{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T13:14:12Z","timestamp":1783602852406,"version":"3.55.0"},"reference-count":77,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2318053"],"award-info":[{"award-number":["DMS-2318053"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2054347"],"award-info":[{"award-number":["DMS-2054347"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1817156"],"award-info":[{"award-number":["DMS-1817156"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2318051"],"award-info":[{"award-number":["DMS-2318051"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2318052"],"award-info":[{"award-number":["DMS-2318052"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1817156"],"award-info":[{"award-number":["DMS-1817156"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2026,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Bacteriophages, viruses that infect bacteria, store their micron long DNA inside an icosahedral capsid with a typical diameter of 40\u00a0nm to 100\u00a0nm.\u00a0Consistent with experimental observations, such confinement conditions induce an arrangement of DNA that corresponds to a hexagonal chromonic liquid-crystalline phase, and increase the topological complexity of the genome in the form of knots.\u00a0A mathematical model that implements a chromonic liquid-crystalline phase and that captures the changes in topology has been lacking.\u00a0We adopt a mathematical model that represents the viral DNA as a pair of a vector field and a line.\u00a0The vector field is a minimizer of the total Oseen\u2013Frank energy for nematic liquid crystals under chromonic constraints, while the line is identified with the tangent to the field at selected locations, representing the central axis of the DNA molecule.\u00a0The fact that the Oseen\u2013Frank functional assigns infinite energy to topological defects (point defects in two dimensions and line defects in three dimensions) precludes the presence of singularities and, in particular, of knot structures. To overcome this limitation, we develop an algorithm that starts from the optimal vector field and an associated helical curve and introduces knots through stochastic perturbations driven by splay and twist deformations, modeled via a Langevin system.\u00a0We conclude by comparing the resulting knot distributions with experimentally observed data and by interpreting the results in light of previously published measurements.\u00a0Overall, the proposed approach highlights the interplay of modeling, analysis, and computation in the study of viral DNA organization within capsids.<\/jats:p>","DOI":"10.1137\/25m1798216","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T12:22:14Z","timestamp":1783599734000},"page":"1570-1592","source":"Crossref","is-referenced-by-count":0,"title":["Knotted DNA Configurations in Bacteriophage Capsids: A Liquid Crystal Theory Approach"],"prefix":"10.1137","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8777-6757","authenticated-orcid":true,"given":"Pei","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6266-772X","authenticated-orcid":true,"given":"Zhijie","family":"Wang","sequence":"additional","affiliation":[{"name":"Graduate Program in Applied Mathematics, University of California, Davis, CA 95616 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tamara","family":"Christiani","sequence":"additional","affiliation":[{"name":"Integrative Genetics and Genomics Graduate Group, University of California, Davis, CA 95616 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mariel","family":"V\u00e1zquez","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Department of Microbiology and Molecular Genetics, University of California, Davis, CA 95616 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9117-7439","authenticated-orcid":true,"given":"M. Carme","family":"Calderer","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Minnesota, Minneapolis, MN 55442 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"Arsuaga","sequence":"additional","affiliation":[{"name":"Department of Molecular and Cellular Biology and Department of Mathematics, University of California, Davis, CA 95616 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1928-1501429-1"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/39\/002"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1080\/17486700802167801"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-4622(02)00197-7"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0409323102"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.032095099"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1039\/C8SM00734A"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad6c01"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.12775\/TMNA.1995.011"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8674(00)81931-5"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.virol.2007.07.035"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1417178112"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1006\/jmbi.1999.2771"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2020.03.030"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1063\/1.2808028"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.55.6245"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.2478\/mlbmb-2014-0002"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216594000307"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00380413"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s41468-017-0007-8"},{"key":"ref21","volume-title":"Firedrake User Manual","author":"Ham D. A.","year":"2023","edition":"1"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01238933"},{"key":"ref23","first-page":"20200111","volume":"379","author":"Hiltner L.","year":"2021","journal-title":"Philos. Trans. A"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.261560398"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aa6a4f"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1142\/9789812385215_0048"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-71266-1_2"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.241486298"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5096(03)00071-1"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1039\/D2SM00712F"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1126\/science.1127981"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/0248-4900(91)90058-U"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(93)81063-4"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0901240106"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1002\/j.1460-2075.1987.tb02393.x"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.032502"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/9.16.3979"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.78.9.5498"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2021.07.006"},{"key":"ref41","first-page":"20220047","volume":"478","author":"Liu P.","year":"2022","journal-title":"Proc. A"},{"key":"ref42","unstructured":"P. Liu, T. Christiani, Z. Wang, F. Guo, M. V\u00e1zquez, M. C Calderer, and J. Arsuaga, Twist dominates bending in the liquid crystal organization of bacteriophage DNA, preprint, arXiv:2510.04408, 2025."},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/746\/15000"},{"key":"ref44","first-page":"300","volume":"33","author":"Livolant F.","year":"1984","journal-title":"Eur. J. Cell Biol."},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1007\/BF00330370"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1038\/339724a0"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/gkr1237"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.cocis.2004.01.006"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0907524106"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2011.03.003"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.108.137653"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/746\/15004"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1074\/jbc.271.10.5656"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsb.2007.08.012"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsb.2010.11.007"},{"key":"ref56","volume-title":"Knotted Fields. Lecture Notes in Mathematics 2344","author":"Rawdon E. J."},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.83.2.342"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.90.11.5307"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-57985-1_8"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms4057"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1126\/science.8475384"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1308450110"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.75.1.400"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1038\/331457a0"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1126\/science.aay1638"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-30494-2"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.49.868"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2024.04.002"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(03)74971-6"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/gkz491"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmb.2011.05.048"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022703"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1051\/jphys:01987004802031900"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9258(18)54963-2"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1038\/171737a0"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/13.18.6695"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-13-S12-A22"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T12:22:20Z","timestamp":1783599740000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1798216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,9]]},"references-count":77,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8,31]]}},"alternative-id":["10.1137\/25M1798216"],"URL":"https:\/\/doi.org\/10.1137\/25m1798216","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,9]]}}}