Pi helix

<h2 id="standard-structure">Standard structure</h2>
The <a href="/facts/Amino_acid/WDxYwBny">amino acids</a> in a standard π-helix are arranged in a right-handed <a href="/facts/Helix/BqC4AKwL">helical</a> 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 <a href="/facts/%25C3%2585ngstr%25C3%25B6m/T5mjdd97">Å</a> (0.115 <a href="/facts/Nanometre/a98sjHyu">nm</a>) along the helical axis. Most importantly, the <a href="/facts/Amine/JvfYJfP6">N-H</a> group of an amino acid forms a <a href="/facts/Hydrogen_bond/85V86IIg">hydrogen bond</a> with the <a href="/facts/Carbonyl/KJ71bo3X">C=O</a> group of the amino acid five residues earlier; this repeated i + 5 → i hydrogen bonding defines a π-helix. Similar structures include the <a href="/facts/310_helix/2S3njI8s">310 helix</a> (i + 3 → i hydrogen bonding) and the <a href="/facts/Alpha_helix/7CESPIYJ">α-helix</a> (i + 4 → i hydrogen bonding).

The majority of π-helices are only 7 residues in length and do adopt regularly repeating (φ, ψ) <a href="/facts/Dihedral_angle/C9WEJsuS">dihedral angles</a> 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 <a href="/facts/Dihedral_angle/C9WEJsuS">dihedral angle</a> 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 310 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

3
        cos
        ⁡
        Ω
        =
        1
        −
        4
        
          cos
          
            2
          
        
        ⁡
        
          (
          
            
              
                ϕ
                +
                ψ
              
              2
            
          
          )
        
        .
      
    
    {\displaystyle 3\cos \Omega =1-4\cos ^{2}\left({\frac {\phi +\psi }{2}}\right).}

<h2 id="left-handed-structure">Left-handed structure</h2>
In principle, a left-handed version of the π-helix is possible by reversing the sign of the (φ, ψ) <a href="/facts/Dihedral_angle/C9WEJsuS">dihedral angles</a> to (55°, 70°). This pseudo-"mirror-image" helix has roughly the same number of residues per turn (4.1) and helical pitch (1.5 Å [150 pm]). It is not a true mirror image, because the <a href="/facts/Amino_acid/WDxYwBny">amino-acid</a> residues still have a left-handed <a href="/facts/Chirality_(chemistry)/p5a9pftB">chirality</a>. A long left-handed π-helix is unlikely to be observed in proteins because, among the naturally occurring amino acids, only <a href="/facts/Glycine/3nXI1hqW">glycine</a> is likely to adopt positive φ dihedral angles such as 55°.

<h2 id="-helices-in-nature">π-helices in nature</h2>

Commonly used automated secondary structure assignment programs, such as <a href="/facts/DSSP_(algorithm)/U9pEU7SJ">DSSP</a>, 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 to 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 (around 15%) do in fact contain at least one π-helical segment.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a>
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.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> 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.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a><a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> Given both the relatively high rate of occurrence of π-helices and their noted association with functional sites (i.e. active sites) of proteins, this ability to interconvert between α-helices and π-helices has been an important mechanism of altering and diversifying protein functionality over the course of evolution.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a>
One of the most notable group of proteins whose functional diversification appears to have been heavily influenced by such an evolutionary mechanism is the <a href="/facts/Ferritin/w7G85xJg">ferritin</a>-like superfamily, which includes <a href="/facts/Ferritin/w7G85xJg">ferritins</a>, <a href="/facts/Bacterioferritin/55lW84uw">bacterioferritins</a>, <a href="/facts/Rubrerythrin/0Cx7HYqr">rubrerythrins</a>, class I <a href="/facts/Ribonucleotide_reductase/DlS3f14z">ribonucleotide reductases</a> and <a href="/facts/Methane_monooxygenase/7p7dTntP">soluble methane monooxygenases</a>. Soluble methane monooxygenase is the current record holder for the most number of π-helices in a single enzyme with 13 (<a href="/facts/Protein_Data_Bank/oUhq4ABD">PDB</a> code 1MTY). However, the bacterial homologue of a Na+/Cl− dependent neurotransmitter transporter (PDB code 2A65) holds the record for the most π-helices in a single peptide chain with 8.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Alpha_helix/7CESPIYJ">alpha helix</a></li>
<li><a href="/facts/3_10_helix/2S3njI8s">310 helix</a></li>
<li><a href="/facts/Secondary_structure/VaN6MEYh">secondary structure</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">"(IUCr) Barbara Wharton Low (1920-2019)". www.iucr.org. Retrieved 2019-10-02. <a href="https://www.iucr.org/news/newsletter/volume-27/number-2/barbara-w.-low-1920-2019" target="_blank">https://www.iucr.org/news/newsletter/volume-27/number-2/barbara-w.-low-1920-2019</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Keefe LJ, Sondek J, Shortle D, Lattman EE (2000). "The alpha aneurism: a structural motif revealed in an insertion mutant of staphylococcal nuclease". Proc. Natl. Acad. Sci. U.S.A. 90 (8): 3275–3279. doi:10.1073/pnas.90.8.3275. PMC 46282. PMID 8475069. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC46282" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC46282</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Weaver TM (2000). "The pi-helix translates structure into function". Protein Science. 9 (1): 201–206. doi:10.1110/ps.9.1.201. PMC 2144447. PMID 10739264. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2144447" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2144447</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Fodje MN, Al-Karadaghi S (2002). "Occurrence, conformational features and amino acid propensities for the pi-helix". Protein Eng. 15 (5): 353–358. doi:10.1093/protein/15.5.353. PMID 12034854. <a href="https://doi.org/10.1093%2Fprotein%2F15.5.353" target="_blank">https://doi.org/10.1093%2Fprotein%2F15.5.353</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Mohapatra, Samar Bhallabha; Manoj, Narayanan (January 2021). "A conserved π-helix plays a key role in thermoadaptation of catalysis in the glycoside hydrolase family 4". Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics. 1869 (1): 140523. doi:10.1016/j.bbapap.2020.140523. PMID 32853774. S2CID 221358131. <a href="https://linkinghub.elsevier.com/retrieve/pii/S1570963920301709" target="_blank">https://linkinghub.elsevier.com/retrieve/pii/S1570963920301709</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Keefe LJ, Sondek J, Shortle D, Lattman EE (2000). "The alpha aneurism: a structural motif revealed in an insertion mutant of staphylococcal nuclease". Proc. Natl. Acad. Sci. U.S.A. 90 (8): 3275–3279. doi:10.1073/pnas.90.8.3275. PMC 46282. PMID 8475069. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC46282" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC46282</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Cooley RB, Arp DJ, Karplus PA (2010). "Evolutionary origin of a secondary structure: π-helices as cryptic but widespread insertional variations of α-helices enhancing protein functionality". J Mol Biol. 404 (2): 232–246. doi:10.1016/j.jmb.2010.09.034. PMC 2981643. PMID 20888342. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981643</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
</ol>

Pi helix open-in-new

Pi helix