An Exploration of the Universe of Polyglutamine Structures
Identifieur interne : 000F85 ( Pmc/Corpus ); précédent : 000F84; suivant : 000F86An Exploration of the Universe of Polyglutamine Structures
Auteurs : Àngel G Mez-Sicilia ; Mateusz Sikora ; Marek Cieplak ; Mariano Carri N-VázquezSource :
- PLoS Computational Biology [ 1553-734X ] ; 2015.
Abstract
Deposits of misfolded proteins in the human brain are associated with the development of many neurodegenerative diseases. Recent studies show that these proteins have common traits even at the monomer level. Among them, a polyglutamine region that is present in huntingtin is known to exhibit a correlation between the length of the chain and the severity as well as the earliness of the onset of Huntington disease. Here, we apply bias exchange molecular dynamics to generate structures of polyglutamine expansions of several lengths and characterize the resulting independent conformations. We compare the properties of these conformations to those of the standard proteins, as well as to other homopolymeric tracts. We find that, similar to the previously studied polyvaline chains, the set of possible transient folds is much broader than the set of known-to-date folds, although the conformations have different structures. We show that the mechanical stability is not related to any simple geometrical characteristics of the structures. We demonstrate that long polyglutamine expansions result in higher mechanical stability than the shorter ones. They also have a longer life span and are substantially more prone to form knotted structures. The knotted region has an average length of 35 residues, similar to the typical threshold for most polyglutamine-related diseases. Similarly, changes in shape and mechanical stability appear once the total length of the peptide exceeds this threshold of 35 glutamine residues. We suggest that knotted conformers may also harm the cellular machinery and thus lead to disease.
Url:
DOI: 10.1371/journal.pcbi.1004541
PubMed: 26495838
PubMed Central: 4619799
Links to Exploration step
PMC:4619799Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">An Exploration of the Universe of Polyglutamine Structures</title><author><name sortKey="G Mez Sicilia, Angel" sort="G Mez Sicilia, Angel" uniqKey="G Mez Sicilia A" first="Àngel" last="G Mez-Sicilia">Àngel G Mez-Sicilia</name><affiliation><nlm:aff id="aff001"><addr-line>Intituto Cajal/CSIC, Madrid, Spain</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff002"><addr-line>Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nanociencia),Madrid, Spain</addr-line></nlm:aff></affiliation></author><author><name sortKey="Sikora, Mateusz" sort="Sikora, Mateusz" uniqKey="Sikora M" first="Mateusz" last="Sikora">Mateusz Sikora</name><affiliation><nlm:aff id="aff003"><addr-line>Institute of Science and Technology Austria, Klosterneuburg, Austria</addr-line></nlm:aff></affiliation></author><author><name sortKey="Cieplak, Marek" sort="Cieplak, Marek" uniqKey="Cieplak M" first="Marek" last="Cieplak">Marek Cieplak</name><affiliation><nlm:aff id="aff004"><addr-line>Instytut Fizyki PAN, Warsaw, Poland</addr-line></nlm:aff></affiliation></author><author><name sortKey="Carri N Vazquez, Mariano" sort="Carri N Vazquez, Mariano" uniqKey="Carri N Vazquez M" first="Mariano" last="Carri N-Vázquez">Mariano Carri N-Vázquez</name><affiliation><nlm:aff id="aff001"><addr-line>Intituto Cajal/CSIC, Madrid, Spain</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff002"><addr-line>Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nanociencia),Madrid, Spain</addr-line></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">26495838</idno><idno type="pmc">4619799</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4619799</idno><idno type="RBID">PMC:4619799</idno><idno type="doi">10.1371/journal.pcbi.1004541</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000F85</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000F85</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">An Exploration of the Universe of Polyglutamine Structures</title><author><name sortKey="G Mez Sicilia, Angel" sort="G Mez Sicilia, Angel" uniqKey="G Mez Sicilia A" first="Àngel" last="G Mez-Sicilia">Àngel G Mez-Sicilia</name><affiliation><nlm:aff id="aff001"><addr-line>Intituto Cajal/CSIC, Madrid, Spain</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff002"><addr-line>Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nanociencia),Madrid, Spain</addr-line></nlm:aff></affiliation></author><author><name sortKey="Sikora, Mateusz" sort="Sikora, Mateusz" uniqKey="Sikora M" first="Mateusz" last="Sikora">Mateusz Sikora</name><affiliation><nlm:aff id="aff003"><addr-line>Institute of Science and Technology Austria, Klosterneuburg, Austria</addr-line></nlm:aff></affiliation></author><author><name sortKey="Cieplak, Marek" sort="Cieplak, Marek" uniqKey="Cieplak M" first="Marek" last="Cieplak">Marek Cieplak</name><affiliation><nlm:aff id="aff004"><addr-line>Instytut Fizyki PAN, Warsaw, Poland</addr-line></nlm:aff></affiliation></author><author><name sortKey="Carri N Vazquez, Mariano" sort="Carri N Vazquez, Mariano" uniqKey="Carri N Vazquez M" first="Mariano" last="Carri N-Vázquez">Mariano Carri N-Vázquez</name><affiliation><nlm:aff id="aff001"><addr-line>Intituto Cajal/CSIC, Madrid, Spain</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff002"><addr-line>Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nanociencia),Madrid, Spain</addr-line></nlm:aff></affiliation></author></analytic><series><title level="j">PLoS Computational Biology</title><idno type="ISSN">1553-734X</idno><idno type="eISSN">1553-7358</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Deposits of misfolded proteins in the human brain are associated with the development of many neurodegenerative diseases. Recent studies show that these proteins have common traits even at the monomer level. Among them, a polyglutamine region that is present in huntingtin is known to exhibit a correlation between the length of the chain and the severity as well as the earliness of the onset of Huntington disease. Here, we apply bias exchange molecular dynamics to generate structures of polyglutamine expansions of several lengths and characterize the resulting independent conformations. We compare the properties of these conformations to those of the standard proteins, as well as to other homopolymeric tracts. We find that, similar to the previously studied polyvaline chains, the set of possible transient folds is much broader than the set of known-to-date folds, although the conformations have different structures. We show that the mechanical stability is not related to any simple geometrical characteristics of the structures. We demonstrate that long polyglutamine expansions result in higher mechanical stability than the shorter ones. They also have a longer life span and are substantially more prone to form knotted structures. The knotted region has an average length of 35 residues, similar to the typical threshold for most polyglutamine-related diseases. Similarly, changes in shape and mechanical stability appear once the total length of the peptide exceeds this threshold of 35 glutamine residues. We suggest that knotted conformers may also harm the cellular machinery and thus lead to disease.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Chothia, C" uniqKey="Chothia C">C Chothia</name></author><author><name sortKey="Finkelstein, Av" uniqKey="Finkelstein A">AV Finkelstein</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chothia, C" uniqKey="Chothia C">C Chothia</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sillitoe, I" uniqKey="Sillitoe I">I Sillitoe</name></author><author><name sortKey="Cuff, Al" uniqKey="Cuff A">AL Cuff</name></author><author><name sortKey="Dessailly, Bh" uniqKey="Dessailly B">BH Dessailly</name></author><author><name sortKey="Dawson, Nl" uniqKey="Dawson N">NL Dawson</name></author><author><name sortKey="Furnham, N" uniqKey="Furnham N">N Furnham</name></author><author><name sortKey="Lee, D" uniqKey="Lee D">D Lee</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cossio, P" uniqKey="Cossio P">P Cossio</name></author><author><name sortKey="Trovato, A" uniqKey="Trovato A">A Trovato</name></author><author><name sortKey="Pietrucci, F" uniqKey="Pietrucci F">F Pietrucci</name></author><author><name sortKey="Seno, F" uniqKey="Seno F">F Seno</name></author><author><name sortKey="Maritan, A" uniqKey="Maritan A">A Maritan</name></author><author><name sortKey="Laio, A" uniqKey="Laio A">A Laio</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhang, Y" uniqKey="Zhang Y">Y Zhang</name></author><author><name sortKey="Skolnick, J" uniqKey="Skolnick J">J Skolnick</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Magrane, M" uniqKey="Magrane M">M Magrane</name></author><author><name sortKey="Consortium, U" uniqKey="Consortium U">U Consortium</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nasir, J" uniqKey="Nasir J">J Nasir</name></author><author><name sortKey="Floresco, Sb" uniqKey="Floresco S">SB Floresco</name></author><author><name sortKey="O Usky, Jr" uniqKey="O Usky J">JR O’Kusky</name></author><author><name sortKey="Diewert, Vm" uniqKey="Diewert V">VM Diewert</name></author><author><name sortKey="Richman, Jm" uniqKey="Richman J">JM Richman</name></author><author><name sortKey="Zeisler, J" uniqKey="Zeisler J">J Zeisler</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zuccato, C" uniqKey="Zuccato C">C Zuccato</name></author><author><name sortKey="Ciammola, A" uniqKey="Ciammola A">A Ciammola</name></author><author><name sortKey="Rigamonti, D" uniqKey="Rigamonti D">D Rigamonti</name></author><author><name sortKey="Leavitt, Br" uniqKey="Leavitt B">BR Leavitt</name></author><author><name sortKey="Goffredo, D" uniqKey="Goffredo D">D Goffredo</name></author><author><name sortKey="Conti, L" uniqKey="Conti L">L Conti</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Velier, J" uniqKey="Velier J">J Velier</name></author><author><name sortKey="Kim, M" uniqKey="Kim M">M Kim</name></author><author><name sortKey="Schwarz, C" uniqKey="Schwarz C">C Schwarz</name></author><author><name sortKey="Kim, Tw" uniqKey="Kim T">TW Kim</name></author><author><name sortKey="Sapp, E" uniqKey="Sapp E">E Sapp</name></author><author><name sortKey="Chase, K" uniqKey="Chase K">K Chase</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Petruska, J" uniqKey="Petruska J">J Petruska</name></author><author><name sortKey="Hartenstine, Mj" uniqKey="Hartenstine M">MJ Hartenstine</name></author><author><name sortKey="Goodman, Mf" uniqKey="Goodman M">MF Goodman</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ross, Ca" uniqKey="Ross C">CA Ross</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pla, P" uniqKey="Pla P">P Pla</name></author><author><name sortKey="Orvoen, S" uniqKey="Orvoen S">S Orvoen</name></author><author><name sortKey="Saudou, F" uniqKey="Saudou F">F Saudou</name></author><author><name sortKey="David, Dj" uniqKey="David D">DJ DAVID</name></author><author><name sortKey="Humbert, S" uniqKey="Humbert S">S Humbert</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Fan, Hc" uniqKey="Fan H">HC Fan</name></author><author><name sortKey="Ho, Li" uniqKey="Ho L">LI Ho</name></author><author><name sortKey="Chi, Cs" uniqKey="Chi C">CS Chi</name></author><author><name sortKey="Chen, Sj" uniqKey="Chen S">SJ Chen</name></author><author><name sortKey="Peng, Gs" uniqKey="Peng G">GS Peng</name></author><author><name sortKey="Chan, Tm" uniqKey="Chan T">TM Chan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Albrecht, A" uniqKey="Albrecht A">A Albrecht</name></author><author><name sortKey="Mundlos, S" uniqKey="Mundlos S">S Mundlos</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Amiel, J" uniqKey="Amiel J">J Amiel</name></author><author><name sortKey="Trochet, D" uniqKey="Trochet D">D Trochet</name></author><author><name sortKey="Clement Ziza, M" uniqKey="Clement Ziza M">M Clément-Ziza</name></author><author><name sortKey="Munnich, A" uniqKey="Munnich A">A Munnich</name></author><author><name sortKey="Lyonnet, S" uniqKey="Lyonnet S">S Lyonnet</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hervas, R" uniqKey="Hervas R">R Hervás</name></author><author><name sortKey="Oroz, J" uniqKey="Oroz J">J Oroz</name></author><author><name sortKey="Galera Prat, A" uniqKey="Galera Prat A">A Galera-Prat</name></author><author><name sortKey="Go I, O" uniqKey="Go I O">O Goñi</name></author><author><name sortKey="Valbuena, A" uniqKey="Valbuena A">A Valbuena</name></author><author><name sortKey="Vera, Am" uniqKey="Vera A">AM Vera</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Piana, S" uniqKey="Piana S">S Piana</name></author><author><name sortKey="Laio, A" uniqKey="Laio A">A Laio</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sulkowska, Ji" uniqKey="Sulkowska J">JI Sułkowska</name></author><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sikora, M" uniqKey="Sikora M">M Sikora</name></author><author><name sortKey="Sulkowska, Ji" uniqKey="Sulkowska J">JI Sułkowska</name></author><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ferreon, Acm" uniqKey="Ferreon A">ACM Ferreon</name></author><author><name sortKey="Moran, Cr" uniqKey="Moran C">CR Moran</name></author><author><name sortKey="Gambin, Y" uniqKey="Gambin Y">Y Gambin</name></author><author><name sortKey="Deniz, Aa" uniqKey="Deniz A">AA Deniz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hess, B" uniqKey="Hess B">B Hess</name></author><author><name sortKey="Kutzner, C" uniqKey="Kutzner C">C Kutzner</name></author><author><name sortKey="Van Der Spoel, D" uniqKey="Van Der Spoel D">D van der Spoel</name></author><author><name sortKey="Lindahl, E" uniqKey="Lindahl E">E Lindahl</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bonomi, M" uniqKey="Bonomi M">M Bonomi</name></author><author><name sortKey="Branduardi, D" uniqKey="Branduardi D">D Branduardi</name></author><author><name sortKey="Bussi, G" uniqKey="Bussi G">G Bussi</name></author><author><name sortKey="Camilloni, C" uniqKey="Camilloni C">C Camilloni</name></author><author><name sortKey="Provasi, D" uniqKey="Provasi D">D Provasi</name></author><author><name sortKey="Raiteri, P" uniqKey="Raiteri P">P Raiteri</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cornell, Wd" uniqKey="Cornell W">WD Cornell</name></author><author><name sortKey="Cieplak, P" uniqKey="Cieplak P">P Cieplak</name></author><author><name sortKey="Bayly, Ci" uniqKey="Bayly C">CI Bayly</name></author><author><name sortKey="Gould, Ir" uniqKey="Gould I">IR Gould</name></author><author><name sortKey="Merz, Km" uniqKey="Merz K">KM Merz</name></author><author><name sortKey="Ferguson, Dm" uniqKey="Ferguson D">DM Ferguson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Qiu, D" uniqKey="Qiu D">D Qiu</name></author><author><name sortKey="Shenkin, Ps" uniqKey="Shenkin P">PS Shenkin</name></author><author><name sortKey="Hollinger, Fp" uniqKey="Hollinger F">FP Hollinger</name></author><author><name sortKey="Still, Wc" uniqKey="Still W">WC Still</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pietrucci, F" uniqKey="Pietrucci F">F Pietrucci</name></author><author><name sortKey="Laio, A" uniqKey="Laio A">A Laio</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Eswar, N" uniqKey="Eswar N">N Eswar</name></author><author><name sortKey="Webb, B" uniqKey="Webb B">B Webb</name></author><author><name sortKey="Marti Renom, Ma" uniqKey="Marti Renom M">MA Marti-Renom</name></author><author><name sortKey="Madhusudhan, Ms" uniqKey="Madhusudhan M">MS Madhusudhan</name></author><author><name sortKey="Eramian, D" uniqKey="Eramian D">D Eramian</name></author><author><name sortKey="Shen, My" uniqKey="Shen M">My Shen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hestenes, Mr" uniqKey="Hestenes M">MR Hestenes</name></author><author><name sortKey="Stiefel, E" uniqKey="Stiefel E">E Stiefel</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Miettinen, Ms" uniqKey="Miettinen M">MS Miettinen</name></author><author><name sortKey="Knecht, V" uniqKey="Knecht V">V Knecht</name></author><author><name sortKey="Monticelli, L" uniqKey="Monticelli L">L Monticelli</name></author><author><name sortKey="Ignatova, Z" uniqKey="Ignatova Z">Z Ignatova</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Khare, Sd" uniqKey="Khare S">SD Khare</name></author><author><name sortKey="Ding, F" uniqKey="Ding F">F Ding</name></author><author><name sortKey="Gwanmesia, Kn" uniqKey="Gwanmesia K">KN Gwanmesia</name></author><author><name sortKey="Dokholyan, Nv" uniqKey="Dokholyan N">NV Dokholyan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Laghaei, R" uniqKey="Laghaei R">R Laghaei</name></author><author><name sortKey="Mousseau, N" uniqKey="Mousseau N">N Mousseau</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author><author><name sortKey="Allan, Db" uniqKey="Allan D">DB Allan</name></author><author><name sortKey="Leheny, Rl" uniqKey="Leheny R">RL Leheny</name></author><author><name sortKey="Reich, Dh" uniqKey="Reich D">DH Reich</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sikora, M" uniqKey="Sikora M">M Sikora</name></author><author><name sortKey="Szymczak, P" uniqKey="Szymczak P">P Szymczak</name></author><author><name sortKey="Thompson, D" uniqKey="Thompson D">D Thompson</name></author><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Joosten, Rp" uniqKey="Joosten R">RP Joosten</name></author><author><name sortKey="Te Beek, Tah" uniqKey="Te Beek T">TAH te Beek</name></author><author><name sortKey="Krieger, E" uniqKey="Krieger E">E Krieger</name></author><author><name sortKey="Hekkelman, Ml" uniqKey="Hekkelman M">ML Hekkelman</name></author><author><name sortKey="Hooft, Rww" uniqKey="Hooft R">RWW Hooft</name></author><author><name sortKey="Schneider, R" uniqKey="Schneider R">R Schneider</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Tsai, J" uniqKey="Tsai J">J Tsai</name></author><author><name sortKey="Taylor, R" uniqKey="Taylor R">R Taylor</name></author><author><name sortKey="Chothia, C" uniqKey="Chothia C">C Chothia</name></author><author><name sortKey="Gerstein, M" uniqKey="Gerstein M">M Gerstein</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Maxwell, Jc" uniqKey="Maxwell J">JC Maxwell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author><author><name sortKey="Robbins, Mo" uniqKey="Robbins M">MO Robbins</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sulkowska, Ji" uniqKey="Sulkowska J">JI Sułkowska</name></author><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Plaxco, Kw" uniqKey="Plaxco K">KW Plaxco</name></author><author><name sortKey="Simons, Kt" uniqKey="Simons K">KT Simons</name></author><author><name sortKey="Baker, D" uniqKey="Baker D">D Baker</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kesner, Ba" uniqKey="Kesner B">BA Kesner</name></author><author><name sortKey="Ding, F" uniqKey="Ding F">F Ding</name></author><author><name sortKey="Temple, Br" uniqKey="Temple B">BR Temple</name></author><author><name sortKey="Dokholyan, Nv" uniqKey="Dokholyan N">NV Dokholyan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author><author><name sortKey="Hoang, Tx" uniqKey="Hoang T">TX Hoang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Berkovich, R" uniqKey="Berkovich R">R Berkovich</name></author><author><name sortKey="Garcia Manyes, S" uniqKey="Garcia Manyes S">S Garcia-Manyes</name></author><author><name sortKey="Klafter, J" uniqKey="Klafter J">J Klafter</name></author><author><name sortKey="Urbakh, M" uniqKey="Urbakh M">M Urbakh</name></author><author><name sortKey="Fernandez, Jm" uniqKey="Fernandez J">JM Fernández</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Rief, M" uniqKey="Rief M">M Rief</name></author><author><name sortKey="Gautel, M" uniqKey="Gautel M">M Gautel</name></author><author><name sortKey="Oesterhelt, F" uniqKey="Oesterhelt F">F Oesterhelt</name></author><author><name sortKey="Fernandez, Jm" uniqKey="Fernandez J">JM Fernandez</name></author><author><name sortKey="Gaub, He" uniqKey="Gaub H">HE Gaub</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Carrion Vazquez, M" uniqKey="Carrion Vazquez M">M Carrion-Vazquez</name></author><author><name sortKey="Oberhauser, Af" uniqKey="Oberhauser A">AF Oberhauser</name></author><author><name sortKey="Fowler, Sb" uniqKey="Fowler S">SB Fowler</name></author><author><name sortKey="Marszalek, Pe" uniqKey="Marszalek P">PE Marszalek</name></author><author><name sortKey="Broedel, Se" uniqKey="Broedel S">SE Broedel</name></author><author><name sortKey="Clarke, J" uniqKey="Clarke J">J Clarke</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sulkowska, Ji" uniqKey="Sulkowska J">JI Sułkowska</name></author><author><name sortKey="Sulkowski, P" uniqKey="Sulkowski P">P Sułkowski</name></author><author><name sortKey="Szymczak, P" uniqKey="Szymczak P">P Szymczak</name></author><author><name sortKey="Cieplak, M" uniqKey="Cieplak M">M Cieplak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Taylor, Wr" uniqKey="Taylor W">WR Taylor</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Virnau, P" uniqKey="Virnau P">P Virnau</name></author><author><name sortKey="Mirny, La" uniqKey="Mirny L">LA Mirny</name></author><author><name sortKey="Kardar, M" uniqKey="Kardar M">M Kardar</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sulkowska, Ji" uniqKey="Sulkowska J">JI Sułkowska</name></author><author><name sortKey="Rawdon, Ej" uniqKey="Rawdon E">EJ Rawdon</name></author><author><name sortKey="Millett, Kc" uniqKey="Millett K">KC Millett</name></author><author><name sortKey="Onuchic, Jn" uniqKey="Onuchic J">JN Onuchic</name></author><author><name sortKey="Stasiak, A" uniqKey="Stasiak A">A Stasiak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Humphrey, W" uniqKey="Humphrey W">W Humphrey</name></author><author><name sortKey="Dalke, A" uniqKey="Dalke A">A Dalke</name></author><author><name sortKey="Schulten, K" uniqKey="Schulten K">K Schulten</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nagai, Y" uniqKey="Nagai Y">Y Nagai</name></author><author><name sortKey="Inui, T" uniqKey="Inui T">T Inui</name></author><author><name sortKey="Popiel, Ha" uniqKey="Popiel H">HA Popiel</name></author><author><name sortKey="Fujikake, N" uniqKey="Fujikake N">N Fujikake</name></author><author><name sortKey="Hasegawa, K" uniqKey="Hasegawa K">K Hasegawa</name></author><author><name sortKey="Urade, Y" uniqKey="Urade Y">Y Urade</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ripaud, L" uniqKey="Ripaud L">L Ripaud</name></author><author><name sortKey="Chumakova, V" uniqKey="Chumakova V">V Chumakova</name></author><author><name sortKey="Antonin, M" uniqKey="Antonin M">M Antonin</name></author><author><name sortKey="Hastie, Ar" uniqKey="Hastie A">AR Hastie</name></author><author><name sortKey="Pinkert, S" uniqKey="Pinkert S">S Pinkert</name></author><author><name sortKey="Korner, R" uniqKey="Korner R">R Körner</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS Comput Biol</journal-id><journal-id journal-id-type="iso-abbrev">PLoS Comput. Biol</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">ploscomp</journal-id><journal-title-group><journal-title>PLoS Computational Biology</journal-title></journal-title-group><issn pub-type="ppub">1553-734X</issn><issn pub-type="epub">1553-7358</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, CA USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">26495838</article-id><article-id pub-id-type="pmc">4619799</article-id><article-id pub-id-type="publisher-id">PCOMPBIOL-D-15-00695</article-id><article-id pub-id-type="doi">10.1371/journal.pcbi.1004541</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>An Exploration of the Universe of Polyglutamine Structures</article-title><alt-title alt-title-type="running-head">An Exploration of the Universe of Polyglutamine Structures</alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Gómez-Sicilia</surname><given-names>Àngel</given-names></name><xref ref-type="aff" rid="aff001"><sup>1</sup></xref><xref ref-type="aff" rid="aff002"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Sikora</surname><given-names>Mateusz</given-names></name><xref ref-type="aff" rid="aff003"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Cieplak</surname><given-names>Marek</given-names></name><xref ref-type="aff" rid="aff004"><sup>4</sup></xref><xref ref-type="corresp" rid="cor001">*</xref></contrib><contrib contrib-type="author"><name><surname>Carrión-Vázquez</surname><given-names>Mariano</given-names></name><xref ref-type="aff" rid="aff001"><sup>1</sup></xref><xref ref-type="aff" rid="aff002"><sup>2</sup></xref></contrib></contrib-group><aff id="aff001"><label>1</label><addr-line>Intituto Cajal/CSIC, Madrid, Spain</addr-line></aff><aff id="aff002"><label>2</label><addr-line>Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nanociencia),Madrid, Spain</addr-line></aff><aff id="aff003"><label>3</label><addr-line>Institute of Science and Technology Austria, Klosterneuburg, Austria</addr-line></aff><aff id="aff004"><label>4</label><addr-line>Instytut Fizyki PAN, Warsaw, Poland</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Wei</surname><given-names>Guanghong</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1"><addr-line>Fudan University, CHINA</addr-line></aff><author-notes><fn fn-type="COI-statement" id="coi001"><p>The authors have declared that no competing interests exist.</p></fn><fn fn-type="con" id="contrib001"><p>Conceived and designed the experiments: ÀGS MC MCV. Performed the experiments: ÀGS MS. Analyzed the data: ÀGS MC. Contributed reagents/materials/analysis tools: MS MC. Wrote the paper: ÀGS MC MCV MS.</p></fn><corresp id="cor001">* E-mail: <email>mc@ifpan.edu.pl</email></corresp></author-notes><pub-date pub-type="collection"><month>10</month><year>2015</year></pub-date><pub-date pub-type="epub"><day>23</day><month>10</month><year>2015</year></pub-date><volume>11</volume><issue>10</issue><elocation-id>e1004541</elocation-id><history><date date-type="received"><day>30</day><month>4</month><year>2015</year></date><date date-type="accepted"><day>8</day><month>9</month><year>2015</year></date></history><permissions><copyright-statement>© 2015 Gómez-Sicilia et al</copyright-statement><copyright-year>2015</copyright-year><copyright-holder>Gómez-Sicilia et al</copyright-holder><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:type="simple" xlink:href="pcbi.1004541.pdf"></self-uri><abstract><p>Deposits of misfolded proteins in the human brain are associated with the development of many neurodegenerative diseases. Recent studies show that these proteins have common traits even at the monomer level. Among them, a polyglutamine region that is present in huntingtin is known to exhibit a correlation between the length of the chain and the severity as well as the earliness of the onset of Huntington disease. Here, we apply bias exchange molecular dynamics to generate structures of polyglutamine expansions of several lengths and characterize the resulting independent conformations. We compare the properties of these conformations to those of the standard proteins, as well as to other homopolymeric tracts. We find that, similar to the previously studied polyvaline chains, the set of possible transient folds is much broader than the set of known-to-date folds, although the conformations have different structures. We show that the mechanical stability is not related to any simple geometrical characteristics of the structures. We demonstrate that long polyglutamine expansions result in higher mechanical stability than the shorter ones. They also have a longer life span and are substantially more prone to form knotted structures. The knotted region has an average length of 35 residues, similar to the typical threshold for most polyglutamine-related diseases. Similarly, changes in shape and mechanical stability appear once the total length of the peptide exceeds this threshold of 35 glutamine residues. We suggest that knotted conformers may also harm the cellular machinery and thus lead to disease.</p></abstract><abstract abstract-type="summary"><title>Author Summary</title><p>Misfolding and aggregation of several proteins are known to be related to neurodegenerative diseases. Among them, polyglutamine expansions are known to be responsible for at least 9 diseases, including Huntington. Nonetheless, the structural properties of these intrinsically disordered proteins are difficult to study using classical techniques because of their rapid fluctuations that result in high conformational polymorphism. Here, we use molecular dynamics simulations to study polyglutamines of different chain lengths, starting with short non-pathogenic ones, and study the independent structures they are able to form. We characterize all structures by their geometrical properties, connectivity, putative mechanical stability and residence time (life span). Similar to the findings of a previous study with polyvalines, only some of the conformers are similar to those found in natural globular proteins. Moreover, we find structures that contain knots in both polyglutamine and polyvaline 60-mers, although the former contains many more knotted conformers than the latter. We suggest that these knotted conformers may impair the cell machinery for degradation and eventually lead to toxicity.</p></abstract><funding-group><funding-statement>We acknowledge the support by the EU Joint Programme in Neurodegenerative Diseases (JPND AC14/00037) project. The project is supported through the following funding organisations under the aegis of JPND—<ext-link ext-link-type="uri" xlink:href="http://www.jpnd.eu">www.jpnd.eu</ext-link>: Ireland, HRB; Poland, National Science Centre; and Spain, ISCIII. MCV acknowledges a grant by the Spanish Ministry of Economy (MINECO SAF2013-49179-C2-1-R). ÀGS was recipient of JAE-Pre and EMBO Short Term fellowships. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.</funding-statement></funding-group><counts><fig-count count="5"></fig-count><table-count count="0"></table-count><page-count count="17"></page-count></counts><custom-meta-group><custom-meta id="data-availability"><meta-name>Data Availability</meta-name><meta-value>For the studied sets of Qn with n = 16, 20, 25, 30, 33, 38, 40, 60 and 80, as well as for V60, the independent conformers can be found in <ext-link ext-link-type="uri" xlink:href="http://www.ifpan.edu.pl/~cieplak/POLYQ">www.ifpan.edu.pl/~cieplak/POLYQ</ext-link>.</meta-value></custom-meta></custom-meta-group></article-meta><notes><title>Data Availability</title><p>For the studied sets of Qn with n = 16, 20, 25, 30, 33, 38, 40, 60 and 80, as well as for V60, the independent conformers can be found in <ext-link ext-link-type="uri" xlink:href="http://www.ifpan.edu.pl/~cieplak/POLYQ">www.ifpan.edu.pl/~cieplak/POLYQ</ext-link>.</p></notes></front><body><sec sec-type="intro" id="sec001"><title>Introduction</title><p>Less than two thousands protein folds have been identified in nature [<xref rid="pcbi.1004541.ref001" ref-type="bibr">1</xref>, <xref rid="pcbi.1004541.ref002" ref-type="bibr">2</xref>], indicating that similar folds can be adopted by large numbers of sequences. These folds have been characterized and classified in the CATH database [<xref rid="pcbi.1004541.ref003" ref-type="bibr">3</xref>]. Recently, Cossio <italic>et al</italic>. [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>] considered a single sequence—polyvaline (polyV) 60-mer (denoted here as V<sub>60</sub>)—and generated, through all-atom simulations, an exhaustive database with 30 063 conformations. Interestingly, only a small fraction of the V<sub>60</sub> conformations turned out to be CATH-like in that they had at least one similar structure in the CATH database. The similarity was assessed by a TM-score being higher than 45%. The score is obtained through an algorithm for protein comparison based on secondary structure alignment [<xref rid="pcbi.1004541.ref005" ref-type="bibr">5</xref>]. Thus they explored, in their own words [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>], the universe of protein structures beyond the Protein Data Bank. They argued that there must be an evolutionary principle that favors shorter loops and directs the evolution to a certain spot in the universe of possible conformations.</p><p>Long polyV chains do not exist in nature. However, many proteins in eukaryotic cells contain homopolymeric tracts, defined as repetitions of the same residue. In particular, upon inspection of the revised human proteome stored in UniProt Knowledge Database [<xref rid="pcbi.1004541.ref006" ref-type="bibr">6</xref>], we found that 18.9% of the human proteome involves homopolymeric tracts of size 5 or greater, while the probability of one happening by chance is 6 ⋅ 10<sup>−6</sup>. Among these, the longest chains have been found for polyserine (polyS, 58 repeats, in the TNRC18 protein, with a random probability of 4 ⋅ 10<sup>−76</sup>) and polyglutamine (polyQ, 40 repeats, in FOXP2 protein, random probability of 9 ⋅ 10<sup>−53</sup>).</p><p>PolyQ chains are known to be responsible for several brain disorders, including Huntington disease (HD). HD is caused by a protein in the human brain known as huntingtin (HTT)—of, as yet, not fully elucidated function. HTT is known to be highly involved in development [<xref rid="pcbi.1004541.ref007" ref-type="bibr">7</xref>], and is thought to be related to gene expression regulation [<xref rid="pcbi.1004541.ref008" ref-type="bibr">8</xref>] and to anchoring or transport of vesicles [<xref rid="pcbi.1004541.ref009" ref-type="bibr">9</xref>]. A HTT mutant with an expansion of polyQ that exceeds the threshold of about 35-mer was linked to the disease [<xref rid="pcbi.1004541.ref010" ref-type="bibr">10</xref>]. Even though polyQ tracts have been extensively studied [<xref rid="pcbi.1004541.ref011" ref-type="bibr">11</xref>–<xref rid="pcbi.1004541.ref013" ref-type="bibr">13</xref>], the molecular physiopathology behind the connection between sequence length and disease remains elusive.</p><p>Another example of disease-related homopolymeric tracts is polyalanine (polyA), occurring in transcription factors. Expansions of the polyA tracts beyond certain thresholds (<italic>e.g</italic>. 19) have been recognized as the cause of congenital malformation syndromes, skeletal dysplasia and nervous system anomalies [<xref rid="pcbi.1004541.ref014" ref-type="bibr">14</xref>, <xref rid="pcbi.1004541.ref015" ref-type="bibr">15</xref>]. The strong evolutionary conservation of the polyA tracts suggests the existence of critical structural or functional constraints [<xref rid="pcbi.1004541.ref014" ref-type="bibr">14</xref>]. It should be noted that in human proteins the polyA tracts are short compared to those of polyQ [<xref rid="pcbi.1004541.ref015" ref-type="bibr">15</xref>].</p><p>Here, we focus on polyQ chains of various lengths, Q<sub><italic>n</italic></sub>, where <italic>n</italic> goes from 16 to 80. The case of <italic>n</italic> = 62 was the subject of a recent single-molecule force spectroscopy study [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>] that revealed a large conformational polymorphism (monitored as a spectrum of different breaking points and characteristic force-peak heights, up to 800 pN). The questions we ask are as follows: 1) can we explain this conformational polymorphism? 2) can polyQ tracts generate non-CATH-like conformers? 3) what are the structural and mechanical properties of the polyQ structures? In order to answer them, we follow a bias exchange molecular dynamics approach (BEMD) [<xref rid="pcbi.1004541.ref017" ref-type="bibr">17</xref>] also used by Cossio <italic>et al</italic>. [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>]—one of the meta dynamics approaches—and explore the structural and dynamical properties of Q<sub><italic>n</italic></sub> with a particular focus on Q<sub>20</sub> and Q<sub>60</sub>, representative examples below and above the HD’s pathological threshold.</p><p>We take two perspectives in our analysis: 1) making comparisons of Q<sub>60</sub> to V<sub>60</sub> and to the similar-sized proteins from the CATH database; 2) investigating the changes in the physical properties of the conformations corresponding to Q<sub><italic>n</italic></sub> as one varies <italic>n</italic>. The dynamical properties can be conveniently captured by their mechanical stability, as characterized by the characteristic force, <italic>F</italic><sub>max</sub>, needed to unravel a structure by pulling by its termini at a constant speed, <italic>v</italic><sub><italic>p</italic></sub>. This part of our studies makes use of a structure-based coarse-grained model [<xref rid="pcbi.1004541.ref018" ref-type="bibr">18</xref>, <xref rid="pcbi.1004541.ref019" ref-type="bibr">19</xref>] to access the regime of near-experimental speeds and to deal with the large statistics. It should be noted that typical fluctuation times of these structures are much smaller than those needed to fully unravel them [<xref rid="pcbi.1004541.ref020" ref-type="bibr">20</xref>]. Thus, the results on <italic>F</italic><sub>max</sub> are merely indicators of the putative mechanical stability of each specific conformer that do not take the intrinsic evolution of the disordered protein into account.</p><p>We find that relatively large mechanical stability may arise not only from structures with large secondary structure content (<inline-formula id="pcbi.1004541.e001"><alternatives><graphic xlink:href="pcbi.1004541.e001.jpg" id="pcbi.1004541.e001g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M1"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>, measured as the percentages of residues belonging to <italic>α</italic>-helices, <italic>β</italic>-strands and hydrogen-bonded turns) but also from those with <inline-formula id="pcbi.1004541.e002"><alternatives><graphic xlink:href="pcbi.1004541.e002.jpg" id="pcbi.1004541.e002g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M2"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> of about 30%. Interestingly, we also find spontaneous generation of knotted structures for <italic>n</italic> = 60, which tend to be of a size of 36 residues, about HD’s threshold. This is a novel feature in neurotoxic proteins that needs further investigation.</p></sec><sec sec-type="materials|methods" id="sec002"><title>Methods</title><sec id="sec003"><title>Generation and selection of structures</title><p>Our BEMD [<xref rid="pcbi.1004541.ref017" ref-type="bibr">17</xref>] simulations were carried out using the GROMACS molecular dynamics package [<xref rid="pcbi.1004541.ref021" ref-type="bibr">21</xref>] and the PLUMED extension [<xref rid="pcbi.1004541.ref022" ref-type="bibr">22</xref>]. The force field used is AMBER99SB [<xref rid="pcbi.1004541.ref023" ref-type="bibr">23</xref>] and the implicit solvent model is the generalized Born surface area method [<xref rid="pcbi.1004541.ref024" ref-type="bibr">24</xref>]. The same force field has been used before in folding simulations with explicit solvent [<xref rid="pcbi.1004541.ref017" ref-type="bibr">17</xref>, <xref rid="pcbi.1004541.ref025" ref-type="bibr">25</xref>], but implicit solvent is preferred in order to efficiently explore the energy landscape [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>]. Structures were initialized randomly using the MODELLER software [<xref rid="pcbi.1004541.ref026" ref-type="bibr">26</xref>]: 10 off-template models were done for each protein; the models that contained knots were discarded and the remaining ones were minimized through up to 1000 steps of the steepest descent method followed by up to 4000 steps of the conjugate gradient algorithm [<xref rid="pcbi.1004541.ref027" ref-type="bibr">27</xref>]. The system which acquired the smallest potential energy after the two minimization stages was chosen for further studies.</p><p>In order to generate a variety of Q<sub><italic>n</italic></sub> structures, we applied the BEMD method with six replicas, each with a different secondary structure bias: the first one with no bias; the next three with a preference to <italic>α</italic>-helix in the first, second and last third of the chain sequence; the fifth with a preference to anti-parallel <italic>β</italic>-strands and the last one with parallel <italic>β</italic>-strands. The method is explained in detail in the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>.</p><p>We first obtained a number of conformations with a varying secondary structure content. To select the structures of interest, we followed the three-sieve protocol used in [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>], described in the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>, that yields structures with <inline-formula id="pcbi.1004541.e003"><alternatives><graphic xlink:href="pcbi.1004541.e003.jpg" id="pcbi.1004541.e003g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M3"><mml:mrow><mml:mtext mathvariant="double-struck">SS</mml:mtext><mml:mrow></mml:mrow><mml:mo>></mml:mo><mml:mn>30</mml:mn><mml:mspace width="3.33333pt"></mml:mspace><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> which are temporally and structurally independent. From a 2 <italic>μ</italic>s simulation of Q<sub>60</sub>, 246 independent conformers were obtained from 953 time clusters. For Q<sub>20</sub>, a 0.66 <italic>μ</italic>s simulation resulted into 491 independent conformers out of 517 time clusters. Interestingly, half the simulation time for the short peptide yielded twice as many independent conformations as the longer one, which indicates higher polymorphism and faster dynamics in Q<sub>20</sub>. The procedure led to the emergence of some knotted structures even though there were no knots present in the initial homology-derived conformers.</p><p>After clustering, all independent structures underwent a minimization process of 10 000 steepest descent steps or until the maximum force between a pair of atoms was smaller than 0.25 J/(mol nm) so that the structure in the closest energy minimum is obtained. In this process, some of the residues may form or break contacts, thus changing their secondary structure content slightly. Therefore, even though the structures were selected with <inline-formula id="pcbi.1004541.e004"><alternatives><graphic xlink:href="pcbi.1004541.e004.jpg" id="pcbi.1004541.e004g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M4"><mml:mrow><mml:mtext mathvariant="double-struck">SS</mml:mtext><mml:mrow></mml:mrow><mml:mo>≥</mml:mo><mml:mn>30</mml:mn><mml:mspace width="3.33333pt"></mml:mspace><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> before the first clustering, some of the final structures may have a smaller <inline-formula id="pcbi.1004541.e005"><alternatives><graphic xlink:href="pcbi.1004541.e005.jpg" id="pcbi.1004541.e005g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M5"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> content.</p><p>The structures of V<sub>60</sub> were taken from ref. [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>]. Their 50 <italic>μ</italic>s simulation yielded 30 063 time clusters. We have applied the structural clustering to this set and obtained 7076 independent conformers—as these were not available. All the independent structures generated are provided in the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>.</p><p>Three previous works have explored the aggregation properties of Q<sub><italic>n</italic></sub> by computer simulations. In the first of them, the focus is on the temporal stability of the structures and on the evaluation of their amyloidogenesis and fibrillation capabilites [<xref rid="pcbi.1004541.ref028" ref-type="bibr">28</xref>]. The second study explores the landscape of possible conformations by simplifying the structure of glutamine and generating a model that efficiently samples many conformations [<xref rid="pcbi.1004541.ref029" ref-type="bibr">29</xref>]. Finally, the third one applies replica exchange molecular dynamics to explore the dimerization of polyQ [<xref rid="pcbi.1004541.ref030" ref-type="bibr">30</xref>]. The three works show structures such as steric zippers and a <italic>β</italic>-helix, which have been found in our sampling among the strongest Q<sub>60</sub> and Q<sub>20</sub> conformations shown in <xref ref-type="supplementary-material" rid="pcbi.1004541.s002">S1</xref> and <xref ref-type="supplementary-material" rid="pcbi.1004541.s003">S2</xref> Figs. Furthermore, rod-like conformers with close to 100% <italic>α</italic>-helical content were also described in the aforementioned works and have likewise been found in this sampling. Our simulations did not find the mainly <italic>β</italic> conformations suggested in Ref. [<xref rid="pcbi.1004541.ref030" ref-type="bibr">30</xref>] because we consider monomers instead of dimers.</p></sec><sec id="sec004"><title>Descriptors of the structures</title><p>Our structural analysis deals with several descriptors. One is the radius of gyration, <italic>R</italic><sub><italic>g</italic></sub>, which characterizes the linear size of the molecule. Another is the <italic>w</italic> parameter which describes the shape [<xref rid="pcbi.1004541.ref031" ref-type="bibr">31</xref>, <xref rid="pcbi.1004541.ref032" ref-type="bibr">32</xref>], which is defined through the diagonalization of the tensor of inertia and by making combinations of the three main radii such that a near-zero <italic>w</italic> corresponds to a globular shape, a positive <italic>w</italic> to an elongated one, and a negative <italic>w</italic> to a flattened object. The third descriptor is the <inline-formula id="pcbi.1004541.e006"><alternatives><graphic xlink:href="pcbi.1004541.e006.jpg" id="pcbi.1004541.e006g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M6"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> parameter, which is determined by using the DSSP procedure [<xref rid="pcbi.1004541.ref033" ref-type="bibr">33</xref>]. This parameter is a sum of several ingredients: the <italic>α</italic>-helical content, the <italic>β</italic>-content (strands and bridges), and the hydrogen-bonded turn content.</p><p>The next two descriptors are <italic>F</italic><sub>max</sub> and ⟨<italic>z</italic>⟩—the average coordination number. The former relates to the dynamics directly, while the latter relates to it indirectly since <italic>z</italic> measures the number of residues a given residue interacts with. These interactions are of two kinds: through the peptide bond with the two nearest residues along the sequence and through contact interactions with residues which are not sequential neighbors. The contacts play a dynamical role in coarse-grained structure-based models but they can also be used as descriptors in all-atom models. The specific definition of the contacts we use is based on enlarged van der Waals spheres associated with the heavy atoms [<xref rid="pcbi.1004541.ref018" ref-type="bibr">18</xref>, <xref rid="pcbi.1004541.ref019" ref-type="bibr">19</xref>] and the radii of the spheres are given in ref. [<xref rid="pcbi.1004541.ref034" ref-type="bibr">34</xref>]: a contact between two residues exists if there is at least one pair of heavy atoms with overlapping spheres.</p><p>In the structure-based model, we assign Lennard-Jones potentials of depth <italic>ɛ</italic> to these contacts (the potential minimum is at the distance between the C<sub>α</sub> atoms in the reference structure) so that larger values of ⟨<italic>z</italic>⟩ are expected to correspond to more stable structures. Maxwell demonstrated [<xref rid="pcbi.1004541.ref035" ref-type="bibr">35</xref>] that large three-dimensional systems of particles with pairwise interactions are stable provided the ⟨<italic>z</italic>⟩ is bigger than 6. In particular, this finding has been shown to be consistent with the behavior of virus capsids [<xref rid="pcbi.1004541.ref036" ref-type="bibr">36</xref>]. In our case, the structures are much smaller than the capsids and, therefore, the threshold value of ⟨<italic>z</italic>⟩ is reduced, as explained in the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>. Furthermore, the systems we study are also endowed with the local backbone stiffness—a four-particle interaction [<xref rid="pcbi.1004541.ref037" ref-type="bibr">37</xref>]—which favors the local chirality of the reference state. Thus non-zero values of <italic>F</italic><sub>max</sub> for structures with ⟨<italic>z</italic>⟩ smaller than 6 are allowed.</p><p>A stretching force (<italic>F</italic>) <italic>vs</italic>. displacement (<italic>d</italic>) curve may include articulated force peaks –which exceed the thermal noise level of about 0.1 <italic>ɛ</italic>/Å—before the <italic>F</italic> raises indefinitely due to stretching of the peptide bonds. The calculations are done at the temperature of 0.3 <italic>ɛ</italic>/<italic>k</italic><sub>B</sub>, where <italic>k</italic><sub>B</sub> denotes the Boltzmann constant. The number of peaks is denoted by <italic>n</italic><sub>p</sub>. <italic>F</italic><sub>max</sub> is defined as the height of the largest peak. If none exists then <italic>F</italic><sub>max</sub> is defined to be zero, even though it could take any value below the baseline of the curve (around 0.4 <italic>ɛ</italic>/Å). We simulate stretching at <italic>v</italic><sub><italic>p</italic></sub> of 5 ⋅ 10<sup>−3</sup> Å/<italic>τ</italic>, where <italic>τ</italic> is of order 1 ns. Experimental <italic>v</italic><sub><italic>p</italic></sub>’s are typically lower, <italic>e.g</italic>. 4 ⋅ 10<sup>−6</sup> Å/ns in ref. [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>]. We have calibrated [<xref rid="pcbi.1004541.ref019" ref-type="bibr">19</xref>] <italic>ɛ</italic> to be 110 pN Å (with a 25% error bar) by comparing theoretical and experimental values of <italic>F</italic><sub>max</sub> in 38 proteins (the theoretical results involved extrapolation to the experimental <italic>v</italic><sub><italic>p</italic></sub>’s). The temperature in the coarse-grained simulations is in the vicinity of the room temperature.</p><p>Finally, one can consider the contact order (<italic>CO</italic>) as yet another structural descriptor. It is related to the number of contacts as well as the average distance along the sequence between the contacting residues, as defined in Ref. [<xref rid="pcbi.1004541.ref038" ref-type="bibr">38</xref>] as <inline-formula id="pcbi.1004541.e007"><alternatives><graphic xlink:href="pcbi.1004541.e007.jpg" id="pcbi.1004541.e007g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M7"><mml:mrow><mml:mi>C</mml:mi><mml:mi>O</mml:mi><mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>L</mml:mi><mml:mo>·</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:mfrac><mml:msub><mml:mo>∑</mml:mo><mml:mi>k</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, where <italic>S</italic><sub><italic>k</italic></sub> is the distance between the residues that form contact <italic>k</italic>, <italic>L</italic> is the number of residues in the protein and <italic>N</italic> the number of contacts. There is a question whether <italic>CO</italic> correlates with the folding time or not (see [<xref rid="pcbi.1004541.ref039" ref-type="bibr">39</xref>] and [<xref rid="pcbi.1004541.ref040" ref-type="bibr">40</xref>] for the arguments for and against it), so one may also inquire whether <italic>F</italic><sub>max</sub> correlates with <italic>CO</italic>. It seems unlikely that the free energy barrier to mechanical unfolding is of the same nature as the one for folding (or thermal unfolding) [<xref rid="pcbi.1004541.ref041" ref-type="bibr">41</xref>] but this does not preclude a correlation with <italic>CO</italic>. However, we do not find the correlation to be valid (see the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>) which is consistent with the fact that the green fluorescent protein (PDB code 1GFL) has a bigger <italic>F</italic><sub>max</sub> than the I27 domain of titin (the PDB code 1TIT), 2.7 <italic>vs</italic>. 2.1 <italic>ɛ</italic>/Å [<xref rid="pcbi.1004541.ref019" ref-type="bibr">19</xref>], whereas its <italic>CO</italic> is smaller, 0.22 <italic>vs</italic>. 0.36.</p></sec></sec><sec sec-type="results" id="sec005"><title>Results</title><sec id="sec006"><title>Properties of Q<sub>60</sub> and Q<sub>20</sub></title><p>We first consider the Q<sub>60</sub> set, so that one can compare with V<sub>60</sub> from [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>] and with the experimental results on Q<sub>62</sub> in [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>]. <xref ref-type="supplementary-material" rid="pcbi.1004541.s002">S1 Fig</xref> shows structures corresponding to the top five values of <italic>F</italic><sub>max</sub>. Similar figures for other sets studied are shown in <xref ref-type="supplementary-material" rid="pcbi.1004541.s003">S2</xref> and <xref ref-type="supplementary-material" rid="pcbi.1004541.s004">S3</xref> Figs. The values range between 2.1 and 2.3 <italic>ɛ</italic>/Å (approximately between 230 and 250 pN) which is of the order of what has been found—about 200 pN—for the I27 domain of titin [<xref rid="pcbi.1004541.ref042" ref-type="bibr">42</xref>, <xref rid="pcbi.1004541.ref043" ref-type="bibr">43</xref>] at smaller <italic>v</italic><sub><italic>p</italic></sub>’s. The fact that these values are much smaller than the ones found experimentally in [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>] can be attributed to a small statistics, since the experimental systems yielded high force only with low probability (<italic>p</italic>(<italic>F</italic><sub>max</sub> > 200 pN) = 7 ± 6%). The figure also shows the corresponding <italic>F</italic> − <italic>d</italic> patterns together with distances at which particular contacts break down (the distance in the contact exceeds the reference distance by 50%) for the last time. The contacts are labeled by the sequential distances ∣<italic>i</italic> − <italic>j</italic>∣ between residues <italic>i</italic> and <italic>j</italic>. The number of force peaks varies between 1 and 4, corresponding to several substructures forming in each conformer. The third column of panels in <xref ref-type="supplementary-material" rid="pcbi.1004541.s002">S1 Fig</xref> provides the values of the relevant descriptors. <italic>R</italic><sub><italic>g</italic></sub> is seen to range between 11.05 and 14.20 Å and the values of <italic>w</italic> indicate that the fifth structure is elongated while the other four are nearly globular. The most stable structure of the five shown (the top row of panels) corresponds to the largest ⟨<italic>z</italic>⟩ (7.67), and <inline-formula id="pcbi.1004541.e008"><alternatives><graphic xlink:href="pcbi.1004541.e008.jpg" id="pcbi.1004541.e008g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M8"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> (66.7%)—the secondary structure is, in this case, exclusively of the <italic>β</italic> type.</p><p>Interestingly, the second most robust structure, as judged by the value of <italic>F</italic><sub>max</sub>, has very low ⟨<italic>z</italic>⟩ (5.33) and <inline-formula id="pcbi.1004541.e009"><alternatives><graphic xlink:href="pcbi.1004541.e009.jpg" id="pcbi.1004541.e009g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M9"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> (28.3%).</p><p>This system was compared to Q<sub>20</sub>, which is unrelated to disease and is close to Q<sub>19</sub>, which was studied experimentally [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>]. The two left columns of <xref ref-type="fig" rid="pcbi.1004541.g001">Fig 1</xref> refer to all structures in sets Q<sub>20</sub> and Q<sub>60</sub>. In particular, the first row represents the geometries obtained on the <italic>R</italic><sub><italic>g</italic></sub>—<italic>w</italic> plane. The convention we use is that we represent the data corresponding to structures with <inline-formula id="pcbi.1004541.e010"><alternatives><graphic xlink:href="pcbi.1004541.e010.jpg" id="pcbi.1004541.e010g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M10"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> of at least 50% and those with lower <inline-formula id="pcbi.1004541.e011"><alternatives><graphic xlink:href="pcbi.1004541.e011.jpg" id="pcbi.1004541.e011g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M11"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> by filled and open symbols, respectively. The structures from Q<sub>60</sub> are seen to overlap with the region taken by Q<sub>20</sub> but they also extend to much larger <italic>R</italic><sub><italic>g</italic></sub> and to bigger <italic>w</italic>. The largest value of <italic>R</italic><sub><italic>g</italic></sub> corresponds to a low <inline-formula id="pcbi.1004541.e012"><alternatives><graphic xlink:href="pcbi.1004541.e012.jpg" id="pcbi.1004541.e012g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M12"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>, while high <italic>w</italic> can be achieved with any value of <inline-formula id="pcbi.1004541.e013"><alternatives><graphic xlink:href="pcbi.1004541.e013.jpg" id="pcbi.1004541.e013g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M13"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>.</p><fig id="pcbi.1004541.g001" orientation="portrait" position="float"><object-id pub-id-type="doi">10.1371/journal.pcbi.1004541.g001</object-id><label>Fig 1</label><caption><title>Scatter plot relating the specified variables for four differentsets, from left to right, Q<sub>20</sub>, Q<sub>60</sub>, V<sub>60</sub> and CATH.</title><p>The empty black points represent the conformers with less than 50% secondary structure content, while the filled red dots represent the more structured conformers. The vertical dotted lines in the middle panels mark the simply stiff limits of stability for each case (see the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>). The conformers to the left of this line are more volatile. The horizontal dashed lines in the middle and bottom panels mark off the top five conformers with respect to the value of <italic>F</italic><sub>max</sub>.</p></caption><graphic xlink:href="pcbi.1004541.g001"></graphic></fig><p>The two bottom rows of <xref ref-type="fig" rid="pcbi.1004541.g001">Fig 1</xref> show scatter plots that compare the values of <italic>F</italic><sub>max</sub> in Q<sub>60</sub> to those in Q<sub>20</sub> when represented as a function of ⟨<italic>z</italic>⟩ and <inline-formula id="pcbi.1004541.e014"><alternatives><graphic xlink:href="pcbi.1004541.e014.jpg" id="pcbi.1004541.e014g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M14"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>. <xref ref-type="supplementary-material" rid="pcbi.1004541.s005">S4 Fig</xref> provides a continuation in which <italic>F</italic><sub>max</sub> is plotted against the <italic>α</italic>-, <italic>β</italic>-, and turns (<italic>τ</italic>) content. It is clear that, for a given <italic>n</italic>, the mechanical stability is not related in any simple manner to either ⟨<italic>z</italic>⟩, <italic>CO</italic> or <inline-formula id="pcbi.1004541.e015"><alternatives><graphic xlink:href="pcbi.1004541.e015.jpg" id="pcbi.1004541.e015g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M15"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> content. This is because typical high-force motifs include <italic>β</italic>-structured regions, while high ⟨<italic>z</italic>⟩ and <inline-formula id="pcbi.1004541.e016"><alternatives><graphic xlink:href="pcbi.1004541.e016.jpg" id="pcbi.1004541.e016g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M16"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> can be achieved with <italic>α</italic>-structure and hydrogen-bonded turns [<xref rid="pcbi.1004541.ref043" ref-type="bibr">43</xref>]. <xref ref-type="supplementary-material" rid="pcbi.1004541.s005">S4 Fig</xref> shows that mechanical stability has no direct correlation to <italic>α</italic>-content or hydrogen-bonded turns (<italic>τ</italic>), and while most of the high <italic>β</italic>-content conformers lead to high forces, these can also be observed in cases with no <italic>β</italic>-content. Similar results are shown in the top panels of <xref ref-type="supplementary-material" rid="pcbi.1004541.s006">S5 Fig</xref> for the <italic>CO</italic>.</p><p>Furthermore, in the top left panel of <xref ref-type="fig" rid="pcbi.1004541.g002">Fig 2</xref> there is a comparison of the distributions of <italic>F</italic><sub>max</sub> for Q<sub>60</sub> and Q<sub>20</sub>. We observe that although our BEMD simulations bias the chain towards the acquisition of <inline-formula id="pcbi.1004541.e017"><alternatives><graphic xlink:href="pcbi.1004541.e017.jpg" id="pcbi.1004541.e017g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M17"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>, many conformers do not produce any articulated force peaks above the 10% noise level (<italic>F</italic><sub>max</sub> = 0). In particular, Q<sub>20</sub> presents (79 ± 2)% of this kind of conformers, while Q<sub>60</sub> only contains (34 ± 3)% of them. This result is consistent with the experimental data [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>], where no force peaks were detected in Q<sub>19</sub>, while some were found in Q<sub>62</sub>. Remarkably, although the diversity in mechanical stability for Q<sub>20</sub> is smaller than for Q<sub>60</sub>, the frequency of independent structure generation is greater in the former (see <xref ref-type="supplementary-material" rid="pcbi.1004541.s007">S6 Fig</xref>), so its conformational polymorphism should be higher. The volatility of each conformer, as assessed by ⟨<italic>z</italic>⟩ lower than their threshold, also agrees with this result, with (49 ± 2)% volatile conformers in Q<sub>20</sub><italic>vs</italic>. (13 ± 2)% in Q<sub>60</sub>.</p><fig id="pcbi.1004541.g002" orientation="portrait" position="float"><object-id pub-id-type="doi">10.1371/journal.pcbi.1004541.g002</object-id><label>Fig 2</label><caption><title>Distributions of <italic>F</italic><sub>max</sub> for the studied species.</title><p>The top left panel shows the distribution for Q<sub>20</sub> in a thick line. The conformations with no force peaks are not plotted in the histograms but contribute to normalization. The amount of such non-mechanostable conformers is (79 ± 2)% for Q<sub>20</sub>, (34 ± 3)% for Q<sub>60</sub>, (16.5 ± 0.2)% for V<sub>60</sub>, and (47 ± 3)% and (20.2 ± 0.5)% for CATH<sub>60</sub> and CATH, respectively. The errors were computed using a bootstrapping method and the size of the error bar indicates the standard deviation.</p></caption><graphic xlink:href="pcbi.1004541.g002"></graphic></fig><p>Taken together, these results show that <italic>F</italic><sub>max</sub> is inherently different in Q<sub>20</sub> and Q<sub>60</sub> sets, even when <inline-formula id="pcbi.1004541.e018"><alternatives><graphic xlink:href="pcbi.1004541.e018.jpg" id="pcbi.1004541.e018g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M18"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> is similar. This further points to <italic>F</italic><sub>max</sub> not being related to hydrogen-bonded turns, <italic>α</italic> helices and even <italic>β</italic>-strand content and <inline-formula id="pcbi.1004541.e019"><alternatives><graphic xlink:href="pcbi.1004541.e019.jpg" id="pcbi.1004541.e019g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M19"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>, and also neither to <italic>CO</italic> nor to ⟨<italic>z</italic>⟩.</p></sec><sec id="sec007"><title>Comparisons of Q<sub>60</sub> to the remaining sets of structures</title><p><xref ref-type="fig" rid="pcbi.1004541.g002">Fig 2</xref> shows the normalized distributions of <italic>F</italic><sub>max</sub> within the Q<sub>60</sub>, Q<sub>20</sub>, V<sub>60</sub>, CATH<sub>60</sub>, and CATH sets. The distributions do not show the peak at <italic>F</italic><sub>max</sub> = 0, but its value is shown in the caption and contributes to the normalization. CATH<sub>60</sub> is defined as structures containing between 57 and 63 residues and it contains 256 proteins. In order to exclude short peptides and most multidomain proteins we take CATH to represent all those proteins in the CATH database that are 40 to 250 residue long. This set comprises 5403 structures.</p><p>The characteristic forces grow on moving from Q<sub>20</sub> to Q<sub>60</sub>. However, in all sets but Q<sub>20</sub>, the most probable <italic>F</italic><sub>max</sub> is about the same, 1.2 <italic>ɛ</italic>/Å, but the shapes of the distributions differ. The distributions are comparably broad for CATH and CATH<sub>60</sub> and comparably narrower for Q<sub>60</sub> and V<sub>60</sub>, indicating the role of the stronger compositional homogeneity in the latter two sets. The rougher look of the distribution for Q<sub>60</sub> is likely due to the one order of magnitude smaller statistics. Furthermore, it should be noted that, among the systems of about 60 residues, CATH<sub>60</sub> leads to the biggest number of situations with no force peaks, (47 ± 3)%; and V<sub>60</sub> to the smallest, (16.5 ± 0.2)%.</p><p>Despite the similarity of the distribution of the forces between Q<sub>60</sub> and V<sub>60</sub>, the geometrical character of structures in the two sets are distinct. <xref ref-type="fig" rid="pcbi.1004541.g001">Fig 1</xref> shows that V<sub>60</sub> conformers are more compact and less elongated than Q<sub>60</sub> or CATH<sub>60</sub>. Furthermore, this figure indicates that size and shape of a chain need not be correlated.</p><p><xref ref-type="fig" rid="pcbi.1004541.g001">Fig 1</xref> further shows that most of the structures in the 60-sized sets, and also for CATH, come with ⟨<italic>z</italic>⟩ between 5.5 and 8.5. However, the largest values of <italic>F</italic><sub>max</sub> arise for ⟨<italic>z</italic>⟩ between 6.3 and 8.1 and many large ⟨<italic>z</italic>⟩ structures come with average or even small forces, including <italic>F</italic><sub>max</sub> of 0. Similarly, <xref ref-type="fig" rid="pcbi.1004541.g001">Fig 1</xref> also demonstrates that large <inline-formula id="pcbi.1004541.e020"><alternatives><graphic xlink:href="pcbi.1004541.e020.jpg" id="pcbi.1004541.e020g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M20"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> may come with low or zero forces and large <italic>F</italic><sub>max</sub> may arise when <inline-formula id="pcbi.1004541.e021"><alternatives><graphic xlink:href="pcbi.1004541.e021.jpg" id="pcbi.1004541.e021g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M21"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> is at its lower range. Furthermore, the scattering of the data points in the <italic>F</italic><sub>max</sub>–<italic>CO</italic> plane shown in Fig. [<xref rid="pcbi.1004541.ref038" ref-type="bibr">38</xref>] also points in the direction of statistical independence. This observation further proves that there is no correlation between <italic>F</italic><sub>max</sub> and ⟨<italic>z</italic>⟩, <italic>CO</italic> or <inline-formula id="pcbi.1004541.e022"><alternatives><graphic xlink:href="pcbi.1004541.e022.jpg" id="pcbi.1004541.e022g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M22"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>. Interestingly, none of the independent V<sub>60</sub> structures obtained from [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>] have ⟨<italic>z</italic>⟩ below the volatility threshold, while (5.5 ± 1.4)% of the ones in CATH<sub>60</sub> and (2.3 ± 0.2)% of CATH do. Our comparison reinforces the remarkable conclusion that <italic>F</italic><sub>max</sub> is unrelated to <italic>CO</italic>, <inline-formula id="pcbi.1004541.e023"><alternatives><graphic xlink:href="pcbi.1004541.e023.jpg" id="pcbi.1004541.e023g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M23"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> or ⟨<italic>z</italic>⟩ and extends it to general globular proteins instead of being a property specific for polyQ. This is further discussed in the <xref ref-type="supplementary-material" rid="pcbi.1004541.s001">S1 Text</xref>, where the independence of <italic>F</italic><sub>max</sub> with the rest of parameters is proved.</p></sec><sec id="sec008"><title>Life span of the structures</title><p>In order to test whether the coordination number is actually related to temporal stability, we performed 10 ns free-dynamics simulations on 100 structures chosen randomly from each set: Q<sub>20</sub>, Q<sub>60</sub> and V<sub>60</sub>. We have studied the time dependence of RMSD relative to the initial structure and the last time that it fluctuated below 2 Å was recorded for each conformer as its time of residence (<italic>t</italic><sub>R</sub>). Similarly, we define the escape probability (<italic>P</italic><sub>e</sub>(<italic>t</italic>)) as the probability of leaving the initial conformation before time <italic>t</italic>.</p><p><xref ref-type="fig" rid="pcbi.1004541.g003">Fig 3</xref> shows the results of this study. The top panel shows that Q<sub>60</sub> conformers last longer than Q<sub>20</sub> in a specific state, while the average escape probability of V<sub>60</sub> initially is lower but soon rises much faster than the other two sets. For completeness, we run the same study on three regular proteins: Trp-cage (PDB code 1L2Y, 20 residues long), an immunoglobulin binding domain of protein G (1GB1, 56 residues) and the 27th immunoglobulin domain of human cardiac titin (1TIT, 89 residues). All of them remained in the same conformation for longer than 10 ns: their RMSD was never higher than 2 Å.</p><fig id="pcbi.1004541.g003" orientation="portrait" position="float"><object-id pub-id-type="doi">10.1371/journal.pcbi.1004541.g003</object-id><label>Fig 3</label><caption><title>Time evolution of the studied structures.</title><p>For each set in Q<sub>60</sub>, Q<sub>20</sub> and V<sub>60</sub>, 100 randomly chosen structures have been placed under a free-dynamics evolution for 10 ns. After that, the RMSD has been studied and the last time when it fluctuates above 2 Å is recorded as the residence time (<italic>t</italic><sub>R</sub>). The top graph shows the escape probability (<italic>P</italic><sub>e</sub>(<italic>t</italic>)), defined as the probability of having left the initial state of a conformer at time <italic>t</italic>. We can see how Q<sub>20</sub> fluctuates out of the initial structure much faster than Q<sub>60</sub>, while V<sub>60</sub> starts more slowly but rapidly outruns both Q<sub>60</sub> and Q<sub>20</sub>. The inset shows the average evolution of the RMSD for the three sets compared to an example of a similar-sized globular protein, an immunoglobulin binding domain of protein G (PDB code 1GB1, 56 residues). The latter lasts for longer than 10 ns fluctuating around 2 Å, while the other three rapidly evolve out of the initial structure. The bottom graphs show scatter plots of ⟨<italic>z</italic>⟩ <italic>vs</italic>. <italic>t</italic><sub>R</sub>. No simple relation can be established between these two quantities above the stiff limit (dashed vertical lines), while below it residence times never exceed 1 ns.</p></caption><graphic xlink:href="pcbi.1004541.g003"></graphic></fig><p>The bottom panels of <xref ref-type="fig" rid="pcbi.1004541.g003">Fig 3</xref> show scatter plots of <italic>t</italic><sub>R</sub><italic>vs</italic>. ⟨<italic>z</italic>⟩. This figure shows that ⟨<italic>z</italic>⟩ is not only unrelated to <italic>F</italic><sub>max</sub>, but also to the temporal stability of the conformers (as measured by <italic>t</italic><sub>R</sub>) in the cases where ⟨<italic>z</italic>⟩ is above the simply stiff limit. In the case of conformers with ⟨<italic>z</italic>⟩ below this limit, however, <italic>t</italic><sub>R</sub> is always below 1 ns, reinforcing Maxwell’s theory on frame stiffness [<xref rid="pcbi.1004541.ref035" ref-type="bibr">35</xref>].</p><p>Interestingly, both theoretical and especially experimental pulling experiments are typically done at <italic>v</italic><sub><italic>p</italic></sub>’s such that the time the protein is being pulled is far longer than 10 ns. In particular, the pulling simulations performed in this work take ≈ 50 <italic>μ</italic>s to completely extend a protein with 60 residues, while experiments such as the ones performed in [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>] take around 60 ms to accomplish the same task. This leads to question whether the force peaks present in the experimental traces really relate to the initial conformers or have actually been formed while the molecule was being pulled.</p><p>Therefore, one must look at <italic>F</italic><sub>max</sub> carefully since it has different meaning in this kind of simulation than in experiments such as those in [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>]: Here, mechanical stability is associated directly with a conformer, since simulations are based on the initial contact map. On the other hand, in experiments, molecules are subjected to fluctuations with a characteristic time of 1 ns and the <italic>F</italic>–<italic>d</italic> curves carry information not only about the initial conformer but also about the stretching-unrelated intrinsic shape transformations that the protein may undergo. All in all, we observe that disordered proteins such as polyglutamines are not long lasting when compared to structured globular ones, and that mechanical stabilities need to be looked at in the context of how they were measured, either referred to the initial conformer if done through structure-based modelling, or including bond formation during the stretching if performed experimentally.</p></sec><sec id="sec009"><title>Structures with knots</title><p>Even though the starting structures were not knotted, our BEMD simulation yielded some knotted conformers. In particular, (9.3 ± 1.8)% of the independent Q<sub>60</sub> conformers have a knot, while Q<sub>20</sub> include no knotted conformers. Moreover, only (3.6 ± 0.5)% of the V<sub>60</sub> structures contain a knot, and none of the CATH structures have one. All knots generated in V<sub>60</sub> are trefoil (3<sub>1</sub>), while Q<sub>60</sub> also contains one three-twist (5<sub>2</sub>). Upon stretching, only (13 ± 7)% of the Q<sub>60</sub> knotted structures untie, while (45 ± 6)% of the V<sub>60</sub> ones do. As shown in ref. [<xref rid="pcbi.1004541.ref044" ref-type="bibr">44</xref>], tightening of knots may be associated with force peaks. Both for Q<sub>60</sub> and V<sub>60</sub>, knot tightening yields <italic>F</italic><sub>max</sub> from 0.9 to 2.4 <italic>ɛ</italic>/Å.</p><p><xref ref-type="fig" rid="pcbi.1004541.g004">Fig 4</xref> shows an example of a 3<sub>1</sub> knotted conformer found in Q<sub>60</sub> plus a histogram of the ends of the knots (<italic>k</italic><sub>−</sub>, <italic>k</italic><sub>+</sub>) and their extension (Δ<italic>k</italic>, measured as the number of residues contained inside the knot) in the structures formed by sets Q<sub>60</sub> and V<sub>60</sub>. An example of a 5<sub>2</sub> one from Q<sub>60</sub> and a 3<sub>1</sub> from V<sub>60</sub> are shown in <xref ref-type="supplementary-material" rid="pcbi.1004541.s008">S7 Fig</xref> Significantly, not only does V<sub>60</sub> form fewer and less stable knots than Q<sub>60</sub>, but also the extension of the V<sub>60</sub> knots is typically larger than the Q<sub>60</sub> ones. Furthermore, the average extension of the knotted Q<sub>60</sub> conformers is 36 (with a 0.12% error), which corresponds to the median threshold value for most polyglutamine-expansion-related diseases such as HD. We note that knotted structures would have been found experimentally as putative events in [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>], since the final length would be reduced and thus they would render molecules with lower total contour length increase. Furthermore, knotted proteins have previously been found in nature especially in enzymes such as methyltransferases and carbonic anhydrases [<xref rid="pcbi.1004541.ref045" ref-type="bibr">45</xref>–<xref rid="pcbi.1004541.ref047" ref-type="bibr">47</xref>]. Nonetheless, the only hypothesized function of the knot itself—as opposed to the whole protein—is to prevent the unfolding of the protein in a case where the proteasome were to try to degrade it [<xref rid="pcbi.1004541.ref046" ref-type="bibr">46</xref>].</p><fig id="pcbi.1004541.g004" orientation="portrait" position="float"><object-id pub-id-type="doi">10.1371/journal.pcbi.1004541.g004</object-id><label>Fig 4</label><caption><title>Knots in the studied conformers.</title><p>The top left panel shows an example of a Q<sub>60</sub> conformation containing a trefoil (3<sub>1</sub>) knot with the knot ends highlighted with yellow spheres. To its right, the same conformation has been partially stretched, and the region inside the knot is highlighted in red and zoomed in. The middle panels represent histograms of the knot end positions, <italic>k</italic><sub>±</sub>, for Q<sub>60</sub> (left) and V<sub>60</sub> (right). The bottom panel shows their corresponding extension, Δ<italic>k</italic>. The percentage of knotted structures relative to to the total number of independent conformers found for Q<sub>60</sub> and V<sub>60</sub> are (9.3 ± 1.8)% and (3.6 ± 0.5)%, respectively. Shallow knots have an extension closer to 60 (the system size). Protein representations have been done with VMD [<xref rid="pcbi.1004541.ref048" ref-type="bibr">48</xref>].</p></caption><graphic xlink:href="pcbi.1004541.g004"></graphic></fig><p>The presence of knots on its own is not indicative of their relevance: they need to last long enough to be able to have any effect. To that end, we performed 200 ns all-atom simulations with explicit TIP3P water of three randomly chosen knotted conformers to see the behaviour of these knots with time. The knot ends fluctuate along the protein as does the knot size, and in some cases the knot unties just to be formed again some time later –the time of the protein being in the untied conformation lasting for as long as 200 ps. Also, in two of the three cases, preferred places for the left and right ends can be seen, the right end being the same for both of them. The results of these simulations can be seen in <xref ref-type="supplementary-material" rid="pcbi.1004541.s009">S8 Fig</xref>.</p></sec><sec id="sec010"><title>Other lengths in polyQ chains</title><p>Given that the average extension of the knots corresponds with the median of the threshold of the polyQ diseases, we applied the same methodology to other Q<sub><italic>n</italic></sub> tracts, with <italic>n</italic> = 16, 25, 33, 38, 40 and 80. As expected, no knots were found for <italic>n</italic> < 35; but there were no knots in sets Q<sub>38</sub>, Q<sub>40</sub> or Q<sub>80</sub> either. This may be attributed to a low probability of knot formation combined with small statistics, which would imply that BEMD took Q<sub>60</sub> through a knot-forming path while taking the rest of Q<sub><italic>n</italic></sub> studied through non-forming ones. This is reinforced by the fact that the greater statistics of V<sub>60</sub> do find knotted conformers. Therefore, an increase in the sampling may catch these knotted structures in Q<sub>80</sub> and Q<sub>40</sub>, while their formation is fairly improbable for <italic>n</italic> below 35 since the typical knot size is about this length.</p><p><xref ref-type="fig" rid="pcbi.1004541.g005">Fig 5</xref> shows the evolution of the mechanical stability and shape with the chain length. In particular, the fraction of conformers with <italic>F</italic><sub>max</sub> > 0, which we name <italic>χ</italic><sub>F</sub>, follow a logarithmic law, while the maximum <italic>F</italic><sub>max</sub> for each set, denoted as <inline-formula id="pcbi.1004541.e024"><alternatives><graphic xlink:href="pcbi.1004541.e024.jpg" id="pcbi.1004541.e024g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M24"><mml:msubsup><mml:mi>F</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mtext>M</mml:mtext></mml:msubsup></mml:math></alternatives></inline-formula> behaves like an avalanche system: it has a constant value until <italic>n</italic> = 33, and then starts growing as a power law with exponent 0.562. The average <italic>R</italic><sub><italic>g</italic></sub> appears to be saturating as <italic>n</italic> approaches 40, but it suddenly jumps for <italic>n</italic> = 60 and 80. Judging by <italic>w</italic>, the shapes of the conformers change around <italic>n</italic> = 35 from elongated to more globular. Interestingly, V<sub>60</sub> behaves differently than Q<sub>60</sub> except that the average <italic>w</italic> (lower right panel) is similar, suggesting the similarity of shapes. We also conclude that the fraction of mechanically stable conformers increases uniformly with <italic>n</italic>, while the maximum <italic>F</italic><sub>max</sub> presents an avalanche behaviour for <italic>n</italic> > 30, once again close to HD’s threshold of 35.</p><fig id="pcbi.1004541.g005" orientation="portrait" position="float"><object-id pub-id-type="doi">10.1371/journal.pcbi.1004541.g005</object-id><label>Fig 5</label><caption><title>Variability of the specified parameters with the length, <italic>n</italic>, of the polyQ chain (circles).</title><p>The values for V<sub>60</sub> are indicated by a square. <italic>χ</italic><sub><italic>F</italic></sub> represents the fraction of conformers with at least one force peak for that particular length. The dotted fits correspond to a logarithmic function (top left.352 ln(<italic>x</italic>/8.115)) and a polynomial behavior (top right, <italic>y</italic> = 0.236<italic>x</italic><sup>0.562</sup>), which is typical for avalanches. The bottom panels show average over the structures of <italic>R</italic><sub><italic>g</italic></sub> and <italic>w</italic>. ⟨<italic>R</italic><sub><italic>g</italic></sub>⟩ has a saturating behavior up to <italic>n</italic> = 40, but jumps for higher values. ⟨<italic>w</italic>⟩ presents a transition around <italic>n</italic> = 35 from slightly elongated to more globular proteins.</p></caption><graphic xlink:href="pcbi.1004541.g005"></graphic></fig></sec></sec><sec sec-type="conclusions" id="sec011"><title>Discussion</title><p>In this study, we have generated an ensemble of structurally independent conformers for glutamine expansions with <italic>n</italic> residues. We have focused on <italic>n</italic> = 60 which, if present in huntingtin protein, would result in Huntington disease, and on <italic>n</italic> = 20, which would not.</p><p>We have then expanded the study to <italic>n</italic> = 16, 25, 30, 33, 38, 40 and 80 in order to further explore the structural nature of the <italic>n</italic> ≈ 35 threshold in most polyQ-related diseases.</p><p>We find that proteins related to the disease exhibit less conformational polymorphism than the ones unrelated to it in terms of independent structures and transition kinetics, even though the former show much more mechanical variability (in terms of <italic>F</italic><sub>max</sub> and <italic>n</italic><sub>p</sub>) as well as structural (measured by <inline-formula id="pcbi.1004541.e025"><alternatives><graphic xlink:href="pcbi.1004541.e025.jpg" id="pcbi.1004541.e025g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M25"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> and ⟨<italic>z</italic>⟩). We also conclude that, contrary to intuition, ⟨<italic>z</italic>⟩, <italic>CO</italic>, <inline-formula id="pcbi.1004541.e026"><alternatives><graphic xlink:href="pcbi.1004541.e026.jpg" id="pcbi.1004541.e026g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M26"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> and <italic>β</italic>-content are not good predictors of either temporal or mechanical stability. This conclusion extends not only for polyQ but also generally for all proteins in CATH.</p><p>Finally, we prove the presence of knots of length 35 at least in Q<sub>60</sub>. The sequential size of these knots suggests a relationship to HD. One of the possible mechanisms for the relevance of the knots in pathology is impairing the process of proteasomal degradation, as suggested in [<xref rid="pcbi.1004541.ref046" ref-type="bibr">46</xref>] and [<xref rid="pcbi.1004541.ref016" ref-type="bibr">16</xref>]. Moreover, although there is evidence for the toxicity of the monomeric polyQ species [<xref rid="pcbi.1004541.ref049" ref-type="bibr">49</xref>], even if the toxicity was due mainly to the oligomers (see <italic>e.g</italic>. Ref. [<xref rid="pcbi.1004541.ref050" ref-type="bibr">50</xref>]), the blockade of the degradation machinery by a knotted monomer would induce an increase of the concentration of aggregating protein, and thus toxicity may be caused by the monomers even if they are not toxic themselves.</p></sec><sec sec-type="supplementary-material" id="sec012"><title>Supporting Information</title><supplementary-material content-type="local-data" id="pcbi.1004541.s001"><label>S1 Text</label><caption><title>The details of structure generation and selection are explained here, together with the stability associated to the coordination number.</title><p>Furthermore, a statistical analysis of the lack of relation between <italic>F</italic><sub>max</sub> and the rest of the descriptors used in this work is also presented.</p><p>(PDF)</p></caption><media xlink:href="pcbi.1004541.s001.pdf"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s002"><label>S1 Fig</label><caption><title>Five conformers with highest mechanical stability in set Q<sub>60</sub>.</title><p>The structure with the biggest <italic>F</italic><sub>max</sub> is at the top. The left column shows snapshots of the structures. The red ribbons represent β strands and the red lines correspond to β bridges. The black lines indicate hydrogen-bonded turns. The orange spheres mark the termini, from which the molecule is pulled. The center column displays the unfolding <italic>F</italic> − <italic>d</italic> curve (left axis) together with the unfolding scenario diagram (right axis), <italic>i.e</italic>. the time a contact is broken <italic>vs</italic>. the distance between the residues that are in contact. The column on the right shows the values of the relevant descriptors. All molecule cartoons were generated using VMD [<xref rid="pcbi.1004541.ref048" ref-type="bibr">48</xref>].</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s002.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s003"><label>S2 Fig</label><caption><title>Five conformers with highest mechanical stability in set Q<sub>20</sub>.</title><p>The structure with the biggest <italic>F</italic><sub>max</sub> is at the top. The left column shows snapshots of the structures. The red ribbons represent β strands and the red lines correspond to β bridges, while blue helices are α helices. The black lines indicate hydrogen-bonded turns. The center column displays the unfolding <italic>F</italic> − <italic>d</italic> curve (left axis) together with the unfolding scenario diagram (right axis). The column on the right shows the values of the relevant descriptors.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s003.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s004"><label>S3 Fig</label><caption><title>Five conformers with highest mechanical stability in set V<sub>60</sub>.</title><p>The structure with the biggest <italic>F</italic><sub>max</sub> is at the top. The left column shows snapshots of the structures. The red ribbons represent β strands and the red lines correspond to β bridges. The black lines indicate hydrogen-bonded turns and α-helices are depicted in blue. The center column displays the unfolding <italic>F</italic> − <italic>d</italic> curve (left axis) together with the unfolding scenario diagram (right axis). The column on the right shows the values of the relevant descriptors.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s004.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s005"><label>S4 Fig</label><caption><title>Scatter plot of <italic>F</italic><sub>max</sub><italic>vs</italic>. α, β and hydrogen-bonded turns (τ) content for polyQ chains.</title><p>The horizontal dashed lines mark off the top five values of <italic>F</italic><sub>max</sub>.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s005.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s006"><label>S5 Fig</label><caption><title>Scatter plot of <italic>F</italic><sub>max</sub><italic>vs</italic>. <italic>CO</italic> for the specified sets.</title><p>The horizontal dashed lines mark off the top five values of <italic>F</italic><sub>max</sub>.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s006.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s007"><label>S6 Fig</label><caption><title>Kinetics of independent structure formation for Q<sub>60</sub> (circles), V<sub>60</sub> (triangles) and Q<sub>20</sub> (diamonds).</title><p>Although more complete plots should be fit with a double exponential function [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>], short trajectories correspond to a linear behavior. The fitted slopes are .28, .62 and .98 respectively. Data for V<sub>60</sub> were taken from [<xref rid="pcbi.1004541.ref004" ref-type="bibr">4</xref>].</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s007.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s008"><label>S7 Fig</label><caption><title>Examples of knotted structures.</title><p>The top structure corresponds to a three-twist (5<sub>2</sub>) knot in Q<sub>60</sub>, while the lower panels are for a trefoil knot from V<sub>60</sub>, where no other knots were found. Left column shows a representation of the molecule before stretching, with the knot ends highlighted with yellow spheres. Right panels show the molecules partially stretched, and the region inside the knot is highlighted in red and zoomed in.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s008.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s009"><label>S8 Fig</label><caption><title>Time evolution of the knots.</title><p>Three randomly chosen knotted conformers were simulated with all-atom and explicit solvent. One of them is shown in <xref ref-type="fig" rid="pcbi.1004541.g004">Fig 4</xref>. The top panel shows the evolution of the knot size with time for one of the simulations. The middle panel shows a histogram of the knot sizes along this time for the three simulations, each with a different color. The bottom panel shows a histogram of the respective knot ends, the left end (<italic>k</italic><sub>−</sub>, inverted) and the right ones (<italic>k</italic><sub>+</sub>).</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s009.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s010"><label>S9 Fig</label><caption><title>An example of the <inline-formula id="pcbi.1004541.e027"><alternatives><graphic xlink:href="pcbi.1004541.e027.jpg" id="pcbi.1004541.e027g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M27"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> sieve and time clustering stages.</title><p>The gray line in the top panel shows evolution of <inline-formula id="pcbi.1004541.e028"><alternatives><graphic xlink:href="pcbi.1004541.e028.jpg" id="pcbi.1004541.e028g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M28"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> with time for one of the replicas. Structures with <inline-formula id="pcbi.1004541.e029"><alternatives><graphic xlink:href="pcbi.1004541.e029.jpg" id="pcbi.1004541.e029g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M29"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> > 30% (the thin horizontal line) are taken for clustering. A cluster ends whenever the gap between successive structured conformers becomes greater than 50 ps. The black dots correspond to structures that represent clusters: these are the structures with the highest <inline-formula id="pcbi.1004541.e030"><alternatives><graphic xlink:href="pcbi.1004541.e030.jpg" id="pcbi.1004541.e030g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M30"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula> in the cluster. The red box in the top panel is shown zoomed in the middle panel, where clusters are represented by red lines. The bottom panel shows the RMSD of each cluster representative relative to the previous one. All of these RMSD’s are greater than 2 Å so the clusters can be considered to be uncorrelated in time.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s010.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s011"><label>S10 Fig</label><caption><title>Color-map plots of the difference between the joint CDF and the product of the independent CDFs of <italic>F</italic><sub>max</sub> and the specified descriptor.</title><p>Differences are always below 0.1, and below 0.05 in three of the descriptors (<inline-formula id="pcbi.1004541.e031"><alternatives><graphic xlink:href="pcbi.1004541.e031.jpg" id="pcbi.1004541.e031g" mimetype="image" position="anchor" orientation="portrait"></graphic><mml:math id="M31"><mml:mtext mathvariant="double-struck">SS</mml:mtext></mml:math></alternatives></inline-formula>, <italic>CO</italic> and τ). Therefore, <italic>F</italic><sub>max</sub> is statistically independent of the descriptors studied.</p><p>(TIF)</p></caption><media xlink:href="pcbi.1004541.s011.tif"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="pcbi.1004541.s012"><label>S1 Table</label><caption><title>Parameters of a linear regression for the dependence of <italic>F</italic><sub>max</sub> on various structural descriptors.</title><p>The top panel lists the values of the Pearson <italic>R</italic><sup>2</sup> coefficients with a 95% confidence interval. The lower panel lists the slopes of the linear fits together with the error bars. The number in the parenthesis is the corresponding <italic>p</italic>-value. Even though the slope for each correlation is significantly different from zero; <italic>R</italic><sup>2</sup> is never close to one, so no correlation can be established between the descriptors and <italic>F</italic><sub>max</sub>. This is also assessed in <xref ref-type="supplementary-material" rid="pcbi.1004541.s011">S10 Fig</xref>.</p><p>(PDF)</p></caption><media xlink:href="pcbi.1004541.s012.pdf"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material></sec></body><back><ack><p>We thank many critical discussions with P. Cossio, R. Hervás, A. Rodríguez and J.M. Ortiz. We also acknowledge the contribution of TeideHPC and SVG High-Performance Computing facilities. TeideHPC facilities are provided by the Instituto Tecnolgico y de Energas Renovables (ITER), S.A., <ext-link ext-link-type="uri" xlink:href="http://www.iter.es">www.iter.es</ext-link>. SVG HPC facilities are provided by the Galician Supercomputing Center (CESGA), <ext-link ext-link-type="uri" xlink:href="http://www.cesga.es">www.cesga.es</ext-link>.</p></ack><ref-list><title>References</title><ref id="pcbi.1004541.ref001"><label>1</label><mixed-citation publication-type="journal"><name><surname>Chothia</surname><given-names>C</given-names></name>, <name><surname>Finkelstein</surname><given-names>AV</given-names></name>. <article-title>The classification and origins of protein folding patterns</article-title>. <source>Annual Review of Biochemistry</source>. <year>1990</year>;<volume>59</volume>(<issue>1</issue>):<fpage>1007</fpage>–<lpage>1035</lpage>.
<pub-id pub-id-type="pmid">2197975</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref002"><label>2</label><mixed-citation publication-type="journal"><name><surname>Chothia</surname><given-names>C</given-names></name>. <article-title>One thousand families for the molecular biologist</article-title>. <source>Nature</source>. <year>1992</year><month>6</month>;<volume>357</volume>(<issue>6379</issue>):<fpage>543</fpage>–<lpage>544</lpage>. <pub-id pub-id-type="doi">10.1038/357543a0</pub-id><pub-id pub-id-type="pmid">1608464</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref003"><label>3</label><mixed-citation publication-type="journal"><name><surname>Sillitoe</surname><given-names>I</given-names></name>, <name><surname>Cuff</surname><given-names>AL</given-names></name>, <name><surname>Dessailly</surname><given-names>BH</given-names></name>, <name><surname>Dawson</surname><given-names>NL</given-names></name>, <name><surname>Furnham</surname><given-names>N</given-names></name>, <name><surname>Lee</surname><given-names>D</given-names></name>, <etal>et al</etal><article-title>New functional families (FunFams) in CATH to improve the mapping of conserved functional sites to 3D structures</article-title>. <source>Nucleic Acids Research</source>. <year>2013</year>;<volume>41</volume>(<issue>D1</issue>):<fpage>D490</fpage>–<lpage>D498</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://nar.oxfordjournals.org/content/41/D1/D490.abstract">http://nar.oxfordjournals.org/content/41/D1/D490.abstract</ext-link>. <pub-id pub-id-type="doi">10.1093/nar/gks1211</pub-id><pub-id pub-id-type="pmid">23203873</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref004"><label>4</label><mixed-citation publication-type="journal"><name><surname>Cossio</surname><given-names>P</given-names></name>, <name><surname>Trovato</surname><given-names>A</given-names></name>, <name><surname>Pietrucci</surname><given-names>F</given-names></name>, <name><surname>Seno</surname><given-names>F</given-names></name>, <name><surname>Maritan</surname><given-names>A</given-names></name>, <name><surname>Laio</surname><given-names>A</given-names></name>. <article-title>Exploring the universe of protein structures beyond the Protein Data Bank</article-title>. <source>PLoS Comput Biol</source>. <year>2010</year>;<volume>6</volume>(<issue>11</issue>):<fpage>e1000957</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000957</pub-id><pub-id pub-id-type="pmid">21079678</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref005"><label>5</label><mixed-citation publication-type="journal"><name><surname>Zhang</surname><given-names>Y</given-names></name>, <name><surname>Skolnick</surname><given-names>J</given-names></name>. <article-title>Scoring function for automated assessment of protein structure template quality</article-title>. <source>Proteins: Structure, Function, and Bioinformatics</source>. <year>2004</year>;<volume>57</volume>(<issue>4</issue>):<fpage>702</fpage>–<lpage>710</lpage>. <pub-id pub-id-type="doi">10.1002/prot.20264</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref006"><label>6</label><mixed-citation publication-type="journal"><name><surname>Magrane</surname><given-names>M</given-names></name>, <name><surname>Consortium</surname><given-names>U</given-names></name>. <article-title>UniProt Knowledgebase: a hub of integrated protein data</article-title>. <source>Database</source>. <year>2011</year>;<volume>2011</volume><pub-id pub-id-type="doi">10.1093/database/bar009</pub-id><pub-id pub-id-type="pmid">21447597</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref007"><label>7</label><mixed-citation publication-type="journal"><name><surname>Nasir</surname><given-names>J</given-names></name>, <name><surname>Floresco</surname><given-names>SB</given-names></name>, <name><surname>O’Kusky</surname><given-names>JR</given-names></name>, <name><surname>Diewert</surname><given-names>VM</given-names></name>, <name><surname>Richman</surname><given-names>JM</given-names></name>, <name><surname>Zeisler</surname><given-names>J</given-names></name>, <etal>et al</etal><article-title>Targeted disruption of the Huntington’s disease gene results in embryonic lethality and behavioral and morphological changes in heterozygotes</article-title>. <source>Cell</source>. <year>1995</year>;<volume>81</volume>(<issue>5</issue>):<fpage>811</fpage>—<lpage>823</lpage>. <pub-id pub-id-type="doi">10.1016/0092-8674(95)90542-1</pub-id><pub-id pub-id-type="pmid">7774020</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref008"><label>8</label><mixed-citation publication-type="journal"><name><surname>Zuccato</surname><given-names>C</given-names></name>, <name><surname>Ciammola</surname><given-names>A</given-names></name>, <name><surname>Rigamonti</surname><given-names>D</given-names></name>, <name><surname>Leavitt</surname><given-names>BR</given-names></name>, <name><surname>Goffredo</surname><given-names>D</given-names></name>, <name><surname>Conti</surname><given-names>L</given-names></name>, <etal>et al</etal><article-title>Loss of Huntingtin-Mediated BDNF Gene Transcription in Huntington’s Disease</article-title>. <source>Science</source>. <year>2001</year>;<volume>293</volume>(<issue>5529</issue>):<fpage>493</fpage>–<lpage>498</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.sciencemag.org/content/293/5529/493.abstract">http://www.sciencemag.org/content/293/5529/493.abstract</ext-link>. <pub-id pub-id-type="doi">10.1126/science.1059581</pub-id><pub-id pub-id-type="pmid">11408619</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref009"><label>9</label><mixed-citation publication-type="journal"><name><surname>Velier</surname><given-names>J</given-names></name>, <name><surname>Kim</surname><given-names>M</given-names></name>, <name><surname>Schwarz</surname><given-names>C</given-names></name>, <name><surname>Kim</surname><given-names>TW</given-names></name>, <name><surname>Sapp</surname><given-names>E</given-names></name>, <name><surname>Chase</surname><given-names>K</given-names></name>, <etal>et al</etal><article-title>Wild-Type and Mutant Huntingtins Function in Vesicle Trafficking in the Secretory and Endocytic Pathways</article-title>. <source>Experimental Neurology</source>. <year>1998</year>;<volume>152</volume>(<issue>1</issue>):<fpage>34</fpage>—<lpage>40</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.sciencedirect.com/science/article/pii/S0014488698968327">http://www.sciencedirect.com/science/article/pii/S0014488698968327</ext-link>. <pub-id pub-id-type="doi">10.1006/exnr.1998.6832</pub-id><pub-id pub-id-type="pmid">9682010</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref010"><label>10</label><mixed-citation publication-type="journal"><name><surname>Petruska</surname><given-names>J</given-names></name>, <name><surname>Hartenstine</surname><given-names>MJ</given-names></name>, <name><surname>Goodman</surname><given-names>MF</given-names></name>. <article-title>Analysis of Strand Slippage in DNA Polymerase Expansions of CAG/CTG Triplet Repeats Associated with Neurodegenerative Disease</article-title>. <source>Journal of Biological Chemistry</source>. <year>1998</year>;<volume>273</volume>(<issue>9</issue>):<fpage>5204</fpage>–<lpage>5210</lpage>. <pub-id pub-id-type="doi">10.1074/jbc.273.9.5204</pub-id><pub-id pub-id-type="pmid">9478975</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref011"><label>11</label><mixed-citation publication-type="journal"><name><surname>Ross</surname><given-names>CA</given-names></name>. <article-title>Polyglutamine Pathogenesis: Emergence of Unifying Mechanisms for Huntington’s Disease and Related Disorders</article-title>. <source>Neuron</source>. <year>2002</year>;<volume>35</volume>(<issue>5</issue>):<fpage>819</fpage>—<lpage>822</lpage>. <pub-id pub-id-type="doi">10.1016/S0896-6273(02)00872-3</pub-id><pub-id pub-id-type="pmid">12372277</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref012"><label>12</label><mixed-citation publication-type="journal"><name><surname>Pla</surname><given-names>P</given-names></name>, <name><surname>Orvoen</surname><given-names>S</given-names></name>, <name><surname>Saudou</surname><given-names>F</given-names></name>, <name><surname>DAVID</surname><given-names>DJ</given-names></name>, <name><surname>Humbert</surname><given-names>S</given-names></name>. <article-title>Mood disorders in Huntington’s disease: from behavior to cellular and molecular mechanisms</article-title>. <source>Frontiers in Behavioral Neuroscience</source>. <year>2014</year>;<volume>8</volume>(<issue>135</issue>). <pub-id pub-id-type="doi">10.3389/fnbeh.2014.00135</pub-id><pub-id pub-id-type="pmid">24795586</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref013"><label>13</label><mixed-citation publication-type="journal"><name><surname>Fan</surname><given-names>HC</given-names></name>, <name><surname>Ho</surname><given-names>LI</given-names></name>, <name><surname>Chi</surname><given-names>CS</given-names></name>, <name><surname>Chen</surname><given-names>SJ</given-names></name>, <name><surname>Peng</surname><given-names>GS</given-names></name>, <name><surname>Chan</surname><given-names>TM</given-names></name>, <etal>et al</etal><article-title>Polyglutamine (PolyQ) Diseases: Genetics to Treatments</article-title>. <source>Cell Transplantation</source>. 2014-04-09T00:00:00;<volume>23</volume>(<issue>4–5</issue>):<fpage>441</fpage>–<lpage>458</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.ingentaconnect.com/content/cog/ct/2014/00000023/F0020004/art00006">http://www.ingentaconnect.com/content/cog/ct/2014/00000023/F0020004/art00006</ext-link>.
<pub-id pub-id-type="pmid">24816443</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref014"><label>14</label><mixed-citation publication-type="journal"><name><surname>Albrecht</surname><given-names>A</given-names></name>, <name><surname>Mundlos</surname><given-names>S</given-names></name>. <article-title>The other trinucleotide repeat: polyalanine expansion disorders</article-title>. <source>Current Opinion in Genetics & Development</source>. <year>2005</year>;<volume>15</volume>(<issue>3</issue>):<fpage>285</fpage>—<lpage>293</lpage>. Genetics of disease. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.sciencedirect.com/science/article/pii/S0959437X05000559">http://www.sciencedirect.com/science/article/pii/S0959437X05000559</ext-link>. <pub-id pub-id-type="doi">10.1016/j.gde.2005.04.003</pub-id><pub-id pub-id-type="pmid">15917204</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref015"><label>15</label><mixed-citation publication-type="journal"><name><surname>Amiel</surname><given-names>J</given-names></name>, <name><surname>Trochet</surname><given-names>D</given-names></name>, <name><surname>Clément-Ziza</surname><given-names>M</given-names></name>, <name><surname>Munnich</surname><given-names>A</given-names></name>, <name><surname>Lyonnet</surname><given-names>S</given-names></name>. <article-title>Polyalanine expansions in human</article-title>. <source>Human Molecular Genetics</source>. <year>2004</year>;<volume>13</volume>(<issue>suppl 2</issue>):<fpage>R235</fpage>–<lpage>R243</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://hmg.oxfordjournals.org/content/13/suppl_2/R235.abstract">http://hmg.oxfordjournals.org/content/13/suppl_2/R235.abstract</ext-link>. <pub-id pub-id-type="doi">10.1093/hmg/ddh251</pub-id><pub-id pub-id-type="pmid">15358730</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref016"><label>16</label><mixed-citation publication-type="journal"><name><surname>Hervás</surname><given-names>R</given-names></name>, <name><surname>Oroz</surname><given-names>J</given-names></name>, <name><surname>Galera-Prat</surname><given-names>A</given-names></name>, <name><surname>Goñi</surname><given-names>O</given-names></name>, <name><surname>Valbuena</surname><given-names>A</given-names></name>, <name><surname>Vera</surname><given-names>AM</given-names></name>, <etal>et al</etal><article-title>Common features at the start of the neurodegeneration cascade</article-title>. <source>PLoS Biol</source>. <year>2012</year>;<volume>10</volume>(<issue>5</issue>):<fpage>e1001335</fpage><pub-id pub-id-type="doi">10.1371/journal.pbio.1001335</pub-id><pub-id pub-id-type="pmid">22666178</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref017"><label>17</label><mixed-citation publication-type="journal"><name><surname>Piana</surname><given-names>S</given-names></name>, <name><surname>Laio</surname><given-names>A</given-names></name>. <article-title>A bias-exchange approach to protein folding</article-title>. <source>The Journal of Physical Chemistry B</source>. <year>2007</year><month>5</month>;<volume>111</volume>(<issue>17</issue>):<fpage>4553</fpage>–<lpage>4559</lpage>. <pub-id pub-id-type="doi">10.1021/jp067873l</pub-id><pub-id pub-id-type="pmid">17419610</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref018"><label>18</label><mixed-citation publication-type="journal"><name><surname>Sułkowska</surname><given-names>JI</given-names></name>, <name><surname>Cieplak</surname><given-names>M</given-names></name>. <article-title>Mechanical stretching of proteins—a theoretical survey of the Protein Data Bank</article-title>. <source>Journal of Physics: Condensed Matter</source>. <year>2007</year>;<volume>19</volume>(<issue>28</issue>):<fpage>283201</fpage>.</mixed-citation></ref><ref id="pcbi.1004541.ref019"><label>19</label><mixed-citation publication-type="journal"><name><surname>Sikora</surname><given-names>M</given-names></name>, <name><surname>Sułkowska</surname><given-names>JI</given-names></name>, <name><surname>Cieplak</surname><given-names>M</given-names></name>. <article-title>Mechanical strength of 17,134 model proteins and cysteine slipknots</article-title>. <source>PLoS Comput Biol</source>. <year>2009</year><month>10</month>;<volume>5</volume>(<issue>10</issue>):<fpage>e1000547</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000547</pub-id><pub-id pub-id-type="pmid">19876372</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref020"><label>20</label><mixed-citation publication-type="journal"><name><surname>Ferreon</surname><given-names>ACM</given-names></name>, <name><surname>Moran</surname><given-names>CR</given-names></name>, <name><surname>Gambin</surname><given-names>Y</given-names></name>, <name><surname>Deniz</surname><given-names>AA</given-names></name>. <article-title>Single-molecule fluorescence studies of intrinsically disordered proteins</article-title>. <source>Methods in Enzymology</source>. <year>2010</year>;<volume>472</volume>:<fpage>179</fpage>–<lpage>204</lpage>. <pub-id pub-id-type="doi">10.1016/S0076-6879(10)72010-3</pub-id><pub-id pub-id-type="pmid">20580965</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref021"><label>21</label><mixed-citation publication-type="journal"><name><surname>Hess</surname><given-names>B</given-names></name>, <name><surname>Kutzner</surname><given-names>C</given-names></name>, <name><surname>van der Spoel</surname><given-names>D</given-names></name>, <name><surname>Lindahl</surname><given-names>E</given-names></name>. <article-title>GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation</article-title>. <source>Journal of Chemical Theory and Computation</source>. <year>2008</year>;<volume>4</volume>(<issue>3</issue>):<fpage>435</fpage>–<lpage>447</lpage>. <pub-id pub-id-type="doi">10.1021/ct700301q</pub-id><pub-id pub-id-type="pmid">26620784</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref022"><label>22</label><mixed-citation publication-type="journal"><name><surname>Bonomi</surname><given-names>M</given-names></name>, <name><surname>Branduardi</surname><given-names>D</given-names></name>, <name><surname>Bussi</surname><given-names>G</given-names></name>, <name><surname>Camilloni</surname><given-names>C</given-names></name>, <name><surname>Provasi</surname><given-names>D</given-names></name>, <name><surname>Raiteri</surname><given-names>P</given-names></name>, <etal>et al</etal><article-title>PLUMED: A portable plugin for free-energy calculations with molecular dynamics</article-title>. <source>Computer Physics Communications</source>. <year>2009</year>;<volume>180</volume>(<issue>10</issue>):<fpage>1961</fpage>–<lpage>1972</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.sciencedirect.com/science/article/pii/S001046550900157X">http://www.sciencedirect.com/science/article/pii/S001046550900157X</ext-link>. <pub-id pub-id-type="doi">10.1016/j.cpc.2009.05.011</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref023"><label>23</label><mixed-citation publication-type="journal"><name><surname>Cornell</surname><given-names>WD</given-names></name>, <name><surname>Cieplak</surname><given-names>P</given-names></name>, <name><surname>Bayly</surname><given-names>CI</given-names></name>, <name><surname>Gould</surname><given-names>IR</given-names></name>, <name><surname>Merz</surname><given-names>KM</given-names></name>, <name><surname>Ferguson</surname><given-names>DM</given-names></name>, <etal>et al</etal><article-title>A second generation force field for the simulation of proteins, nucleic acids, and organic molecules</article-title>. <source>Journal of the American Chemical Society</source>. <year>1995</year>;<volume>117</volume>(<issue>19</issue>):<fpage>5179</fpage>–<lpage>5197</lpage>. <pub-id pub-id-type="doi">10.1021/ja00124a002</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref024"><label>24</label><mixed-citation publication-type="journal"><name><surname>Qiu</surname><given-names>D</given-names></name>, <name><surname>Shenkin</surname><given-names>PS</given-names></name>, <name><surname>Hollinger</surname><given-names>FP</given-names></name>, <name><surname>Still</surname><given-names>WC</given-names></name>. <article-title>The GB/SA continuum model for solvation. A fast analytical method for the calculation of approximate Born radii</article-title>. <source>The Journal of Physical Chemistry A</source>. <year>1997</year>;<volume>101</volume>(<issue>16</issue>):<fpage>3005</fpage>–<lpage>3014</lpage>. <pub-id pub-id-type="doi">10.1021/jp961992r</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref025"><label>25</label><mixed-citation publication-type="journal"><name><surname>Pietrucci</surname><given-names>F</given-names></name>, <name><surname>Laio</surname><given-names>A</given-names></name>. <article-title>A Collective Variable for the Efficient Exploration of Protein Beta-Sheet Structures: Application to SH3 and GB1</article-title>. <source>Journal of Chemical Theory and Computation</source>. <year>2009</year>;<volume>5</volume>(<issue>9</issue>):<fpage>2197</fpage>–<lpage>2201</lpage>. <pub-id pub-id-type="doi">10.1021/ct900202f</pub-id><pub-id pub-id-type="pmid">26616604</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref026"><label>26</label><mixed-citation publication-type="book"><name><surname>Eswar</surname><given-names>N</given-names></name>, <name><surname>Webb</surname><given-names>B</given-names></name>, <name><surname>Marti-Renom</surname><given-names>MA</given-names></name>, <name><surname>Madhusudhan</surname><given-names>MS</given-names></name>, <name><surname>Eramian</surname><given-names>D</given-names></name>, <name><surname>Shen</surname><given-names>My</given-names></name>, <etal>et al</etal> In: <source>Comparative Protein Structure Modeling Using Modeller</source>. <publisher-name>John Wiley & Sons, Inc</publisher-name>; <year>2002</year> Available from: <pub-id pub-id-type="doi">10.1002/0471250953.bi0506s15</pub-id>.</mixed-citation></ref><ref id="pcbi.1004541.ref027"><label>27</label><mixed-citation publication-type="book"><name><surname>Hestenes</surname><given-names>MR</given-names></name>, <name><surname>Stiefel</surname><given-names>E</given-names></name>. <source>Methods of conjugate gradients for solving linear systems</source>. <volume>vol. 49</volume><publisher-name>National Bureau of Standards Washington, DC</publisher-name>; <year>1952</year>.</mixed-citation></ref><ref id="pcbi.1004541.ref028"><label>28</label><mixed-citation publication-type="journal"><name><surname>Miettinen</surname><given-names>MS</given-names></name>, <name><surname>Knecht</surname><given-names>V</given-names></name>, <name><surname>Monticelli</surname><given-names>L</given-names></name>, <name><surname>Ignatova</surname><given-names>Z</given-names></name>. <article-title>Assessing polyglutamine conformation in the nucleating event by molecular dynamics simulations</article-title>. <source>The Journal of Physical Chemistry B</source>. <year>2012</year>;<volume>116</volume>(<issue>34</issue>):<fpage>10259</fpage>–<lpage>10265</lpage>. <pub-id pub-id-type="doi">10.1021/jp305065c</pub-id><pub-id pub-id-type="pmid">22770401</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref029"><label>29</label><mixed-citation publication-type="journal"><name><surname>Khare</surname><given-names>SD</given-names></name>, <name><surname>Ding</surname><given-names>F</given-names></name>, <name><surname>Gwanmesia</surname><given-names>KN</given-names></name>, <name><surname>Dokholyan</surname><given-names>NV</given-names></name>. <article-title>Molecular origin of polyglutamine aggregation in neurodegenerative diseases</article-title>. <source>PLoS Comput Biol</source>. <year>2005</year>;<volume>1</volume>(<issue>3</issue>):<fpage>230</fpage>–<lpage>235</lpage>. <pub-id pub-id-type="doi">10.1371/journal.pcbi.0010030</pub-id><pub-id pub-id-type="pmid">16158094</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref030"><label>30</label><mixed-citation publication-type="journal"><name><surname>Laghaei</surname><given-names>R</given-names></name>, <name><surname>Mousseau</surname><given-names>N</given-names></name>. <article-title>Spontaneous formation of polyglutamine nanotubes with molecular dynamics simulations</article-title>. <source>The Journal of Chemical Physics</source>. <year>2010</year>;<volume>132</volume>(<issue>16</issue>):<fpage>165102</fpage><pub-id pub-id-type="doi">10.1063/1.3383244</pub-id><pub-id pub-id-type="pmid">20441310</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref031"><label>31</label><mixed-citation publication-type="journal"><name><surname>Cieplak</surname><given-names>M</given-names></name>, <name><surname>Allan</surname><given-names>DB</given-names></name>, <name><surname>Leheny</surname><given-names>RL</given-names></name>, <name><surname>Reich</surname><given-names>DH</given-names></name>. <article-title>Proteins at Air–Water Interfaces: A Coarse-Grained Model</article-title>. <source>Langmuir</source>. <year>2014</year>;<volume>30</volume>:<fpage>1288</fpage>–<lpage>96</lpage>. Available from: <pub-id pub-id-type="doi">10.1021/la502465m</pub-id>.</mixed-citation></ref><ref id="pcbi.1004541.ref032"><label>32</label><mixed-citation publication-type="journal"><name><surname>Sikora</surname><given-names>M</given-names></name>, <name><surname>Szymczak</surname><given-names>P</given-names></name>, <name><surname>Thompson</surname><given-names>D</given-names></name>, <name><surname>Cieplak</surname><given-names>M</given-names></name>. <article-title>Linker-mediated assembly of gold nanoparticles into multimeric motifs</article-title>. <source>Nanotechnology</source>. <year>2011</year>;<volume>22</volume>(<issue>44</issue>):<fpage>445601</fpage><pub-id pub-id-type="doi">10.1088/0957-4484/22/44/445601</pub-id><pub-id pub-id-type="pmid">21979426</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref033"><label>33</label><mixed-citation publication-type="journal"><name><surname>Joosten</surname><given-names>RP</given-names></name>, <name><surname>te Beek</surname><given-names>TAH</given-names></name>, <name><surname>Krieger</surname><given-names>E</given-names></name>, <name><surname>Hekkelman</surname><given-names>ML</given-names></name>, <name><surname>Hooft</surname><given-names>RWW</given-names></name>, <name><surname>Schneider</surname><given-names>R</given-names></name>, <etal>et al</etal><article-title>A series of PDB related databases for everyday needs</article-title>. <source>Nucleic Acids Res</source>. <year>2011</year><month>1</month>;<volume>39</volume>(<issue>Database issue</issue>):<fpage>D411</fpage>–<lpage>D419</lpage>. <pub-id pub-id-type="doi">10.1093/nar/gkq1105</pub-id><pub-id pub-id-type="pmid">21071423</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref034"><label>34</label><mixed-citation publication-type="journal"><name><surname>Tsai</surname><given-names>J</given-names></name>, <name><surname>Taylor</surname><given-names>R</given-names></name>, <name><surname>Chothia</surname><given-names>C</given-names></name>, <name><surname>Gerstein</surname><given-names>M</given-names></name>. <article-title>The packing density in proteins: standard radii and volumes</article-title>. <source>Journal of Molecular Biology</source>. <year>1999</year>;<volume>290</volume>(<issue>1</issue>):<fpage>253</fpage>–<lpage>266</lpage>. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.sciencedirect.com/science/article/pii/S0022283699928292">http://www.sciencedirect.com/science/article/pii/S0022283699928292</ext-link>. <pub-id pub-id-type="doi">10.1006/jmbi.1999.2829</pub-id><pub-id pub-id-type="pmid">10388571</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref035"><label>35</label><mixed-citation publication-type="journal"><name><surname>Maxwell</surname><given-names>JC</given-names></name>. <article-title>L. on the calculation of the equilibrium and stiffness of frames</article-title>. <source>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Sciences</source>. <year>1864</year>;<volume>27</volume>(<issue>182</issue>):<fpage>294</fpage>–<lpage>299</lpage>.</mixed-citation></ref><ref id="pcbi.1004541.ref036"><label>36</label><mixed-citation publication-type="journal"><name><surname>Cieplak</surname><given-names>M</given-names></name>, <name><surname>Robbins</surname><given-names>MO</given-names></name>. <article-title>Nanoindentation of 35 virus capsids in a molecular model: relating mechanical properties to structure</article-title>. <source>PloS One</source>. <year>2013</year>;<volume>8</volume>(<issue>6</issue>):<fpage>e63640</fpage><pub-id pub-id-type="doi">10.1371/journal.pone.0063640</pub-id><pub-id pub-id-type="pmid">23785395</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref037"><label>37</label><mixed-citation publication-type="journal"><name><surname>Sułkowska</surname><given-names>JI</given-names></name>, <name><surname>Cieplak</surname><given-names>M</given-names></name>. <article-title>Selection of optimal variants of Gō-like models of proteins through studies of stretching</article-title>. <source>Biophysical Journal</source>. <year>2008</year>;<volume>95</volume>(<issue>7</issue>):<fpage>3174</fpage>–<lpage>3191</lpage>. <pub-id pub-id-type="doi">10.1529/biophysj.107.127233</pub-id><pub-id pub-id-type="pmid">18567634</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref038"><label>38</label><mixed-citation publication-type="journal"><name><surname>Plaxco</surname><given-names>KW</given-names></name>, <name><surname>Simons</surname><given-names>KT</given-names></name>, <name><surname>Baker</surname><given-names>D</given-names></name>. <article-title>Contact order, transition state placement and the refolding rates of single domain proteins</article-title>. <source>Journal of Molecular Biology</source>. <year>1998</year>;<volume>277</volume>(<issue>4</issue>):<fpage>985</fpage>–<lpage>994</lpage>. <pub-id pub-id-type="doi">10.1006/jmbi.1998.1645</pub-id><pub-id pub-id-type="pmid">9545386</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref039"><label>39</label><mixed-citation publication-type="journal"><name><surname>Kesner</surname><given-names>BA</given-names></name>, <name><surname>Ding</surname><given-names>F</given-names></name>, <name><surname>Temple</surname><given-names>BR</given-names></name>, <name><surname>Dokholyan</surname><given-names>NV</given-names></name>. <article-title>N-terminal strands of filamin Ig domains act as a conformational switch under biological forces</article-title>. <source>Proteins: Structure, Function, and Bioinformatics</source>. <year>2010</year>;<volume>78</volume>(<issue>1</issue>):<fpage>12</fpage>–<lpage>24</lpage>. <pub-id pub-id-type="doi">10.1002/prot.22479</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref040"><label>40</label><mixed-citation publication-type="journal"><name><surname>Cieplak</surname><given-names>M</given-names></name>, <name><surname>Hoang</surname><given-names>TX</given-names></name>. <article-title>Universality classes in folding times of proteins</article-title>. <source>Biophysical Journal</source>. <year>2003</year>;<volume>84</volume>(<issue>1</issue>):<fpage>475</fpage>–<lpage>488</lpage>. <pub-id pub-id-type="doi">10.1016/S0006-3495(03)74867-X</pub-id><pub-id pub-id-type="pmid">12524300</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref041"><label>41</label><mixed-citation publication-type="journal"><name><surname>Berkovich</surname><given-names>R</given-names></name>, <name><surname>Garcia-Manyes</surname><given-names>S</given-names></name>, <name><surname>Klafter</surname><given-names>J</given-names></name>, <name><surname>Urbakh</surname><given-names>M</given-names></name>, <name><surname>Fernández</surname><given-names>JM</given-names></name>. <article-title>Hopping around an entropic barrier created by force</article-title>. <source>Biochemical and Biophysical Research Communications</source>. <year>2010</year>;<volume>403</volume>(<issue>1</issue>):<fpage>133</fpage>–<lpage>137</lpage>. <pub-id pub-id-type="doi">10.1016/j.bbrc.2010.10.133</pub-id><pub-id pub-id-type="pmid">21050839</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref042"><label>42</label><mixed-citation publication-type="journal"><name><surname>Rief</surname><given-names>M</given-names></name>, <name><surname>Gautel</surname><given-names>M</given-names></name>, <name><surname>Oesterhelt</surname><given-names>F</given-names></name>, <name><surname>Fernandez</surname><given-names>JM</given-names></name>, <name><surname>Gaub</surname><given-names>HE</given-names></name>. <article-title>Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM</article-title>. <source>Science</source>. <year>1997</year>;<volume>276</volume>(<issue>5315</issue>):<fpage>1109</fpage>–<lpage>1112</lpage>. <pub-id pub-id-type="doi">10.1126/science.276.5315.1109</pub-id><pub-id pub-id-type="pmid">9148804</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref043"><label>43</label><mixed-citation publication-type="journal"><name><surname>Carrion-Vazquez</surname><given-names>M</given-names></name>, <name><surname>Oberhauser</surname><given-names>AF</given-names></name>, <name><surname>Fowler</surname><given-names>SB</given-names></name>, <name><surname>Marszalek</surname><given-names>PE</given-names></name>, <name><surname>Broedel</surname><given-names>SE</given-names></name>, <name><surname>Clarke</surname><given-names>J</given-names></name>, <etal>et al</etal><article-title>Mechanical and chemical unfolding of a single protein: A comparison</article-title>. <source>Proceedings of the National Academy of Sciences USA</source>. <year>1999</year>;<volume>96</volume>(<issue>7</issue>):<fpage>3694</fpage>–<lpage>3699</lpage>. <pub-id pub-id-type="doi">10.1073/pnas.96.7.3694</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref044"><label>44</label><mixed-citation publication-type="journal"><name><surname>Sułkowska</surname><given-names>JI</given-names></name>, <name><surname>Sułkowski</surname><given-names>P</given-names></name>, <name><surname>Szymczak</surname><given-names>P</given-names></name>, <name><surname>Cieplak</surname><given-names>M</given-names></name>. <article-title>Tightening of knots in proteins</article-title>. <source>Physical Review Letters</source>. <year>2008</year>;<volume>100</volume>(<issue>5</issue>):<fpage>058106</fpage><pub-id pub-id-type="doi">10.1103/PhysRevLett.100.058106</pub-id><pub-id pub-id-type="pmid">18352439</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref045"><label>45</label><mixed-citation publication-type="journal"><name><surname>Taylor</surname><given-names>WR</given-names></name>. <article-title>A deeply knotted protein structure and how it might fold</article-title>. <source>Nature</source>. <year>2000</year>;<volume>406</volume>(<issue>6798</issue>):<fpage>916</fpage>–<lpage>919</lpage>. <pub-id pub-id-type="doi">10.1038/35022623</pub-id><pub-id pub-id-type="pmid">10972297</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref046"><label>46</label><mixed-citation publication-type="journal"><name><surname>Virnau</surname><given-names>P</given-names></name>, <name><surname>Mirny</surname><given-names>LA</given-names></name>, <name><surname>Kardar</surname><given-names>M</given-names></name>. <article-title>Intricate knots in proteins: Function and evolution</article-title>. <source>PLoS Computational Biology</source>. <year>2006</year>;<volume>2</volume>(<issue>9</issue>):<fpage>e122</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.0020122</pub-id><pub-id pub-id-type="pmid">16978047</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref047"><label>47</label><mixed-citation publication-type="journal"><name><surname>Sułkowska</surname><given-names>JI</given-names></name>, <name><surname>Rawdon</surname><given-names>EJ</given-names></name>, <name><surname>Millett</surname><given-names>KC</given-names></name>, <name><surname>Onuchic</surname><given-names>JN</given-names></name>, <name><surname>Stasiak</surname><given-names>A</given-names></name>. <article-title>Conservation of complex knotting and slipknotting patterns in proteins</article-title>. <source>Proceedings of the National Academy of Sciences USA</source>. <year>2012</year>;<volume>109</volume>(<issue>26</issue>):<fpage>E1715</fpage>–<lpage>E1723</lpage>. <pub-id pub-id-type="doi">10.1073/pnas.1205918109</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref048"><label>48</label><mixed-citation publication-type="journal"><name><surname>Humphrey</surname><given-names>W</given-names></name>, <name><surname>Dalke</surname><given-names>A</given-names></name>, <name><surname>Schulten</surname><given-names>K</given-names></name>. <article-title>VMD: visual molecular dynamics</article-title>. <source>Journal of Molecular Graphics</source>. <year>1996</year>;<volume>14</volume>(<issue>1</issue>):<fpage>33</fpage>–<lpage>38</lpage>. <pub-id pub-id-type="doi">10.1016/0263-7855(96)00018-5</pub-id><pub-id pub-id-type="pmid">8744570</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref049"><label>49</label><mixed-citation publication-type="journal"><name><surname>Nagai</surname><given-names>Y</given-names></name>, <name><surname>Inui</surname><given-names>T</given-names></name>, <name><surname>Popiel</surname><given-names>HA</given-names></name>, <name><surname>Fujikake</surname><given-names>N</given-names></name>, <name><surname>Hasegawa</surname><given-names>K</given-names></name>, <name><surname>Urade</surname><given-names>Y</given-names></name>, <etal>et al</etal><article-title>A toxic monomeric conformer of the polyglutamine protein</article-title>. <source>Nature Structural & Molecular Biology</source>. <year>2007</year>;<volume>14</volume>(<issue>4</issue>):<fpage>332</fpage>–<lpage>340</lpage>. <pub-id pub-id-type="doi">10.1038/nsmb1215</pub-id></mixed-citation></ref><ref id="pcbi.1004541.ref050"><label>50</label><mixed-citation publication-type="journal"><name><surname>Ripaud</surname><given-names>L</given-names></name>, <name><surname>Chumakova</surname><given-names>V</given-names></name>, <name><surname>Antonin</surname><given-names>M</given-names></name>, <name><surname>Hastie</surname><given-names>AR</given-names></name>, <name><surname>Pinkert</surname><given-names>S</given-names></name>, <name><surname>Körner</surname><given-names>R</given-names></name>, <etal>et al</etal><article-title>Overexpression of Q-rich prion-like proteins suppresses polyQ cytotoxicity and alters the polyQ interactome</article-title>. <source>Proceedings of the National Academy of Sciences</source>. <year>2014</year>;<volume>111</volume>(<issue>51</issue>):<fpage>18219</fpage>–<lpage>18224</lpage>. <pub-id pub-id-type="doi">10.1073/pnas.1421313111</pub-id></mixed-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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