Boolean modeling of biological regulatory networks: a methodology tutorial

PseudoCell: A Multivalued Logical Regulatory Network to Investigate Premature Senescence Dynamics and Heterogeneity

Purpose

Premature cellular senescence is a pivotal process in aging and age-related diseases, triggered by various stressors. However, this is not a homogeneous phenotype, but a heterogeneous cellular state composed of multiple senescence programs with different compositions. Therefore, understanding the complex dynamics of senescence programs requires a systemic approach. We introduce PseudoCell, a multivalued logical regulatory network designed to explore the molecular intricacies of premature senescence.

Methods

PseudoCell integrates key senescence signaling pathways and molecular mechanisms, offering a versatile platform for investigating diverse premature senescence programs initiated by different stimuli.

Results

Validation through simulation of classical senescence programs, including oxidative stress-induced senescence and oncogene-induced senescence, demonstrates its ability to replicate molecular signatures consistent with empirical data. Additionally, we explore the role of CCL11, a novel senescence-associated molecule, through simulations that reveal potential pathways and mechanisms underlying CCL11-mediated senescence induction.

Conclusions

In conclusion, PseudoCell provides a systematic approach to dissecting premature senescence programs and uncovering novel regulatory mechanisms.

How the dynamic interplay of cortico-basal ganglia-thalamic pathways shapes the time course of deliberation and commitment

Although the cortico-basal ganglia-thalamic (CBGT) network is identified as a central circuit for decision-making, the dynamic interplay of multiple control pathways within this network in shaping decision trajectories remains poorly understood. Here we develop and apply a novel computational framework - CLAW (Circuit Logic Assessed via Walks) - for tracing the instantaneous flow of neural activity as it progresses through CBGT networks engaged in a virtual decision-making task. Our CLAW analysis reveals that the complex dynamics of network activity is functionally dissectible into two critical phases: deliberation and commitment. These two phases are governed by distinct contributions of underlying CBGT pathways, with indirect and pallidostriatal pathways influencing deliberation, while the direct pathway drives action commitment. We translate CBGT dynamics into the evolution of decision-related policies, based on three previously identified control ensembles (responsiveness, pliancy, and choice) that encapsulate the relationship between CBGT activity and the evidence accumulation process. Our results demonstrate two contrasting strategies for decision-making. Fast decisions, with direct pathway dominance, feature an early response in both boundary height and drift rate, leading to a rapid collapse of decision boundaries and a clear directional bias. In contrast, slow decisions, driven by indirect and pallidostriatal pathway dominance, involve delayed changes in both decision policy parameters, allowing for an extended period of deliberation before commitment to an action. These analyses provide important insights into how the CBGT circuitry can be tuned to adopt various decision strategies and how the decision-making process unfolds within each regime.

Operating principles of interconnected feedback loops driving cell fate transitions

Interconnected feedback loops are prevalent across biological mechanisms, including cell fate transitions enabled by epigenetic mechanisms in carcinomas. However, the operating principles of these networks remain largely unexplored. Here, we identify numerous interconnected feedback loops implicated in cell lineage decisions, which we discover to be the hallmarks of lower- and higher-dimensional state space. We demonstrate that networks having higher centrality nodes have restricted state space while those with lower centrality nodes have higher dimensional state space. The topologically distinct networks with identical node or loop counts have different steady-state distributions, highlighting the crucial influence of network structure on emergent dynamics. Further, regardless of topology, networks with autoregulated nodes exhibit multiple steady states, thereby "liberating" network dynamics from absolute topological control. These findings unravel the design principles of multistable networks implicated in fate decisions and can have crucial implications in engineering or comprehending multi-fate decision circuits.

A Computational Protocol for the Knowledge-Based Assessment and Capture of Pathologies

We propose that one of the main hurdles in delivering comprehensively informed care results from the challenges surrounding the extraction, representation, and retention of prior clinical experience and basic medical knowledge, as well as its translation into time- and context-informed actionable interventions. While emerging applications in artificial intelligence-based techniques, for example, large language models, offer impressive pattern association capabilities, they often fall short in producing human-readable explanations crucial to their integration into clinical care. Moreover, they require large well-defined and well-integrated data sets that typically conflict with the availability of such data in all but a few areas of medicine, for example, medical imaging and neuroimaging, noninvasive monitoring of bio-electrical activity, etc. In this chapter, we argue that approximate reasoning rooted in the knowledge that is explainable to the human clinician may offer attractive avenues for the introduction of such knowledge in a systematic way that supports formal retention, sharing, and reuse of new clinical and basic medical experience. We outline a conceptual protocol that targets the use of sparse and disparate data of different types and from different sources, seamlessly drawing on our collective experience and that of others. We illustrate the utility of such an integrative approach by applying the latter to the assessment and reconciliation of data from different experimental models, human and animal, in the example use case of a complex health condition.

Approaches for Benchmarking Single-Cell Gene Regulatory Network Methods

Gene regulatory networks are powerful tools for modeling genetic interactions that control the expression of genes driving cell differentiation, and single-cell sequencing offers a unique opportunity to build these networks with high-resolution genomic data. There are many proposed computational methods to build these networks using single-cell data, and different approaches are used to benchmark these methods. However, a comprehensive discussion specifically focusing on benchmarking approaches is missing. In this article, we lay the GRN terminology, present an overview of common gold-standard studies and data sets, and define the performance metrics for benchmarking network construction methodologies. We also point out the advantages and limitations of different benchmarking approaches, suggest alternative ground truth data sets that can be used for benchmarking, and specify additional considerations in this context.

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.

Evolving higher-order synergies reveals a trade-off between stability and information-integration capacity in complex systems

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

The art of modeling gene regulatory circuits

The amazing complexity of gene regulatory circuits, and biological systems in general, makes mathematical modeling an essential tool to frame and develop our understanding of their properties. Here, we present some fundamental considerations to develop and analyze a model of a gene regulatory circuit of interest, either representing a natural, synthetic, or theoretical system. A mathematical model allows us to effectively evaluate the logical implications of our hypotheses. Using our models to systematically perform in silico experiments, we can then propose specific follow-up assessments of the biological system as well as to reformulate the original assumptions, enriching both our knowledge and our understanding of the system. We want to invite the community working on different aspects of gene regulatory circuits to explore the power and benefits of mathematical modeling in their system.

A perfectly imperfect engine: Utilizing the digital twin paradigm in pulmonary hypertension

Pulmonary hypertension (PH) is a severe medical condition with a number of treatment options, the majority of which are introduced without consideration of the underlying mechanisms driving it within an individual and thus a lack of tailored approach to treatment. The one exception is a patient presenting with apparent pulmonary arterial hypertension and shown to have vaso-responsive disease, whose clinical course and prognosis is significantly improved by high dose calcium channel blockers. PH is however characterized by a relative abundance of available data from patient cohorts, ranging from molecular data characterizing gene and protein expression in different tissues to physiological data at the organ level and clinical information. Integrating available data with mechanistic information at the different scales into computational models suggests an approach to a more personalized treatment of the disease using model-based optimization of interventions for individual patients. That is, constructing digital twins of the disease, customized to a patient, promises to be a key technology for personalized medicine, with the aim of optimizing use of existing treatments and developing novel interventions, such as new drugs. This article presents a perspective on this approach in the context of a review of existing computational models for different aspects of the disease, and it lays out a roadmap for a path to realizing it.

Modulating the dynamics of NFκB and PI3K enhances the ensemble-level TNFR1 signaling mediated apoptotic response

Cell-to-cell variability during TNFα stimulated Tumor Necrosis Factor Receptor 1 (TNFR1) signaling can lead to single-cell level pro-survival and apoptotic responses. This variability stems from the heterogeneity in signal flow through intracellular signaling entities that regulate the balance between these two phenotypes. Using systematic Boolean dynamic modeling of a TNFR1 signaling network, we demonstrate that the signal flow path variability can be modulated to enable cells favour apoptosis. We developed a computationally efficient approach "Boolean Modeling based Prediction of Steady-state probability of Phenotype Reachability (BM-ProSPR)" to accurately predict the network's ability to settle into different phenotypes. Model analysis juxtaposed with the experimental observations revealed that NFκB and PI3K transient responses guide the XIAP behaviour to coordinate the crucial dynamic cross-talk between the pro-survival and apoptotic arms at the single-cell level. Model predicted the experimental observations that ~31% apoptosis increase can be achieved by arresting Comp1 - IKK* activity which regulates the NFκB and PI3K dynamics. Arresting Comp1 - IKK* activity causes signal flow path re-wiring towards apoptosis without significantly compromising NFκB levels, which govern adequate cell survival. Priming an ensemble of cancerous cells with inhibitors targeting the specific interaction involving Comp1 and IKK* prior to TNFα exposure could enable driving them towards apoptosis.

iLSGRN: inference of large-scale gene regulatory networks based on multi-model fusion

MOTIVATION

Gene regulatory networks (GRNs) are a way of describing the interaction between genes, which contribute to revealing the different biological mechanisms in the cell. Reconstructing GRNs based on gene expression data has been a central computational problem in systems biology. However, due to the high dimensionality and non-linearity of large-scale GRNs, accurately and efficiently inferring GRNs is still a challenging task.

RESULTS

In this article, we propose a new approach, iLSGRN, to reconstruct large-scale GRNs from steady-state and time-series gene expression data based on non-linear ordinary differential equations. Firstly, the regulatory gene recognition algorithm calculates the Maximal Information Coefficient between genes and excludes redundant regulatory relationships to achieve dimensionality reduction. Then, the feature fusion algorithm constructs a model leveraging the feature importance derived from XGBoost (eXtreme Gradient Boosting) and RF (Random Forest) models, which can effectively train the non-linear ordinary differential equations model of GRNs and improve the accuracy and stability of the inference algorithm. The extensive experiments on different scale datasets show that our method makes sensible improvement compared with the state-of-the-art methods. Furthermore, we perform cross-validation experiments on the real gene datasets to validate the robustness and effectiveness of the proposed method.

AVAILABILITY AND IMPLEMENTATION

The proposed method is written in the Python language, and is available at: https://github.com/lab319/iLSGRN.

Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics

Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.

Collective behavior and self-organization in neural rosette morphogenesis

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Predicting attractors from spectral properties of stylized gene regulatory networks

How the architecture of gene regulatory networks shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify nonrandom features in these networks and then argue for the function of these features using mechanistic modeling. Here we establish the foundation of an alternative approach by studying the correlation of network eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics: Boolean threshold dynamics in signed directed graphs. We show that eigenvectors of the network adjacency matrix can predict collective states (attractors). However, the overall predictive power depends on details of the network architecture, namely the fraction of positive 3-cycles, in a predictable fashion. Our results are a set of statistical observations, providing a systematic step towards a further theoretical understanding of the role of network eigenvectors in dynamics on graphs.

In silico investigation of molecular networks linking gastrointestinal diseases, malnutrition, and sarcopenia

Malnutrition (MN) is a common primary or secondary complication in gastrointestinal diseases. The patient’s nutritional status also influences muscle mass and function, which can be impaired up to the degree of sarcopenia. The molecular interactions in diseases leading to sarcopenia are complex and multifaceted, affecting muscle physiology, the intestine (nutrition), and the liver at different levels. Although extensive knowledge of individual molecular factors is available, their regulatory interplay is not yet fully understood. A comprehensive overall picture of pathological mechanisms and resulting phenotypes is lacking. In silico approaches that convert existing knowledge into computationally readable formats can help unravel mechanisms, underlying such complex molecular processes. From public literature, we manually compiled experimental evidence for molecular interactions involved in the development of sarcopenia into a knowledge base, referred to as the Sarcopenia Map. We integrated two diseases, namely liver cirrhosis (LC), and intestinal dysfunction, by considering their effects on nutrition and blood secretome. We demonstrate the performance of our model by successfully simulating the impact of changing dietary frequency, glycogen storage capacity, and disease severity on the carbohydrate and muscle systems. We present the Sarcopenia Map as a publicly available, open-source, and interactive online resource, that links gastrointestinal diseases, MN, and sarcopenia. The map provides tools that allow users to explore the information on the map and perform in silico simulations.

Filter feature selection based Boolean Modelling for Genetic Network Inference

The reconstruction of Gene Regulatory Networks (GRNs) from time series gene expression data is highly relevant for the discovery of complex biological interactions and dynamics. Various computational strategies have been developed for this task, but most approaches have low computational efficiency and are not able to cope with high-dimensional, low sample-number, gene expression data. In this paper, we introduce a novel combined filter feature selection approach for efficient and accurate inference of GRNs. A Boolean framework for network modelling is used to demonstrate the efficacy of the proposed approach. Using discretized microarray expression data, the genes most relevant to each target gene are first filtered using ReliefF, an instance-based feature ranking method that is here applied for the first time to GRN inference. Then, further gene selection from the filtered-gene list is done using a mutual information-based min-redundancy max-relevance criterion by eliminating irrelevant genes. This combined method is executed on resampled datasets to finalize the optimal set of regulatory genes. Building upon our previous research, a Pearson correlation coefficient-based Boolean modelling approach is utilized for the efficient identification of the optimal regulatory rules associated with selected regulatory genes. The proposed approach was evaluated using gene expression datasets from small-scale and medium-scale real gene networks, and was observed to be more effective than Linear Discriminant Analysis, performed better than the individual feature selection methods, and obtained improved Structural Accuracy with a higher number of true positives than other state-of-the-art methods, while outperforming these methods with respect to Dynamic Accuracy and efficiency.

A probabilistic Boolean model on hair follicle cell fate regulation by TGF-β

Hair follicles (HFs) are mini skin organs that undergo cyclic growth. Various signals regulate HF cell fate decisions jointly. Recent experimental results suggest that transforming growth factor beta (TGF-β) exhibits a dual role in HF cell fate regulation that can be either anti- or pro-apoptosis. To understand the underlying mechanisms of HF cell fate control, we develop a novel probabilistic Boolean network (pBN) model on the HF epithelial cell gene regulation dynamics. First, the model is derived from literature, then refined using single-cell RNA sequencing data. Using the model, we both explore the mechanisms underlying HF cell fate decisions and make predictions that could potentially guide future experiments: 1) we propose that a threshold-like switch in the TGF-β strength may necessitate the dual roles of TGF-β in either activating apoptosis or cell proliferation, in cooperation with bone morphogenetic protein (BMP) and tumor necrosis factor (TNF) and at different stages of a follicle growth cycle; 2) our model shows concordance with the high-activator-low-inhibitor theory of anagen initiation; 3) we predict that TNF may be more effective in catagen initiation than TGF-β, and they may cooperate in a two-step fashion; 4) finally, predictions of gene knockout and overexpression reveal the roles in HF cell fate regulations of each gene. Attractor and motif analysis from the associated Boolean networks reveal the relations between the topological structure of the gene regulation network and the cell fate regulation mechanism. A discrete spatial model equipped with the pBN illustrates how TGF-β and TNF cooperate in initiating and driving the apoptosis wave during catagen.

SNAIL driven by a feed forward loop motif promotes TGFβinduced epithelial to mesenchymal transition

Epithelial to Mesenchymal Transition (EMT) plays an important role in tissue regeneration, embryonic development, and cancer metastasis. Several signaling pathways are known to regulate EMT, among which the modulation of TGFβ(Transforming Growth Factor-β) induced EMT is crucial in several cancer types. Several mathematical models were built to explore the role of core regulatory circuit of ZEB/miR-200, SNAIL/miR-34 double negative feedback loops in modulating TGFβinduced EMT. Different emergent behavior including tristability, irreversible switching, existence of hybrid EMT states were inferred though these models. Some studies have explored the role of TGFβreceptor activation, SMADs nucleocytoplasmic shuttling and complex formation. Recent experiments have revealed that MDM2 along with SMAD complex regulates SNAIL expression driven EMT. Encouraged by this, in the present study we developed a mathematical model for p53/MDM2 dependent TGFβinduced EMT regulation. Inclusion of p53 brings in an additional mechanistic perspective in exploring the EM transition. The network formulated comprises a C1FFL moderating SNAIL expression involving MDM2 and SMAD complex, which functions as a noise filter and persistent detector. The C1FFL was also observed to operate as a coincidence detector driving the SNAIL dependent downstream signaling into phenotypic switching decision. Systems modelling and analysis of the devised network, displayed interesting dynamic behavior, systems response to various inputs stimulus, providing a better understanding of p53/MDM2 dependent TGF-βinduced Epithelial to Mesenchymal Transition.

Inference of a Boolean Network From Causal Logic Implications

Biological systems contain a large number of molecules that have diverse interactions. A fruitful path to understanding these systems is to represent them with interaction networks, and then describe flow processes in the network with a dynamic model. Boolean modeling, the simplest discrete dynamic modeling framework for biological networks, has proven its value in recapitulating experimental results and making predictions. A first step and major roadblock to the widespread use of Boolean networks in biology is the laborious network inference and construction process. Here we present a streamlined network inference method that combines the discovery of a parsimonious network structure and the identification of Boolean functions that determine the dynamics of the system. This inference method is based on a causal logic analysis method that associates a logic type (sufficient or necessary) to node-pair relationships (whether promoting or inhibitory). We use the causal logic framework to assimilate indirect information obtained from perturbation experiments and infer relationships that have not yet been documented experimentally. We apply this inference method to a well-studied process of hormone signaling in plants, the signaling underlying abscisic acid (ABA)—induced stomatal closure. Applying the causal logic inference method significantly reduces the manual work typically required for network and Boolean model construction. The inferred model agrees with the manually curated model. We also test this method by re-inferring a network representing epithelial to mesenchymal transition based on a subset of the information that was initially used to construct the model. We find that the inference method performs well for various likely scenarios of inference input information. We conclude that our method is an effective approach toward inference of biological networks and can become an efficient step in the iterative process between experiments and computations.

Identification of condition-specific regulatory mechanisms in normal and cancerous human lung tissue

Background

Lung cancer is the leading cause of cancer death in both men and women. The most common lung cancer subtype is non-small cell lung carcinoma (NSCLC) comprising about 85% of all cases. NSCLC can be further divided into three subtypes: adenocarcinoma (LUAD), squamous cell carcinoma (LUSC), and large cell lung carcinoma. Specific genetic mutations and epigenetic aberrations play an important role in the developmental transition to a specific tumor subtype. The elucidation of normal lung versus lung tumor gene expression patterns and regulatory targets yields biomarker systems that discriminate lung phenotypes (i.e., biomarkers) and provide a foundation for the discovery of normal and aberrant gene regulatory mechanisms.

Results

We built condition-specific gene co-expression networks (csGCNs) for normal lung, LUAD, and LUSC conditions. Then, we integrated normal lung tissue-specific gene regulatory networks (tsGRNs) to elucidate control-target biomarker systems for normal and cancerous lung tissue. We characterized co-expressed gene edges, possibly under common regulatory control, for relevance in lung cancer.

Conclusions

Our approach demonstrates the ability to elucidate csGCN:tsGRN merged biomarker systems based on gene expression correlation and regulation. The biomarker systems we describe can be used to classify and further describe lung specimens. Our approach is generalizable and can be used to discover and interpret complex gene expression patterns for any condition or species.

Supplementary Information

The online version contains available at 10.1186/s12864-022-08591-9.

Learning Asynchronous Boolean Networks From Single-Cell Data Using Multiobjective Cooperative Genetic Programming

Recent advances in high-throughput single-cell technologies provide new opportunities for computational modeling of gene regulatory networks (GRNs) with an unprecedented amount of gene expression data. Current studies on the Boolean network (BN) modeling of GRNs mostly depend on bulk time-series data and focus on the synchronous update scheme due to its computational simplicity and tractability. However, such synchrony is a strong and rarely biologically realistic assumption. In this study, we adopt the asynchronous update scheme instead and propose a novel framework called SgpNet to infer asynchronous BNs from single-cell data by formulating it into a multiobjective optimization problem. SgpNet aims to find BNs that can match the asynchronous state transition graph (STG) extracted from single-cell data and retain the sparsity of GRNs. To search the huge solution space efficiently, we encode each Boolean function as a tree in genetic programming and evolve all functions of a network simultaneously via cooperative coevolution. Besides, we develop a regulator preselection strategy in view of GRN sparsity to further enhance learning efficiency. An error threshold estimation heuristic is also proposed to ease tedious parameter tuning. SgpNet is compared with the state-of-the-art method on both synthetic data and experimental single-cell data. Results show that SgpNet achieves comparable inference accuracy, while it has far fewer parameters and eliminates artificial restrictions on the Boolean function structures. Furthermore, SgpNet can potentially scale to large networks via straightforward parallelization on multiple cores.

Discrete Logic Modeling of Cell Signaling Pathways

Cell signaling pathways often crosstalk generating complex biological behaviors observed in different cellular contexts. Frequently, laboratory experiments focus on a few putative regulators, alone unable to predict the molecular mechanisms behind the observed phenotypes. Here, systems biology complements these approaches by giving a holistic picture to complex signaling crosstalk. In particular, Boolean network models are a meaningful tool to study large network behaviors and can cope with incomplete kinetic information. By introducing a model describing pathways involved in hematopoietic stem cell maintenance, we present a general approach on how to model cell signaling pathways with Boolean network models.

Modelling of glucose repression signalling in yeast Saccharomyces cerevisiae

Saccharomyces cerevisiae has a sophisticated signalling system that plays a crucial role in cellular adaptation to changing environments. The SNF1 pathway regulates energy homeostasis upon glucose derepression; hence, it plays an important role in various processes, such as metabolism, cell cycle and autophagy. To unravel its behaviour, SNF1 signalling has been extensively studied. However, the pathway components are strongly interconnected and inconstant; therefore, elucidating its dynamic behaviour based on experimental data only is challenging. To tackle this complexity, systems biology approaches have been successfully employed. This review summarizes the progress, advantages and disadvantages of the available mathematical modelling frameworks covering Boolean, dynamic kinetic, single-cell models, which have been used to study processes and phenomena ranging from crosstalks to sources of cell-to-cell variability in the context of SNF1 signalling. Based on the lessons from existing models, we further discuss how to develop a consensus dynamic mechanistic model of the entire SNF1 pathway that can provide novel insights into the dynamics of nutrient signalling.

Patient-specific Boolean models of signalling networks guide personalised treatments

Prostate cancer is the second most occurring cancer in men worldwide. To better understand the mechanisms of tumorigenesis and possible treatment responses, we developed a mathematical model of prostate cancer which considers the major signalling pathways known to be deregulated. We personalised this Boolean model to molecular data to reflect the heterogeneity and specific response to perturbations of cancer patients. A total of 488 prostate samples were used to build patient-specific models and compared to available clinical data. Additionally, eight prostate cell line-specific models were built to validate our approach with dose-response data of several drugs. The effects of single and combined drugs were tested in these models under different growth conditions. We identified 15 actionable points of interventions in one cell line-specific model whose inactivation hinders tumorigenesis. To validate these results, we tested nine small molecule inhibitors of five of those putative targets and found a dose-dependent effect on four of them, notably those targeting HSP90 and PI3K. These results highlight the predictive power of our personalised Boolean models and illustrate how they can be used for precision oncology.

Dynamic Boolean modelling reveals the influence of energy supply on bacterial efflux pump expression

Antimicrobial resistance (AMR) is a global health issue. One key factor contributing to AMR is the ability of bacteria to export drugs through efflux pumps, which relies on the ATP-dependent expression and interaction of several controlling genes. Recent studies have shown that significant cell-to-cell ATP variability exists within clonal bacterial populations, but the contribution of intrinsic cell-to-cell ATP heterogeneity is generally overlooked in understanding efflux pumps. Here, we consider how ATP variability influences gene regulatory networks controlling expression of efflux pump genes in two bacterial species. We develop and apply a generalizable Boolean modelling framework, developed to incorporate the dependence of gene expression dynamics on available cellular energy supply. Theoretical results show that differences in energy availability can cause pronounced downstream heterogeneity in efflux gene expression. Cells with higher energy availability have a superior response to stressors. Furthermore, in the absence of stress, model bacteria develop heterogeneous pulses of efflux pump gene expression which contribute to a sustained sub-population of cells with increased efflux expression activity, potentially conferring a continuous pool of intrinsically resistant bacteria. This modelling approach thus reveals an important source of heterogeneity in cell responses to antimicrobials and sheds light on potentially targetable aspects of efflux pump-related antimicrobial resistance.

Inference of regulatory networks through temporally sparse data

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs leads to a large possible topology candidate space, which often cannot be exhaustively searched due to the limitation in computational resources. This paper develops a scalable and efficient topology inference for GRNs using Bayesian optimization and kernel-based methods. Rather than an exhaustive search over possible topologies, the proposed method constructs a Gaussian Process (GP) with a topology-inspired kernel function to account for correlation in the likelihood function. Then, using the posterior distribution of the GP model, the Bayesian optimization efficiently searches for the topology with the highest likelihood value by optimally balancing between exploration and exploitation. The performance of the proposed method is demonstrated through comprehensive numerical experiments using a well-known mammalian cell-cycle network.

An Integrated View of Virus-Triggered Cellular Plasticity Using Boolean Networks

Virus-related mortality and morbidity are due to cell/tissue damage caused by replicative pressure and resource exhaustion, e.g., HBV or HIV; exaggerated immune responses, e.g., SARS-CoV-2; and cancer, e.g., EBV or HPV. In this context, oncogenic and other types of viruses drive genetic and epigenetic changes that expand the tumorigenic program, including modifications to the ability of cancer cells to migrate. The best-characterized group of changes is collectively known as the epithelial–mesenchymal transition, or EMT. This is a complex phenomenon classically described using biochemistry, cell biology and genetics. However, these methods require enormous, often slow, efforts to identify and validate novel therapeutic targets. Systems biology can complement and accelerate discoveries in this field. One example of such an approach is Boolean networks, which make complex biological problems tractable by modeling data (“nodes”) connected by logical operators. Here, we focus on virus-induced cellular plasticity and cell reprogramming in mammals, and how Boolean networks could provide novel insights into the ability of some viruses to trigger uncontrolled cell proliferation and EMT, two key hallmarks of cancer.

Network-Based Systems Analysis Explains Sequence-Dependent Synergism of Bortezomib and Vorinostat in Multiple Myeloma

Bortezomib and vorinostat exhibit synergistic effects in multiple myeloma (MM) cells when given in sequence, and the purpose of this study was to evaluate the molecular determinants of the interaction using a systems pharmacology approach. A Boolean network model consisting of 79 proteins and 225 connections was developed using literature information characterizing mechanisms of drug action and intracellular signal transduction. Network visualization and structural analysis were conducted, and model simulations were compared with experimental data. Critical biomarkers, such as pNFκB, p53, cellular stress, and p21, were identified using measures of network centrality and model reduction. U266 cells were then exposed to bortezomib (3 nM) and vorinostat (2 μM) as single agents or in simultaneous and sequential (bortezomib for first 24 h, followed by addition of vorinostat for another 24 h) combinations. Temporal changes for nine of the critical proteins in the reduced Boolean model were measured over 48 h, and cellular proliferation was measured over 96 h. A mechanism-based systems model was developed that captured the biological basis of a bortezomib and vorinostat sequence-dependent pharmacodynamic interaction. The model was further extended in vivo by linking in vitro parameter values and dynamics of p21, caspase-3, and pAKT biomarkers to tumor growth in xenograft mice reported in the literature. Network-based methodologies and pharmacodynamic principles were integrated successfully to evaluate bortezomib and vorinostat interactions in a mechanistic and quantitative manner. The model can be potentially applied to evaluate their combination regimens and explore in vivo dosing regimens.

Unsupervised logic-based mechanism inference for network-driven biological processes

Modern analytical techniques enable researchers to collect data about cellular states, before and after perturbations. These states can be characterized using analytical techniques, but the inference of regulatory interactions that explain and predict changes in these states remains a challenge. Here we present a generalizable, unsupervised approach to generate parameter-free, logic-based models of cellular processes, described by multiple discrete states. Our algorithm employs a Hamming-distance based approach to formulate, test, and identify optimized logic rules that link two states. Our approach comprises two steps. First, a model with no prior knowledge except for the mapping between initial and attractor states is built. We then employ biological constraints to improve model fidelity. Our algorithm automatically recovers the relevant dynamics for the explored models and recapitulates key aspects of the biochemical species concentration dynamics in the original model. We present the advantages and limitations of our work and discuss how our approach could be used to infer logic-based mechanisms of signaling, gene-regulatory, or other input-output processes describable by the Boolean formalism.

Computational systems-biology approaches for modeling gene networks driving epithelial-mesenchymal transitions

Epithelial-mesenchymal transition (EMT) is an important biological process through which epithelial cells undergo phenotypic transitions to mesenchymal cells by losing cell-cell adhesion and gaining migratory properties that cells use in embryogenesis, wound healing, and cancer metastasis. An important research topic is to identify the underlying gene regulatory networks (GRNs) governing the decision making of EMT and develop predictive models based on the GRNs. The advent of recent genomic technology, such as single-cell RNA sequencing, has opened new opportunities to improve our understanding about the dynamical controls of EMT. In this article, we review three major types of computational and mathematical approaches and methods for inferring and modeling GRNs driving EMT. We emphasize (1) the bottom-up approaches, where GRNs are constructed through literature search; (2) the top-down approaches, where GRNs are derived from genome-wide sequencing data; (3) the combined top-down and bottom-up approaches, where EMT GRNs are constructed and simulated by integrating bioinformatics and mathematical modeling. We discuss the methodologies and applications of each approach and the available resources for these studies.

TaBooN Boolean Network Synthesis Based on Tabu Search

Recent developments in Omics-technologies revolutionized the investigation of biology by producing molecular data in multiple dimensions and scale. This breakthrough in biology raises the crucial issue of their interpretation based on modelling. In this undertaking, network provides a suitable framework for modelling the interactions between molecules. Basically a Biological network is composed of nodes referring to the components such as genes or proteins, and the edges/arcs formalizing interactions between them. The evolution of the interactions is then modelled by the definition of a dynamical system. Among the different categories of network, the Boolean network offers a reliable qualitative framework for the modelling. Automatically synthesizing a Boolean network from experimental data therefore remains a necessary but challenging issue. In this study, we present Taboon, an original work-flow for synthesizing Boolean Networks from biological data. The methodology uses the data in the form of boolean profiles for inferring all the potential local formula inference. They combine to form the model space from which the most truthful model with regards to biological knowledge and experiments must be found. In the TaBooN work-flow the selection of the fittest model is achieved by a Tabu-search algorithm. TaBooN is an automated method for Boolean Network inference from.

Impact of explicit area scaling on kinetic models involving multiple compartments

BACKGROUND

Computational modelling of cell biological processes is a frequently used technique to analyse the underlying mechanisms and to generally understand the behaviour of these processes in the context of a pathway, network or even the whole cell. The most common technique in this context is the usage of ordinary differential equations that describe the kinetics of the relevant processes in mechanistic detail. Here, it is usually assumed that the content of the cell is well-stirred and thus homogeneous - which is of course an over-simplification, but often worked in the past. However, many processes happen at membranes and thus not in 3D, but in 2D. The scaling of the rates of these processes poses a special problem, if volumes of compartments are changed. They will typically scale with an area, but not with the volume of the involved compartment. However, commonly, this is neglected when setting up models and/or volume scaling also sometimes automatically happens when using modelling software in the field.

RESULTS

Here, we investigate generic as well as specific, realistic cases to find out, how strong the impact of the wrong scaling is for the outcome of simulations. We show that the importance of correct area scaling depends on the architecture of the reaction site and its changes upon volume alterations and it is hard to foresee, if it has a significant impact or not just by looking at the original model set-up. Moreover, scaled rates might exhibit more or less control over the behaviour of the system and therefore, accordingly, incorrect scaling will have more or less influence.

CONCLUSIONS

Working with multi-compartment reactions requires a careful consideration of the correct scaling of the rates when changing the volumes of the involved compartments. The error following incorrect scaling - often done by scaling with the volume of the respective compartments can lead to significant aberrations of model behaviour.

Personalized logical models to investigate cancer response to BRAF treatments in melanomas and colorectal cancers

The study of response to cancer treatments has benefited greatly from the contribution of different omics data but their interpretation is sometimes difficult. Some mathematical models based on prior biological knowledge of signaling pathways facilitate this interpretation but often require fitting of their parameters using perturbation data. We propose a more qualitative mechanistic approach, based on logical formalism and on the sole mapping and interpretation of omics data, and able to recover differences in sensitivity to gene inhibition without model training. This approach is showcased by the study of BRAF inhibition in patients with melanomas and colorectal cancers who experience significant differences in sensitivity despite similar omics profiles. We first gather information from literature and build a logical model summarizing the regulatory network of the mitogen-activated protein kinase (MAPK) pathway surrounding BRAF, with factors involved in the BRAF inhibition resistance mechanisms. The relevance of this model is verified by automatically assessing that it qualitatively reproduces response or resistance behaviors identified in the literature. Data from over 100 melanoma and colorectal cancer cell lines are then used to validate the model's ability to explain differences in sensitivity. This generic model is transformed into personalized cell line-specific logical models by integrating the omics information of the cell lines as constraints of the model. The use of mutations alone allows personalized models to correlate significantly with experimental sensitivities to BRAF inhibition, both from drug and CRISPR targeting, and even better with the joint use of mutations and RNA, supporting multi-omics mechanistic models. A comparison of these untrained models with learning approaches highlights similarities in interpretation and complementarity depending on the size of the datasets. This parsimonious pipeline, which can easily be extended to other biological questions, makes it possible to explore the mechanistic causes of the response to treatment, on an individualized basis.

Single-cell network biology for resolving cellular heterogeneity in human diseases

Understanding cellular heterogeneity is the holy grail of biology and medicine. Cells harboring identical genomes show a wide variety of behaviors in multicellular organisms. Genetic circuits underlying cell-type identities will facilitate the understanding of the regulatory programs for differentiation and maintenance of distinct cellular states. Such a cell-type-specific gene network can be inferred from coregulatory patterns across individual cells. Conventional methods of transcriptome profiling using tissue samples provide only average signals of diverse cell types. Therefore, reconstructing gene regulatory networks for a particular cell type is not feasible with tissue-based transcriptome data. Recently, single-cell omics technology has emerged and enabled the capture of the transcriptomic landscape of every individual cell. Although single-cell gene expression studies have already opened up new avenues, network biology using single-cell transcriptome data will further accelerate our understanding of cellular heterogeneity. In this review, we provide an overview of single-cell network biology and summarize recent progress in method development for network inference from single-cell RNA sequencing (scRNA-seq) data. Then, we describe how cell-type-specific gene networks can be utilized to study regulatory programs specific to disease-associated cell types and cellular states. Moreover, with scRNA data, modeling personal or patient-specific gene networks is feasible. Therefore, we also introduce potential applications of single-cell network biology for precision medicine. We envision a rapid paradigm shift toward single-cell network analysis for systems biology in the near future.

Gene regulatory networks reconstructed from single-cell RNA sequencing datasets are allowing researchers to better understand the molecular circuits and cell states that contribute to complex human disease. Junha Cha and Insuk Lee from Yonsei University in Seoul, South Korea, review the concept of ‘single-cell network biology’, which involves using computational algorithms on genetic expression data from thousands of cells to infer functional interactions in various biological contexts. This systems biology approach to analyzing the profiles of messenger RNA in single cells is helping researchers discover new signaling pathways that could serve as disease biomarkers or therapeutic targets. In the future, patient-specific models of personal gene networks could explain why certain genetic variants affect disease risk. This research could also eventually lead to new types of individualized medical treatments.

Inference of gene regulatory networks based on nonlinear ordinary differential equations

Motivation

Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks.

Results

In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity.

Availability and implementation

The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs

Supplementary information

Supplementary data are available at Bioinformatics online.

ATEN: And/Or tree ensemble for inferring accurate Boolean network topology and dynamics

MOTIVATION

Inferring gene regulatory networks from gene expression time series data is important for gaining insights into the complex processes of cell life. A popular approach is to infer Boolean networks. However, it is still a pressing open problem to infer accurate Boolean networks from experimental data that are typically short and noisy.

RESULTS

To address the problem, we propose a Boolean network inference algorithm which is able to infer accurate Boolean network topology and dynamics from short and noisy time series data. The main idea is that, for each target gene, we use an And/Or tree ensemble algorithm to select prime implicants of which each is a conjunction of a set of input genes. The selected prime implicants are important features for predicting the states of the target gene. Using these important features we then infer the Boolean function of the target gene. Finally, the Boolean functions of all target genes are combined as a Boolean network. Using the data generated from artificial and real-world gene regulatory networks, we show that our algorithm can infer more accurate Boolean network topology and dynamics from short and noisy time series data than other algorithms. Our algorithm enables us to gain better insights into complex regulatory mechanisms of cell life.

AVAILABILITY AND IMPLEMENTATION

Package ATEN is freely available at https://github.com/ningshi/ATEN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Local and global features of genetic networks supporting a phenotypic switch

Phenotypic switches are associated with alterations in the cell's gene expression profile and are vital to many aspects of biology. Previous studies have identified local motifs of the genetic regulatory network that could underlie such switches. Recent advancements allowed the study of networks at the global, many-gene, level; however, the relationship between the local and global scales in giving rise to phenotypic switches remains elusive. In this work, we studied the epithelial-mesenchymal transition (EMT) using a gene regulatory network model. This model supports two clusters of stable steady-states identified with the epithelial and mesenchymal phenotypes, and a range of intermediate less stable hybrid states, whose importance in cancer has been recently highlighted. Using an array of network perturbations and quantifying the resulting landscape, we investigated how features of the network at different levels give rise to these landscape properties. We found that local connectivity patterns affect the landscape in a mostly incremental manner; in particular, a specific previously identified double-negative feedback motif is not required when embedded in the full network, because the landscape is maintained at a global level. Nevertheless, despite the distributed nature of the switch, it is possible to find combinations of a few local changes that disrupt it. At the level of network architecture, we identified a crucial role for peripheral genes that act as incoming signals to the network in creating clusters of states. Such incoming signals are a signature of modularity and are expected to appear also in other biological networks. Hybrid states between epithelial and mesenchymal arise in the model due to barriers in the interaction between genes, causing hysteresis at all connections. Our results suggest emergent switches can neither be pinpointed to local motifs, nor do they arise as typical properties of random network ensembles. Rather, they arise through an interplay between the nature of local interactions, and the core-periphery structure induced by the modularity of the cell.

Modified Half-System Based Method for Reverse Engineering of Gene Regulatory Networks

The accurate reconstruction of gene regulatory networks for proper understanding of the intricacies of complex biological mechanisms still provides motivation for researchers. Due to accessibility of various gene expression data, we can now attempt to computationally infer genetic interactions. Among the established network inference techniques, S-system is preferred because of its efficiency in replicating biological systems though it is computationally more expensive. This provides motivation for us to develop a similar system with lesser computational load. In this work, we have proposed a novel methodology for reverse engineering of gene regulatory networks based on a new technique: half-system. Half-systems use half the number of parameters compared to S-systems and thus significantly reduce the computational complexity. We have implemented our proposed technique for reconstructing four benchmark networks from their corresponding temporal expression profiles: an 8-gene, a 10-gene, and two 20-gene networks. Being a new technique, to the best of our knowledge, there are no comparable results for this in the contemporary literature. Therefore, we have compared our results with those obtained from the contemporary literature using other methodologies, including the state-of-the-art method, GENIE3. The results obtained in this work stack favourably against the competition, even showing quantifiable improvements in some cases.

Phenotype stability under dynamic brain-tumor environment stimuli maps glioblastoma progression in patients

Although tumor invasiveness is known to drive glioblastoma (GBM) recurrence, current approaches to treatment assume a fairly simple GBM phenotype transition map. We provide new analyses to estimate the likelihood of reaching or remaining in a phenotype under dynamic, physiologically likely perturbations of stimuli ("phenotype stability"). We show that higher stability values of the motile phenotype (Go) are associated with reduced patient survival. Moreover, induced motile states are capable of driving GBM recurrence. We found that the Dormancy and Go phenotypes are equally represented in advanced GBM samples, with natural transitioning between the two. Furthermore, Go and Grow phenotype transitions are mostly driven by tumor-brain stimuli. These are difficult to regulate directly, but could be modulated by reprogramming tumor-associated cell types. Our framework provides a foundation for designing targeted perturbations of the tumor-brain environment, by assessing their impact on GBM phenotypic plasticity, and is corroborated by analyses of patient data.

Multi-parameter exploration of dynamics of regulatory networks

Over the last twenty years advances in systems biology have changed our views on microbial communities and promise to revolutionize treatment of human diseases. In almost all scientific breakthroughs since time of Newton, mathematical modeling has played a prominent role. Regulatory networks emerged as preferred descriptors of how abundances of molecular species depend on each other. However, the central question on how cellular phenotypes emerge from dynamics of these network remains elusive. The principal reason is that differential equation models in the field of biology (while so successful in areas of physics and physical chemistry), do not arise from first principles, and these models suffer from lack of proper parameterization. In response to these challenges, discrete time models based on Boolean networks have been developed. In this review, we discuss an emerging modeling paradigm that combines ideas from differential equations and Boolean models, and has been developed independently within dynamical systems and computer science communities. The result is an approach that can associate a range of potential dynamical behaviors to a network, arrange the descriptors of the dynamics in a searchable database, and allows for multi-parameter exploration of the dynamics akin to bifurcation theory. Since this approach is computationally accessible for moderately sized networks, it allows, perhaps for the first time, to rationally compare different network topologies based on their dynamics.

Characterization and synthetic biology of lipase from Bacillus amyloliquefaciens strain

Lipases with high tolerance to temperature play a significant role in industry from food manufacturing to waste management systems. Thus, there is a need to investigate these enzymes from different geographical areas to look out for a more thermo-stable one. Characterization of lipases through experimental approaches is time consuming process and sometimes the results are ambiguous due to errors. However, integration of computational technologies is quite useful for prediction of optimized conditions. Such technologies can be applied as synthetic biology, which has many major applications in engineered biological approaches for accurate prediction of effects of different physical and chemical parameters on the system. In this study, cloning and expression of a lipase gene from Bacillus amyloliquefaciens, isolated from a novel geographical region of Pakistan, in Escherichia coli DH5α cells followed by sequencing was carried out. To isolate thermostable lipase producing strains, all the samples were kept at 50 °C. Genomic DNA was isolated and signal peptide (1-32 residues) sequence was chopped (ΔSPLipase). The ΔSPLipase was amplified and expressed in Linearized p15TV-L vector. The purified lipase appeared as single band of approximately 26 kDa. Suitable conditions of factors required for maximum lipase activity such as temperature, pH, substrate, organic solvent, detergents and metal ions were predicted through synthetic biology approach and further confirmed in wet lab. The predicted suitable factors for enzyme were almost similar to those determined experimentally. The optimum enzyme activity was recorded at pH 8 and 50 °C temperature. Interestingly, the activity of enzyme was found on a number of solvents, metal ions, detergents, and surfactants. The predicted optimum values and their experimental confirmations highlights the importance of integrated synthetic biology approaches in wet lab experiments. The characterized lipase of B. amyloliquefaciens at molecular level from Pakistani strains displayed good activity on a range of factors that implies this strain to be used for application in industrial level production.

Concepts in Boolean network modeling: What do they all mean?

Boolean network models are one of the simplest models to study complex dynamic behavior in biological systems. They can be applied to unravel the mechanisms regulating the properties of the system or to identify promising intervention targets. Since its introduction by Stuart Kauffman in 1969 for describing gene regulatory networks, various biologically based networks and tools for their analysis were developed. Here, we summarize and explain the concepts for Boolean network modeling. We also present application examples and guidelines to work with and analyze Boolean network models.

Computation capacities of a broad class of signaling networks are higher than their communication capacities

Due to structural and functional abnormalities or genetic variations and mutations, there may be dysfunctional molecules within an intracellular signaling network that do not allow the network to correctly regulate its output molecules, such as transcription factors. This disruption in signaling interrupts normal cellular functions and may eventually develop some pathological conditions. In this paper, computation capacity of signaling networks is introduced as a fundamental limit on signaling capability and performance of such networks. In simple terms, the computation capacity measures the maximum number of computable inputs, that is, the maximum number of input values for which the correct functional output values can be recovered from the erroneous network outputs, when the network contains some dysfunctional molecules. This contrasts with the conventional communication capacity that measures instead the maximum number of input values that can be correctly distinguished based on the erroneous network outputs. The computation capacity is higher than the communication capacity whenever the network response function is not a one-to-one function of the input signals, and, unlike the communication capacity, it takes into account the input-output functional relationships of the network. By explicitly incorporating the effect of signaling errors that result in the network dysfunction, the computation capacity provides more information about the network and its malfunction. Two examples of signaling networks are considered in the paper, one regulating caspase3 and another regulating NFκB, for which computation and communication capacities are investigated. Higher computation capacities are observed for both networks. One biological implication of this finding is that signaling networks may have more 'capacity' than that specified by the conventional communication capacity metric. The effect of feedback is studied as well. In summary, this paper reports findings on a new fundamental feature of the signaling capability of cell signaling networks.

WASABI: a dynamic iterative framework for gene regulatory network inference

BACKGROUND

Inference of gene regulatory networks from gene expression data has been a long-standing and notoriously difficult task in systems biology. Recently, single-cell transcriptomic data have been massively used for gene regulatory network inference, with both successes and limitations.

RESULTS

In the present work we propose an iterative algorithm called WASABI, dedicated to inferring a causal dynamical network from time-stamped single-cell data, which tackles some of the limitations associated with current approaches. We first introduce the concept of waves, which posits that the information provided by an external stimulus will affect genes one-by-one through a cascade, like waves spreading through a network. This concept allows us to infer the network one gene at a time, after genes have been ordered regarding their time of regulation. We then demonstrate the ability of WASABI to correctly infer small networks, which have been simulated in silico using a mechanistic model consisting of coupled piecewise-deterministic Markov processes for the proper description of gene expression at the single-cell level. We finally apply WASABI on in vitro generated data on an avian model of erythroid differentiation. The structure of the resulting gene regulatory network sheds a new light on the molecular mechanisms controlling this process. In particular, we find no evidence for hub genes and a much more distributed network structure than expected. Interestingly, we find that a majority of genes are under the direct control of the differentiation-inducing stimulus.

CONCLUSIONS

Together, these results demonstrate WASABI versatility and ability to tackle some general gene regulatory networks inference issues. It is our hope that WASABI will prove useful in helping biologists to fully exploit the power of time-stamped single-cell data.

A compositional framework for Boolean networks

Boolean networks are a widely used qualitative approach for modelling and analysing biological systems. However, their application is restricted by the well-known state space explosion problem which means that modelling large-scale, realistic biological systems is challenging. In this paper we set out to facilitate the construction and analysis of large scale biological models by developing a formal framework for the composition of Boolean networks. The compositional approach we present is based on merging entities between Boolean networks using a binary Boolean operator and we formalise the preservation of behaviour under composition using a notion of compatibility. We investigate characterising compatibility in terms of the composed models by developing a trace alignment property. In particular, we use a formalisation of the interference that can occur in a composed model to define an extended trace alignment property that we show completely characterises compatibility.

Personalization of Logical Models With Multi-Omics Data Allows Clinical Stratification of Patients

Logical models of cancer pathways are typically built by mining the literature for relevant experimental observations. They are usually generic as they apply for large cohorts of individuals. As a consequence, they generally do not capture the heterogeneity of patient tumors and their therapeutic responses. We present here a novel framework, referred to as PROFILE, to tailor logical models to a particular biological sample such as a patient tumor. This methodology permits to compare the model simulations to individual clinical data, i.e., survival time. Our approach focuses on integrating mutation data, copy number alterations (CNA), and expression data (transcriptomics or proteomics) to logical models. These data need first to be either binarized or set between 0 and 1, and can then be incorporated in the logical model by modifying the activity of the node, the initial conditions or the state transition rates. The use of MaBoSS, a tool based on Monte-Carlo kinetic algorithm to perform stochastic simulations on logical models results in model state probabilities, and allows for a semi-quantitative study of the model phenotypes and perturbations. As a proof of concept, we use a published generic model of cancer signaling pathways and molecular data from METABRIC breast cancer patients. For this example, we test several combinations of data incorporation and discuss that, with these data, the most comprehensive patient-specific cancer models are obtained by modifying the nodes' activity of the model with mutations, in combination or not with CNA data, and altering the transition rates with RNA expression. We conclude that these model simulations show good correlation with clinical data such as patients' Nottingham prognostic index (NPI) subgrouping and survival time. We observe that two highly relevant cancer phenotypes derived from personalized models, Proliferation and Apoptosis, are biologically consistent prognostic factors: patients with both high proliferation and low apoptosis have the worst survival rate, and conversely. Our approach aims to combine the mechanistic insights of logical modeling with multi-omics data integration to provide patient-relevant models. This work leads to the use of logical modeling for precision medicine and will eventually facilitate the choice of patient-specific drug treatments by physicians.

BioLQM: A Java Toolkit for the Manipulation and Conversion of Logical Qualitative Models of Biological Networks

Here we introduce bioLQM, a new Java software toolkit for the conversion, modification, and analysis of Logical Qualitative Models of biological regulatory networks. BioLQM provides core modeling operations as building blocks for the development of integrated modeling software, or for the assembly of heterogeneous analysis workflows involving several complementary tools. Based on the definition of multi-valued logical models, bioLQM implements import and export facilities, notably for the recent SBML qual exchange format, as well as for formats used by several popular tools, facilitating the design of workflows combining these tools. Model modifications enable the definition of various perturbations, as well as model reduction, easing the analysis of large models. Another modification enables the study of multi-valued models with tools limited to the Boolean case. Finally, bioLQM provides a framework for the development of novel analysis tools. The current version implements various updating modes for model simulation (notably synchronous, asynchronous, and random asynchronous), as well as some static analysis features for the identification of attractors. The bioLQM software can be integrated into analysis workflows through command line and scripting interfaces. As a Java library, it further provides core data structures to the GINsim and EpiLog interactive tools, which supply graphical interfaces and additional analysis methods for cellular and multi-cellular qualitative models.