A reaction-diffusion model of the cadherin-catenin system: a possible mechanism for contact inhibition and implications for tumorigenesis

Modeling the influence of cell-cell contact and TGF-β signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells

The epithelial mesenchymal transition (EMT) is a process by which cells lose their adhesive nature and gain the migratory properties associated with mesenchymal cells. This transition allows cells to migrate away from a primary tumor while maintaining their newly acquired invasive behavior, suggesting that there is a bistable switch between the epithelial and mesenchymal phenotypes. In recent experimental work, we found evidence of this bistability in the MCF7 breast carcinoma cell line (Gasior et al., 2019). Underlying the complex processes governing EMT, we identify a feedback loop between E-cadherin, a protein involved in cellular adhesion, and Slug, a transcription factor that is upregulated during EMT. Here, we present a simple mathematical model that examines the relationship between E-cadherin and Slug in response to pro-epithelial and pro-mesenchymal factors, cell-cell contact and TGF-β, respectively. We hypothesize that cell-cell contact is a critical component in the transition from the epithelial to the mesenchymal phenotype and that it is possible to initiate EMT with the loss of cell-cell contact or the activation of the TGF-β signaling pathway. We propose a reversible bistable switch in response to a loss of cell-cell contact but an irreversible bistable switch when the cell is exposed to TGF-β. Taken together, this model shows that acquiring and retaining invasive behavior by cells with high levels of cell-cell contact is not impossible but, instead, depends on the cooperation between the two switches. The predictions of this model for E-cadherin and Slug levels were compared against relative gene expression data from our recent experiments with MCF7 cells (Gasior et al., 2019). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments, while also highlighting issues that arise when comparing in vitro experimental results to theoretical predictions.

Paracrine SPARC signaling dysregulates alveolar epithelial barrier integrity and function in lung fibrosis

Idiopathic pulmonary fibrosis (IPF) is a chronic scarring disease in which aging, environmental exposure(s) and genetic susceptibility have been implicated in disease pathogenesis, however, the causes and mechanisms of the progressive fibrotic cascade are still poorly understood. As epithelial-mesenchymal interactions are essential for normal wound healing, through human 2D and 3D in vitro studies, we tested the hypothesis that IPF fibroblasts (IPFFs) dysregulate alveolar epithelial homeostasis. Conditioned media from IPFFs exaggerated the wound-healing response of primary human Type II alveolar epithelial cells (AECs). Furthermore, AECs co-cultured with IPFFs exhibited irregular epithelialization compared with those co-cultured with control fibroblasts (NHLFs) or AECs alone, suggesting that epithelial homeostasis is dysregulated in IPF as a consequence of the abnormal secretory phenotype of IPFFs. Secretome analysis of IPFF conditioned media and functional studies identified the matricellular protein, SPARC, as a key mediator in the epithelial-mesenchymal paracrine signaling, with increased secretion of SPARC by IPFFs promoting persistent activation of alveolar epithelium via an integrin/focal adhesion/cellular-junction axis resulting in disruption of epithelial barrier integrity and increased macromolecular permeability. These findings suggest that in IPF fibroblast paracrine signaling promotes persistent alveolar epithelial activation, so preventing normal epithelial repair responses and restoration of tissue homeostasis. Furthermore, they identify SPARC-mediated paracrine signaling as a potential therapeutic target to promote the restoration of lung epithelial homoestasis in IPF patients.

PCDHGA9 acts as a tumor suppressor to induce tumor cell apoptosis and autophagy and inhibit the EMT process in human gastric cancer

The results of a cDNA  array revealed that protocadherin gamma subfamily A, 9 (PCDHGA9) was significantly decreased in SGC-7901 gastric cancer (GC) cells compared with GES-1 normal gastric cells and was strongly associated with the Wnt/β-catenin and transforming growth factor-β (TGF-β)/Smad2/3 signaling pathway. As a member of the cadherin family, PCDHGA9 functions in both cell-cell adhesion and nuclear signaling. However, its role in tumorigenicity or metastasis has not been reported. In the present study, we found that PCDHGA9 was decreased in GC tissues compared with corresponding normal mucosae and its expression was correlated with the GC TNM stage, the UICC stage, differentiation, relapse, and metastasis (p < 0.01). Multivariate Cox analysis revealed that PCDHGA9 was an independent prognostic indicator for overall survival (OS) and disease-free survival (DFS) (p < 0.01). The effects of PCDHGA9 on GC tumor growth and metastasis were examined both in vivo and in vitro. PCDHGA9 knockdown promoted GC cell proliferation, migration, and invasion, whereas PCDHGA9 overexpression inhibited GC tumor growth and metastasis but induced apoptosis, autophagy, and G1 cell cycle arrest. Furthermore, PCDHGA9 suppressed epithelial-mesenchymal transition (EMT) induced by TGF-β, decreased the phosphorylation of Smad2/3, and inhibited the nuclear translocation of pSmad2/3. Our results suggest that PCDHGA9 might interact with β-catenin to prevent β-catenin from dissociating in the cytoplasm and translocating to the nucleus. Moreover, PCDHGA9 overexpression restrained cell proliferation and reduced the nuclear β-catenin, an indicator of Wnt/β-catenin pathway activation, suggesting that PCDHGA9 negatively regulates Wnt signaling. Together, these data indicate that PCDHGA9 acts as a tumor suppressor with anti-proliferative activity and anti-invasive ability, and the reduction of PCDHGA9 could serve as an independent prognostic biomarker in GC.

A Theoretical Model of the Wnt Signaling Pathway in the Epithelial Mesenchymal Transition

BACKGROUND

Following the formation of a primary carcinoma, neoplastic cells metastasize by undergoing the epithelial mesenchymal transition (EMT), which is triggered by cues from inflammatory and stromal cells in the microenvironment. EMT allows epithelial cells to lose their highly adhesive nature and instead adopt the spindle-like appearance, as well as the invasive and migratory behavior, of mesenchymal cells. We hypothesize that a bistable switch between the epithelial and mesenchymal phenotypes governs EMT, allowing the cell to maintain its mesenchymal phenotype even after it leaves the primary tumor microenvironment and EMT-inducing extracellular signal.

RESULTS

This work presents a simple mathematical model of EMT, specifically the roles played by four key proteins in the Wnt signaling pathway: Dishevelled (Dvl), E-cadherin, β-catenin, and Slug. The model predicts that following activation of the Wnt pathway, an epithelial cell in the primary carcinoma must attain a threshold level of membrane-bound Dvl to convert to the mesenchymal-like phenotype and maintain that phenotype once it has migrated away from the primary tumor. Furthermore, sensitivity analysis of the model suggests that in both the epithelial and the mesenchymal states, the steady state behavior of E-cadherin and the transcription factor Slug are sensitive to changes in the degradation rate of Slug, while E-cadherin is also sensitive to the IC₅₀ (half-maximal) concentration of Slug necessary to inhibit E-cadherin production. The steady state behavior of Slug exhibits sensitivity to changes in the rate at which it is induced by β-catenin upon activation of the Wnt pathway. In the presence of sufficient amount of Wnt ligand, E-cadherin levels are sensitive to the ratio of the rate of Slug activation via β-catenin to the IC₅₀ concentration of Slug necessary to inhibit E-cadherin production.

CONCLUSIONS

The sensitivity of E-cadherin to the degradation rate of Slug, as well as the IC₅₀ concentration of Slug necessary to inhibit E-cadherin production, shows how the adhesive nature of the cell depends on finely-tuned regulation of Slug. By highlighting the role of β-catenin in the activation of EMT and the relationship between E-cadherin and Slug, this model identifies critical parameters of therapeutic concern, such as the threshold level of Dvl necessary to inactivate the GSK-3β complex mediating β-catenin degradation, the rate at which β-catenin translocates to the nucleus, and the IC₅₀ concentration of Slug needed to inhibit E-cadherin production.

Beyond a tumor suppressor: Soluble E-cadherin promotes the progression of cancer

E-cadherin (E-cad) plays important roles in tumorigenesis as well as in tumor progression, invasion and metastasis. This protein exists in two forms: a membrane-tethered form and a soluble form. Full-length E-cad is membrane tethered. As a type I transmembrane glycoprotein, E-cad mainly mediates adherens junctions between cells and is involved in maintaining the normal structure of epithelial tissues. Soluble E-cad (sE-cad) is the extracellular fragment of the protein that is cleaved from the membrane after proteolysis of full-length E-cad. The production of sE-cad undermines adherens junctions, causing a reduction in cell aggregation capacity; furthermore, sE-cad can diffuse into the extracellular environment and the blood. As a paracrine/autocrine signaling molecule, sE-cad activates or inhibits multiple signaling pathways and participates in the progression of various types of cancer, such as breast cancer, ovarian cancer, and lung cancer, by promoting invasion and metastasis. This article briefly reviews the role of sE-cad in tumorigenesis and tumor progression and its significance in clinical therapeutics.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Interlocked positive and negative feedback network motifs regulate β-catenin activity in the adherens junction pathway

The integrity of epithelial tissue architecture is maintained through adherens junctions that are created through extracellular homotypic protein-protein interactions between cadherin molecules. Cadherins also provide an intracellular scaffold for the formation of a multiprotein complex that contains signaling proteins, including β-catenin. Environmental factors and controlled tissue reorganization disrupt adherens junctions by cleaving the extracellular binding domain and initiating a series of transcriptional events that aim to restore tissue homeostasis. However, it remains unclear how alterations in cell adhesion coordinate transcriptional events, including those mediated by β-catenin in this pathway. Here were used quantitative single-cell and population-level in vitro assays to quantify the endogenous pathway dynamics after the proteolytic disruption of the adherens junctions. Using prior knowledge of isolated elements of the overall network, we interpreted these data using in silico model-based inference to identify the topology of the regulatory network. Collectively the data suggest that the regulatory network contains interlocked network motifs consisting of a positive feedback loop, which is used to restore the integrity of adherens junctions, and a negative feedback loop, which is used to limit β-catenin-induced gene expression.

Analysis of Wnt signaling β-catenin spatial dynamics in HEK293T cells

Background

Wnt/β-catenin signaling is involved in different stages of mammalian development and implicated in various cancers (e.g. colorectal cancer). Recent experimental and computational studies have revealed characteristics of the pathway, however a cell-specific spatial perspective is lacking. In this study, a novel 3D confocal quantitation protocol is developed to acquire spatial (two cellular compartments: nucleus and cytosol-membrane) and temporal quantitative data on target protein (e.g. β-catenin) concentrations in Human Epithelial Kidney cells (HEK293T) during perturbation (with either cycloheximide or Wnt3A). Computational models of the Wnt pathway are constructed and interrogated based on this data.

Results

A single compartment Wnt pathway model is compared with a simple β-catenin two compartment model to investigate Wnt3A signaling in HEK293T cells. When protein synthesis is inhibited, β-catenin decreases at the same rate in both cellular compartments, suggesting diffusional transport is fast compared to β-catenin degradation in the cytosol. With Wnt3A stimulation, the total amount of β-catenin rises throughout the cell, however the increase is initially (~first hour) faster in the nuclear compartment. While both models were able to reproduce the whole cell changes in β-catenin, only the compartment model reproduced the Wnt3A induced changes in β-catenin distribution and it was also the best fit for the data obtained when active transport was included alongside passive diffusion transport.

Conclusions

This integrated 3D quantitation imaging protocol and computational modeling approach allowed cell-specific compartment models of the signaling pathways to be constructed and analyzed. The Wnt models constructed in this study are the first for HEK293T and have suggested potential roles of inter-compartment transport to the dynamics of signaling.

Toward a quantitative understanding of the Wnt/β-catenin pathway through simulation and experiment

Wnt signaling regulates cell survival, proliferation, and differentiation throughout development and is aberrantly regulated in cancer. The pathway is activated when Wnt ligands bind to specific receptors on the cell surface, resulting in the stabilization and nuclear accumulation of the transcriptional co-activator β-catenin. Mathematical and computational models have been used to study the spatial and temporal regulation of the Wnt/β-catenin pathway and to investigate the functional impact of mutations in key components. Such models range in complexity, from time-dependent, ordinary differential equations that describe the biochemical interactions between key pathway components within a single cell, to complex, multiscale models that incorporate the role of the Wnt/β-catenin pathway target genes in tissue homeostasis and carcinogenesis. This review aims to summarize recent progress in mathematical modeling of the Wnt pathway and to highlight new biological results that could form the basis for future theoretical investigations designed to increase the utility of theoretical models of Wnt signaling in the biomedical arena.

Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing

Recent experiments have shown that spreading epithelial sheets exhibit a long-range coordination of motility forces that leads to a buildup of tension in the tissue, which may enhance cell division and the speed of wound healing. Furthermore, the edges of these epithelial sheets commonly show finger-like protrusions whereas the bulk often displays spontaneous swirls of motile cells. To explain these experimental observations, we propose a simple flocking-type mechanism, in which cells tend to align their motility forces with their velocity. Implementing this idea in a mechanical tissue simulation, the proposed model gives rise to efficient spreading and can explain the experimentally observed long-range alignment of motility forces in highly disordered patterns, as well as the buildup of tensile stress throughout the tissue. Our model also qualitatively reproduces the dependence of swirl size and swirl velocity on cell density reported in experiments and exhibits an undulation instability at the edge of the spreading tissue commonly observed in vivo. Finally, we study the dependence of colony spreading speed on important physical and biological parameters and derive simple scaling relations that show that coordination of motility forces leads to an improvement of the wound healing process for realistic tissue parameters.

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

The surface epithelium lining the intestinal tract renews itself rapidly by a coordinated programme of cell proliferation, migration and differentiation events that is initiated in the crypts of Lieberkühn. It is generally believed that colorectal cancer arises due to mutations that disrupt the normal cellular dynamics of the crypts. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and the proliferative and adhesive properties of the mutant cells, to obtain statistical distributions for the probability of their domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion. By comparing simulation results with those from a simple one-dimensional stochastic model of population dynamics at the base of the crypt, we infer that this sensitivity is due to direct competition between wild-type and mutant cells at the base of the crypt. We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate can give rise to counter-intuitive, non-linear changes to the probability of their fixation, due to effects that cannot be captured in simpler models.

β-Catenin signaling initiates the activation of astrocytes and its dysregulation contributes to the pathogenesis of astrocytomas

Astrocytes are the most abundant cell of the CNS and demonstrate contact inhibition in which a nonproliferative, nonmotile cellular state is achieved once stable intercellular contacts are formed between mature cells. Cellular injury disrupts these intercellular contacts, causing a loss of contact inhibition and the rapid initiation of healing. Dysregulation of the molecular pathways involved in this process is thought to lead to an aggressive cellular state associated with neoplasia. We investigated whether a comparable correlation exists between the response of astrocytes to injury and the malignant phenotype of astrocytomas. We discovered that the loss of contact inhibition plays a critical role in the initiation and regulation of reactive astrocytes in the healing of wounds. In particular, injury of the astrocytes interrupts and destabilizes the cadherin-catenin complexes at the cell membrane leading to nuclear translocation of β-catenin and characteristic changes associated with the activation of astrocytes. Similar signaling pathways are found to be active--but dysregulated--in astrocytomas. Inhibition of β-catenin signaling diminished both the response of astrocytes to injury and induction of the malignant phenotype of astrocytomas. The findings shed light on a unique mechanism associated with the pathogenesis of astrocytomas and provide a model for the loss of contact inhibition that may broadly apply to understanding the mechanisms of tissue repair and tumorigenesis in the brain.