{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T11:06:26Z","timestamp":1785323186819,"version":"3.55.0"},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Small"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Viewing molecular active matter by analogy with micro\u2010 and mesoscopic scale active matter has led to confusion in the field regarding the importance of phoretic or hydrodynamic forces. Here we discuss how kinetic asymmetry and diffusion asymmetry combine with dissipation to provide the necessary time and space symmetry breaking to give rise to directional motion for nanoscale enzymes. Thus, this mechanism enables the generation of higher\u2010order tensorial outputs from scalar energy input. Our model is sufficient to explain both positive and negative chemotaxis of molecular catalysts, as well as the emergence of non\u2010reciprocal interaction between enzymes that share substrates and products. We end by speculating how non\u2010reciprocal interaction at the molecular scale can lead to the generation of memory and order, ingredients that are key to the transition from matter to life.<\/jats:p>","DOI":"10.1002\/smll.74782","type":"journal-article","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T10:47:10Z","timestamp":1785322030000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Molecular Active Matter, Kinetic Asymmetry, and Non\u2010Reciprocal Interactions"],"prefix":"10.1002","author":[{"given":"Niladri Sekhar","family":"Mandal","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering The Pennsylvania State University  University Park Pennsylvania USA"},{"name":"Department of Chemical Engineering Indian Institute of Technology Roorkee Roorkee Uttarakhand India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaotian","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering The Pennsylvania State University  University Park Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ayusman","family":"Sen","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering The Pennsylvania State University  University Park Pennsylvania USA"},{"name":"Department of Chemistry The Pennsylvania State University  University Park Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7472-187X","authenticated-orcid":false,"given":"R. Dean","family":"Astumian","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy University of Maine  Orono Maine USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevX.12.010501","article-title":"Symmetry, Thermodynamics, and Topology in Active Matter","volume":"12","author":"Bowick M. J.","year":"2022","journal-title":"Physical Review X"},{"key":"e_1_2_8_3_1","doi-asserted-by":"crossref","first-page":"6416","DOI":"10.1103\/PhysRevA.39.6416","article-title":"Effects of Oscillations and Energy\u2010Driven Fluctuations on the Dynamics of Enzyme Catalysis and Free\u2010Energy Transduction","volume":"39","author":"Astumian R. D.","year":"1989","journal-title":"Physical Review A"},{"key":"e_1_2_8_4_1","doi-asserted-by":"crossref","first-page":"12263","DOI":"10.1021\/acs.langmuir.1c01360","article-title":"Relative Diffusivities of Bound and Unbound Protein Can Control Chemotactic Directionality","volume":"37","author":"Mandal N. S.","year":"2021","journal-title":"Langmuir"},{"key":"e_1_2_8_5_1","doi-asserted-by":"crossref","first-page":"3837","DOI":"10.1038\/s41467-019-11402-7","article-title":"Kinetic Asymmetry Allows Macromolecular Catalysts to Drive an Information Ratchet","volume":"10","author":"Astumian R. D.","year":"2019","journal-title":"Nature Communications"},{"key":"e_1_2_8_6_1","doi-asserted-by":"crossref","first-page":"5730","DOI":"10.1021\/jacs.2c11945","article-title":"Kinetic Asymmetry versus Dissipation in the Evolution of Chemical Systems as Exemplified by Single Enzyme Chemotaxis","volume":"145","author":"Mandal N. S.","year":"2023","journal-title":"Journal of the American Chemical Society"},{"key":"e_1_2_8_7_1","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.chempr.2023.11.017","article-title":"A Molecular Origin of Non\u2010Reciprocal Interactions between Interacting Active Catalysts","volume":"10","author":"Mandal N. S.","year":"2024","journal-title":"Chem"},{"key":"e_1_2_8_8_1","doi-asserted-by":"crossref","first-page":"14775","DOI":"10.1021\/acsnano.6c03464","article-title":"Emergent Nonlinearity in Active Molecular Chemotaxis","volume":"5","author":"Lu X.","year":"2026","journal-title":"ACS Nano"},{"key":"e_1_2_8_9_1","doi-asserted-by":"crossref","DOI":"10.1039\/c1cp00003a","article-title":"A Mesoscopic Model for Protein Enzymatic Dynamics in Solution","volume":"13","author":"Echeverria C.","year":"2011","journal-title":"Physical Chemistry Chemical Physics"},{"key":"e_1_2_8_10_1","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1038\/s42005-025-02303-x","article-title":"Interpreting Molecular Ratchets, Directionality, and Kinetic Asymmetry through the Work of Curie, Einstein, and Lewis","volume":"8","author":"Astumian R. D.","year":"2025","journal-title":"Communications Physics"},{"key":"e_1_2_8_11_1","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1021\/acs.nanolett.8b00717","article-title":"Phoresis and Enhanced Diffusion Compete in Enzyme Chemotaxis","volume":"18","author":"Agudo\u2010Canalejo J.","year":"2018","journal-title":"Nano Letters"},{"key":"e_1_2_8_12_1","doi-asserted-by":"crossref","first-page":"4496","DOI":"10.1038\/s41467-023-40241-w","article-title":"Self\u2010Organization of Primitive Metabolic Cycles due to Non\u2010Reciprocal Interactions","volume":"14","author":"Ouazan\u2010Reboul V.","year":"2023","journal-title":"Nature Communications"},{"key":"e_1_2_8_13_1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1038\/s44286-026-00368-1","article-title":"Chemically Powered Active Particle Colonies","volume":"3","author":"Lu X.","year":"2026","journal-title":"Nature Chemical Engineering"},{"key":"e_1_2_8_14_1","doi-asserted-by":"crossref","DOI":"10.1002\/smll.202600030","article-title":"Biomolecular Machines as Active Matter: Kinetic Asymmetry and Nonequilibrium Function","volume":"22","author":"Astumian R. D.","year":"2026","journal-title":"Small"},{"key":"e_1_2_8_15_1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1146\/annurev-biophys-121219-081535","article-title":"Enhanced Diffusion and Chemotaxis of Enzymes","volume":"49","author":"Feng M.","year":"2020","journal-title":"Annual Review of Biophysics"},{"key":"e_1_2_8_16_1","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1038\/s41570-021-00281-6","article-title":"Chemically\u2010Powered Swimming and Diffusion in the Microscopic World","volume":"5","author":"Zhang Y.","year":"2021","journal-title":"Nature Reviews Chemistry"},{"key":"e_1_2_8_17_1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1038\/s41586-021-03375-9","article-title":"Non\u2010Reciprocal Phase Transitions","volume":"592","author":"Fruchart M.","year":"2021","journal-title":"Nature"},{"key":"e_1_2_8_18_1","doi-asserted-by":"crossref","first-page":"7035","DOI":"10.1038\/s41467-023-42713-5","article-title":"Non\u2010Reciprocity across Scales in Active Mixtures","volume":"14","author":"Dinelli A.","year":"2023","journal-title":"Nature Communications"},{"key":"e_1_2_8_19_1","doi-asserted-by":"crossref","DOI":"10.1103\/gphr-d1bc","article-title":"Phase Transitions in Nonreciprocal Driven\u2010Dissipative Condensates","volume":"135","author":"Belyansky R.","year":"2025","journal-title":"Physical Review Letters"},{"key":"e_1_2_8_20_1","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1038\/nchem.2905","article-title":"Substrate\u2010Driven Chemotactic Assembly in an Enzyme Cascade","volume":"10","author":"Zhao X.","year":"2018","journal-title":"Nature Chemistry"},{"key":"e_1_2_8_21_1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1038\/s41565-022-01258-2","article-title":"Non\u2010Reciprocal Multifarious Self\u2010Organization","volume":"18","author":"Osat S.","year":"2023","journal-title":"Nature Nanotechnology"},{"key":"e_1_2_8_22_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.xcrp.2025.102666","article-title":"Non\u2010Reciprocal Chemotactic Movement in Enzyme Cascade under Flow\u2010Free Conditions","volume":"6","author":"Sapre A.","year":"2025","journal-title":"Cell Reports Physical Science"},{"key":"e_1_2_8_23_1","doi-asserted-by":"crossref","DOI":"10.1080\/23746149.2019.1602480","article-title":"Thermodynamics and Statistical Mechanics of Chemically Powered Synthetic Nanomotors","volume":"4","author":"Gaspard P.","year":"2019","journal-title":"Advances in Physics X"},{"key":"e_1_2_8_24_1","doi-asserted-by":"crossref","first-page":"1406","DOI":"10.1021\/ja3091615","article-title":"Enzyme Molecules as Nanomotors","volume":"135","author":"Sengupta S.","year":"2013","journal-title":"Journal of the American Chemical Society"},{"key":"e_1_2_8_25_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.02.001","article-title":"Escapement Mechanisms and the Conversion of Disequilibria; the Engines of Creation","volume":"677","author":"Branscomb E.","year":"2017","journal-title":"Physics Reports"},{"key":"e_1_2_8_26_1","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.3390\/life13112171","article-title":"On the Emergence of Autonomous Chemical Systems through Dissipation Kinetics","volume":"13","author":"Pross A.","year":"2023","journal-title":"Life"}],"container-title":["Small"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/smll.74782","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/smll.74782","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/smll.74782","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T10:47:14Z","timestamp":1785322034000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/smll.74782"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,29]]},"references-count":25,"alternative-id":["10.1002\/smll.74782"],"URL":"https:\/\/doi.org\/10.1002\/smll.74782","archive":["Portico"],"relation":{},"ISSN":["1613-6810","1613-6829"],"issn-type":[{"value":"1613-6810","type":"print"},{"value":"1613-6829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,29]]},"assertion":[{"value":"2026-02-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e74782"}}