Logical modelling of gene regulatory networks with GINsim

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.

Race-specific coregulatory and transcriptomic profiles associated with DNA methylation and androgen receptor in prostate cancer

BACKGROUND

Prostate cancer is a significant health concern, particularly among African American (AA) men who exhibit higher incidence and mortality compared to European American (EA) men. Understanding the molecular mechanisms underlying these disparities is imperative for enhancing clinical management and achieving better outcomes.

METHODS

Employing a multi-omics approach, we analyzed prostate cancer in both AA and EA men. Using Illumina methylation arrays and RNA sequencing, we investigated DNA methylation and gene expression in tumor and non-tumor prostate tissues. Additionally, Boolean analysis was utilized to unravel complex networks contributing to racial disparities in prostate cancer.

RESULTS

When comparing tumor and adjacent non-tumor prostate tissues, we found that DNA hypermethylated regions are enriched for PRC2/H3K27me3 pathways and EZH2/SUZ12 cofactors. Olfactory/ribosomal pathways and distinct cofactors, including CTCF and KMT2A, were enriched in DNA hypomethylated regions in prostate tumors from AA men. We identified race-specific inverse associations of DNA methylation with expression of several androgen receptor (AR) associated genes, including the GATA family of transcription factors and TRIM63. This suggests that race-specific dysregulation of the AR signaling pathway exists in prostate cancer. To investigate the effect of AR inhibition on race-specific gene expression changes, we generated in-silico patient-specific prostate cancer Boolean networks. Our simulations revealed prolonged AR inhibition causes significant dysregulation of TGF-β, IDH1, and cell cycle pathways specifically in AA prostate cancer. We further quantified global gene expression changes, which revealed differential expression of genes related to microtubules, immune function, and TMPRSS2-fusion pathways, specifically in prostate tumors of AA men. Enrichment of these pathways significantly correlated with an altered risk of disease progression in a race-specific manner.

CONCLUSIONS

Our study reveals unique signaling networks underlying prostate cancer biology in AA and EA men, offering potential insights for clinical management strategies tailored to specific racial groups. Targeting AR and associated pathways could be particularly beneficial in addressing the disparities observed in prostate cancer outcomes in the context of AA and EA men. Further investigation into these identified pathways may lead to the development of personalized therapeutic approaches to improve outcomes for prostate cancer patients across different racial backgrounds.

Drug-target identification in COVID-19 disease mechanisms using computational systems biology approaches

Introduction

The COVID-19 Disease Map project is a large-scale community effort uniting 277 scientists from 130 Institutions around the globe. We use high-quality, mechanistic content describing SARS-CoV-2-host interactions and develop interoperable bioinformatic pipelines for novel target identification and drug repurposing.

Methods

Extensive community work allowed an impressive step forward in building interfaces between Systems Biology tools and platforms. Our framework can link biomolecules from omics data analysis and computational modelling to dysregulated pathways in a cell-, tissue- or patient-specific manner. Drug repurposing using text mining and AI-assisted analysis identified potential drugs, chemicals and microRNAs that could target the identified key factors.

Results

Results revealed drugs already tested for anti-COVID-19 efficacy, providing a mechanistic context for their mode of action, and drugs already in clinical trials for treating other diseases, never tested against COVID-19.

Discussion

The key advance is that the proposed framework is versatile and expandable, offering a significant upgrade in the arsenal for virus-host interactions and other complex pathologies.

Cyclone: open-source package for simulation and analysis of finite dynamical systems

MOTIVATION

While there are software packages that analyze Boolean, ternary, or other multi-state models, none compute the complete state space of function-based models over any finite set. Results: We propose Cyclone, a simple light-weight software package which simulates the complete state space for a finite dynamical system over any finite set.

AVAILABILITY AND IMPLEMENTATION

Source code is freely available at https://github.com/discretedynamics/cyclone under the Apache-2.0 license.

A large-scale Boolean model of the rheumatoid arthritis fibroblast-like synoviocytes predicts drug synergies in the arthritic joint

Rheumatoid arthritis (RA) is a complex autoimmune disease with an unknown aetiology. However, rheumatoid arthritis fibroblast-like synoviocytes (RA-FLS) play a significant role in initiating and perpetuating destructive joint inflammation by expressing immuno-modulating cytokines, adhesion molecules, and matrix remodelling enzymes. In addition, RA-FLS are primary drivers of inflammation, displaying high proliferative rates and an apoptosis-resistant phenotype. Thus, RA-FLS-directed therapies could become a complementary approach to immune-directed therapies by predicting the optimal conditions that would favour RA-FLS apoptosis, limit inflammation, slow the proliferation rate and minimise bone erosion and cartilage destruction. In this paper, we present a large-scale Boolean model for RA-FLS that consists of five submodels focusing on apoptosis, cell proliferation, matrix degradation, bone erosion and inflammation. The five-phenotype-specific submodels can be simulated independently or as a global model. In silico simulations and perturbations reproduced the expected biological behaviour of the system under defined initial conditions and input values. The model was then used to mimic the effect of mono or combined therapeutic treatments and predict novel targets and drug candidates through drug repurposing analysis.

Reducing Boolean networks with backward equivalence

BACKGROUND

Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis.

RESULTS

We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance.

CONCLUSIONS

BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

Metabolomics meets systems immunology

Metabolic processes play a critical role in immune regulation. Metabolomics is the systematic analysis of small molecules (metabolites) in organisms or biological samples, providing an opportunity to comprehensively study interactions between metabolism and immunity in physiology and disease. Integrating metabolomics into systems immunology allows the exploration of the interactions of multilayered features in the biological system and the molecular regulatory mechanism of these features. Here, we provide an overview on recent technological developments of metabolomic applications in immunological research. To begin, two widely used metabolomics approaches are compared: targeted and untargeted metabolomics. Then, we provide a comprehensive overview of the analysis workflow and the computational tools available, including sample preparation, raw spectra data preprocessing, data processing, statistical analysis, and interpretation. Third, we describe how to integrate metabolomics with other omics approaches in immunological studies using available tools. Finally, we discuss new developments in metabolomics and its prospects for immunology research. This review provides guidance to researchers using metabolomics and multiomics in immunity research, thus facilitating the application of systems immunology to disease research.

An integrated in silico-in vitro approach for identifying therapeutic targets against osteoarthritis

Background

Without the availability of disease-modifying drugs, there is an unmet therapeutic need for osteoarthritic patients. During osteoarthritis, the homeostasis of articular chondrocytes is dysregulated and a phenotypical transition called hypertrophy occurs, leading to cartilage degeneration. Targeting this phenotypic transition has emerged as a potential therapeutic strategy. Chondrocyte phenotype maintenance and switch are controlled by an intricate network of intracellular factors, each influenced by a myriad of feedback mechanisms, making it challenging to intuitively predict treatment outcomes, while in silico modeling can help unravel that complexity. In this study, we aim to develop a virtual articular chondrocyte to guide experiments in order to rationalize the identification of potential drug targets via screening of combination therapies through computational modeling and simulations.

Results

We developed a signal transduction network model using knowledge-based and data-driven (machine learning) modeling technologies. The in silico high-throughput screening of (pairwise) perturbations operated with that network model highlighted conditions potentially affecting the hypertrophic switch. A selection of promising combinations was further tested in a murine cell line and primary human chondrocytes, which notably highlighted a previously unreported synergistic effect between the protein kinase A and the fibroblast growth factor receptor 1.

Conclusions

Here, we provide a virtual articular chondrocyte in the form of a signal transduction interactive knowledge base and of an executable computational model. Our in silico-in vitro strategy opens new routes for developing osteoarthritis targeting therapies by refining the early stages of drug target discovery.

Graphical Abstract

Addressing barriers in comprehensiveness, accessibility, reusability, interoperability and reproducibility of computational models in systems biology

Computational models are often employed in systems biology to study the dynamic behaviours of complex systems. With the rise in the number of computational models, finding ways to improve the reusability of these models and their ability to reproduce virtual experiments becomes critical. Correct and effective model annotation in community-supported and standardised formats is necessary for this improvement. Here, we present recent efforts toward a common framework for annotated, accessible, reproducible and interoperable computational models in biology, and discuss key challenges of the field.

Model-checking ecological state-transition graphs

Model-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transition graph satisfies a dynamical property written as a temporal logic formula. The dynamics of ecosystems have been drawn as state-transition graphs for more than a century, ranging from state-and-transition models to assembly graphs. Model-checking can provide insights into both empirical data and theoretical models, as long as they sum up into state-transition graphs. While model-checking proved to be a valuable tool in systems biology, it remains largely underused in ecology apart from precursory applications. This article proposes to address this situation, through an inventory of existing ecological STGs and an accessible presentation of the model-checking methodology. This overview is illustrated by the application of model-checking to assess the dynamics of a vegetation pathways model. We select management scenarios by model-checking Computation Tree Logic formulas representing management goals and built from a proposed catalogue of patterns. In discussion, we sketch bridges between existing studies in ecology and available model-checking frameworks. In addition to the automated analysis of ecological state-transition graphs, we believe that defining ecological concepts with temporal logics could help clarify and compare them.

Exploring attractor bifurcations in Boolean networks

Background

Boolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors–subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks.

Results

In this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method’s applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus.

Conclusions

The proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system’s stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

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.

Inference of an Integrative, Executable Network for Rheumatoid Arthritis Combining Data-Driven Machine Learning Approaches and a State-of-the-Art Mechanistic Disease Map

Rheumatoid arthritis (RA) is a multifactorial, complex autoimmune disease that involves various genetic, environmental, and epigenetic factors. Systems biology approaches provide the means to study complex diseases by integrating different layers of biological information. Combining multiple data types can help compensate for missing or conflicting information and limit the possibility of false positives. In this work, we aim to unravel mechanisms governing the regulation of key transcription factors in RA and derive patient-specific models to gain more insights into the disease heterogeneity and the response to treatment. We first use publicly available transcriptomic datasets (peripheral blood) relative to RA and machine learning to create an RA-specific transcription factor (TF) co-regulatory network. The TF cooperativity network is subsequently enriched in signalling cascades and upstream regulators using a state-of-the-art, RA-specific molecular map. Then, the integrative network is used as a template to analyse patients' data regarding their response to anti-TNF treatment and identify master regulators and upstream cascades affected by the treatment. Finally, we use the Boolean formalism to simulate in silico subparts of the integrated network and identify combinations and conditions that can switch on or off the identified TFs, mimicking the effects of single and combined perturbations.

Discrete Dynamic Model of the Mammalian Sperm Acrosome Reaction: The Influence of Acrosomal pH and Physiological Heterogeneity

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse physiological changes (biochemical, biophysical, and morphological) that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the physiological heterogeneity within a sperm population has not been studied. Here, we present a discrete mathematical model for the human sperm AR based on the physiological interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pH a ) and cell heterogeneity regulate AR. Our results confirm that a pH a increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known natural inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population physiological heterogeneity.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

Logical modeling of thymus and natural killer lymphocyte differentiation

Thymus (T) and natural killer (NK) lymphocytes are important barriers against diseases. Therefore, it is necessary to understand regulatory mechanisms related to the cell fate decisions involved in the production of these cells. Although some individual information related to T and NK lymphocyte cell fate decisions have been revealed, the related network and its dynamical characteristics still have not been well understood. By integrating individual information and comparing with experimental data, we construct a comprehensive regulatory network and a logical model related to T and NK lymphocyte differentiation. We aim to explore possible mechanisms of how each lineage differentiation is realized by systematically screening individual perturbations. When determining the perturbation strategies, the state transition can be used to identify the roles of specific genes in cell type selection and reprogramming. In agreement with experimental observations, the dynamics of the model correctly restates the cell differentiation processes from common lymphoid progenitors to CD4+ T cells, CD8+ T cells, and NK cells. Our analysis reveals that some specific perturbations can give rise to directional cell differentiation or reprogramming. We test our in silico results by using known experimental observations. The integrated network and the logical model presented here might be a good candidate for providing qualitative mechanisms of cell fate specification involved in T and NK lymphocyte cell fate decisions.

Automated inference of Boolean models from molecular interaction maps using CaSQ

Motivation

Molecular interaction maps have emerged as a meaningful way of representing biological mechanisms in a comprehensive and systematic manner. However, their static nature provides limited insights to the emerging behaviour of the described biological system under different conditions. Computational modelling provides the means to study dynamic properties through in silico simulations and perturbations. We aim to bridge the gap between static and dynamic representations of biological systems with CaSQ, a software tool that infers Boolean rules based on the topology and semantics of molecular interaction maps built with CellDesigner.

Results

We developed CaSQ by defining conversion rules and logical formulas for inferred Boolean models according to the topology and the annotations of the starting molecular interaction maps. We used CaSQ to produce executable files of existing molecular maps that differ in size, complexity and the use of Systems Biology Graphical Notation (SBGN) standards. We also compared, where possible, the manually built logical models corresponding to a molecular map to the ones inferred by CaSQ. The tool is able to process large and complex maps built with CellDesigner (either following SBGN standards or not) and produce Boolean models in a standard output format, Systems Biology Marked Up Language-qualitative (SBML-qual), that can be further analyzed using popular modelling tools. References, annotations and layout of the CellDesigner molecular map are retained in the obtained model, facilitating interoperability and model reusability.

Availability and implementation

The present tool is available online: https://lifeware.inria.fr/∼soliman/post/casq/ and distributed as a Python package under the GNU GPLv3 license. The code can be accessed here: https://gitlab.inria.fr/soliman/casq.

Supplementary information

Supplementary data are available at Bioinformatics online.

Tools for time-course simulation in systems biology: a brief overview

Dynamic modeling of biological systems is essential for understanding all properties of a given organism as it allows us to look not only at the static picture of an organism but also at its behavior under various conditions. With the increasing amount of experimental data, the number of tools that enable dynamic analysis also grows. However, various tools are based on different approaches, use different types of data and offer different functions for analyses; so it can be difficult to choose the most suitable tool for a selected type of model. Here, we bring a brief overview containing descriptions of 50 tools for the reconstruction of biological models, their time-course simulation and dynamic analysis. We examined each tool using test data and divided them based on the qualitative and quantitative nature of the mathematical apparatus they use.

Symbolic Coloured SCC Decomposition

Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.

We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(p\cdot n\cdot \log n)$$\end{document}O(p·n·logn) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{48}$$\end{document}248) coloured graphs produced by models appearing in systems biology.

Modelling of Immune Checkpoint Network Explains Synergistic Effects of Combined Immune Checkpoint Inhibitor Therapy and the Impact of Cytokines in Patient Response

Simple Summary

The future of cancer immunotherapy relies on a combination of individually targeted therapies. However, a lot of experiments are needed to define the most effective combinations of drugs. A computational and modelling approach could help reduce the number of experiments and suggest optimal treatments to test. This article presents a logical model of T cell activation influenced by immune checkpoints, and explores the effect of these checkpoints, suggests mechanisms that would explain why some treatments might be better suited than others. The model includes not only programmed cell death protein 1 (PD1) and cytotoxic T-lymphocyte-associated protein 4 (CTL4) downstream pathways but also those of other immune checkpoints such as T cell immunoglobulin and ITIM (immunoreceptor tyrosine-based inhibition motif) domain (TIGIT), lymphocyte activation gene 3 (LAG3), T cell immunoglobulin and mucin domain-containing protein 3 (TIM3), cluster of differentiation 226 (CD226), inducible T-cell costimulator (ICOS), and tumour necrosis factor receptors (TNFRs).

Abstract

After the success of the new generation of immune therapies, immune checkpoint receptors have become one important center of attention of molecular oncologists. The initial success and hopes of anti-programmed cell death protein 1 (anti-PD1) and anti-cytotoxic T-lymphocyte-associated protein 4 (anti-CTLA4) therapies have shown some limitations since a majority of patients have continued to show resistance. Other immune checkpoints have raised some interest and are under investigation, such as T cell immunoglobulin and ITIM (immunoreceptor tyrosine-based inhibition motif) domain (TIGIT), inducible T-cell costimulator (ICOS), and T cell immunoglobulin and mucin domain-containing protein 3 (TIM3), which appear as promising targets for immunotherapy. To explore their role and study possible synergetic effects of these different checkpoints, we have built a model of T cell receptor (TCR) regulation including not only PD1 and CTLA4, but also other well studied checkpoints (TIGIT, TIM3, lymphocyte activation gene 3 (LAG3), cluster of differentiation 226 (CD226), ICOS, and tumour necrosis factor receptors (TNFRs)) and simulated different aspects of T cell biology. Our model shows good correspondence with observations from available experimental studies of anti-PD1 and anti-CTLA4 therapies and suggest efficient combinations of immune checkpoint inhibitors (ICI). Among the possible candidates, TIGIT appears to be the most promising drug target in our model. The model predicts that signal transducer and activator of transcription 1 (STAT1)/STAT4-dependent pathways, activated by cytokines such as interleukin 12 (IL12) and interferon gamma (IFNG), could improve the effect of ICI therapy via upregulation of Tbet, suggesting that the effect of the cytokines related to STAT3/STAT1 activity is dependent on the balance between STAT1 and STAT3 downstream signalling.

Simulation of multiple microenvironments shows a pivot role of RPTPs on the control of Epithelial-to-Mesenchymal Transition

Epithelial-to-Mesenchymal Transition (EMT) is a natural and reversible process involved in embryogenesis, wound healing and thought to participate in the process of metastasis. Multiple signals from the microenvironment have been reported to drive EMT. However, the tight control of this process on physiological scenarios and how it is disrupted during cancer progression is not fully understood. Here, we analysed a regulatory network of EMT accounting for 10 key microenvironment signals focusing on the impact of two cell contact signals on the reversibility of EMT and the stability of resulting phenotypes. The analysis showed that the microenvironment is not enough for stabilizing Hybrid and Amoeboid-like phenotypes, requiring intracellular de-regulations as reported during cancer progression. Our simulations demonstrated that RPTP activation by cell contacts have the potential to inhibit the process of EMT and trigger its reversibility under tissue growth and chronic inflammation scenarios. Simulations also showed that hypoxia inhibits the capacity of RPTPs to control EMT. Our analysis further provided a theoretical explanation for the observed correlation between hypoxia and metastasis under chronic inflammation, and predicted that de-regulations in FAT4 signalling may promote Hybrid stabilization. Taken together, we propose a natural control mechanism of EMT that supports the idea that EMT is tightly regulated by the microenvironment.

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

Conceptual and computational framework for logical modelling of biological networks deregulated in diseases

Mathematical models can serve as a tool to formalize biological knowledge from diverse sources, to investigate biological questions in a formal way, to test experimental hypotheses, to predict the effect of perturbations and to identify underlying mechanisms. We present a pipeline of computational tools that performs a series of analyses to explore a logical model's properties. A logical model of initiation of the metastatic process in cancer is used as a transversal example. We start by analysing the structure of the interaction network constructed from the literature or existing databases. Next, we show how to translate this network into a mathematical object, specifically a logical model, and how robustness analyses can be applied to it. We explore the visualization of the stable states, defined as specific attractors of the model, and match them to cellular fates or biological read-outs. With the different tools we present here, we explain how to assign to each solution of the model a probability and how to identify genetic interactions using mutant phenotype probabilities. Finally, we connect the model to relevant experimental data: we present how some data analyses can direct the construction of the network, and how the solutions of a mathematical model can also be compared with experimental data, with a particular focus on high-throughput data in cancer biology. A step-by-step tutorial is provided as a Supplementary Material and all models, tools and scripts are provided on an accompanying website: https://github.com/sysbio-curie/Logical_modelling_pipeline.

A Robustness Analysis of Dynamic Boolean Models of Cellular Circuits

With ever growing amounts of omics data, the next challenge in biological research is the interpretation of these data to gain mechanistic insights about cellular function. Dynamic models of cellular circuits that capture the activity levels of proteins and other molecules over time offer great expressive power by allowing the simulation of the effects of specific internal or external perturbations on the workings of the cell. However, the study of such models is at its infancy and no large-scale analysis of the robustness of real models to changing conditions has been conducted to date. Here we provide a computational framework to study the robustness of such models using a combination of stochastic simulations and integer linear programming techniques. We apply our framework to a large collection of cellular circuits and benchmark the results against randomized models. We find that the steady states of real circuits tend to be more robust in multiple aspects compared with their randomized counterparts.

AEON: Attractor Bifurcation Analysis of Parametrised Boolean Networks

Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for analysing bifurcations in asynchronous parametrised Boolean networks. To fight the state-space and parameter-space explosion problem the tool uses a parallel semi-symbolic algorithm.

PlantSimLab - a modeling and simulation web tool for plant biologists

BACKGROUND

At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists.

RESULTS

This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers.

CONCLUSIONS

Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise.

Dynamics of the feedback loops required for the phenotypic stabilization in the epithelial-mesenchymal transition

The epithelial-mesenchymal transition (EMT) is a complex mechanism in which cells undergo a transition from epithelial to mesenchymal phenotypes (there is also an intermediary hybrid state) in response to microenvironmental alterations and aberrant stimuli triggered by molecules such as TGF-β. Recent studies in breast cancer progression reported new feedback loops and new participant molecules such as microRNAs 340 and 1199. In this work, we propose a logical model of EMT contemplating the influence of these new published molecules on the regulatory core of EMT. The model results were compared with theoretical and experimental data for the human breast epithelial cell line MCF10A presenting excellent agreement. We propose that the miRNAs 340 and 1199 should be considered phenotypic stability factors of the hybrid state based on the positive feedback loops they form with ZEB1. In addition, the model allows the prediction of phenotype probabilities at the coexistence region. For the tristable dynamics when epithelial, hybrid, and mesenchymal phenotypes coexist, we found that the hybrid state is the most probable, agreeing with experiments. Our results highlight new mechanisms related to the EMT dynamics in response to TGF-β stimulus in epithelial breast cells and might help the design of therapeutic strategies for breast cancer.

Logical modelling uncovers developmental constraints for primary sex determination of chicken gonads

In the chicken, sex determination relies on a ZZ (male)/ZW (female) chromosomal system, but underlying mechanisms are still not fully understood. The Z-dosage and the dominant W-chromosome hypotheses have been proposed to underlie primary sex determination. We present a modelling approach, which assembles the current knowledge and permits exploration of the regulation of this process in chickens. Relying on published experimental data, we assembled a gene network, which led to a logical model that integrates both the Z-dosage and dominant W hypotheses. This model showed that the sexual fate of chicken gonads results from the resolution of the mutual inhibition between DMRT1 and FOXL2, where the initial amount of DMRT1 product determines the development of the gonads. In this respect, at the initiation step, a W-factor would function as a secondary device, by reducing the amount of DMRT1 in ZW gonads when the sexual fate of the gonad is settled, that is when the SOX9 functional level is established. Developmental constraints that are instrumental in this resolution were identified. These constraints establish qualitative restrictions regarding the relative transcription rates of the genes DMRT1, FOXL2 and HEMGN. Our model further clarified the role of OESTROGEN in maintaining FOXL2 function during ovary development.

Modeling genotypes in their microenvironment to predict single- and multi-cellular behavior

A cell's phenotype is the set of observable characteristics resulting from the interaction of the genotype with the surrounding environment, determining cell behavior. Deciphering genotype-phenotype relationships has been crucial to understanding normal and disease biology. Analysis of molecular pathways has provided an invaluable tool to such understanding; however, typically it does not consider the physical microenvironment, which is a key determinant of phenotype. In this study, we present a novel modeling framework that enables the study of the link between genotype, signaling networks, and cell behavior in a three-dimensional microenvironment. To achieve this, we bring together Agent-Based Modeling, a powerful computational modeling technique, and gene networks. This combination allows biological hypotheses to be tested in a controlled stepwise fashion, and it lends itself naturally to model a heterogeneous population of cells acting and evolving in a dynamic microenvironment, which is needed to predict the evolution of complex multi-cellular dynamics. Importantly, this enables modeling co-occurring intrinsic perturbations, such as mutations, and extrinsic perturbations, such as nutrient availability, and their interactions. Using cancer as a model system, we illustrate how this framework delivers a unique opportunity to identify determinants of single-cell behavior, while uncovering emerging properties of multi-cellular growth. This framework is freely available at http://www.microc.org.

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.

Towards the contribution of the p38MAPK pathway to the dual role of TGFβ in cancer: A boolean model approach

The transforming growth factor-beta (TGF-β) pathway is involved in the regulation of cell growth and differentiation. In normal cells or in the early stages of cancer, this pathway can control proliferation stimuli by inducing cell cycle arrest or apoptosis (through the MAP-kinase protein p38MAPK), while in late stages it seems to act as a tumor promoter. This feature is known as the TGF-β dual role in cancer and it is not completely explained. This seems to arise through the accumulation of mutations in cancer development that affect the normal function of these pathways. In this work we propose a Boolean model of the crosstalk between the TGF-β, p38 MAPK and cell cycle checkpoint pathways which qualitatively describes this dual behavior. The model shows that for the wild type case, TGF-β acts as tumor supressor by inducing cell cycle arrest or apoptosis, as expected. However, the loss of function (LoF) of its two signaling proteins: SMAD2 and SMAD3 has immortalization effects due to the activation of the PI3K/AKT pathway that contributes to inhibit apoptosis. In silico mutations of the model elements were compared with cell phenotypes in experiments presenting agreement. In addition, we performed a series of double gene perturbations (that simulate random deleterious mutations) to determine the main regulators of the network. The results suggest that SMAD2/3 and p38MAPK are key players in processing the network input. In addition, when the LoF of SMAD2/3 is combined with the LoF of p38MAPK and p53, cell cycle arrest is completely abrogated. In conclusion, the model allows to visualize, through in silico mutations, the dual role of TGF-β: for the wild-type case TGF-β is able to block proliferation, however deleterious mutations can impair cell cycle arrest promoting cellular proliferation.

Gene Regulatory Network Modeling of Macrophage Differentiation Corroborates the Continuum Hypothesis of Polarization States

Macrophages derived from monocyte precursors undergo specific polarization processes which are influenced by the local tissue environment: classically activated (M1) macrophages, with a pro-inflammatory activity and a role of effector cells in Th1 cellular immune responses, and alternatively activated (M2) macrophages, with anti-inflammatory functions and involved in immunosuppression and tissue repair. At least three different subsets of M2 macrophages, namely, M2a, M2b, and M2c, are characterized in the literature based on their eliciting signals. The activation and polarization of macrophages is achieved through many, often intertwined, signaling pathways. To describe the logical relationships among the genes involved in macrophage polarization, we used a computational modeling methodology, namely, logical (Boolean) modeling of gene regulation. We integrated experimental data and knowledge available in the literature to construct a logical network model for the gene regulation driving macrophage polarization to the M1, M2a, M2b, and M2c phenotypes. Using the software GINsim and BoolNet, we analyzed the network dynamics under different conditions and perturbations to understand how they affect cell polarization. Dynamic simulations of the network model, enacting the most relevant biological conditions, showed coherence with the observed behavior of in vivo macrophages. The model could correctly reproduce the polarization toward the four main phenotypes as well as to several hybrid phenotypes, which are known to be experimentally associated to physiological and pathological conditions. We surmise that shifts among different phenotypes in the model mimic the hypothetical continuum of macrophage polarization, with M1 and M2 being the extremes of an uninterrupted sequence of states. Furthermore, model simulations suggest that anti-inflammatory macrophages are resilient to shift back to the pro-inflammatory phenotype.

Integrative workflows for network analysis

Due to genetic heterogeneity across patients, the identification of effective disease signatures and therapeutic targets is challenging. Addressing this challenge, we have previously developed a network-based approach, which integrates heterogeneous sources of biological information to identify disease specific core-regulatory networks. In particular, our workflow uses a multi-objective optimization function to calculate a ranking score for network components (e.g. feedback/feedforward loops) based on network properties, biomedical and high-throughput expression data. High ranked network components are merged to identify the core-regulatory network(s) that is then subjected to dynamical analysis using stimulus–response and in silico perturbation experiments for the identification of disease gene signatures and therapeutic targets. In a case study, we implemented our workflow to identify bladder and breast cancer specific core-regulatory networks underlying epithelial–mesenchymal transition from the E2F1 molecular interaction map.

In this study, we review our workflow and described how it has developed over time to understand the mechanisms underlying disease progression and prediction of signatures for clinical decision making.

General method to find the attractors of discrete dynamic models of biological systems

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

Estimating Attractor Reachability in Asynchronous Logical Models

Logical models are well-suited to capture salient dynamical properties of regulatory networks. For networks controlling cell fate decisions, cell fates are associated with model attractors (stable states or cyclic attractors) whose identification and reachability properties are particularly relevant. While synchronous updates assume unlikely instantaneous or identical rates associated with component changes, the consideration of asynchronous updates is more realistic but, for large models, may hinder the analysis of the resulting non-deterministic concurrent dynamics. This complexity hampers the study of asymptotical behaviors, and most existing approaches suffer from efficiency bottlenecks, being generally unable to handle cyclical attractors and quantify attractor reachability. Here, we propose two algorithms providing probability estimates of attractor reachability in asynchronous dynamics. The first algorithm, named Firefront, exhaustively explores the state space from an initial state, and provides quasi-exact evaluations of the reachability probabilities of model attractors. The algorithm progresses in breadth, propagating the probabilities of each encountered state to its successors. Second, Avatar is an adapted Monte Carlo approach, better suited for models with large and intertwined transient and terminal cycles. Avatar iteratively explores the state space by randomly selecting trajectories and by using these random walks to estimate the likelihood of reaching an attractor. Unlike Monte Carlo simulations, Avatar is equipped to avoid getting trapped in transient cycles and to identify cyclic attractors. Firefront and Avatar are validated and compared to related methods, using as test cases logical models of synthetic and biological networks. Both algorithms are implemented as new functionalities of GINsim 3.0, a well-established software tool for logical modeling, providing executable GUI, Java API, and scripting facilities.

Dynamical Analysis of the Regulatory Network Controlling Natural Killer Cells Differentiation

Many disease fighting strategies have focused on the generation of NK cells, since they constitute the main immune barrier against cancer and intracellular pathogens such as viruses. Therefore, a predictive model for the development of NK cells would constitute a useful tool to test several hypotheses regarding the production of these cells during both physiological and pathological conditions. Here, we present a boolean network model that reproduces experimental results reported on the literature regarding the progressive stages of the development of NK cells in wild-type and mutant backgrounds. The model allows for the simulation of different conditions, including extracellular micro-environment as well as the simulation of genetic alterations. It also describes how NK cell differentiation depends on a molecular regulatory network that controls the specification of lymphoid lineages, such as T and B cells, which share a common progenitor with NKs. Furthermore, the study shows that the structure of the regulatory network strongly determines the stability of the expression patterns against perturbations.

Modeling and analysis of the impacts of jet lag on circadian rhythm and its role in tumor growth

Circadian rhythms maintain a 24 h oscillation pattern in metabolic, physiological and behavioral processes in all living organisms. Circadian rhythms are organized as biochemical networks located in hypothalamus and peripheral tissues. Rhythmicity in the expression of circadian clock genes plays a vital role in regulating the process of cell division and DNA damage control. The oncogenic protein, MYC and the tumor suppressor, p53 are directly influenced by the circadian clock. Jet lag and altered sleep/wake schedules prominently affect the expression of molecular clock genes. This study is focused on developing a Petri net model to analyze the impacts of long term jet lag on the circadian clock and its probable role in tumor progression. The results depict that jet lag disrupts the normal rhythmic behavior and expression of the circadian clock proteins. This disruption leads to persistent expression of MYC and suppressed expression of p53. Thus, it is inferred that jet lag altered circadian clock negatively affects the expressions of cell cycle regulatory genes and contribute in uncontrolled proliferation of tumor cells.

Logical modeling of lymphoid and myeloid cell specification and transdifferentiation

Blood cells are derived from a common set of hematopoietic stem cells, which differentiate into more specific progenitors of the myeloid and lymphoid lineages, ultimately leading to differentiated cells. This developmental process is controlled by a complex regulatory network involving cytokines and their receptors, transcription factors, and chromatin remodelers. Using public data and data from our own molecular genetic experiments (quantitative PCR, Western blot, EMSA) or genome-wide assays (RNA-sequencing, ChIP-sequencing), we have assembled a comprehensive regulatory network encompassing the main transcription factors and signaling components involved in myeloid and lymphoid development. Focusing on B-cell and macrophage development, we defined a qualitative dynamical model recapitulating cytokine-induced differentiation of common progenitors, the effect of various reported gene knockdowns, and the reprogramming of pre-B cells into macrophages induced by the ectopic expression of specific transcription factors. The resulting network model can be used as a template for the integration of new hematopoietic differentiation and transdifferentiation data to foster our understanding of lymphoid/myeloid cell-fate decisions.

A Network-Based Integrative Workflow to Unravel Mechanisms Underlying Disease Progression

Unraveling mechanisms underlying diseases has motivated the development of systems biology approaches. The key challenges for the development of mathematical models and computational tool are (1) the size of molecular networks, (2) the nonlinear nature of spatio-temporal interactions, and (3) feedback loops in the structure of interaction networks. We here propose an integrative workflow that combines structural analyses of networks, high-throughput data, and mechanistic modeling. As an illustration of the workflow, we use prostate cancer as a case study with the aim of identifying key functional components associated with primary to metastasis transitions. Analysis carried out by the workflow revealed that HOXD10, BCL2, and PGR are the most important factors affected in primary prostate samples, whereas, in the metastatic state, STAT3, JUN, and JUNB are playing a central role. The identified key elements of each network are validated using patient survival analysis. The workflow presented here allows experimentalists to use heterogeneous data sources for the identification of diagnostic and prognostic signatures.

Computational Systems Biology Approach for the Study of Rheumatoid Arthritis: From a Molecular Map to a Dynamical Model

In this work we present a systematic effort to summarize current biological pathway knowledge concerning Rheumatoid Arthritis (RA). We are constructing a detailed molecular map based on exhaustive literature scanning, strict curation criteria, re-evaluation of previously published attempts and most importantly experts' advice. The RA map will be web-published in the coming months in the form of an interactive map, using the MINERVA platform, allowing for easy access, navigation and search of all molecular pathways implicated in RA, serving thus, as an on line knowledgebase for the disease. Moreover the map could be used as a template for Omics data visualization offering a first insight about the pathways affected in different experimental datasets. The second goal of the project is a dynamical study focused on synovial fibroblasts' behavior under different initial conditions specific to RA, as recent studies have shown that synovial fibroblasts play a crucial role in driving the persistent, destructive characteristics of the disease. Leaning on the RA knowledgebase and using the web platform Cell Collective, we are currently building a Boolean large scale dynamical model for the study of RA fibroblasts' activation.

Maximal aggregation of polynomial dynamical systems

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

BACKGROUND

This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.

RESULTS

We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.

CONCLUSION

The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

Logical model specification aided by model-checking techniques: application to the mammalian cell cycle regulation

MOTIVATION

Understanding the temporal behaviour of biological regulatory networks requires the integration of molecular information into a formal model. However, the analysis of model dynamics faces a combinatorial explosion as the number of regulatory components and interactions increases.

RESULTS

We use model-checking techniques to verify sophisticated dynamical properties resulting from the model regulatory structure in the absence of kinetic assumption. We demonstrate the power of this approach by analysing a logical model of the molecular network controlling mammalian cell cycle. This approach enables a systematic analysis of model properties, the delineation of model limitations, and the assessment of various refinements and extensions based on recent experimental observations. The resulting logical model accounts for the main irreversible transitions between cell cycle phases, the sequential activation of cyclins, and the inhibitory role of Skp2, and further emphasizes the multifunctional role for the cell cycle inhibitor Rb.

AVAILABILITY AND IMPLEMENTATION

The original and revised mammalian cell cycle models are available in the model repository associated with the public modelling software GINsim (http://ginsim.org/node/189).

CONTACT

thieffry@ens.fr

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Formal reasoning about systems biology using theorem proving

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients.

Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli

The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.

Modeling Asymmetric Cell Division in Caulobacter crescentus Using a Boolean Logic Approach

Caulobacter crescentus is a model organism for the study of asymmetric division and cell type differentiation, as its cell division cycle generates a pair of daughter cells that differ from one another in their morphology and behavior. One of these cells (called stalked) develops a structure that allows it to attach to solid surfaces and is the only one capable of dividing, while the other (called swarmer) develops a flagellum that allows it to move in liquid media and divides only after differentiating into a stalked cell type. Although many genes, proteins, and other molecules involved in the asymmetric division exhibited by C. crescentus have been discovered and characterized for several decades, it remains as a challenging task to understand how cell properties arise from the high number of interactions between these molecular components. This chapter describes a modeling approach based on the Boolean logic framework that provides a means for the integration of knowledge and study of the emergence of asymmetric division. The text illustrates how the simulation of simple logic models gives valuable insight into the dynamic behavior of the regulatory and signaling networks driving the emergence of the phenotypes exhibited by C. crescentus. These models provide useful tools for the characterization and analysis of other complex biological networks.

Formal modeling and analysis of the hexosamine biosynthetic pathway: role of O-linked N-acetylglucosamine transferase in oncogenesis and cancer progression

The alteration of glucose metabolism, through increased uptake of glucose and glutamine addiction, is essential to cancer cell growth and invasion. Increased flux of glucose through the Hexosamine Biosynthetic Pathway (HBP) drives increased cellular O-GlcNAcylation (hyper-O-GlcNAcylation) and contributes to cancer progression by regulating key oncogenes. However, the association between hyper-O-GlcNAcylation and activation of these oncogenes remains poorly characterized. Here, we implement a qualitative modeling framework to analyze the role of the Biological Regulatory Network in HBP activation and its potential effects on key oncogenes. Experimental observations are encoded in a temporal language format and model checking is applied to infer the model parameters and qualitative model construction. Using this model, we discover step-wise genetic alterations that promote cancer development and invasion due to an increase in glycolytic flux, and reveal critical trajectories involved in cancer progression. We compute delay constraints to reveal important associations between the production and degradation rates of proteins. O-linked N-acetylglucosamine transferase (OGT), an enzyme used for addition of O-GlcNAc during O-GlcNAcylation, is identified as a key regulator to promote oncogenesis in a feedback mechanism through the stabilization of c-Myc. Silencing of the OGT and c-Myc loop decreases glycolytic flux and leads to programmed cell death. Results of network analyses also identify a significant cycle that highlights the role of p53-Mdm2 circuit oscillations in cancer recovery and homeostasis. Together, our findings suggest that the OGT and c-Myc feedback loop is critical in tumor progression, and targeting these mediators may provide a mechanism-based therapeutic approach to regulate hyper-O-GlcNAcylation in human cancer.