{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T02:56:25Z","timestamp":1768532185178,"version":"3.49.0"},"reference-count":66,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["814426"],"award-info":[{"award-number":["814426"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["953152"],"award-info":[{"award-number":["953152"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>The lack of knowledge about the uptake of NPs by biological cells poses a significant problem for drug delivery. For this reason, designing an appropriate model is the main challenge for modelers. To address this problem, molecular modeling studies that can describe the mechanism of cellular uptake of drug-loaded nanoparticles have been conducted in recent decades. In this context, we developed three different models for the amphipathic nature of drug-loaded nanoparticles (MTX-SS-\u03b3-PGA), whose cellular uptake mechanism was predicted by molecular dynamics studies. Many factors affect nanoparticle uptake, including nanoparticle physicochemical properties, protein\u2013particle interactions, and subsequent agglomeration, diffusion, and sedimentation. Therefore, the scientific community needs to understand how these factors can be controlled and the NP uptake of nanoparticles. Based on these considerations, in this study, we investigated for the first time the effects of the selected physicochemical properties of the anticancer drug methotrexate (MTX) grafted with hydrophilic-\u03b3-polyglutamic acid (MTX-SS-\u03b3-PGA) on its cellular uptake at different pH values. To answer this question, we developed three theoretical models describing drug-loaded nanoparticles (MTX-SS-\u03b3-PGA) at three different pH values, such as (1) pH 7.0 (the so-called neutral pH model), (2) pH 6.4 (the so-called tumor pH model), and (3) pH 2.0 (the so-called stomach pH model). Exceptionally, the electron density profile shows that the tumor model interacts more strongly with the head groups of the lipid bilayer than the other models due to charge fluctuations. Hydrogen bonding and RDF analyses provide information about the solution of the NPs with water and their interaction with the lipid bilayer. Finally, dipole moment and HOMO-LUMO analysis showed the free energy of the solution in the water phase and chemical reactivity, which are particularly useful for determining the cellular uptake of the NPs. The proposed study provides fundamental insights into molecular dynamics (MD) that will allow researchers to determine the influence of pH, structure, charge, and energetics of NPs on the cellular uptake of anticancer drugs. We believe that our current study will be useful in developing a new model for drug delivery to cancer cells with a much more efficient and less time-consuming model.<\/jats:p>","DOI":"10.3390\/ijms24043479","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T02:56:13Z","timestamp":1675997773000},"page":"3479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["How Does the Study MD of pH-Dependent Exposure of Nanoparticles Affect Cellular Uptake of Anticancer Drugs?"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1264-6901","authenticated-orcid":false,"given":"Selvaraj","family":"Sengottiyan","sequence":"first","affiliation":[{"name":"Laboratory of Environmental Chemoinformatics, Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0019-8323","authenticated-orcid":false,"given":"Alicja","family":"Mikolajczyk","sequence":"additional","affiliation":[{"name":"Laboratory of Environmental Chemoinformatics, Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0449-8339","authenticated-orcid":false,"given":"Tomasz","family":"Puzyn","sequence":"additional","affiliation":[{"name":"Laboratory of Environmental Chemoinformatics, Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.jcrpr.2017.07.001","article-title":"Review of cancer from perspective of molecular","volume":"4","author":"Hassanpour","year":"2017","journal-title":"J. Cancer Res. Pract."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.3389\/fonc.2020.01734","article-title":"Polymeric nanoscale drug carriers mediate methotrexate delivery for developing therapeutic interventions against cancer and rheumatoid arthritis","volume":"10","author":"Yu","year":"2020","journal-title":"Front. Oncol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/S0169-409X(02)00044-3","article-title":"Nanoparticles in cancer therapy and diagnosis","volume":"54","author":"Brigger","year":"2002","journal-title":"Adv. Drug Deliv. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.canlet.2014.03.013","article-title":"Multi-drug resistance in cancer chemotherapeutics: Mechanisms and lab approaches","volume":"347","author":"Wu","year":"2014","journal-title":"Cancer Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/0885328215578111","article-title":"Functional liposomes in the cancer-targeted drug delivery","volume":"30","author":"Tila","year":"2015","journal-title":"J. Biomater. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10272","DOI":"10.1021\/acsnano.8b05373","article-title":"Synthetic charge-invertible polymer for rapid and complete implantation of layer-by-layer microneedle drug films for enhanced transdermal vaccination","volume":"12","author":"He","year":"2018","journal-title":"ACS Nano"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4923","DOI":"10.2147\/IJN.S69493","article-title":"Self-assembled micelles based on pH-sensitive PAE-g-MPEG-cholesterol block copolymer for anticancer drug delivery","volume":"9","author":"Zhang","year":"2014","journal-title":"Int. J. Nanomed."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6556","DOI":"10.1016\/j.biomaterials.2009.08.022","article-title":"Computational studies on self-assembled paclitaxel structures: Templates for hierarchical block copolymer assemblies and sustained drug release","volume":"30","author":"Guo","year":"2009","journal-title":"Biomaterials"},{"key":"ref_9","first-page":"618","article-title":"Methotrexate and epirubicin conjugates as potential antitumor drugs","volume":"71","author":"Kmiecik","year":"2017","journal-title":"Adv. Hyg. Exp. Med.\/Postep. Hig. I Med. Dosw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3107","DOI":"10.1021\/nn500962q","article-title":"Nanoparticles for imaging, sensing, and therapeutic intervention","volume":"8","author":"Bogart","year":"2014","journal-title":"ACS Nano"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1021\/mp800035h","article-title":"Computational model for predicting chemical substituent effects on passive drug permeability across parallel artificial membranes","volume":"5","author":"Acharya","year":"2008","journal-title":"Mol. Pharm."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ejps.2010.05.014","article-title":"Prediction of the in vitro permeability determined in Caco-2 cells by using artificial neural networks","volume":"41","author":"Gouveia","year":"2010","journal-title":"Eur. J. Pharm. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1007\/s10822-011-9480-7","article-title":"Modeling the pharmacodynamics of passive membrane permeability","volume":"25","author":"Swift","year":"2011","journal-title":"J. Comput. Aided Mol. Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.bpc.2009.01.001","article-title":"Influence of a lipid bilayer on the conformational behavior of amphotericin B derivatives\u2014A molecular dynamics study","volume":"141","author":"Czub","year":"2009","journal-title":"Biophys. Chem."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3918","DOI":"10.1021\/jp211904j","article-title":"Structure and elasticity of lipid membranes with genistein and daidzein bioflavinoids using X-ray scattering and MD simulations","volume":"116","author":"Raghunathan","year":"2012","journal-title":"J. Phys. Chem. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1021\/js950285r","article-title":"Correlation of drug absorption with molecular surface properties","volume":"85","author":"Palm","year":"1996","journal-title":"J. Pharm. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1021\/jm00135a001","article-title":"A practitioner\u2019s perspective of the role of quantitative structure-activity analysis in medicinal chemistry","volume":"24","author":"Martin","year":"1981","journal-title":"J. Med. Chem."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1021\/jm970530e","article-title":"Physicochemical high throughput screening: Parallel artificial membrane permeation assay in the description of passive absorption processes","volume":"41","author":"Kansy","year":"1998","journal-title":"J. Med. Chem."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1016\/S0016-5085(89)80072-1","article-title":"Characterization of the human colon carcinoma cell line (Caco-2) as a model system for intestinal epithelial permeability","volume":"96","author":"Hidalgo","year":"1989","journal-title":"Gastroenterology"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1002\/jps.2600790604","article-title":"Epithelial transport of drugs in cell culture. I: A model for studying the passive diffusion of drugs over intestinal absorbtive (Caco-2) cells","volume":"79","author":"Artursson","year":"1990","journal-title":"J. Pharm. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6485","DOI":"10.1166\/jnn.2013.7525","article-title":"Influence of nanoparticle shape, size, and surface functionalization on cellular uptake","volume":"13","author":"Ma","year":"2013","journal-title":"J. Nanosci. Nanotechnol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.2147\/IJN.S152312","article-title":"Design of pH-sensitive methotrexate prodrug-targeted curcumin nanoparticles for efficient dual-drug delivery and combination cancer therapy","volume":"13","author":"Xie","year":"2018","journal-title":"Int. J. Nanomed."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.jconrel.2004.02.003","article-title":"Folate receptor targeted biodegradable polymeric doxorubicin micelles","volume":"96","author":"Yoo","year":"2004","journal-title":"J. Control. Release"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14480","DOI":"10.1021\/acs.langmuir.7b03544","article-title":"Understanding the cellular uptake of pH-responsive zwitterionic gold nanoparticles: A computer simulation study","volume":"33","author":"Quan","year":"2017","journal-title":"Langmuir"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1080\/10667857.2021.1908769","article-title":"A new type of glutathione-responsive anti-osteosarcoma prodrug nanoparticles","volume":"37","author":"Zheng","year":"2021","journal-title":"Mater. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1021\/nn304439f","article-title":"Nanoparticle geometry and surface orientation influence mode of cellular uptake","volume":"7","author":"Herd","year":"2013","journal-title":"ACS Nano"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4131","DOI":"10.1038\/s41598-017-03834-2","article-title":"A comparison between sphere and rod nanoparticles regarding their in vivo biological behavior and pharmacokinetics","volume":"7","author":"Zhao","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3373","DOI":"10.2174\/0929867324666170404142840","article-title":"Peptide-drug conjugate: A novel drug design approach","volume":"24","author":"Ma","year":"2017","journal-title":"Curr. Med. Chem."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"17554","DOI":"10.1021\/bi981802y","article-title":"Lipid properties and the orientation of aromatic residues in OmpF, influenza M2, and alamethicin systems: Molecular dynamics simulations","volume":"37","author":"Tieleman","year":"1998","journal-title":"Biochemistry"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1021\/bi00456a027","article-title":"Organization and interaction of cholesterol and phosphatidylcholine in model bilayer membranes","volume":"29","author":"Hyslop","year":"1990","journal-title":"Biochemistry"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4000","DOI":"10.1103\/PhysRevE.62.4000","article-title":"Structural information from multilamellar liposomes at full hydration: Full q-range fitting with high quality x-ray data","volume":"62","author":"Pabst","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6667","DOI":"10.1002\/ange.201411615","article-title":"Acylsulfonamide-functionalized Zwitterionic gold nanoparticles for enhanced cellular uptake at tumor pH","volume":"127","author":"Mizuhara","year":"2015","journal-title":"Angew. Chem."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"664","DOI":"10.3390\/membranes5040664","article-title":"Effect of cholesterol on the structure of a five-component mitochondria-like phospholipid membrane","volume":"5","author":"Cathcart","year":"2015","journal-title":"Membranes"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00232-005-7006-8","article-title":"Structure of fully hydrated fluid phase lipid bilayers with monounsaturated chains","volume":"208","author":"Nagle","year":"2006","journal-title":"J. Membr. Biol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3148","DOI":"10.1021\/acs.jpcb.5b12337","article-title":"Effect of cholesterol on cellular uptake of cancer drugs pirarubicin and ellipticine","volume":"120","author":"Zhang","year":"2016","journal-title":"J. Phys. Chem. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1976","DOI":"10.1039\/C2CP42738A","article-title":"Cholesterol and POPC segmental order parameters in lipid membranes: Solid state 1H\u201313C NMR and MD simulation studies","volume":"15","author":"Ferreira","year":"2013","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1007\/s00249-007-0192-9","article-title":"Acyl chain order parameter profiles in phospholipid bilayers: Computations from molecular dynamics simulations and comparison with 2H NMR experiments","volume":"36","author":"Vermeer","year":"2007","journal-title":"Eur. Biophys. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.chemphyslip.2006.02.011","article-title":"Lipid lateral diffusion in bilayers with phosphatidylcholine, sphingomyelin and cholesterol: An NMR study of dynamics and lateral phase separation","volume":"141","author":"Lindblom","year":"2006","journal-title":"Chem. Phys. Lipids"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4155","DOI":"10.1021\/j100066a040","article-title":"Simulation of water transport through a lipid membrane","volume":"98","author":"Marrink","year":"1994","journal-title":"J. Phys. Chem."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0005-2760(97)00070-2","article-title":"Permeability of Lipid Bilayer to Anthracycline Derivatives. Role of the Bilayer Composition and of the Temperature","volume":"1389","author":"Frezard","year":"1998","journal-title":"Biochim. Biophys. Acta Lipids Lipid Metab."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.bpj.2011.06.015","article-title":"Structural Effects and Translocation of Doxorubicin in a Dppc\/Chol Bilayer: The Role of Cholesterol","volume":"101","author":"Yacoub","year":"2011","journal-title":"Biophys. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.1038\/s41598-019-39411-y","article-title":"A computational study of Anthracyclines interacting with lipid bilayers: Correlation of membrane insertion rates, orientation effects and localisation with cytotoxicity","volume":"9","author":"Toroz","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Caruso, U., Di Costanzo, L., Concilio, S., Piotto, S., Sessa, L., and Panunzi, B. (2022). A Water Soluble 2-Phenyl-5-(pyridin-3-yl)-1, 3, 4-oxadiazole Based Probe: Antimicrobial Activity and Colorimetric\/Fluorescence pH Response. Molecules, 27.","DOI":"10.3390\/molecules27061824"},{"key":"ref_44","unstructured":"Fong, C. (2020). Inhibition of COVID-2019 3C-Like Protease: Structure Activity Relationship Using Quantum Mechanics. [Ph.D. Thesis, The University of Adelaide]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4218","DOI":"10.1039\/C6CS00636A","article-title":"Cellular uptake of nanoparticles: Journey inside the cell","volume":"46","author":"Behzadi","year":"2017","journal-title":"Chem. Soc. Rev."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/0005-2736(91)90268-D","article-title":"Uptake of liposomes by cultured mouse bone marrow macrophages: Influence of liposome composition and size","volume":"1061","author":"Allen","year":"1991","journal-title":"Biochim. Biophys. Acta"},{"key":"ref_47","first-page":"487","article-title":"Biochemical, morphological, and ultrastructural studies on the uptake of liposomes by murine macrophages","volume":"41","author":"Raz","year":"1981","journal-title":"Cancer Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"4600","DOI":"10.1016\/j.biomaterials.2007.07.029","article-title":"Protein adsorption and cellular uptake of cerium oxide nanoparticles as a function of zeta potential","volume":"28","author":"Patil","year":"2007","journal-title":"Biomaterials"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1016\/S0142-9612(02)00440-4","article-title":"Intracellular uptake of anionic superparamagnetic nanoparticles as a function of their surface coating","volume":"24","author":"Wilhelm","year":"2003","journal-title":"Biomaterials"},{"key":"ref_50","first-page":"87","article-title":"The effect of nanoparticle uptake on cellular behavior: Disrupting or enabling functions?","volume":"5","author":"Panariti","year":"2012","journal-title":"Nanotechnol. Sci. Appl."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s00204-010-0546-4","article-title":"Nanoparticles: Molecular targets and cell signalling","volume":"85","author":"Marano","year":"2011","journal-title":"Arch Toxicol."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1186\/s13321-019-0336-9","article-title":"Dimorphite-DL: An open-source program for enumerating the ionization states of drug-like small molecules","volume":"11","author":"Ropp","year":"2019","journal-title":"J. Cheminform."},{"key":"ref_53","unstructured":"Frisch, M., Trucks, G., Schlegel, H.E.A., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Montgomery, J.A., Vreven, T.K.K.N., Kudin, K.N., and Burant, J.C. (2009). Gaussian 09, Revision B.01, Gaussian, Inc."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1002\/jcc.540141112","article-title":"General atomic and molecular electronic structure system","volume":"14","author":"Schmidt","year":"1993","journal-title":"J. Comput. Chem."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1002\/jcc.20945","article-title":"CHARMM-GUI: A web-based graphical user interface for CHARMM","volume":"29","author":"Jo","year":"2008","journal-title":"J. Comput. Chem."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.bpj.2014.05.034","article-title":"CHARMM all-atom additive force field for sphingomyelin: Elucidation of hydrogen bonding and of positive curvature","volume":"107","author":"Venable","year":"2014","journal-title":"Biophys. J."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1063\/1.445869","article-title":"Comparison of simple potential functions for simulating liquid water","volume":"79","author":"Jorgensen","year":"1983","journal-title":"J. Chem. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmgm.2019.02.009","article-title":"Conformational perturbation of peptides in presence of polar organic solvents","volume":"89","author":"Yadav","year":"2019","journal-title":"J. Mol.Graph. Model."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"4177","DOI":"10.1063\/1.467468","article-title":"Constant pressure molecular dynamics algorithms","volume":"101","author":"Martyna","year":"1994","journal-title":"J. Chem. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1063\/1.463137","article-title":"Reversible multiple time scale molecular dynamics","volume":"97","author":"Tuckerman","year":"1992","journal-title":"J. Chem. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"9537","DOI":"10.1021\/acs.jpcb.1c03665","article-title":"Nonconverged Constraints Cause Artificial Temperature Gradients in Lipid Bilayer Simulations","volume":"125","author":"Thallmair","year":"2021","journal-title":"J. Phys. Chem. B"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1002\/jcc.20290","article-title":"The Amber biomolecular simulation programs","volume":"26","author":"Case","year":"2005","journal-title":"J. Comput. Chem."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0021-9991(77)90098-5","article-title":"Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes","volume":"23","author":"Ryckaert","year":"1977","journal-title":"J. Comput. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1021\/ct700301q","article-title":"GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation","volume":"4","author":"Hess","year":"2008","journal-title":"J. Chem. Theory Comput."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1021\/ct0502864","article-title":"Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations","volume":"3","author":"Chodera","year":"2007","journal-title":"J. Chem. Theory Comput."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1002\/jcc.540130812","article-title":"The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method","volume":"13","author":"Kumar","year":"1992","journal-title":"J. Comput. Chem."}],"container-title":["International Journal of Molecular Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1422-0067\/24\/4\/3479\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:28:27Z","timestamp":1760120907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1422-0067\/24\/4\/3479"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,9]]},"references-count":66,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["ijms24043479"],"URL":"https:\/\/doi.org\/10.3390\/ijms24043479","relation":{},"ISSN":["1422-0067"],"issn-type":[{"value":"1422-0067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,9]]}}}