{"month":"01","has_accepted_license":"1","external_id":{"arxiv":["2510.24536"]},"article_type":"original","quality_controlled":"1","status":"public","project":[{"grant_number":"101118866","name":"Transcription in 4D: the dynamic interplay between chromatin architecture and gene expression in developing pseudo-embryos","_id":"7bfe6a29-9f16-11ee-852c-c0da5e2045d9"}],"abstract":[{"lang":"eng","text":"Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes—as well as the continuum of intermediate cases—can be conceptualized as information-processing systems, whose operation can be described using “Marr's three levels of analysis”: the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information-processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models."}],"OA_type":"gold","acknowledgement":"We thank Edouard Hannezo, Anna Kicheva, Fridtjof Brauns, and all members of the Brückner and Tkačik groups for feedback and inspiring discussions. This work was supported in part by European Research Council ERC-2023-SyG “Dynatrans” Grant No. 101118866 (G.T.). This work was conducted while visiting the Okinawa Institute of Science and Technology (OIST) through the Theoretical Sciences Visiting Program (TSVP); at the Kavli Institute for Theoretical Physics (KITP) Santa Barbara, supported by NSF Grant No. PHY-1748958 and the Gordon and Betty Moore Foundation Grant No. 2919.02; and at Lucullus, Vienna.","citation":{"chicago":"Brückner, David, and Gašper Tkačik. “Marr’s Three Levels for Embryonic Development: Information, Dynamical Systems, Gene Networks.” <i>PRX Life</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/fdcf-dkws\">https://doi.org/10.1103/fdcf-dkws</a>.","ista":"Brückner D, Tkačik G. 2026. Marr’s three levels for embryonic development: Information, dynamical systems, gene networks. PRX Life. 4, 017001.","mla":"Brückner, David, and Gašper Tkačik. “Marr’s Three Levels for Embryonic Development: Information, Dynamical Systems, Gene Networks.” <i>PRX Life</i>, vol. 4, 017001, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/fdcf-dkws\">10.1103/fdcf-dkws</a>.","apa":"Brückner, D., &#38; Tkačik, G. (2026). Marr’s three levels for embryonic development: Information, dynamical systems, gene networks. <i>PRX Life</i>. American Physical Society. <a href=\"https://doi.org/10.1103/fdcf-dkws\">https://doi.org/10.1103/fdcf-dkws</a>","ama":"Brückner D, Tkačik G. Marr’s three levels for embryonic development: Information, dynamical systems, gene networks. <i>PRX Life</i>. 2026;4. doi:<a href=\"https://doi.org/10.1103/fdcf-dkws\">10.1103/fdcf-dkws</a>","ieee":"D. Brückner and G. Tkačik, “Marr’s three levels for embryonic development: Information, dynamical systems, gene networks,” <i>PRX Life</i>, vol. 4. American Physical Society, 2026.","short":"D. Brückner, G. Tkačik, PRX Life 4 (2026)."},"date_updated":"2026-02-24T07:00:16Z","file_date_updated":"2026-02-24T06:57:44Z","article_number":"017001","arxiv":1,"_id":"21282","publication":"PRX Life","department":[{"_id":"GaTk"}],"date_created":"2026-02-17T08:29:10Z","oa":1,"volume":4,"ddc":["570"],"date_published":"2026-01-23T00:00:00Z","day":"23","DOAJ_listed":"1","oa_version":"Published Version","title":"Marr's three levels for embryonic development: Information, dynamical systems, gene networks","article_processing_charge":"Yes","PlanS_conform":"1","publication_identifier":{"eissn":["2835-8279"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"author":[{"id":"e1e86031-6537-11eb-953a-f7ab92be508d","last_name":"Brückner","first_name":"David","full_name":"Brückner, David","orcid":"0000-0001-7205-2975"},{"full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455","first_name":"Gašper","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","last_name":"Tkačik"}],"file":[{"file_id":"21352","date_updated":"2026-02-24T06:57:44Z","success":1,"date_created":"2026-02-24T06:57:44Z","checksum":"99ef02dd741c4536eeefd12d409d5269","file_name":"2026_PRXLife_Brueckner.pdf","relation":"main_file","content_type":"application/pdf","file_size":1147994,"creator":"dernst","access_level":"open_access"}],"publication_status":"published","type":"journal_article","OA_place":"publisher","language":[{"iso":"eng"}],"corr_author":"1","publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1103/fdcf-dkws","intvolume":"         4","year":"2026"}