{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T14:03:17Z","timestamp":1791468197812,"version":"4.3.4"},"reference-count":69,"publisher":"American Chemical Society (ACS)","issue":"40","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["R01-GM158907"],"award-info":[{"award-number":["R01-GM158907"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["R35-GM144089"],"award-info":[{"award-number":["R35-GM144089"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Systems in which the free energy density is nonuniform in space are familiar; the surface tension of a water droplet and the surface energy of a solid are good examples. Some such cases can be treated with prior theory, notably inhomogeneous solvation theory (IST), but IST is applicable only to liquids. Despite this limitation, IST has proven useful as a guide to the design of ligands to bind a targeted protein, based on the idea that ligands that displace high free energy water will tend to bind more tightly, other things being equal. Here, we present Generalized Thermodynamic Mapping (GTM) theory, a more general theory that is applicable to the entirety of a biomolecular or other chemical system, and which thus may provide additional guidance for molecular design. For example, it might highlight parts of a ligand whose local free energy rises on binding, thus suggesting where modifications could improve affinity. Starting from classical statistical thermodynamics, we derive structural decompositions that assign energy and entropy to individual atoms or to larger chemical components, such as amino acid residues, and spatial decompositions that define continuously varying thermodynamic densities throughout the system. The potential energy is decomposed via the multibody expansion, and the entropy via the mutual information expansion. The resulting thermodynamic densities satisfy key desiderata: their spatial integrals yield the correct total thermodynamic quantities, the densities vanish where the atomic number density is zero, and all entropy terms above first order go to zero in the absence of correlation. The entropy decomposition in GTM theory is closely related to that of IST, but it is simpler, largely because it expresses the entropy in terms of normalized probability density functions instead of nonnormalized correlation functions. We show that GTM theory is formally exact for any number of particles, N, whereas IST is not. The unified framework presented here enables thermodynamic mapping of solute and solvent alike and is expected to support a range of applications, including in structure-based drug design, protein design, the analysis of allostery, and materials science. The use of GTM theory to gain insight into protein-ligand binding is illustrated here with an initial case study.<\/jats:p>","DOI":"10.1021\/acs.jpcb.6c02416","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T18:02:06Z","timestamp":1790704926000},"page":"10383-10402","source":"Crossref","is-referenced-by-count":0,"title":["A Generalized Theory\nfor the Structural and Spatial\nMapping of Energy, Entropy, and Free Energy"],"prefix":"10.1021","volume":"130","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3375-1738","authenticated-orcid":true,"given":"Michael K.","family":"Gilson","sequence":"first","affiliation":[{"name":"University of California San Diego , , , ,","place":["La Jolla, California, United States, 92093"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joe","family":"Cruz","sequence":"additional","affiliation":[{"name":"The Graduate Center of the City University of New York , , , ,","place":["New York, New York, United States, 10016"]},{"name":"Lehman College, The City University of New York , , , ,","place":["Bronx, New York, United States, 10468"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6042-5594","authenticated-orcid":true,"given":"Kunhuan","family":"Liu","sequence":"additional","affiliation":[{"name":"University of California San Diego , , , ,","place":["La Jolla, California, United States, 92093"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5925-2052","authenticated-orcid":true,"given":"Samrat","family":"Lohar","sequence":"additional","affiliation":[{"name":"The Graduate Center of the City University of New York , , , ,","place":["New York, New York, United States, 10016"]},{"name":"Lehman College, The City University of New York , , , ,","place":["Bronx, New York, United States, 10468"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helmut","family":"Carter","sequence":"additional","affiliation":[{"name":"The Graduate Center of the City University of New York , , , ,","place":["New York, New York, United States, 10016"]},{"name":"Lehman College, The City University of New York , , , ,","place":["Bronx, New York, United States, 10468"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5834-2447","authenticated-orcid":true,"given":"Daniel R.","family":"Roe","sequence":"additional","affiliation":[{"name":"National Institutes of Health , , , ,","place":["Bethesda, Maryland, United States, 20892"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0900-772X","authenticated-orcid":true,"given":"Tom","family":"Kurtzman","sequence":"additional","affiliation":[{"name":"The Graduate Center of the City University of New York , , , ,","place":["New York, New York, United States, 10016"]},{"name":"Lehman College, The City University of New York , , , ,","place":["Bronx, New York, United States, 10468"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"issue":"8","key":"2026100809100778300_cit1","doi-asserted-by":"publisher","first-page":"627","DOI":"10.4236\/jmp.2014.58073","article-title":"Simulating Grain Boundary\nEnergy Using Molecular Dynamics","volume":"5","author":"Movahedi-Rad","year":"2014","journal-title":"J. Mod. Phys."},{"issue":"18","key":"2026100809100778300_cit2","doi-asserted-by":"publisher","first-page":"3542","DOI":"10.1021\/jp972358w","article-title":"Inhomogeneous\nFluid Approach to Solvation Thermodynamics. 2. Applications to Simple\nFluids","volume":"102","author":"Lazaridis","year":"1998","journal-title":"J. Phys. Chem. B"},{"issue":"18","key":"2026100809100778300_cit3","doi-asserted-by":"publisher","first-page":"3531","DOI":"10.1021\/jp9723574","article-title":"Innhomogeneous\nFluid Approach to Solvation Thermodynamics. 1. Theory","volume":"102","author":"Lazaridis","year":"1998","journal-title":"J. Phys. Chem. B"},{"issue":"4","key":"2026100809100778300_cit4","doi-asserted-by":"publisher","first-page":"1424","DOI":"10.1021\/jm2010332","article-title":"Rational Approaches\nto Improving\nSelectivity in Drug Design","volume":"55","author":"Huggins","year":"2012","journal-title":"J. Med. Chem."},{"issue":"6","key":"2026100809100778300_cit5","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1080\/17460441.2025.2497912","article-title":"Water in drug design: pitfalls and\ngood practices","volume":"20","author":"Zolta\u0301n Zsido\u0301","year":"2025","journal-title":"Expert Opin. Drug Discovery"},{"key":"2026100809100778300_cit6","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1002\/cmdc.201700718","article-title":"Discovery of Rogaratinib (BAY 1163877):\na pan-FGFR\nInhibitor","volume":"13","author":"Collin","year":"2018","journal-title":"ChemMedchem"},{"issue":"3","key":"2026100809100778300_cit7","doi-asserted-by":"publisher","first-page":"960","DOI":"10.1039\/D0SC04938G","article-title":"Ligand design by targeting\na binding site water","volume":"12","author":"Matricon","year":"2021","journal-title":"Chem. Sci."},{"issue":"1","key":"2026100809100778300_cit8","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1080\/17460441.2023.2267015","article-title":"The application of WaterMap-guided\nstructure-based virtual screening in novel drug discovery","volume":"19","author":"Kaczor","year":"2024","journal-title":"Expert Opin. Drug Discovery"},{"issue":"33","key":"2026100809100778300_cit9","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.1703287114","article-title":"Testing\ninhomogeneous solvation theory in structure-based ligand discovery","volume":"114","author":"Balius","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"9","key":"2026100809100778300_cit10","doi-asserted-by":"publisher","first-page":"2817","DOI":"10.1021\/ja0771033","article-title":"The role\nof the active site solvent in the thermodynamics of factor Xa-ligand\nbinding","volume":"130","author":"Abel","year":"2008","journal-title":"J. Am. Chem. Soc."},{"issue":"7","key":"2026100809100778300_cit11","doi-asserted-by":"publisher","first-page":"2769","DOI":"10.1021\/ct401110x","article-title":"Thermodynamics of Water\nin an Enzyme Active Site: Grid-Based Hydration Analysis of Coagulation\nFactor Xa","volume":"10","author":"Nguyen","year":"2014","journal-title":"J. Chem. Theory Comput."},{"issue":"35","key":"2026100809100778300_cit12","doi-asserted-by":"publisher","DOI":"10.1002\/anie.202505713","article-title":"Thermodynamics of\nWater Displacement from Binding Sites and its Contributions to Supramolecular\nand Biomolecular Affinity","volume":"64","author":"Setiadi","year":"2025","journal-title":"Angew. Chem. Int.\nEd."},{"key":"2026100809100778300_cit13","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/0097-8485(84)85020-2","article-title":"Ligand-Receptor Interactions","volume":"8","author":"Tembre","year":"1984","journal-title":"Comput. Chem."},{"key":"2026100809100778300_cit14","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1126\/science.3576184","article-title":"Free energy calculations\nby computer simulation","volume":"236","author":"Bash","year":"1987","journal-title":"Science"},{"issue":"12","key":"2026100809100778300_cit15","doi-asserted-by":"publisher","first-page":"2911","DOI":"10.1021\/acs.jcim.7b00564","article-title":"Relative Binding\nFree Energy Calculations\nin Drug Discovery: Recent Advances and Practical Considerations","volume":"57","author":"Cournia","year":"2017","journal-title":"J. Chem. Inf. Model."},{"issue":"11","key":"2026100809100778300_cit16","doi-asserted-by":"publisher","first-page":"5457","DOI":"10.1021\/acs.jcim.0c00900","article-title":"Large-Scale\nAssessment of Binding Free Energy Calculations in Active Drug Discovery\nProjects","volume":"60","author":"Schindler","year":"2020","journal-title":"J. Chem. Inf. 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A."},{"issue":"5535","key":"2026100809100778300_cit21","doi-asserted-by":"publisher","first-page":"1657","DOI":"10.1126\/science.1062246","article-title":"Allosteric\nactivation of a spring-loaded natriuretic peptide receptor dimer by\nhormone","volume":"293","author":"He","year":"2001","journal-title":"Science"},{"issue":"7","key":"2026100809100778300_cit22","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1016\/j.str.2017.05.018","article-title":"A Spring-Loaded\nMechanism Governs the Clamp-like Dynamics of the Skp Chaperone","volume":"25","author":"Holdbrook","year":"2017","journal-title":"Structure"},{"issue":"2","key":"2026100809100778300_cit23","doi-asserted-by":"publisher","first-page":"461a","DOI":"10.1016\/j.bpj.2013.11.2611","article-title":"Calculation and\nvisualization of\natomistic mechanical stresses in biomolecules","volume":"106","author":"Fenley","year":"2014","journal-title":"Biophys. J."},{"issue":"2","key":"2026100809100778300_cit24","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.jmb.2009.04.003","article-title":"Configurational Entropy in Protein-Peptide Binding.\nComputational Study of Tsg101 UEV Domain with an HIV-derived PTAP\nNonapeptide","volume":"389","author":"Killian","year":"2009","journal-title":"J. Mol. Biol."},{"issue":"7","key":"2026100809100778300_cit25","doi-asserted-by":"publisher","first-page":"2871","DOI":"10.1021\/acs.jctc.3c01173","article-title":"Free energy density\nof a fluid and its role in solvation\nand binding","volume":"20","author":"Gilson","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"2026100809100778300_cit26","doi-asserted-by":"publisher","first-page":"4052","DOI":"10.1103\/PhysRevE.56.4052","article-title":"Information Content of Signals using\nCorrelation Function Expansions of the Entropy","volume":"56","author":"Attard","year":"1997","journal-title":"Phys. Rev. E"},{"issue":"3","key":"2026100809100778300_cit27","doi-asserted-by":"publisher","first-page":"3096","DOI":"10.1103\/PhysRevE.62.3096","article-title":"Physical nature\nof higher-order mutual information: Intrinsic correlations and frustration","volume":"62","author":"Matsuda","year":"2000","journal-title":"Phys. Rev. E"},{"issue":"2","key":"2026100809100778300_cit28","doi-asserted-by":"publisher","first-page":"024107","DOI":"10.1063\/1.2746329","article-title":"Extraction\nof configurational entropy\nfrom molecular simulations via an expansion approximation","volume":"127","author":"Killian","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2026100809100778300_cit29","volume-title":"Statistical Mechanics","author":"McQuarrie","year":"1973"},{"issue":"3","key":"2026100809100778300_cit30","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1021\/jp0135407","article-title":"Coordinate systems and the calculation of molecular\nproperties","volume":"106","author":"Potter","year":"2002","journal-title":"J. Phys. Chem. A"},{"issue":"6","key":"2026100809100778300_cit31","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1063\/1.1747782","article-title":"The Statistical\nMechanical Theory of Transport Processes.\nIV. The Equations of Hydrodynamics","volume":"18","author":"Irving","year":"1950","journal-title":"J. Chem.\nPhys."},{"issue":"1","key":"2026100809100778300_cit32","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/S0301-4622(02)00293-4","article-title":"Thermodynamics of protein folding: a microscopic view","volume":"100","author":"Lazaridis","year":"2002","journal-title":"Biophys. Chem."},{"issue":"4","key":"2026100809100778300_cit33","doi-asserted-by":"publisher","first-page":"044101","DOI":"10.1063\/1.4733951","article-title":"Grid inhomogeneous solvation theory:\nHydration structure and thermodynamics of the miniature receptor cucurbit[7]uril","volume":"137","author":"Nguyen","year":"2012","journal-title":"J. Chem. Phys."},{"issue":"4","key":"2026100809100778300_cit34","doi-asserted-by":"publisher","first-page":"2282","DOI":"10.1063\/1.453158","article-title":"On the\nrole of density fluctuations in the entropy of a fluid","volume":"87","author":"Wallace","year":"1987","journal-title":"J. Chem. Phys."},{"key":"2026100809100778300_cit35","first-page":"409","article-title":"The entropy\nof systems with a random number of particles","volume":"28","author":"Stratonovich","year":"1955","journal-title":"Sov. Phys. JETP"},{"issue":"7","key":"2026100809100778300_cit36","doi-asserted-by":"publisher","first-page":"3817","DOI":"10.1103\/PhysRevA.40.3817","article-title":"Direct entropy calculation from computer simulation\nof liquids","volume":"40","author":"Baranyai","year":"1989","journal-title":"Phys. Rev. A"},{"issue":"15","key":"2026100809100778300_cit37","doi-asserted-by":"publisher","first-page":"154107","DOI":"10.1063\/1.3245303","article-title":"General formulation\nof pressure and\nstress tensor for arbitrary many-body interaction potentials under\nperiodic boundary conditions","volume":"131","author":"Thompson","year":"2009","journal-title":"J. Chem. Phys."},{"issue":"18","key":"2026100809100778300_cit38","doi-asserted-by":"publisher","first-page":"184106","DOI":"10.1063\/1.3582905","article-title":"Stress and heat flux for arbitrary\nmultibody potentials: A unified framework","volume":"134","author":"Chandra Admal","year":"2011","journal-title":"J.\nChem. Phys."},{"issue":"1\u20132","key":"2026100809100778300_cit39","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s10659-010-9249-6","article-title":"A Unified Interpretation of Stress\nin Molecular Systems","volume":"100","author":"Chandra Admal","year":"2010","journal-title":"J. Elast."},{"key":"2026100809100778300_cit40","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1021\/jp056020a","article-title":"Thermodynamics\nof Buried Water Clusters at a Protein-Ligand\nBinding Interface","volume":"110","author":"Li","year":"2006","journal-title":"J. Phys. Chem. B"},{"issue":"1","key":"2026100809100778300_cit41","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.33011\/livecoms.4.1.1497","article-title":"Best Practices for Constructing,\nPreparing, and Evaluating Protein-Ligand Binding Affinity Benchmarks\n[Article v1.0]","volume":"4","author":"Hahn","year":"2022","journal-title":"Living J. Comput. Mol. Sci."},{"issue":"11","key":"2026100809100778300_cit42","doi-asserted-by":"publisher","first-page":"4521","DOI":"10.1021\/jm400266t","article-title":"Lead Optimization of a 4-Aminopyridine Benzamide\nScaffold To Identify Potent, Selective, and Orally Bioavailable TYK2\nInhibitors","volume":"56","author":"Liang","year":"2013","journal-title":"J. Med. Chem."},{"key":"2026100809100778300_cit43","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.ejmech.2013.03.070","article-title":"Lead identification of novel and selective\nTYK2 inhibitors","volume":"67","author":"Liang","year":"2013","journal-title":"Eur. J. Med. Chem."},{"issue":"7","key":"2026100809100778300_cit44","doi-asserted-by":"publisher","first-page":"2695","DOI":"10.1021\/ja512751q","article-title":"Accurate and Reliable\nPrediction of Relative Ligand Binding Potency in Prospective Drug\nDiscovery by Way of a Modern Free-Energy Calculation Protocol and\nForce Field","volume":"137","author":"Wang","year":"2015","journal-title":"J. Am. Chem. Soc."},{"key":"2026100809100778300_cit45","doi-asserted-by":"publisher","DOI":"10.26434\/chemrxiv.15008034\/v1","article-title":"Atomic decomposition and mapping of\nsolute thermodynamics","author":"Cruz","year":"2026","journal-title":"ChemRxiv"},{"issue":"7","key":"2026100809100778300_cit46","doi-asserted-by":"publisher","first-page":"3084","DOI":"10.1021\/ct400341p","article-title":"PTRAJ and CPPTRAJ: Software for Processing\nand Analysis\nof Molecular Dynamics Trajectory Data","volume":"9","author":"Roe","year":"2013","journal-title":"J. Chem.\nTheory Comput."},{"issue":"25","key":"2026100809100778300_cit47","doi-asserted-by":"publisher","first-page":"2110","DOI":"10.1002\/jcc.25382","article-title":"Parallelization of CPPTRAJ enables large scale analysis\nof molecular dynamics trajectory data","volume":"39","author":"Roe","year":"2018","journal-title":"J. Comput.\nChem."},{"key":"2026100809100778300_cit48","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1080\/01966324.2003.10737616","article-title":"Nearest neighbor estimates of entropy","volume":"23","author":"Singh","year":"2003","journal-title":"Am. J. Math. Manag. Sci."},{"issue":"3","key":"2026100809100778300_cit49","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1002\/jcc.20589","article-title":"Nearest-neighbor nonparametric\nmethod for estimating the configurational\nentropy of complex molecules","volume":"28","author":"Hnizdo","year":"2007","journal-title":"J. Comput. Chem."},{"issue":"10","key":"2026100809100778300_cit50","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1002\/jcc.20919","article-title":"Efficient calculation of configurational\nentropy from molecular simulations by combining the mutual-information\nexpansion and nearest-neighbor methods","volume":"29","author":"Hnizdo","year":"2008","journal-title":"J. Comput.\nChem."},{"key":"2026100809100778300_cit100","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1002\/jcc.21787","article-title":"A Toolkit\nfor the Analysis of Molecular Dynamics Simulations","volume":"32","author":"Michaud-Agrawal","year":"2011","journal-title":"J. Comput. Chem."},{"key":"2026100809100778300_cit101","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1002\/jcc.540150503","article-title":"ICM\u2500A\nnew method for protein modeling and design: Applications to docking\nand structure prediction from the distorted native conformation","volume":"15","author":"Abagyan","year":"1994","journal-title":"J. Comput. Chem."},{"key":"2026100809100778300_cit102","doi-asserted-by":"publisher","first-page":"5990","DOI":"10.1021\/acs.jctc.6b00563","article-title":"Computational Methods\nfor Configurational Entropy Using Internal and Cartesian Coordinates","volume":"12","author":"Hikiri","year":"2016","journal-title":"J. Chem. Theory Comput."},{"issue":"3","key":"2026100809100778300_cit51","doi-asserted-by":"publisher","first-page":"808","DOI":"10.1073\/pnas.0610202104","article-title":"Motifs\nfor molecular recognition exploiting hydrophobic enclosure in protein-ligand\nbinding","volume":"104","author":"Young","year":"2007","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100809100778300_cit52","doi-asserted-by":"publisher","first-page":"2029","DOI":"10.1002\/jcc.24417","article-title":"Solvation thermodynamic mapping of molecular surfaces\nin AmberTools: GIST","volume":"37","author":"Ramsey","year":"2016","journal-title":"J. Comput. Chem."},{"issue":"1","key":"2026100809100778300_cit53","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1021\/acs.jctc.7b00592","article-title":"Solvation\nStructure and Thermodynamic Mapping (SSTMap): An Open-Source, Flexible\nPackage for the Analysis of Water in Molecular Dynamics Trajectories","volume":"14","author":"Haider","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2026100809100778300_cit54","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/978-1-61779-465-0_24","article-title":"Computing\nthe thermodynamic contributions of interfacial\nwater","volume":"819","author":"Li","year":"2012","journal-title":"Methods Mol. 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