[{"oa":1,"author":[{"full_name":"Isakova, Lada H.","first_name":"Lada H.","last_name":"Isakova"},{"full_name":"Streltsova, Elizaveta","first_name":"Elizaveta","id":"57a170da-dc96-11ea-b7c8-ab3565071bf7","last_name":"Streltsova"},{"id":"C4558D3C-6102-11E9-A62E-F418E6697425","full_name":"Bochkareva, Olga","first_name":"Olga","orcid":"0000-0003-1006-6639","last_name":"Bochkareva"},{"first_name":"Peter K.","full_name":"Vlasov, Peter K.","last_name":"Vlasov"},{"id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","full_name":"Kondrashov, Fyodor","first_name":"Fyodor","orcid":"0000-0001-8243-4694","last_name":"Kondrashov"}],"ddc":["570"],"language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"date_updated":"2026-05-04T06:57:31Z","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_created":"2026-04-12T22:01:47Z","publisher":"National Academy of Sciences","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","intvolume":"       123","external_id":{"pmid":["41915737"]},"page":"e2532018123","citation":{"mla":"Isakova, Lada H., et al. “Descent from a Common Ancestor Restricts Exploration of Protein Sequence Space.” <i>Proceedings of the National Academy of Sciences</i>, vol. 123, no. 14, National Academy of Sciences, 2026, p. e2532018123, doi:<a href=\"https://doi.org/10.1073/pnas.2532018123\">10.1073/pnas.2532018123</a>.","short":"L.H. Isakova, E. Streltsova, O. Bochkareva, P.K. Vlasov, F. Kondrashov, Proceedings of the National Academy of Sciences 123 (2026) e2532018123.","chicago":"Isakova, Lada H., Elizaveta Streltsova, Olga Bochkareva, Peter K. Vlasov, and Fyodor Kondrashov. “Descent from a Common Ancestor Restricts Exploration of Protein Sequence Space.” <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences, 2026. <a href=\"https://doi.org/10.1073/pnas.2532018123\">https://doi.org/10.1073/pnas.2532018123</a>.","ama":"Isakova LH, Streltsova E, Bochkareva O, Vlasov PK, Kondrashov F. Descent from a common ancestor restricts exploration of protein sequence space. <i>Proceedings of the National Academy of Sciences</i>. 2026;123(14):e2532018123. doi:<a href=\"https://doi.org/10.1073/pnas.2532018123\">10.1073/pnas.2532018123</a>","apa":"Isakova, L. H., Streltsova, E., Bochkareva, O., Vlasov, P. K., &#38; Kondrashov, F. (2026). Descent from a common ancestor restricts exploration of protein sequence space. <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2532018123\">https://doi.org/10.1073/pnas.2532018123</a>","ieee":"L. H. Isakova, E. Streltsova, O. Bochkareva, P. K. Vlasov, and F. Kondrashov, “Descent from a common ancestor restricts exploration of protein sequence space,” <i>Proceedings of the National Academy of Sciences</i>, vol. 123, no. 14. National Academy of Sciences, p. e2532018123, 2026.","ista":"Isakova LH, Streltsova E, Bochkareva O, Vlasov PK, Kondrashov F. 2026. Descent from a common ancestor restricts exploration of protein sequence space. Proceedings of the National Academy of Sciences. 123(14), e2532018123."},"fulldoi":"https://doi.org/10.1073/pnas.2532018123","OA_type":"hybrid","title":"Descent from a common ancestor restricts exploration of protein sequence space","OA_place":"publisher","scopus_import":"1","_id":"21704","year":"2026","file":[{"file_size":3355016,"file_id":"21783","date_updated":"2026-05-04T06:46:31Z","file_name":"2026_PNAS_Isakova.pdf","checksum":"11b7a13a359e302498b2367906093a6b","access_level":"open_access","creator":"dernst","date_created":"2026-05-04T06:46:31Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"type":"journal_article","status":"public","acknowledgement":"We thank Olga Kalinina for feedback on our manuscript, Vsevolod Kuksin for fruitful discussions and Lev Tsarin for participation in the design of our models. This work was supported by Japan Science and Technology Agency as part of Adopting Sustainable Partnerships for Innovative Research Ecosystem, Grant No. JPMJAP24B2 (F.A.K. and L.H.I.), and Fonds Zur Förderung der Wissenschaftlichen Forschung Grant ESP253-B (O.O.B.)","date_published":"2026-04-07T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","pmid":1,"month":"04","quality_controlled":"1","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","publication_identifier":{"eissn":["1091-6490"]},"doi":"10.1073/pnas.2532018123","day":"07","issue":"14","file_date_updated":"2026-05-04T06:46:31Z","volume":123,"publication":"Proceedings of the National Academy of Sciences","abstract":[{"lang":"eng","text":"How functional protein sequences are distributed in sequence space is fundamentally important for evolutionary theory and protein design, particularly if a large diversity of protein functions are hidden in evolutionarily unexplored areas of the sequence space. However, this question is understudied in part because experimental and computational studies use extant sequences as a starting point to study sequence space. Here, we study whether extant sequences are representative of the entire functional sequence space. Across thousands of protein families from vertebrates and bacteria we calculate the dimensionality and the volume of sequence space occupied by extant homologs. We find that the observed dimensionality and volume of extant sequence space are minuscule, many orders of magnitude smaller than what we estimated using a model of protein evolution. Simulating sequence evolution we then quantify the impact of phylogeny, selection, and epistasis on restricting the evolutionary exploration of sequence space. We find that sequence evolution from a single common ancestor, or a single point of origin in sequence space, is by far the largest limiting factor that reduces the dimensionality and volume of extant sequence space. These results indicate that there are vast areas of functional sequence space that have not been explored in evolution because of the excessive restrictions on natural exploration of the protein sequence space imposed by the point of origin effect. We suggest that protein design methods that rely on extant sequences may be limited in their ability to discover truly novel functions."}],"oa_version":"Published Version"},{"fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2025.75","citation":{"ista":"Streltsova E, Wagner U. 2025. Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 75.","ieee":"E. Streltsova and U. Wagner, “Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers,” in <i>41st International Symposium on Computational Geometry</i>, Kanazawa, Japan, 2025, vol. 332.","apa":"Streltsova, E., &#38; Wagner, U. (2025). Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. In <i>41st International Symposium on Computational Geometry</i> (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.75\">https://doi.org/10.4230/LIPIcs.SoCG.2025.75</a>","ama":"Streltsova E, Wagner U. Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. In: <i>41st International Symposium on Computational Geometry</i>. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.75\">10.4230/LIPIcs.SoCG.2025.75</a>","chicago":"Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers.” In <i>41st International Symposium on Computational Geometry</i>, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.75\">https://doi.org/10.4230/LIPIcs.SoCG.2025.75</a>.","short":"E. Streltsova, U. Wagner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","mla":"Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers.” <i>41st International Symposium on Computational Geometry</i>, vol. 332, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2025.75\">10.4230/LIPIcs.SoCG.2025.75</a>."},"external_id":{"arxiv":["2504.07752","2504.07770"]},"corr_author":"1","intvolume":"       332","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_created":"2025-07-13T22:01:22Z","department":[{"_id":"UlWa"}],"language":[{"iso":"eng"}],"date_updated":"2026-07-07T13:03:16Z","ddc":["510"],"author":[{"id":"57a170da-dc96-11ea-b7c8-ab3565071bf7","full_name":"Streltsova, Elizaveta","first_name":"Elizaveta","last_name":"Streltsova"},{"last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"oa":1,"oa_version":"Published Version","das_tickbox":"1","abstract":[{"text":"A long-standing conjecture of Eckhoff, Linhart, and Welzl, which would generalize McMullen’s Upper Bound Theorem for polytopes and refine asymptotic bounds due to Clarkson, asserts that for k ⩽ ⌊(n-d-2)/2⌋, the complexity of the (⩽ k)-level in a simple arrangement of n hemispheres in S^d is maximized for arrangements that are polar duals of neighborly d-polytopes. We prove this conjecture in the case n = d+4. By Gale duality, this implies the following result about crossing numbers: In every spherical arc drawing of K_n in S² (given by a set V ⊂ S² of n unit vectors connected by spherical arcs), the number of crossings is at least 1/4 ⌊n/2⌋ ⌊(n-1)/2⌋ ⌊(n-2)/2⌋ ⌊(n-3)/2⌋. This lower bound is attained if every open linear halfspace contains at least ⌊(n-2)/2⌋ of the vectors in V.\r\nMoreover, we determine the space of all linear and affine relations that hold between the face numbers of levels in simple arrangements of n hemispheres in S^d. This completes a long line of research on such relations, answers a question posed by Andrzejak and Welzl in 2003, and generalizes the classical fact that the Dehn-Sommerville relations generate all linear relations between the face numbers of simple polytopes (which correspond to the 0-level).\r\nTo prove these results, we introduce the notion of the g-matrix, which encodes the face numbers of levels in an arrangement and generalizes the classical g-vector of a polytope.","lang":"eng"}],"file_date_updated":"2025-07-14T07:11:04Z","volume":332,"publication":"41st International Symposium on Computational Geometry","day":"20","doi":"10.4230/LIPIcs.SoCG.2025.75","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773706"]},"has_accepted_license":"1","article_processing_charge":"Yes","quality_controlled":"1","month":"06","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"start_date":"2025-06-23","location":"Kanazawa, Japan","name":"SoCG: Symposium on Computational Geometry","end_date":"2025-06-27"},"date_published":"2025-06-20T00:00:00Z","status":"public","type":"conference","file":[{"creator":"dernst","file_size":952807,"checksum":"a8f7feb1aa3b896e31195841a989d622","file_id":"20015","date_updated":"2025-07-14T07:11:04Z","file_name":"2025_LIPIcs.SoCG_Streltsova.pdf","access_level":"open_access","success":1,"relation":"main_file","date_created":"2025-07-14T07:11:04Z","content_type":"application/pdf"}],"year":"2025","article_number":"75","_id":"20004","scopus_import":"1","OA_place":"publisher","title":"Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers","OA_type":"gold"}]