Reducing Boolean Networks with Backward Boolean Equivalence

Argyris, Georgios; Lafuente, Alberto Lluch; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea

doi:10.1007/978-3-030-85633-5_1

Cited by 3 publications

(7 citation statements)

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“…They are usually associated with important behaviours of the underlying system: for instance, different attractors correspond to different cell types in cell differentiation processes [2]. In [1], we present cases wherein BBE reduction can enable of facilitate these tasks. Input and Output Variables.…”

Section: An Illustration Of Bbe Reductionmentioning

confidence: 99%

“…Given a BBE partition, we can create a BBE-reduced BN containing one variable per partition block. We have shown in [1] that this can be used to study selected part of the original dynamics.…”

Section: Preliminariesmentioning

confidence: 99%

“…The splitting is done by an iterative partition refinement algorithm [17]. In each iteration, the Z3 SAT solver [7], integrated in ERODE, checks the validity of the SAT-encoding of the BBE criterion (see [1]); if valid, the current partition is a BBE; if invalid, Z3 returns a counter-example according to which the splitting is performed. Once we get to a partition for which the formula is valid, (iii) ERODE produces the reduced BN according to the resulting BBE partition by collapsing all variables that belong to the same block into single variable components.…”

Section: An Illustration Of Bbe Reductionmentioning

confidence: 99%

“…1; the BN has 6 variables, leading to 2 6 states. For the tractability of large BNs, several reduction techniques have been proposed (e.g., [1,16,19]). One of the most popular reduction methods is based on fast-slow decomposition, studied in [16,19] Her6 (t +1 ) = ¬miR9 (t) ∧ ¬N (t) HuC (t +1 ) = ¬miR9 (t) ∧ ¬P (t) N (t +1 ) = HuC (t)…”

Section: Introductionmentioning

confidence: 99%

“…and implemented in GINsim [5]. Here, we present an extension of ERODE [3], a tool for modelling, analysis, and reduction of biological models that implements a complementary method of reduction for BNs called Boolean Backward Equivalence (BBE) [1]. Originally, ERODE was developed to support chemical reaction networks, and systems of ordinary differential equations [3].…”

Section: Introductionmentioning

confidence: 99%

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An Extension of ERODE to Reduce Boolean Networks By Backward Boolean Equivalence

Argyris

Lafuente

Tribastone

et al. 2022

Computational Methods in Systems Biology

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Boolean Networks (BN) are established tools for modelling biological systems. However, their analysis is hindered by the state space explosion: the exponentially many states on the variables of a BN. We present an extension of the tool for model reduction ERODE with support for BNs and their reduction with a recent method called Backward Boolean Equivalence (BBE). BBE identifies maximal sets of variables that retain the same value whenever initialized equally. ERODE has been also extended to support importing and exporting between different formats and model repositories, enhancing interoperability with other tools.

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Section: An Illustration Of Bbe Reductionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: An Illustration Of Bbe Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Extension of ERODE to Reduce Boolean Networks By Backward Boolean Equivalence

Argyris

Lafuente

Tribastone

et al. 2022

Computational Methods in Systems Biology

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Minimization of Dynamical Systems over Monoids

Argyris

Lafuente

Robayo

et al. 2023

2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Reducing Boolean networks with backward equivalence

et al. 2023

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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.

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Reducing Boolean Networks with Backward Boolean Equivalence

Cited by 3 publications

References 48 publications

An Extension of ERODE to Reduce Boolean Networks By Backward Boolean Equivalence

An Extension of ERODE to Reduce Boolean Networks By Backward Boolean Equivalence

Minimization of Dynamical Systems over Monoids

Reducing Boolean networks with backward equivalence

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