{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:57:53Z","timestamp":1791392273529,"version":"4.3.3"},"reference-count":59,"publisher":"National Academy of Sciences","issue":"41","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:p>The composition of a polyclonal antibody response is hard to measure experimentally but contains vital information about the robustness of immunity. Here, we argue that the statistics of neutralization titers alone can be used to make quantitative predictions about the composition of the response, circumventing challenges arising through sequencing and monoclonal antibody expression. We show that the response against influenza within a cohort can be either driven by a collective phenomenon where many antibodies contribute to neutralization, or dominated by just a few strong binders, leading to a broad distribution of titers across individuals described by a Gumbel distribution from extreme value theory. Comparing titers across cohorts, we find that Gumbel statistics accurately describe individuals prior to an immune challenge. We propose an equilibrium binding model that quantitatively captures titer data and illustrates the structure of the polyclonal response. Our approach extends generically to immune responses to other pathogens.<\/jats:p>","DOI":"10.1073\/pnas.2612096123","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:35:51Z","timestamp":1791390951000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Neutralization titers reveal the structure of polyclonal antibody responses"],"prefix":"10.1073","volume":"123","author":[{"given":"Henry","family":"Alston","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02en5vm52","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire de physique de l\u2019\u00c9cole normale sup\u00e9rieure, CNRS, Universit\u00e9 Paris Sciences et Lettres, Sorbonne Universit\u00e9, Universit\u00e9 Paris-Cit\u00e9","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5456-9361","authenticated-orcid":false,"given":"Thierry","family":"Mora","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02en5vm52","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire de physique de l\u2019\u00c9cole normale sup\u00e9rieure, CNRS, Universit\u00e9 Paris Sciences et Lettres, Sorbonne Universit\u00e9, Universit\u00e9 Paris-Cit\u00e9","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2686-5702","authenticated-orcid":false,"given":"Aleksandra M.","family":"Walczak","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02en5vm52","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire de physique de l\u2019\u00c9cole normale sup\u00e9rieure, CNRS, Universit\u00e9 Paris Sciences et Lettres, Sorbonne Universit\u00e9, Universit\u00e9 Paris-Cit\u00e9","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.41.11.849"},{"key":"e_1_3_4_2_2","first-page":"67","article-title":"A modification of Jerne\u2019s theory of antibody production using the concept of clonal selection","volume":"20","author":"Burnet F. M.","year":"1957","unstructured":"F. M. Burnet, A modification of Jerne\u2019s theory of antibody production using the concept of clonal selection. Aust. J. Sci. 20, 67\u20139 (1957).","journal-title":"Aust. J. Sci."},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/302575a0"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5699(92)90043-7"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.49324"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.61346"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chom.2021.02.003"},{"key":"e_1_3_4_8_2","first-page":"2666","article-title":"Serotypic evolution of measles virus is constrained by multiple co-dominant b cell epitopes on its surface glycoproteins","volume":"2","author":"Mu\u00f1oz-Al\u00eda M. \u00c1.","year":"2021","unstructured":"M. \u00c1. Mu\u00f1oz-Al\u00eda, R. A. Nace, L. Zhang, S. J. Russell, Serotypic evolution of measles virus is constrained by multiple co-dominant b cell epitopes on its surface glycoproteins. Cell Rep. Med. 2, 2666\u20133791 (2021).","journal-title":"Cell Rep. Med."},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2113512119"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2020.08.012"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chom.2020.11.007"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-04385-3"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-022-04980-y"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature07930"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1093\/ve\/veac110"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1213737110"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1038\/nm.4224"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.106811.4"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1093\/ve\/veaf086"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007830"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.45.79"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.24.2613"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.84.21.7524"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1749933"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1002\/prot.340210302"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.physchem.48.1.545"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.192693599"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1088\/1478-3975\/4\/2\/006"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0805909105"},{"key":"e_1_3_4_30_2","first-page":"031026","article-title":"Nonequilibrium antigen recognition during infections and vaccinations","volume":"14","author":"Mor\u00e1n-Tovar R.","year":"2024","unstructured":"R. Mor\u00e1n-Tovar, M. L\u00e4ssig, Nonequilibrium antigen recognition during infections and vaccinations. Phys. Rev. X 14, 031026 (2024).","journal-title":"Phys. Rev. X"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-34471-3"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2020.604053"},{"key":"e_1_3_4_33_2","doi-asserted-by":"crossref","unstructured":"W. S. DeWitt Replaying germinal center evolution on a quantified affinity landscape. bioRxiv [Preprint] (2025). https:\/\/doi.org\/10.1101\/2025.06.02.656870 (Accessed 13 April 2026).","DOI":"10.1101\/2025.06.02.656870"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.adr6896"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1421827112"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1600663113"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41559-017-0077"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1920263117"},{"key":"e_1_3_4_39_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2103398118"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2307712120"},{"key":"e_1_3_4_41_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-immunol-120419-022408"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000800"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.immuni.2015.06.013"},{"key":"e_1_3_4_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.immuni.2016.02.010"},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2022.11.032"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.immuni.2023.02.003"},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2023.10.022"},{"key":"e_1_3_4_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.celrep.2023.112256"},{"key":"e_1_3_4_49_2","doi-asserted-by":"crossref","unstructured":"A. Schiepers van\u2019t Wout MF Hobbs A Mesin L Victora GD Opposing effects of pre-existing antibody and memory t cell help on the dynamics of recall germinal centers. Immunity 57 1618\u20131628.e4 (2024).","DOI":"10.1016\/j.immuni.2024.05.009"},{"key":"e_1_3_4_50_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-08687-8"},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1093\/cid\/ciae380"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2205598119"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-026-10248-6"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.coviro.2016.12.004"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.3390\/vaccines6020028"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1126\/scitranslmed.abd3601"},{"key":"e_1_3_4_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1074-7613(00)80580-4"},{"key":"e_1_3_4_58_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature09385"},{"key":"e_1_3_4_59_2","doi-asserted-by":"publisher","DOI":"10.1051\/jphyslet:01985004609040100"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2612096123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:36:02Z","timestamp":1791390962000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2612096123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,7]]},"references-count":59,"journal-issue":{"issue":"41","published-print":{"date-parts":[[2026,10,13]]}},"alternative-id":["10.1073\/pnas.2612096123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2612096123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,7]]},"assertion":[{"value":"2026-04-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2612096123"}}