2026-10-14T14:37:53Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34025314 2026-09-29T17:10:55Z category_1 category_4 category_915 category_15 category_873 category_734 category_931 category_135 portal_63 item_type_6 month_year_09_2026

A Generalized Theory for the Structural and Spatial Mapping of Energy, Entropy, and Free Energy Michael K. Gilson (673405) Joe Cruz (25138093) Kunhuan Liu (9452799) Samrat Lohar (25138096) Helmut Carter (21687524) Daniel R. Roe (1899412) Tom Kurtzman (1325889) Biophysics Biochemistry Physical Sciences not elsewhere classified Neuroscience Chemical Sciences not elsewhere classified Biological Sciences not elsewhere classified Information Systems not elsewhere classified Computational Biology unified framework presented might highlight parts initial case study first order go classical statistical thermodynamics amino acid residues mutual information expansion larger chemical components enables thermodynamic mapping spatial integrals yield free energy systems free energy density nonnormalized correlation functions atomic number density >, whereas ist derive structural decompositions based drug design spatial mapping spatial decompositions multibody expansion surface energy potential energy assign energy water droplet thus suggesting surface tension solvent alike proven useful n </ molecular design materials science individual atoms good examples gain insight formally exact densities vanish decomposed via closely related chemical system 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, <i>N</i>, 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. 2026-09-29T00:00:00Z Text Journal contribution 10.1021/acs.jpcb.6c02416.s001 https://figshare.com/articles/journal_contribution/A_Generalized_Theory_for_the_Structural_and_Spatial_Mapping_of_Energy_Entropy_and_Free_Energy/34025314 CC BY-NC 4.0