{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:11Z","timestamp":1760242331545,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T00:00:00Z","timestamp":1492128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a mathematical model describing the formation of micellar forms\u2014whether spherical, globular, cylindrical, or ribbonlike\u2014as well as its adaptation to protein structure. Our model, based on the fuzzy oil drop paradigm, assumes that in a spherical micelle the distribution of hydrophobicity produced by the alignment of polar molecules with the external water environment can be modeled by a 3D Gaussian function. Perturbing this function by changing the values of its sigma parameters leads to a variety of conformations\u2014the model is therefore applicable to globular, cylindrical, and ribbonlike micelles. In the context of protein structures ranging from globular to ribbonlike, our model can explain the emergence of fibrillar forms; particularly amyloids.<\/jats:p>","DOI":"10.3390\/e19040167","type":"journal-article","created":{"date-parts":[[2017,4,18]],"date-time":"2017-04-18T11:22:04Z","timestamp":1492514524000},"page":"167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Application of the Fuzzy Oil Drop Model Describes Amyloid as a Ribbonlike Micelle"],"prefix":"10.3390","volume":"19","author":[{"given":"Irena","family":"Roterman","sequence":"first","affiliation":[{"name":"Department of Bioinformatics and Telemedicine, Collegium Medium, Jagiellonian University, Lazarza 16, 31-530 Krakow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1806-9877","authenticated-orcid":false,"given":"Mateusz","family":"Banach","sequence":"additional","affiliation":[{"name":"Department of Bioinformatics and Telemedicine, Collegium Medium, Jagiellonian University, Lazarza 16, 31-530 Krakow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leszek","family":"Konieczny","sequence":"additional","affiliation":[{"name":"Chair of Medical Biochemistry, Collegium Medicum, Jagiellonian University, Kopernika 7, 31-034 Krakow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1126\/science.6801762","article-title":"Novel proteinaceous infectious particles cause scrapie","volume":"216","author":"Prusiner","year":"1982","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1038\/scientificamerican0704-86","article-title":"Detecting madcow disease","volume":"291","author":"Prusiner","year":"2004","journal-title":"Sci. Am."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11025","DOI":"10.1073\/pnas.1206555109","article-title":"Purified and synthetic Alzheimer\u2019s amyloid \u03b2 (A\u03b2) prions","volume":"109","author":"Watts","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1126\/science.271.5255.1493","article-title":"Misfolding the way to disease","volume":"271","author":"Taubes","year":"1996","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5566","DOI":"10.1073\/pnas.091431798","article-title":"Evaluating the binding selectivity of transthyretin amyloid fibril inhibitors in blood plasma","volume":"98","author":"Purkey","year":"2001","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6313","DOI":"10.1126\/science.aah4949","article-title":"De novo design of a biologically active amyloid","volume":"354","author":"Gallardo","year":"2016","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3233\/ISB-00217","article-title":"Gauss-function-based model of hydrophobicity density in proteins","volume":"6","author":"Konieczny","year":"2006","journal-title":"In Silico Biol."},{"key":"ref_8","unstructured":"Roterman, I. (2012). Ligand-binding site recognition. Protein Folding in Silico\u2014Protein Folding Versus Protein Structure Prediction, Woodhead Publishing."},{"key":"ref_9","unstructured":"Roterman, I. (2012). Use of the \u201cfuzzy oil drop\u201d model to identify the complexation area in protein homodimers. Protein Folding in Silico\u2014Protein Folding Versus Protein Structure Prediction, Woodhead Publishing."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dygut, J., Kalinowska, B., Banach, M., Piwowar, M., Konieczny, L., and Roterman, I. (2016). Structural Interface Forms and Their Involvement in Stabilization of Multidomain Proteins or Protein Complexes. Int. J. Mol. Sci., 17.","DOI":"10.3390\/ijms17101741"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8037","DOI":"10.1021\/acs.jpcb.5b00171","article-title":"Modeling Protein\u2013Micelle Systems in Implicit Water","volume":"119","author":"Versace","year":"2015","journal-title":"J. Phys. Chem. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1006\/jmbi.1998.1640","article-title":"Folding of \u03b2-sheet membrane proteins: A hydrophobic hexapeptide model","volume":"277","author":"Wimley","year":"1998","journal-title":"J. Mol. Biol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Di Bartolo, N., Compton, E.L., Warne, T., Edwards, P.C., Tate, C.G., Schertler, G.F., and Booth, P.J. (2016). Complete Reversible Refolding of a G-Protein Coupled Receptor on a Solid Support. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0151582"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1111\/jphp.12545","article-title":"Synthesis and in vitro evaluation of pH-sensitive PEG-I-dC16 block polymer micelles for anticancer drug delivery","volume":"68","author":"Huang","year":"2016","journal-title":"J. Pharm. Pharmacol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.biomaterials.2016.03.010","article-title":"Thailandepsin A-loaded and octreotide-functionalized unimolecular micelles for targeted neuroendocrine cancer therapy","volume":"91","author":"Xu","year":"2016","journal-title":"Biomaterials"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"23322","DOI":"10.18632\/oncotarget.8019","article-title":"\u03b2-casein nanovehicles for oral delivery of chemotherapeutic Drug combinations overcoming P-glycoprotein-mediated multidrug resistance in human gastric cancer cells","volume":"7","author":"Assaraf","year":"2016","journal-title":"Oncotarget"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1111\/cas.12926","article-title":"Enhanced efficacy against cervical carcinomas through polymeric micelles physically incorporating the proteasome inhibitor MG132","volume":"107","author":"Matsumoto","year":"2016","journal-title":"Cancer Sci."},{"key":"ref_18","first-page":"703","article-title":"Development of a robust pH-sensitive polyelectrolyte ionomer complex for anticancer nanocarriers","volume":"11","author":"Lim","year":"2016","journal-title":"Int. J. Nanomed."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chren, Y., Huang, Y., Qin, D., Liu, W., Song, C., Lou, K., Wang, W., and Gao, F. (2016). \u03b2-Cyclodextrin-Based Inclusion Complexation Bridged Biodegradable Self-Assembly Macromolecular Micelle for the Delivery of Paclitaxel. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0150877"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1822","DOI":"10.1021\/acs.molpharmaceut.5b00971","article-title":"Micelle Mixtures for Coadministration of Gemcitabine and GDC-0449 to Treat Pancreatic Cancer","volume":"13","author":"Karaca","year":"2016","journal-title":"Mol. Pharm."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8307","DOI":"10.1063\/1.1689293","article-title":"Thermodynamics of \u03b2-amyloid fibril formation","volume":"120","author":"Tiana","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10866","DOI":"10.1073\/pnas.1605104113","article-title":"A\u03b242 assembles into specific \u03b2-barrel pore-forming oligomers in membrane-mimicking environments","volume":"113","author":"Bayoumi","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"9973","DOI":"10.1021\/acs.langmuir.5b02186","article-title":"Supersaturation-Limited and Unlimited Phase Spaces Compete to Produce Maximal Amyloid Fibrillation near the Critical Micelle Concentration of Sodium Dodecyl Sulfate","volume":"31","author":"So","year":"2015","journal-title":"Langmuir"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"16094","DOI":"10.1021\/bi961598j","article-title":"Three-dimensional structures of the amyloid \u03b2 peptide (25\u201335) in membrane-mimicking environment","volume":"35","author":"Kohno","year":"1996","journal-title":"Biochemistry"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1038\/nature20416","article-title":"The activities of amyloids from a structural perspective","volume":"339","author":"Riek","year":"2016","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1038\/nsmb.2991","article-title":"A\u03b2(1\u201342) fibril structure illuminates self-recognition and replication of amyloid in Alzheimer\u2019s disease","volume":"22","author":"Xiao","year":"2015","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1006\/jmbi.1999.3292","article-title":"Crystal structure of chondroitinase B from Flavobacterium heparinum and its complex with a disaccharide product at 1.7 A resolution","volume":"294","author":"Huang","year":"1999","journal-title":"J. Mol. Biol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1038\/nature03680","article-title":"Structure of the cross-\u03b2 spine of amyloid-like fibrils","volume":"435","author":"Nelson","year":"2005","journal-title":"Nature"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"16938","DOI":"10.1073\/pnas.1112600108","article-title":"Molecular basis for amyloid-\u03b2 polymorphism","volume":"108","author":"Colletier","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1038\/nsmb.1643","article-title":"Molecular mechanisms for protein-encoded inheritance","volume":"16","author":"Wiltzius","year":"2009","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1038\/nsmb.1948","article-title":"\u03b22-microglobulin forms three-dimensional domain-swapped amyloid fibrils with disulfide linkages","volume":"18","author":"Liu","year":"2011","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2456","DOI":"10.1021\/bi101803k","article-title":"Atomic structures suggest determinants of transmission barriers in mammalian prion disease","volume":"50","author":"Apostol","year":"2011","journal-title":"Biochemistry"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"29671","DOI":"10.1074\/jbc.C110.158303","article-title":"Crystallographic studies of prion protein (PrP) segments suggest how structural changes encoded by polymorphism at residue 129 modulate susceptibility to human prion disease","volume":"285","author":"Apostol","year":"2010","journal-title":"J. Biol. Chem."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1038\/381090a0","article-title":"Structure of Bordetella pertussis virulence factor P.69 pertactin","volume":"381","author":"Emsley","year":"1996","journal-title":"Nature"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.3390\/e17031477","article-title":"Application of Divergence Entropy to Characterize the Structure of the Hydrophobic Core in DNA Interacting Proteins","volume":"17","author":"Kalinowska","year":"2015","journal-title":"Entropy"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Roterman, I., Banach, M., Kalinowska, B., and Konieczny, L. (2016). Influence of the Aqueous Environment on Protein Structure\u2014A Plausible Hypothesis Concerning the Mechanism of Amyloidogenesis. Entropy, 18.","DOI":"10.3390\/e18100351"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1023\/B:JCAM.0000022562.76762.f0","article-title":"Force-field parametrization and molecular dynamics simulations of Congo red","volume":"18","author":"Borowski","year":"2004","journal-title":"J. Comput. Aided Mol. Des."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s00894-011-1033-4","article-title":"Fuzzy oil drop model to interpret the structure of antifreeze proteins and their mutants","volume":"18","author":"Banach","year":"2012","journal-title":"J. Mol. Model."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.jtbi.2011.05.027","article-title":"Two-intermediate model to characterize the structure of fast-folding proteins","volume":"283","author":"Roterman","year":"2011","journal-title":"J. Theor. Biol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.jmb.2009.01.054","article-title":"Molecular dynamism of fe-S cluster biosynthesis implicated by the structure of the sufc2-Sufd2 complex","volume":"387","author":"Wada","year":"2009","journal-title":"J. Mol. Biol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/128_2011_287","article-title":"Protein structure determination by solid-state NMR","volume":"326","author":"Zhao","year":"2012","journal-title":"Top. Curr. Chem."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1038\/nmeth.2635","article-title":"Solid-state NMR spectroscopy structure determination of a lipid-embedded heptahelical membrane protein","volume":"10","author":"Wang","year":"2013","journal-title":"Nat. Methods"},{"key":"ref_44","unstructured":"Roterman, I., Banach, M., and Konieczny, L. (2017). Stop signals preventing the linear propagation of hydrophobicity in proteins. IJMS, submitted."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.jtbi.2014.05.007","article-title":"The fuzzy oil drop model, based on hydrophobicity density distribution, generalizes the influence of water environment on protein structure and function","volume":"359","author":"Banach","year":"2014","journal-title":"J. Theor. Biol."},{"key":"ref_46","first-page":"44","article-title":"Are there pathways for protein folding","volume":"65","author":"Levinthal","year":"1968","journal-title":"J. Chem. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0065-3233(08)60401-5","article-title":"Protein denaturation","volume":"23","author":"Tanford","year":"1968","journal-title":"Adv. Protein Chem."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1038\/377754a0","article-title":"Initial hydrophobic collapse in the folding of barstar","volume":"377","author":"Agashe","year":"1995","journal-title":"Nature"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1126\/science.282.5389.740","article-title":"Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution","volume":"282","author":"Duan","year":"1998","journal-title":"Science"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"13928","DOI":"10.1073\/pnas.1936025100","article-title":"Differential hydrophobicity drives self-assembly in Huntington\u2019s disease","volume":"100","author":"Burke","year":"2003","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1002\/prot.20002","article-title":"Conformational subspace in simulation of early-stage protein folding","volume":"55","author":"Jurkowski","year":"2004","journal-title":"Proteins"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/S0925-4439(00)00029-6","article-title":"Alzheimer\u2019s amyloid fibrils: Structure and assembly","volume":"1502","author":"Serpell","year":"2000","journal-title":"Biochim. Biophys. Acta"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"11158","DOI":"10.1002\/anie.201310958","article-title":"The hydrophobic effect revisited\u2014Studies with supramolecular complexes imply high-energy water as a noncovalent driving force","volume":"53","author":"Biedermann","year":"2014","journal-title":"Angew. Chem."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"7412","DOI":"10.1063\/1.456221","article-title":"Solvent-induced interactions: Hydrophobic and Hydrophilic Phenomena","volume":"90","year":"1989","journal-title":"J. Chem. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.bbamem.2009.12.012","article-title":"Membrane charge dependent states of the \u03b2-amyloid fragment A\u03b2 (16\u201335) with differently charged micelle aggregates","volume":"1798","author":"Grimaldi","year":"2010","journal-title":"Biochim. Biophys. Acta"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3480","DOI":"10.1016\/S0006-3495(03)70068-X","article-title":"Micelle formation by a fragment of human islet amyloid polypeptide","volume":"84","author":"Rhoades","year":"2003","journal-title":"Biophys. J."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1110\/ps.052048706","article-title":"Structure and topology of the non-amyloid-\u03b2 component fragment of human alpha-synuclein bound to micelles: Implications for the aggregation process","volume":"15","author":"Bisaglia","year":"2006","journal-title":"Protein Sci."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"3521","DOI":"10.1021\/bi061716v","article-title":"Structural chracterisation of the partially folder intermediates of an immunoglobulin Ligot chain leading to amyloid fibrillation and amorphous aggregation","volume":"46","author":"Qin","year":"2007","journal-title":"Biochemistry"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1038\/nature02264","article-title":"Folding proteins in fatal ways","volume":"426","author":"Selkoe","year":"2003","journal-title":"Nature"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/4\/167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:32:41Z","timestamp":1760207561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/4\/167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,14]]},"references-count":59,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["e19040167"],"URL":"https:\/\/doi.org\/10.3390\/e19040167","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,4,14]]}}}