{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T13:01:01Z","timestamp":1785243661597,"version":"3.55.0"},"reference-count":43,"publisher":"American Chemical Society (ACS)","issue":"14","license":[{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101097272"],"award-info":[{"award-number":["101097272"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We introduce force-kernel extended-system adaptive biasing force (FK-eABF), a force-based kernel reformulation of eABF that replaces the histogram-based mean-force accumulator of conventional eABF with a sparse population of Gaussian kernels storing local running-mean forces. Biasing forces are recovered by Nadaraya\u2013Watson regression, yielding smooth estimates from the earliest stages of a simulation without a minimum-count threshold, while the same kernel population also defines an auxiliary, self-attenuating exploration force that requires no prior knowledge of barrier heights. On N-acetyl-N\u2032-methylalanylamide in explicit water, FK-eABF achieves full free-energy landscape coverage faster than well-tempered metadynamics (WT-MetaD), on-the-fly probability enhanced sampling (OPES), and WTM-eABF, while all four methods converge to comparable accuracy given sufficient time. FK-eABF also retains long-time accuracy: on the DFG-in\/out transition of Abl1 kinase, multimicrosecond simulations recover the established near-isoenergetic balance between states. At the opposite extreme, applied to the electrocyclic ring closure of 1,3-butadiene at the ab initio molecular dynamics level, FK-eABF recovers the free-energy landscape within 30 ps. Together, these benchmarks, spanning more than 4 orders of magnitude in simulation time, establish FK-eABF as more than a kernelized implementation of eABF: A force-based kernel reformulation that delivers faster early time convergence without sacrificing long-time quantitative accuracy.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c00879","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T07:19:28Z","timestamp":1783408768000},"page":"7313-7325","source":"Crossref","is-referenced-by-count":0,"title":["A Force-Kernel\nReformulation of the Extended-System\nAdaptive Biasing Force for Free-Energy Calculations"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9245-8101","authenticated-orcid":true,"given":"Christopher","family":"Kang","sequence":"first","affiliation":[{"name":"North Carolina State University , , , ,","place":["Raleigh, North Carolina, United States, 27695"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-8376","authenticated-orcid":true,"given":"Rahul","family":"Verma","sequence":"additional","affiliation":[{"name":"North Carolina State University , , , ,","place":["Raleigh, North Carolina, United States, 27695"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4317-1654","authenticated-orcid":true,"given":"Aditya","family":"Sonpal","sequence":"additional","affiliation":[{"name":"North Carolina State University , , , ,","place":["Raleigh, North Carolina, United States, 27695"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0536-149X","authenticated-orcid":true,"given":"Alyson","family":"Shoji","sequence":"additional","affiliation":[{"name":"North Carolina State University , , , ,","place":["Raleigh, North Carolina, United States, 27695"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9122-1698","authenticated-orcid":true,"given":"Christophe","family":"Chipot","sequence":"additional","affiliation":[{"name":"Universite\u0301 de Lorraine , , ,","place":["Vand\u0153uvre-le\u0300s-Nancy Cedex, France, 54506"]},{"name":"Beckman Institute, University of Illinois at Urbana\u2212Champaign , , , ,","place":["Urbana, Illinois, United States, 61801"]},{"name":"University of Illinois at Urbana\u2212Champaign , , , ,","place":["Urbana, Illinois, United States, 61801"]},{"name":"The University of Chicago , , , ,","place":["Chicago, Illinois, United States, 60637"]},{"name":"The University of Hawai\u2018i at Ma\u0305noa , , , ,","place":["Honolulu, Hawaii, United States, 96822"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6727-2957","authenticated-orcid":true,"given":"Jim","family":"Pfaendtner","sequence":"additional","affiliation":[{"name":"North Carolina State University , , , ,","place":["Raleigh, North Carolina, United States, 27695"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,7]]},"reference":[{"key":"2026072808090616200_cit1","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1021\/ct3008099","article-title":"Standard binding free energies from\ncomputer simulations: What is the best strategy?","volume":"9","author":"Gumbart","year":"2013","journal-title":"J. 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