Boolean Network Model Research Articles

A Computational Model of the Endothelial to Mesenchymal Transition.

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.

The Impact of Self-Loops on Boolean Networks Attractor Landscape and Implications for Cell Differentiation Modelling.

Boolean networks are a notable model of gene regulatory networks and, particularly, prominent theories discuss how they can capture cellular differentiation processes. One frequent motif in gene regulatory networks, especially in those circuits involved in cell differentiation, is autoregulation. In spite of this, the impact of autoregulation on Boolean network attractor landscape has not yet been extensively discussed in literature. In this paper we propose to model autoregulation as self-loops, and analyse how the number of attractors and their robustness may change once they are introduced in a well-known and widely used Boolean networks model, namely random Boolean networks. Results show that self-loops provide an evolutionary advantage in dynamic mechanisms of cells, by increasing both number and maximal robustness of attractors. These results provide evidence to the hypothesis that autoregulation is a straightforward functional component to consolidate cell dynamics, mainly in differentiation processes.

Boolean model of anchorage dependence and contact inhibition points to coordinated inhibition but semi-independent induction of proliferation and migration

Epithelial cells respond to their physical neighborhood with mechano-sensitive behaviors required for development and tissue maintenance. These include anchorage dependence, matrix stiffness-dependent proliferation, contact inhibition of proliferation and migration, and collective migration that balances cell crawling with the maintenance of cell junctions. While required for development and tissue repair, these coordinated responses to the microenvironment also contribute to cancer metastasis. Predictive models of the signaling networks that coordinate these behaviors are critical in controlling cell behavior to halt disease. Here we propose a Boolean regulatory network model that synthesizes mechanosensitive signaling that links anchorage to a matrix of varying stiffness and cell density sensing to contact inhibition, proliferation, migration, and apoptosis. Our model can reproduce anchorage dependence and anoikis, detachment-induced cytokinesis errors, the effect of matrix stiffness on proliferation, and contact inhibition of proliferation and migration by two mechanisms that converge on the YAP transcription factor. In addition, we offer testable predictions related to cell cycle-dependent anoikis sensitivity, the molecular requirements for abolishing contact inhibition, and substrate stiffness dependent expression of the catalytic subunit of PI3K. Moreover, our model predicts heterogeneity in migratory vs. non-migratory phenotypes in sub-confluent monolayers, and co-inhibition but semi-independent induction of proliferation vs. migration as a function of cell density and mitogenic stimulation. Our model serves as a stepping-stone towards modeling mechanosensitive routes to the epithelial to mesenchymal transition, capturing the effects of the mesenchymal state on anoikis resistance, and understanding the balance between migration versus proliferation at each stage of the epithelial to mesenchymal transition.

Deriving a Boolean dynamics to reveal macrophage activation with in vitro temporal cytokine expression profiles

BackgroundMacrophages show versatile functions in innate immunity, infectious diseases, and progression of cancers and cardiovascular diseases. These versatile functions of macrophages are conducted by different macrophage phenotypes classified as classically activated macrophages and alternatively activated macrophages due to different stimuli in the complex in vivo cytokine environment. Dissecting the regulation of macrophage activations will have a significant impact on disease progression and therapeutic strategy. Mathematical modeling of macrophage activation can improve the understanding of this biological process through quantitative analysis and provide guidance to facilitate future experimental design. However, few results have been reported for a complete model of macrophage activation patterns.ResultsWe globally searched and reviewed literature for macrophage activation from PubMed databases and screened the published experimental results. Temporal in vitro macrophage cytokine expression profiles from published results were selected to establish Boolean network models for macrophage activation patterns in response to three different stimuli. A combination of modeling methods including clustering, binarization, linear programming (LP), Boolean function determination, and semi-tensor product was applied to establish Boolean networks to quantify three macrophage activation patterns. The structure of the networks was confirmed based on protein-protein-interaction databases, pathway databases, and published experimental results. Computational predictions of the network evolution were compared against real experimental results to validate the effectiveness of the Boolean network models.ConclusionThree macrophage activation core evolution maps were established based on the Boolean networks using Matlab. Cytokine signatures of macrophage activation patterns were identified, providing a possible determination of macrophage activations using extracellular cytokine measurements.

Automated inference of gene regulatory networks using explicit regulatory modules

Gene regulatory networks are a popular tool for modelling important biological phenomena, such as cell differentiation or oncogenesis. Efficient identification of the causal connections between genes, their products and regulating transcription factors, is key to understanding how defects in their function may trigger diseases. Modelling approaches should keep up with the ever more detailed descriptions of the biological phenomena at play, as provided by new experimental findings and technical improvements. In recent years, we have seen great improvements in mapping of specific binding sites of many transcription factors to distinct regulatory regions. Recent gene regulatory network models use binding measurements; but usually only to define gene-to-gene interactions, ignoring regulatory module structure. Moreover, current huge amount of transcriptomic data, and exploration of all possible cis-regulatory arrangements which can lead to the same transcriptomic response, makes manual model building both tedious and time-consuming.In our paper, we propose a method to specify possible regulatory connections in a given Boolean network, based on transcription factor binding evidence. This is implemented by an algorithm which expands a regular Boolean network model into a “cis-regulatory” Boolean network model. This expanded model explicitly defines regulatory regions as additional nodes in the network, and adds new, valuable biological insights to the system dynamics. The expanded model can automatically be compared with expression data. And, for each node, a regulatory function, consistent with the experimental data, can be found. The resulting models are usually more constrained (by biologically-motivated metadata), and can then be inspected in in silico simulations.The fully automated method for model identification has been implemented in Python, and the expansion algorithm in R. The method resorts to the Z3 Satisfiability Modulo Theories (SMT) solver, and is similar to the RE:IN application (Yordanov et al., 2016).It is available on https://github.com/regulomics/expansion-network.

OPTIMIZING INDIVIDUALS’ DAILY FUNCTION: A BOOLEAN NETWORK APPROACH FOR IDENTIFYING INTERVENTION SEQUENCES

Development and aging are the product of a process wherein an individuals’ functional components co-act to produce change. System dynamics can be described using a variety of methods. In this paper we illustrate how Boolean network methods may be used to describe the sequences of emotion and behavior states that lead to a stable equilibrium – e.g., healthy function; and the interventions needed to push an individual toward healthier equilibria. We applied Boolean network models to intensive longitudinal data obtained from 150 participants (age 18-89 years) to describe individuals’ on-going psychosocial dynamics and identify the specific social behaviors that may be driving them toward undesirable and/or desirable equilibria (e.g., high and low negative emotions). Results are discussed with respect to how they inform theory about developmental systems, and construction of interventions meant to guide individuals toward healthy aging.

Topological features determining the error in the inference of networks using transfer entropy

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.

WIP1 Contributes to the Adaptation of Fanconi Anemia Cells to DNA Damage as Determined by the Regulatory Network of the Fanconi Anemia and Checkpoint Recovery Pathways.

DNA damage adaptation (DDA) allows the division of cells with unrepaired DNA damage. DNA repair deficient cells might take advantage of DDA to survive. The Fanconi anemia (FA) pathway repairs DNA interstrand crosslinks (ICLs), and deficiencies in this pathway cause a fraction of breast and ovarian cancers as well as FA, a chromosome instability syndrome characterized by bone marrow failure and cancer predisposition. FA cells are hypersensitive to ICLs; however, DDA might promote their survival. We present the FA-CHKREC Boolean Network Model, which explores how FA cells might use DDA. The model integrates the FA pathway with the G2 checkpoint and the checkpoint recovery (CHKREC) processes. The G2 checkpoint mediates cell-cycle arrest (CCA) and the CHKREC activates cell-cycle progression (CCP) after resolution of DNA damage. Analysis of the FA-CHKREC network indicates that CHKREC drives DDA in FA cells, ignoring the presence of unrepaired DNA damage and allowing their division. Experimental inhibition of WIP1, a CHKREC component, in FA lymphoblast and cancer cell lines prevented division of FA cells, in agreement with the prediction of the model.

Boolean network modeling of \u03b2-cell apoptosis and insulin resistance in type 2 diabetes mellitus

BackgroundMajor alteration in lifestyle of human population has promoted Type 2 diabetes mellitus (T2DM) to the level of an epidemic. This metabolic disorder is characterized by insulin resistance and pancreatic β-cell dysfunction and apoptosis, triggered by endoplasmic reticulum (ER) stress, oxidative stress and cytokines. Computational modeling is necessary to consolidate information from various sources in order to obtain a comprehensive understanding of the pathogenesis of T2DM and to investigate possible interventions by performing in silico simulations.ResultsIn this paper, we propose a Boolean network model integrating the insulin resistance pathway with pancreatic β-cell apoptosis pathway which are responsible for T2DM. The model has five input signals, i.e. ER stress, oxidative stress, tumor necrosis factor α (TNF α), Fas ligand (FasL), and interleukin-6 (IL-6). We performed dynamical simulations using random order asynchronous update and with different combinations of the input signals. From the results, we observed that the proposed model made predictions that closely resemble the expression levels of genes in T2DM as reported in the literature.ConclusionThe proposed model can make predictions about expression levels of genes in T2DM that are in concordance with literature. Although experimental validation of the model is beyond the scope of this study, the model can be useful for understanding the aetiology of T2DM and discovery of therapeutic intervention for this prevalent complex disease. The files of our model and results are available at https://github.com/JieZheng-ShanghaiTech/boolean-t2dm.

RMut: R package for a Boolean sensitivity analysis against various types of mutations.

There have been many in silico studies based on a Boolean network model to investigate network sensitivity against gene or interaction mutations. However, there are no proper tools to examine the network sensitivity against many different types of mutations, including user-defined ones. To address this issue, we developed RMut, which is an R package to analyze the Boolean network-based sensitivity by efficiently employing not only many well-known node-based and edgetic mutations but also novel user-defined mutations. In addition, RMut can specify the mutation area and the duration time for more precise analysis. RMut can be used to analyze large-scale networks because it is implemented in a parallel algorithm using the OpenCL library. In the first case study, we observed that the real biological networks were most sensitive to overexpression/state-flip and edge-addition/-reverse mutations among node-based and edgetic mutations, respectively. In the second case study, we showed that edgetic mutations can predict drug-targets better than node-based mutations. Finally, we examined the network sensitivity to double edge-removal mutations and found an interesting synergistic effect. Taken together, these findings indicate that RMut is a flexible R package to efficiently analyze network sensitivity to various types of mutations. RMut is available at https://github.com/csclab/RMut.

Fault detection and therapeutic intervention in gene regulatory networks using SAT solvers

Random somatic mutations disrupt homeostasis of the cell resulting in various undesirable phenotypes including proliferation. One of the most important questions in systems medicine research is the therapeutic intervention design, which requires the knowledge of these mutations. A single or multiple mutations can occur in the diseases like cancer. These mutations have been successfully modeled as stuck-at faults in the Boolean network model of the underlying regulatory system. Identification of these fault types for multiple stuck-at faults is a non-trivial problem and requires some system theoretic introspection. This manuscript addresses the dual problem of the fault identification and the therapeutic intervention. Both the problems are mapped to the Boolean satisfiability (SAT) problem. The underlying problems are solved using a fast SAT solver. The synthetic and biological examples elucidate the effectiveness of the mapping.

Generation and robustness of Boolean networks to model Clostridium difficile infection

One of the more common healthcare associated infection is Chronic diarrhea. This disease is caused by the bacterium Clostridium difficile which alters the normal composition of the human gut flora. The most successful therapy against this infection is the fecal microbial transplant (FMT). They displace C. difficile and contribute to gut microbiome resilience, stability and prevent further episodes of diarrhea. The microorganisms in the FMT their interactions and inner dynamics reshape the gut microbiome to a healthy state. Even though microbial interactions play a key role in the development of the disease, currently, little is known about their dynamics and properties. In this context, a Boolean network model for C. difficile infection (CDI) describing one set of possible interactions was recently presented. To further explore the space of possible microbial interactions, we propose the construction of a neutral space conformed by a set of models that differ in their interactions, but share the final community states of the gut microbiome under antibiotic perturbation and CDI. To begin with the analysis, we use the previously described Boolean network model and we demonstrate that this model is in fact a threshold Boolean network (TBN). Once the TBN model is set, we generate and use an evolutionary algorithm to explore to identify alternative TBNs. We organize the resulting TBNs into clusters that share similar dynamic behaviors. For each cluster, the associated neutral graph is constructed and the most relevant interactions are identified. Finally, we discuss how these interactions can either affect or prevent CDI.

Reconstructing Gene Regulatory Networks That Control Hematopoietic Commitment.

Hematopoietic stem cells (HSCs) reside at the apex of the hematopoietic hierarchy, possessing the ability to self-renew and differentiate toward all mature blood lineages. Along with more specialized progenitor cells, HSCs have an essential role in maintaining a healthy blood system. Incorrect regulation of cell fate decisions in stem/progenitor cells can lead to an imbalance of mature blood cell populations-a situation seen in diseases such as leukemia. Transcription factors, acting as part of complex regulatory networks, are known to play an important role in regulating hematopoietic cell fate decisions. Yet, discovering the interactions present in these networks remains a big challenge. Here, we discuss a computational method that uses single-cell gene expression data to reconstruct Boolean gene regulatory network models and show how this technique can be applied to enhance our understanding of transcriptional regulation in hematopoiesis.

On the stability of multilayer Boolean networks under targeted immunization

In this paper, we study targeted immunization in a multilayer Boolean network model for genetic regulatory networks. Given a specific set of nodes immune to perturbations, we find that the stability of a multilayer Boolean network is determined by the largest eigenvalue of the weighted non-backtracking matrix of corresponding aggregated network. Aimed to minimize this largest eigenvalue, we developed the metric of multilayer collective influence (MCI) to quantify the impact of immunizing individual nodes on the stability of the system. Compared with other competing heuristics, immunizing nodes with high MCI scores can stabilize an unstable multilayer network with higher efficiency on both synthetic and real-world networks. Moreover, despite that coupling nodes can exert direct influence across multiple layers, they are found to exhibit less importance as measured by the MCI score. Our work reveals the mechanism of maintaining the stability of multilayer Boolean networks and provides an efficient targeted immunization strategy, which can be potentially applied to the location of pathogenesis of diseases and the development of targeted therapy.

On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors

It is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In order to cope with this intrinsic difficulty, we consider a special case of the control problem in which the targets are restricted to attractors. For this special case, we mathematically prove under the uniform distribution of states in basins that the expected number of driver nodes is only O(log2N+log2M) for controlling Boolean networks, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, the new model requires a much smaller number of driver nodes. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector’s problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.

Information Flow in a Boolean Network Model of Collective Behavior

In animal groups, leaders have often been proposed to be those individuals who possess additional knowledge about their surroundings, such as the location of a food source or a potential predator. Understanding how this information propagates through the group to shape collective response is an important step to elucidate the evolutionary basis of leadership. In this paper, we study a Boolean model of collective behavior, in which a single leader interacts with a group of followers in a binary decision-making process. Through an analytical treatment of the associated Markov chain, we establish closed-form solutions for the transition probability matrix and the stationary distribution, as functions of the noise in the decision-making process and the size of the group. We leverage these expressions to quantify information transfer within the group, measured through the information-theoretic construct of transfer entropy. We find that information transfer depends nonlinearly on the group size and noise. For low noise intensities, the system is nearly deterministic, such that no information is shared within the group; an equivalent effect is observed for large noise intensities, which mask the information transfer. We determine the existence of critical noise intensities at which the leader maximizes information transfer to a follower or followers maximize information sharing between each other for a given group size. These analytical findings suggest that noise might have a positive role in collective behavior, facilitating the transfer of knowledge within the group, from leaders to followers.

Inference of time-varying networks through transfer entropy, the case of a Boolean network model.

Inferring network topologies from the time series of individual units is of paramount importance in the study of biological and social networks. Despite considerable progress, our success in network inference is largely limited to static networks and autonomous node dynamics, which are often inadequate to describe complex systems. Here, we explore the possibility of reconstructing time-varying weighted topologies through the information-theoretic notion of transfer entropy. We focus on a Boolean network model in which the weight of the links and the spontaneous activity periodically vary in time. For slowly-varying dynamics, we establish closed-form expressions for the stationary periodic distribution and transfer entropy between each pair of nodes. Our results indicate that the instantaneous weight of each link is mapped into a corresponding transfer entropy value, thereby affording the possibility of pinpointing the dominant weights at each time. However, comparing transfer entropy readings at different times may provide erroneous estimates of the strength of the links in time, due to a counterintuitive modulation of the information flow by the non-autonomous dynamics. In fact, this time variation should be used to scale transfer entropy values toward the correct inference of the time evolution of the network weights. This study constitutes a necessary step toward a mathematically-principled use of transfer entropy to reconstruct time-varying networks.

Criticality Distinguishes the Ensemble of Biological Regulatory Networks.

The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

CANA: A Python Package for Quantifying Control and Canalization in Boolean Networks.

Logical models offer a simple but powerful means to understand the complex dynamics of biochemical regulation, without the need to estimate kinetic parameters. However, even simple automata components can lead to collective dynamics that are computationally intractable when aggregated into networks. In previous work we demonstrated that automata network models of biochemical regulation are highly canalizing, whereby many variable states and their groupings are redundant (Marques-Pita and Rocha, 2013). The precise charting and measurement of such canalization simplifies these models, making even very large networks amenable to analysis. Moreover, canalization plays an important role in the control, robustness, modularity and criticality of Boolean network dynamics, especially those used to model biochemical regulation (Gates and Rocha, 2016; Gates et al., 2016; Manicka, 2017). Here we describe a new publicly-available Python package that provides the necessary tools to extract, measure, and visualize canalizing redundancy present in Boolean network models. It extracts the pathways most effective in controlling dynamics in these models, including their effective graph and dynamics canalizing map, as well as other tools to uncover minimum sets of control variables.

Determining Relative Dynamic Stability of Cell States Using Boolean Network Model

Cell state transition is at the core of biological processes in metazoan, which includes cell differentiation, epithelial-to-mesenchymal transition (EMT) and cell reprogramming. In these cases, it is important to understand the molecular mechanism of cellular stability and how the transitions happen between different cell states, which is controlled by a gene regulatory network (GRN) hard-wired in the genome. Here we use Boolean modeling of GRN to study the cell state transition of EMT and systematically compare four available methods to calculate the cellular stability of three cell states in EMT in both normal and genetically mutated cases. The results produced from four methods generally agree but do not totally agree with each other. We show that distribution of one-degree neighborhood of cell states, which are the nearest states by Hamming distance, causes the difference among the methods. From that, we propose a new method based on one-degree neighborhood, which is the simplest one and agrees with other methods to estimate the cellular stability in all scenarios of our EMT model. This new method will help the researchers in the field of cell differentiation and cell reprogramming to calculate cellular stability using Boolean model, and then rationally design their experimental protocols to manipulate the cell state transition.