{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T16:40:30Z","timestamp":1786466430704,"version":"build-2736575974"},"reference-count":96,"publisher":"American Chemical Society (ACS)","issue":"15","license":[{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100001403","name":"Indian Institute of Technology Kanpur","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001403","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["SRG\/2022\/000548"],"award-info":[{"award-number":["SRG\/2022\/000548"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Membrane curvature plays a central role in a wide range of biological processes, yet a quantitative and transferable description of its underlying energetics remains challenging. In this work, we develop a \u201creaction coordinate\u201d within the Umbrella-Sampling framework to compute the free-energy cost associated with local membrane bending in both coarse-grained and atomistic simulations. The methodology is systematically validated across diverse lipid environments, including pure bilayers with varying tail unsaturation, tail length, and headgroup chemistry, where it reproduces established trends in membrane-mechanical rigidity. Extension to mixed lipid systems further captures composition-dependent modulation of bending energetics, including cholesterol-induced responses. Finally, we apply the framework to membrane-active proteins with distinct curvature-generation mechanisms and demonstrate that the method successfully captures the protein modulation of the free-energy cost of local membrane deformation. Furthermore, the method is transferable to atomistic membrane systems while maintaining reasonable computational efficiency, providing a unified approach for quantifying membrane bending energetics across lipids, proteins, and simulation scales.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c00977","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T13:15:39Z","timestamp":1785849339000},"page":"8013-8025","source":"Crossref","is-referenced-by-count":0,"title":["Quantifying the\nEnergetics of Protein-Mediated Stabilization\nof Membrane Deformation"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8207-4060","authenticated-orcid":true,"given":"Rupam","family":"Dey","sequence":"first","affiliation":[{"name":"Indian Institute of Technology Kanpur , , ,","place":["Kanpur, India, 208016"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-1166-6929","authenticated-orcid":true,"given":"Jatin","family":"Soni","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Kanpur , , ,","place":["Kanpur, India, 208016"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9902-2415","authenticated-orcid":true,"given":"Taraknath","family":"Mandal","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Kanpur , , ,","place":["Kanpur, India, 208016"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"key":"2026081111100993100_cit1","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1146\/annurev.cellbio.042308.113324","article-title":"Mechanisms shaping the membranes\nof cellular organelles","volume":"25","author":"Shibata","year":"2009","journal-title":"Annu. Rev. Cell Dev.\nBiol."},{"issue":"7068","key":"2026081111100993100_cit2","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1038\/nature04396","article-title":"Membrane curvature and mechanisms of dynamic cell membrane\nremodelling","volume":"438","author":"McMahon","year":"2005","journal-title":"Nature"},{"issue":"1","key":"2026081111100993100_cit3","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1038\/nrm1784","article-title":"How proteins produce\ncellular membrane curvature","volume":"7","author":"Zimmerberg","year":"2006","journal-title":"Nat. Rev. Mol.\nCell Biol."},{"issue":"3","key":"2026081111100993100_cit4","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1034\/j.1600-0854.2000.010302.x","article-title":"Role of membrane organization and membrane domains\nin endocytic lipid trafficking","volume":"1","author":"Mukherjee","year":"2000","journal-title":"Traffic"},{"issue":"10","key":"2026081111100993100_cit5","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1038\/35096054","article-title":"The endocytic\npathway: a mosaic of domains","volume":"2","author":"Gruenberg","year":"2001","journal-title":"Nat. Rev. Mol.\nCell Biol."},{"issue":"12","key":"2026081111100993100_cit6","doi-asserted-by":"publisher","first-page":"872","DOI":"10.1038\/nrm3013","article-title":"Mitochondrial\nfusion and fission in cell life and death","volume":"11","author":"Westermann","year":"2010","journal-title":"Nat.\nRev. Mol. Cell Biol."},{"issue":"6","key":"2026081111100993100_cit7","doi-asserted-by":"publisher","DOI":"10.1101\/cshperspect.a011072","article-title":"Mechanisms of mitochondrial\nfission and fusion","volume":"5","author":"Van der Bliek","year":"2013","journal-title":"Cold Spring Harbor Perspect.\nBiol."},{"issue":"7","key":"2026081111100993100_cit8","doi-asserted-by":"publisher","first-page":"2658","DOI":"10.1016\/j.bpj.2008.11.073","article-title":"The fusion of membranes\nand vesicles:\npathway and energy barriers from dissipative particle dynamics","volume":"96","author":"Grafmu\u0308ller","year":"2009","journal-title":"Biophys. J."},{"issue":"7419","key":"2026081111100993100_cit9","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1038\/nature11320","article-title":"Molecular\nmachines governing exocytosis of synaptic\nvesicles","volume":"490","author":"Jahn","year":"2012","journal-title":"Nature"},{"issue":"10","key":"2026081111100993100_cit10","doi-asserted-by":"publisher","first-page":"2136","DOI":"10.1016\/j.bpj.2010.01.059","article-title":"Mechanisms\ncontrolling\ncell size and shape during isotropic cell spreading","volume":"98","author":"Xiong","year":"2010","journal-title":"Biophys. J."},{"issue":"4","key":"2026081111100993100_cit11","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1016\/j.bpj.2010.12.3732","article-title":"Signaling\nnetwork triggers and membrane\nphysical properties control the actin cytoskeleton-driven isotropic\nphase of cell spreading","volume":"100","author":"Rangamani","year":"2011","journal-title":"Biophys. J."},{"key":"2026081111100993100_cit12","volume-title":"Signal Transduction","author":"Gomperts","year":"2009"},{"issue":"6","key":"2026081111100993100_cit13","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1016\/S0955-0674(99)00045-9","article-title":"Cell adhesion\nmolecules, signal transduction\nand cell growth","volume":"11","author":"Aplin","year":"1999","journal-title":"Curr. Opin. Cell Biol."},{"issue":"4","key":"2026081111100993100_cit14","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1002595","article-title":"Defective membrane\nremodeling in neuromuscular diseases: insights from animal models","volume":"8","author":"Cowling","year":"2012","journal-title":"PLoS Genet."},{"issue":"10","key":"2026081111100993100_cit15","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1056\/NEJMra0910494","article-title":"Mendelian disorders of membrane trafficking","volume":"365","author":"De Matteis","year":"2011","journal-title":"N. Engl. J. Med."},{"issue":"6","key":"2026081111100993100_cit16","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1038\/nrm1940","article-title":"Harnessing\nactin dynamics for clathrin-mediated\nendocytosis","volume":"7","author":"Kaksonen","year":"2006","journal-title":"Nat. Rev. Mol. Cell Biol."},{"key":"2026081111100993100_cit17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ceb.2017.11.007","article-title":"Membrane\nbending by actin polymerization","volume":"50","author":"Carlsson","year":"2018","journal-title":"Curr. Opin.\nCell Biol."},{"issue":"11","key":"2026081111100993100_cit18","doi-asserted-by":"publisher","first-page":"6493","DOI":"10.1073\/pnas.1031670100","article-title":"Compression forces generated by actin\ncomet tails on lipid vesicles","volume":"100","author":"Giardini","year":"2003","journal-title":"Proc. Natl. Acad.\nSci. U.S.A."},{"issue":"7","key":"2026081111100993100_cit19","doi-asserted-by":"publisher","first-page":"1619","DOI":"10.1016\/j.bbamem.2016.02.003","article-title":"Continuum descriptions\nof membranes and their interaction with proteins: Towards chemically\naccurate models","volume":"1858","author":"Argudo","year":"2016","journal-title":"Biochim. Biophys. Acta, Biomembr."},{"issue":"22","key":"2026081111100993100_cit20","doi-asserted-by":"publisher","first-page":"4021","DOI":"10.1039\/D3SM00218G","article-title":"Differential\nmembrane curvature induced\nby distinct protein conformers","volume":"19","author":"Malshikare","year":"2023","journal-title":"Soft Matter"},{"issue":"1","key":"2026081111100993100_cit21","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.bpj.2018.11.3127","article-title":"Interplay between membrane\ncurvature and cholesterol:\nRole of palmitoylated caveolin-1","volume":"116","author":"Krishna","year":"2019","journal-title":"Biophys. J."},{"key":"2026081111100993100_cit22","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1039\/D0FD00062K","article-title":"Caveolin induced membrane curvature\nand lipid clustering: two sides of the same coin?","volume":"232","author":"Prakash","year":"2021","journal-title":"Faraday Discuss."},{"issue":"3","key":"2026081111100993100_cit23","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2017.11.3283","article-title":"The role of traction in membrane curvature generation","volume":"114","author":"Alimohamadi","year":"2018","journal-title":"Biophys. J."},{"issue":"2","key":"2026081111100993100_cit24","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BF00275981","article-title":"Static\nequilibrium configurations of a model red blood cell","volume":"4","author":"Jenkins","year":"1977","journal-title":"J. Math. Biol."},{"issue":"28","key":"2026081111100993100_cit25","doi-asserted-by":"publisher","first-page":"L313","DOI":"10.1088\/0305-4470\/37\/28\/L02","article-title":"Membrane geometry\nwith auxiliary variables and quadratic constraints","volume":"37","author":"Guven","year":"2004","journal-title":"J. Phys. A: Math. Gen."},{"issue":"33","key":"2026081111100993100_cit26","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adv1499","article-title":"Membrane\ncurvature association of amphipathic\nhelix 8 drives constitutive endocytosis of gpcrs","volume":"11","author":"Schmidt","year":"2025","journal-title":"Sci. Adv."},{"issue":"15","key":"2026081111100993100_cit27","doi-asserted-by":"publisher","DOI":"10.3390\/ijms23158098","article-title":"Molecular\ndynamics simulations of curved lipid membranes","volume":"23","author":"Larsen","year":"2022","journal-title":"Int. J. Mol. Sci."},{"issue":"5","key":"2026081111100993100_cit28","doi-asserted-by":"publisher","first-page":"2325","DOI":"10.1529\/biophysj.108.133173","article-title":"The hydrophobic insertion mechanism\nof membrane curvature generation by proteins","volume":"95","author":"Campelo","year":"2008","journal-title":"Biophys. J."},{"issue":"6905","key":"2026081111100993100_cit29","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1038\/nature01020","article-title":"Curvature of clathrin-coated\npits\ndriven by epsin","volume":"419","author":"Ford","year":"2002","journal-title":"Nature"},{"issue":"21","key":"2026081111100993100_cit30","doi-asserted-by":"publisher","DOI":"10.1063\/5.0049448","article-title":"Identifying systematic\nerrors in a power spectral analysis\nof simulated lipid membranes","volume":"154","author":"Ergu\u0308der","year":"2021","journal-title":"J. Chem. Phys."},{"issue":"4","key":"2026081111100993100_cit31","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s101890070003","article-title":"Elastic energy of\ntilt and bending of fluid membranes","volume":"3","author":"Hamm","year":"2000","journal-title":"Eur. Phys.\nJ. E"},{"issue":"9","key":"2026081111100993100_cit32","doi-asserted-by":"publisher","first-page":"944","DOI":"10.1038\/ncb2561","article-title":"Membrane\nbending by protein\u2013protein crowding","volume":"14","author":"Stachowiak","year":"2012","journal-title":"Nat. Cell Biol."},{"issue":"4","key":"2026081111100993100_cit33","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/S0955-0674(03)00073-5","article-title":"Mechanisms of membrane deformation","volume":"15","author":"Farsad","year":"2003","journal-title":"Curr. Opin. Cell Biol."},{"key":"2026081111100993100_cit34","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1146\/annurev-cellbio-100617-060558","article-title":"Curving cells\ninside and out: Roles of bar domain proteins in membrane shaping and\nits cellular implications","volume":"35","author":"Simunovic","year":"2019","journal-title":"Annu. Rev. Cell Dev.\nBiol."},{"issue":"1\u201315","key":"2026081111100993100_cit35","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002892","article-title":"Membrane sculpting\nby f-bar domains studied by molecular\ndynamics simulations","volume":"9","author":"Yu","year":"2013","journal-title":"PLoS Comput. Biol."},{"key":"2026081111100993100_cit36","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1146\/annurev-biochem-062917-012644","article-title":"Regulation\nof clathrin-mediated endocytosis","volume":"87","author":"Mettlen","year":"2018","journal-title":"Annu. Rev.\nBiochem."},{"issue":"1","key":"2026081111100993100_cit37","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms6974","article-title":"Membrane tension and\nperipheral protein density mediate\nmembrane shape transitions","volume":"6","author":"Shi","year":"2015","journal-title":"Nat. Commun."},{"key":"2026081111100993100_cit38","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.sbi.2018.03.018","article-title":"Organizing membrane-curving proteins:\nthe emerging dynamical picture","volume":"51","author":"Simunovic","year":"2018","journal-title":"Curr. Opin.\nStruct. Biol."},{"key":"2026081111100993100_cit39","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.sbi.2016.06.007","article-title":"Molecular dynamics simulations of\nmembrane proteins and their interactions: from nanoscale to mesoscale","volume":"40","author":"Chavent","year":"2016","journal-title":"Curr. Opin. Struct. Biol."},{"issue":"7","key":"2026081111100993100_cit40","doi-asserted-by":"publisher","first-page":"1635","DOI":"10.1016\/j.bbamem.2015.12.032","article-title":"Molecular\ndynamics simulations of biological membranes and membrane proteins\nusing enhanced conformational sampling algorithms","volume":"1858","author":"Mori","year":"2016","journal-title":"Biochim. Biophys. Acta, Biomembr."},{"key":"2026081111100993100_cit41","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.sbi.2016.11.007","article-title":"Survey\nof adaptive biasing potentials: comparisons and outlook","volume":"43","author":"Dickson","year":"2017","journal-title":"Curr. Opin. Struct. Biol."},{"issue":"3","key":"2026081111100993100_cit42","doi-asserted-by":"publisher","DOI":"10.1063\/1.4811677","article-title":"A guiding\npotential\nmethod for evaluating the bending rigidity of tensionless lipid membranes\nfrom molecular simulation","volume":"139","author":"Kawamoto","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2026081111100993100_cit43","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.chemphyslip.2015.07.014","article-title":"Mechanical properties of lipid bilayers\nfrom molecular dynamics simulation","volume":"192","author":"Venable","year":"2015","journal-title":"Chem. Phys.\nLipids"},{"issue":"2","key":"2026081111100993100_cit44","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1021\/acs.jctc.0c00800","article-title":"Encurv: Simple technique of maintaining global membrane\ncurvature in molecular dynamics simulations","volume":"17","author":"Yesylevskyy","year":"2021","journal-title":"J. Chem. Theory Comput."},{"issue":"2","key":"2026081111100993100_cit45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.028102","article-title":"Determining biomembrane\nbending rigidities from simulations of modest size","volume":"109","author":"Watson","year":"2012","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"2026081111100993100_cit46","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.1016\/j.bpj.2012.02.013","article-title":"Determining the gaussian curvature\nmodulus of lipid membranes in simulations","volume":"102","author":"Hu","year":"2012","journal-title":"Biophys.\nJ."},{"issue":"39","key":"2026081111100993100_cit47","doi-asserted-by":"publisher","first-page":"13582","DOI":"10.1021\/ja507910r","article-title":"Determination\nof biomembrane bending\nmoduli in fully atomistic simulations","volume":"136","author":"Levine","year":"2014","journal-title":"J. Am.\nChem. Soc."},{"issue":"24","key":"2026081111100993100_cit48","doi-asserted-by":"publisher","DOI":"10.1063\/1.4938383","article-title":"Calculation of membrane bending rigidity using field-theoretic\numbrella sampling","volume":"143","author":"Smirnova","year":"2015","journal-title":"J. Chem. Phys."},{"issue":"10","key":"2026081111100993100_cit49","doi-asserted-by":"publisher","first-page":"2202","DOI":"10.1016\/j.bpj.2013.03.048","article-title":"Bending free energy from simulation: correspondence\nof planar and inverse hexagonal lipid phases","volume":"104","author":"Sodt","year":"2013","journal-title":"Biophys. J."},{"issue":"18","key":"2026081111100993100_cit50","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.188102","article-title":"Exploiting\nlipid permutation symmetry\nto compute membrane remodeling free energies","volume":"117","author":"Bubnis","year":"2016","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"2026081111100993100_cit51","doi-asserted-by":"publisher","first-page":"2240","DOI":"10.1021\/acs.jctc.8b00012","article-title":"Bending\nlipid bilayers: a closed-form\ncollective variable for effective free-energy landscapes in quantitative\nbiology","volume":"14","author":"Masone","year":"2018","journal-title":"J. Chem. Theory Comput."},{"issue":"12","key":"2026081111100993100_cit52","doi-asserted-by":"publisher","first-page":"6551","DOI":"10.1021\/acs.jctc.9b00716","article-title":"Curvature\nas a collective coordinate in enhanced sampling membrane simulations","volume":"15","author":"Bouvier","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"2026081111100993100_cit53","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1021\/acs.jctc.5c01709","article-title":"Exploring the energetics\nof membrane fission using\nmolecular simulations","volume":"22","author":"Dey","year":"2026","journal-title":"J. Chem. Theory Comput."},{"key":"2026081111100993100_cit54","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.softx.2015.06.001","article-title":"Gromacs: High performance\nmolecular simulations through multi-level parallelism from laptops\nto supercomputers","volume":"1\u20132","author":"Abraham","year":"2015","journal-title":"SoftwareX"},{"issue":"27","key":"2026081111100993100_cit55","doi-asserted-by":"publisher","first-page":"7812","DOI":"10.1021\/jp071097f","article-title":"The martini\nforce field: coarse grained model for biomolecular simulations","volume":"111","author":"Marrink","year":"2007","journal-title":"J. Phys. Chem. B"},{"issue":"16","key":"2026081111100993100_cit56","doi-asserted-by":"publisher","first-page":"6801","DOI":"10.1039\/c3cs60093a","article-title":"Perspective on the\nmartini model","volume":"42","author":"Marrink","year":"2013","journal-title":"Chem. Soc. Rev."},{"issue":"9","key":"2026081111100993100_cit57","doi-asserted-by":"publisher","first-page":"5775","DOI":"10.1021\/acs.chemrev.8b00451","article-title":"Emerging\ndiversity\nin lipid-protein interactions","volume":"119","author":"Corradi","year":"2019","journal-title":"Chem. Rev."},{"issue":"5","key":"2026081111100993100_cit58","doi-asserted-by":"publisher","first-page":"2144","DOI":"10.1021\/acs.jctc.5b00209","article-title":"Computational\nlipidomics with insane: a versatile tool for generating custom membranes\nfor molecular simulations","volume":"11","author":"Wassenaar","year":"2015","journal-title":"J. Chem. Theory Comput."},{"issue":"1","key":"2026081111100993100_cit59","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1021\/acs.jcim.0c01291","article-title":"Concerted\ninteractions between multiple gp41 trimers and the target cell lipidome\nmay be required for hiv-1 entry","volume":"61","author":"Gorai","year":"2021","journal-title":"J. Chem. Inf.\nModel."},{"issue":"1","key":"2026081111100993100_cit60","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1021\/ct300646g","article-title":"Improved parameters for the martini coarse-grained\nprotein force field","volume":"9","author":"de Jong","year":"2013","journal-title":"J. Chem. Theory Comput."},{"issue":"4","key":"2026081111100993100_cit61","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1038\/s41592-021-01098-3","article-title":"Martini 3: a general purpose force field\nfor coarse-grained molecular\ndynamics","volume":"18","author":"Souza","year":"2021","journal-title":"Nat. Methods"},{"issue":"21","key":"2026081111100993100_cit62","doi-asserted-by":"publisher","first-page":"9673","DOI":"10.1021\/acs.jctc.4c00645","article-title":"Recalibration\nof martini-3 parameters\nfor improved interactions between peripheral proteins and lipid bilayers","volume":"20","author":"Soni","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"2026081111100993100_cit63","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.90627.4","article-title":"Martinize2 and vermouth provide a\nunified framework\nfor molecular topology generation","volume":"12","author":"Kroon","year":"2025","journal-title":"eLife"},{"issue":"9","key":"2026081111100993100_cit64","doi-asserted-by":"publisher","first-page":"2531","DOI":"10.1021\/ct9002114","article-title":"Combining\nan elastic\nnetwork with a coarse-grained molecular force field: structure, dynamics,\nand intermolecular recognition","volume":"5","author":"Periole","year":"2009","journal-title":"J. Chem. Theory\nComput."},{"issue":"1","key":"2026081111100993100_cit65","doi-asserted-by":"publisher","DOI":"10.1063\/1.2408420","article-title":"Canonical sampling through velocity\nrescaling","volume":"126","author":"Bussi","year":"2007","journal-title":"J. Chem. Phys."},{"issue":"8","key":"2026081111100993100_cit66","doi-asserted-by":"publisher","first-page":"3684","DOI":"10.1063\/1.448118","article-title":"Molecular dynamics with coupling\nto an external bath","volume":"81","author":"Berendsen","year":"1984","journal-title":"J. Chem. Phys."},{"issue":"12","key":"2026081111100993100_cit67","doi-asserted-by":"publisher","first-page":"7182","DOI":"10.1063\/1.328693","article-title":"Polymorphic transitions\nin single crystals: A new molecular\ndynamics method","volume":"52","author":"Parrinello","year":"1981","journal-title":"J. Appl. Phys."},{"issue":"1","key":"2026081111100993100_cit68","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0263-7855(96)00018-5","article-title":"Vmd: visual\nmolecular dynamics","volume":"14","author":"Humphrey","year":"1996","journal-title":"J. Mol. Graphics"},{"issue":"3","key":"2026081111100993100_cit69","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2015.11.3431","article-title":"Charmm-gui input generator\nfor namd,\ngromacs, amber, openmm, and charmm\/openmm simulations using the charmm36\nadditive force field","volume":"110","author":"Lee","year":"2016","journal-title":"Biophys. J."},{"issue":"9","key":"2026081111100993100_cit70","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0000880","article-title":"Automated\nbuilder and database of protein\/membrane\ncomplexes for molecular dynamics simulations","volume":"2","author":"Jo","year":"2007","journal-title":"PLoS One"},{"issue":"11","key":"2026081111100993100_cit71","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1002\/jcc.20945","article-title":"Charmm-gui: a web-based\ngraphical\nuser interface for charmm","volume":"29","author":"Jo","year":"2008","journal-title":"J. Comput. Chem."},{"issue":"1","key":"2026081111100993100_cit72","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.bpj.2014.05.034","article-title":"Charmm all-atom\nadditive force field for sphingomyelin: elucidation of hydrogen bonding\nand of positive curvature","volume":"107","author":"Venable","year":"2014","journal-title":"Biophys. J."},{"issue":"23","key":"2026081111100993100_cit73","doi-asserted-by":"publisher","first-page":"7830","DOI":"10.1021\/jp101759q","article-title":"Update of the charmm all-atom additive\nforce field for lipids: validation on six lipid types","volume":"114","author":"Klauda","year":"2010","journal-title":"J. Phys. Chem. B"},{"issue":"2","key":"2026081111100993100_cit74","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1063\/1.445869","article-title":"Comparison\nof simple potential functions for simulating liquid water","volume":"79","author":"Jorgensen","year":"1983","journal-title":"J. Chem. Phys."},{"issue":"1","key":"2026081111100993100_cit75","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1063\/1.447334","article-title":"A unified\nformulation of the constant temperature molecular dynamics methods","volume":"81","author":"Nose\u0301","year":"1984","journal-title":"J. Chem. Phys."},{"issue":"3","key":"2026081111100993100_cit76","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.31.1695","article-title":"Canonical\ndynamics: Equilibrium phase-space distributions","volume":"31","author":"Hoover","year":"1985","journal-title":"Phys. Rev. A"},{"issue":"12","key":"2026081111100993100_cit77","doi-asserted-by":"publisher","first-page":"1463","DOI":"10.1002\/(SICI)1096-987X(199709)18:12&lt;1463::AID-JCC4&gt;3.0.CO;2-H","article-title":"Lincs: A linear\nconstraint solver for molecular simulations","volume":"18","author":"Hess","year":"1997","journal-title":"J. Comput. Chem."},{"issue":"2","key":"2026081111100993100_cit78","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1016\/j.cpc.2013.09.018","article-title":"Plumed 2: New feathers for an old\nbird","volume":"185","author":"Tribello","year":"2014","journal-title":"Comput.\nPhys. Commun."},{"issue":"2","key":"2026081111100993100_cit79","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0021-9991(77)90121-8","article-title":"Nonphysical sampling distributions\nin monte carlo free-energy\nestimation: Umbrella sampling","volume":"23","author":"Torrie","year":"1977","journal-title":"J. Comput. Phys."},{"issue":"1\u20133","key":"2026081111100993100_cit80","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0010-4655(95)00053-I","article-title":"The calculation\nof the potential of mean force using computer simulations","volume":"91","author":"Roux","year":"1995","journal-title":"Comput. Phys. Commun."},{"key":"2026081111100993100_cit81","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.chemphyslip.2017.04.006","article-title":"Experimentally\ndetermined tilt and bending moduli of single-component lipid bilayers","volume":"205","author":"Nagle","year":"2017","journal-title":"Chem. Phys. Lipids"},{"issue":"1","key":"2026081111100993100_cit82","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1140\/epje\/i2007-10315-0","article-title":"Bending modulus\nof lipid bilayers in a liquid-crystalline phase including an anomalous\nswelling regime estimated by neutron spin echo experiments","volume":"26","author":"Seto","year":"2008","journal-title":"Eur. Phys. J. E"},{"issue":"8","key":"2026081111100993100_cit83","doi-asserted-by":"publisher","first-page":"732","DOI":"10.1007\/s00249-004-0420-5","article-title":"Vesicle fluctuation\nanalysis of the\neffects of sterols on membrane bending rigidity","volume":"33","author":"Henriksen","year":"2004","journal-title":"Eur. Biophys. J."},{"issue":"7","key":"2026081111100993100_cit84","doi-asserted-by":"publisher","DOI":"10.1140\/epje\/i2013-13075-2","article-title":"Bending stiffness of\nbiological membranes: What can be measured by neutron spin echo?","volume":"36","author":"Mell","year":"2013","journal-title":"Eur. Phys. J. E"},{"issue":"9","key":"2026081111100993100_cit85","doi-asserted-by":"publisher","first-page":"3629","DOI":"10.1016\/j.bpj.2009.01.045","article-title":"Stiffening effect of\ncholesterol on disordered lipid\nphases: a combined neutron spin echo+ dynamic light scattering analysis\nof the bending elasticity of large unilamellar vesicles","volume":"96","author":"Arriaga","year":"2009","journal-title":"Biophys. J."},{"issue":"1","key":"2026081111100993100_cit86","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0263119","article-title":"Effects of\ncholesterol on the size\ndistribution and bending modulus of lipid vesicles","volume":"17","author":"Karal","year":"2022","journal-title":"PLoS One"},{"issue":"31","key":"2026081111100993100_cit87","doi-asserted-by":"publisher","first-page":"28993","DOI":"10.1074\/jbc.M302865200","article-title":"Contrasting\nmembrane interaction\nmechanisms of ap180 n-terminal homology (anth) and epsin n-terminal\nhomology (enth) domains","volume":"278","author":"Stahelin","year":"2003","journal-title":"J. Biol. Chem."},{"issue":"2","key":"2026081111100993100_cit88","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1083\/jcb.200107075","article-title":"Generation of high curvature membranes mediated by\ndirect endophilin bilayer interactions","volume":"155","author":"Farsad","year":"2001","journal-title":"J. Cell\nBiol."},{"issue":"37","key":"2026081111100993100_cit89","doi-asserted-by":"publisher","first-page":"13710","DOI":"10.1021\/ja400146z","article-title":"Influenza\nvirus a m2 protein generates negative gaussian membrane curvature\nnecessary for budding and scission","volume":"135","author":"Schmidt","year":"2013","journal-title":"J. Am. Chem.\nSoc."},{"issue":"2","key":"2026081111100993100_cit90","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1021\/acs.jctc.4c01026","article-title":"The role of cholesterol in m2 clustering and viral\nbudding explained","volume":"21","author":"Kolokouris","year":"2025","journal-title":"J. Chem. Theory Comput."},{"issue":"6","key":"2026081111100993100_cit91","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1038\/nsmb762","article-title":"The stalk region\nof dynamin drives the constriction of dynamin tubes","volume":"11","author":"Chen","year":"2004","journal-title":"Nat. Struct. Mol. Biol."},{"issue":"1","key":"2026081111100993100_cit92","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1146\/annurev.biochem.72.121801.161504","article-title":"Protein-lipid interplay\nin fusion and fission of biological\nmembranes","volume":"72","author":"Chernomordik","year":"2003","journal-title":"Annu. Rev. Biochem."},{"issue":"2","key":"2026081111100993100_cit93","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1038\/nrm1313","article-title":"The dynamin superfamily:\nuniversal membrane tubulation\nand fission molecules?","volume":"5","author":"Praefcke","year":"2004","journal-title":"Nat. Rev. Mol. Cell\nBiol."},{"issue":"6518","key":"2026081111100993100_cit94","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1038\/374186a0","article-title":"Tubular membrane\ninvaginations coated by dynamin rings are induced by gtp-\u03b3s\nin nerve terminals","volume":"374","author":"Takei","year":"1995","journal-title":"Nature"},{"issue":"1","key":"2026081111100993100_cit95","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-022-26633-w","article-title":"Interplay of membrane crosslinking\nand curvature induction by annexins","volume":"12","author":"Mularski","year":"2022","journal-title":"Sci. Rep."},{"issue":"36","key":"2026081111100993100_cit96","doi-asserted-by":"publisher","first-page":"8701","DOI":"10.1021\/acs.jpcb.4c02318","article-title":"Modulation of annexin-induced membrane curvature by\ncholesterol and the anionic lipid headgroup during plasma membrane\nrepair","volume":"128","author":"Hakami Zanjani","year":"2024","journal-title":"J. Phys. Chem. B"}],"container-title":["Journal of Chemical Theory\nand Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jctc.6c00977","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/15\/8013\/66323993\/acs.jctc.6c00977.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/15\/8013\/66323993\/acs.jctc.6c00977.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T15:43:45Z","timestamp":1786463025000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jctcce\/article\/22\/15\/8013\/5236347\/Quantifying-the-Energetics-of-Protein-Mediated"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,29]]},"references-count":96,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,7,29]]},"published-print":{"date-parts":[[2026,8,11]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jctc.6c00977","relation":{},"ISSN":["1549-9618","1549-9626"],"issn-type":[{"value":"1549-9618","type":"print"},{"value":"1549-9626","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,29]]}}}