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This minimal framework incorporates the essential parameters governing such transitions: two characteristic lengths, two elastic force constants, a free-energy difference between states, and a nearest-neighbor interaction energy that accounts for cooperativity. Chain stiffness is introduced through a bending potential. In the long-chain limit, exact equations are derived for both the molecular extension and the state populations as functions of the applied force. In the absence of bending rigidity, the model reduces to the two-state Elastic Freely Jointed Chain (EFJC). Within this approximation, it accurately reproduces the experimental force\u2013extension behavior of poly(ethylene glycol) (PEG) and hyaluronic acid (HA), revealing the absence of cooperativity in PEG and the presence of negative cooperativity in HA. The model also captures the positive cooperativity of the B-DNA-to-S-DNA conformational transition when chain semiflexibility is taken into account. Within the EFJC framework, we further examine the mathematical conditions necessary for the occurrence of a transition and identify two fundamental driving mechanisms: differences in Kuhn lengths and differences in elastic force constants. Possible extensions to systems with more than two conformational states are also considered. The results apply equally to transitions intrinsic to the macromolecular architecture and to those induced by ligand\u2013receptor interactions, providing a unified and thermodynamically consistent framework for describing both phenomena.<\/jats:p>","DOI":"10.1063\/5.0352573","type":"journal-article","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T10:46:27Z","timestamp":1791542787000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Cooperative conformational transitions in macromolecules under mechanical stretching: Exact solution and validation of a two-state model against single-molecule experiments"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4673-534X","authenticated-orcid":false,"given":"Javier","family":"Orradre","sequence":"first","affiliation":[{"name":"Department of Materials Science and Physical Chemistry and Institute of Theoretical and Computational Chemistry (IQTC), University of Barcelona 1 , Barcelona, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7603-8617","authenticated-orcid":false,"given":"Pablo M.","family":"Blanco","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Physics and Environmental and Soil Sciences and Agrotecnio, University of Lleida 2 , Lleida, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8135-7057","authenticated-orcid":false,"given":"Sergio","family":"Madurga","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Physical Chemistry and Institute of Theoretical and Computational Chemistry (IQTC), University of Barcelona 1 , Barcelona, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0815-742X","authenticated-orcid":false,"given":"Marina I.","family":"Giannotti","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Physical Chemistry and Institute of Theoretical and Computational Chemistry (IQTC), University of Barcelona 1 , Barcelona, Catalonia,","place":["Spain"]},{"name":"Nanoprobes and Nanoswitches Group, Institute for Bioengineering of Catalunya (IBEC), The Barcelona Institute of Science and Technology (BIST) 3 , Barcelona, Catalonia,","place":["Spain"]},{"name":"CIBER-BBN, ISCIII 4 , Barcelona, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1362-4002","authenticated-orcid":false,"given":"Francesc","family":"Mas","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Physical Chemistry and Institute of Theoretical and Computational Chemistry (IQTC), University of Barcelona 1 , Barcelona, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0650-8473","authenticated-orcid":false,"given":"Josep Llu\u00eds","family":"Garc\u00e9s","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Physics and Environmental and Soil Sciences and Agrotecnio, University of Lleida 2 , Lleida, Catalonia,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"key":"2026100906462298400_c1","doi-asserted-by":"publisher","first-page":"1835","DOI":"10.1126\/science.271.5257.1835","article-title":"The elasticity of a single supercoiled DNA molecule","volume":"271","year":"1996","journal-title":"Science"},{"key":"2026100906462298400_c2","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1016\/s0006-3495(97)78780-0","article-title":"Stretching DNA with optical tweezers","volume":"72","year":"1997","journal-title":"Biophys. 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