---
OA_place: publisher
OA_type: hybrid
_id: '19854'
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.'
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.
article_number: '11'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Samuel
full_name: Pastva, Samuel
id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
last_name: Pastva
orcid: 0000-0003-1993-0331
- first_name: Kyu Hyong
full_name: Park, Kyu Hyong
last_name: Park
- first_name: Ondřej
full_name: Huvar, Ondřej
last_name: Huvar
- first_name: Jordan C.
full_name: Rozum, Jordan C.
last_name: Rozum
- first_name: Réka
full_name: Albert, Réka
last_name: Albert
citation:
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? Journal of Mathematical
Biology. 2025;91. doi:10.1007/s00285-025-02235-8'
apa: 'Pastva, S., Park, K. H., Huvar, O., Rozum, J. C., & Albert, R. (2025).
An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean
networks? Journal of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s00285-025-02235-8'
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?” Journal of Mathematical Biology. Springer Nature, 2025.
https://doi.org/10.1007/s00285-025-02235-8.'
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?,”
Journal of Mathematical Biology, vol. 91. Springer Nature, 2025.'
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.'
mla: 'Pastva, Samuel, et al. “An Open Problem: Why Are Motif-Avoidant Attractors
so Rare in Asynchronous Boolean Networks?” Journal of Mathematical Biology,
vol. 91, 11, Springer Nature, 2025, doi:10.1007/s00285-025-02235-8.'
short: S. Pastva, K.H. Park, O. Huvar, J.C. Rozum, R. Albert, Journal of Mathematical
Biology 91 (2025).
corr_author: '1'
date_created: 2025-06-22T22:02:05Z
date_published: 2025-06-12T00:00:00Z
date_updated: 2025-09-30T13:36:46Z
day: '12'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/s00285-025-02235-8
ec_funded: 1
external_id:
arxiv:
- '2410.03976'
isi:
- '001507009300001'
file:
- access_level: open_access
checksum: a385ef2662f1d0c3497ed3f2721fe594
content_type: application/pdf
creator: dernst
date_created: 2025-06-23T11:10:01Z
date_updated: 2025-06-23T11:10:01Z
file_id: '19871'
file_name: 2025_JourMathBiology_Pastva.pdf
file_size: 1243163
relation: main_file
success: 1
file_date_updated: 2025-06-23T11:10:01Z
has_accepted_license: '1'
intvolume: ' 91'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Journal of Mathematical Biology
publication_identifier:
eissn:
- 1432-1416
issn:
- 0303-6812
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'An open problem: Why are motif-avoidant attractors so rare in asynchronous
Boolean networks?'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 91
year: '2025'
...