{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T15:40:27Z","timestamp":1793893227515,"version":"4.8.0"},"reference-count":147,"publisher":"IOP Publishing","issue":"6","license":[{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":7,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"tdm","delay-in-days":7,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":7,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"},{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":7,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"}],"funder":[{"name":"National Science Foundation","award":["MCB-2227268"],"award-info":[{"award-number":["MCB-2227268"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"crossref","award":["R01NS121114"],"award-info":[{"award-number":["R01NS121114"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Rep. Prog. Phys."],"published-print":{"date-parts":[[2026,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Intrinsically disordered prion-like low complexity domains (PLCDs) drive phase transitions that underlie the biogenesis of many biomolecular condensates. Here, we report results from large-scale Monte Carlo simulations on lattices aided by computations of Binder cumulants and rigorous finite-size scaling. These approaches enable accurate mapping of the critical regime and computations of the full binodal of an archetypal PLCD. This weakly associating polymer undergoes phase separation coupled to percolation. Between the lowest temperature and the critical point, the concentrations along the left arm of the binodal vary by four orders of magnitude. The overlap line intersects the left arm of the binodal well below the critical point. This, taken together with the intersection of the percolation line and the left arm of the binodal, leads to demarcation of the binodal into three regimes. Regime I is farthest from the critical point. Here, the coexisting dilute phase is akin to a gas of dispersed polymers. The dilute arm of the binodal lies above the overlap line in Regimes II and III. Here, the semidilute nature of dilute phases enables clustering of polymers that is enhanced by intermolecular associations. The coexisting dense phases form confined percolated networks in Regimes I and II. In Regime III, which is closest to the critical point, the dense phase becomes unconfined and fragmented, and the system is defined by two interconnected, system-spanning networks. In addition to mapping the critical point accurately, we evaluated methods for identifying the theta temperature. We find that scaling approaches based on assumptions from two-parameter theories for homopolymers yield erroneous estimates of the theta temperature of an archetypal PLCD. Accurate estimation of the theta temperature requires direct calculation of the temperature dependence of the two-body interaction coefficient. We discuss implications for inferring solvent quality from scaling analysis of segmental distances of disordered proteins.<\/jats:p>","DOI":"10.1088\/1361-6633\/ae70d6","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T22:53:31Z","timestamp":1779317611000},"page":"068101","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Distinguishing near- versus off-critical phase behaviors of intrinsically disordered proteins"],"prefix":"10.1088","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8340-4016","authenticated-orcid":true,"given":"Gaurav","family":"Mitra","sequence":"first","affiliation":[{"name":"Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5454-7891","authenticated-orcid":false,"given":"Souradeep","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3240-1856","authenticated-orcid":false,"given":"Kiersten M","family":"Ruff","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2247-201X","authenticated-orcid":false,"given":"Ruoyao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2510-8635","authenticated-orcid":true,"given":"Gaurav","family":"Chauhan","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis"},{"name":"Indian Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2568-1378","authenticated-orcid":true,"given":"Rohit V","family":"Pappu","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"key":"ropae70d6bib1","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1038\/nrm.2017.7","type":"journal-article","volume":"18","author":"Banani","year":"2017","journal-title":"Nat. Rev. Mol. Cell Biol."},{"key":"ropae70d6bib2","doi-asserted-by":"publisher","first-page":"eaaf4382","DOI":"10.1126\/science.aaf4382","type":"journal-article","volume":"357","author":"Shin","year":"2017","journal-title":"Science"},{"key":"ropae70d6bib3","doi-asserted-by":"publisher","first-page":"1729","DOI":"10.1126\/science.1172046","type":"journal-article","volume":"324","author":"Brangwynne","year":"2009","journal-title":"Science"},{"key":"ropae70d6bib4","doi-asserted-by":"publisher","first-page":"4334","DOI":"10.1073\/pnas.1017150108","type":"journal-article","volume":"108","author":"Brangwynne","year":"2011","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib5","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1038\/nature10879","type":"journal-article","volume":"483","author":"Li","year":"2012","journal-title":"Nature"},{"key":"ropae70d6bib6","doi-asserted-by":"publisher","first-page":"8945","DOI":"10.1021\/acs.chemrev.2c00814","type":"journal-article","volume":"123","author":"Pappu","year":"2023","journal-title":"Chem. Rev."},{"key":"ropae70d6bib7","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1146\/annurev-biophys-121219-081629","type":"journal-article","volume":"49","author":"Choi","year":"2020","journal-title":"Annu. Rev. Biophys."},{"key":"ropae70d6bib8","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.cell.2016.06.010","type":"journal-article","volume":"166","author":"Banani","year":"2016","journal-title":"Cell"},{"key":"ropae70d6bib9","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.30294","type":"journal-article","volume":"6","author":"Harmon","year":"2017","journal-title":"eLife"},{"key":"ropae70d6bib10","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1126\/science.aat5671","type":"journal-article","volume":"361","author":"Milovanovic","year":"2018","journal-title":"Science"},{"key":"ropae70d6bib11","doi-asserted-by":"publisher","first-page":"4466","DOI":"10.1073\/pnas.1321007111","type":"journal-article","volume":"111","author":"Mitrea","year":"2014","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib12","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.cell.2020.03.050","type":"journal-article","volume":"181","author":"Sanders","year":"2020","journal-title":"Cell"},{"key":"ropae70d6bib13","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.cell.2020.03.049","type":"journal-article","volume":"181","author":"Guill\u00e9n-Boixet","year":"2020","journal-title":"Cell"},{"key":"ropae70d6bib14","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.molcel.2019.06.044","type":"journal-article","volume":"76","author":"Powers","year":"2019","journal-title":"Mol. Cell"},{"key":"ropae70d6bib15","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1016\/j.bpj.2020.08.002","type":"journal-article","volume":"120","author":"Jang","year":"2021","journal-title":"Biophys. J."},{"key":"ropae70d6bib16","doi-asserted-by":"publisher","first-page":"688","DOI":"10.1016\/j.cell.2018.06.006","type":"journal-article","volume":"174","author":"Wang","year":"2018","journal-title":"Cell"},{"key":"ropae70d6bib17","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1126\/science.aaw8653","type":"journal-article","volume":"367","author":"Martin","year":"2020","journal-title":"Science"},{"key":"ropae70d6bib18","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1016\/j.molcel.2020.01.025","type":"journal-article","volume":"77","author":"Greig","year":"2020","journal-title":"Mol. Cell"},{"key":"ropae70d6bib19","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1038\/s41586-023-06329-5","type":"journal-article","volume":"619","author":"Galvanetto","year":"2023","journal-title":"Nature"},{"key":"ropae70d6bib20","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005941","type":"journal-article","volume":"14","author":"Dignon","year":"2018","journal-title":"PLOS Comput. Biol."},{"key":"ropae70d6bib21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.042403","type":"journal-article","volume":"102","author":"Choi","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ropae70d6bib22","doi-asserted-by":"publisher","first-page":"2201","DOI":"10.1016\/j.molcel.2022.05.018","type":"journal-article","volume":"82","author":"Mittag","year":"2022","journal-title":"Mol. Cell"},{"key":"ropae70d6bib23","doi-asserted-by":"publisher","first-page":"1236","DOI":"10.1038\/s41557-025-01847-3","type":"journal-article","volume":"17","author":"Mahendran","year":"2025","journal-title":"Nat. Chem."},{"key":"ropae70d6bib24","doi-asserted-by":"publisher","first-page":"5237","DOI":"10.1038\/s41467-025-60345-9","type":"journal-article","volume":"16","author":"Liao","year":"2025","journal-title":"Nat. Commun."},{"key":"ropae70d6bib25","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.81907","type":"journal-article","volume":"12","author":"Shen","year":"2023","journal-title":"eLife"},{"key":"ropae70d6bib26","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/(95)00275-8","type":"journal-article","volume":"63","author":"Tanaka","year":"1996","journal-title":"Adv. Colloid Interface Sci."},{"key":"ropae70d6bib27","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007028","type":"journal-article","volume":"15","author":"Choi","year":"2019","journal-title":"PLOS Comput. Biol."},{"key":"ropae70d6bib28","doi-asserted-by":"publisher","first-page":"1988","DOI":"10.1021\/ma00194a077","type":"journal-article","volume":"22","author":"Tanaka","year":"1989","journal-title":"Macromolecules"},{"key":"ropae70d6bib29","doi-asserted-by":"publisher","first-page":"2663","DOI":"10.1039\/FT9959102663","type":"journal-article","volume":"91","author":"Tanaka","year":"1995","journal-title":"J. Chem. Soc. Faraday Trans."},{"key":"ropae70d6bib30","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1021\/ma970616h","type":"journal-article","volume":"31","author":"Semenov","year":"1998","journal-title":"Macromolecules"},{"key":"ropae70d6bib31","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1295\/polymj.34.479","type":"journal-article","volume":"34","author":"Tanaka","year":"2002","journal-title":"Polym. J."},{"key":"ropae70d6bib32","doi-asserted-by":"publisher","first-page":"1420","DOI":"10.1038\/s41589-024-01717-y","type":"journal-article","volume":"20","author":"Dai","year":"2024","journal-title":"Nat. Chem. Biol."},{"key":"ropae70d6bib33","doi-asserted-by":"publisher","first-page":"7678","DOI":"10.1038\/s41467-023-43489-4","type":"journal-article","volume":"14","author":"Lin","year":"2023","journal-title":"Nat. Commun."},{"key":"ropae70d6bib34","doi-asserted-by":"publisher","DOI":"10.7554\/elife.67176","type":"journal-article","volume":"10","author":"Chattaraj","year":"2021","journal-title":"eLife"},{"key":"ropae70d6bib35","doi-asserted-by":"publisher","first-page":"1678","DOI":"10.1016\/j.bpj.2023.03.036","type":"journal-article","volume":"122","author":"Chattaraj","year":"2023","journal-title":"Biophys. J."},{"key":"ropae70d6bib36","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2100099118","type":"journal-article","volume":"118","author":"Deviri","year":"2021","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib37","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2407453121","type":"journal-article","volume":"121","author":"Qian","year":"2024","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib38","doi-asserted-by":"publisher","first-page":"3031","DOI":"10.1080\/00268970500186045","type":"journal-article","volume":"103","author":"Cheong","year":"2005","journal-title":"Mol. Phys."},{"key":"ropae70d6bib39","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1038\/s42004-025-01502-5","type":"journal-article","volume":"8","author":"Zeng","year":"2025","journal-title":"Commun. Chem."},{"key":"ropae70d6bib40","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1038\/nchem.2803","type":"journal-article","volume":"9","author":"Wei","year":"2017","journal-title":"Nat. Chem."},{"key":"ropae70d6bib41","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.90.031001","type":"journal-article","volume":"90","author":"Munoz","year":"2018","journal-title":"Rev. Mod. Phys."},{"key":"ropae70d6bib42","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1038\/s41586-021-03905-5","type":"journal-article","volume":"599","author":"Shimobayashi","year":"2021","journal-title":"Nature"},{"key":"ropae70d6bib43","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2103401118","type":"journal-article","volume":"118","author":"Rouches","year":"2021","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib44","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2102772118","type":"journal-article","volume":"118","author":"Fritsch","year":"2025","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.033144","type":"journal-article","volume":"4","author":"Graf","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"ropae70d6bib46","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2220014120","type":"journal-article","volume":"120","author":"Pyo","year":"2023","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib47","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1021\/acs.biomac.4c01201","type":"journal-article","volume":"26","author":"Smokers","year":"2024","journal-title":"Biomacromolecules"},{"key":"ropae70d6bib48","doi-asserted-by":"publisher","first-page":"17650","DOI":"10.1073\/pnas.0703513104","type":"journal-article","volume":"104","author":"Veatch","year":"2007","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib49","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.cell.2015.09.015","type":"journal-article","volume":"163","author":"Molliex","year":"2015","journal-title":"Cell"},{"key":"ropae70d6bib50","first-page":"pp 21","author":"Lundberg","year":"1980","type":"book"},{"key":"ropae70d6bib51","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1038\/s41557-021-00840-w","type":"journal-article","volume":"14","author":"Bremer","year":"2021","journal-title":"Nat. Chem."},{"key":"ropae70d6bib52","doi-asserted-by":"publisher","first-page":"7722","DOI":"10.1038\/s41467-022-35370-7","type":"journal-article","volume":"13","author":"Farag","year":"2022","journal-title":"Nat. Commun."},{"key":"ropae70d6bib53","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmb.2025.168987","type":"journal-article","volume":"437","author":"Hoffmann","year":"2025","journal-title":"J. Mol. Biol."},{"key":"ropae70d6bib54","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmb.2021.167373","type":"journal-article","volume":"434","author":"Cohan","year":"2022","journal-title":"J. Mol. Biol."},{"key":"ropae70d6bib55","doi-asserted-by":"publisher","first-page":"4936","DOI":"10.1016\/j.cell.2023.08.032","type":"journal-article","volume":"186","author":"Patil","year":"2023","journal-title":"Cell"},{"key":"ropae70d6bib56","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.cell.2025.10.019","type":"journal-article","volume":"189","author":"Ruff","year":"2026","journal-title":"Cell"},{"key":"ropae70d6bib57","doi-asserted-by":"publisher","first-page":"9929","DOI":"10.1073\/pnas.1804177115","type":"journal-article","volume":"115","author":"Dignon","year":"2018","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib58","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1146\/annurev-physchem-071819-113553","type":"journal-article","volume":"71","author":"Dignon","year":"2020","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ropae70d6bib59","doi-asserted-by":"publisher","first-page":"732","DOI":"10.1038\/s43588-021-00155-3","type":"journal-article","volume":"1","author":"Joseph","year":"2021","journal-title":"Nat. Comput. Sci."},{"key":"ropae70d6bib60","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.99068.2","type":"journal-article","volume":"13","author":"Maristany","year":"2025","journal-title":"Phys. Living Syst."},{"key":"ropae70d6bib61","doi-asserted-by":"publisher","first-page":"eadj2448","DOI":"10.1126\/sciadv.adj2448","type":"journal-article","volume":"10","author":"An","year":"2024","journal-title":"Sci. Adv."},{"key":"ropae70d6bib62","doi-asserted-by":"publisher","first-page":"5527","DOI":"10.1038\/s41467-023-41274-x","type":"journal-article","volume":"14","author":"Farag","year":"2023","journal-title":"Nat. Commun."},{"key":"ropae70d6bib63","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1080\/00268976.2016.1262075","type":"journal-article","volume":"115","author":"Silmore","year":"2017","journal-title":"Mol. Phys."},{"key":"ropae70d6bib64","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BF01293604","type":"journal-article","volume":"43","author":"Binder","year":"1981","journal-title":"Z. f\u00fcr Phys. B Condens. Matter"},{"key":"ropae70d6bib65","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","type":"journal-article","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib66","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1063\/1.1741967","type":"journal-article","volume":"23","author":"Rosenbluth","year":"1955","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib67","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1080\/00268979200100061","type":"journal-article","volume":"75","author":"Siepmann","year":"1992","journal-title":"Mol. Phys."},{"key":"ropae70d6bib68","doi-asserted-by":"publisher","first-page":"2819","DOI":"10.1021\/ma00187a030","type":"journal-article","volume":"21","author":"Carmesin","year":"1988","journal-title":"Macromolecules"},{"key":"ropae70d6bib69","doi-asserted-by":"publisher","first-page":"4205","DOI":"10.1063\/1.467470","type":"journal-article","volume":"101","author":"Shaffer","year":"1994","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib70","doi-asserted-by":"publisher","DOI":"10.1063\/1.4935066","type":"journal-article","volume":"143","author":"Ruff","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib71","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1080\/00268976.2010.495734","type":"journal-article","volume":"108","author":"Binder","year":"2010","journal-title":"Mol. Phys."},{"key":"ropae70d6bib72","doi-asserted-by":"publisher","first-page":"16155","DOI":"10.1073\/pnas.1207719109","type":"journal-article","volume":"109","author":"Hofmann","year":"2012","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib73","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1146\/annurev-biophys-120221-095357","type":"journal-article","volume":"51","author":"Ghosh","year":"2022","journal-title":"Annu. Rev. Biophys."},{"key":"ropae70d6bib74","doi-asserted-by":"publisher","first-page":"3219","DOI":"10.1063\/1.1671544","type":"journal-article","volume":"50","author":"Fisk","year":"1969","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib75","doi-asserted-by":"publisher","first-page":"2396","DOI":"10.1016\/j.bpj.2023.05.007","type":"journal-article","volume":"122","author":"Farag","year":"2023","journal-title":"Biophys. J."},{"key":"ropae70d6bib76","doi-asserted-by":"publisher","first-page":"4722","DOI":"10.1063\/1.451748","type":"journal-article","volume":"85","author":"Muthukumar","year":"1986","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib77","doi-asserted-by":"publisher","DOI":"10.1063\/5.0105540","type":"journal-article","volume":"157","author":"Bauer","year":"2022","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib78","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1012826","type":"journal-article","volume":"21","author":"Biswas","year":"2025","journal-title":"PLOS Comput. Biol."},{"key":"ropae70d6bib79","doi-asserted-by":"publisher","first-page":"13190","DOI":"10.1021\/jp9536460","type":"journal-article","volume":"100","author":"Widom","year":"1996","journal-title":"J. Phys. Chem."},{"key":"ropae70d6bib80","doi-asserted-by":"publisher","DOI":"10.1063\/1.5141095","type":"journal-article","article-title":"Brangwynne C P and Panagiotopoulos A Z 2020","volume":"152","author":"Statt","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib81","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022413","type":"journal-article","volume":"101","author":"Nilsson","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ropae70d6bib82","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2111696118","type":"journal-article","volume":"118","author":"Tesei","year":"2021","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib83","author":"Rubinstein","year":"2003","type":"book"},{"key":"ropae70d6bib84","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1126\/science.157.3787.375","type":"journal-article","volume":"157","author":"Widom","year":"1967","journal-title":"Science"},{"key":"ropae70d6bib85","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1126\/science.1097116","type":"journal-article","volume":"304","author":"Aarts","year":"2004","journal-title":"Science"},{"key":"ropae70d6bib86","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.molcel.2016.05.042","type":"journal-article","volume":"63","author":"Pak","year":"2016","journal-title":"Mol. Cell"},{"key":"ropae70d6bib87","doi-asserted-by":"publisher","first-page":"1686","DOI":"10.1016\/j.cell.2016.04.047","type":"journal-article","volume":"165","author":"Feric","year":"2016","journal-title":"Cell"},{"key":"ropae70d6bib88","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2407423122","type":"journal-article","volume":"122","author":"Cheng","year":"2025","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib89","doi-asserted-by":"publisher","first-page":"1516","DOI":"10.1103\/PhysRevLett.28.1516","type":"journal-article","volume":"28","author":"Fisher","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ropae70d6bib90","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1051\/jphys:0198200430101500","type":"journal-article","volume":"43","author":"Br\u00e9zin","year":"1982","journal-title":"J. Phys. Fr."},{"key":"ropae70d6bib91","first-page":"pp 85","author":"Malthe-S\u00f8renssen","year":"2024","type":"book"},{"key":"ropae70d6bib92","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.043301","type":"journal-article","volume":"97","author":"Ferrenberg","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ropae70d6bib93","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1103\/PhysRevLett.26.957","type":"journal-article","volume":"26","author":"Mermin","year":"1971","journal-title":"Phys. Rev. Lett."},{"key":"ropae70d6bib94","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1063\/1.1678352","type":"journal-article","volume":"57","author":"Zollweg","year":"1972","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib95","doi-asserted-by":"publisher","first-page":"2123","DOI":"10.1073\/pnas.1216979110","type":"journal-article","volume":"110","author":"Meng","year":"2013","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib96","doi-asserted-by":"publisher","first-page":"4030","DOI":"10.1103\/PhysRevB.29.4030","type":"journal-article","volume":"29","author":"Pawley","year":"1984","journal-title":"Phys. Rev. B"},{"key":"ropae70d6bib97","doi-asserted-by":"publisher","first-page":"3331","DOI":"10.1021\/acs.macromol.4c03065","type":"journal-article","volume":"58","author":"Chen","year":"2025","journal-title":"Macromolecules"},{"key":"ropae70d6bib98","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1142\/S0129183198000261","type":"journal-article","volume":"09","author":"Jan","year":"1998","journal-title":"Int. J. Mod. Phys. C"},{"key":"ropae70d6bib99","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1021\/acspolymersau.2c00020","type":"journal-article","volume":"2","author":"Li","year":"2022","journal-title":"ACS Polym. Au"},{"key":"ropae70d6bib100","doi-asserted-by":"publisher","first-page":"6479","DOI":"10.1063\/1.474306","type":"journal-article","volume":"107","author":"Raos","year":"1997","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib101","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1016\/j.bpj.2020.06.014","type":"journal-article","volume":"119","author":"Zeng","year":"2020","journal-title":"Biophys. J."},{"key":"ropae70d6bib102","first-page":"pp 255","author":"Kolb","year":"1990","type":"book"},{"key":"ropae70d6bib103","first-page":"pp 437","author":"Sch\u00e4fer","year":"1999","type":"book"},{"key":"ropae70d6bib104","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1042\/BJ20121346","type":"journal-article","volume":"449","author":"Mao","year":"2012","journal-title":"Biochem. J."},{"key":"ropae70d6bib105","doi-asserted-by":"publisher","DOI":"10.1063\/1.1846651","type":"journal-article","volume":"122","author":"Steinhauser","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib106","doi-asserted-by":"publisher","first-page":"1475","DOI":"10.1021\/ma071443r","type":"journal-article","volume":"41","author":"Shirvanyants","year":"2008","journal-title":"Macromolecules"},{"key":"ropae70d6bib107","doi-asserted-by":"publisher","first-page":"900","DOI":"10.1063\/1.446748","type":"journal-article","volume":"80","author":"Kholodenko","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib108","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1002\/jcc.540161104","type":"journal-article","volume":"16","author":"Kumar","year":"1995","journal-title":"J. Comput. Chem."},{"key":"ropae70d6bib109","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0010-4655(95)00053-I","type":"journal-article","volume":"91","author":"Roux","year":"1995","journal-title":"Comput. Phys. Commun."},{"key":"ropae70d6bib110","article-title":"2.1.0","author":"Grossfield","year":"2014","type":"other"},{"key":"ropae70d6bib111","article-title":"bioRxiv","author":"Varma","year":"2026","type":"other"},{"key":"ropae70d6bib112","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.39695.001","type":"journal-article","volume":"8","author":"Narayanan","year":"2019","journal-title":"Elife"},{"key":"ropae70d6bib113","doi-asserted-by":"publisher","first-page":"4831","DOI":"10.1038\/s41467-023-40540-2","type":"journal-article","volume":"14","author":"Lan","year":"2023","journal-title":"Nat. Commun."},{"key":"ropae70d6bib114","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1126\/science.aar4199","type":"journal-article","volume":"361","author":"Cho","year":"2018","journal-title":"Science"},{"key":"ropae70d6bib115","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.cels.2024.01.005","type":"journal-article","volume":"15","author":"Mumford","year":"2024","journal-title":"Cell Syst."},{"key":"ropae70d6bib116","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1101\/gad.350828.123","type":"journal-article","volume":"38","author":"Zolotarev","year":"2024","journal-title":"Genes Dev."},{"key":"ropae70d6bib117","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1016\/j.cell.2025.11.026","type":"journal-article","volume":"189","author":"Shinn","year":"2026","journal-title":"Cell"},{"key":"ropae70d6bib118","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2202222119","type":"journal-article","volume":"119","author":"Kar","year":"2022","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib119","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2120799119","type":"journal-article","volume":"119","author":"Seim","year":"2022","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib120","doi-asserted-by":"publisher","first-page":"4408","DOI":"10.1038\/s41467-024-48775-3","type":"journal-article","volume":"15","author":"Kar","year":"2024","journal-title":"Nat. Commun."},{"key":"ropae70d6bib121","doi-asserted-by":"publisher","first-page":"5714","DOI":"10.1016\/j.cub.2024.10.055","type":"journal-article","volume":"34","author":"Yanas","year":"2024","journal-title":"Curr. Biol."},{"key":"ropae70d6bib122","doi-asserted-by":"publisher","first-page":"3640","DOI":"10.1016\/j.molcel.2025.08.034","type":"journal-article","volume":"85","author":"Sprunger","year":"2025","journal-title":"Mol. Cell"},{"key":"ropae70d6bib123","doi-asserted-by":"publisher","first-page":"9956","DOI":"10.1038\/s41467-025-64909-7","type":"journal-article","volume":"16","author":"Ge","year":"2025","journal-title":"Nat. Commun."},{"key":"ropae70d6bib124","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1038\/s41567-025-02827-7","type":"journal-article","volume":"21","author":"Wu","year":"2025","journal-title":"Nat. Phys."},{"key":"ropae70d6bib125","article-title":"bioRxiv","author":"Linsenmeier","year":"2025","type":"other"},{"key":"ropae70d6bib126","doi-asserted-by":"publisher","DOI":"10.1063\/5.0223001","type":"journal-article","volume":"161","author":"Cohen","year":"2024","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib127","doi-asserted-by":"publisher","first-page":"20837","DOI":"10.1002\/anie.202006711","type":"journal-article","volume":"59","author":"Ghosh","year":"2020","journal-title":"Angew. Chem. Int. Edn"},{"key":"ropae70d6bib128","doi-asserted-by":"publisher","first-page":"5995","DOI":"10.1038\/s41467-021-26274-z","type":"journal-article","volume":"12","author":"Ghosh","year":"2021","journal-title":"Nat. Commun."},{"key":"ropae70d6bib129","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1038\/s41567-024-02558-1","type":"journal-article","volume":"20","author":"Alshareedah","year":"2024","journal-title":"Nat. Phys."},{"key":"ropae70d6bib130","doi-asserted-by":"publisher","first-page":"3413","DOI":"10.1038\/s41467-024-47602-z","type":"journal-article","volume":"15","author":"Dar","year":"2024","journal-title":"Nat. Commun."},{"key":"ropae70d6bib131","doi-asserted-by":"publisher","first-page":"19795","DOI":"10.1039\/D4SC03564J","type":"journal-article","volume":"15","author":"Fisher","year":"2024","journal-title":"Chem. Sci."},{"key":"ropae70d6bib132","doi-asserted-by":"publisher","first-page":"4488","DOI":"10.1016\/j.cell.2022.09.042","type":"journal-article","volume":"185","author":"Boyd-Shiwarski","year":"2022","journal-title":"Cell"},{"key":"ropae70d6bib133","doi-asserted-by":"publisher","first-page":"R207","DOI":"10.1088\/0953-8984\/12\/15\/201","type":"journal-article","volume":"12","author":"Tanaka","year":"2000","journal-title":"J. Phys.: Condens. Matter"},{"key":"ropae70d6bib134","doi-asserted-by":"publisher","first-page":"eaat8715","DOI":"10.1126\/scisignal.aat8715","type":"journal-article","volume":"12","author":"Lin","year":"2019","journal-title":"Sci. Signal."},{"key":"ropae70d6bib135","doi-asserted-by":"publisher","DOI":"10.1063\/1.5110393","type":"journal-article","volume":"151","author":"Midya","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib136","doi-asserted-by":"publisher","first-page":"10748","DOI":"10.1063\/1.1809588","type":"journal-article","volume":"121","author":"Cecchini","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ropae70d6bib137","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1126\/science.aan5774","type":"journal-article","volume":"358","author":"Riback","year":"2017","journal-title":"Science"},{"key":"ropae70d6bib138","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1038\/s41586-023-07004-5","type":"journal-article","volume":"626","author":"Tesei","year":"2024","journal-title":"Nature"},{"key":"ropae70d6bib139","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1038\/s41592-023-02159-5","type":"journal-article","volume":"21","author":"Lotthammer","year":"2024","journal-title":"Nat. Methods"},{"key":"ropae70d6bib140","doi-asserted-by":"publisher","first-page":"4729","DOI":"10.1021\/jacsau.4c00673","type":"journal-article","volume":"4","author":"Holla","year":"2024","journal-title":"JACS Au"},{"key":"ropae70d6bib141","doi-asserted-by":"publisher","first-page":"e4986","DOI":"10.1002\/pro.4986","type":"journal-article","volume":"33","author":"Baxa","year":"2024","journal-title":"Protein Sci."},{"key":"ropae70d6bib142","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbc.2021.100998","type":"journal-article","volume":"297","author":"Safari","year":"2021","journal-title":"J. Biol. Chem."},{"key":"ropae70d6bib143","doi-asserted-by":"publisher","first-page":"20075","DOI":"10.1073\/pnas.1320626110","type":"journal-article","volume":"110","author":"Crick","year":"2013","journal-title":"Proc. Natl Acad. Sci."},{"key":"ropae70d6bib144","doi-asserted-by":"publisher","first-page":"1979","DOI":"10.1016\/j.bpj.2026.03.037","type":"journal-article","volume":"125","author":"Zhang","year":"2026","journal-title":"Biophys. J."},{"key":"ropae70d6bib145","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1021\/acscentsci.4c01617","type":"journal-article","volume":"11","author":"Tejedor","year":"2025","journal-title":"ACS Cent. Sci."},{"key":"ropae70d6bib146","doi-asserted-by":"publisher","first-page":"e5172","DOI":"10.1002\/pro.5172","type":"journal-article","volume":"33","author":"Cao","year":"2024","journal-title":"Protein Sci."},{"key":"ropae70d6bib147","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2417920122","type":"journal-article","volume":"122","author":"von Bulow","year":"2025","journal-title":"Proc. Natl Acad. Sci."}],"container-title":["Reports on Progress in Physics"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T06:55:23Z","timestamp":1780901723000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6633\/ae70d6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,1]]},"references-count":147,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6,8]]},"published-print":{"date-parts":[[2026,6,1]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6633\/ae70d6","relation":{},"ISSN":["0034-4885","1361-6633"],"issn-type":[{"value":"0034-4885","type":"print"},{"value":"1361-6633","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,1]]},"assertion":[{"value":"Distinguishing near- versus off-critical phase behaviors of intrinsically disordered proteins","name":"article_title","label":"Article Title"},{"value":"Reports on Progress in Physics","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2026 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2026-03-09","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-05-20","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-06-08","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}