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AbstractAlthough there is a plethora of methods to estimate sensitivity indices associated with individual inputs, there is much less work on interaction effects of every order, especially when it comes to make inferences about the true underlying values of the indices. To fill this gap, a method that allows one to make such inferences simultaneously from a Monte Carlo sample is given. One advantage of this method is its simplicity: it leverages the fact that Shapley effects and Sobol indices are only linear transformations of total indices, so that standard asymptotic theory suffices to get confidence intervals and to carry out statistical tests. To perform the numerical computations efficiently, Möbius inversion formulas are used, and linked to the fast Möbius transform algorithm. The method is illustrated on two dynamical systems, both with an application in life sciences: a Boolean network modeling a cellular decision-making process involving 12 inputs, and a system of ordinary differential equations modeling some population dynamics involving 10 inputs. [ABSTRACT FROM AUTHOR]

The cell cycle of budding yeast is governed by an intricate protein regulatory network whose dysregulation can lead to lethal mistakes or aberrant cell division cycles. In this work, we model this network in a Boolean framework for stochastic simulations. Our model is sufficiently detailed to account for the phenotypes of 40 mutant yeast strains (83% of the experimentally characterized strains that we simulated) and also to simulate an endoreplicating strain (multiple rounds of DNA synthesis without mitosis) and a strain that exhibits 'Cdc14 endocycles' (periodic transitions between metaphase and anaphase). Because our model successfully replicates the observed properties of both wild-type yeast cells and many mutant strains, it provides a reasonable, validated starting point for more comprehensive stochastic-Boolean models of cell cycle controls. Such models may provide a better understanding of cell cycle anomalies in budding yeast and ultimately in mammalian cells. [ABSTRACT FROM AUTHOR]

In-field trees are thought to buffer arable crops from climate extremes through the creation of microclimates that may reduce the impacts of heat, wind, and cold. Much less is known about how trees and their biotic interactions (e.g. with natural enemies of pests and wild understory plants) impact crop yield stability to biotic stresses such as crop pests and disease. Modelling these interactions using conventional approaches is complex and time consuming, and we take a simplified approach, representing the agroecosystem as a Boolean regulatory network and parameterising Boolean functions using expert opinion. This allies our approach with decision analysis, which is increasingly finding applications in agriculture. Despite the naivety of our model, we demonstrate that it outputs complex and realistic agroecosystem dynamics. It predicts that, in English silvoarable, the biotic interactions of in-field trees boost arable crop yield overall, but they do not increase yield stability to biotic stress. Sensitivity analysis shows that arable crop yield is very sensitive to disease and weeds. We suggest that the focus of studies and debate on ecosystem service provision by English agroforestry needs to shift from natural enemies and pests to these ecosystem components. We discuss how our model can be improved through validation and parameterisation using real field data. Finally, we discuss how our approach can be used to rapidly model systems (agricultural or otherwise) than can be represented as dynamic interaction networks. [ABSTRACT FROM AUTHOR]

In this paper, the minimal observability of switching Boolean networks (SBNs) is investigated. Firstly, applying the semi‐tensor product (STP) method of matrices, a parallel extension system is constructed, based on which a necessary and sufficient condition to detect the observability of the SBNs is given. Secondly, when an SBN is unobservable, the specific steps to obtain the required measurements to make the system observable are given using the set reachable method; however, the measurements given in this part are not necessarily the fewest. Then, a criterion for determining the minimum number of measurements is further proposed through a constructed indicator matrix. Lastly, the effectiveness of the new results is verified by an example. [ABSTRACT FROM AUTHOR]

The article titled "A Criterion of Properness for a Family of Functions" explores the concept of proper families of functions and their applications in different areas, such as cryptography. It introduces the idea of properness and investigates the actions and transformations that maintain properness. The article also discusses the isometry group of the space and its connection to weak isometries. It concludes by stating that properness-preserving transformations can be represented as compositions of reencodings and consistent renumberings of families. The text acknowledges that there are other types of transformations not covered in the paper. [Extracted from the article]

ABSTRACT With the rise of the Internet and electronic devices, the security of network information is gaining attention, and the true random number generator (TRNG) is playing an increasingly crucial role in information security. TRNG, based on Boolean chaotic entropy source, has drawn significant interest due to its uncomplicated circuit design and minimal hardware resource usage. However, most existing structures consist of two‐input or three‐input logic devices, forming a complex multinode, geometrically symmetric Boolean chaotic network using multiple logic devices. This network configuration results in increased complexity and reduced throughput. This study introduces an entropy source based on Boolean chaos utilizing single‐node and four‐input XOR gates, which can be easily placed and routed on Xilinx Artix‐7 FPGA. It requires only 29 LUTs and 5 DFFs without any postprocessing, achieving a throughput of up to 700 Mb/s. The output of TRNG has successfully passed various tests including the autocorrelation test, NIST SP800‐22, NIST SP800‐90B, AIS‐31, and TESTU01 tests with favorable results. Furthermore, by applying a three‐stage XOR chain postprocessing on Xilinx Spartan‐6 FPGA and Xilinx Virtex‐6 FPGA, it has passed the NIST SP800‐22 and NIST SP800‐90B tests at 300 Mb/s. The structure was also tested using Xilinx Virtex‐6 FPGA under different temperature and voltage conditions, passing the NIST SP800‐90B IID test. [ABSTRACT FROM AUTHOR]

This paper develops a parameter tuning method for solving the set restabilization problem of perturbed Boolean control networks (BCNs). First, the absorbable attractor, which we previously proposed, is recalled. Based on the relationship between attractors, a necessary and sufficient restabilizability criterion is derived. This criterion is used to check whether a perturbed BCN can be stabilized to the original target set by modifying the least number of parameters to the old controller. Furthermore, a constructive method for fine-tuning the old controller is provided if the criterion condition derived above is satisfied. Compared with the existing relevant results, ours have clear advantages, since they can address the set restabilization problem of BCNs subject to multi-column function perturbations, which has not been solved yet. Finally, two examples are employed to show the effectiveness and advantages of our results. [ABSTRACT FROM AUTHOR]

The tendency for cell fate to be robust to most perturbations, yet sensitive to certain perturbations raises intriguing questions about the existence of a key path within the underlying molecular network that critically determines distinct cell fates. Reprogramming and trans-differentiation clearly show examples of cell fate change by regulating only a few or even a single molecular switch. However, it is still unknown how to identify such a switch, called a master regulator, and how cell fate is determined by its regulation. Here, we present CAESAR, a computational framework that can systematically identify master regulators and unravel the resulting canalizing kernel, a key substructure of interconnected feedbacks that is critical for cell fate determination. We demonstrate that CAESAR can successfully predict reprogramming factors for de-differentiation into mouse embryonic stem cells and trans-differentiation of hematopoietic stem cells, while unveiling the underlying essential mechanism through the canalizing kernel. CAESAR provides a system-level understanding of how complex molecular networks determine cell fates. [ABSTRACT FROM AUTHOR]

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans , achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans , where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git. [ABSTRACT FROM AUTHOR]

This study addresses a problem of correspondence between dynamics of a parameterized system and the structure of interactions within that system. The structure of interactions is captured by a signed network. A network dynamics is parameterized by collections of multi-level monotone Boolean functions (MBFs), which are organized in a parameter graph PG. Each collection generates dynamics which are captured in a structure of recurrent sets called a Morse graph. We study two operations on signed graphs, switching and subnetwork inclusion, and show that these induce dynamics-preserving maps between parameter graphs. We show that duality, a standard operation on MBFs, and switching are dynamically related: If M is the switch of N, then duality gives an isomorphism between PG(N) and PG(A4) which preserves dynamics and thus Morse graphs. We then show that for each subnetwork M c N, there are embeddings of the parameter graph PG(A4) into PG(N) that preserve the Morse graph. Since our combinatorial description of network dynamics is closely related to switching ODE network models, our results suggest similar results for parameterized sets of smooth ODE network models of the network dynamics. [ABSTRACT FROM AUTHOR]

Asynchronous temporal Boolean Networks (ATBNs) are more complex in structure and have different linear expressions compared to traditional synchronous Boolean networks. The complexity depends on the number of updated nodes. The main contribution of this paper is to propose results of synchronization and anti-synchronization problems of ATBNs. First, this paper abstracts two Temporal Boolean Networks (TBNs) into a mathematical model, and provides a linear expression of the network by means of the semi-tensor product (STP) tool. Second, based on the asynchronous updating scheme of temporal Boolean networks, we investigate the synchronization (including complete synchronization and anti-synchronization) of ATBNs, and provide two results to guarantee the synchronization and anti-synchronization. Finally, we provide two examples to verify the correctness of our theorems and corollaries. [ABSTRACT FROM AUTHOR]

Simple Summary: Boolean modeling is a graphical analytic approach used for analyzing qualitative models of biological systems, including protein–protein interaction networks. This study performed an analysis of the protein–protein interaction network related to four individuals diagnosed with Autism Spectrum Disorder (ASD) to identify the underlying etiology of the observed phenotype. The genetic mutations in each of these patients have been found to be convergent with the widely recognized Wnt and mTOR signaling pathways, which have previously been implicated in the development of ASD. The disturbance in the activity of these genetic mutations caused abnormal activation levels of critical proteins such as β-catenin, MTORC1, RPS6, eIF4E, Cadherin, and SMAD, which regulate gene expression, translation, cell adhesion, shape, and migration. The varied functions of these proteins contribute to the observed traits in these individuals, yet they reveal potential therapeutic options for them. Cellular molecules interact with one another in a structured manner, defining a regulatory network topology that describes cellular mechanisms. Genetic mutations alter these networks' pathways, generating complex disorders such as autism spectrum disorder (ASD). Boolean models have assisted in understanding biological system dynamics since Kauffman's 1969 discovery, and various analytical tools for regulatory networks have been developed. This study examined the protein–protein interaction network created in our previous publication of four ASD patients using the SPIDDOR R package, a Boolean model-based method. The aim is to examine how patients' genetic variations in INTS6L, USP9X, RSK4, FGF5, FLNA, SUMF1, and IDS affect mTOR and Wnt cell signaling convergence. The Boolean network analysis revealed abnormal activation levels of essential proteins such as β-catenin, MTORC1, RPS6, eIF4E, Cadherin, and SMAD. These proteins affect gene expression, translation, cell adhesion, shape, and migration. Patients 1 and 2 showed consistent patterns of increased β-catenin activity and decreased MTORC1, RPS6, and eIF4E activity. However, patient 2 had an independent decrease in Cadherin and SMAD activity due to the FLNA mutation. Patients 3 and 4 have an abnormal activation of the mTOR pathway, which includes the MTORC1, RPS6, and eIF4E genes. The shared mTOR pathway behavior in these patients is explained by a shared mutation in two closely related proteins (SUMF1 and IDS). Diverse activities in β-catenin, MTORC1, RPS6, eIF4E, Cadherin, and SMAD contributed to the reported phenotype in these individuals. Furthermore, it unveiled the potential therapeutic options that could be suggested to these individuals. [ABSTRACT FROM AUTHOR]

This paper devotes to the design of all feasible output feedback controllers for the robust output tracking of Boolean control networks with disturbances (DBCNs). First, the output feedback–based robust control invariant set (RCIS) is defined, and a calculation method to find all output feedback–based RCISs of a given set is derived via the truth matrix technique. Second, a class of complete family of robust reachable sets (CFRRSs) is developed; the solvability of robust output tracking problem by output feedback control is verified. Furthermore, a constructive algorithm of all feasible output feedback controllers is presented. Finally, the study of a network about Escherichia coli lactose operon shows the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

We study relationships between lower estimates for the energy complexity E(Σ), the switching complexity S(Σ) of a normalized Boolean network Σ, and the positive sensitivity ps(f) of the Boolean function f implemented by this circuit. The lower estimate E (Σ) ⩾ ⌊ ps (f) − 1 m ⌋ is proved for a sufficiently wide class of bases consisting of monotone Boolean functions of at most m variables, the negation gate, and the Boolean constants 0 and 1. For the switching complexity of circuits, we construct a counterexample which shows that, for the standard basis of elements of the disjunction, conjunction, and negation, there do not exist a linear (with respect to ps(f)) lower estimate for the switching complexity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of Boolean networks by using their matrices of support. We derive properties about the transients, fixed points, and limit cycles. We also study the graph properties of the phase spaces of Boolean networks, and show how to use matrices of support to construct Boolean networks with prescribed dynamics. [ABSTRACT FROM AUTHOR]

This paper investigates the one-bit function perturbation (OBFP) impact on the robust set stability of Boolean networks with disturbances (DBNs). Firstly, the dynamics of these networks are converted into the algebraic forms utilizing the semi-tensor product (STP) method. Secondly, OBFP's impact on the robust set stability of DBNs is divided into two situations. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions to guarantee that a DBN under OBFP can stay robust set stable unchanged are provided. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Boolean networks are largely employed to model the qualitative dynamics of cell fate processes by describing the change of binary activation states of genes and transcription factors with time. Being able to bridge such qualitative states with quantitative measurements of gene expressions in cells, as scRNA-seq, is a cornerstone for data-driven model construction and validation. On one hand, scRNA-seq binarisation is a key step for inferring and validating Boolean models. On the other hand, the generation of synthetic scRNA-seq data from baseline Boolean models provides an important asset to benchmark inference methods. However, linking characteristics of scRNA-seq datasets, including dropout events, with Boolean states is a challenging task. We present scBoolSeq, a method for the bidirectional linking of scRNA-seq data and Boolean activation state of genes. Given a reference scRNA-seq dataset, scBoolSeq computes statistical criteria to classify the empirical gene pseudocount distributions as either unimodal, bimodal, or zero-inflated, and fit a probabilistic model of dropouts, with gene-dependent parameters. From these learnt distributions, scBoolSeq can perform both binarisation of scRNA-seq datasets, and generate synthetic scRNA-seq datasets from Boolean traces, as issued from Boolean networks, using biased sampling and dropout simulation. We present a case study demonstrating the application of scBoolSeq's binarisation scheme in data-driven model inference. Furthermore, we compare synthetic scRNA-seq data generated by scBoolSeq with BoolODE's, data for the same Boolean Network model. The comparison shows that our method better reproduces the statistics of real scRNA-seq datasets, such as the mean-variance and mean-dropout relationships while exhibiting clearly defined trajectories in two-dimensional projections of the data. Author summary: The qualitative and logical modelling of cell dynamics has brought precious insight into gene regulatory mechanisms that drive cellular differentiation and fate decisions by predicting cellular trajectories and mutations for their control. However, the design and validation of these models is impeded by the quantitative nature of experimental measurements of cellular states. In this paper, we provide and assess a new methodology, scBoolSeq for bridging single-cell level pseudocounts of RNA transcripts with Boolean classification of gene activity levels. Our method, implemented as a Python package, enables both to binarise scRNA-seq data in order to match quantitative measurements with states of logical models, and to generate synthetic data from Boolean traces to benchmark inference methods. We show that scBoolSeq accurately captures the main statistical features of scRNA-seq data, including measurement dropouts, improving significantly the state of the art. Overall, scBoolSeq brings a statistically-grounded method for enabling the inference and validation of qualitative models from scRNA-seq data. [ABSTRACT FROM AUTHOR]

Reconstructing the topology of gene regulatory network from gene expression data has been extensively studied. With the abundance functional transcriptomic data available, it is now feasible to systematically decipher regulatory interaction dynamics in a logic form such as a Boolean network (BN) framework, which qualitatively indicates how multiple regulators aggregated to affect a common target gene. However, inferring both the network topology and gene interaction dynamics simultaneously is still a challenging problem since gene expression data are typically noisy and data discretization is prone to information loss. We propose a new method for BN inference from time-series transcriptional profiles, called LogicGep. LogicGep formulates the identification of Boolean functions as a symbolic regression problem that learns the Boolean function expression and solve it efficiently through multi-objective optimization using an improved gene expression programming algorithm. To avoid overly emphasizing dynamic characteristics at the expense of topology structure ones, as traditional methods often do, a set of promising Boolean formulas for each target gene is evolved firstly, and a feed-forward neural network trained with continuous expression data is subsequently employed to pick out the final solution. We validated the efficacy of LogicGep using multiple datasets including both synthetic and real-world experimental data. The results elucidate that LogicGep adeptly infers accurate BN models, outperforming other representative BN inference algorithms in both network topology reconstruction and the identification of Boolean functions. Moreover, the execution of LogicGep is hundreds of times faster than other methods, especially in the case of large network inference. [ABSTRACT FROM AUTHOR]

Tissue-scale multicellular information processing in plants remains poorly understood. Universal principles of distributed information processing can be applied to plant tissues. Modelling approaches, including cellular automata and Boolean networks, can be used to understand plant tissue behaviour. The algorithmic nature of information processing in plants merits further investigation. Molecular motifs can explain information processing within single cells, while how assemblies of cells collectively achieve this remains less well understood. Plant fitness and survival depend upon robust and accurate decision-making in their decentralised multicellular organ systems. Mobile agents, including hormones, metabolites, and RNAs, have a central role in coordinating multicellular collective decision-making, yet mechanisms describing how cell–cell communication scales to organ-level transitions is poorly understood. Here, we explore how unified outputs may emerge in plant organs by distributed information processing across different scales and using different modalities. Mathematical and computational representations of these events are also explored toward understanding how these events take place and are leveraged to manipulate plant development in response to the environment. [ABSTRACT FROM AUTHOR]

BackgroundComputational models of cell signaling networks are extremely useful tools for the exploration of underlying system behavior and prediction of response to various perturbations. By representing signaling cascades as executable Boolean networks, the previously developed rxncon ("reaction-contingency") formalism and associated Python package enable accurate and scalable modeling of signal transduction even in large (thousands of components) biological systems. The models are split into reactions, which generate states, and contingencies, that impinge on reactions; this avoids the so-called "combinatorial explosion" of system size. Boolean description of the biological system compensates for the poor availability of kinetic parameters which are necessary for quantitative models. Unfortunately, few tools are available to support rxncon model development, especially for large, intricate systems.ResultsWe present the kboolnet toolkit ( https://github.com/Kufalab-UCSD/kboolnet , complete documentation at https://github.com/Kufalab-UCSD/kboolnet/wiki ), an R package and a set of scripts that seamlessly integrate with the python-based rxncon software and collectively provide a complete workflow for the verification, validation, and visualization of rxncon models. The verification script VerifyModel.R checks for responsiveness to repeated stimulations as well as consistency of steady state behavior. The validation scripts TruthTable.R, SensitivityAnalysis.R, and ScoreNet.R provide various readouts for the comparison of model predictions to experimental data. In particular, ScoreNet.R compares model predictions to a cloud-stored MIDAS-format experimental database to provide a numerical score for tracking model accuracy. Finally, the visualization scripts allow for graphical representations of model topology and behavior. The entire kboolnet toolkit is cloud-enabled, allowing for easy collaborative development; most scripts also allow for the extraction and analysis of individual user-defined "modules".ConclusionThe kboolnet toolkit provides a modular, cloud-enabled workflow for the development of rxncon models, as well as their verification, validation, and visualization. This will enable the creation of larger, more comprehensive, and more rigorous models of cell signaling using the rxncon formalism in the future.

Biological networks, such as gene regulatory networks, possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated into biological networks. A recent meta-analysis of published, expert-curated Boolean biological network models has revealed several such features, often referred to as design principles. Among others, the biological networks are enriched for certain recurring network motifs, the dynamic update rules are more redundant, more biased, and more canalizing than expected, and the dynamics of biological networks are better approximable by linear and lower-order approximations than those of comparable random networks. Since most of these features are interrelated, it is paramount to disentangle cause and effect, that is, to understand which features evolution actively selects for, and thus truly constitute evolutionary design principles. Here, we compare published Boolean biological network models with different ensembles of null models and show that the abundance of canalization in biological networks can almost completely explain their recently postulated high approximability. Moreover, an analysis of random N–K Kauffman models reveals a strong dependence of approximability on the dynamical robustness of a network. [ABSTRACT FROM AUTHOR]

Boolean networks provide an effective mechanism for describing interactions and dynamics of gene regulatory networks (GRNs). Deriving accurate Boolean descriptions of GRNs is a challenging task. The number of experiments is usually much smaller than the number of genes. In addition, binarization leads to a loss of information and inconsistencies arise in binarized time-series data. The inference of Boolean networks from binarized time-series data alone often leads to complex and overfitted models. To obtain relevant Boolean models of gene regulatory networks, inference methods could incorporate data from multiple sources and prior knowledge in terms of general network structure and/or exact interactions. We propose the Boolean network inference method SAILoR (Structure-Aware Inference of Logic Rules). SAILoR incorporates time-series gene expression data in combination with provided reference networks to infer accurate Boolean models. SAILoR automatically extracts topological properties from reference networks. These can describe a more general structure of the GRN or can be more precise and describe specific interactions. SAILoR infers a Boolean network by learning from both continuous and binarized time-series data. It navigates between two main objectives, topological similarity to reference networks and correspondence with gene expression data. By incorporating the NSGA-II multi-objective genetic algorithm, SAILoR relies on the wisdom of crowds. Our results indicate that SAILoR can infer accurate and biologically relevant Boolean descriptions of GRNs from both a static and a dynamic perspective. We show that SAILoR improves the static accuracy of the inferred network compared to the network inference method dynGENIE3. Furthermore, we compared the performance of SAILoR with other Boolean network inference approaches including Best-Fit, REVEAL, MIBNI, GABNI, ATEN, and LogBTF. We have shown that by incorporating prior knowledge about the overall network structure, SAILoR can improve the structural correctness of the inferred Boolean networks while maintaining dynamic accuracy. To demonstrate the applicability of SAILoR, we inferred context-specific Boolean subnetworks of female Drosophila melanogaster before and after mating. [ABSTRACT FROM AUTHOR]

Recent technological advances have made it possible to produce tiny robots equipped with simple sensors and effectors. Micro-robots are particularly suitable for scenarios such as exploration of hostile environments, and emergency intervention, e.g., in areas subject to earthquakes or fires. A crucial desirable feature of such a robot is the capability of adapting to the specific environment in which it has to operate. Given the limited computational capabilities of a micro-robot, this property cannot be achieved by complicated software but it rather should come from the flexibility of simple control mechanisms, such as the sensory–motor loop. In this work, we explore the possibility of equipping simple robots controlled by Boolean networks with the capability of modulating their sensory–motor loop such that their behavior adapts to the incumbent environmental conditions. This study builds upon the cybernetic concept of homeostasis, which is the property of maintaining essential parameters inside vital ranges, and analyzes the performance of adaptive mechanisms intervening in the sensory–motor loop. In particular, we focus on the possibility of maneuvering the robot's effectors such that both their connections to network nodes and environmental features can be adapted. As the actions the robot takes have a feedback effect to its sensors mediated by the environment, this mechanism makes it possible to tune the sensory–motor loop, which, in turn, determines the robot's behavior. We study this general setting in simulation and assess to what extent this mechanism can sustain the homeostasis of the robot. Our results show that controllers made of random Boolean networks in critical and chaotic regimes can be tuned such that their homeostasis in different environments is kept. This outcome is a step towards the design and deployment of controllers for micro-robots able to adapt to different environments. [ABSTRACT FROM AUTHOR]

There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems comprised of many interacting elements (often called "synergistic" information). This "emergent" organization has been found in a variety of natural and artificial systems, although at present, the field lacks a unified understanding of what the consequences of higher-order synergies and redundancies are for systems under study. Typical research treats the presence (or absence) of synergistic information as a dependent variable and report changes in the level of synergy in response to some change in the system. Here, we attempt to flip the script: rather than treating higher-order information as a dependent variable, we use evolutionary optimization to evolve boolean networks with significant higher-order redundancies, synergies, or statistical complexity. We then analyze these evolved populations of networks using established tools for characterizing discrete dynamics: the number of attractors, the average transient length, and the Derrida coefficient. We also assess the capacity of the systems to integrate information. We find that high-synergy systems are unstable and chaotic, but with a high capacity to integrate information. In contrast, evolved redundant systems are extremely stable, but have negligible capacity to integrate information. Finally, the complex systems that balance integration and segregation (known as Tononi–Sporns–Edelman complexity) show features of both chaosticity and stability, with a greater capacity to integrate information than the redundant systems while being more stable than the random and synergistic systems. We conclude that there may be a fundamental trade-off between the robustness of a system's dynamics and its capacity to integrate information (which inherently requires flexibility and sensitivity) and that certain kinds of complexity naturally balance this trade-off. [ABSTRACT FROM AUTHOR]

This paper forges a strong connection between two well known computational frameworks for representing biological systems, in order to facilitate the seamless transfer of techniques between them. Boolean networks are a well established formalism employed from biologists. They have been studied under different (synchronous and asynchronous) update semantics, enabling the observation and characterisation of distinct facets of system behaviour. Recently, a new semantics for Boolean networks has been proposed, called most permissive semantics, that enables a more faithful representation of biological phenomena. Reaction systems offer a streamlined formalism inspired by biochemical reactions in living cells. Reaction systems support a full range of analysis techniques that can help for gaining deeper insights into the underlying biological phenomena. Our goal is to leverage the available toolkit for predicting and comprehending the behaviour of reaction systems within the realm of Boolean networks. In this paper, we first extend the behaviour of reaction systems to several asynchronous semantics, including the most permissive one, and then we demonstrate that Boolean networks and reaction systems exhibit isomorphic behaviours under the synchronous, general/fully asynchronous and most permissive semantics. [ABSTRACT FROM AUTHOR]

Single-cell transcriptomic studies of differentiating systems allow meaningful understanding, especially in human embryonic development and cell fate determination. We present an innovative method aimed at modeling these intricate processes by leveraging scRNAseq data from various human developmental stages. Our implemented method identifies pseudo-perturbations, since actual perturbations are unavailable due to ethical and technical constraints. By integrating these pseudo-perturbations with prior knowledge of gene interactions, our framework generates stage-specific Boolean networks (BNs). We apply our method to medium and late trophectoderm developmental stages and identify 20 pseudo-perturbations required to infer BNs. The resulting BN families delineate distinct regulatory mechanisms, enabling the differentiation between these developmental stages. We show that our program outperforms existing pseudo-perturbation identification tool. Our framework contributes to comprehending human developmental processes and holds potential applicability to diverse developmental stages and other research scenarios. [ABSTRACT FROM AUTHOR]

There is a growing interest in inferring context specific gene regulatory networks from single-cell RNA sequencing (scRNA-seq) data. This involves identifying the regulatory relationships between transcription factors (TFs) and genes in individual cells, and then characterizing these relationships at the level of specific cell types or cell states. In this study, we introduce scGATE (single-cell gene regulatory gate) as a novel computational tool for inferring TF–gene interaction networks and reconstructing Boolean logic gates involving regulatory TFs using scRNA-seq data. In contrast to current Boolean models, scGATE eliminates the need for individual formulations and likelihood calculations for each Boolean rule (e.g. AND, OR, XOR). By employing a Bayesian framework, scGATE infers the Boolean rule after fitting the model to the data, resulting in significant reductions in time-complexities for logic-based studies. We have applied assay for transposase-accessible chromatin with sequencing (scATAC-seq) data and TF DNA binding motifs to filter out non-relevant TFs in gene regulations. By integrating single-cell clustering with these external cues, scGATE is able to infer context specific networks. The performance of scGATE is evaluated using synthetic and real single-cell multi-omics data from mouse tissues and human blood, demonstrating its superiority over existing tools for reconstructing TF-gene networks. Additionally, scGATE provides a flexible framework for understanding the complex combinatorial and cooperative relationships among TFs regulating target genes by inferring Boolean logic gates among them. [ABSTRACT FROM AUTHOR]

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using |$10$| reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's |$Z$| -parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states. [ABSTRACT FROM AUTHOR]

Lyapunov-based approach to sampled-data set stabilisation of constrained delayed Boolean control networks (DBCNs) is investigated in this paper. The main mathematical tool is semi-tensor product (STP) of matrices. Since the sampling interval is selected from a finite set, the STP method is adopted to convert the dynamics of constrained DBCNs under nonuniform sampled-data control into a switched Boolean network (SBN). It is worth noting that the switches can only occur at the sampling instant. Using the techniques of Lyapunov function and average dwell time, several sufficient conditions are proposed for the global stability of SBN. Moreover, by virtue of reachable set approach, a procedure is established to design state feedback sampled-data stabilisers for constrained DBCNs. The obtained results are applied to the cell survival regulation of apoptosis networks. [ABSTRACT FROM AUTHOR]

Multi-layer Complex networks are commonly used for modeling and analysing biological entities. This paper presents the advantage of using COMBO (Combining Multi Bio Omics) to suggest a new role of the chromosomal aberration as a cancer driver factor. Exploiting the heterogeneous multi-layer networks, COMBO integrates gene expression and DNA-methylation data in order to identify complex bilateral relationships between transcriptome and epigenome. We evaluated the multi-layer networks generated by COMBO on different TCGA cancer datasets (COAD, BLCA, BRCA, CESC, STAD) focusing on the effect of a specific chromosomal numerical aberration, broad gain in chromosome 20, on different cancer histotypes. In addition, the effect of chromosome 8q amplification was tested in the same TCGA cancer dataset. The results demonstrate the ability of COMBO to identify the chromosome 20 amplification cancer driver force in the different TCGA Pan Cancer project datasets. [ABSTRACT FROM AUTHOR]

Background: Prostate cancer is a significant health concern, particularly among African American (AA) men who exhibit higher incidence and mortality compared to European American (EA) men. Understanding the molecular mechanisms underlying these disparities is imperative for enhancing clinical management and achieving better outcomes. Methods: Employing a multi-omics approach, we analyzed prostate cancer in both AA and EA men. Using Illumina methylation arrays and RNA sequencing, we investigated DNA methylation and gene expression in tumor and non-tumor prostate tissues. Additionally, Boolean analysis was utilized to unravel complex networks contributing to racial disparities in prostate cancer. Results: When comparing tumor and adjacent non-tumor prostate tissues, we found that DNA hypermethylated regions are enriched for PRC2/H3K27me3 pathways and EZH2/SUZ12 cofactors. Olfactory/ribosomal pathways and distinct cofactors, including CTCF and KMT2A, were enriched in DNA hypomethylated regions in prostate tumors from AA men. We identified race-specific inverse associations of DNA methylation with expression of several androgen receptor (AR) associated genes, including the GATA family of transcription factors and TRIM63. This suggests that race-specific dysregulation of the AR signaling pathway exists in prostate cancer. To investigate the effect of AR inhibition on race-specific gene expression changes, we generated in-silico patient-specific prostate cancer Boolean networks. Our simulations revealed prolonged AR inhibition causes significant dysregulation of TGF-β, IDH1, and cell cycle pathways specifically in AA prostate cancer. We further quantified global gene expression changes, which revealed differential expression of genes related to microtubules, immune function, and TMPRSS2-fusion pathways, specifically in prostate tumors of AA men. Enrichment of these pathways significantly correlated with an altered risk of disease progression in a race-specific manner. Conclusions: Our study reveals unique signaling networks underlying prostate cancer biology in AA and EA men, offering potential insights for clinical management strategies tailored to specific racial groups. Targeting AR and associated pathways could be particularly beneficial in addressing the disparities observed in prostate cancer outcomes in the context of AA and EA men. Further investigation into these identified pathways may lead to the development of personalized therapeutic approaches to improve outcomes for prostate cancer patients across different racial backgrounds. [ABSTRACT FROM AUTHOR]

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid‐index model of impulsive Boolean networks with state‐triggered impulses. Based on this model, the time‐domain output controllability is investigated. Using the quotient mapping method, the hybrid‐domain solutions of this model are mapped to the time‐domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract Boolean networks (BNs) have been extensively used to model gene regulatory networks (GRNs). The dynamics of BNs depend on the network architecture and regulatory logic rules (Boolean functions (BFs)) associated with nodes. Nested canalyzing functions (NCFs) have been shown to be enriched among the BFs in the large-scale studies of reconstructed Boolean models. The central question we address here is whether that enrichment is due to certain sub-types of NCFs. We build on one sub-type of NCFs, the chain functions (or chain-0 functions) proposed by Gat-Viks and Shamir. First, we propose two other sub-types of NCFs, namely, the class of chain-1 functions and generalized chain functions, the union of the chain-0 and chain-1 types. Next, we find that the fraction of NCFs that are chain-0 (also holds for chain-1) functions decreases exponentially with the number of inputs. We provide analytical treatment for this and other observations on BFs. Then, by analyzing three different datasets of reconstructed Boolean models we find that generalized chain functions are significantly enriched within the NCFs. Lastly we illustrate that upon imposing the constraints of generalized chain functions on three different GRNs we are able to obtain biologically viable Boolean models.

Reservoir Computing (RC) is a paradigmin artificial intelligence where a recurrent neural network (RNN) is used to process temporal data, leveraging the inherent dynamical properties of the reservoir to perform complex computations. In the realm of RC, the excitatory-inhibitory balance b has been shown to be pivotal for driving the dynamics and performance of Echo State Networks (ESN) and, more recently, Random Boolean Network (RBN). However, the relationship between b and other parameters of the network is still poorly understood. This article explores how the interplay of the balance b, the connectivity degree K (i.e., the number of synapses per neuron) and the size of the network (i.e., the number of neurons N) influences the dynamics and performance (memory and prediction) of an RBN reservoir. Our findings reveal that K and b are strongly tied in optimal reservoirs. Reservoirs with high K have two optimal balances, one for globally inhibitory networks (b < 0), and the other one for excitatory networks (b > 0). Both show asymmetric performances about a zero balance. In contrast, for moderate K, the optimal value being K = 4, best reservoirs are obtained when excitation and inhibition almost, but not exactly, balance each other. For almost all K, the influence of the size is such that increasing N leads to better performance, even with very large values of N. Our investigation provides clear directions to generate optimal reservoirs or reservoirs with constraints on size or connectivity. [ABSTRACT FROM AUTHOR]

Deregulated metabolism is one of the hallmarks of cancer. It is well-known that tumour cells tend to metabolize glucose via glycolysis even when oxygen is available and mitochondrial respiration is functional. However, the lower energy efficiency of aerobic glycolysis with respect to mitochondrial respiration makes this behaviour, namely the Warburg effect, counter-intuitive, although it has now been recognized as source of anabolic precursors. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from glycolysis. We employed a multi-scale approach that integrates multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks to study metabolic cooperation between hypoxic and oxygenated cells exposed to varying oxygen, nutrient, and inhibitor concentrations. The results show that the cooperation reduces the depletion of environmental glucose, resulting in an overall advantage of using aerobic glycolysis. In addition, the oxygen level was found to be decreased by symbiosis, promoting a further shift towards anaerobic glycolysis. However, the oxygenated and hypoxic populations may gradually reach quasi-equilibrium. A sensitivity analysis using Latin hypercube sampling and partial rank correlation shows that the symbiotic dynamics depends on properties of the specific cell such as the minimum glucose level needed for glycolysis. Our results suggest that strategies that block glucose transporters may be more effective to reduce tumour growth than those blocking lactate intake transporters. Author summary: Metabolic alteration is one of the hallmarks of cancer and the well-known metabolic alteration of tumour cells is that cells prefer to do glycolysis over mitochondrial respiration even under well-oxygenated and functional mitochondrial conditions. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from hypoxic glycolytic cells in which it can create a metabolic co-operation between oxygenated and hypoxic cell populations. This metabolic co-operation could allow tumour cells to economically share oxygen and glucose and promote tumour survival. Using a multi-scale approach combining multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks representing cell regulatory mechanisms, we studied this metabolic co-operation between different populations of cells, exposed to a changing microenvironment. We predict that the tumour environmental glucose depletion is decreased while the oxygen depletion is increased by this metabolic symbiosis, promoting a further shift towards glycolysis. Our results also show that blocking glucose transporters could be more effective than blocking lactate intake transporters, because the former would disrupt both glycolysis and lactate production, drastically reducing tumour growth. [ABSTRACT FROM AUTHOR]

A True Random Number Generator (TRNG) is an important component in cryptographic algorithms and protocols. The Rosin Autonomous Boolean Network (ABN) digital TRNG has been widely studied due to its nice properties, such as low energy consumption, high speed, strong platform portability, and strong randomness. However, there is still a lack of suitable entropy models to deduce the requirement of design parameters to ensure true randomness. The current model to evaluate the entropy of oscillator-based TRNGs is not applicable for Rosin ABN TRNGs due to low-frequency noise. This work presents a new, suitable stochastic model to evaluate the entropy of Rosin ABN TRNGs. Theoretical analysis and simulation experiments verify the correctness and the effectiveness of the model, and, finally, the appropriate sampling parameters for Rosin ABN TRNGs are given for sufficient entropy per random bit to ensure true randomness. [ABSTRACT FROM AUTHOR]

A technology for automating structural-parametric synthesis of a Boolean network with a given periodic trajectory is proposed. This technology provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. The proposed technology is based on the author's method of Boolean restrictions. According to this method, all conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. A software implementation of the proposed technology using microserviceoriented tools is presented. All stages of the parametric synthesis of a Boolean network in accordance with the proposed technology are demonstrated in the example of a one-step linear system. [ABSTRACT FROM AUTHOR]

For an asynchronous Boolean network with step-by-step updating only one state vector variable, a Boolean dynamic model was built with the update schedule control over a finite time. Following the authors' method of Boolean constraints. constructive methods were obtained for studying various attractor types in terms of Boolean models of their dynamic properties. The most important for practice property of controllability concerning initial and target states is considered. Illustrative examples demonstrating the technology for using the obtained theoretical results are given. [ABSTRACT FROM AUTHOR]

Using the Boolean constraint method, we consider dynamics and control problems on a finite time interval for controlled singular Boolean networks. The models of local dynamical properties, periodicity properties of trajectories, and properties of controllability type are obtained as Boolean constraints. Depending on the property, the Boolean constraints solvability is reduced to the Boolean satisfiability problem or problem of verifying the truth of a quantified Boolean formula. The proposed approach is focused on systems with a high dimension of state and control vectors and a large interval of discrete time variation. The software implementation of the proposed approach is performed using a microservice architecture and is aimed at application in a high-performance hybrid computing environment. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of optimal preview pinning control for Boolean networks. The primary objective is to design efficient control strategies that leverage future reference information for improved control performance. We propose a policy iteration algorithm specifically for Boolean networks based on an augmented error system, constructed using the state augmentation technique in combination with the Exclusive-Or operator approach. The algorithm effectively optimizes control policies using future information. Finally, an example is presented to illustrate the effectiveness of the proposed algorithm. • First study of optimal preview pinning control problem of BNs. • Transformation using the semi-tensor product and exclusive-OR operator. • Deduction of a policy iteration algorithm for BNs. [ABSTRACT FROM AUTHOR]

Multiplication is a fundamental arithmetic operation in electronic processing units such as microprocessors and digital signal processors as it plays an important role in various computational tasks and applications. There exist many designs of synchronous multipliers in the literature. However, in the domain of Input–Output Mode (IOM) asynchronous design, there is relatively less published research on multipliers. Some existing works have considered quasi-delay-insensitive (QDI) asynchronous implementations of multipliers. However, the QDI asynchronous design paradigm, in general, is not area- and speed-efficient. This article presents an efficient alternative implementation of IOM asynchronous multipliers based on the concept of monotonic Boolean networks. The array multiplier architecture has been considered for demonstrating the usefulness of our proposition. The building blocks of the multiplier, such as the partial product generator, half adder, and full adder, were implemented monotonically. The popular dual-rail encoding scheme was considered for encoding the multiplier inputs and outputs, and four-phase return-to-zero handshaking (RZH) and return-to-one handshaking (ROH) were separately considered for communication. Compared to the best of the existing QDI asynchronous array multipliers, the proposed monotonic asynchronous array multiplier achieves the following reductions in design metrics: (i) a 40.1% (44.3%) reduction in cycle time (which is the asynchronous equivalent of synchronous clock timing), a 37.7% (37.7%) reduction in area, and a 4% (4.5%) reduction in power for 4 × 4 multiplication corresponding to RZH (ROH), and (ii) a 58.1% (60.2%) reduction in cycle time, a 45.2% (45.2%) reduction in area, and a 10.3% (11%) reduction in power for 8 × 8 multiplication corresponding to RZH (ROH). The multipliers were implemented using a 28 nm CMOS process technology. [ABSTRACT FROM AUTHOR]

Introduction: The vagus nerve innervates multiple organs, but its role in regulating cross-tissue spread of inflammation is as yet unclear. We hypothesized that the vagus nerve may regulate cross-tissue inflammation via modulation of the putatively neurally regulated chemokine IP-10/CXCL10. Methods: Rate-of-change analysis, dynamic network analysis, and dynamic hypergraphs were used to model intra- and inter-tissue trends, respectively, in inflammatory mediators from mice that underwent either vagotomy or sham surgery. Results: This analysis suggested that vagotomy primarily disrupts the cross-tissue attenuation of inflammatory networks involving IP-10 as well as the chemokines MIG/CXCL9 and CCL2/MCP-1 along with the cytokines IFN-γ and IL-6. Computational analysis also suggested that the vagus-dependent rate of expression of IP-10 and MIG/CXCL9 in the spleen impacts the trajectory of chemokine expression in other tissues. Perturbation of this complex system with bacterial lipopolysaccharide (LPS) revealed a vagally regulated role for MIG in the heart. Further, LPS-stimulated expression of IP-10 was inferred to be vagusindependent across all tissues examined while reducing connectivity to IL-6 and MCP-1, a hypothesis supported by Boolean network modeling. Discussion: Together, these studies define novel spatiotemporal dimensions of vagus-regulated acute inflammation. [ABSTRACT FROM AUTHOR]

Megaphylls, present in the majority of vascular plants, show in many plant lineages an abaxial-adaxial polarity in their dorsoventral axis. This polarity commonly translates into different tissues developing on each side of the leaf blade. This is important because it promotes better photosynthetic efficiency as related to light absorption and gas exchange. Many researchers have studied the molecular bases of the emergence of leaf abaxial-adaxial polarity, showing that it is produced by the interaction and differential expression of particular genes and other molecules. However, until now, it is still unclear if the molecular components documented thus far are sufficient to explain the emergence of leaf polarity. In this work, we integrated the available experimental data to construct a graph of the Gene Regulatory Network (GRN) involved in the formation of abaxial-adaxial polarity in the leaf primordium of Arabidopsis thaliana. This graph consisted of 21 nodes and 47 regulations. We extracted the main components of the graph to obtain a Minimum Network consisting of six genes and 22 possible regulations. Then, we used the Boolean network (BN) formalism to describe the dynamics of this Minimum Network. We identified 1905 distinct BNs that comprised the regulations of the Minimum Network and exclusively generated the two attractors representing the abaxial and adaxial cell types. This highlights the fact that most graphs, including our network, can describe experimentally observed behaviors with many BN dynamics. By performing mutant simulations and robustness analysis, we found that two of the 1905 BNs better reproduce experimentally available information. To produce the expected attractors, both BNs predict the same missing regulations, which we propose should be experimentally analyzed to confirm their existence. Interestingly, these two BNs have low robustness to perturbations compared with previously analyzed GRNs. This was an unexpected result since abaxialadaxial polarity is a robust biological trait, which suggests more components or regulations of the network are missing. [ABSTRACT FROM AUTHOR]