Boolean Model Research Articles

A Model for the Gene Regulatory Network Along the Arabidopsis Fruit Medio-Lateral Axis: Rewiring the Pod Shatter Process.

Different convergent evolutionary strategies adopted by angiosperm fruits lead to diverse functional seed dispersal units. Dry dehiscent fruits are a common type of fruit, characterized by their lack of fleshy pericarp and the release of seeds at maturity through openings (dehiscence zones, DZs) in their structure. In previous decades, a set of core players in DZ formation have been intensively characterized in Arabidopsis and integrated in a gene regulatory network (GRN) that explains the morphogenesis of these tissues. In this work, we compile all the experimental data available to date to build a discrete Boolean model as a mechanistic approach to validate the network and, if needed, to identify missing components of the GRN and/or propose new hypothetical regulatory interactions, but also to provide a new formal framework to feed further work in Brassicaceae fruit development and the evolution of seed dispersal mechanisms. Hence, by means of exhaustive in-silico validations and experimental evidence, we are able to incorporate both the NO TRANSMITTING TRACT (NTT) transcription factor as a new additional node, and a new set of regulatory hypothetical rules to uncover the dynamics of Arabidopsis DZ specification.

Stochastic Boolean model of normal and aberrant cell cycles in budding yeast

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

Macrophages on the run: Exercise balances macrophage polarization for improved health

ObjectiveExercise plays a crucial role in maintaining and improving human health. However, the precise molecular mechanisms that govern the body’s response to exercise or/compared to periods of inactivity remain elusive. Current evidence appears to suggest that exercise exerts a seemingly dual influence on macrophage polarization states, inducing both pro-immune response M1 activation and cell-repair-focused M2 activation. To reconcile this apparent paradox, we leveraged a comprehensive meta-analysis of 75 diverse exercise and immobilization published datasets (7000+ samples), encompassing various exercise modalities, sampling techniques, and species. Methods75 exercise and immobilization expression datasets were identified and processed for analysis. The data was analyzed using boolean relationships which uses binary gene expression relationships in order to increase the signal to noise achieved from the data, allowing for the use of comparison across such a diverse set of datasets. We utilized a boolean relationship-aided macrophage gene model [1], to model the macrophage polarization state in pre and post exercise samples in both immediate exercise and long term training. ResultsOur modeling uncovered a key temporal dynamic: exercise triggers an immediate M1 surge, while long term training transitions to sustained M2 activation. These patterns were consistent across different species (human vs mouse), sampling methods (blood vs muscle biopsy), and exercise type (resistance vs endurance), and routinely showed statistically significant results. Immobilization was shown to have the opposite effect of exercise by triggering an immediate M2 activation. Individual characteristics like gender, exercise intensity and age were found to impact the degree of polarization without changing the overall patterns. To model macrophages within the specific context of muscle tissue, we identified a focused gene set signature of muscle resident macrophage polarization, allowing for the precise measurement of macrophage activity in response to exercise within the muscle. ConclusionsThese consistent patterns across all 75 examined studies suggest that the long term health benefits of exercise stem from its ability to orchestrate a balanced and temporally-regulated interplay between pro-immune response (M1) and reparative macrophage activity (M2). Similarly, it suggests that an imbalance between pro-immune and cell repair responses could facilitate disease development. Our findings shed light on the intricate molecular choreography behind exercise-induced health benefits with a particular insight on its effect on the macrophages within the muscle.

A Boolean model explains phenotypic plasticity changes underlying hepatic cancer stem cells emergence

In several carcinomas, including hepatocellular carcinoma, it has been demonstrated that cancer stem cells (CSCs) have enhanced invasiveness and therapy resistance compared to differentiated cancer cells. Mathematical-computational tools could be valuable for integrating experimental results and understanding the phenotypic plasticity mechanisms for CSCs emergence. Based on the literature review, we constructed a Boolean model that recovers eight stable states (attractors) corresponding to the gene expression profile of hepatocytes and mesenchymal cells in senescent, quiescent, proliferative, and stem-like states. The epigenetic landscape associated with the regulatory network was analyzed. We observed that the loss of p53, p16, RB, or the constitutive activation of β-catenin and YAP1 increases the robustness of the proliferative stem-like phenotypes. Additionally, we found that p53 inactivation facilitates the transition of proliferative hepatocytes into stem-like mesenchymal phenotype. Thus, phenotypic plasticity may be altered, and stem-like phenotypes related to CSCs may be easier to attain following the mutation acquisition.

Unlocking mitochondrial dysfunction-associated senescence (MiDAS) with NAD+ – A Boolean model of mitochondrial dynamics and cell cycle control

The steady accumulation of senescent cells with aging creates tissue environments that aid cancer evolution. Aging cell states are highly heterogeneous. 'Deep senescent' cells rely on healthy mitochondria to fuel a strong proinflammatory secretome, including cytokines, growth and transforming signals. Yet, the physiological triggers of senescence such as reactive oxygen species (ROS) can also trigger mitochondrial dysfunction, and sufficient energy deficit to alter their secretome and cause chronic oxidative stress – a state termed Mitochondrial Dysfunction-Associated Senescence (MiDAS). Here, we offer a mechanistic hypothesis for the molecular processes leading to MiDAS, along with testable predictions. To do this we have built a Boolean regulatory network model that qualitatively captures key aspects of mitochondrial dynamics during cell cycle progression (hyper-fusion at the G1/S boundary, fission in mitosis), apoptosis (fission and dysfunction) and glucose starvation (reversible hyper-fusion), as well as MiDAS in response to SIRT3 knockdown or oxidative stress. Our model reaffirms the protective role of NAD+ and external pyruvate. We offer testable predictions about the growth factor- and glucose-dependence of MiDAS and its reversibility at different stages of reactive oxygen species (ROS)-induced senescence. Our model provides mechanistic insights into the distinct stages of DNA-damage induced senescence, the relationship between senescence and epithelial-to-mesenchymal transition in cancer and offers a foundation for building multiscale models of tissue aging.

LncRNA PTENP1/miR-21/PTEN Axis Modulates EMT and Drug Resistance in Cancer: Dynamic Boolean Modeling for Cell Fates in DNA Damage Response.

It is well established that microRNA-21 (miR-21) targets phosphatase and tensin homolog (PTEN), facilitating epithelial-to-mesenchymal transition (EMT) and drug resistance in cancer. Recent evidence indicates that PTEN activates its pseudogene-derived long non-coding RNA, PTENP1, which in turn inhibits miR-21. However, the dynamics of PTEN, miR-21, and PTENP1 in the DNA damage response (DDR) remain unclear. Thus, we propose a dynamic Boolean network model by integrating the published literature from various cancers. Our model shows good agreement with the experimental findings from breast cancer, hepatocellular carcinoma (HCC), and oral squamous cell carcinoma (OSCC), elucidating how DDR activation transitions from the intra-S phase to the G2 checkpoint, leading to a cascade of cellular responses such as cell cycle arrest, senescence, autophagy, apoptosis, drug resistance, and EMT. Model validation underscores the roles of PTENP1, miR-21, and PTEN in modulating EMT and drug resistance. Furthermore, our analysis reveals nine novel feedback loops, eight positive and one negative, mediated by PTEN and implicated in DDR cell fate determination, including pathways related to drug resistance and EMT. Our work presents a comprehensive framework for investigating cellular responses following DDR, underscoring the therapeutic potential of targeting PTEN, miR-21, and PTENP1 in cancer treatment.

Corrections: On the capacity functional of the infinite cluster of a Boolean model

Corrections: On the capacity functional of the infinite cluster of a Boolean model

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.

Using Pattern Counts to Quantify the Difference Between a Pair of Three-Dimensional Realizations

When comparing different ways of modeling discrete three-dimensional realizations such as facies, it is useful to have a measure of difference (or similarity) in the geometry of these realizations. We propose a method for evaluating such difference by comparing pattern counts for a small template. Tests on synthetic datasets demonstrate that the proposed difference effectively differentiates between realizations of a Boolean model and those generated using multiple-point statistics with the Boolean realizations as training images. We also observed that multiple-point statistics realizations based on similar training images yield smaller differences to one another compared to those based on training images from dissimilar concepts. This suggests that the proposed difference is a useful tool for comparing discrete three-dimensional realizations.

Comprehensive molecular interaction map of TGFβ induced epithelial to mesenchymal transition in breast cancer

Breast cancer is one of the prevailing cancers globally, with a high mortality rate. Metastatic breast cancer (MBC) is an advanced stage of cancer, characterised by a highly nonlinear, heterogeneous process involving numerous singling pathways and regulatory interactions. Epithelial–mesenchymal transition (EMT) emerges as a key mechanism exploited by cancer cells. Transforming Growth Factor-β (TGFβ)-dependent signalling is attributed to promote EMT in advanced stages of breast cancer. A comprehensive regulatory map of TGFβ induced EMT was developed through an extensive literature survey. The network assembled comprises of 312 distinct species (proteins, genes, RNAs, complexes), and 426 reactions (state transitions, nuclear translocations, complex associations, and dissociations). The map was developed by following Systems Biology Graphical Notation (SBGN) using Cell Designer and made publicly available using MINERVA (http://35.174.227.105:8080/minerva/?id=Metastatic_Breast_Cancer_1). While the complete molecular mechanism of MBC is still not known, the map captures the elaborate signalling interplay of TGFβ induced EMT-promoting MBC. Subsequently, the disease map assembled was translated into a Boolean model utilising CaSQ and analysed using Cell Collective. Simulations of these have captured the known experimental outcomes of TGFβ induced EMT in MBC. Hub regulators of the assembled map were identified, and their transcriptome-based analysis confirmed their role in cancer metastasis. Elaborate analysis of this map may help in gaining additional insights into the development and progression of metastatic breast cancer.

A network-based modeling framework reveals the core signal transduction network underlying high carbon dioxide-induced stomatal closure in guard cells.

Stomata are pores on plant aerial surfaces, each bordered by a pair of guard cells. They control gas exchange vital for plant survival. Understanding how guard cells respond to environmental signals such as atmospheric carbon dioxide (CO2) levels is not only insightful to fundamental biology but also relevant to real-world issues of crop productivity under global climate change. In the past decade, multiple important signaling elements for stomatal closure induced by elevated CO2 have been identified. Yet, there is no comprehensive understanding of high CO2-induced stomatal closure. In this work, we assemble a cellular signaling network underlying high CO2-induced stomatal closure by integrating evidence from a comprehensive literature analysis. We further construct a Boolean dynamic model of the network, which allows in silico simulation of the stomatal closure response to high CO2 in wild-type Arabidopsis thaliana plants and in cases of pharmacological or genetic manipulation of network nodes. Our model has a 91% accuracy in capturing known experimental observations. We perform network-based logical analysis and reveal a feedback core of the network, which dictates cellular decisions in closure response to high CO2. Based on these analyses, we predict and experimentally confirm that applying nitric oxide (NO) induces stomatal closure in ambient CO2 and causes hypersensitivity to elevated CO2. Moreover, we predict a negative regulatory relationship between NO and the protein phosphatase ABI2 and find experimentally that NO inhibits ABI2 phosphatase activity. The experimental validation of these model predictions demonstrates the effectiveness of network-based modeling and highlights the decision-making role of the feedback core of the network in signal transduction. We further explore the model's potential in predicting targets of signaling elements not yet connected to the CO2 network. Our combination of network science, in silico model simulation, and experimental assays demonstrates an effective interdisciplinary approach to understanding system-level biology.

The contact process on scale-free geometric random graphs

We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on Rd. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.

Research on Complex Network Models and Characteristics of Building Material Enterprises Based on Competitive Relationships

Based on complex network theory, this paper establishes a Boolean competitive relationship network model and a weighted competitive relationship network model for building material enterprises based on big data and performs empirical analyses with construction prefabricated component (PC) enterprises in the Beijing–Tianjin–Hebei region as research samples. Results show the competitive relationship network of PC enterprises in the Beijing–Tianjin–Hebei region is characterised by the development of a small-world network, and its cumulative degree and out-degree (in-degree) intensity distributions are single-scale networks with fast-decaying tails. The network has strong network clustering and assortativity, and it can truly reflect the competitive status and dynamics of the enterprises.

Wetting of alginate aerogels, from mesoporous solids to hydrogels: a small-angle scattering analysis

Mesoporous polysaccharide aerogels are versatile functional materials for drug delivery and wound dressing devices. The hydration and wetting of these aerogels control their application-related performance, e.g. the release of encapsulated drugs. Reported here is a detailed small-angle neutron scattering (SANS) analysis of the hydration mechanism of a calcium alginate aerogel, based on mathematical modelling of the scattering. The model accounts for the hierarchical structure of the material comprising a mesoporous structure, the solid skeleton of which is made up of water-swollen polymers. At large scale, the mesoporous structure is modelled as a random collection of elongated cylinders, which grow in size as they absorb water and aggregate. The small-scale inner structure of the skeleton is described as a Boolean model of polymer coils, which captures the progressive transition from a dense dry polymer to a fully hydrated gel. Using known physico-chemical characteristics of the alginate, the SANS data are fitted using the size of the cylinders as the only adjustable parameter. The alginate aerogel maintains a nanometre-scale, albeit altered, structure for low water contents but it collapses into micrometre-sized structures when the water content approaches one gram of water per gram of alginate. In addition to the wetting of aerogels, the model might be useful for the small-angle scattering analysis of the supercritical drying of gels.

Automated code development based on genetic programming in graphical programming language: A pilot study.

Continual technological advances associated with the recent automation revolution have tremendously increased the impact of computer technology in the industry. Software development and testing are time-consuming processes, and the current market faces a lack of specialized experts. Introducing automation to this field could, therefore, improve software engineers' common workflow and decrease the time to market. Even though many code-generating algorithms have been proposed in textual-based programming languages, to the best of the authors' knowledge, none of the studies deals with the implementation of such algorithms in graphical programming environments, especially LabVIEW. Due to this fact, the main goal of this study is to conduct a proof-of-concept for a requirement-based automated code-developing system within the graphical programming environment LabVIEW. The proposed framework was evaluated on four basic benchmark problems, encompassing a string model, a numeric model, a boolean model and a mixed-type problem model, which covers fundamental programming scenarios. In all tested cases, the algorithm demonstrated an ability to create satisfying functional and errorless solutions that met all user-defined requirements. Even though the generated programs were burdened with redundant objects and were much more complex compared to programmer-developed codes, this fact has no effect on the code's execution speed or accuracy. Based on the achieved results, we can conclude that this pilot study not only proved the feasibility and viability of the proposed concept, but also showed promising results in solving linear and binary programming tasks. Furthermore, the results revealed that with further research, this poorly explored field could become a powerful tool not only for application developers but also for non-programmers and low-skilled users.

Boolean modeling of breast cancer signaling pathways uncovers mechanisms of drug synergy.

Breast cancer is one of the most common types of cancer in females. While drug combinations have shown potential in breast cancer treatments, identifying new effective drug pairs is challenging due to the vast number of possible combinations among available compounds. Efforts have been made to accelerate the process with in silico predictions. Here, we developed a Boolean model of signaling pathways in breast cancer. The model was tailored to represent five breast cancer cell lines by integrating information about cell-line specific mutations, gene expression, and drug treatments. The models reproduced cell-line specific protein activities and drug-response behaviors in agreement with experimental data. Next, we proposed a calculation of protein synergy scores (PSSs), determining the effect of drug combinations on individual proteins' activities. The PSSs of selected proteins were used to investigate the synergistic effects of 150 drug combinations across five cancer cell lines. The comparison of the highest single agent (HSA) synergy scores between experiments and model predictions from the MDA-MB-231 cell line achieved the highest Pearson's correlation coefficient of 0.58 with a great balance among the classification metrics (AUC = 0.74, sensitivity = 0.63, and specificity = 0.64). Finally, we clustered drug pairs into groups based on the selected PSSs to gain further insights into the mechanisms underlying the observed synergistic effects of drug pairs. Clustering analysis allowed us to identify distinct patterns in the protein activities that correspond to five different modes of synergy: 1) synergistic activation of FADD and BID (extrinsic apoptosis pathway), 2) synergistic inhibition of BCL2 (intrinsic apoptosis pathway), 3) synergistic inhibition of MTORC1, 4) synergistic inhibition of ESR1, and 5) synergistic inhibition of CYCLIN D. Our approach offers a mechanistic understanding of the efficacy of drug combinations and provides direction for selecting potential drug pairs worthy of further laboratory investigation.

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.

Network dynamics investigation of omics-data-driven circadian-hypoxia crosstalk logical model in gallbladder cancer reveals key therapeutic target combinations.

Recent findings in cancer research have pointed towards the bidirectional interaction between circadian and hypoxia pathways. However, little is known about their crosstalk mechanism. In this work, we aimed to investigate this crosstalk at a network level utilizing the omics information of gallbladder cancer. Differential gene expression and pathway enrichment analysis were used for selecting the crucial genes from both the pathways, followed by the construction of a logical crosstalk model using GINsim. Functional circuit identification and node perturbations were then performed. Significant node combinations were used to investigate the temporal behavior of the network through MaBoSS. Lastly, the model was validated using published in vitro experimentations. Four new positive circuits and a new axis viz. BMAL1/ HIF1αβ/ NANOG, responsible for stemness were identified. Through triple node perturbations viz.a. BMAL:CLOCK (KO or E1) + P53 (E1) + HIF1α (KO); b. P53 (E1) + HIF1α (KO) + MYC (E1); and c. HIF1α (KO) + MYC (E1) + EGFR (KO), the model was able to inhibit cancer growth and maintain a homeostatic condition. This work provides an architecture for drug simulation analysis to entrainment circadian rhythm and in vitro experiments for chronotherapy-related studies. Insight Box. Circadian rhythm and hypoxia are the key dysregulated processes which fuels-up the cancer growth. In the present work we have developed a gallbladder cancer (GBC) specific Boolean model, utilizing the RNASeq data from GBC dataset and tissue specific interactions. This work adequately models the bidirectional nature of interactions previously illustrated in experimental papers showing the effect of hypoxia on dysregulation of circadian rhythm and the influence of this disruption on progression towards metastasis. Through the dynamical study of the model and its response to different perturbations, we report novel triple node combinations that can be targeted to efficiently reduce GBC growth. This network can be used as a generalized framework to investigate different crosstalk pathways linked with cancer progression.

Boolean model of the gene regulatory network of Pseudomonas aeruginosa CCBH4851.

Pseudomonas aeruginosa infections are one of the leading causes of death in immunocompromised patients with cystic fibrosis, diabetes, and lung diseases such as pneumonia and bronchiectasis. Furthermore, P. aeruginosa is one of the main multidrug-resistant bacteria responsible for nosocomial infections worldwide, including the multidrug-resistant CCBH4851 strain isolated in Brazil. One way to analyze their dynamic cellular behavior is through computational modeling of the gene regulatory network, which represents interactions between regulatory genes and their targets. For this purpose, Boolean models are important predictive tools to analyze these interactions. They are one of the most commonly used methods for studying complex dynamic behavior in biological systems. Therefore, this research consists of building a Boolean model of the gene regulatory network of P. aeruginosa CCBH4851 using data from RNA-seq experiments. Next, the basins of attraction are estimated, as these regions and the transitions between them can help identify the attractors, representing long-term behavior in the Boolean model. The essential genes of the basins were associated with the phenotypes of the bacteria for two conditions: biofilm formation and polymyxin B treatment. Overall, the Boolean model and the analysis method proposed in this work can identify promising control actions and indicate potential therapeutic targets, which can help pinpoint new drugs and intervention strategies.