regular structure comprising six or more residues that lacks well-defined dihedral angles or a pattern of hydrogen bonding, but is often found to have limited flexibility. It can be identified by the fact that the first and last residue of the loop are in close vicinity to each other; they act as hinge points and gives rise to the loop's eponymous shape that resembles a Greek omega, Ω (Papaleo et al. 2016).