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Reducing Boolean networks with backward equivalence

BACKGROUND: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space expl...

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Autores principales: Argyris, Georgios A., Lluch Lafuente, Alberto, Tribastone, Mirco, Tschaikowski, Max, Vandin, Andrea
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BioMed Central 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10207686/
https://www.ncbi.nlm.nih.gov/pubmed/37221494
http://dx.doi.org/10.1186/s12859-023-05326-9
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author Argyris, Georgios A.
Lluch Lafuente, Alberto
Tribastone, Mirco
Tschaikowski, Max
Vandin, Andrea
author_facet Argyris, Georgios A.
Lluch Lafuente, Alberto
Tribastone, Mirco
Tschaikowski, Max
Vandin, Andrea
author_sort Argyris, Georgios A.
collection PubMed
description BACKGROUND: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. RESULTS: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. CONCLUSIONS: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12859-023-05326-9.
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spelling pubmed-102076862023-05-25 Reducing Boolean networks with backward equivalence Argyris, Georgios A. Lluch Lafuente, Alberto Tribastone, Mirco Tschaikowski, Max Vandin, Andrea BMC Bioinformatics Research BACKGROUND: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. RESULTS: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. CONCLUSIONS: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12859-023-05326-9. BioMed Central 2023-05-23 /pmc/articles/PMC10207686/ /pubmed/37221494 http://dx.doi.org/10.1186/s12859-023-05326-9 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/ (https://creativecommons.org/publicdomain/zero/1.0/) ) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
spellingShingle Research
Argyris, Georgios A.
Lluch Lafuente, Alberto
Tribastone, Mirco
Tschaikowski, Max
Vandin, Andrea
Reducing Boolean networks with backward equivalence
title Reducing Boolean networks with backward equivalence
title_full Reducing Boolean networks with backward equivalence
title_fullStr Reducing Boolean networks with backward equivalence
title_full_unstemmed Reducing Boolean networks with backward equivalence
title_short Reducing Boolean networks with backward equivalence
title_sort reducing boolean networks with backward equivalence
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10207686/
https://www.ncbi.nlm.nih.gov/pubmed/37221494
http://dx.doi.org/10.1186/s12859-023-05326-9
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