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| [[Image:Pi helix neg55 neg70 sideview.png|thumb|right|250px|Side view of a standard π-helix of L-[[alanine]] residues in [[atom]]ic detail. Two [[hydrogen bond]]s to the same [[peptide bond|peptide group]] are highlighted in magenta; the oxygen-hydrogen distance is 1.65 Å (165 pm). The [[protein]] chain runs upwards, i.e., its N-terminus is at the bottom and its C-terminus at the top of the figure. Note that the sidechains point slightly ''downwards'', i.e., towards the N-terminus.]]
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| A '''pi helix''' (or '''π-helix''') is a type of [[secondary structure]] found in [[protein]]s.<ref name="pmid14816373">{{cite journal |doi=10.1073/pnas.37.4.205 |author=Pauling L, Corey RB, Branson HR |year=1951 |title=The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=37 |issue=4 |pages=205–211 |pmid=14816373 |pmc=1063337}}</ref> Although thought to be rare, π-helices are actually 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]].<ref name="pmid20888342">{{cite journal |doi=10.1016/j.jmb.2010.09.034 |author=Cooley RB, Arp DJ, Karplus PA |year=2010 |title=Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality|journal=J Mol Biol |volume=404 |issue=2 |pages=232–246 |pmid=20888342 |pmc=2981643}}</ref> Because such insertions are highly destabilizing,<ref name="pmid8475069">{{cite journal |author=Keefe LJ, Sondek J, Shortle D, and Lattman EE |year=2000 |title=The alpha aneurism: a structural motif revealed in an insertion mutant of staphylococcal nuclease|journal=Proc. Natl. Acad. Sci. U.S.A. |volume=90 |issue=8 |pages=3275–3279 |pmid=8475069 |pmc=46282 |doi=10.1073/pnas.90.8.3275}}</ref> 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.<ref name="pmid20888342" /><ref name="pmid10739264">{{cite journal |author=Weaver TM |year=2000 |title=The pi-helix translates structure into function|journal=[[Protein Science]] |volume=9 |issue=1 |pages=201–206 |pmid=10739264 |pmc=2144447 |doi=10.1110/ps.9.1.201}}</ref><ref name="pmid12034854">{{cite journal |author=Fodje MN, Al-Karadaghi S |year=2002 |title=Occurrence, conformational features and amino acid propensities for the pi-helix|journal=Protein Eng |volume=15 |issue=5 |pages=353–358 |pmid=12034854 |doi=10.1093/protein/15.5.353 }}</ref>
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| ==Standard structure==
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| The [[amino acid]]s in a standard π-helix are arranged in a right-handed [[helix|helical]] structure. Each amino acid corresponds to an 87° turn in the helix (i.e., the helix has 4.1 residues per turn), and a translation of 1.15 [[Ångström|Å]] (=0.115 [[Nanometre|nm]]) along the helical axis. Most importantly, the [[amine|N-H]] group of an amino acid forms a [[hydrogen bond]] with the [[carbonyl|C=O]] group of the amino acid ''five'' residues earlier; this repeated ''i''+5→''i'' hydrogen bonding '''defines''' a π-helix. Similar structures include the [[310 helix|3<sub>10</sub> helix]] (''i''+3→''i'' hydrogen bonding) and the [[Alpha helix|α-helix]] (''i''+4→''i'' hydrogen bonding).
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| [[Image:Pi helix topview.png|thumb|left|150px|Top view of the same helix shown above. Four [[carbonyl]] groups are pointing upwards towards the viewer, spaced roughly 87° apart on the circle, corresponding to 4.1 [[amino acid|amino-acid]] residues per turn of the helix.]]
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| The majority of π-helices are only 7 residues in length and do not adopt regularly repeating (φ, ψ) [[dihedral angle]]s throughout the entire structure like that of α-helices or β-sheets. Because of this, textbooks that provide single dihedral values for all residues in the π-helix are misleading. Some generalizations can be made, however. When the first and last residue pairs are excluded, dihedral angles exist such that the ψ [[dihedral angle]] of one residue and the φ dihedral angle of the ''next'' residue sum to roughly -125°. The first and last residue pairs sum to -95° and -105°, respectively. For comparison, the sum of the dihedral angles for a 3<sub>10</sub> helix is roughly -75°, whereas that for the α-helix is roughly -105°. Proline is often seen immediately following the end of π-helices. The general formula for the rotation angle Ω per residue of any polypeptide helix with ''trans'' isomers is given by the equation
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| :<math>
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| 3 \cos \Omega = 1 - 4 \cos^{2} \left[ \left(\phi + \psi \right)/2 \right]
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| </math>
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| ==Left-handed structure==
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| In principle, a left-handed version of the π-helix is possible by reversing the sign of the (φ, ψ) [[dihedral angle]]s to (55°, 70°). This pseudo-"mirror-image" helix has roughly the same number of residues per turn (4.1) and helical pitch (1.5 angstroms or 150 [[picometer]]s). It is not a true mirror image, because the [[amino acid|amino-acid]] residues still have a left-handed [[chirality (chemistry)|chirality]]. <!-- Need to make the image, and check whether hydrogen bonds are still made. --> A long left-handed π-helix is unlikely to be observed in proteins because, among the naturally occurring amino acids, only [[glycine]] is likely to adopt positive φ dihedral angles such as 55°.
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| ==π-helices in nature==
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| [[File:Pi-helix within an alpha-helix.jpg|thumb|left|A short, 7 residue π-helix (orange) is embedded within a longer, α-helix (green). The "bulge" of the π-helix can be clearly seen, and was created as the result of a single amino acid that has been inserted into an α-helix. PBD code 3QHB.]]
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| Commonly used automated secondary structure assignment programs, such as [[DSSP (protein)|DSSP]], suggest <1% of proteins contain a π-helix. This mis-characterization results from the fact that naturally occurring π-helices are typically short in length (7-10 residues) and are almost always associated with (i.e. flanked by) α-helices on either end. Nearly all π-helices are therefore cryptic in that the π-helical residues are incorrectly assigned as either α-helical or as "turns". Recently developed programs have been written to properly annotate π-helices in protein structures and they have found that 1 in 6 proteins (~15%) do in fact contain at least one π-helical segment.<ref name="pmid20888342"/>
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| Natural π-helices can easily be identified in a structure as a "bulge" within a longer α-helix. Such helical bulges have previously been referred to as α-aneurisms, α-bulges, π-bulges, wide-turns,looping outs and π-turns, but in fact are π-helices as determined by their repeating ''i''+5→''i'' hydrogen bonds.<ref name="pmid20888342"/> Evidence suggests that these bulges, or π-helices, are created by the insertion of a single additional amino acid into a pre-existing α-helix. Thus, α-helices and π-helices can be inter-converted by the insertion and deletion of a single amino acid.<ref name="pmid20888342"/><ref name="pmid8475069"/> Given both the relatively high rate of occurrence of π-helices and their noted associtation with functional sites (i.e. active sites) of proteins, this ability to inter-convert between α-helices and π-helices has been an important mechanism of altering and diversifying protein functionality over the course of evolution.<ref name="pmid20888342"/>
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| One of the most notable group of proteins whose functional diversification appears to have been heavily influenced by such an evolutionary mechanism is the ferritin-like superfamily, which includes [[ferritin]]s, [[bacterioferritin]]s, rubrerythrins, class I [[ribonucleotide reductase]]s and [[Methane monooxygenase#Soluble methane Monooxygenase .28MMO.29 Systems|soluble methane monooxygenases]]. Soluble methane monooxygenase is the current record holder for the most number of π-helices in a single enzyme with 13 (PDB code 1MTY). However, the bacterial homologue of a Na+/Cl− dependent neurotransmitter transporter (PDB code 2A65) holds the record for the most number of π-helices in a single peptide chain with 8.<ref name="pmid20888342"/>
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| ==See also==
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| * [[alpha helix]]
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| * [[3 10 helix]]
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| * [[secondary structure]]
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| == References ==
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| {{reflist}}
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| {{Protein secondary structure}}
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| [[Category:Protein structural motifs]]
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| [[Category:Helices]]
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