{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:08:55Z","timestamp":1785431335369,"version":"3.56.0"},"reference-count":43,"publisher":"International Union of Crystallography (IUCr)","issue":"3","license":[{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html#TDM"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-00277-24-00"],"award-info":[{"award-number":["075-00277-24-00"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["iucr.org","wiley.com","iucrj.org"],"crossmark-restriction":true},"short-container-title":["Acta Crystallogr A Found Adv","Acta Crystallogr A","Acta Crystallogr A Found Crystallogr","Acta Cryst A","Acta Cryst A Found Adv","Acta Cryst Sect A","Acta Cryst Sect A Found Adv","Acta Crystallogr Sect A","Acta Crystallogr Sect A Found Adv","Acta Crystallogr Sect A Found Crystallogr"],"accepted":{"date-parts":[[2025,2,24]]},"published-print":{"date-parts":[[2025,5,1]]},"abstract":"<jats:p>\n                    In a 4D polytope {3, 3, 5}, a 40-vertex toroidal helix is selected that unites the vertices of two orbits of the axis 20\/9 with the angle of rotation 9\u2005\u00d7\u2005360\u00b0\/20 = 162\u00b0. Symmetrization of this helix allows one to select in the 3D spherical space a helix {40\/11} with the angle of rotation of 99\u00b0. Its mapping into the 3D Euclidean space E\n                    <jats:sup>3<\/jats:sup>\n                    determines the helix {40\/11}, which coincides with the helix of atoms C\n                    <jats:sub>\u03b1<\/jats:sub>\n                    in the \u03b1-helix. A tube polytope with the symmetry group \u00b1[O\u00d7D\n                    <jats:sub>20<\/jats:sub>\n                    ] contains a toroidal helix {40\/11}, constructed of 40 prismatic cells. The symmetry of the polytope, as well as the partition it induces on the lateral face of the prismatic cell, allow one to find additional vertices that do not belong to the polytope. Putting the vertices of the helix {40\/11} in correspondence with the atoms C\n                    <jats:sub>\u03b1<\/jats:sub>\n                    and the additional vertices with the atoms O, C\u2032, N, H, determines the peptide plane of the \u03b1-helix; its multiplication by the axis 40\/11 leads to a polytope model of the \u03b1-helix. A radial contraction of the polytope model, with subsequent mapping into E\n                    <jats:sup>3<\/jats:sup>\n                    , leads to its densely packed structural realization \u2013 the \u03b1-helix that is universal in proteins. A polytope with the group of symmetry \u00b1[O\u00d7D\n                    <jats:sub>20<\/jats:sub>\n                    ] arises in the family of tube polytopes with the starting group \u00b11\/2[O\u00d7C\n                    <jats:sub>\n                      2\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    ] at\n                    <jats:italic>n<\/jats:italic>\n                    = 5. Along with the axis 40\/11 of a single \u03b1-helix, the screw axes of this family of polytopes determine the axes 7\/2, 11\/3, 15\/4, 18\/5 realized as the axes of the \u03b1-helices included in superhelices.\n                  <\/jats:p>","DOI":"10.1107\/s2053273325001743","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T04:00:59Z","timestamp":1743652859000},"page":"211-220","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":0,"title":["Helical substructures of 4D constructions that determine the structure of \u03b1-helices"],"prefix":"10.1107","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0147-6102","authenticated-orcid":true,"given":"Alexander","family":"Talis","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03jzs4815","id-type":"ROR","asserted-by":"publisher"}],"department":["Laboratory for Physical Chemistry of Polymers"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"329","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"nv5018_bb1","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1038\/143663a0","volume":"143","author":"Bernal","year":"1939","journal-title":"Nature"},{"key":"nv5018_bb2","unstructured":"Brian, H. (2013). Tetrahedra with a Twist, http:\/\/bit-player.org\/2013\/tetrahedra-with-a-twist."},{"key":"nv5018_bb3","unstructured":"Cartan, E. (1983). Geometry of Riemannian Spaces. Mathematical Sciences Press, Brookline."},{"key":"nv5018_bb4","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1038\/357543a0","volume":"357","author":"Chothia","year":"1992","journal-title":"Nature"},{"key":"nv5018_bb5","unstructured":"Coxeter, H. S. M. (1973). Regular Polytopes. New York: Dover Publications."},{"key":"nv5018_bb7","doi-asserted-by":"crossref","unstructured":"Coxeter, H. S. M. & Moser, W. O. J. (1980). Generators and Relations for Discrete Groups. Berlin: Springer.","DOI":"10.1007\/978-3-662-21943-0"},{"key":"nv5018_bb8","first-page":"686","volume":"6","author":"Crick","year":"1953","journal-title":"Acta Cryst."},{"key":"nv5018_bb9","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1038\/35068645","volume":"410","author":"Denton","year":"2001","journal-title":"Nature"},{"key":"nv5018_bb10","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1006\/jtbi.2002.3128","volume":"219","author":"Denton","year":"2002","journal-title":"J. Theor. Biol."},{"key":"nv5018_bb11","unstructured":"Du Val, P. (1964). Homographies Quaternions and Rotations. Clarendon Press, Oxford University Press."},{"key":"nv5018_bb12","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1107\/S1600576724003418","volume":"57","author":"Flor","year":"2024","journal-title":"J. Appl. Cryst."},{"key":"nv5018_bb13","unstructured":"Fomenko, A. T. & Tuzhilin, A. A. (1992). Editors. Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space. Translations of Mathematical Monographs, Vol. 93. Providence: American Mathematical Society."},{"key":"nv5018_bb15","doi-asserted-by":"crossref","first-page":"e11861","DOI":"10.7554\/eLife.11861","volume":"5","author":"Hartmann","year":"2016","journal-title":"eLife"},{"key":"nv5018_bb16","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1295\/polymj.14.753","volume":"14","author":"Ichikawa","year":"1982","journal-title":"Polym. J."},{"key":"nv5018_bb17","doi-asserted-by":"crossref","unstructured":"Koshy, T. (2019). Fibonacci and Lucas Numbers with Applications, 2nd ed. Hoboken: John Wiley & Sons.","DOI":"10.1002\/9781118742297"},{"key":"nv5018_bb18","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1016\/S0006-3495(98)77634-9","volume":"75","author":"Kumar","year":"1998","journal-title":"Biophys. J."},{"key":"nv5018_bb19","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1038\/261552a0","volume":"261","author":"Levitt","year":"1976","journal-title":"Nature"},{"key":"nv5018_bb21","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1023\/A:1015863923728","volume":"13","author":"Lord","year":"2002","journal-title":"Struct. Chem."},{"key":"nv5018_bb20","first-page":"335","volume":"D15","author":"Lord","year":"2001","journal-title":"Eur. Phys. J."},{"key":"nv5018_bb22","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-3-319-49674-0_4","volume":"82","author":"Lupas","year":"2017","journal-title":"Subcell. Biochem."},{"key":"nv5018_bb23","unstructured":"Milo\u0161evi\u0107, I., Damjanovi\u0107, A. & Damnjanovi\u0107, M. (1996). Quantum Mechanical Simulation Methods for Studying Biological Systems, edited by D. Bicout & M. Field. Berlin: Springer."},{"key":"nv5018_bb24","doi-asserted-by":"crossref","first-page":"3974","DOI":"10.1103\/PhysRevB.32.3974","volume":"32","author":"Mosseri","year":"1985","journal-title":"Phys. Rev. B"},{"key":"nv5018_bb25","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1107\/S2052520617001901","volume":"73","author":"M\u00fcller","year":"2017","journal-title":"Acta Cryst. B"},{"key":"nv5018_bb26","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00214-009-0639-4","volume":"125","author":"Olsen","year":"2010","journal-title":"Theor. Chem. Acc."},{"key":"nv5018_bb27","unstructured":"Oss, S. L. van (1899). Das regelm\u00e4ssige Sechshundertzell und seine Selbstdeckenden Bewegungen. Amsterdam: J. M\u00fcller."},{"key":"nv5018_bb28","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1073\/pnas.37.4.205","volume":"37","author":"Pauling","year":"1951","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"nv5018_bb30","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1524\/zkri.1970.132.1-6.152","volume":"132","author":"Ramachandran","year":"1970","journal-title":"Z. Kristallogr."},{"key":"nv5018_bb31","unstructured":"Rastanawi, L. & Rote, G. (2022). arXiv:2205.04965V1."},{"key":"nv5018_bb32","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1146\/annurev.bb.06.060177.001055","volume":"6","author":"Richards","year":"1977","journal-title":"Annu. Rev. Biophys. Bioeng."},{"key":"nv5018_bb50","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s101890170040","volume":"5","author":"Sadoc","year":"2001","journal-title":"Eur. Phys. J. E"},{"key":"nv5018_bb34","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s100510051009","volume":"12","author":"Sadoc","year":"1999","journal-title":"Eur. Phys. J. B"},{"key":"nv5018_bb35","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1107\/S2053273313033822","volume":"70","author":"Samoylovich","year":"2014","journal-title":"Acta Cryst. A"},{"key":"nv5018_bb36","unstructured":"Samoylovich, M. & Talis, A. (2016). arXiv:1606.01237."},{"key":"nv5018_bb37","doi-asserted-by":"crossref","first-page":"22326","DOI":"10.1021\/acsnano.3c04283","volume":"17","author":"Sari","year":"2023","journal-title":"ACS Nano"},{"key":"nv5018_bb39","doi-asserted-by":"crossref","unstructured":"\u0160krbi\u0107, T., Maritan, A., Giacometti, A., Rose, G. D. & Banavar, J. R. (2021). Phys. Rev. E, 104, 014402.","DOI":"10.1103\/PhysRevE.104.014402"},{"key":"nv5018_bb40","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1126\/science.1106243","volume":"307","author":"Snir","year":"2005","journal-title":"Science"},{"key":"nv5018_bb41","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1107\/S2053273320012978","volume":"77","author":"Talis","year":"2021","journal-title":"Acta Cryst. A"},{"key":"nv5018_bb42","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1107\/S2052520623009393","volume":"79","author":"Talis","year":"2023","journal-title":"Acta Cryst. B"},{"key":"nv5018_bb43","unstructured":"Talis, A. L. (2012). Proceedings of the IX All-Russian Fersman Scientific Session, pp. 307-312. Apatity: Geological Institute, Kola Science Centre RAS."},{"key":"nv5018_bb44","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1007\/s11041-024-01052-y","volume":"66","author":"Talis","year":"2024","journal-title":"Met. Sci. Heat Treat."},{"key":"nv5018_bb45","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1134\/S106377451903026X","volume":"64","author":"Talis","year":"2019","journal-title":"Crystallogr. Rep."},{"key":"nv5018_bb46","unstructured":"Vainshtein, B. K. (1981). Modern Crystallography I: Symmetry of Crystals, Methods of Structural Crystallography. Berlin: Springer."},{"key":"nv5018_bb47","unstructured":"Webb, R. (2014). https:\/\/www.software3d.com\/Stella.php."}],"container-title":["Acta Crystallographica Section A Foundations and Advances"],"original-title":[],"link":[{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2025\/03\/00\/nv5018\/nv5018.pdf","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2025\/03\/00\/nv5018\/nv5018.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T05:01:41Z","timestamp":1747630901000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.iucr.org\/paper?S2053273325001743"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,3]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["S2053273325001743"],"URL":"https:\/\/doi.org\/10.1107\/s2053273325001743","relation":{},"ISSN":["2053-2733"],"issn-type":[{"value":"2053-2733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,3]]},"assertion":[{"value":"Acta Crystallographica Section A: Foundations and Advances","order":0,"name":"journal","label":"Publication","explanation":{"URL":"https:\/\/journals.iucr.org\/a"},"group":{"name":"general","label":"General"}},{"value":"research papers","order":1,"name":"content_type","label":"Content type","explanation":{"URL":"https:\/\/journals.iucr.org\/a\/services\/notesforauthors.html"},"group":{"name":"general","label":"General"}},{"value":"Available","URL":"https:\/\/scripts.iucr.org\/cgi-bin\/citedin?nv5018","order":2,"name":"article_metrics","label":"Article metrics","group":{"name":"general","label":"General"}},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"4 June 2024","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication history"}},{"value":"24 February 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication history"}},{"value":"3 April 2025","order":2,"name":"published_online","label":"Published online","group":{"name":"publication_history","label":"Publication history"}},{"value":"\u00a9 Alexander Talis","order":0,"name":"copyright","label":"Copyright","explanation":{"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},"group":{"name":"copyright_and_licensing","label":"Copyright and licencing"}},{"value":"IUCr licence to publish","order":1,"name":"license","label":"Licence","explanation":{"URL":"https:\/\/journals.iucr.org\/copyright\/licencetopublish.html"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}}]}}