{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T02:30:20Z","timestamp":1778034620349,"version":"3.51.4"},"reference-count":40,"publisher":"Proceedings of the National Academy of Sciences","issue":"13","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2005,3,29]]},"abstract":"<jats:p>\n                    The presence of macromolecules in cells geometrically restricts the available space for poplypeptide chains. To study the effects of macromolecular crowding on folding thermodynamics and kinetics, we used an off-lattice model of the all-\u03b2-sheet WW domain in the presence of large spherical particles whose interaction with the polypeptide chain is purely repulsive. At all volume fractions, \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    , of the crowding agents the stability of the native state is enhanced. Remarkably, the refolding rates, which are larger than the value at \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    = 0, increase nonmonotonically as \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    increases, reaching a maximum at\n                    <jats:inline-formula>\n                      <jats:tex-math notation=\"LaTeX\">\\documentclass[12pt]{minimal}\n\\usepackage{amsmath}\n\\usepackage{wasysym} \n\\usepackage{amsfonts} \n\\usepackage{amssymb} \n\\usepackage{amsbsy}\n\\usepackage{mathrsfs}\n\\setlength{\\oddsidemargin}{-69pt}\n\\begin{document}\n\\begin{equation*}{\\varphi}_{{\\mathrm{c}}}={\\varphi}_{{\\mathrm{c}}}^{*}\\end{equation*}\\end{document}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . At high values of \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    , the depletion-induced intramolecular attraction produces compact structures with considerable structure in the denatured state. Changes in native state stability and folding kinetics at \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    can be quantitatively mapped onto confinement in a volume-fraction-dependent spherical pore with radius\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    \u2248 (4\u03c0\/3\u03d5\n                    <jats:sub>c<\/jats:sub>\n                    )\n                    <jats:sup>1\/3<\/jats:sup>\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>c<\/jats:sub>\n                    (\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>c<\/jats:sub>\n                    is the radius of the crowding particles) as long as\n                    <jats:inline-formula>\n                      <jats:tex-math notation=\"LaTeX\">\\documentclass[12pt]{minimal}\n\\usepackage{amsmath}\n\\usepackage{wasysym} \n\\usepackage{amsfonts} \n\\usepackage{amssymb} \n\\usepackage{amsbsy}\n\\usepackage{mathrsfs}\n\\setlength{\\oddsidemargin}{-69pt}\n\\begin{document}\n\\begin{equation*}{\\varphi}_{{\\mathrm{c}}}{\\leq}{\\varphi}_{{\\mathrm{c}}}^{*}\\end{equation*}\\end{document}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . We show that the extent of native state stabilization at finite \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    is comparable with that in a spherical pore. In both situations, rate enhancement is due to destabilization of the denatured states with respect to \u03d5\n                    <jats:sub>c<\/jats:sub>\n                    = 0.\n                  <\/jats:p>","DOI":"10.1073\/pnas.0409630102","type":"journal-article","created":{"date-parts":[[2005,3,21]],"date-time":"2005-03-21T20:33:31Z","timestamp":1111437211000},"page":"4753-4758","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":527,"title":["Molecular crowding enhances native state stability and refolding rates of globular proteins"],"prefix":"10.1073","volume":"102","author":[{"given":"Margaret S.","family":"Cheung","sequence":"first","affiliation":[{"name":"Biophysics Program, Institute of Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742"}]},{"given":"Dmitri","family":"Klimov","sequence":"additional","affiliation":[{"name":"Biophysics Program, Institute of Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742"}]},{"given":"D.","family":"Thirumalai","sequence":"additional","affiliation":[{"name":"Biophysics Program, Institute of Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742"}]}],"member":"341","published-online":{"date-parts":[[2005,3,21]]},"reference":[{"key":"e_1_3_2_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/425027a"},{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0968-0004(01)01938-7"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-440X(99)00045-7"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-440X(00)00172-X"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1093\/emboj\/19.15.3870"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.37.269"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1021\/bi0155504"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.072220699"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmbi.1999.2591"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1831920100"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1564048"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.97.6.2544"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1021\/jp034441r"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmbi.2001.4873"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1333907100"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0731771100"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1110\/ps.8.2.361"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/bip.1978.360170612"},{"key":"e_1_3_2_19_2","unstructured":"Allen M. 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