{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:31:45Z","timestamp":1760146305940,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T00:00:00Z","timestamp":1729209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Institutes of Health Grant","award":["R35-GM124818","2019\/35\/B\/ST4\/02086"],"award-info":[{"award-number":["R35-GM124818","2019\/35\/B\/ST4\/02086"]}]},{"name":"Narodowe Centrum Nauki (NCN) in Poland","award":["R35-GM124818","2019\/35\/B\/ST4\/02086"],"award-info":[{"award-number":["R35-GM124818","2019\/35\/B\/ST4\/02086"]}]},{"name":"TASK Supercomputer Center in Gdansk and PLGrid Infrastructure, Poland","award":["R35-GM124818","2019\/35\/B\/ST4\/02086"],"award-info":[{"award-number":["R35-GM124818","2019\/35\/B\/ST4\/02086"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomolecules"],"abstract":"<jats:p>Single-molecule force spectroscopy (SMFS) experiments can monitor protein refolding by applying a small force of a few piconewtons (pN) and slowing down the folding process. Bell theory predicts that in the narrow force regime where refolding can occur, the folding time should increase exponentially with increased external force. In this work, using coarse-grained molecular dynamics simulations, we compared the refolding pathways of SARS-CoV-1 RBD and SARS-CoV-2 RBD (RBD refers to the receptor binding domain) starting from unfolded conformations with and without a force applied to the protein termini. For SARS-CoV-2 RBD, the number of trajectories that fold is significantly reduced with the application of a 5 pN force, indicating that, qualitatively consistent with Bell theory, refolding is slowed down when a pulling force is applied to the termini. In contrast, the refolding times of SARS-CoV-1 RBD do not change meaningfully when a force of 5 pN is applied. How this lack of a Bell response could arise at the molecular level is unknown. Analysis of the entanglement changes of the folded conformations revealed that in the case of SARS-CoV-1 RBD, an external force minimizes misfolding into kinetically trapped states, thereby promoting efficient folding and offsetting any potential slowdown due to the external force. These misfolded states contain non-native entanglements that do not exist in the native state of either SARS-CoV-1-RBD or SARS-CoV-2-RBD. These results indicate that non-Bell behavior can arise from this class of misfolding and, hence, may be a means of experimentally detecting these elusive, theoretically predicted states.<\/jats:p>","DOI":"10.3390\/biom14101327","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T03:57:09Z","timestamp":1729483029000},"page":"1327","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pulling Forces Differentially Affect Refolding Pathways Due to Entangled Misfolded States in SARS-CoV-1 and SARS-CoV-2 Receptor Binding Domain"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1197-0307","authenticated-orcid":false,"given":"Pham Dang","family":"Lan","sequence":"first","affiliation":[{"name":"Institute for Computational Sciences and Technology, Ho Chi Minh City 71506, Vietnam"},{"name":"Faculty of Physics and Engineering Physics, VNUHCM-University of Science, 227, Nguyen Van Cu Street, District 5, Ho Chi Minh City 72700, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edward P.","family":"O\u2019Brien","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Pennsylvania State University, University Park, PA 16802, USA"},{"name":"Bioinformatics and Genomics Graduate Program, The Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, PA 16802, USA"},{"name":"Institute for Computational and Data Sciences, Pennsylvania State University, University Park, PA 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mai Suan","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"504001","DOI":"10.1088\/1751-8121\/aa97e7","article-title":"Exploring the correlation between the folding rates of proteins and the entanglement of their native states","volume":"50","author":"Baiesi","year":"2017","journal-title":"J. Phys. A Math. Theor."},{"doi-asserted-by":"crossref","unstructured":"Salicari, L., Baiesi, M., Orlandini, E., and Trovato, A. (2023). Folding kinetics of an entangled protein. PLoS Comput. Biol., 19.","key":"ref_2","DOI":"10.1101\/2023.04.17.537117"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3081","DOI":"10.1038\/s41467-022-30548-5","article-title":"Universal protein misfolding intermediates can bypass the proteostasis network and remain soluble and less functional","volume":"13","author":"Nissley","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1038\/s41557-022-01091-z","article-title":"How synonymous mutations alter enzyme structure and function over long timescales","volume":"15","author":"Jiang","year":"2023","journal-title":"Nat. Chem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1674","DOI":"10.1126\/science.1092497","article-title":"Force-clamp spectroscopy monitors the folding trajectory of a single protein","volume":"303","author":"Fernandez","year":"2004","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1073\/pnas.0503758103","article-title":"Multiple stepwise refolding of immunoglobulin domain I27 upon force quench depends on initial conditions","volume":"103","author":"Li","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/S0140-6736(20)30251-8","article-title":"Genomic characterisation and epidemiology of 2019 novel coronavirus: Implications for virus origins and receptor binding","volume":"395","author":"Lu","year":"2020","journal-title":"Lancet"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1126\/science.abb2507","article-title":"Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation","volume":"367","author":"Wrapp","year":"2020","journal-title":"Science"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.cell.2020.02.058","article-title":"Structure, function, and antigenicity of the SARS-CoV-2 spike glycoprotein","volume":"181","author":"Walls","year":"2020","journal-title":"Cell"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1038\/s41586-020-2179-y","article-title":"Structural basis of receptor recognition by SARS-CoV-2","volume":"581","author":"Shang","year":"2020","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1038\/s41586-020-2180-5","article-title":"Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor","volume":"581","author":"Lan","year":"2020","journal-title":"Nature"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7336","DOI":"10.1021\/acs.jpcb.0c04511","article-title":"Does SARS-CoV-2 bind to human ACE2 more strongly than does SARS-CoV?","volume":"124","author":"Nguyen","year":"2020","journal-title":"J. Phys. Chem. B"},{"doi-asserted-by":"crossref","unstructured":"Prentiss, M.C., Wales, D.J., and Wolynes, P.G. (2010). The energy landscape, folding pathways and the kinetics of a knotted protein. PLoS Comput. Biol., 6.","key":"ref_13","DOI":"10.1371\/journal.pcbi.1000835"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"354101","DOI":"10.1088\/0953-8984\/27\/35\/354101","article-title":"Molecular knots in biology and chemistry","volume":"27","author":"Lim","year":"2015","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4761","DOI":"10.1021\/acs.jpcb.3c01694","article-title":"Is Posttranslational Folding More Efficient Than Refolding from a Denatured State: A Computational Study","volume":"127","author":"Vu","year":"2023","journal-title":"J. Phys. Chem. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3689","DOI":"10.1038\/s41467-023-38962-z","article-title":"How soluble misfolded proteins bypass chaperones at the molecular level","volume":"14","author":"Halder","year":"2023","journal-title":"Nat. Commun."},{"doi-asserted-by":"crossref","unstructured":"Lan, P.D., Nissley, D.A., Sitarik, I., Vu, Q.V., Jiang, Y., To, P., Xia, Y., Fried, S.D., Li, M.S., and O\u2019Brien, E.P. (2024). Synonymous mutations can alter protein dimerization through localized interface misfolding involving self-entanglements. J. Mol. Biol., 436.","key":"ref_17","DOI":"10.1016\/j.jmb.2024.168487"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"D384","DOI":"10.1093\/nar\/gkac1096","article-title":"The conserved domain database in 2023","volume":"51","author":"Wang","year":"2023","journal-title":"Nucleic Acids Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"W521","DOI":"10.1093\/nar\/gkae241","article-title":"The EMBL-EBI Job Dispatcher sequence analysis tools framework in 2024","volume":"52","author":"Madeira","year":"2024","journal-title":"Nucleic Acids Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","article-title":"Highly accurate protein structure prediction with AlphaFold","volume":"596","author":"Jumper","year":"2021","journal-title":"Nature"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"334a","DOI":"10.1016\/j.bpj.2023.11.2036","article-title":"COSMIC2: A global resource for structure prediction and structural analysis","volume":"123","author":"Cianfrocco","year":"2024","journal-title":"Biophys. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3696","DOI":"10.1021\/acs.jctc.5b00255","article-title":"ff14SB: Improving the accuracy of protein side chain and backbone parameters from ff99SB","volume":"11","author":"Maier","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1063\/1.445869","article-title":"Comparison of simple potential functions for simulating liquid water","volume":"79","author":"Jorgensen","year":"1983","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1002\/jcc.20945","article-title":"CHARMM-GUI: A web-based graphical user interface for CHARMM","volume":"29","author":"Jo","year":"2008","journal-title":"J. Comput. Chem."},{"unstructured":"Spoel, V.D. (2021). Gromacs 2020.5 Source Code, Zenodo.","key":"ref_25"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1002\/(SICI)1096-987X(199709)18:12<1463::AID-JCC4>3.0.CO;2-H","article-title":"LINCS: A linear constraint solver for molecular simulations","volume":"18","author":"Hess","year":"1997","journal-title":"J. Comput. Chem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1063\/1.447334","article-title":"A unified formulation of the constant temperature molecular dynamics methods","volume":"81","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7182","DOI":"10.1063\/1.328693","article-title":"Polymorphic transitions in single crystals: A new molecular dynamics method","volume":"52","author":"Parrinello","year":"1981","journal-title":"J. Appl. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"10920","DOI":"10.1021\/ja302305u","article-title":"Trigger factor slows co-translational folding through kinetic trapping while sterically protecting the nascent chain from aberrant cytosolic interactions","volume":"134","author":"Christodoulou","year":"2012","journal-title":"J. Am. Chem. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6103","DOI":"10.1021\/jacs.9b12264","article-title":"Electrostatic interactions govern extreme nascent protein ejection times from ribosomes and can delay ribosome recycling","volume":"142","author":"Nissley","year":"2020","journal-title":"J. Am. Chem. Soc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5523","DOI":"10.1073\/pnas.1813003116","article-title":"Domain topology, stability, and translation speed determine mechanical force generation on the ribosome","volume":"116","author":"Leininger","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"doi-asserted-by":"crossref","unstructured":"Eastman, P., Friedrichs, M., Chodera, J.D., Radmer, R., McGibbon, R.T., Zhao, Y., Beauchamp, K.A., Wang, L.-P., Simmonett, A.C., and Harrigan, M.P. (2017). OpenMM 7: Rapid development of high-performance algorithms for molecular dynamics. PLoS Comput. Biol., 13.","key":"ref_32","DOI":"10.1371\/journal.pcbi.1005659"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1063\/1.2809632","article-title":"Knots and Physics","volume":"45","author":"Kauffman","year":"1992","journal-title":"Phys. Today"},{"doi-asserted-by":"crossref","unstructured":"Vu, Q.V., Sitarik, I., Jiang, Y., Yadav, D., Sharma, P., Fried, S.D., Li, M.S., and O\u2019Brien, E.P. (2022). A Newly Identified Class of Protein Misfolding in All-atom Folding Simulations Consistent with Limited Proteolysis Mass Spectrometry. bioRxiv.","key":"ref_34","DOI":"10.1101\/2022.07.19.500586"},{"doi-asserted-by":"crossref","unstructured":"Niemyska, W., Millett, K.C., and Sulkowska, J.I. (2020). GLN: A method to reveal unique properties of lasso-type topology in proteins. Sci. Rep., 10.","key":"ref_35","DOI":"10.1038\/s41598-020-71874-2"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1002\/(SICI)1521-3773(19990115)38:1\/2<236::AID-ANIE236>3.0.CO;2-M","article-title":"Peptide folding: When simulation meets experiment","volume":"38","author":"Daura","year":"1999","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1038\/nature01891","article-title":"Rationalization of the effects of mutations on peptide and protein aggregation rates","volume":"424","author":"Chiti","year":"2003","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1146\/annurev-biochem-060208-092442","article-title":"Molecular chaperone functions in protein folding and proteostasis","volume":"82","author":"Kim","year":"2013","journal-title":"Annu. Rev. Biochem."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2739","DOI":"10.1016\/j.jmb.2014.04.018","article-title":"Active cage mechanism of chaperonin-assisted protein folding demonstrated at the single-molecule level","volume":"426","author":"Gupta","year":"2014","journal-title":"J. Mol. Biol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/S0959-440X(00)00176-7","article-title":"Mechanisms of protein folding","volume":"11","author":"Grantcharova","year":"2001","journal-title":"Curr. Opin. Struct. Biol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6539","DOI":"10.1074\/jbc.M512345200","article-title":"Trigger factor forms a protective shield for nascent polypeptides at the ribosome","volume":"281","author":"Hoffmann","year":"2006","journal-title":"J. Biol. Chem."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"E2794","DOI":"10.1073\/pnas.1601846113","article-title":"Hsp70 biases the folding pathways of client proteins","volume":"113","author":"Sekhar","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3796","DOI":"10.1073\/pnas.1115519109","article-title":"The molten globule state is unusually deformable under mechanical force","volume":"109","author":"Elms","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"17820","DOI":"10.1073\/pnas.1201800109","article-title":"Direct observation of a force-induced switch in the anisotropic mechanical unfolding pathway of a protein","volume":"109","author":"Jagannathan","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1038\/nmat1825","article-title":"Polyprotein of GB1 is an ideal artificial elastomeric protein","volume":"6","author":"Cao","year":"2007","journal-title":"Nat. Mater."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3694","DOI":"10.1073\/pnas.96.7.3694","article-title":"Mechanical and chemical unfolding of a single protein: A comparison","volume":"96","author":"Oberhauser","year":"1999","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3540","DOI":"10.1021\/ja5119368","article-title":"Dynamics of equilibrium folding and unfolding transitions of titin immunoglobulin domain under constant forces","volume":"137","author":"Chen","year":"2015","journal-title":"J. Am. Chem. Soc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"198101","DOI":"10.1103\/PhysRevLett.125.198101","article-title":"Hidden intermediate state and second pathway determining folding and unfolding dynamics of GB1 protein at low forces","volume":"125","author":"Guo","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6117","DOI":"10.1002\/anie.201610648","article-title":"Single-Molecule Force Spectroscopy Trajectories of a Single Protein and Its Polyproteins Are Equivalent: A Direct Experimental Validation Based on A Small Protein NuG2","volume":"56","author":"Lei","year":"2017","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"078201","DOI":"10.1088\/1674-1056\/abfb56","article-title":"Equilibrium folding and unfolding dynamics to reveal detailed free energy landscape of src SH3 protein by magnetic tweezers","volume":"30","author":"Su","year":"2021","journal-title":"Chin. Phys. B"},{"doi-asserted-by":"crossref","unstructured":"Rivera, M., Hao, Y., Maillard, R.A., and Baez, M. (2020). Mechanical unfolding of a knotted protein unveils the kinetic and thermodynamic consequences of threading a polypeptide chain. Sci. Rep., 10.","key":"ref_51","DOI":"10.1038\/s41598-020-66258-5"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1096\/fasebj.10.1.8566547","article-title":"In vitro folding of inclusion body proteins","volume":"10","author":"Rudolph","year":"1996","journal-title":"FASEB J."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"6447","DOI":"10.1038\/s41467-021-26531-1","article-title":"Nascent chains can form co-translational folding intermediates that promote post-translational folding outcomes in a disease-causing protein","volume":"12","author":"Plessa","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/10409230490892496","article-title":"Chaperone-assisted folding of newly synthesized proteins in the cytosol","volume":"39","author":"Deuerling","year":"2004","journal-title":"Crit. Rev. Biochem. Mol. Biol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1038\/nsmb.2466","article-title":"Evolutionary conservation of codon optimality reveals hidden signatures of cotranslational folding","volume":"20","author":"Pechmann","year":"2013","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1888","DOI":"10.1126\/science.286.5446.1888","article-title":"Posttranslational quality control: Folding, refolding, and degrading proteins","volume":"286","author":"Wickner","year":"1999","journal-title":"Science"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1110\/ps.9.6.1254","article-title":"Assisted folding of D-glyceraldehyde-3-phosphate dehydrogenase by trigger factor","volume":"9","author":"Huang","year":"2000","journal-title":"Protein Sci."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1006\/jmbi.2000.5192","article-title":"Dynamic association of trigger factor with protein substrates","volume":"314","author":"Maier","year":"2001","journal-title":"J. Mol. Biol."},{"doi-asserted-by":"crossref","unstructured":"Baiesi, M., Orlandini, E., Seno, F., and Trovato, A. (2019). Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding. Sci. Rep., 9.","key":"ref_59","DOI":"10.1038\/s41598-019-44928-3"}],"container-title":["Biomolecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-273X\/14\/10\/1327\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:16:27Z","timestamp":1760112987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-273X\/14\/10\/1327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,18]]},"references-count":59,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["biom14101327"],"URL":"https:\/\/doi.org\/10.3390\/biom14101327","relation":{},"ISSN":["2218-273X"],"issn-type":[{"type":"electronic","value":"2218-273X"}],"subject":[],"published":{"date-parts":[[2024,10,18]]}}}