Nikola Beneš’s research while affiliated with Masaryk University and other places

Partially specified Boolean networks (PSBNs) represent a promising framework for the qualitative modelling of biological systems in which the logic of interactions is not completely known. Phenotype control aims to stabilise the network in states exhibiting specific traits.In this paper, we define the phenotype control problem in the context of asynchronous PSBNs and propose a novel semi-symbolic algorithm for solving this problem with permanent variable perturbations.

Recent developments in both computational analysis and data-driven synthesis enable a new era of automated reasoning with logical models (Boolean networks in particular) in systems biology. However, these advancements also motivate an increased focus on quality control and performance comparisons between tools. At the moment, to illustrate real-world applicability, authors typically test their approaches on small sets of manually curated models that are inherently limited in scope. This further complicates reuse and comparisons, because benchmark models often contain ad hoc modifications or are outright not available. In this paper, we describe a new, comprehensive, open source dataset of 210+ Boolean network models compiled from available databases and a literature survey. The models are available in a wide range of formats. Furthermore, the dataset is accompanied by a validation pipeline that ensures the integrity and logical consistency of each model. Using this pipeline, we identified and repaired 400+ potential problems in a number of widely used models.

Motivation: The problem of model inference is of fundamental importance to systems biology. Logical models (e.g., Boolean networks; BNs) represent a computationally attractive approach capable of handling large biological networks. The models are typically inferred from experimental data. However, even with a substantial amount of experimental data supported by some prior knowledge, existing inference methods often focus on a small sample of admissible candidate models only. Results: We propose Boolean network sketches as a new formal instrument for the inference of Boolean networks. A sketch integrates (typically partial) knowledge about the network's topology and the update logic (obtained through, e.g., a biological knowledge base or a literature search), as well as further assumptions about the properties of the network's transitions (e.g., the form of its attractor landscape), and additional restrictions on the model dynamics given by the measured experimental data. Our new BNs inference algorithm starts with an initial sketch which is extended by adding restrictions representing experimental data to a data-informed sketch and subsequently computes all BNs consistent with the data-informed sketch. Our algorithm is based on a symbolic representation and coloured model-checking. Our approach is unique in its ability to cover a broad spectrum of knowledge and efficiently produce a compact representation of all inferred BNs. We evaluate the method on a non-trivial collection of real-world and simulated data. Availability: All software and data are freely available as a reproducible artefact at https://doi.org/10.5281/zenodo.7688740. Supplementary information: Supplementary data available online through Bioinformatics.

AEON.py is a Python library for the analysis of the long-term behaviour in very large asynchronous Boolean networks. It provides significant computational improvements over the state of the art methods for attractor detection. Furthermore, it admits the analysis of partially specified Boolean networks with uncertain update functions. It also includes techniques for identifying viable source-target control strategies and the assessment of their robustness with respect to parameter perturbations. Availability and Implementation All relevant results are available in supplementary materials. The tool is accessible through https://github.com/sybila/biodivine-aeon-py. Supplementary information Supplementary data are available online through Bioinformatics.

Background Boolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors–subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks. Results In this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method’s applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus. Conclusions The proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system’s stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where p is the number of colours and n is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

Aeon is a recent tool which enables efficient analysis of long-term behaviour of asynchronous Boolean networks with unknown parameters. In this tool paper, we present a novel major release of Aeon (Aeon 2021) which introduces substantial new features compared to the original version. These include (i) enhanced static analysis functionality that verifies integrity of the Boolean network with its regulatory graph; (ii) state-space visualisation of individual attractors; (iii) stability analysis of network variables with respect to parameters; and finally, (iv) a novel decision-tree based interactive visualisation module allowing the exploration of complex relationships between parameters and network behaviour. Aeon 2021 is open-source, fully compatible with SBML-qual models, and available as an online application with an independent native compute engine responsible for resource-intensive tasks. The paper artefact is available via https://doi.org/10.5281/zenodo.5008293.

Edge-coloured directed graphs provide an essential structure for modelling and computing complex problems arising in many scientific disciplines. The size of edge-coloured graphs appearing in practice can be enormous in the number of both vertices and colours. An important fundamental problem that needs to be solved over edge-coloured graphs is detecting strongly connected components. The problem becomes challenging for large graphs with a large number of colours. In this paper, we describe a novel symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot \log n)$ symbolic steps, where p is the number of colours and n is the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $2^{48}$) coloured graphs produced by models appearing in systems biology.

Detection of bottom strongly connected components (BSCC) in state-transition graphs is an important problem with many applications, such as detecting recurrent states in Markov chains or attractors in dynamical systems. However, these graphs’ size is often entirely out of reach for algorithms using explicit state-space exploration, necessitating alternative approaches such as the symbolic one. Symbolic methods for BSCC detection often show impressive performance, but can sometimes take a long time to converge in large graphs. In this paper, we provide a symbolic state-space reduction method for labelled transition systems, called interleaved transition guided reduction (ITGR), which aims to alleviate current problems of BSCC detection by efficiently identifying large portions of the non-BSCC states. We evaluate the suggested heuristic on an extensive collection of 125 real-world biologically motivated systems. We show that ITGR can easily handle all these models while being either the only method to finish, or providing at least an order-of-magnitude speedup over existing state-of-the-art methods. We then use a set of synthetic benchmarks to demonstrate that the technique also consistently scales to graphs with more than $2^{1000}$ 2 1000 vertices, which was not possible using previous methods.