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Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a limited number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. The exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.<\/jats:p>","DOI":"10.1002\/advs.202301501","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T22:39:59Z","timestamp":1686177599000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantification of Surface Tension Effects and Nucleation\u2010and\u2010Growth Rates during Self\u2010Assembly of Biological Condensates"],"prefix":"10.1002","volume":"10","author":[{"given":"Zsuzsa","family":"S\u00e1rk\u00e1ny","sequence":"first","affiliation":[{"name":"IBMC \u2212 Instituto de Biologia Molecular e Celular Universidade do Porto  Porto 4150\u2013180 Portugal"},{"name":"i3S \u2212 Instituto de Investiga\u00e7\u00e3o e Inova\u00e7\u00e3o em Sa\u00fade Universidade do Porto  Porto 4150\u2013180 Portugal"}]},{"given":"Fernando","family":"Rocha","sequence":"additional","affiliation":[{"name":"LEPABE \u2212 Laboratory for Process Engineering Environment Biotechnology and Energy Faculdade de Engenharia da Universidade do Porto  Porto 4200\u2010465 Portugal"}]},{"given":"Anna","family":"Bratek\u2010Skicki","sequence":"additional","affiliation":[{"name":"Jerzy Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences  Niezapominajek 8 Krakow PL30239 Poland"},{"name":"VIB\u2010VUB Center for Structural Biology Vlaams Instituut voor Biotechnology  Brussels 1050 Ixelles Belgium"},{"name":"Structural Biology Brussels (SBB) Bioengineering Sciences Department Vrije Universiteit Brussel (VUB)  Brussels B\u20101050 Belgium"}]},{"given":"Peter","family":"Tompa","sequence":"additional","affiliation":[{"name":"VIB\u2010VUB Center for Structural Biology Vlaams Instituut voor Biotechnology  Brussels 1050 Ixelles Belgium"},{"name":"Structural Biology Brussels (SBB) Bioengineering Sciences Department Vrije Universiteit Brussel (VUB)  Brussels B\u20101050 Belgium"},{"name":"Institute of Enzymology Research Centre for Natural Sciences  Budapest 1117 Hungary"}]},{"given":"Sandra","family":"Macedo\u2010Ribeiro","sequence":"additional","affiliation":[{"name":"IBMC \u2212 Instituto de Biologia Molecular e Celular Universidade do Porto  Porto 4150\u2013180 Portugal"},{"name":"i3S \u2212 Instituto de Investiga\u00e7\u00e3o e Inova\u00e7\u00e3o em Sa\u00fade Universidade do Porto  Porto 4150\u2013180 Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6908-1828","authenticated-orcid":false,"given":"Pedro M.","family":"Martins","sequence":"additional","affiliation":[{"name":"IBMC \u2212 Instituto de Biologia Molecular e Celular Universidade do Porto  Porto 4150\u2013180 Portugal"},{"name":"i3S \u2212 Instituto de Investiga\u00e7\u00e3o e Inova\u00e7\u00e3o em Sa\u00fade Universidade do Porto  Porto 4150\u2013180 Portugal"}]}],"member":"311","published-online":{"date-parts":[[2023,6,6]]},"reference":[{"key":"e_1_2_14_1_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaf4382"},{"key":"e_1_2_14_2_1","doi-asserted-by":"publisher","DOI":"10.3389\/fnmol.2020.582488"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.1074\/jbc.M115.699348"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1074\/jbc.M112.375345"},{"key":"e_1_2_14_5_1","doi-asserted-by":"publisher","DOI":"10.1021\/ja9705102"},{"key":"e_1_2_14_6_1","doi-asserted-by":"publisher","DOI":"10.1021\/ja8017412"},{"key":"e_1_2_14_7_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1218402110"},{"key":"e_1_2_14_8_1","doi-asserted-by":"publisher","DOI":"10.3390\/biom8040108"},{"key":"e_1_2_14_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/anie.201707345"},{"key":"e_1_2_14_10_1","doi-asserted-by":"publisher","DOI":"10.1021\/bi049621l"},{"key":"e_1_2_14_11_1","doi-asserted-by":"publisher","DOI":"10.1110\/ps.041266605"},{"key":"e_1_2_14_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.xcrp.2020.100014"},{"key":"e_1_2_14_13_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1404855111"},{"key":"e_1_2_14_14_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/aaa61e"},{"key":"e_1_2_14_15_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcb.0c09225"},{"key":"e_1_2_14_16_1","doi-asserted-by":"publisher","DOI":"10.1038\/s42003-020-01596-8"},{"key":"e_1_2_14_17_1","doi-asserted-by":"publisher","DOI":"10.1021\/jacs.9b03083"},{"key":"e_1_2_14_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2019.08.037"},{"key":"e_1_2_14_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.molcel.2015.09.017"},{"key":"e_1_2_14_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2016.06.010"},{"key":"e_1_2_14_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2018.12.035"},{"key":"e_1_2_14_22_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-biophys-121219-081629"},{"key":"e_1_2_14_23_1","volume-title":"Methods in Enzymology","author":"Posey A. 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