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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]

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]

Objectives. The problem of choosing the best methods and programs for circuit implementation as part of digital ASIC (Application-Specific Integrated Circuit) sparse systems of disjunctive normal forms (DNF) of completely defined Boolean functions is considered. For matrix forms of sparse DNF systems, the ternary matrix specifying elementary conjunctions contains a large proportion of undefined values corresponding to missing literals of Boolean input variables, and the Boolean matrix specifying the occurrences of conjunctions in DNF functions contains a large proportion of zero values.Methods. It is proposed to investigate various methods of technologically independent logical optimization performed at the first stage of logical synthesis: joint minimization of systems of functions in the DNF class, separate and joint minimization in classes of multilevel representations in the form of Boolean networks and BDD representations using mutually inverse cofactors, as well as the division of a system of functions into subsystems with a limited number of input variables and the method of block cover of DNF systems, focused on minimizing the total area of the blocks forming the cover.Results. When implementing sparse DNF systems of Boolean functions in ASIC, along with traditional methods of joint minimization of systems of functions in the DNF class, methods for optimizing multilevel representations of Boolean function systems based on Shannon expansions can be used for technologically independent optimization, while separate minimization and joint minimization of the entire system as a whole turn out to be less effective compared with block partitions and coatings of the DNF system and subsequent minimization of multilevel representations. Schemes obtained as a result of synthesis using minimized representations of Boolean networks often have a smaller area than schemes obtained using minimized BDD representations.Conclusion. For the design of digital ASIC, the effectiveness of combined approach is shown, when initially the block coverage programs of the DNF system is used, followed by the use of programs to minimize multilevel block representations in the form of Boolean networks minimized based on Shannon expansion.

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]

Models of gene regulatory networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understanding the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing (scRNA-Seq). We demonstrate the effectiveness of these tools using simulated data, and in addition a publicly available scRNA-Seq dataset and the GRN that is associated with it. Our methodology will enable researchers to obtain a better understanding of the dynamics of GRNs and their biological role. [ABSTRACT FROM AUTHOR]

We investigate the optimal preview control problem of Boolean Networks (BNs) in this paper. An augmented system, which can control BNs with a minimal cost function, is established through a model transformation based on the semi-tensor product of matrices and the Exclusive-Or operator. Then the optimal preview controller that is equipped with various features such as state feedback, integrator, and preview feedforward is given for BNs. Finally, we present a numerical example to illustrate the validity of the proposed optimal preview controller of BNs. [ABSTRACT FROM AUTHOR]

Abstract Background Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. Results We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. Conclusions BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

The asynchronous automaton of a Boolean network f : { 0 , 1 } n → { 0 , 1 } n , considered in many applications, is the finite deterministic automaton where the set of states is { 0 , 1 } n , the alphabet is [ n ] , and the action of letter i on a state x consists in either switching the i th component if f i (x) ≠ x i or doing nothing otherwise. In this paper, we ask for the existence of synchronizing words for this automaton, and their minimal length, when f is the and-net over an arc-signed digraph G on [ n ] : for every i ∈ [ n ] , f i (x) = 1 if and only if x j = 1 (x j ≠ 0) for every positive (negative) arc from j to i. Our main result is that if G is strongly connected and has no positive cycles, then either there exists a synchronizing word of length at most 10 (5 + 1) n or G is a cycle and there are no synchronizing words. We also give complexity results showing that the situation is much more complex if one of the two hypothesis made on G is removed. [ABSTRACT FROM AUTHOR]

This article concentrates on the function perturbation impact on robust stability and robust stabilization of Boolean networks with disturbance inputs (DBNs). First, using the semi-tensor product (STP) of matrices, the algebraic representation of DBNs with function perturbation is given. Second, a state set is determined to detect the robust stability of DBNs subject to function perturbation. The result shows that the robust stability of DBNs remains unchanged if and only if the perturbed point is not in the constructed state set. Third, DBNs with control inputs (DBCNs) are considered, and several criteria to verify whether DBCNs with function perturbation can still maintain robust stabilization under a given state feedback stabilizer are presented. Finally, two examples are provided to illustrate the validity of the theoretical results.

Background: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. Results: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. Conclusions: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs. [ABSTRACT FROM AUTHOR]

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality—a balance between change and stability, order and chaos—is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks—a general model of discrete dynamical systems—we show that heterogeneity—in time, structure, and function—can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic. [ABSTRACT FROM AUTHOR]

Anaerobic Porphyromonas gingivalis is a rod-shaped bacterium and is a primary agent of periodontal inflammation and thus periodontitis. This bacterium disturbs the normal flora of the oral cavity and causes dysbiosis. Databases including Google Scholar Scopus and PubMed were employed to find the evidence by using keywords like 'Porphyromonas gingivalis,' 'Boolean network,' 'inflammatory response and Porphyromonas gingivalis,' 'inflammation and Porphyromonas gingivalis. Only articles that reviewed the role of Porphyromonas gingivalis in oral inflammation were selected. Porphyromonas gingivalis promotes and reorganizes host immune systems against normal host flora, which causes a dysbiotic state. A reorganized immune system induces dysbiosis and periodontitis. Specifically, the role of the C5a receptor in the complement system is vital in this mechanism. P. gingivalis can change the metabolic pathways of phagocytic cells without impeding inflammation. Toll-like receptor and complement signaling are inverted by Porphyromonas gingivalis, which aids them in overcoming immunological responses. However, they sustain the inflammation process, which promotes dysbiosis. Instead of a subjective approach, a systems perspective is required to comprehend this intricate process. A Boolean network is a system approach that seems to be a better approach to understanding this complicated interaction process of Porphyromonas gingivalis with the immune system and inflammation. In short, attempts to understand the complex process using the Boolean network will ultimately help in the early detection of periodontitis, and immediate treatment can prevent soft tissue destruction and dentition loss. [ABSTRACT FROM AUTHOR]

The Boolean network (BN) is a mathematical model used to represent various biological processes such as gene regulatory networks. The state of a BN is determined from the previous state and eventually reaches a stable state called an attractor. Due to its significance for elucidating the whole system, extensive studies have been conducted on analysis of attractors. However, the problem of detecting an attractor from a given BN has been shown to be NP-hard, and for general BNs, the time complexity of most existing algorithms is not guaranteed to be less than O(2n). Therefore, the computational difficulty of attractor detection has been a big obstacle for analysis of BNs. This review highlights singleton/periodic attractor detection algorithms that have guaranteed computational complexities less than O(2n) time for particular classes of BNs under synchronous update in which the maximum indegree is limited to a constant, each Boolean function is AND or OR of literals, or each Boolean function is given as a nested canalyzing function. We also briefly review practically efficient algorithms for the problem.

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

As a class of state estimation issues, detectability is widely used in fault diagnosis, circuit design, and disease status detection. This brief analyzes the robust weak detectability of Boolean networks (BNs) under function perturbation. A simplified parallel system is constructed for BNs. Based on the transition of state pairs in the simplified parallel system, a new criterion is proposed for the weak detectability of BNs. Using the reachability from perturbed state pairs to attractors in indistinguishable pairs, the robust weak detectability of BNs subject to function perturbation is analyzed. A practical example of p53-MDM2 negative feedback regulatory loop is used to illustrate the obtained criteria. [ABSTRACT FROM AUTHOR]

Due to advances in computing power and internet technology, various industrial sectors are adopting IT infrastructure and artificial intelligence (AI) technologies. Recently, data-driven predictions have attracted interest in high-stakes decision-making. Despite this, advanced AI methods are less often used for such tasks. This is because AI technology is a black box for the social systems it is meant to support; trustworthiness and fairness have not yet been established. Meanwhile in the field of marketing, strategic decision-making is a high-stakes problem that has a significant impact on business trends. For global marketing, with its diverse cultures and market environments, future decision-making is likely to focus on building consensus on the formulation of the problem itself rather than on solutions for achieving the goal. There are two important and conflicting facts: the fact that the core of domestic strategic decision-making comes down to the formulation of the problem itself, and the fact that it is difficult to realize AI technology that can achieve problem formulation. How can we resolve this difficulty with current technology? This is the main challenge for the realization of high-level human-AI systems in the marketing field. Thus, we propose customer journey mapping (CJM) automation through model-level data fusion, a process for the practical problem formulation known as explainable alignment. Using domain-specific requirements and observations as inputs, the system automatically outputs a CJM. Explainable alignment corresponds with both human and AI perspectives and in formulating the problem, thereby improving strategic decision-making in marketing. Following preprocessing to make latent variables and their dynamics transparent with latent Dirichlet allocation and a variational autoencoder, a post-hoc explanation is implemented in which a hidden Markov model and learning from an interpretation transition are combined with a long short-term memory architecture that learns sequential data between touchpoints for extracting attitude rules for CJM. Finally, we realize the application of human-AI systems to strategic decision-making in marketing with actual logs in over-the-top media services, in which the dynamic behavior of customers for CJM can be automatically extracted.

Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification usually focus either on attractor or phenotype control, and are unable to deal with more complex control problems, for instance phenotype avoidance. They also fail to capture, in many situations, all possible minimal strategies, finding instead only sub-optimal solutions. In order to fill these gaps, we present a novel approach to control strategy identification in Boolean networks based on model checking. The method is guaranteed to identify all minimal control strategies, and provides maximal flexibility in the definition of the control target. We investigate the applicability of the approach by considering a range of control problems for different biological systems, comparing the results, where possible, to those obtained by alternative control methods.

Adaptability, heterogeneity, and plasticity are the hallmarks of macrophages. How these complex properties emerge from the molecular interactions is an open question. Thus, in this study we propose an actualized regulatory network of cytokines, signaling pathways, and transcription factors to survey the differentiation, heterogeneity, and plasticity of macrophages. The network recovers attractors, which in regulatory networks correspond to cell types, that correspond to M0, M1, M2a, M2b, M2c, M2d, M2-like, and IL-6 producing cells, including multiple cyclic attractors that are stable to perturbations. These cyclic attractors reproduce experimental observations and show that oscillations result from the structure of the network. We also study the effect of the environment in the differentiation and plasticity of macrophages, showing that the observed heterogeneity in macrophage populations is a result of the regulatory network and its interaction with the micro-environment. The macrophage regulatory network gives a mechanistic explanation to the heterogeneity and plasticity of macrophages seen in vivo and in vitro, and offers insights into the mechanism that allows the immune system to react to a complex dynamic environment.

Background: A novel data-driven Boolean model, namely, the fundamental Boolean model (FBM), has been proposed to draw genetic regulatory insights into gene activation, inhibition, and protein decay, published in 2018. This novel Boolean model facilitates the analysis of the activation and inhibition pathways. However, the novel model does not handle the situation well, where genetic regulation might require more time steps to complete. Methods: Here, we propose extending the fundamental Boolean modelling to address the issue that some gene regulations might require more time steps to complete than others. We denoted this extension model as the temporal fundamental Boolean model (TFBM) and related networks as the temporal fundamental Boolean networks (TFBNs). The leukaemia microarray datasets downloaded from the National Centre for Biotechnology Information have been adopted to demonstrate the utility of the proposed TFBM and TFBNs. Results: We developed the TFBNs that contain 285 components and 2775 Boolean rules based on TFBM on the leukaemia microarray datasets, which are in the form of short-time series. The data contain gene expression measurements for 13 GC-sensitive children under therapy for acute lymphoblastic leukaemia, and each sample has three time points: 0 hour (before GC treatment), 6/8 hours (after GC treatment) and 24 hours (after GC treatment). Conclusion: We conclude that the proposed TFBM unlocks their predecessor's limitation, i.e., FBM, that could help pharmaceutical agents identify any side effects on clinic-related data. New hypotheses could be identified by analysing the extracted fundamental Boolean networks and analysing their up-regulatory and down-regulatory pathways. [ABSTRACT FROM AUTHOR]

The problem of inferring interactions from observations of individual behavior in networked dynamical systems is ubiquitous in science and engineering. From brain circuits to financial networks, there is a dire need for robust methodologies that can unveil network structures from individual time series. Originally formulated to identify asymmetries in pairs of coupled dynamical systems, transfer entropy has been proposed as a model-free, computationally-inexpensive framework for network inference. While previous studies have cataloged a library of pathological instances in which transfer entropy-based network reconstruction can fail, we presently lack analytical results that can help quantify the accuracy of the identification and pinpoint scenarios where false inferences results are more likely to be registered. Here, we present a detailed analytical study of a Boolean network model of policy diffusion. Through perturbation theory, we establish a closed-form expression for the transfer entropy between any pair of nodes in the network up to the third order in an expansion parameter that is associated with the spontaneous activity of the nodes. While for slowly-varying dynamics transfer entropy is successful in capturing the weight of any link, for faster dynamics the error in the inference is controlled by local topological features of the node pair. Specifically, the error in the inference of a weight between two nodes depends on the mismatch between their weighted indegrees that serves as a common uncertainty bath upon which we must tackle the inference problem. Interestingly, an equivalent result is discovered when numerically studying a network of coupled chaotic tent maps, suggesting that heterogeneity in the in-degree is a critical factor that can undermine the success of transfer entropy-based network inference.

In this paper, the synchronization of coupled Boolean networks with asynchronous update scheme is investigated. First, the asynchronous Boolean dynamics is transformed into a linear expression with the semi-tensor product technique. Then, the synchronization cycle is proposed to establish the synchronization conditions of asynchronous Boolean networks. Furthermore, an algorithm is given, which can be used to quickly check whether there exists the synchronization cycle in the coefficient matrix of the Boolean function. Finally, an example is provided to verify the efficiency of the theoretical analysis.

Background: How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling. Methods: We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable. Results: Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved. Conclusion: The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality—a balance between change and stability, order and chaos—is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks—a general model of discrete dynamical systems—we show that heterogeneity—in time, structure, and function—can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the “optimal” balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.

In this brief, the service function chain (SFC) routing in network function virtualization (NFV) with server capacity limitation and user minimum target rate constraint is investigated simultaneously. After relaxing the constraints by the addition of extra cost terms, an extended NFV game incorporating the coupled constraints is formulated. By using semi-tensor product of matrices, we prove that the formulated game is a potential game which possesses at least one Nash equilibrium. We then present the equilibrium point algorithm for solving the SFC routes problem. The numerical simulation of two cases with constraints and without constraints illustrates the influence of coupled limitations on the SFC routing. [ABSTRACT FROM AUTHOR]

This paper presents mutual time-varying delay-coupled temporal Boolean network model and investigates synchronization issue for mutual time-varying delay-coupled temporal Boolean networks. The necessary and sufficient conditions for the synchronization are given, and the check criterion of the upper bound is presented. An example is given to illustrate the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract Background In silico experiments, with the aid of computer simulation, speed up the process of in vitro or in vivo experiments. Cancer therapy design is often based on signalling pathway. MicroRNAs (miRNA) are small non-coding RNA molecules. In several kinds of diseases, including cancer, hepatitis and cardiovascular diseases, they are often deregulated, acting as oncogenes or tumor suppressors. miRNA therapeutics is based on two main kinds of molecules injection: miRNA mimics, which consists of injection of molecules that mimic the targeted miRNA, and antagomiR, which consists of injection of molecules inhibiting the targeted miRNA. Nowadays, the research is focused on miRNA therapeutics. This paper addresses cancer related signalling pathways to investigate miRNA therapeutics. Results In order to prove our approach, we present two different case studies: non-small cell lung cancer and melanoma. KEGG signalling pathways are modelled by a digital circuit. A logic value of 1 is linked to the expression of the corresponding gene. A logic value of 0 is linked to the absence (not expressed) gene. All possible relationships provided by a signalling pathway are modelled by logic gates. Mutations, derived according to the literature, are introduced and modelled as well. The modelling approach and analysis are widely discussed within the paper. MiRNA therapeutics is investigated by the digital circuit analysis. The most effective miRNA and combination of miRNAs, in terms of reduction of pathogenic conditions, are obtained. A discussion of obtained results in comparison with literature data is provided. Results are confirmed by existing data. Conclusions The proposed study is based on drug discovery and miRNA therapeutics and uses a digital circuit simulation of a cancer pathway. Using this simulation, the most effective combination of drugs and miRNAs for mutated cancer therapy design are obtained and these results were validated by the literature. The proposed modelling and analysis approach can be applied to each human disease, starting from the corresponding signalling pathway.

Using the semi-tensor product method, this paper studies the set stability of Boolean networks (BNs) with stochastic function perturbations. First, the definition of one-column function perturbation for BNs is defined, and two kinds of stochastic function perturbations are formulated. Second, by constructing a state transition matrix, a new criterion is proposed for the set stability of BNs with probabilistic function perturbation. Third, the set stability of BNs with Markov jump function perturbation is studied by calculating the state probability distribution. Finally, the obtained results are applied to D. melanogaster segmentation polarity gene network.

This paper investigates the time-variant state feedback stabilization of constrained delayed Boolean control networks under nonuniform sampled-data control. Firstly, using the augmented algebraic form of constrained delayed Boolean control networks, the constrained nonuniform sampled-data controllability matrix is constructed. Secondly, based on the controllability matrix, a necessary and sufficient condition is proposed for the nonuniform sampled-data reachability of constrained delayed Boolean control networks. Thirdly, by virtue of the nonuniform sampled-data reachability, a new procedure is established to design time-variant state feedback sampled-data stabilizers via reachable set approach. The obtained results are applied to the cell survival regulation of apoptosis networks. [ABSTRACT FROM AUTHOR]

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization- the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular. [ABSTRACT FROM AUTHOR]

As the world faces unprecedented ecological and social changes, there is a need to better understand the complex dynamics of social-ecological systems (SES) and the mechanisms that underlie their resilience. In Mexico, Natural Protected Areas (NPAs) constitute complex SES as they are generally established on territories that different peoples have historically inhabited and managed. They generally manage their resources following a multiple use strategy (MUS), which involves local traditional agricultural practices and has been proposed as a resilience-enhancing mechanism. In this paper we study the MUS as practiced by the Yucatec Maya communities that inhabit the NPA Otoch Ma'ax Yetel Kooh and its buffer zone in the Yucatan Peninsula, Mexico. Due to the restrictions imposed by the decree of the reserve and the growth of tourism in the region, some of these communities have started to abandon the MUS and specialize on tourism-related activities. To study the consequences of these changes and to better understand the mechanisms by which the MUS may enhance the resilience of this SES, we built an evidence-based dynamical computational model that allows us to explore different virtual scenarios. The model, through the incorporation of agent-based and boolean network modeling, explores the interaction between the forest, the monkey population and some productive activities done by the households (milpa agriculture, ecotourism, agriculture, charcoal production). We calibrated the model, explored its sensibility, compared it with empirical data and simulated different management scenarios. Our results support the hypothesis that the MUS enhances the resilience of this SES in terms of income and food availability, as it increases the system's response diversity and functional redundancy, thus reducing income variability and increasing the resistance to natural and anthropogenic disturbances. We also identify other possible mechanisms related with the MUS that provide a more nuanced understanding of the resilience of this SES. Our study, in addition to highlighting the importance of local management practices for resilience, also puts forward a novel integration of diverse mathematical formalisms and illustrates how computational modeling and a systems perspective are effective means of integrating and synthesizing information from different sources.

Stomatal pores play a central role in the control of carbon assimilation and plant water status. The guard cell pair that borders each pore integrates information from environmental and endogenous signals and accordingly swells or deflates, thereby increasing or decreasing the stomatal aperture. Prior research shows that there is a complex cellular network underlying this process. We have previously constructed a signal transduction network and a Boolean dynamic model describing stomatal closure in response to signals including the plant hormone abscisic acid (ABA), calcium or reactive oxygen species (ROS). Here, we improve the Boolean network model such that it captures the biologically expected response of the guard cell in the absence or following the removal of a closure-inducing signal such as ABA or external Ca2+. The expectation from the biological system is reversibility, i.e., the stomata should reopen after the closing signal is removed. We find that the model’s reversibility is obstructed by the previously assumed persistent activity of four nodes. By introducing time-dependent Boolean functions for these nodes, the model recapitulates stomatal reopening following the removal of a signal. The previous version of the model predicts ∼20% closure in the absence of any signal due to uncertainty regarding the initial conditions of multiple network nodes. We systematically test and adjust these initial conditions to find the minimally restrictive combinations that appropriately result in open stomata in the absence of a closure signal. We support these results by an analysis of the successive stabilization of feedback motifs in the network, illuminating the system’s dynamic progression toward the open or closed stomata state. This analysis particularly highlights the role of cytosolic calcium oscillations in causing and maintaining stomatal closure. Overall, we illustrate the strength of the Boolean network modeling framework to efficiently capture cellular phenotypes as emergent outcomes of intracellular biological processes.

Hematopoietic stem cells (HSCs) provide all types of blood cells during the entire life of the organism. HSCs are mainly quiescent and can eventually enter the cell cycle to differentiate. HSCs are maintained and tightly regulated in a particular environment. The stem cell niche regulates dormancy and awakening. Deregulations of this interplay can lead to hematopoietic failure and diseases. In this paper, we present a Boolean network model that recapitulates HSC regulation in virtue of external signals coming from the niche. This Boolean network integrates and summarizes the current knowledge of HSC regulation and is based on extensive literature research. Furthermore, dynamic simulations suggest a novel systemic regulation of TP53 in homeostasis. Thereby, our model indicates that TP53 activity is balanced depending on external stimulations, engaging a regulatory mechanism involving ROS regulators and RAS activated transcription factors. Finally, we investigated different mouse models and compared them to in silico knockout simulations. Here, the model could recapitulate in vivo observed behaviors and thus sustains our results.

Endothelial cells (ECs) form the lining of lymph and blood vessels. Changes in tissue requirements or wounds may cause ECs to behave as tip or stalk cells. Alternatively, they may differentiate into mesenchymal cells (MCs). These processes are known as EC activation and endothelial-to-mesenchymal transition (EndMT), respectively. EndMT, Tip, and Stalk EC behaviors all require SNAI1, SNAI2, and Matrix metallopeptidase (MMP) function. However, only EndMT inhibits the expression of VE-cadherin, PECAM1, and VEGFR2, and also leads to EC detachment. Physiologically, EndMT is involved in heart valve development, while a defective EndMT regulation is involved in the physiopathology of cardiovascular malformations, congenital heart disease, systemic and organ fibrosis, pulmonary arterial hypertension, and atherosclerosis. Therefore, the control of EndMT has many promising potential applications in regenerative medicine. Despite the fact that many molecular components involved in EC activation and EndMT have been characterized, the system-level molecular mechanisms involved in this process have not been elucidated. Toward this end, hereby we present Boolean network model of the molecular involved in the regulation of EC activation and EndMT. The simulated dynamic behavior of our model reaches fixed and cyclic patterns of activation that correspond to the expected EC and MC cell types and behaviors, recovering most of the specific effects of simple gain and loss-of-function mutations as well as the conditions associated with the progression of several diseases. Therefore, our model constitutes a theoretical framework that can be used to generate hypotheses and guide experimental inquiry to comprehend the regulatory mechanisms behind EndMT. Our main findings include that both the extracellular microevironment and the pattern of molecular activity within the cell regulate EndMT. EndMT requires a lack of VEGFA and sufficient oxygen in the extracellular microenvironment as well as no FLI1 and GATA2 activity within the cell. Additionally Tip cells cannot undergo EndMT directly. Furthermore, the specific conditions that are sufficient to trigger EndMT depend on the specific pattern of molecular activation within the cell.

Abstract In this paper we describe the application of a learning classifier system (LCS) variant known as the eXtended classifier system (XCS) to evolve a set of ‘control rules’ for a number of Boolean network instances. We show that (1) it is possible to take the system to an attractor, from any given state, by applying a set of ‘control rules’ consisting of ternary conditions strings (i.e. each condition component in the rule has three possible states; 0, 1 or #) with associated bit-flip actions, and (2) that it is possible to discover such rules using an evolutionary approach via the application of a learning classifier system. The proposed approach builds on learning (reinforcement learning) and discovery (a genetic algorithm) and therefore the series of interventions for controlling the network are determined but are not fixed. System control rules evolve in such a way that they mirror both the structure and dynamics of the system, without having ‘direct’ access to either.

Abstract Background During the last years, several approaches were applied on biomedical data to detect disease specific proteins and genes in order to better target drugs. It was shown that statistical and machine learning based methods use mainly clinical data and improve later their results by adding omics data. This work proposes a new method to discriminate the response of Acute Myeloid Leukemia (AML) patients to treatment. The proposed approach uses proteomics data and prior regulatory knowledge in the form of networks to predict cancer treatment outcomes by finding out the different Boolean networks specific to each type of response to drugs. To show its effectiveness we evaluate our method on a dataset from the DREAM 9 challenge. Results The results are encouraging and demonstrate the benefit of our approach to distinguish patient groups with different response to treatment. In particular each treatment response group is characterized by a predictive model in the form of a signaling Boolean network. This model describes regulatory mechanisms which are specific to each response group. The proteins in this model were selected from the complete dataset by imposing optimization constraints that maximize the difference in the logical response of the Boolean network associated to each group of patients given the omic dataset. This mechanistic and predictive model also allow us to classify new patients data into the two different patient response groups. Conclusions We propose a new method to detect the most relevant proteins for understanding different patient responses upon treatments in order to better target drugs using a Prior Knowledge Network and proteomics data. The results are interesting and show the effectiveness of our method.

In this brief, observability of Boolean networks (BNs) with redundant channels is considered. Each output node with multi-channels is designed to receive the system state information under certain probabilities. By resorting to the semi-tensor product of matrices, the algebraic form of the proposed model is provided. An algorithm to verify the observability of the proposed model is then given by fully considering the randomness properties of the proposed model. In addition, a new observable BN with a set of redundant channels is proposed to improve the reliability of the BNs. Finally, two numerical examples are presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

Stomatal pores play a central role in the control of carbon assimilation and plant water status. The guard cell pair that borders each pore integrates information from environmental and endogenous signals and accordingly swells or deflates, thereby increasing or decreasing the stomatal aperture. Prior research shows that there is a complex cellular network underlying this process. We have previously constructed a signal transduction network and a Boolean dynamic model describing stomatal closure in response to signals including the plant hormone abscisic acid (ABA), calcium or reactive oxygen species (ROS). Here, we improve the Boolean network model such that it captures the biologically expected response of the guard cell in the absence or following the removal of a closure-inducing signal such as ABA or external Ca2+. The expectation from the biological system is reversibility, i.e., the stomata should reopen after the closing signal is removed. We find that the model's reversibility is obstructed by the previously assumed persistent activity of four nodes. By introducing time-dependent Boolean functions for these nodes, the model recapitulates stomatal reopening following the removal of a signal. The previous version of the model predicts ∼20% closure in the absence of any signal due to uncertainty regarding the initial conditions of multiple network nodes. We systematically test and adjust these initial conditions to find the minimally restrictive combinations that appropriately result in open stomata in the absence of a closure signal. We support these results by an analysis of the successive stabilization of feedback motifs in the network, illuminating the system's dynamic progression toward the open or closed stomata state. This analysis particularly highlights the role of cytosolic calcium oscillations in causing and maintaining stomatal closure. Overall, we illustrate the strength of the Boolean network modeling framework to efficiently capture cellular phenotypes as emergent outcomes of intracellular biological processes. [ABSTRACT FROM AUTHOR]

This paper presents mutual time-varying delay-coupled temporal Boolean network model and investigates synchronization issue for mutual time-varying delay-coupled temporal Boolean networks. The necessary and sufficient conditions for the synchronization are given, and the check criterion of the upper bound is presented. An example is given to illustrate the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Hematopoietic stem cells (HSCs) provide all types of blood cells during the entire life of the organism. HSCs are mainly quiescent and can eventually enter the cell cycle to differentiate. HSCs are maintained and tightly regulated in a particular environment. The stem cell niche regulates dormancy and awakening. Deregulations of this interplay can lead to hematopoietic failure and diseases. In this paper, we present a Boolean network model that recapitulates HSC regulation in virtue of external signals coming from the niche. This Boolean network integrates and summarizes the current knowledge of HSC regulation and is based on extensive literature research. Furthermore, dynamic simulations suggest a novel systemic regulation of TP53 in homeostasis. Thereby, our model indicates that TP53 activity is balanced depending on external stimulations, engaging a regulatory mechanism involving ROS regulators and RAS activated transcription factors. Finally, we investigated different mouse models and compared them to in silico knockout simulations. Here, the model could recapitulate in vivo observed behaviors and thus sustains our results. [ABSTRACT FROM AUTHOR]

This paper studies the delay partial synchronization for mutual delay-coupled Boolean networks. First, the mutual delay-coupled Boolean network model is presented. Second, some necessary and sufficient conditions are derived to ensure the delay partial synchronization of the mutual delay-coupled Boolean networks. The upper bound of synchronization time is obtained. Finally, an example is provided to illustrate the efficiency of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Background: How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling. Methods: We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable. Results: Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved. Conclusion: The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network. [ABSTRACT FROM AUTHOR]

Endothelial cells (ECs) form the lining of lymph and blood vessels. Changes in tissue requirements or wounds may cause ECs to behave as tip or stalk cells. Alternatively, they may differentiate into mesenchymal cells (MCs). These processes are known as EC activation and endothelial-to-mesenchymal transition (EndMT), respectively. EndMT, Tip, and Stalk EC behaviors all require SNAI1, SNAI2, and Matrix metallopeptidase (MMP) function. However, only EndMT inhibits the expression of VE-cadherin, PECAM1, and VEGFR2, and also leads to EC detachment. Physiologically, EndMT is involved in heart valve development, while a defective EndMT regulation is involved in the physiopathology of cardiovascular malformations, congenital heart disease, systemic and organ fibrosis, pulmonary arterial hypertension, and atherosclerosis. Therefore, the control of EndMT has many promising potential applications in regenerative medicine. Despite the fact that many molecular components involved in EC activation and EndMT have been characterized, the system-level molecular mechanisms involved in this process have not been elucidated. Toward this end, hereby we present Boolean network model of the molecular involved in the regulation of EC activation and EndMT. The simulated dynamic behavior of our model reaches fixed and cyclic patterns of activation that correspond to the expected EC and MC cell types and behaviors, recovering most of the specific effects of simple gain and loss-of-function mutations as well as the conditions associated with the progression of several diseases. Therefore, our model constitutes a theoretical framework that can be used to generate hypotheses and guide experimental inquiry to comprehend the regulatory mechanisms behind EndMT. Our main findings include that both the extracellular microevironment and the pattern of molecular activity within the cell regulate EndMT. EndMT requires a lack of VEGFA and sufficient oxygen in the extracellular microenvironment as well as no FLI1 and GATA2 activity within the cell. Additionally Tip cells cannot undergo EndMT directly. Furthermore, the specific conditions that are sufficient to trigger EndMT depend on the specific pattern of molecular activation within the cell. [ABSTRACT FROM AUTHOR]

We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional consequences of a given structural feature, for example a scale free architecture. A key step is to construct an algorithm that allows us to efficiently sample from a maximum entropy distribution on the space of Boolean dynamical networks constrained to perform a specific function, or cascade of gene expression. Such a distribution can act as a "functional null model" to test the significance of any given network feature, and can aid in revealing underlying evolutionary selection pressures on various network properties. Although our methods are general, we illustrate them in an analysis of the yeast cell cycle cascade. This analysis uncovers strong constraints on the architecture of the cell cycle regulatory network as well as significant selection pressures on this network to maintain ordered and convergent dynamics, possibly at the expense of sacrificing robustness to structural perturbations.