{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T17:26:49Z","timestamp":1787851609895,"version":"build-2784847793"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["25-24-00991"],"award-info":[{"award-number":["25-24-00991"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"award":["25-24-00991"],"award-info":[{"award-number":["25-24-00991"]}],"id":[{"id":"https:\/\/ror.org\/03y2gwe85","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomolecules"],"abstract":"<jats:p>Hydration plays an essential role in protein\u2013protein interactions. Coarse-grained modeling provides an efficient way to treat hydrated protein complexes without the use of extra-large computational resources. To enhance the capabilities of coarse-grained modeling, we developed an integral equation theory based on the solution of the Ornstein\u2013Zerinke equation to evaluate the hydration structure of peptides and proteins within the framework of coarse-grained modeling. Our current version is based on the SPICA force field, which considers distance-dependent interaction potentials between solvent particles and amino acid segments. Our approach involves two key procedures: an accurate estimation of the structure factor of the uniform fluid and the specific construction of bridge functions obtained from MD simulations. The use of a special hybrid closure allows us to reproduce not only the details of the structure factor, but also the isothermal compressibility obtained from the simulations. The developed bridge functions include two components: an analytical repulsive contribution, which is primarily responsible for the thermodynamic properties, and an attractive contribution obtained from MD simulations. The main assumption in the construction is that the contribution of individual amino acids to the attractive bridge function is additive. By parameterizing the bridge functions, we reproduced details of the hydration structure and accurately calculated the hydration energy for various peptides and proteins. Our method is computationally inexpensive and appears to be suitable for the rapid processing of hydrated proteins of any size.<\/jats:p>","DOI":"10.3390\/biom16091242","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T16:47:13Z","timestamp":1787849233000},"page":"1242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Integral Equation Theory for Coarse-Grained Modeling of Protein Hydration"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8608-3753","authenticated-orcid":false,"given":"Gennady N.","family":"Chuev","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Experimental Biophysics, The Russian Academy of Sciences, Institutskaya St., 142290 Pushchino, Moscow Region, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Timur V.","family":"Mamedov","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Experimental Biophysics, The Russian Academy of Sciences, Institutskaya St., 142290 Pushchino, Moscow Region, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dmitry O.","family":"Morozov","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Experimental Biophysics, The Russian Academy of Sciences, Institutskaya St., 142290 Pushchino, Moscow Region, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"ref_1","unstructured":"Franks, F. 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