Boolean Models Research Articles

Boolean network modeling and its integration with experimental read-outs : An interdisciplinary presentation using a leukemia model.

The limited availability of suitable animal models and cell lines often impedes experimental cancer research. Wet-laboratory experiments are also time-consuming and cost-intensive. In this review, we present an in silico modeling strategy, namely, Boolean network (BN) models, and demonstrate how it could be applied to streamline experimental design and to focus the effort of experimental read-outs. Boolean network models allow for the dynamic analysis of large molecular signaling pathways and their crosstalks. After establishing and validating aspecific tumor model, mechanistic insights into the tumor cell behavior can be gained by studying the trajectories of different tumor phenotypes. Also, tumor driver and drug target screenings can be performed. These automatic screenings can help to identify new intervention targets and putative biomarkers for tumor evolution, hence guiding new wet-laboratory experiments. The goal of this round-up is to demonstrate how to establish, validate, and use BN modeling and its crosstalks in classic wet-laboratory research using achronic lymphocytic leukemia (CLL) BN model.

Abstract 4125893: Deciphering the Mechanism of Action of Drug Combinations by Boolean Modeling of Transcriptomes: a Case Study of Atorvastatin/Simvastatin and Ezetimibe

Introduction: Drug combinations offer increased therapeutic efficacy and reduced toxicity and plays a vital role in treating chronic complex diseases. Understanding a drug combination's mechanism of action (MoA) can provide important insights into its therapeutic efficacy. The MoA of many FDA-approved drugs, however, often remains unclear. Methods: In this study, we investigated the combination of a statin [atorvastatin (ATO) or simvastatin (SIM) plus ezetimibe (EZE)] and utilized drug-treated RNA-seq transcriptome data from SOAT2-only-HepG2 cells (treated with ATO 5 umol/L, EZE, 25 umol/L, their combination or vehicle) and from liver biopsies of patients with uncomplicated cholesterol gallstone disease in the Stockholm Study (a single-blind, randomized trial with SIM 80 mg daily, EZE 10 mg daily, their combination, or placebo) to decipher the underlying molecular mechanisms of the drug combination. We proposed a Boolean logical modeling framework to simulate the MoA of a drug combination. Specifically, fourteen two-variable Boolean models were used to describe the combinatory relationships of ATO/SIM and EZE. Thereafter, a pattern matching approach was applied to associate drug-induced differentially expressed genes with the idealized differential expression templates derived from Boolean models. Results: We found 1,560 and 594 genes differentially expressed in at least one treatment condition in SOAT2-only-HepG2 cells and liver biopsies, respectively. Our analysis revealed both expected and novel combinatorial modes of ATO/SIM and EZE. For example, ATO independently activates downstream genes (i.e. B 4 (ATO,EZE)=ATO), and ATO and EZE synergistically inhibits downstream genes (i.e. B 15 (ATO,EZE)=NOT (ATO AND EZE)) , as the two most prevalent MoAs in SOAT2-only-HepG2 cells (Figure 1). Similarly, the combination of SIM and EZE synergistically inhibiting downstream genes was also the most prevalent MoA in the liver biopsies. We mapped the downstream genes of each combinatorial mode to the human interactome and obtained underlying subnetworks, which are important for understanding the therapeutic effects of the drug combination. Functional enrichment and disease-association analyses of the downstream suggest the additional therapeutic indications of the drugs. Conclusion: Drug-induced transcriptomes are informative in deciphering the MoA of drug combinations using Boolean logical modeling. This framework can be easily extended to the combinations of three drugs.

HHIP's Dynamic Role in Epithelial Wound Healing Reveals a Potential Mechanism of COPD Susceptibility.

A genetic variant near HHIP has been consistently identified as associated with increased risk for Chronic Obstructive Pulmonary Disease (COPD), the third leading cause of death worldwide. However HHIP's role in COPD pathogenesis remains elusive. Canonically, HHIP is a negative regulator of the hedgehog pathway and downstream GLI1 and GLI2 activation. The hedgehog pathway plays an important role in wound healing, specifically in activating transcription factors that drive the epithelial mesenchymal transition (EMT), which in its intermediate state (partial EMT) is necessary for the collective movement of cells closing the wound. Herein, we propose a mechanism to explain HHIP's role in faulty epithelial wound healing, which could contribute to the development of emphysema, a key feature of COPD. Using two different Boolean models compiled from the literature, we show dysfunctional HHIP results in a lack of negative feedback on GLI, triggering a full EMT, where cells become mesenchymal and do not properly close the wound. We validate these Boolean models with experimental evidence gathered from published scientific literature. We also experimentally test if low HHIP expression is associated with EMT at the edge of wounds by using a scratch assay in a human lung epithelial cell line. Finally, we show evidence supporting our hypothesis in bulk and single cell RNA-Seq data from different COPD cohorts. Overall, our analyses suggest that aberrant wound healing due to dysfunctional HHIP, combined with chronic epithelial damage through cigarette smoke exposure, may be a primary cause of COPD-associated emphysema.

Building multiscale models with PhysiBoSS, an agent-based modeling tool.

Multiscale models provide a unique tool for analyzing complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. These models aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms-coupled with a graphical interface-is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to construct these models more easily, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as Supplementary Material and all models are provided at https://physiboss.github.io/tutorial/.

Cohort-specific boolean models highlight different regulatory modules during Parkinson’s disease progression

Parkinson's disease (PD) involves complex molecular interactions and diverse comorbidities. To better understand its molecular mechanisms, we employed systems medicine approaches using the PD map, a detailed repository of PD-related interactions and applied Probabilistic Boolean Networks (PBNs) to capture the stochastic nature of molecular dynamics. By integrating cohort-level and real-world patient data, we modeled PD's subtype-specific pathway deregulations, providing a refined representation of its molecular landscape. Our study identifies key regulatory biomolecules and pathways that vary across PD subtypes, offering insights into the disease's progression and patient stratification. These findings have significant implications for the development of targeted therapeutic interventions.

Bayesian Lookahead Perturbation Policy for Inference of Regulatory Networks.

The complexity, scale, and uncertainty in regulatory networks (e.g., gene regulatory networks and microbial networks) regularly pose a huge uncertainty in their models. These uncertainties often cannot be entirely reduced using limited and costly data acquired from the normal condition of systems. Meanwhile, regulatory networks often suffer from the non-identifiability issue, which refers to scenarios where the true underlying network model cannot be clearly distinguished from other possible models. Perturbation or excitation is a well-known process in systems biology for acquiring targeted data to reveal the complex underlying mechanisms of regulatory networks and overcome the non-identifiability issue. We consider a general class of Boolean network models for capturing the activation and inactivation of components and their complex interactions. Assuming partial available knowledge about the interactions between components of the networks, this paper formulates the inference process through the maximum aposteriori (MAP) criterion. We develop a Bayesian lookahead policy that systematically perturbs regulatory networks to maximize the performance of MAP inference under the perturbed data. This is achieved by optimally formulating the perturbation process in a reinforcement learning context and deriving a scalable deep reinforcement learning perturbation policy to compute near-optimal Bayesian policy. The proposed method learns the perturbation policy through planning without the need for any real data. The high performance of the proposed approach is demonstrated by comprehensive numerical experiments using the well-known mammalian cell cycle and gut microbial community networks.

Modular construction of Boolean networks

Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as dynamical systems have been studied through simulation studies, due to a lack of mathematical structure. This paper uses a common mathematical technique to identify a class of Boolean networks with a “simple” structure and describes an algorithm to construct arbitrary extensions of a collection of simple Boolean networks. In this way, all Boolean networks can be obtained from a collection of simple Boolean networks as building blocks. The paper furthermore provides a formula for the number of extensions of given simple networks and, in some cases, provides a parametrization of those extensions. This has potential applications to the construction of networks with particular properties, for instance in synthetic biology, and can also be applied to develop efficient control algorithms for Boolean network models.

ScBoolSeq: Linking scRNA-seq statistics and Boolean dynamics.

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 expression 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.

Characterization of supercritical CO2 heat transfer in microporous media under (T/p)-mutability and integrated random function

The thermophysical properties of supercritical carbon dioxide (sCO2) undergo drastic changes under reservoir conditions, which significantly affects transfer characteristics and the storage efficiency. The present work seeks to identity of the heat transfer response of a mutable sCO2 in porous micromodels with integrated Boolean stochastic models. An upgraded variant of Lattice Boltzmann model is used after a thorough validation with literature experiments. The injection conditions of sCO2 are ranged from 295 to 333 K and 8–10 MPa, with a mass flow rate of 0.05–0.20 kg/min. The thermodynamic instabilities are discussed through the joint bonds between temperature and density, local and overall heat transfer, and pressure drop coefficient, under a series of pore-throats dimension from 7.5 to 401.3 μm. The results showed: (i) the remarkable (T/p)-nature of heat transfer capacity of sCO2 to lead the transfer coefficients with a subordinate impact of thermal conductivity near the Widom line, as long as the convective mode primes with increased temperature and pressure; (ii) The heterogeneity of the microporous media promoted the decrease of the transfer capacity while adjusting the spatiotemporal density and the heat transfer orientations inside the pore bodies; (iii) the growth of the pressure drop under increasing temperature has revealed an equilibrium stage where, neither the mutability of sCO2 properties nor the injection intensity can significantly affect the heat transfer of the integrated microporous.

SAILoR: Structure-Aware Inference of Logic Rules.

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.

Maboss for HPC environments: implementations of the continuous time Boolean model simulator for large CPU clusters and GPU accelerators

BackgroundComputational models in systems biology are becoming more important with the advancement of experimental techniques to query the mechanistic details responsible for leading to phenotypes of interest. In particular, Boolean models are well fit to describe the complexity of signaling networks while being simple enough to scale to a very large number of components. With the advance of Boolean model inference techniques, the field is transforming from an artisanal way of building models of moderate size to a more automatized one, leading to very large models. In this context, adapting the simulation software for such increases in complexity is crucial.ResultsWe present two new developments in the continuous time Boolean simulators: MaBoSS.MPI, a parallel implementation of MaBoSS which can exploit the computational power of very large CPU clusters, and MaBoSS.GPU, which can use GPU accelerators to perform these simulations.ConclusionThese implementations enable simulation and exploration of the behavior of very large models, thus becoming a valuable analysis tool for the systems biology community.

A gray box framework that optimizes a white box logical model using a black box optimizer for simulating cellular responses to perturbations

Predicting cellular responses to perturbations requires interpretable insights into molecular regulatory dynamics to perform reliable cell fate control, despite the confounding non-linearity of the underlying interactions. There is a growing interest in developing machine learning-based perturbation response prediction models to handle the non-linearity of perturbation data, but their interpretation in terms of molecular regulatory dynamics remains a challenge. Alternatively, for meaningful biological interpretation, logical network models such as Boolean networks are widely used in systems biology to represent intracellular molecular regulation. However, determining the appropriate regulatory logic of large-scale networks remains an obstacle due to the high-dimensional and discontinuous search space. To tackle these challenges, we present a scalable derivative-free optimizer trained by meta-reinforcement learning for Boolean network models. The logical network model optimized by the trained optimizer successfully predicts anti-cancer drug responses of cancer cell lines, while simultaneously providing insight into their underlying molecular regulatory mechanisms.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

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.

Single-cell multi-omics analysis identifies context-specific gene regulatory gates and mechanisms.

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.

Preponderance of generalized chain functions in reconstructed Boolean models of biological networks

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.

MetaLo: metabolic analysis of Logical models extracted from molecular interaction maps.

Molecular interaction maps (MIMs) are static graphical representations depicting complex biochemical networks that can be formalized using one of the Systems Biology Graphical Notation languages. Regardless of their extensive coverage of various biological processes, they are limited in terms of dynamic insights. However, MIMs can serve as templates for developing dynamic computational models. We present MetaLo, an open-source Python package that enables the coupling of Boolean models inferred from process description MIMs with generic core metabolic networks. MetaLo provides a framework to study the impact of signaling cascades, gene regulation processes, and metabolic flux distribution of central energy production pathways. MetaLo computes the Boolean model's asynchronous asymptotic behavior, through the identification of trap-spaces, and extracts metabolic constraints to contextualize the generic metabolic network. MetaLo is able to handle large-scale Boolean models and genome-scale metabolic models without requiring kinetic information or manual tuning. The framework behind MetaLo enables in depth analysis of the regulatory model, and may allow tackling a lack of omics data in poorly addressed biological fields to contextualize generic metabolic networks along with improper automatic reconstructions of cell- and/or disease-specific metabolic networks. MetaLo is available at https://pypi.org/project/metalo/ under the terms of the GNU General Public License v3.

Breaking reflection symmetry: evolving long dynamical cycles in Boolean systems

In interacting dynamical systems, specific local interaction rules for system components give rise to diverse and complex global dynamics. Long dynamical cycles are a key feature of many natural interacting systems, especially in biology. Examples of dynamical cycles range from circadian rhythms regulating sleep to cell cycles regulating reproductive behavior. Despite the crucial role of cycles in nature, the properties of network structure that give rise to cycles still need to be better understood. Here, we use a Boolean interaction network model to study the relationships between network structure and cyclic dynamics. We identify particular structural motifs that support cycles, and other motifs that suppress them. More generally, we show that the presence of dynamical reflection symmetry in the interaction network enhances cyclic behavior. In simulating an artificial evolutionary process, we find that motifs that break reflection symmetry are discarded. We further show that dynamical reflection symmetries are over-represented in Boolean models of natural biological systems. Altogether, our results demonstrate a link between symmetry and functionality for interacting dynamical systems, and they provide evidence for symmetry’s causal role in evolving dynamical functionality.

Large-scale computational modelling of the M1 and M2 synovial macrophages in rheumatoid arthritis

Macrophages play an essential role in rheumatoid arthritis. Depending on their phenotype (M1 or M2), they can play a role in the initiation or resolution of inflammation. The M1/M2 ratio in rheumatoid arthritis is higher than in healthy controls. Despite this, no treatment targeting specifically macrophages is currently used in clinics. Thus, devising strategies to selectively deplete proinflammatory macrophages and promote anti-inflammatory macrophages could be a promising therapeutic approach. State-of-the-art molecular interaction maps of M1 and M2 macrophages in rheumatoid arthritis are available and represent a dense source of knowledge; however, these maps remain limited by their static nature. Discrete dynamic modelling can be employed to study the emergent behaviours of these systems. Nevertheless, handling such large-scale models is challenging. Due to their massive size, it is computationally demanding to identify biologically relevant states in a cell- and disease-specific context. In this work, we developed an efficient computational framework that converts molecular interaction maps into Boolean models using the CaSQ tool. Next, we used a newly developed version of the BMA tool deployed to a high-performance computing cluster to identify the models’ steady states. The identified attractors are then validated using gene expression data sets and prior knowledge. We successfully applied our framework to generate and calibrate the M1 and M2 macrophage Boolean models for rheumatoid arthritis. Using KO simulations, we identified NFkB, JAK1/JAK2, and ERK1/Notch1 as potential targets that could selectively suppress proinflammatory macrophages and GSK3B as a promising target that could promote anti-inflammatory macrophages in rheumatoid arthritis.

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks.

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data are sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy, and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.

GatekeepR: an R Shiny application for the identification of nodes with high dynamic impact in Boolean networks.

Boolean networks can serve as straightforward models for understanding processes such as gene regulation, and employing logical rules. These rules can either be derived from existing literature or by data-driven approaches. However, in the context of large networks, the exhaustive search for intervention targets becomes challenging due to the exponential expansion of a Boolean network's state space and the multitude of potential target candidates, along with their various combinations. Instead, we can employ the logical rules and resultant interaction graph as a means to identify targets of specific interest within larger-scale models. This approach not only facilitates the screening process but also serves as a preliminary filtering step, enabling the focused investigation of candidates that hold promise for more profound dynamic analysis. However, applying this method requires a working knowledge of R, thus restricting the range of potential users. We, therefore, aim to provide an application that makes this method accessible to a broader scientific community. Here, we introduce GatekeepR, a graphical, web-based R Shiny application that enables scientists to screen Boolean network models for possible intervention targets whose perturbation is likely to have a large impact on the system's dynamics. This application does not require a local installation or knowledge of R and provides the suggested targets along with additional network information and visualizations in an intuitive, easy-to-use manner. The Supplementary Material describes the underlying method for identifying these nodes along with an example application in a network modeling pancreatic cancer. https://www.github.com/sysbio-bioinf/GatekeepR https://abel.informatik.uni-ulm.de/shiny/GatekeepR/.