4.2: Secondary Structure and Loops

Search Fundamentals of Biochemistry

Learning Goals 

(Learning goals written by Claude, Sonnet 4.6, Anthropic)

Alpha Helices and Other Helical Structures

• Describe the geometry of the α-helix in precise terms — hydrogen bonding pattern (i to i+4 carbonyl O to amide H), φ/ψ angles (−57°, −47°), 3.6 residues/turn, 5.4 Å pitch, and 100° side chain stagger — and explain why the helix core is fully packed with no central cavity, why left-handed α-helices are not observed in natural proteins, and which amino acids are helix-promoting or helix-destabilizing.
• Compare the α-helix, 3₁₀ helix, and π-helix in terms of hydrogen bonding pattern (i to i+3, i+4, or i+5), residues per turn, pitch, φ/ψ angles, relative abundance, and side chain stagger — and explain why α-helices are far more prevalent than 3₁₀ or π helices based on geometric and energetic arguments.
• Explain the origin and magnitude of the helix macrodipole — arising from the parallel alignment of individual amide bond dipoles along the helix axis — and predict how this dipole influences the binding of charged ligands and ions at helix termini.
• Interpret helical wheel projections to identify amphipathic versus fully hydrophobic helices, explain the functional significance of each type, and predict which face of an amphipathic helix is likely to interact with a hydrophobic protein interface or lipid bilayer.

Beta Sheets, Turns, and Connecting Elements

• Compare parallel and antiparallel β-sheets in terms of φ/ψ angles, hydrogen bond geometry (linear in antiparallel, bent in parallel), side chain distribution (hydrophobic on both faces vs. one face), and relative stability — and explain how the inherent right-handed twist of β-strands gives rise to twisted sheets, saddle shapes, and β-barrels depending on strand registration.
• Describe the structural features of Type I and Type II β-turns (four residues, i to i+3 hydrogen bond, characteristic φ/ψ angles at positions 2 and 3), identify the amino acids most commonly found at each position and explain the structural rationale, and distinguish β-turns from γ-turns and ω-loops in terms of residue count and regularity of internal hydrogen bonding.

Amino Acid Propensities and Secondary Structure Prediction

• Use Chou-Fasman propensity values to rationalize why specific amino acids favor or disfavor α-helices or β-sheets — connecting propensity to side chain geometry (β-carbon branching, ring constraints, conformational flexibility) — and explain why glycine and proline are uniquely suited to tight turns and loop regions rather than regular secondary structure elements

Secondary structures are those repetitive structures involving hydrogen bonds between amide Hs and carbonyl Os in the protein backbone. These include

• helices (alpha - α, 3₁₀, and pi - π), in which the hydrogen bonds are within a short continuous stretch of amino acids (a strand),
• beta strands (β sheets) in which the hydrogen bonds are between backbone atoms (again amide Hs and carbonyl Os) on noncontinuous stretches of the protein, and
• reverse turns occur within a very short, continuous stretch of amino acids.

Helices

A schematic showing idealized geometries of helices, with amino acids shown as dots for simplicity, is shown in Figure \(\PageIndex{1}\).

Figure \(\PageIndex{1}\): Helix geometries Open University. https://www.open.edu/openlearn/scien...-section-1.3.1.

The pitch (p) represents the spacing between the chain on one side of the helix, the number of amino acids per turn (n), and handedness (plus = right-handed, minus = left-handed) are shown in the figure. There are three major types of helices in proteins: the alpha helix (n = 3.6), 3₁₀ helix (n = 3), and the pi helix (n = 4.4). Note that n is most commonly not an integer.

Alpha

The alpha helix is the most common type of helix. They are formed when the carbonyl O of the i^th amino acid forms hydrogen bonds to the amide H of the i+4^th amino acid (4 amino acids away). Figure \(\PageIndex{2}\) shows a short section of an alpha helix running from the N-terminal (bottom) to the C-terminal (top) with the sequence DTASDAA. The amino acids i, i+1, ... i+4 are labeled at their alpha carbons. The red oval highlights the intrastrand H bond between the C=O of the i^th amino acid (Asp) and the amide H of the i+4^th amino acid (Ser).

Figure \(\PageIndex{2}\): A short alpha helix

Figure \(\PageIndex{3}\) shows a cartoon image showing a longer helix and a schematic showing hydrogen bonding partners.

Figure \(\PageIndex{3}\): A longer alpha helix Open University. https://www.open.edu/openlearn/scien...-section-1.3.1.

The phi/psi angles for amino acids in the alpha helix are approximately - 57, -47, which emphasize the regular repeating nature of the structure. It can also be characterized by n (the number of amino acid units/turn = 3.6) and the pitch (the helix rise/turn = 5.4 angstroms = 0.54 nm). Since there are 3.6 amino acids per turn, and a full circle or turn is 360⁰, each amino acid is staggered at 100⁰ increments looking down on the helix axis. To refresh your mind, the phi/psi diagram for a fully extended polypeptide chain (phi 180⁰, psi 180⁰) is shown below in Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\): Extended polypeptide with phi/psi planes

Figure \(\PageIndex{5}\) shows the side and end-on view of a helix from the antifreeze protein (1wfa) from the winter flounder. The green coil (often shown in red when displaying alpha helices in full proteins) highlights the backbone's repetitive nature. Note that side chains are pointing away from the helix axis. H-bonds are shown as yellow dotted lines within the backbone (one is also shown between two side chains on the top). The spacefill rendering is shown in colors optimized for colorblind people. The end-on view shows that the helix's center is fully packed with atoms from the helix and is NOT open (a common misconception among students).

Figure \(\PageIndex{5}\): Multiple views and renders of an alpha helix

Some facts:

• The alpha helix is more compact than the fully extended polypeptide chain with phi/psi angles of 180 ^o.
• In proteins, the average number of amino acids per helix is 11, corresponding to three turns.
• The left-handed alpha helix, although allowed by Ramachandran plot analyses, is never observed since the side chains are too close to the backbone.
• The core of the helix is packed tightly. No central cavities or pores are present in the helix.
• All the R-groups extend backward and away from the helix axis.
• Some amino acids are more commonly found in alpha helices. Amino acids can be divided into two kinds: those with branches at the beta C and those with none. Consider first those that aren't branched. Gly is too conformationally flexible to be found with high frequency in alpha helices, while Pro is too rigid. The amino acids with side chains that can H-bond (Ser, Asp, and Asn) and aren't too long appear to act as competitors of main chain H bond donors and acceptors and destabilize alpha helices. The rest with no branches at the beta C can form helices. Those with branches at the beta carbon (Val, Ile) destabilize the alpha helix due to steric interactions of the bulky side chains with the helix backbone. (Remember, left-handed alpha helices are not naturally found for similar reasons.)
• Alpha keratins, the major component of hair, skin, fur, beaks, and fingernails, are almost all alpha helices.

Figure \(\PageIndex{6}\) shows an interactive iCn3D model of an alpha helix from bacteriophage T4 lysozyme (1DYG). Side chains, which are not involved in helix-stabilizing hydrogen bonds, are shown in cyan. H-bonds are shown as green dotted lines.

Figure \(\PageIndex{6}\): An alpha helix from bacteriophage T4 lysozyme (1DYG). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...qhkPT6cMqxvp88 (Copyright; author via source)

The amino acid side chain R groups can be hydrophilic or hydrophobic. They can be localized in specific positions on the helix, forming amphipathic regions on the protein, or fully hydrophobic helices may extend through the plasma membrane as shown in Figure \(\PageIndex{7}\).

 Figure modified from: Khara, J.S., et al. (2017) Acta Biomat 57:103-114 and Ryu, H., et al. (2019) Int J Mol Sci 20 (6) 1437

In amphipathic helices, hydrophilic residues are positioned on one side of the helix and hydrophobic residues on the other, as shown in the side view (A) or top-down views (B & C). R-groups may also be entirely hydrophobic within alpha helices that span the plasma membrane, as shown in (D).

Helical wheel projections can show the polarity of the helix's faces, looking down the helix's axis. Here are two such helical wheel projections:

For the sequence MLQSMVSLLQSLVSLIIQ, Figure \(\PageIndex{8}\) shows that the helix is amphiphilic.

Figure \(\PageIndex{8}\): Helical wheel for MLQSMVSLLQSLVSLIIQ http://lbqp.unb.br/NetWheels/

A helical wheel for the membrane-crossing section of the human receptor-type tyrosine-protein phosphatase C protein, ALIAFLAFLIIVTSIALLVVL, is shown in Figure \(\PageIndex{9}\).

Figure \(\PageIndex{9}\): Helical wheel for a membrane helix

The amide bond in the peptide has a significant permanent dipole moment. Since the dipoles of individual amino acids are oriented in the same direction in an alpha helix, the whole helix has a significant dipole moment. This is illustrated in Figure \(\PageIndex{10}\).

recreate this image:

Figure \(\PageIndex{10}\): Helix Dipole (https://www.sciencedirect.com/scienc...05273612003860; reproduce image)

In the alpha helix, all the amides in the backbone point in one direction from the C-terminus to the N-terminus. This leads effectively to one long dipole of magnitude n(3.5) Debyes, where n is the number of amino acids in the helix. A long helix can produce a significant electric field and affect protein binding properties.

3₁₀ helices

The 3₁₀ (or 3 10)helix is stabilized by hydrogen bonds between the carbonyl O of the i^th amino acid and the amide H of the i+3^th aa (3 amino acids away). It has three residues/turn and a pitch (rise per turn) of 6 angstroms, with a rise of 1.3-2 angstroms/residue. Typical phi/psi angles are -50⁰,-26°. As with the alternative description of the alpha helix, the 3₁₀ helix has three amino acids per turn and 10 atoms in the main chain/turn (counting Cα-N-C-Cα atoms). It is longer (for the same number of amino acids) and thinner. The amino acid side chains are staggered at 120⁰ increments as you look around the helix axis. Although not very prevalent (about 3 percent of protein amino acids are in 3₁₀ helix with an average of 3.3 amino acids in the helix), they presumably serve some function. 3₁₀ helices as long as 11 residues have been found.

A helix will be stable within a protein if the packing and noncovalent interactions favor it over other conformations. Many more alpha-helix side chain interactions with surrounding protein are likely, given a 100⁰ staggering of side chains compared to a 120⁰ staggering in a 3₁₀ helix, which line up in three ridges looking down the helical axis. Molecular dynamics studies suggest that parts of a 3₁₀ helix might reversibly interconvert to an alpha helix, allowing conformational and binding flexibility. The S4 helix in some voltage-sensitive potassium ion channels with a canonical R₁xxR₂xxR₃xxR₄xxK₅xxR₆ (where R and K are Arg and Lys) has been shown to adopt a 3₁₀ helical conformation.

Figure \(\PageIndex{11}\) shows an interactive iCn3D model of a nine amino acids (150-158) 3₁₀ helix from dienelactone hydrolase (1DIN)

Figure \(\PageIndex{11}\): A 3₁₀ helix from from dienelactone hydrolase (1DIN). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...Kufi7gmpSBdjYA (Copyright; author via source)

π (pi) helices

This helix has 4.4 residues/turn and a helix pitch (rise) of about 4.1 nm. It has hydrogen bonds between the carbonyl O of the i^th amino acid and the amide H of the i+5^th amino acid (5 amino acids away). Its rise is about 1.2 angstroms/residue and has approximate phi/psi angles of -55⁰, -70⁰. An alternative designation for the pi helix is 4.4₁₆, with 16 main-chain atoms in 1 full turn (see above for the alpha helix). Some reasons for its low abundance include minimal contact between the main chain atoms, given the larger radius and phi-psi angles close to disallowed values. It might also not form as quickly as the other helices, since its nucleation would be more difficult. At the same time, molecular dynamics simulations show alpha helices can interconvert reversibly with pi helices. They are often found between two alpha helices, again suggesting that dynamic interconversions between the two forms are likely.

About 55% of characterized pi helices contain five amino acids. Each side chain is staggered by 85⁰, with a rise of about 1.3 Angstroms. Figure 12 below shows an interactive iCn3D model of a short pi helix (aa 265-276) from barley beta-D-glucan glucohydrolase (1x38).

Figure \(\PageIndex{12}\): A short pi helix (aa 265-276) from barley beta-D-glucan glucohydrolase (1x38). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...U7H6xjzHd95nbA (Copyright; author via source)

Helices in Proteins: Comparison of alpha, 3₁₀, and pi helices

Beta Structure

Beta Structure: Parallel and antiparallel beta strands are much more extended than alpha helices (phi/psi of -57,-47) but not as extended as a fully extended polypeptide chain (with phi/psi angles of +/- 180), as shown in the figure below. Parallel beta strands have phi/psi angles of -119, +113, while the antiparallel angles are -139, +135. Figure \(\PageIndex{13}\)

Figure \(\PageIndex{13}\)Open University. https://www.open.edu/openlearn/scien...-section-1.3.2

Each single strand of the beta-sheet can be pictured as a twofold helix, i.e., a helix with two residues/turn. The arrangement of each successive peptide plane is pleated due to the tetrahedral nature of the alpha C. Hydrogen bonds are inter-strand, not intra-strand, as in the alpha helix.

The figure below shows how the "pleats" in a sheet containing parallel beta strands can be envisioned as rippled sheets. Figure \(\PageIndex{14}\)

Figure \(\PageIndex{14}\)

They can be visualized by folding a sheet of paper into narrow folds or pleats to form a "pleated sheet" of paper. Each strip of paper can be pictured as a single peptide strand, with the peptide backbone zigzagging along it, the alpha carbons lying at the folds of the pleats. The R groups are attached to the carbons and extend above and below the pleat folds in the trans conformation.

Consider a strand as a continuous, contiguous polypeptide backbone propagating in one direction. Hence, using this definition, a helix consists of a single strand, and all the H-bonds are within the strand (or intrastrand). A beta sheet would then consist of multiple strands since each "strand" is separated from other "strands" by an intervening contiguous stretch of amino acid, which bends within the protein in a way that allows the next section of the peptide backbone, the next "strand," to H-bond with the first "strand." But remember, even in this case, all the H-bonds holding the alpha and beta structures together are intramolecular.

In a parallel beta sheet structure, the optimal H bond pattern leads to a less extended structure (phi/psi of -119, +113) than the optimal arrangement of the H bonds in the antiparallel structure (phi/psi of -139, +135). Also, the H bonds in the parallel sheet are bent significantly. (i.e., the carbonyl O on one strand is not exactly opposite the amide H on the adjacent strand, as it is in the antiparallel sheet.) Hence, antiparallel beta strands are presumably more stable, although both are abundant in nature. Short parallel beta sheets with 4 strands or fewer are uncommon, which may reflect their lower stability.

The side chains in the beta sheet are perpendicular to the sheet's plane, extending out on alternating sides. Parallel sheets characteristically distribute hydrophobic side chains on both sides of the sheet, while antiparallel sheets are usually arranged with all the hydrophobic residues on one side. This requires alternating hydrophilic and hydrophobic amino acid side chains in the primary sequence. Antiparallel sheets are found in silk, running parallel to the silk fibers. The following repeat is found in the primary sequence: (Ser-Gly-Ala-Gly)_n, with Gly pointing out from one face and Ser or Ala from the other.

Unfortunately, no PDB structure of the silk "amyloid" protein shows this repetitive structure. The monomers and aggregates of this protein are quite insoluble, so few X-ray structures for proteins like this are available. Figure \(\PageIndex{15}\) shows an interactive iCn3D model of the N-terminal part (domain) of the Bombyx mori fibroin silk protein (pdb = 3UA0), which gives an excellent example of antiparallel beta sheets. Notice that two chains align to form a face of the curved antiparallel beta sheet.

Figure \(\PageIndex{15}\): N-terminal Domain of the Bombyx mori fibroin silk protein (3UA0). Click the image for a popup or use this external link:https://structure.ncbi.nlm.nih.gov/i...TuDiMoi64TaAx9 (Copyright; author via source)

Figure \(\PageIndex{16}\) shows a more detailed static image of the antiparallel beta sheets in 3UA0. Note the yellow sticks between the strands representing the H-bonds.

Figure \(\PageIndex{16}\):

Beta strands tend to twist in the right-hand direction. This has important consequences for how the beta strands are connected. Parallel strands can form twisted sheets, saddles, and beta barrels.

Figure \(\PageIndex{17}\) shows an interactive iCn3D model of the parallel beta sheet structure from the arabinose binding protein (1ABE).

Figure \(\PageIndex{17}\): Parallel beta sheet structure from the arabinose binding protein (1ABE). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...7A2akqvuCpavu8 (Copyright; author via source)

Figure \(\PageIndex{18}\) shows a static image of the parallel beta sheets in 1ABE. Note the yellow sticks between the strands representing the H-bonds.

Figure \(\PageIndex{18}\): Parallel beta sheet structure from the arabinose binding protein (1ABE)

Figure \(\PageIndex{19}\) shows an interactive iCn3D model of a parallel beta barrel from the triose phosphate isomerase (1WYI).

Figure \(\PageIndex{19}\): Parallel beta barrel from the triose phosphate isomerase (1WYI) (Copyright; author via source)). Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...7dki3WjRDtiaRA

Figure \(\PageIndex{20}\) shows a static image of the parallel beta sheets in triose phosphate isomerase. Note the yellow sticks between the strands representing the H-bonds. Also, note that the barrel is not hollow but is filled with side chains.

Figure \(\PageIndex{20}\): Parallel beta sheets in triose phosphate isomerase

Some facts on parallel beta structure:

• In parallel strands, right-handed connectivity is common.
• In a protein with parallel strands in a register, and given the inherent twist in the strands, the strands arrange to have the H bonds stretched equally at the ends of the chains, giving rise to a twisted saddle shape (top structure above).
• In a protein with parallel strands out of register, and given the inherent twist in the strands, the strands arrange to have the H bonds stretched equally at the ends of the chains, giving rise to a beta barrel (bottom structure above).

Connectors, Loops, Linkers, and Bends

About 50% of the amino acids in a globular (spherical) protein are in regular secondary structure (alpha or beta). The amino acids in helices and beta strands are connected by stretches of amino acids that still retain order. Still, that order is less regular than those found in helices and beta strands, characterized by stretches of amino acids with the same phi/psi angles. Some bear the hallmarks of secondary structure - intrachain hydrogen bonds hold them together. We will consider a few here.

Turns, Reverse Turns, and Hairpins

One example of a connector involving secondary structure (i.e. hydrogen bonds between amide Hs and carbonyl Os of the backbone), is a reverse turn called the beta bend or beta turn. These turns often connect successive antiparallel beta strands and are then called beta hairpins. A hairpin is a special case of a turn in which the direction of the protein backbone reverses, and the flanking secondary structure elements interact. For example, the beta hairpin connects two antiparallel β-strands via hydrogen bonds. The word beta can be confusing. It does not mean the structure has hydrogen-bonded amino acids with the same phi-psi angles as beta strands. It's easy to remember the name beta as the beta bend connects two antiparallel beta strands. The term beta comes from the fact that it is a member of a class of turns named with Greek letters, including alpha-, gamma-, delta-, pi-, and beta- turns.

They are almost always on the surface and usually contain four amino acids. However, several types of beta turns and different ways to classify them exist. One involves the number of residues (n) between the two hydrogen-bonded residues.

n=2: These contain four amino acids. Amino acids 1 and 4 form hydrogen bonds with n=2 amino acids in between. Another way to describe them is that the hydrogen bond between residues 1 and 4 is between the backbone carbonyl O of the i^th amino acid and the amide H of the i+3^th amino acid (three amino acids away), so the structure contains four amino acids (i^th, i+1^th, i+2^th, and i+3^th). There are two common types:

• Type I: phi 2 = -60, psi 2 =-30; phi 3 = -90, psi 3 = 0; The first amino acid in the actual turn (i^th + 1) is in a left-handed alpha helix conformation. Glycine, asparagine, or aspartate are stable at this position since glycine is small and the side chains of Asp and Asn can form hydrogen bonds to the main chain. Glycine is usually found in the second position of the actual turn (i+2^th).
• Type II: phi 2 = -60, psi 2=120; phi 3 = 90, psi 3 = 0; The first residue of the actual turn is typically Gly, while the second often is a polar amino acid such as Ser and Thr

Here are 2D line drawings showing Type I and Type II beta turns. Figure \(\PageIndex{21}\)

Figure \(\PageIndex{21}\)

The figure below shows Type I (left) and Type 2 (right) from human egg white lysozyme. Figure \(\PageIndex{22}\)

Figure \(\PageIndex{22}\)

Figure \(\PageIndex{23}\) shows an interactive iCn3D model showing two reverse turns in hen egg white lysozyme (1dpx). Notice the tightness of the reverse turn and the presence of proline and glycine.

Figure \(\PageIndex{23}\): Two reverse turns in hen egg white lysozyme (1dpx) (Copyright; author via source). Click the image for a popup or use this external link:https://structure.ncbi.nlm.nih.gov/i...U2BzPt98cPYHFA

n=3: These contain five amino acids. Amino acids 1 and 5 form hydrogen bonds with n=3 amino acids between them. Another way to describe them is that the hydrogen bond between residues 1 and 4 is between the backbone carbonyl O of the i^th amino acid and the amide H of the i+4^th amino acid (four amino acids away).

Shifting back to the Greek letter naming system, the gamma turn, the second most common turn, has just three total residues (i^th, i+1^th, and i+2^th) with the hydrogen bond between the backbone carbonyl of the i^th amino acid and the backbone amide H of the i+2^th amino acid.

An ω-loop is a catch-all term for a longer, extended, or irregular loop without fixed internal hydrogen bonding. Turns are sometimes found within flexible linkers or loops connecting protein domains. Linker sequences vary in length and are typically rich in polar uncharged amino acids. Flexible linkers between domains allow twisting and rotation to recruit their binding partners via protein domain dynamics.

Most modeling programs display the linear sequence of a protein, and a linear cartoon rendering shows the alpha structure as squiggles or helices and the beta structure as yellow arrows. The figure below shows a 1D connectivity diagram for part of the protein alpha-lactalbumin (1a4v). Figure \(\PageIndex{24}\)

Figure \(\PageIndex{24}\):

Amino Acid Propensities for Secondary Structures

Finally, what types of amino acids are most likely found in different secondary structures? Some rationales for the "propensity" for secondary structure are shown in the figure below. Figure \(\PageIndex{25}\)

Figure \(\PageIndex{25}\):Amino Acid Propensities for Secondary Structure

 

Chou-Fasman derived a list of propensities for each amino acid for secondary structure, based on their occurrence in determined protein structures..  These values are shown in Figure \(\PageIndex{26}\) below.

 

Figure \(\PageIndex{26}\): Chou-Fasman propensity values.  Higher + values represent higher propensities.  Jain, Vikas & Tu, Raymond. (2011). Coupled Folding and Specific Binding: Fishing for Amphiphilicity. International journal of molecular sciences. 12. 865-89. 10.3390/ijms12031431. Creative Commons Attribution 3.0 Unported

Summary

(Summary written by Claude, Sonnet 4.6, Anthropic)

This chapter provides a detailed treatment of protein secondary structure — the repetitive, hydrogen-bonded arrangements of the polypeptide backbone — encompassing the three major helix types, parallel and antiparallel β-sheets, and the connecting elements that link them. Throughout, structure is analyzed quantitatively in terms of φ/ψ angles, hydrogen bonding geometry, and the resulting physical properties.

Alpha helices are the most abundant secondary structure in proteins. Their defining feature is an intrastrand hydrogen bond between the backbone carbonyl oxygen of residue i and the amide hydrogen of residue i+4, yielding a compact, regular helix with 3.6 residues per turn, a 5.4 Å pitch, and φ/ψ angles of approximately −57°, −47°. Because successive residues are rotated 100° around the helix axis, side chains project outward and backward, leaving the helix core fully packed with no interior cavity — a common student misconception. The average helix in globular proteins contains about 11 residues, corresponding to three turns. Left-handed α-helices, though technically in an allowed region of the Ramachandran plot, are not observed in natural proteins because side chains clash with the backbone. Amino acid propensity for α-helix formation is governed by side chain geometry: β-carbon-branched residues (Val, Ile) destabilize helices sterically, glycine introduces excessive conformational flexibility, proline cannot donate an amide hydrogen and introduces a fixed kink, and residues capable of competing with backbone hydrogen bonds (Ser, Asp, Asn) tend to be helix-destabilizing. Because all amide dipoles point in the same direction along the helix (from C- to N-terminus), their sum produces a significant macrodipole — approximately 3.5n Debyes for an n-residue helix — that creates a partial positive charge at the N-terminus and partial negative charge at the C-terminus, influencing the binding of anions, metal ions, and charged ligands at helix ends. Helical wheel projections reveal the distribution of hydrophilic and hydrophobic residues around the circumference of the helix: amphipathic helices partition polar residues to one face and hydrophobic residues to the other (common at protein-protein interfaces and membrane surfaces), while fully hydrophobic helices span the lipid bilayer in transmembrane proteins.

The 3₁₀ helix differs from the α-helix by forming hydrogen bonds between residue i and i+3, yielding three residues per turn, a 6 Å pitch, and φ/ψ angles of approximately −50°, −26°. Side chains are staggered at 120° increments rather than 100°, aligning in three ridges when viewed down the helix axis. Although comprising only about 3% of protein secondary structure (average length ~3.3 residues), 3₁₀ helices are found at helix termini and in functionally important segments, and molecular dynamics studies show reversible interconversion with α-helices — suggesting a role in conformational flexibility. The π-helix (i to i+5 hydrogen bonds, 4.4 residues/turn, φ/ψ ≈ −55°, −70°) is the rarest of the three, with a wider radius and φ/ψ angles near the boundary of allowed Ramachandran space; it is typically found inserted between two α-helices and may represent a dynamic intermediate.

Beta sheets are far more extended than α-helices, with φ/ψ angles of approximately −119°, +113° for parallel sheets and −139°, +135° for antiparallel sheets — intermediate between the fully extended polypeptide (±180°) and the compact α-helix. Hydrogen bonds are interstrand rather than intrastrand. In antiparallel β-sheets, adjacent strands run in opposite N→C directions, and hydrogen bonds are linear and well-aligned, making antiparallel sheets generally more stable. Hydrophobic side chains typically cluster on one face, enabling membrane-proximal or protein-core burial. In parallel β-sheets, strands run in the same direction, hydrogen bonds are bent and less optimal, and hydrophobic side chains distribute on both faces; short parallel sheets (≤4 strands) are rare, consistent with lower inherent stability. Beta strands have an inherent right-handed twist, a consequence of the chiral L-amino acid backbone geometry, which propagates into twisted sheet structures, saddle configurations, and β-barrels. β-Barrels, formed from parallel strands in register displaced across the barrel circumference, are prominent in proteins such as triose phosphate isomerase (the TIM barrel) and are not hollow — their interiors are packed with side chains.

Connecting elements link helices and strands and account for approximately half of all residues in globular proteins. Beta-turns (β-bends) are the most common reverse turns, consisting of four residues with a hydrogen bond between the carbonyl oxygen of residue i and the amide hydrogen of residue i+3. Type I turns have φ₂/ψ₂ = −60°/−30° and φ₃/ψ₃ = −90°/0°, favoring glycine or asparagine at position 3; Type II turns have φ₂/ψ₂ = −60°/+120° and φ₃/ψ₃ = +90°/0°, typically placing glycine at position 2. Both types are almost always surface-exposed. Gamma-turns involve three residues (i to i+2 hydrogen bond), while ω-loops are longer, irregular connectors lacking fixed internal hydrogen bonding. Flexible linker sequences rich in polar uncharged residues connect protein domains and enable the rotational dynamics that facilitate binding to partners. Amino acid propensities for secondary structure — quantified by Chou-Fasman values derived from statistical analysis of known protein structures — reflect the structural rationale for helix and sheet preferences and underpin computational secondary structure prediction algorithms.

 

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