Boolean network Dotaz Zobrazit nápovědu
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
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
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: 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
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.
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
It has been known for discrete-time recurrent neural networks (NNs) that binary-state models using the Heaviside activation function (with Boolean outputs 0 or 1) are equivalent to finite automata (level 3 in the Chomsky hierarchy), while analog-state NNs with rational weights, employing the saturated-linear function (with real-number outputs in the interval [0,1]), are Turing complete (Chomsky level 0) even for three analog units. However, it is as yet unknown whether there exist subrecursive (i.e. sub-Turing) NN models which occur on Chomsky levels 1 or 2. In this paper, we provide such a model which is a binary-state NN extended with one extra analog unit (1ANN). We achieve a syntactic characterization of languages that are accepted online by 1ANNs in terms of so-called cut languages which are combined in a certain way by usual operations. We employ this characterization for proving that languages accepted by 1ANNs with rational weights are context-sensitive (Chomsky level 1) and we present explicit examples of such languages that are not context-free (i.e. are above Chomsky level 2). In addition, we formulate a sufficient condition when a 1ANN recognizes a regular language (Chomsky level 3) in terms of quasi-periodicity of parameters derived from its real weights, which is satisfied e.g. for rational weights provided that the inverse of the real self-loop weight of the analog unit is a Pisot number.
- Klíčová slova
- Chomsky hierarchy, Cut language, Quasi-periodic number, Recurrent neural network,
- MeSH
- jazyk (prostředek komunikace) * MeSH
- neuronové sítě (počítačové) * MeSH
- teoretické modely * MeSH
- Publikační typ
- časopisecké články MeSH
This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for the extraction of fuzzy rules. Two important theoretical properties of piecewise-linear neural networks are proved, allowing an elaboration of the basic ideas of the approach into several variants of an algorithm for the extraction of Boolean rules. That algorithm has already been used in two real-world applications. Finally, a connection to the extraction of rules of the Łukasiewicz logic is established, relying on recent results about rational McNaughton functions. Based on one of the constructive proofs of the McNaughton theorem, an algorithm is formulated that in principle allows extracting a particular kind of formulas of the Łukasiewicz predicate logic from piecewise-linear neural networks trained with rational data.
- MeSH
- algoritmy * MeSH
- ekologie MeSH
- fuzzy logika MeSH
- interpretace statistických dat * MeSH
- lidé MeSH
- lineární modely * MeSH
- neuronové sítě (počítačové) * MeSH
- rozpoznávání automatizované metody MeSH
- umělá inteligence MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
