[{"external_id":{"arxiv":["2410.03976"],"isi":["001507009300001"]},"OA_place":"publisher","arxiv":1,"publication_identifier":{"issn":["0303-6812"],"eissn":["1432-1416"]},"file_date_updated":"2025-06-23T11:10:01Z","article_type":"original","acknowledgement":"Ondřej Huvar has been supported by the Czech Science Foundation grant No. GA22-10845S. Samuel Pastva received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101034413. Kyu Hyong Park and Réka Albert have been supported by NSF grant MCB 1715826 and ARO grant 79961-SM-MUR. No funding bodies had any role in study design, analysis, decision to publish, or preparation of the manuscript.","day":"12","date_updated":"2025-09-30T13:36:46Z","title":"An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?","author":[{"full_name":"Pastva, Samuel","id":"07c5ea74-f61c-11ec-a664-aa7c5d957b2b","last_name":"Pastva","orcid":"0000-0003-1993-0331","first_name":"Samuel"},{"last_name":"Park","first_name":"Kyu Hyong","full_name":"Park, Kyu Hyong"},{"last_name":"Huvar","first_name":"Ondřej","full_name":"Huvar, Ondřej"},{"last_name":"Rozum","first_name":"Jordan C.","full_name":"Rozum, Jordan C."},{"last_name":"Albert","first_name":"Réka","full_name":"Albert, Réka"}],"doi":"10.1007/s00285-025-02235-8","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"mla":"Pastva, Samuel, et al. “An Open Problem: Why Are Motif-Avoidant Attractors so Rare in Asynchronous Boolean Networks?” <i>Journal of Mathematical Biology</i>, vol. 91, 11, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00285-025-02235-8\">10.1007/s00285-025-02235-8</a>.","ieee":"S. Pastva, K. H. Park, O. Huvar, J. C. Rozum, and R. Albert, “An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?,” <i>Journal of Mathematical Biology</i>, vol. 91. Springer Nature, 2025.","apa":"Pastva, S., Park, K. H., Huvar, O., Rozum, J. C., &#38; Albert, R. (2025). An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks? <i>Journal of Mathematical Biology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00285-025-02235-8\">https://doi.org/10.1007/s00285-025-02235-8</a>","ista":"Pastva S, Park KH, Huvar O, Rozum JC, Albert R. 2025. An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks? Journal of Mathematical Biology. 91, 11.","ama":"Pastva S, Park KH, Huvar O, Rozum JC, Albert R. An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks? <i>Journal of Mathematical Biology</i>. 2025;91. doi:<a href=\"https://doi.org/10.1007/s00285-025-02235-8\">10.1007/s00285-025-02235-8</a>","chicago":"Pastva, Samuel, Kyu Hyong Park, Ondřej Huvar, Jordan C. Rozum, and Réka Albert. “An Open Problem: Why Are Motif-Avoidant Attractors so Rare in Asynchronous Boolean Networks?” <i>Journal of Mathematical Biology</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00285-025-02235-8\">https://doi.org/10.1007/s00285-025-02235-8</a>.","short":"S. Pastva, K.H. Park, O. Huvar, J.C. Rozum, R. Albert, Journal of Mathematical Biology 91 (2025)."},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"volume":91,"department":[{"_id":"ToHe"}],"scopus_import":"1","quality_controlled":"1","oa_version":"Published Version","_id":"19854","oa":1,"type":"journal_article","isi":1,"ec_funded":1,"date_published":"2025-06-12T00:00:00Z","article_number":"11","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file":[{"file_size":1243163,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2025-06-23T11:10:01Z","creator":"dernst","checksum":"a385ef2662f1d0c3497ed3f2721fe594","file_name":"2025_JourMathBiology_Pastva.pdf","date_updated":"2025-06-23T11:10:01Z","file_id":"19871","success":1}],"year":"2025","article_processing_charge":"Yes (in subscription journal)","publication_status":"published","intvolume":"        91","OA_type":"hybrid","language":[{"iso":"eng"}],"publisher":"Springer Nature","has_accepted_license":"1","abstract":[{"lang":"eng","text":"Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular in systems biology due to their ability to model long-term biological phenotypes within a qualitative, predictive framework. Boolean networks model phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable hypercubes in the system’s state space). In biological applications, attractors and minimal trap spaces are typically in one-to-one correspondence. However, this correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside minimal trap spaces are possible. MAAs are rare and poorly understood, despite recent efforts. In this contribution to the BMB & JMB Special Collection “Problems, Progress and Perspectives in Mathematical and Computational Biology”, we summarize the current state of knowledge regarding MAAs and present several novel observations regarding their response to node deletion reductions and linear extensions of edges. We conduct large-scale computational studies on an ensemble of 14 000 models derived from published Boolean models of biological systems, and more than 100 million Random Boolean Networks. Our findings quantify the rarity of MAAs; in particular, we only observed MAAs in biological models after applying standard simplification methods, highlighting the role of network reduction in introducing MAAs into the dynamics. We also show that MAAs are fragile to linear extensions: in sparse networks, even a single linear node can disrupt virtually all MAAs. Motivated by this observation, we improve the upper bound on the number of delays needed to disrupt a motif-avoidant attractor."}],"date_created":"2025-06-22T22:02:05Z","publication":"Journal of Mathematical Biology","status":"public","month":"06","ddc":["000"],"corr_author":"1"}]