Boolean modelling of gene regulation but also of post-transcriptomic systems has proven over the years that it can bring powerful analyses and corresponding insight to the many cases where precise biological data is not sufficiently available to build a detailed quantitative model. This is even more true for very large models where such data is frequently missing and led to a constant increase in size of logical models à la Thomas. Besides simulation, the analysis of such models is mostly based on attractor computation, since those correspond roughly to observable biological phenotypes. The recent use of trap spaces made a real breakthrough in that field allowing to consider medium-sized models that used to be out of reach. However, with the continuing increase in model-size, the state-of-the-art computation of minimal trap spaces based on prime-implicants shows its limits as there can be a huge number of implicants.In this article we present an alternative method to compute minimal trap spaces, and hence complex attractors, of a Boolean model. It replaces the need for prime-implicants by a completely different technique, namely the enumeration of maximal siphons in the Petri net encoding of the original model. After some technical preliminaries, we expose the concrete need for such a method and detail its implementation using Answer Set Programming. We then demonstrate its efficiency and compare it to implicant-based methods on some large Boolean models from the literature.

Boolean Networks (BNs) play a crucial role in modeling, analyzing, and controlling biological systems. One of the most important problems on BNs is to compute all the possible attractors of a BN. There are two popular types of BNs, Synchronous BNs (SBNs) and Asynchronous BNs (ABNs). Although ABNs are considered more suitable than SBNs in modeling real-world biological systems, their attractor computation is more challenging than that of SBNs. Several methods have been proposed for computing attractors of ABNs. However, none of them can robustly handle large and complex models. In this paper, we propose a novel method called mtsNFVS for exactly computing all the attractors of an ABN based on its minimal trap spaces, where a trap space is a subspace of state space that no path can leave. The main advantage of mtsNFVS lies in opening the chance to reach easy cases for the attractor computation. We then evaluate mtsNFVS on a set of large and complex real-world models with crucial biologically motivations as well as a set of randomly generated models. The experimental results show that mtsNFVS can easily handle large-scale models and it completely outperforms the state-of-the-art method CABEAN as well as other recently notable methods.

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Motivation Boolean networks are simple but efficient mathematical formalism for modelling complex biological systems. However, having only two levels of activation is sometimes not enough to fully capture the dynamics of real-world biological systems. Hence, the need for multi-valued networks (MVNs), a generalization of Boolean networks. Despite the importance of MVNs for modelling biological systems, only limited progress has been made on developing theories, analysis methods, and tools that can support them. In particular, the recent use of trap spaces in Boolean networks made a great impact on the field of systems biology, but there has been no similar concept defined and studied for MVNs to date. Results In this work, we generalize the concept of trap spaces in Boolean networks to that in MVNs. We then develop the theory and the analysis methods for trap spaces in MVNs. In particular, we implement all proposed methods in a Python package called trapmvn. Not only showing the applicability of our approach via a realistic case study, we also evaluate the time efficiency of the method on a large collection of real-world models. The experimental results confirm the time efficiency, which we believe enables more accurate analysis on larger and more complex multi-valued models. Availability and implementation Source code and data are freely available at https://github.com/giang-trinh/trap-mvn.