Logical Modeling and Analysis of Cellular Regulatory Networks With GINsim 3.0

LM-Merger: A workflow for merging logical models with an application to gene regulation

Motivation

Gene regulatory network (GRN) models provide mechanistic understanding of genetic interactions that regulate gene expression and, consequently, influence cellular behavior. Dysregulated gene expression plays a critical role in disease progression and treatment response, making GRN models a promising tool for precision medicine. While researchers have built many models to describe specific subsets of gene interactions, more comprehensive models that cover a broader range of genes are challenging to build. This necessitates the development of automated approaches for merging existing models.

Results

We present LM-Merger, a workflow for semi-automatically merging logical GRN models. The workflow consists of five main steps: (a) model identification, (b) model standardization and annotation, (c) model verification, (d) model merging, and (d) model evaluation. We demonstrate the feasibility and benefit of this workflow with two pairs of published models pertaining to acute myeloid leukemia (AML). The integrated models were able to retain the predictive accuracy of the original models, while expanding coverage of the biological system. Notably, when applied to a new dataset, the integrated models outperformed the individual models in predicting patient response. This study highlights the potential of logical model merging to advance systems biology research and our understanding of complex diseases.

Availability and implementation

The workflow and accompanying tools, including modules for model standardization, automated logical model merging, and evaluation, are available at https://github.com/IlyaLab/LogicModelMerger/.

A system-level model reveals that transcriptional stochasticity is required for hematopoietic stem cell differentiation

HSCs differentiation has been difficult to study experimentally due to the high number of components and interactions involved, as well as the impact of diverse physiological conditions. From a 200-node network, that was grounded on experimental data, we derived a 21-node regulatory network by collapsing linear pathways and retaining the functional feedback loops. This regulatory network core integrates key nodes and interactions underlying HSCs differentiation, including transcription factors, metabolic, and redox signaling pathways. We used Boolean, continuous, and stochastic dynamic models to simulate the hypoxic conditions of the HSCs niche, as well as the patterns and temporal sequences of HSCs transitions and differentiation. Our findings indicate that HSCs differentiation is a plastic process in which cell fates can transdifferentiate among themselves. Additionally, we found that cell heterogeneity is fundamental for HSCs differentiation. Lastly, we found that oxygen activates ROS production, inhibiting quiescence and promoting growth and differentiation pathways of HSCs.

Predictive modelling of acute Promyelocytic leukaemia resistance to retinoic acid therapy

Acute Promyelocytic Leukaemia (APL) arises from an aberrant chromosomal translocation involving the Retinoic Acid Receptor Alpha (RARA) gene, predominantly with the Promyelocytic Leukaemia (PML) or Promyelocytic Leukaemia Zinc Finger (PLZF) genes. The resulting oncoproteins block the haematopoietic differentiation program promoting aberrant proliferative promyelocytes. Retinoic Acid (RA) therapy is successful in most of the PML::RARA patients, while PLZF::RARA patients frequently become resistant and relapse. Recent studies pointed to various underlying molecular components, but their precise contributions remain to be deciphered. We developed a logical network model integrating signalling, transcriptional, and epigenetic regulatory mechanisms, which captures key features of the APL cell responses to RA depending on the genetic background. The explicit inclusion of the histone methyltransferase EZH2 allowed the assessment of its role in the resistance mechanism, distinguishing between its canonical and non-canonical activities. The model dynamics was thoroughly analysed using tools integrated in the public software suite maintained by the CoLoMoTo consortium (https://colomoto.github.io/). The model serves as a solid basis to assess the roles of novel regulatory mechanisms, as well as to explore novel therapeutical approaches in silico.

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

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

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

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

A dynamic Boolean network reveals that the BMI1 and MALAT1 axis is associated with drug resistance by limiting miR-145-5p in non-small cell lung cancer

Patients with non-small cell lung cancer (NSCLC) are often treated with chemotherapy. Poor clinical response and the onset of chemoresistance limit the anti-tumor benefits of drugs such as cisplatin. According to recent research, metastasis-associated lung adenocarcinoma transcript 1 (MALAT1) is a long non-coding RNA related to cisplatin resistance in NSCLC. Furthermore, MALAT1 targets microRNA-145-5p (miR-145), which activates Krüppel-like factor 4 (KLF4) in associated cell lines. B lymphoma Mo-MLV insertion region 1 homolog (BMI1), on the other hand, inhibits miR-145 expression, which stimulates Specificity protein 1 (Sp1) to trigger the epithelial-mesenchymal transition (EMT) process in pemetrexed-resistant NSCLC cells. The interplay between these molecules in drug resistance is still unclear. Therefore, we propose a dynamic Boolean network that can encapsulate the complexity of these drug-resistant molecules. Using published clinical data for gain or loss-of-function perturbations, our network demonstrates reasonable agreement with experimental observations. We identify four new positive circuits: miR-145/Sp1/MALAT1, BMI1/miR-145/Myc, KLF4/p53/miR-145, and miR-145/Wip1/p38MAPK/p53. Notably, miR-145 emerges as a central player in these regulatory circuits, underscoring its pivotal role in NSCLC drug resistance. Our circuit perturbation analysis further emphasizes the critical involvement of these new circuits in drug resistance for NSCLC. In conclusion, targeting MALAT1 and BMI1 holds promise for overcoming drug resistance, while activating miR-145 represents a potential strategy to significantly reduce drug resistance in NSCLC.

Breaking reflection symmetry: evolving long dynamical cycles in Boolean systems

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

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

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

The lncRNA DLX6-AS1/miR-16-5p axis regulates autophagy and apoptosis in non-small cell lung cancer: A Boolean model of cell death

Long non-coding RNA (lncRNA) distal-less homeobox 6 antisense RNA 1 (DLX6-AS1) is elevated in a variety of cancers, including non-small cell lung cancer (NSCLC) and cervical cancer. Although it was found that the microRNA-16-5p (miR-16), which is known to regulate autophagy and apoptosis, had been downregulated in similar cancers. Recent research has shown that in tumors with similar characteristics, DLX6-AS1 acts as a sponge for miR-16 expression. However, the cell death-related molecular mechanism of the DLX6-AS1/miR-16 axis has yet to be investigated. Therefore, we propose a dynamic Boolean model to investigate gene regulation in cell death processes via the DLX6-AS1/miR-16 axis. We found the finest concordance when we compared our model to many experimental investigations including gain-of-function genes in NSCLC and cervical cancer. A unique positive circuit involving BMI1/ATM/miR-16 is also something we predict. Our results suggest that this circuit is essential for regulating autophagy and apoptosis under stress signals. Thus, our Boolean network enables an evident cell-death process coupled with NSCLC and cervical cancer. Therefore, our results suggest that DLX6-AS1 targeting may boost miR-16 activity and thereby restrict tumor growth in these cancers by triggering autophagy and apoptosis.

A Boolean model of the oncogene role of FAM111B in lung adenocarcinoma

The ultimate goal of this study is to analyze the gene regulation between FAM111B and p53 in lung adenocarcinoma using Boolean networks. Recent studies have shown that downregulation of FAM111B enhances the G2/M cell cycle checkpoint in the respective cell lines. Upregulation of p53 directly downregulates FAM111B, which is directed to affect cell cycle controllers Cdc25C and Cdk1/CyclinB, thereby controlling G2/M cell cycle arrest. As for apoptosis, down-regulation of FAM111B by p53 directly regulates the BAG3/Bcl-2 axis, which triggers apoptotic cell death. However, the molecular mechanisms involving p53 and FAM111B in G2/M checkpoint regulation are still unknown. Thus, we present a Boolean model of the G2/M checkpoint considering the effect of p53 and FAM111B. Our model indicates that the cell fate between the two cellular phenotypes, arrest, and apoptosis, at the G2/M checkpoint is non-deterministic and is controlled by p53. The model was compared with the experimental data involving gain- or loss-of-function genes and achieved a fair agreement. The model predicts a positive circuit involving p53/FAM111B/BAG3. Our circuit perturbation analysis suggests that this circuit may be essential for controlling cell-fate decisions at the G2/M checkpoint. Our model supports that FAM111B is an engaging target for drug development in lung adenocarcinoma.

A logical model of Ewing sarcoma cell epithelial-to-mesenchymal transition supports the existence of hybrid cellular phenotypes

Ewing sarcoma (ES) is a highly aggressive pediatric tumor driven by the RNA-binding protein EWS (EWS)/friend leukemia integration 1 transcription factor (FLI1) chimeric transcription factor, which is involved in epithelial-mesenchymal transition (EMT). EMT stabilizes a hybrid cell state, boosting metastatic potential and drug resistance. Nevertheless, the mechanisms underlying the maintenance of this hybrid phenotype in ES remain elusive. Our study proposes a logical EMT model for ES, highlighting zinc finger E-box-binding homeobox 2 (ZEB2), miR-145, and miR-200 circuits that maintain hybrid states. The model aligns with experimental findings and reveals a previously unknown circuit supporting the mesenchymal phenotype. These insights emphasize the role of ZEB2 in the maintenance of the hybrid state in ES.

Applications of Boolean modeling to study the dynamics of a complex disease and therapeutics responses

Computational modeling has emerged as a critical tool in investigating the complex molecular processes involved in biological systems and diseases. In this study, we apply Boolean modeling to uncover the molecular mechanisms underlying Parkinson's disease (PD), one of the most prevalent neurodegenerative disorders. Our approach is based on the PD-map, a comprehensive molecular interaction diagram that captures the key mechanisms involved in the initiation and progression of PD. Using Boolean modeling, we aim to gain a deeper understanding of the disease dynamics, identify potential drug targets, and simulate the response to treatments. Our analysis demonstrates the effectiveness of this approach in uncovering the intricacies of PD. Our results confirm existing knowledge about the disease and provide valuable insights into the underlying mechanisms, ultimately suggesting potential targets for therapeutic intervention. Moreover, our approach allows us to parametrize the models based on omics data for further disease stratification. Our study highlights the value of computational modeling in advancing our understanding of complex biological systems and diseases, emphasizing the importance of continued research in this field. Furthermore, our findings have potential implications for the development of novel therapies for PD, which is a pressing public health concern. Overall, this study represents a significant step forward in the application of computational modeling to the investigation of neurodegenerative diseases, and underscores the power of interdisciplinary approaches in tackling challenging biomedical problems.

Verifiable biology

The formalization of biological systems using computational modelling approaches as an alternative to mathematical-based methods has recently received much interest because computational models provide a deeper mechanistic understanding of biological systems. In particular, formal verification, complementary approach to standard computational techniques such as simulation, is used to validate the system correctness and obtain critical information about system behaviour. In this study, we survey the most frequently used computational modelling approaches and formal verification techniques for computational biology. We compare a number of verification tools and software suites used to analyse biological systems and biochemical networks, and to verify a wide range of biological properties. For users who have no expertise in formal verification, we present a novel methodology that allows them to easily apply formal verification techniques to analyse their biological or biochemical system of interest.

Quadra-Stable Dynamics of p53 and PTEN in the DNA Damage Response

Cell fate determination is a complex process that is frequently described as cells traveling on rugged pathways, beginning with DNA damage response (DDR). Tumor protein p53 (p53) and phosphatase and tensin homolog (PTEN) are two critical players in this process. Although both of these proteins are known to be key cell fate regulators, the exact mechanism by which they collaborate in the DDR remains unknown. Thus, we propose a dynamic Boolean network. Our model incorporates experimental data obtained from NSCLC cells and is the first of its kind. Our network's wild-type system shows that DDR activates the G2/M checkpoint, and this triggers a cascade of events, involving p53 and PTEN, that ultimately lead to the four potential phenotypes: cell cycle arrest, senescence, autophagy, and apoptosis (quadra-stable dynamics). The network predictions correspond with the gain-and-loss of function investigations in the additional two cell lines (HeLa and MCF-7). Our findings imply that p53 and PTEN act as molecular switches that activate or deactivate specific pathways to govern cell fate decisions. Thus, our network facilitates the direct investigation of quadruplicate cell fate decisions in DDR. Therefore, we concluded that concurrently controlling PTEN and p53 dynamics may be a viable strategy for enhancing clinical outcomes.

Network analysis reveals that the tumor suppressor lncRNA GAS5 acts as a double-edged sword in response to DNA damage in gastric cancer

The lncRNA GAS5 acts as a tumor suppressor and is downregulated in gastric cancer (GC). In contrast, E2F1, an important transcription factor and tumor promoter, directly inhibits miR-34c expression in GC cell lines. Furthermore, in the corresponding GC cell lines, lncRNA GAS5 directly targets E2F1. However, lncRNA GAS5 and miR-34c remain to be studied in conjunction with GC. Here, we present a dynamic Boolean network to classify gene regulation between these two non-coding RNAs (ncRNAs) in GC. This is the first study to show that lncRNA GAS5 can positively regulate miR-34c in GC through a previously unknown molecular pathway coupling lncRNA/miRNA. We compared our network to several in-vivo/in-vitro experiments and obtained an excellent agreement. We revealed that lncRNA GAS5 regulates miR-34c by targeting E2F1. Additionally, we found that lncRNA GAS5, independently of p53, inhibits GC proliferation through the ATM/p38 MAPK signaling pathway. Accordingly, our results support that E2F1 is an engaging target of drug development in tumor growth and aggressive proliferation of GC, and favorable results can be achieved through tumor suppressor lncRNA GAS5/miR-34c axis in GC. Thus, our findings unlock a new avenue for GC treatment in response to DNA damage by these ncRNAs.

A novel logical model of COVID-19 intracellular infection to support therapies development

In this paper, a logical-based mathematical model of the cellular pathways involved in the COVID-19 infection has been developed to study various drug treatments (single or in combination), in different illness scenarios, providing insights into their mechanisms of action. Drug simulations suggest that the effects of single drugs are limited, or depending on the scenario counterproductive, whereas better results appear combining different treatments. Specifically, the combination of the anti-inflammatory Baricitinib and the anti-viral Remdesivir showed significant benefits while a stronger efficacy emerged from the triple combination of Baricitinib, Remdesivir, and the corticosteroid Dexamethasone. Together with a sensitivity analysis, we performed an analysis of the mechanisms of the drugs to reveal their impact on molecular pathways.

The paper introduces a logical-based mathematical model of the cellular pathways involved in the COVID-19 infection. The aim of the model is to study, in a qualitative but comprehensive way, the cellular mechanisms developed during the virus infection with the principal focus on drug treatments. The model is able to reproduce various illness scenarios: from the early infection stages to the late illness stages characterized by strong immune reaction usually evolving in the so-called cytokine storm. Different drug effects have been tested singularly and in combination treatments. Computational sensitivity analysis was performed on the model along with the analysis of the mechanisms of the drugs to reveal their impact on molecular pathways. The results show that the effect of single drugs may be limited or counterproductive, depending on the illness stage. The highest predicted efficacy is obtained by combining three different treatments: the anti-inflammatory Baricitinib, the anti-viral Remdesivir and the corticosteroid Dexamethasone. This triple combination therapy has been analyzed not only in terms of global cellular effect but also in function of the involved internal pathways, suggesting the rational mechanisms for its successfulness.

Boolean modelling as a logic-based dynamic approach in systems medicine

Molecular mechanisms of health and disease are often represented as systems biology diagrams, and the coverage of such representation constantly increases. These static diagrams can be transformed into dynamic models, allowing for in silico simulations and predictions. Boolean modelling is an approach based on an abstract representation of the system. It emphasises the qualitative modelling of biological systems in which each biomolecule can take two possible values: zero for absent or inactive, one for present or active. Because of this approximation, Boolean modelling is applicable to large diagrams, allowing to capture their dynamic properties. We review Boolean models of disease mechanisms and compare a range of methods and tools used for analysis processes. We explain the methodology of Boolean analysis focusing on its application in disease modelling. Finally, we discuss its practical application in analysing signal transduction and gene regulatory pathways in health and disease.

The Wnt pathway can stabilize hybrid phenotypes in the epithelial-mesenchymal transition: A logical modeling approach

The Wnt pathway is important to regulate a variety of biochemical functions and can contribute to cancer development through its influence on the epithelial-mesenchymal transition (EMT). Multiple circuits have been reported to participate in the regulation of the Wnt signaling, however, the way these circuits coordinately regulate this signaling is still unclear. Moreover, the mechanisms responsible for the appearance of hybrid phenotypes (cells presenting both E and M features) are not well determined. The hybrid phenotype can present much higher metastatic potential than the mesenchymal phenotype. In this study, we propose a Boolean model of the Wnt pathway signaling contemplating recent published biochemical information on hepatocarcinoma. The model presents good coherence with experimental data for perturbed and wild-type cases. With the model, we propose two new molecular circuits involving several molecules that can stabilize hybrid states during the EMT. Moreover, we found that the two well studied circuits, AKT1/β-catenin and SNAIL1/miR-34, can cooperate with the predicted ones to favor the stabilization of the hybrid states. These findings highlight some possible unrecognized mechanisms during Wnt signaling and may provide alternative therapeutic strategies to control cancer metastatization.

Computational Analysis of Cytokine Release Following Bispecific T-Cell Engager Therapy: Applications of a Logic-Based Model

Bispecific T-cell engaging therapies harness the immune system to elicit an effective anticancer response. Modulating the immune activation avoiding potential adverse effects such as cytokine release syndrome (CRS) is a critical aspect to realizing the full potential of this therapy. The use of suitable exogenous intervention strategies to mitigate the CRS risk without compromising the antitumoral capability of bispecific antibody treatment is crucial. To this end, computational approaches can be instrumental to systematically exploring the effects of combining bispecific antibodies with CRS intervention strategies. Here, we employ a logical model to describe the action of bispecific antibodies and the complex interplay of various immune system components and use it to perform simulation experiments to improve the understanding of the factors affecting CRS. We performed a sensitivity analysis to identify the comedications that could ameliorate CRS without impairing tumor clearance. Our results agree with publicly available experimental data suggesting anti-TNF and anti-IL6 as possible co-treatments. Furthermore, we suggest anti-IFNγ as a suitable candidate for clinical studies.

Calcium Signaling Is Impaired in PTEN-Deficient T Cell Acute Lymphoblastic Leukemia

PTEN (Phosphatase and TENsin homolog) is a well-known tumor suppressor involved in numerous types of cancer, including T-cell acute lymphoblastic leukemia (T-ALL). In human, loss-of-function mutations of PTEN are correlated to mature T-ALL expressing a T-cell receptor (TCR) at their cell surface. In accordance with human T-ALL, inactivation of Pten gene in mouse thymocytes induces TCRαβ⁺ T-ALL development. Herein, we explored the functional interaction between TCRαβ signaling and PTEN. First, we performed single-cell RNA sequencing (scRNAseq) of PTEN-deficient and PTEN-proficient thymocytes. Bioinformatic analysis of our scRNAseq data showed that pathological Pten^del thymocytes express, as expected, Myc transcript, whereas inference of pathway activity revealed that these Pten^del thymocytes display a lower calcium pathway activity score compared to their physiological counterparts. We confirmed this result using ex vivo calcium flux assay and showed that upon TCR activation tumor Pten^del blasts were unable to release calcium ions (Ca²⁺) from the endoplasmic reticulum to the cytosol. In order to understand such phenomena, we constructed a mathematical model centered on the mechanisms controlling the calcium flux, integrating TCR signal strength and PTEN interactions. This qualitative model displays a dynamical behavior coherent with the dynamics reported in the literature, it also predicts that PTEN affects positively IP3 (inositol 1,4,5-trisphosphate) receptors (ITPR). Hence, we analyzed Itpr expression and unraveled that ITPR proteins levels are reduced in PTEN-deficient tumor cells compared to physiological and leukemic PTEN-proficient cells. However, calcium flux and ITPR proteins expression are not defective in non-leukemic PTEN-deficient T cells indicating that beyond PTEN loss an additional alteration is required. Altogether, our study shows that ITPR/Calcium flux is a part of the oncogenic landscape shaped by PTEN loss and pinpoints a putative role of PTEN in the regulation of ITPR proteins in thymocytes, which remains to be characterized.

Dynamical modeling of miR-34a, miR-449a, and miR-16 reveals numerous DDR signaling pathways regulating senescence, autophagy, and apoptosis in HeLa cells

Transfection of tumor suppressor miRNAs such as miR-34a, miR-449a, and miR-16 with DNA damage can regulate apoptosis and senescence in cancer cells. miR-16 has been shown to influence autophagy in cervical cancer. However, the function of miR-34a and miR-449a in autophagy remains unknown. The functional and persistent G1/S checkpoint signaling pathways in HeLa cells via these three miRNAs, either synergistically or separately, remain a mystery. As a result, we present a synthetic Boolean network of the functional G1/S checkpoint regulation, illustrating the regulatory effects of these three miRNAs. To our knowledge, this is the first synthetic Boolean network that demonstrates the advanced role of these miRNAs in cervical cancer signaling pathways reliant on or independent of p53, such as MAPK or AMPK. We compared our estimated probability to the experimental data and found reasonable agreement. Our findings indicate that miR-34a or miR-16 may control senescence, autophagy, apoptosis, and the functional G1/S checkpoint. Additionally, miR-449a can regulate just senescence and apoptosis on an individual basis. MiR-449a can coordinate autophagy in HeLa cells in a synergistic manner with miR-16 and/or miR-34a.

A Boolean Model of the Proliferative Role of the lncRNA XIST in Non-Small Cell Lung Cancer Cells

The long non-coding RNA X inactivate-specific transcript (lncRNA XIST) has been verified as an oncogenic gene in non-small cell lung cancer (NSCLC) whose regulatory role is largely unknown. The important tumor suppressors, microRNAs: miR-449a and miR-16 are regulated by lncRNA XIST in NSCLC, these miRNAs share numerous common targets and experimental evidence suggests that they synergistically regulate the cell-fate regulation of NSCLC. LncRNA XIST is known to sponge miR-449a and miR-34a, however, the regulatory network connecting all these non-coding RNAs is still unknown. Here we propose a Boolean regulatory network for the G1/S cell cycle checkpoint in NSCLC contemplating the involvement of these non-coding RNAs. Model verification was conducted by comparison with experimental knowledge from NSCLC showing good agreement. The results suggest that miR-449a regulates miR-16 and p21 activity by targeting HDAC1, c-Myc, and the lncRNA XIST. Furthermore, our circuit perturbation simulations show that five circuits are involved in cell fate determination between senescence and apoptosis. The model thus allows pinpointing the direct cell fate mechanisms of NSCLC. Therefore, our results support that lncRNA XIST is an attractive target of drug development in tumor growth and aggressive proliferation of NSCLC, and promising results can be achieved through tumor suppressor miRNAs.

Dynamical Analysis of a Boolean Network Model of the Oncogene Role of lncRNA ANRIL and lncRNA UFC1 in Non-Small Cell Lung Cancer

Long non-coding RNA (lncRNA) such as ANRIL and UFC1 have been verified as oncogenic genes in non-small cell lung cancer (NSCLC). It is well known that the tumor suppressor microRNA-34a (miR-34a) is downregulated in NSCLC. Furthermore, miR-34a induces senescence and apoptosis in breast, glioma, cervical cancer including NSCLC by targeting Myc. Recent evidence suggests that these two lncRNAs act as a miR-34a sponge in corresponding cancers. However, the biological functions between these two non-coding RNAs (ncRNAs) have not yet been studied in NSCLC. Therefore, we present a Boolean model to analyze the gene regulation between these two ncRNAs in NSCLC. We compared our model to several experimental studies involving gain- or loss-of-function genes in NSCLC cells and achieved an excellent agreement. Additionally, we predict three positive circuits involving miR-34a/E2F1/ANRIL, miR-34a/E2F1/UFC1, and miR-34a/Myc/ANRIL. Our circuit- perturbation analysis shows that these circuits are important for regulating cell-fate decisions such as senescence and apoptosis. Thus, our Boolean network permits an explicit cell-fate mechanism associated with NSCLC. Therefore, our results support that ANRIL and/or UFC1 is an attractive target for drug development in tumor growth and aggressive proliferation of NSCLC, and that a valuable outcome can be achieved through the miRNA-34a/Myc pathway.

UPMaBoSS: A Novel Framework for Dynamic Cell Population Modeling

Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.

Patient-Specific Modeling of Diffuse Large B-Cell Lymphoma

Personalized medicine aims to tailor treatment to patients based on their individual genetic or molecular background. Especially in diseases with a large molecular heterogeneity, such as diffuse large B-cell lymphoma (DLBCL), personalized medicine has the potential to improve outcome and/or to reduce resistance towards treatment. However, integration of patient-specific information into a computational model is challenging and has not been achieved for DLBCL. Here, we developed a computational model describing signaling pathways and expression of critical germinal center markers. The model integrates the regulatory mechanism of the signaling and gene expression network and covers more than 50 components, many carrying genetic lesions common in DLBCL. Using clinical and genomic data of 164 primary DLBCL patients, we implemented mutations, structural variants and copy number alterations as perturbations in the model using the CoLoMoTo notebook. Leveraging patient-specific genotypes and simulation of the expression of marker genes in specific germinal center conditions allows us to predict the consequence of the modeled pathways for each patient. Finally, besides modeling how genetic perturbations alter physiological signaling, we also predicted for each patient model the effect of rational inhibitors, such as Ibrutinib, that are currently discussed as possible DLBCL treatments, showing patient-dependent variations in effectiveness and synergies.

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.

COVID19 Disease Map, a computational knowledge repository of virus-host interaction mechanisms

We need to effectively combine the knowledge from surging literature with complex datasets to propose mechanistic models of SARS-CoV-2 infection, improving data interpretation and predicting key targets of intervention. Here, we describe a large-scale community effort to build an open access, interoperable and computable repository of COVID-19 molecular mechanisms. The COVID-19 Disease Map (C19DMap) is a graphical, interactive representation of disease-relevant molecular mechanisms linking many knowledge sources. Notably, it is a computational resource for graph-based analyses and disease modelling. To this end, we established a framework of tools, platforms and guidelines necessary for a multifaceted community of biocurators, domain experts, bioinformaticians and computational biologists. The diagrams of the C19DMap, curated from the literature, are integrated with relevant interaction and text mining databases. We demonstrate the application of network analysis and modelling approaches by concrete examples to highlight new testable hypotheses. This framework helps to find signatures of SARS-CoV-2 predisposition, treatment response or prioritisation of drug candidates. Such an approach may help deal with new waves of COVID-19 or similar pandemics in the long-term perspective.

Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks

We present new applications of parity inversion and time reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a long-standing open question of how attractor count in critical random Boolean networks scales with network size and whether the scaling matches biological observations. Via 80-fold improvement in probed network size (N = 16,384), we find the unexpectedly low scaling exponent of 0.12 ± 0.05, approximately one-tenth the analytical upper bound. We demonstrate a general principle: A system's relationship to its time reversal and state-space inversion constrains its repertoire of emergent behaviors.

Prediction and Boolean logical modelling of synergistic microRNA regulatory networks during reprogramming of male germline pluripotent stem cells

Unipotent male germline stem (GS) cells can undergo spontaneous reprogramming to germline pluripotent stem (GPS) cells during in vitro culture. In our previous study, we proposed a Boolean logical model of gene regulatory network (GRN) during reprogramming of GS cells to GPS cells. This study was designed to predict and model synergistic microRNA (miRNA) regulatory network during reprogramming of GS cells into GPS cells. The miRNAs targeting differentially expressed genes (DEGs) among GS and GPS cells were predicted by a novel Gene Ontology (GO) enrichment analysis to construct miRNA synergistic networks (MSN) and identify regulatory miRNA modules. Qualitative Boolean logical model of synergistic miRNAs and its regulated genes was then constructed by considering discrete, asynchronous, multivalued logical formalism using the GINsim modeling and simulation tools. Topology, functional and community overlap studies revealed that mmu-miR-200b-3p, mmu-miR-429-3p and mmu-miR-141-3p, mmu-miR-200a-3p and mmu-miR-200c-3p in MSN belongs to the family of miR-200/429/141 and conjectured to control the pluripotency and reprogramming by promoting Mesenchymal to Epithelial Transition (MET). Synergistic network involving mmu-miR-20b-5p, mmu-miR-20a-5p, mmu-miR-106a-5p, mmu-miR-106b-5p, and mmu-miR-17-5p were found to be essential for the maintenance of GS cells. Logical miRNA regulatory network modelling showed that synergistic miRNAs regulates the gene dynamics of MET during GS-GPS reprogramming, as confirmed by perturbation analysis. Taken together, our study predicted novel synergistic miRNAs involved in the regulation of reprogramming and pluripotency in GPS cells. The Boolean logical model of synergistic miRNAs regulatory network further confirms our previous study that gene dynamics of MET regulates GS-GPS reprogramming.

Logical modelling of in vitro differentiation of human monocytes into dendritic cells unravels novel transcriptional regulatory interactions

Dendritic cells (DCs) are the major specialized antigen-presenting cells, thereby connecting innate and adaptive immunity. Because of their role in establishing adaptive immunity, they constitute promising targets for immunotherapy. Monocytes can differentiate into DCs in vitro in the presence of colony-stimulating factor 2 (CSF2) and interleukin 4 (IL4), activating four signalling pathways (MAPK, JAK/STAT, NFKB and PI3K). However, the downstream transcriptional programme responsible for DC differentiation from monocytes (moDCs) remains unknown. By analysing the scientific literature on moDC differentiation, we established a preliminary logical model that helped us identify missing information regarding the activation of genes responsible for this differentiation, including missing targets for key transcription factors (TFs). Using ChIP-seq and RNA-seq data from the Blueprint consortium, we defined active and inactive promoters, together with differentially expressed genes in monocytes, moDCs and macrophages, which correspond to an alternative cell fate. We then used this functional genomic information to predict novel targets for previously identified TFs. By integrating this information, we refined our model and recapitulated the main established facts regarding moDC differentiation. Prospectively, the resulting model should be useful to develop novel immunotherapies targeting moDCs.

Interplay between SMAD2 and STAT5A is a critical determinant of IL-17A/IL-17F differential expression

Interleukins (IL)-17A and F are critical cytokines in anti-microbial immunity but also contribute to auto-immune pathologies. Recent evidence suggests that they may be differentially produced by T-helper (Th) cells, but the underlying mechanisms remain unknown. To address this question, we built a regulatory graph integrating all reported upstream regulators of IL-17A and F, completed by ChIP-seq data analyses. The resulting regulatory graph encompasses 82 components and 136 regulatory links. The graph was then supplemented by logical rules calibrated with original flow cytometry data using naive CD4⁺ T cells, in conditions inducing IL-17A or IL-17F. The model displays specific stable states corresponding to virtual phenotypes explaining IL-17A and IL-17F differential regulation across eight cytokine stimulatory conditions. Our model analysis points to the transcription factors NFAT2A, STAT5A and SMAD2 as key regulators of the differential expression of IL-17A and IL-17F, with STAT5A controlling IL-17F expression, and an interplay of NFAT2A, STAT5A and SMAD2 controlling IL-17A expression. We experimentally observed that the production of IL-17A was correlated with an increase of SMAD2 transcription, and the expression of IL-17F correlated with an increase of BLIMP-1 transcription, together with an increase of STAT5A expression (mRNA), as predicted by our model. Interestingly, RORγt presumably plays a more determinant role in IL-17A expression as compared to IL-17F expression. In conclusion, we propose the first mechanistic model accounting for the differential expression of IL-17A and F in Th cells, providing a basis to design novel therapeutic interventions in auto-immune and inflammatory diseases.

Deciphering and modelling the TGF-β signalling interplays specifying the dorsal-ventral axis of the sea urchin embryo

During sea urchin development, secretion of Nodal and BMP2/4 ligands and their antagonists Lefty and Chordin from a ventral organiser region specifies the ventral and dorsal territories. This process relies on a complex interplay between the Nodal and BMP pathways through numerous regulatory circuits. To decipher the interplay between these pathways, we used a combination of treatments with recombinant Nodal and BMP2/4 proteins and a computational modelling approach. We assembled a logical model focusing on cell responses to signalling inputs along the dorsal-ventral axis, which was extended to cover ligand diffusion and enable multicellular simulations. Our model simulations accurately recapitulate gene expression in wild-type embryos, accounting for the specification of ventral ectoderm, ciliary band and dorsal ectoderm. Our model simulations further recapitulate various morphant phenotypes, reveal a dominance of the BMP pathway over the Nodal pathway and stress the crucial impact of the rate of Smad activation in dorsal-ventral patterning. These results emphasise the key role of the mutual antagonism between the Nodal and BMP2/4 pathways in driving early dorsal-ventral patterning of the sea urchin embryo.

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.

A practical guide to mechanistic systems modeling in biology using a logic-based approach

Mechanistic computational models enable the study of regulatory mechanisms implicated in various biological processes. These models provide a means to analyze the dynamics of the systems they describe, and to study and interrogate their properties, and provide insights about the emerging behavior of the system in the presence of single or combined perturbations. Aimed at those who are new to computational modeling, we present here a practical hands-on protocol breaking down the process of mechanistic modeling of biological systems in a succession of precise steps. The protocol provides a framework that includes defining the model scope, choosing validation criteria, selecting the appropriate modeling approach, constructing a model and simulating the model. To ensure broad accessibility of the protocol, we use a logical modeling framework, which presents a lower mathematical barrier of entry, and two easy-to-use and popular modeling software tools: Cell Collective and GINsim. The complete modeling workflow is applied to a well-studied and familiar biological process-the lac operon regulatory system. The protocol can be completed by users with little to no prior computational modeling experience approximately within 3 h.

Systems biology approach suggests new miRNAs as phenotypic stability factors in the epithelial-mesenchymal transition

The epithelial-mesenchymal transition (EMT) is a cellular programme on which epithelial cells undergo a phenotypic transition to mesenchymal ones acquiring metastatic properties such as mobility and invasion. TGF-β signalling can promote the EMT process. However, the dynamics of the concentration response of TGF-β-induced EMT is not well explained. In this work, we propose a logical model of TGF-β dose dependence of EMT in MCF10A breast cells. The model outcomes agree with experimentally observed phenotypes for the wild-type and perturbed/mutated cases. As important findings of the model, it predicts the coexistence of more than one hybrid state and that the circuit between TWIST1 and miR-129 is involved in their stabilization. Thus, miR-129 should be considered as a phenotypic stability factor. The circuit TWIST1/miR-129 associates with ZEB1-mediated circuits involving miRNAs 200, 1199, 340, and the protein GRHL2 to stabilize the hybrid state. Additionally, we found a possible new autocrine mechanism composed of the circuit involving TGF-β, miR-200, and SNAIL1 that contributes to the stabilization of the mesenchymal state. Therefore, our work can extend our comprehension of TGF-β-induced EMT in MCF10A cells to potentially improve the strategies for breast cancer treatment.

Computational Verification of Large Logical Models-Application to the Prediction of T Cell Response to Checkpoint Inhibitors

At the crossroad between biology and mathematical modeling, computational systems biology can contribute to a mechanistic understanding of high-level biological phenomenon. But as knowledge accumulates, the size and complexity of mathematical models increase, calling for the development of efficient dynamical analysis methods. Here, we propose the use of two approaches for the development and analysis of complex cellular network models. A first approach, called "model verification" and inspired by unitary testing in software development, enables the formalization and automated verification of validation criteria for whole models or selected sub-parts. When combined with efficient analysis methods, this approach is suitable for continuous testing, thereby greatly facilitating model development. A second approach, called "value propagation," enables efficient analytical computation of the impact of specific environmental or genetic conditions on the dynamical behavior of some models. We apply these two approaches to the delineation and the analysis of a comprehensive model for T cell activation, taking into account CTLA4 and PD-1 checkpoint inhibitory pathways. While model verification greatly eases the delineation of logical rules complying with a set of dynamical specifications, propagation provides interesting insights into the different potential of CTLA4 and PD-1 immunotherapies. Both methods are implemented and made available in the all-inclusive CoLoMoTo Docker image, while the different steps of the model analysis are fully reported in two companion interactive jupyter notebooks, thereby ensuring the reproduction of our results.

Towards DNA-damage induced autophagy: A Boolean model of p53-induced cell fate mechanisms

How a cell determines a given phenotype upon damaged DNA is an open problem. Cell fate decisions happen at cell cycle checkpoints and it is becoming clearer that the p53 pathway is a major regulator of cell fate decisions involving apoptosis or senescence upon DNA damage, especially at G1/S. However, recent results suggest that this pathway is also involved in autophagy induction upon DNA damage. To our knowledge, in this work we propose the first model of the DNA damage-induced G1/S checkpoint contemplating the decision between three phenotypes: apoptosis, senescence, and autophagy. The Boolean model is proposed based on experiments with U87 glioblastoma cells using the transfection of miR-16 that can induce a DNA damage response. The wild-type case of the model shows that DNA damage induces the checkpoint and the coexistence of the three phenotypes (tristable dynamics), each with a different probability. We also predict that the positive feedback involving ATM, miR-16, and Wip1 has an influence on the tristable state. The model predictions were compared to experiments of gain and loss of function in other three different cell lines (MCF-7, A549, and U2OS) presenting agreement. For p53-deficient cell lines such as HeLa, H1299, and PC-3, our model contemplates the experimental observation that the alternative AMPK pathway can compensate this deficiency. We conclude that at the G1/S checkpoint the p53 pathway (or, in its absence, the AMPK pathway) can regulate the induction of different phenotypes in a stochastic manner in the U87 cell line and others.

A Boolean Logical model for Reprogramming of Testes-derived male Germline Stem Cells into Germline pluripotent stem cells

BACKGROUND AND OBJECTIVE

Male germline stem (GS) cells are responsible for the maintenance of spermatogenesis throughout the adult life of males. Upon appropriate in vitro culture conditions, these GS cells can undergo reprogramming to become germline pluripotent stem (GPS) cells with the loss of spermatogenic potential. In recent years, voluminous data of gene transcripts in GS and GPS cells have become available. However, the mechanism of reprogramming of GS cells into GPS cells remains elusive. This study was designed to develop a Boolean logical model of gene regulatory network (GRN) that might be involved in the reprogramming of GS cells into GPS cells.

METHODS

The gene expression profile of GS and GPS cells (GSE ID: GSE11274 and GSE74151) were analyzed using R Bioconductor to identify differentially expressed genes (DEGs) and were functionally annotated with DAVID server. Potential pluripotent genes among the DEGs were then predicted using a combination of machine learning [Support Vector Machine (SVM)] and BLAST search. Protein isoforms were identified by pattern matching with UniProt database with in-house scripts written in C++. Both linear and non-linear interaction maps were generated using the STRING server. CellNet is used to study the relationship of GRNs between the GS and GPS cells. Finally, the GRNs involving all the genes from integrated methods and literature was constructed and qualitative modelling for reprogramming of GS to GPS cells were done by considering the discrete, asynchronous, multivalued logical formalism using the GINsim modeling and simulation tool.

RESULTS

Through the use of machine learning and logical modeling, the present study identified 3585 DEGs and 221 novel pluripotent genes including Tet1, Cdh1, Tfap2c, Etv4, Etv5, Prdm14, and Prdm10 in GPS cells. Pathway analysis revealed that important signaling pathways such as core pluripotency network, PI3K-Akt, WNT, GDNF and BMP4 signalling pathways were important for the reprogramming of GS cells to GPS cells. On the other hand, CellNet analysis of GRNs of GS and GPS cells revealed that GS cells were similar to gonads whereas GPS cells were similar to ESCs in gene expression profile. A logical regulatory model was developed, which showed that TGFβ negatively regulated the reprogramming of the GS to GPS cells, as confirmed by perturbations studies.

CONCLUSION

The study identified novel pluripotent genes involved in the reprogramming of GS cells into GPS cells. A multivalued logical model of cellular reprogramming is proposed, which suggests that reprogramming of GS cells to GPS cells involves signalling pathways namely LIF, GDNF, BMP4, and TGFβ along with some novel pluripotency genes.

Exact solving and sensitivity analysis of stochastic continuous time Boolean models

Background

Solutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models.

Results

We show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation’s kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights.

Conclusion

Up to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model’s timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

Setting the basis of best practices and standards for curation and annotation of logical models in biology-highlights of the [BC]2 2019 CoLoMoTo/SysMod Workshop

The fast accumulation of biological data calls for their integration, analysis and exploitation through more systematic approaches. The generation of novel, relevant hypotheses from this enormous quantity of data remains challenging. Logical models have long been used to answer a variety of questions regarding the dynamical behaviours of regulatory networks. As the number of published logical models increases, there is a pressing need for systematic model annotation, referencing and curation in community-supported and standardised formats. This article summarises the key topics and future directions of a meeting entitled 'Annotation and curation of computational models in biology', organised as part of the 2019 [BC]2 conference. The purpose of the meeting was to develop and drive forward a plan towards the standardised annotation of logical models, review and connect various ongoing projects of experts from different communities involved in the modelling and annotation of molecular biological entities, interactions, pathways and models. This article defines a roadmap towards the annotation and curation of logical models, including milestones for best practices and minimum standard requirements.

Contribution of ROS and metabolic status to neonatal and adult CD8+ T cell activation

In neonatal T cells, a low response to infection contributes to a high incidence of morbidity and mortality of neonates. Here we have evaluated the impact of the cytoplasmic and mitochondrial levels of Reactive Oxygen Species of adult and neonatal CD8⁺ T cells on their activation potential. We have also constructed a logical model connecting metabolism and ROS with T cell signaling. Our model indicates the interplay between antigen recognition, ROS and metabolic status in T cell responses. This model displays alternative stable states corresponding to different cell fates, i.e. quiescent, activated and anergic states, depending on ROS levels. Stochastic simulations with this model further indicate that differences in ROS status at the cell population level contribute to the lower activation rate of neonatal, compared to adult, CD8⁺ T cells upon TCR engagement. These results are relevant for neonatal health care. Our model can serve to analyze the impact of metabolic shift during cancer in which, similar to neonatal cells, a high glycolytic rate and low concentrations of glutamine and arginine promote tumor tolerance.

Logical modelling reveals the PDC-PDK interaction as the regulatory switch driving metabolic flexibility at the cellular level

BACKGROUND

Metabolic flexibility is the ability of an organism to switch between substrates for energy metabolism, in response to the changing nutritional state and needs of the organism. On the cellular level, metabolic flexibility revolves around the tricarboxylic acid cycle by switching acetyl coenzyme A production from glucose to fatty acids and vice versa. In this study, we modelled cellular metabolic flexibility by constructing a logical model connecting glycolysis, fatty acid oxidation, fatty acid synthesis and the tricarboxylic acid cycle, and then using network analysis to study the behaviours of the model.

RESULTS

We observed that the substrate switching usually occurs through the inhibition of pyruvate dehydrogenase complex (PDC) by pyruvate dehydrogenase kinases (PDK), which moves the metabolism from glycolysis to fatty acid oxidation. Furthermore, we were able to verify four different regulatory models of PDK to contain known biological observations, leading to the biological plausibility of all four models across different cells and conditions.

CONCLUSION

These results suggest that the cellular metabolic flexibility depends upon the PDC-PDK regulatory interaction as a key regulatory switch for changing metabolic substrates.

The ability of transcription factors to differentially regulate gene expression is a crucial component of the mechanism underlying inversion, a frequently observed genetic interaction pattern

Genetic interactions, a phenomenon whereby combinations of mutations lead to unexpected effects, reflect how cellular processes are wired and play an important role in complex genetic diseases. Understanding the molecular basis of genetic interactions is crucial for deciphering pathway organization as well as understanding the relationship between genetic variation and disease. Several hypothetical molecular mechanisms have been linked to different genetic interaction types. However, differences in genetic interaction patterns and their underlying mechanisms have not yet been compared systematically between different functional gene classes. Here, differences in the occurrence and types of genetic interactions are compared for two classes, gene-specific transcription factors (GSTFs) and signaling genes (kinases and phosphatases). Genome-wide gene expression data for 63 single and double deletion mutants in baker's yeast reveals that the two most common genetic interaction patterns are buffering and inversion. Buffering is typically associated with redundancy and is well understood. In inversion, genes show opposite behavior in the double mutant compared to the corresponding single mutants. The underlying mechanism is poorly understood. Although both classes show buffering and inversion patterns, the prevalence of inversion is much stronger in GSTFs. To decipher potential mechanisms, a Petri Net modeling approach was employed, where genes are represented as nodes and relationships between genes as edges. This allowed over 9 million possible three and four node models to be exhaustively enumerated. The models show that a quantitative difference in interaction strength is a strict requirement for obtaining inversion. In addition, this difference is frequently accompanied with a second gene that shows buffering. Taken together, these results provide a mechanistic explanation for inversion. Furthermore, the ability of transcription factors to differentially regulate expression of their targets provides a likely explanation why inversion is more prevalent for GSTFs compared to kinases and phosphatases.

Cooperation between T cell receptor and Toll-like receptor 5 signaling for CD4+ T cell activation

CD4⁺ T cells recognize antigens through their T cell receptors (TCRs); however, additional signals involving costimulatory receptors, for example, CD28, are required for proper T cell activation. Alternative costimulatory receptors have been proposed, including members of the Toll-like receptor (TLR) family, such as TLR5 and TLR2. To understand the molecular mechanism underlying a potential costimulatory role for TLR5, we generated detailed molecular maps and logical models for the TCR and TLR5 signaling pathways and a merged model for cross-interactions between the two pathways. Furthermore, we validated the resulting model by analyzing how T cells responded to the activation of these pathways alone or in combination, in terms of the activation of the transcriptional regulators CREB, AP-1 (c-Jun), and NF-κB (p65). Our merged model accurately predicted the experimental results, showing that the activation of TLR5 can play a similar role to that of CD28 activation with respect to AP-1, CREB, and NF-κB activation, thereby providing insights regarding the cross-regulation of these pathways in CD4⁺ T cells.

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.

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.

Prediction of Mutations to Control Pathways Enabling Tumor Cell Invasion with the CoLoMoTo Interactive Notebook (Tutorial)

Boolean and multi-valued logical formalisms are increasingly used to model complex cellular networks. To ease the development and analysis of logical models, a series of software tools have been proposed, often with specific assets. However, combining these tools typically implies a series of cumbersome software installation and model conversion steps. In this respect, the CoLoMoTo Interactive Notebook provides a joint distribution of several logical modeling software tools, along with an interactive web Python interface easing the chaining of complementary analyses. Our computational workflow combines (1) the importation of a GINsim model and its display, (2) its format conversion using the Java library BioLQM, (3) the formal prediction of mutations using the OCaml software Pint, (4) the model checking using the C++ software NuSMV, (5) quantitative stochastic simulations using the C++ software MaBoSS, and (6) the visualization of results using the Python library matplotlib. To illustrate our approach, we use a recent Boolean model of the signaling network controlling tumor cell invasion and migration. Our model analysis culminates with the prediction of sets of mutations presumably involved in a metastatic phenotype.