{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T13:48:42Z","timestamp":1782308922864,"version":"3.54.5"},"reference-count":51,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013105","name":"Shanghai Rising-Star Program","doi-asserted-by":"publisher","award":["23QD1400600"],"award-info":[{"award-number":["23QD1400600"]}],"id":[{"id":"10.13039\/501100013105","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFC3400504"],"award-info":[{"award-number":["2022YFC3400504"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>Structure-based drug design (SBDD) has advanced with deep generative models, but bridging the gap between continuous atomic coordinates and discrete atom types remains a challenge. Current approaches, such as diffusion and flow matching models, often fail to unify these heterogeneous modalities, relying on separate strategies or ill-fitting Euclidean metrics for discrete variables. This lack of a consistent framework limits generative models\u2019 ability to capture the geometric and chemical structure of protein\u2013ligand complexes.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>We present MolPIF, a parameter interpolation flow mechanism designed to unify the generation of continuous and discrete molecular variables. Unlike traditional flow models that operate in sample space, MolPIF interpolates between distributions in the parameter space, theoretically recovering Wasserstein-2 optimal transport for continuous coordinates and establishing Fisher\u2013Rao geodesics for discrete atom types. We further incorporate a geometry-enhanced learning strategy to improve the capture of atomic contexts. Extensive evaluations on the CrossDocked2020 dataset demonstrate that MolPIF outperforms baselines in binding affinity, chemical validity, geometric fidelity, and chemical space coverage. Additionally, MolPIF exhibits versatility in lead optimization and offers flexible prior distribution selection (such as Laplace), establishing a robust paradigm for SBDD.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability and implementation<\/jats:title>\n                    <jats:p>Source code is freely available at https:\/\/github.com\/BLEACH366\/MolPIF.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btag323","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T11:44:03Z","timestamp":1779363843000},"source":"Crossref","is-referenced-by-count":0,"title":["MolPIF: a parameter interpolation flow model for molecule generation"],"prefix":"10.1093","volume":"42","author":[{"given":"Yaowei","family":"Jin","sequence":"first","affiliation":[{"name":"Lingang Laboratory , Shanghai 200031,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjie","family":"Wang","sequence":"additional","affiliation":[{"name":"Lingang Laboratory , Shanghai 200031,","place":["China"]},{"name":"School of Information Science and Technology, ShanghaiTech University , Shanghai 201210,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufan","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Artificial Intelligence, Fudan University , Shanghai 200433,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6869-7931","authenticated-orcid":false,"given":"Wenkai","family":"Xiang","sequence":"additional","affiliation":[{"name":"Lingang Laboratory , Shanghai 200031,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Duanhua","family":"Cao","sequence":"additional","affiliation":[{"name":"Drug 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