# 310 helix

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A 310 helix is a type of secondary structure found in proteins and polypeptides. Of the numerous protein secondary structures present, the 310-helix is the fourth most common type observed; following α-helices, β-sheets and reverse turns. 310-helices constitute nearly 10–15% of all helices in protein secondary structures, and are typically observed as extensions of α-helices found at either their N- or C- termini. Because of the α-helices tendency to consistently fold and unfold, it has been proposed that the 310-helix serves as an intermediary conformation of sorts, and provides insight into the initiation of α-helix folding.

## Discovery

Max Perutz, the head of the Medical Research Council Laboratory of Molecular Biology at the University of Cambridge, wrote the first paper documenting the elusive 310-helix. [1] Together with Lawrence Bragg and John Kendrew, Perutz published an exploration of polypeptide chain configurations in 1950, based on cues from noncrystalline diffraction data as well as from small molecule crystal structures such as crystalline found in hair. [2] Their proposals included what is now known as the 310 helix, but did not include the two most common structural motifs now known to occur. The following year, Linus Pauling predicted both of those motifs, the alpha helix [3] and the beta sheet, [4] in work which is now compared in significance [1] to Francis Crick and James D. Watson's publication of the DNA double helix. [5] Pauling was highly critical of the helical structures proposed by Bragg, Kendrew, and Perutz, taking a triumphal tone in declaring them all implausible. [1] [3] Perutz describes in his book I wish I'd made you angry sooner [6] the experience of reading Pauling's paper one Saturday morning:

I was thunderstruck by Pauling and Corey's paper. In contrast to Kendrew's and my helices, theirs was free of strain; all of the amide groups were planar and every carbonyl group formed a perfect hydrogen bond with an amino group four residues further along the chain. The structure looked dead right. How could I have missed it?

Max Perutz, 1998, pp.173-175. [6]

Later that day, an idea for an experiment to confirm Pauling's model occurred to Perutz, and he rushed to the lab to carry it out. Within a few hours, he had the evidence to confirm the alpha helix, which he showed to Bragg first thing on Monday. [1] Perutz' confirmation of the alpha helix structure was published in Nature shortly afterwards. [7] The principles applied in the 1950 paper to theoretical polypeptide structures, true of the 310 helix, included: [2]

• The chains are held together by hydrogen bonding between the hydrogen and oxygen atoms of different by nearby amide (peptide) links formed as the amino acids condense to form the polypeptide chain. These form helical arrangements that cannot be uncoiled without breaking the hydrogen bonds.
• Those structures in which all available NH and CO groups are hydrogen bonded are inherently more probable, because their free energy is presumably lower.

The 310 helix was eventually confirmed by Kendrew in his 1958 structure of myoglobin, [8] and was also found in Perutz' 1960 determination of the structure of haemoglobin [9] [10] [11] and in subsequent work on both its deoxygenated [12] [13] and oxygenated forms. [14] [15]

The 310 helix is now known to be the third principal structure to occur in globular proteins, after the α-helix and β-sheet. [16] They are almost always short sections, with nearly 96% containing four or fewer amino acid residues, [17] :44 appearing in places such as the "corners" where α-helices change direction in the myoglobin structure, for example. [8] Longer sections, in the range of seven to eleven residues, have been observed in the voltage sensor segment of voltage-gated potassium channels in the transmembrane domain of certain helical proteins. [18]

## Structure

The amino acids in a 310-helix are arranged in a right-handed helical structure. Each amino acid corresponds to a 120° turn in the helix (i.e., the helix has three residues per turn), and a translation of 2.0 Å (0.20 nm) along the helical axis, and has 10 atoms in the ring formed by making the hydrogen bond. [17] :39 Most importantly, the N-H group of an amino acid forms a hydrogen bond with the C=O group of the amino acid three residues earlier; this repeated i + 3  i hydrogen bonding defines a 310-helix. Similar structures include the α-helix (i + 4  i hydrogen bonding) and the π-helix i + 5  i hydrogen bonding. [17] :44–45 [19]

Residues in long 310-helices adopt (φ, ψ) dihedral angles near (−49°, −26°). Many 310-helices in proteins are short, so deviate from these values. More generally, residues in long 310-helices adopt dihedral angles such that the ψ dihedral angle of one residue and the φ dihedral angle of the next residue sum to roughly −75°. For comparison, the sum of the dihedral angles for an α-helix is roughly −105°, whereas that for a π-helix is roughly −125°. [17] :45

The general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation: [17] :40

${\displaystyle 3\cos \Omega =1-4\cos ^{2}\left({\frac {\varphi +\psi }{2}}\right)}$

and since Ω = 120° for an ideal 310 helix, it follows that φ and ψ should be related by:

${\displaystyle \cos \left({\frac {\varphi +\psi }{2}}\right)={\frac {\sqrt {10}}{4}},}$

consistent with the observed value of φ + ψ near 75°. [17] :44

The dihedral angles in the 310 helix, relative to those of the α helix, could be attributed to the short lengths of these helices anywhere from 3 to 5 residues long, compared with the 10 to 12 residue lengths of their α-helix contemporaries. 310-helices often arise in transitions, leading to typically short residue lengths that result in deviations in their main-chain torsion angle distributions and thus irregularities. Their hydrogen bond networks are distorted when compared with α-helices, contributing to their instability, though the frequent appearance of the 310-helix in natural proteins demonstrate their importance in transitional structures. [19] [20]

## Stability

Through research carried out by Mary Karpen, Pieter De Haseth and Kenneth Neet, [21] factors in the partial stability in 310-helices were uncovered. The helices are most noticeably stabilized by an aspartate residue at the nonpolar N-terminus that interacts with the amide group at the helical N-cap. This electrostatic interaction stabilizes the peptide dipoles in a parallel orientation. Much like the contiguous helical hydrogen bonds that stabilize α-helices, high levels of aspartate are just as equally important in the survival of the 310-helix. High frequency of aspartate in both 310-helix and α-helices is indicative of its helix initiation, but at the same time suggests that it favors stabilization of the 310-helix by inhibiting the propagation of α-helices. [21]

## Related Research Articles

The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located four residues earlier along the protein sequence.

The beta sheet, (β-sheet) is a common motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands) connected laterally by at least two or three backbone hydrogen bonds, forming a generally twisted, pleated sheet. A β-strand is a stretch of polypeptide chain typically 3 to 10 amino acids long with backbone in an extended conformation. The supramolecular association of β-sheets has been implicated in the formation of the fibrils and protein aggregates observed in amyloidosis, notably Alzheimer's disease.

The collagen triple helix or type-2 helix is the primary secondary structure of various types of fibrous collagen, including type I collagen. It consists of a triple helix made of the repetitious amino acid sequence glycine-X-Y, where X and Y are frequently proline or hydroxyproline. Collagen folded into a triple helix is known as tropocollagen. Collagen triple helices are often bundled into fibrils which themselves form larger fibres, as in tendon.

Protein secondary structure is the three dimensional form of local segments of proteins. The two most common secondary structural elements are alpha helices and beta sheets, though beta turns and omega loops occur as well. Secondary structure elements typically spontaneously form as an intermediate before the protein folds into its three dimensional tertiary structure.

Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction is one of the most important goals pursued by computational biology; and it is important in medicine and biotechnology.

A coiled coil is a structural motif in proteins in which 2–7 alpha-helices are coiled together like the strands of a rope. Many coiled coil-type proteins are involved in important biological functions, such as the regulation of gene expression — e.g., transcription factors. Notable examples are the oncoproteins c-Fos and c-jun, as well as the muscle protein tropomyosin.

In biochemistry, a Ramachandran plot, originally developed in 1963 by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan, is a way to visualize energetically allowed regions for backbone dihedral angles ψ against φ of amino acid residues in protein structure. The figure on the left illustrates the definition of the φ and ψ backbone dihedral angles. The ω angle at the peptide bond is normally 180°, since the partial-double-bond character keeps the peptide planar. The figure in the top right shows the allowed φ,ψ backbone conformational regions from the Ramachandran et al. 1963 and 1968 hard-sphere calculations: full radius in solid outline, reduced radius in dashed, and relaxed tau (N-Cα-C) angle in dotted lines. Because dihedral angle values are circular and 0° is the same as 360°, the edges of the Ramachandran plot "wrap" right-to-left and bottom-to-top. For instance, the small strip of allowed values along the lower-left edge of the plot are a continuation of the large, extended-chain region at upper left.

Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers – specifically polypeptides – formed from sequences of amino acids, the monomers of the polymer. A single amino acid monomer may also be called a residue indicating a repeating unit of a polymer. Proteins form by amino acids undergoing condensation reactions, in which the amino acids lose one water molecule per reaction in order to attach to one another with a peptide bond. By convention, a chain under 30 amino acids is often identified as a peptide, rather than a protein. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions such as hydrogen bonding, ionic interactions, Van der Waals forces, and hydrophobic packing. To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional structure. This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo electron microscopy (cryo-EM) and dual polarisation interferometry to determine the structure of proteins.

A leucine zipper is a common three-dimensional structural motif in proteins. They were first described by Landschulz and collaborators in 1988 when they found that an enhancer binding protein had a very characteristic 30-amino acid segment and the display of these amino acid sequences on an idealized alpha helix revealed a periodic repetition of leucine residues at every seventh position over a distance covering eight helical turns. The polypeptide segments containing these periodic arrays of leucine residues were proposed to exist in an alpha-helical conformation and the leucine side chains from one alpha helix interdigitate with those from the alpha helix of a second polypeptide, facilitating dimerization.

"Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid" was the first article published to describe the discovery of the double helix structure of DNA, using X-ray diffraction and the mathematics of a helix transform. It was published by Francis Crick and James D. Watson in the scientific journal Nature on pages 737–738 of its 171st volume.

A turn is an element of secondary structure in proteins where the polypeptide chain reverses its overall direction.

A polyproline helix is a type of protein secondary structure which occurs in proteins comprising repeating proline residues. A left-handed polyproline II helix is formed when sequential residues all adopt (φ,ψ) backbone dihedral angles of roughly and have trans isomers of their peptide bonds. This PPII conformation is also common in proteins and polypeptides with other amino acids apart from proline. Similarly, a more compact right-handed polyproline I helix is formed when sequential residues all adopt (φ,ψ) backbone dihedral angles of roughly and have cis isomers of their peptide bonds. Of the twenty common naturally occurring amino acids, only proline is likely to adopt the cis isomer of the peptide bond, specifically the X-Pro peptide bond; steric and electronic factors heavily favor the trans isomer in most other peptide bonds. However, peptide bonds that replace proline with another N-substituted amino acid are also likely to adopt the cis isomer.

A pi helix is a type of secondary structure found in proteins. Discovered by crystallographer Barbara Low in 1952 and once thought to be rare, short π-helices are found in 15% of known protein structures and are believed to be an evolutionary adaptation derived by the insertion of a single amino acid into an α-helix. Because such insertions are highly destabilizing, the formation of π-helices would tend to be selected against unless it provided some functional advantage to the protein. π-helices therefore are typically found near functional sites of proteins.

In polymer science, the Lifson–Roig model is a helix-coil transition model applied to the alpha helix-random coil transition of polypeptides; it is a refinement of the Zimm–Bragg model that recognizes that a polypeptide alpha helix is only stabilized by a hydrogen bond only once three consecutive residues have adopted the helical conformation. To consider three consecutive residues each with two states, the Lifson–Roig model uses a 4x4 transfer matrix instead of the 2x2 transfer matrix of the Zimm–Bragg model, which considers only two consecutive residues. However, the simple nature of the coil state allows this to be reduced to a 3x3 matrix for most applications.

Alpha sheet is an atypical secondary structure in proteins, first proposed by Linus Pauling and Robert Corey in 1951. The hydrogen bonding pattern in an alpha sheet is similar to that of a beta sheet, but the orientation of the carbonyl and amino groups in the peptide bond units is distinctive; in a single strand, all the carbonyl groups are oriented in the same direction on one side of the pleat, and all the amino groups are oriented in the same direction on the opposite side of the sheet. Thus the alpha sheet accumulates an inherent separation of electrostatic charge, with one edge of the sheet exposing negatively charged carbonyl groups and the opposite edge exposing positively charged amino groups. Unlike the alpha helix and beta sheet, the alpha sheet configuration does not require all component amino acid residues to lie within a single region of dihedral angles; instead, the alpha sheet contains residues of alternating dihedrals in the traditional right-handed (αR) and left-handed (αL) helical regions of Ramachandran space. Although the alpha sheet is only rarely observed in natural protein structures, it has been speculated to play a role in amyloid disease and it was found to be a stable form for amyloidogenic proteins in molecular dynamics simulations. Alpha sheets have also been observed in X-ray crystallography structures of designed peptides.

β turns are the most common form of turns—a type of non-regular secondary structure in proteins that cause a change in direction of the polypeptide chain. They are very common motifs in proteins and polypeptides. Each consists of four amino acid residues. They can be defined in two ways: 1. By the possession of an intra-main-chain hydrogen bond between the CO of residue i and the NH of residue i+3; Alternatively, 2. By having a distance of less than 7Å between the Cα atoms of residues i and i+3. The hydrogen bond criterion is the one most appropriate for everyday use, partly because it gives rise to four distinct categories; the distance criterion gives rise to the same four categories but yields additional turn types.

Schellman loops are commonly occurring structural features of proteins and polypeptides. Each has six amino acid residues with two specific inter-mainchain hydrogen bonds and a characteristic main chain dihedral angle conformation. The CO group of residue i is hydrogen-bonded to the NH of residue i+5, and the CO group of residue i+1 is hydrogen-bonded to the NH of residue i+4. Residues i+1, i+2, and i+3 have negative φ (phi) angle values and the phi value of residue i+4 is positive. Schellman loops incorporate a three amino acid residue RL nest, in which three mainchain NH groups form a concavity for hydrogen bonding to carbonyl oxygens. About 2.5% of amino acids in proteins belong to Schellman loops. Two websites are available for examining small motifs in proteins, Motivated Proteins: ; or PDBeMotif:.

The Asx turn is a structural feature in proteins and polypeptides. It consists of three amino acid residues in which residue i is an aspartate (Asp) or asparagine (Asn) that forms a hydrogen bond from its sidechain CO group to the mainchain NH group of residue i+2. About 14% of Asx residues present in proteins belong to Asx turns.

The beta bend ribbon, or beta-bend ribbon, is a structural feature in polypeptides and proteins. The shortest possible has six amino acid residues arranged as two overlapping hydrogen bonded beta turns in which the carbonyl group of residue i is hydrogen-bonded to the NH of residue i+3 while the carbonyl group of residue i+2 is hydrogen-bonded to the NH of residue i+5. In longer ribbons, this bonding is continued in peptides of 8, 10, etc., amino acid residues. A beta bend ribbon can be regarded as an aberrant 310 helix (3/10-helix) that has lost some of its hydrogen bonds. Two websites are available to facilitate finding and examining these features in proteins: Motivated Proteins; and PDBeMotif.

The term N cap describes an amino acid in a particular position within a protein or polypeptide. The N cap residue of an alpha helix is the first amino acid residue at the N terminus of the helix. More precisely, it is defined as the first residue (i) whose CO group is hydrogen-bonded to the NH group of residue i+4. Because of this it is sometimes also described as the residue prior to the helix.

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