{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T02:07:08Z","timestamp":1771553228324,"version":"3.50.1"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100024370","name":"Ministero dell'Istruzione dell'Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100024370","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012740","name":"Istituto Nazionale di Alta Matematica Francesco Severi Gruppo Nazionale per l'Analisi Matematica la Probabilita e le loro Applicazioni","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012740","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["2022XZSAFN"],"award-info":[{"award-number":["2022XZSAFN"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Theoretical Biology"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1016\/j.jtbi.2026.112376","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T16:09:02Z","timestamp":1768493342000},"page":"112376","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["On the dynamics of antigen receptors on the B-cell membrane through a two-dimensional stochastic process"],"prefix":"10.1016","volume":"622","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4583-2612","authenticated-orcid":false,"given":"Verdiana","family":"Mustaro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9810-0488","authenticated-orcid":false,"given":"Vincenzo","family":"Casolaro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4751-7341","authenticated-orcid":false,"given":"Antonio","family":"Di Crescenzo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jtbi.2026.112376_bib0001","article-title":"A population dynamics model for clonal diversity in a germinal center","volume":"12","author":"Amitai","year":"2017","journal-title":"Front. Microbiol."},{"key":"10.1016\/j.jtbi.2026.112376_bib0002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11587-020-00548-y","article-title":"A generalized Gompertz growth model with applications and related birth-death processes","volume":"72","author":"Asadi","year":"2023","journal-title":"Ric. Mat."},{"issue":"1-2","key":"10.1016\/j.jtbi.2026.112376_bib0003","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.jim.2011.08.014","article-title":"A new model for the estimation of cell proliferation dynamics using CFSE data","volume":"28","author":"Banks","year":"2011","journal-title":"J. Immunol. Methods"},{"issue":"3","key":"10.1016\/j.jtbi.2026.112376_bib0004","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1239\/jap\/1409932661","article-title":"A stochastic model for virus growth in a cell population","volume":"51","author":"Bj\u00f6rnberg","year":"2014","journal-title":"J. Appl. Probab."},{"issue":"21","key":"10.1016\/j.jtbi.2026.112376_bib0005","article-title":"Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types","volume":"559","author":"Cho","year":"2023","journal-title":"J. Theor. Biol."},{"issue":"2","key":"10.1016\/j.jtbi.2026.112376_bib0006","doi-asserted-by":"crossref","DOI":"10.1002\/wics.1423","article-title":"Computational methods for birth-death processes","volume":"10","author":"Crawford","year":"2018","journal-title":"Wiley Interdiscip. Rev. Comput. Stat."},{"issue":"3","key":"10.1016\/j.jtbi.2026.112376_bib0007","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s00285-011-0471-z","article-title":"Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution","volume":"65","author":"Crawford","year":"2012","journal-title":"J. Math. Biol."},{"issue":"10","key":"10.1016\/j.jtbi.2026.112376_bib0008","doi-asserted-by":"crossref","first-page":"2510","DOI":"10.1007\/s11538-012-9764-7","article-title":"Mathematical determination of cell population doubling times for multiple cell lines","volume":"74","author":"Daukste","year":"2012","journal-title":"Bull. Math. Biol."},{"issue":"10","key":"10.1016\/j.jtbi.2026.112376_bib0009","doi-asserted-by":"crossref","first-page":"4963","DOI":"10.4049\/jimmunol.170.10.4963","article-title":"Stochastic model of T cell proliferation: a calculus revealing IL-2 regulation of precursor frequencies, cell cycle time, and survival","volume":"15","author":"Deenick","year":"2003","journal-title":"J. Immunol."},{"key":"10.1016\/j.jtbi.2026.112376_bib0010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tpb.2024.07.002","article-title":"Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics","volume":"159","author":"DeWitt","year":"2024","journal-title":"Theor. Popul. Biol."},{"issue":"1","key":"10.1016\/j.jtbi.2026.112376_bib0011","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00000070","article-title":"Stochastic population models with interacting species","volume":"42","author":"Di Crescenzo","year":"2001","journal-title":"J. Math. Biol."},{"key":"10.1016\/j.jtbi.2026.112376_bib0012","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1080\/15326340802232293","article-title":"A first-passage-time problem for symmetric and similar two-dimensional birth-death processes","volume":"24","author":"Di Crescenzo","year":"2008","journal-title":"Stoch. Models"},{"key":"10.1016\/j.jtbi.2026.112376_bib0013","doi-asserted-by":"crossref","first-page":"13621","DOI":"10.1002\/mma.10211","article-title":"Modeling the random spreading of fake news through a two-dimensional time-inhomogeneous birth-death process","volume":"47","author":"Di Crescenzo","year":"2024","journal-title":"Math. Methods Appl. Sci."},{"key":"10.1016\/j.jtbi.2026.112376_bib0014","series-title":"Stochastic growth models for the spreading of fake news","first-page":"3597","volume":"11","author":"Di Crescenzo","year":"2023"},{"issue":"1","key":"10.1016\/j.jtbi.2026.112376_bib0015","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1038\/s41467-023-36672-0","article-title":"Antigen footprint governs activation of the B cell receptor","volume":"22","author":"Ferapontov","year":"2023","journal-title":"Nat. Commun."},{"key":"10.1016\/j.jtbi.2026.112376_bib0016","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"Gillespie","year":"1976","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.jtbi.2026.112376_bib0017","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1046\/j.1365-2567.2002.01494.x","article-title":"Life and death within germinal centres: a double-edged sword","volume":"107","author":"Guzman-Rojas","year":"2002","journal-title":"Immunology"},{"issue":"4","key":"10.1016\/j.jtbi.2026.112376_bib0018","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1007\/s00285-017-1160-3","article-title":"Birth\/birth-death processes and their computable transition probabilities with biological applications","volume":"76","author":"Ho","year":"2017","journal-title":"J. Math. Biol."},{"issue":"7","key":"10.1016\/j.jtbi.2026.112376_bib0019","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1371\/journal.pbio.0040200","article-title":"B cell antigen receptor signaling and internalization are mutually exclusive events","volume":"4","author":"Hou","year":"2006","journal-title":"PLoS Biol."},{"key":"10.1016\/j.jtbi.2026.112376_bib0020","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s11009-013-9372-5","article-title":"A quasi random walk to model a biological transport process","volume":"17","author":"Keller","year":"2015","journal-title":"Methodol. Comput. Appl. Probab."},{"issue":"1","key":"10.1016\/j.jtbi.2026.112376_bib0021","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10928-011-9230-4","article-title":"Multi-response model for rheumatoid arthritis based on delay differential equations in collagen-induced arthritic mice treated with an anti-GM-CSF antibody","volume":"39","author":"Koch","year":"2012","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"10.1016\/j.jtbi.2026.112376_bib0022","series-title":"Advanced Engineering Mathematics","author":"Kreyszig","year":"2011"},{"key":"10.1016\/j.jtbi.2026.112376_bib0023","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.55678","article-title":"Quantitative modeling of the effect of antigen dosage on B-cell affinity distributions in maturating germinal centers","volume":"9","author":"Molari","year":"2020","journal-title":"eLife"},{"key":"10.1016\/j.jtbi.2026.112376_bib0024","series-title":"Janeway\u2019s Immunobiology","author":"Murphy","year":"2017"},{"key":"10.1016\/j.jtbi.2026.112376_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.jtbi.2021.110620","article-title":"Mathematical modelling of the hematopoietic stem cell-niche system: clonal dominance based on stem cell fitness","volume":"518","author":"Pedersen","year":"2021","journal-title":"J. Theor. Biol."},{"issue":"6","key":"10.1016\/j.jtbi.2026.112376_bib0026","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.3390\/cells9061448","article-title":"Computational model reveals a stochastic mechanism behind germinal center clonal bursts","volume":"9","author":"P\u00e9lissier","year":"2020","journal-title":"Cells"},{"key":"10.1016\/j.jtbi.2026.112376_bib0027","series-title":"Global sensitivity analysis: the primer","author":"Saltelli","year":"2008"},{"key":"10.1016\/j.jtbi.2026.112376_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.epidem.2024.100795","article-title":"Estimating pathogen spread using structured coalescent and birth-death models: a quantitative comparison","volume":"49","author":"Seidel","year":"2024","journal-title":"Epidemic"},{"key":"10.1016\/j.jtbi.2026.112376_bib0029","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0378-4754(00)00270-6","article-title":"Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates","volume":"55","author":"Sobol\u2019","year":"2001","journal-title":"Math. Comput. Simul."},{"issue":"11","key":"10.1016\/j.jtbi.2026.112376_bib0030","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1007\/s11538-014-0026-8","article-title":"A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate","volume":"76","author":"Spina","year":"2014","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.jtbi.2026.112376_bib0031","series-title":"Essential Mathematics for Economic Analysis","author":"Sydsaeter","year":"2021"},{"issue":"2","key":"10.1016\/j.jtbi.2026.112376_bib0032","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s00285-011-0459-8","article-title":"Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system","volume":"65","author":"Terry","year":"2011","journal-title":"J. Math. Biol."},{"issue":"4","key":"10.1016\/j.jtbi.2026.112376_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.celrep.2023.112256","article-title":"Antigen presentation dynamics shape the antibody response to variants like SARS-COV-2 Omicron after multiple vaccinations with the original strain","volume":"42","author":"Yang","year":"2023","journal-title":"Cell Rep."}],"container-title":["Journal of Theoretical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519326000020?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519326000020?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T01:28:20Z","timestamp":1771550900000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0022519326000020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":33,"alternative-id":["S0022519326000020"],"URL":"https:\/\/doi.org\/10.1016\/j.jtbi.2026.112376","relation":{},"ISSN":["0022-5193"],"issn-type":[{"value":"0022-5193","type":"print"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the dynamics of antigen receptors on the B-cell membrane through a two-dimensional stochastic process","name":"articletitle","label":"Article Title"},{"value":"Journal of Theoretical Biology","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jtbi.2026.112376","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"112376"}}