{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T18:09:44Z","timestamp":1789754984927,"version":"4.0.1"},"reference-count":21,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T00:00:00Z","timestamp":1789689600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n Surface charge is widely regarded as a primary determinant of nanoparticle\u2013immune cell interactions, yet nanocarriers with similar physicochemical profiles often exhibit markedly different biological outcomes. Here, we show that ligand conformational diversity, quantified through an information-theoretic descriptor (\n \n \n \n \n \n \n H<\/mml:mi>\n \n \n l<\/mml:mi>\n i<\/mml:mi>\n g<\/mml:mi>\n a<\/mml:mi>\n n<\/mml:mi>\n d<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ), is strongly associated with a regime transition in the relationship between surface charge and cellular uptake. Analysis of 105 gold nanoparticles from a benchmark protein corona dataset identifies a critical threshold at\n \n \n \n \n \n \n H<\/mml:mi>\n \n \n l<\/mml:mi>\n i<\/mml:mi>\n g<\/mml:mi>\n a<\/mml:mi>\n n<\/mml:mi>\n d<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n \n *<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msubsup>\n \u2248<\/mml:mo>\n 1.76<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bits (\n F<\/jats:italic>\n \u2009=\u200947.3,\n p<\/jats:italic>\n \u2009<\u200910\n \u221214<\/jats:sup>\n ): below this value, zeta potential is positively associated with uptake (\n r<\/jats:italic>\n \u2009=\u2009+0.70), whereas above it the relationship reverses (\n \n \n \n \n \n r<\/mml:mi>\n =<\/mml:mo>\n \u2212<\/mml:mo>\n 0.58<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ), consistent with steric shielding by flexible surface ligands. Entropy-derived descriptors improve predictive performance across multiple model classes (\n \n \n \n \n \n \u0394<\/mml:mo>\n \n R<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n up to +0.118), with gains concentrated in high-entropy regimes where physicochemical descriptors alone are insufficient. An analytical competition model captures this transition in a compact form (\n R<\/jats:italic>\n 2<\/jats:sup>\n \u2009=\u20090.550), with\n \n \n \n \n \n \n 2<\/mml:mn>\n \n \n H<\/mml:mi>\n \n *<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:msup>\n \u2248<\/mml:mo>\n 3.4<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n effective microstates marking a numerical balance point between electrostatic and steric contributions. Cross-dataset validation on 652 multi-material nanoparticles supports transferability of the descriptor framework (\n \n \n \n \n \n \u0394<\/mml:mo>\n \n R<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n =<\/mml:mo>\n +<\/mml:mo>\n 0.181<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ). We emphasize that\n \n \n \n \n \n \n H<\/mml:mi>\n \n \n l<\/mml:mi>\n i<\/mml:mi>\n g<\/mml:mi>\n a<\/mml:mi>\n n<\/mml:mi>\n d<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a constructed information-theoretic descriptor rather than a thermodynamic entropy, and that all findings are derived from retrospective analysis of in vitro datasets and not from controlled experimental manipulation. The identified threshold therefore represents a reproducible statistical pattern and a testable hypothesis for how ligand flexibility modulates interaction regimes. This framework provides a computable basis for organizing nanocarrier design hypotheses and motivates prospective validation in more complex carrier systems.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0358239","type":"journal-article","created":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T17:33:54Z","timestamp":1789752834000},"page":"e0358239","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ligand conformational entropy as a regime-switching descriptor of the electrostatic\u2013uptake relationship in nanocarrier\u2013immune cell interactions"],"prefix":"10.1371","volume":"21","author":[{"given":"Quynh Hoa","family":"Truong","sequence":"first","affiliation":[{"name":"Clevix Lab, Clevix LLC","place":["Hanoi, Vietnam"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4876-2610","authenticated-orcid":true,"given":"Xuan Khanh","family":"Truong","sequence":"additional","affiliation":[{"name":"Clevix Lab, Clevix LLC","place":["Hanoi, Vietnam"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,9,18]]},"reference":[{"issue":"1","key":"pone.0358239.ref001","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1038\/nrc.2016.108","article-title":"Cancer nanomedicine: progress, challenges and opportunities","volume":"17","author":"J Shi","year":"2017","journal-title":"Nat Rev Cancer"},{"issue":"4","key":"pone.0358239.ref002","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1021\/ja2084338","article-title":"Nanoparticle size and surface chemistry determine serum protein adsorption and macrophage uptake","volume":"134","author":"CD Walkey","year":"2012","journal-title":"J Am Chem 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