Boolean network
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Boolean networks (BNs) are a well-accepted modelling formalism in computational systems biology. Nevertheless, modellers often cannot identify only a single BN that matches the biological reality. The typical reasons for this is insufficient knowledge or a lack of experimental data. Formally, this uncertainty can be expressed using partially specified Boolean networks (PSBNs), which encode the wide range of network candidates into a single structure. In this paper, we target the control of PSBNs. The goal of BN control is to find perturbations which guarantee stabilisation of the system in the desired state. Specifically, we consider variable perturbations (gene knock-out and over-expression) with three types of application time-window: one-step, temporary, and permanent. While the control of fully specified BNs is a thoroughly explored topic, control of PSBNs introduces additional challenges that we address in this paper. In particular, the unspecified components of the model cause a significant amount of additional state space explosion. To address this issue, we propose a fully symbolic methodology that can represent the numerous system variants in a compact form. In fully specified models, the efficiency of a perturbation is characterised by the count of perturbed variables (the perturbation size). However, in the case of a PSBN, a perturbation might work only for a subset of concrete BN models. To that end, we introduce and quantify perturbation robustness. This metric characterises how efficient the given perturbation is with respect to the model uncertainty. Finally, we evaluate the novel control methods using non-trivial real-world PSBN models. We inspect the method's scalability and efficiency with respect to the size of the state space and the number of unspecified components. We also compare the robustness metrics for all three perturbation types. Our experiments support the hypothesis that one-step perturbations are significantly less robust than temporary and permanent ones.
- Klíčová slova
- Boolean network, Permanent control, Perturbation, Symbolic algorithm, Temporary control,
- MeSH
- algoritmy MeSH
- genové regulační sítě * MeSH
- systémová biologie * MeSH
- Publikační typ
- časopisecké články MeSH
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 AND IMPLEMENTATION: All software and data are freely available as a reproducible artefact at https://doi.org/10.5281/zenodo.7688740.
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.
- Klíčová slova
- Attractor bifurcation, Boolean networks, Software tool, Symbolic computation, type-1 interferons,
- MeSH
- algoritmy MeSH
- aniliny MeSH
- benzamidy MeSH
- COVID-19 * MeSH
- genové regulační sítě * MeSH
- lidé MeSH
- modely genetické MeSH
- naftaleny MeSH
- SARS-CoV-2 MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- Názvy látek
- 5-amino-2-methyl-N-((R)-1-(1-naphthyl)ethyl)benzamide MeSH Prohlížeč
- aniliny MeSH
- benzamidy MeSH
- naftaleny MeSH
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.
- Klíčová slova
- Biomolecular networks, Boolean models, Boolean networks, Complex systems, Discrete dynamics, Stable motif, Trap spaces,
- MeSH
- biologické modely * MeSH
- fenotyp MeSH
- genové regulační sítě MeSH
- lidé MeSH
- matematické pojmy MeSH
- počítačová simulace MeSH
- systémová biologie statistika a číselné údaje MeSH
- výpočetní biologie MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
MOTIVATION: Boolean networks are popular dynamical models of cellular processes in systems biology. Their attractors model phenotypes that arise from the interplay of key regulatory subcircuits. A succession diagram (SD) describes this interplay in a discrete analog of Waddington's epigenetic attractor landscape that allows for fast identification of attractors and attractor control strategies. Efficient computational tools for studying SDs are essential for the understanding of Boolean attractor landscapes and connecting them to their biological functions. RESULTS: We present a new approach to SD construction for asynchronously updated Boolean networks, implemented in the biologist's Boolean attractor landscape mapper, biobalm. We compare biobalm to similar tools and find a substantial performance increase in SD construction, attractor identification, and attractor control. We perform the most comprehensive comparative analysis to date of the SD structure in experimentally-validated Boolean models of cell processes and random ensembles. We find that random models (including critical Kauffman networks) have relatively small SDs, indicating simple decision structures. In contrast, nonrandom models from the literature are enriched in extremely large SDs, indicating an abundance of decision points and suggesting the presence of complex Waddington landscapes in nature. AVAILABILITY AND IMPLEMENTATION: The tool biobalm is available online at https://github.com/jcrozum/biobalm. Further data, scripts for testing, analysis, and figure generation are available online at https://github.com/jcrozum/biobalm-analysis and in the reproducibility artefact at https://doi.org/10.5281/zenodo.13854760.
BACKGROUND: Computational models in systems biology are becoming more important with the advancement of experimental techniques to query the mechanistic details responsible for leading to phenotypes of interest. In particular, Boolean models are well fit to describe the complexity of signaling networks while being simple enough to scale to a very large number of components. With the advance of Boolean model inference techniques, the field is transforming from an artisanal way of building models of moderate size to a more automatized one, leading to very large models. In this context, adapting the simulation software for such increases in complexity is crucial. RESULTS: We present two new developments in the continuous time Boolean simulators: MaBoSS.MPI, a parallel implementation of MaBoSS which can exploit the computational power of very large CPU clusters, and MaBoSS.GPU, which can use GPU accelerators to perform these simulations. CONCLUSION: These implementations enable simulation and exploration of the behavior of very large models, thus becoming a valuable analysis tool for the systems biology community.
- Klíčová slova
- Boolean models, Computational biology, High performance computing,
- MeSH
- algoritmy MeSH
- počítačová grafika MeSH
- počítačová simulace * MeSH
- software * MeSH
- systémová biologie metody MeSH
- výpočetní biologie metody MeSH
- Publikační typ
- časopisecké články MeSH
SUMMARY: 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 at Bioinformatics online.
- MeSH
- genová knihovna MeSH
- software * MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Computational models of gene regulations help to understand regulatory mechanisms and are extensively used in a wide range of areas, e.g., biotechnology or medicine, with significant benefits. Unfortunately, there are only a few computational gene regulatory models of whole genomes allowing static and dynamic analysis due to the lack of sophisticated tools for their reconstruction. Here, we describe Augusta, an open-source Python package for Gene Regulatory Network (GRN) and Boolean Network (BN) inference from the high-throughput gene expression data. Augusta can reconstruct genome-wide models suitable for static and dynamic analyses. Augusta uses a unique approach where the first estimation of a GRN inferred from expression data is further refined by predicting transcription factor binding motifs in promoters of regulated genes and by incorporating verified interactions obtained from databases. Moreover, a refined GRN is transformed into a draft BN by searching in the curated model database and setting logical rules to incoming edges of target genes, which can be further manually edited as the model is provided in the SBML file format. The approach is applicable even if information about the organism under study is not available in the databases, which is typically the case for non-model organisms including most microbes. Augusta can be operated from the command line and, thus, is easy to use for automated prediction of models for various genomes. The Augusta package is freely available at github.com/JanaMus/Augusta. Documentation and tutorials are available at augusta.readthedocs.io.
- Klíčová slova
- Databases, Gene interactions, Mutual information, Python package, Transcription factor binding motifs,
- Publikační typ
- časopisecké články MeSH
We give upper bounds on rates of approximation of real-valued functions of d Boolean variables by one-hidden-layer perceptron networks. Our bounds are of the form c/n where c depends on certain norms of the function being approximated and n is the number of hidden units. We describe sets of functions where these norms grow either polynomially or exponentially with d.
- Publikační typ
- časopisecké články MeSH
We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET). The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network.
