A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix

Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed to the more usual Differentiated Cancer Cells (DCCs), they exhibit higher motility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the CSCs is not completely clear; they seem to stem from the DCCs via a transition process related to the Epithelial-Mesenchymal Transition (EMT) that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting "ensemble" invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion

Advances in modelling of epithelial to mesenchymal transition

Epithelial to Mesenchymal Transition (EMT) is a cellular transformation process that is employed repeatedly and ubiquitously during vertebrate morphogenesis to build complex tissues and organs. Cellular transformations that occur during cancer cell invasion are phenotypically similar to developmental EMT, and involve the same molecular signalling pathways. EMT processes are diverse, but are characterised by: a loss of cell-cell adhesion; a gain in cell-matrix adhesion; an increase in cell motility; the secretion of proteases that degrade basement membrane proteins; an increased resistance to apoptosis; a loss of polarisation; increased production of extracellular matrix components; a change from a rounded to a fibroblastic morphology; and an invasive phenotype. This thesis focuses explicitly on endocardial EMT, which is the EMT that occurs during vertebrate embryonic heart development. The embryonic heart initially forms as a tube, with myocardium externally, endocardium internally, with these tissue layers separated by a thick extracellular matrix termed the cardiac jelly. Some of the endocardial cells in specific regions of the embryonic heart tube undergo EMT and invade the cardiac jelly. This causes cellularised swellings inside the embryonic heart tube termed the endocardial cushions. The emergence of the four chambered double pump heart of mammals involves a complex remodelling that the endocardial cushions play an active role in. Even while heart remodelling is taking place, the heart tube is operating as a single-circulation pump, and the endocardial cushions are performing a valve-like function that is critical to the survival of the embryo (Nomura-Kitabayashi et al. 2009). As the endocardial cushions grow and remodel, they become the valve leaflets of the foetal heart. The endocardial cushions also contribute tissue to the septa (walls) of the heart. Their correct formation is thus essential to the development of a fully functional, fully divided, double-pump system. It has been shown that genetic mutations that cause impaired endocardial EMT lead to the development of a range of congenital heart defects (Fischer et al. 2007). An extensive review is conducted of existing experimental investigations into endocardial EMT. The information extracted from this review is used to develop a multiscale conceptual model of endocardial EMT, including the major protein signalling pathways involved, and the cellular phenotypes that they induce or inhibit. After considering the requirements for computational simulations of EMT, and reviewing the various techniques and simulation packages available for multi-cell modelling, cellular Potts modelling is selected as having the most appropriate combination of features. The open source simulation platform Compucell3D is selected for model development, due to the flexibility, range of features provided and an existing implementation of multiscale models; that include subcellular models of reaction pathways. Based on the conceptual model of endocardial EMT, abstract computational simulations of key aspects are developed, in order to investigate qualitative behaviour under different simulated conditions. The abstract simulations include a 2D multiscale model of Notch signalling lateral induction, which is the mechanism by which the embryonic heart tube is patterned into cushion and non-cushion forming regions. Additionally, a 3D simulation is used to investigate the possible role of contact-inhibited mitosis, upregulated by the VEGF protein, in maintaining an epithelial phenotype. One particular in vitro investigation of endocardial EMT (Luna-Zurita et al. 2010) is used to develop quantitative simulations. The quantitative data used for fitting the simulations consist of cell shape metrics that are derived from simple processing of the imaging results. Single cell simulations are used to investigate the relationship between cell motility and cell shape in the cellular Potts model. The findings are then implemented in multi-cell models, in order to investigate the relationship between cell-cell adhesion, cell-matrix adhesion, cell motility and cell shape during EMT

Generative models of morphogenesis in developmental biology

Understanding the mechanism by which cells coordinate their differentiation and migration is critical to our understanding of many fundamental processes such as wound healing, disease progression, and developmental biology. Mathematical models have been an essential tool for testing and developing our understanding, such as models of cells as soft spherical particles, reaction-diffusion systems that couple cell movement to environmental factors, and multi-scale multi-physics simulations that combine bottom-up rule-based models with continuum laws. However, mathematical models can often be loosely related to data or have so many parameters that model behaviour is weakly constrained. Recent methods in machine learning introduce new means by which models can be derived and deployed. In this review, we discuss examples of mathematical models of aspects of developmental biology, such as cell migration, and how these models can be combined with these recent machine learning methods

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematics and physics backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges, and includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and classical systems typically studied in non-equilibrium statistical and quantum mechanics.Comment: 73 pages, 12 figure

Cell signaling stabilizes morphogenesis against noise

Embryonic development involves gene networks, extracellular signaling, cell behaviors (cell division, adhesion, etc.) and mechanical interactions. How should these be coordinated to lead to complex and robust morphologies? To explore this question, we randomly wired genes and cell behaviors into a huge number of networks in EmbryoMaker. EmbryoMaker is a computational model of animal development that simulates how the 3D positions of cells, i.e. morphology, change over time due to such networks. We found that any gene network can lead to complex morphologies if this activates cell behaviors over large regions of the embryo. Importantly, however, for such complex morphologies to be robust to noise, gene networks should include cell signaling that compartmentalizes the embryo into small regions where cell behaviors are regulated differently. If, instead, cell behaviors are equally regulated over large regions, complex but non-robust morphologies arise. We explain how compartmentalization enhances robustness and why it is a general feature of animal development. Our results are consistent with theories proposing that robustness evolved by the co-option of gene networks and extracellular cell signaling in early animal evolution.Peer reviewe

Transcriptional regulatory network analysis during epithelial-mesenchymal transformation of retinal pigment epithelium

PURPOSE: Phenotypic transformation of retinal pigment epithelial (RPE) cells contributes to the onset and progression of ocular proliferative disorders such as proliferative vitreoretinopathy (PVR). The formation of epiretinal membranes in PVR may involve an epithelial-mesenchymal transformation (EMT) of RPE cells as part of an aberrant wound healing response. While the underlying mechanism remains unclear, this likely involves changes in RPE cell gene expression under the control of specific transcription factors (TFs). Thus, the purpose of the present study was to identify TFs that may play a role in this process. METHODS: Regulatory regions of genes that are differentially regulated during phenotypic transformation of ARPE-19 cells, a human RPE cell line, were subjected to computational analysis using the promoter analysis and interaction network toolset (PAINT). The PAINT analysis was used to identify transcription response elements (TREs) statistically overrepresented in the promoter and first intron regions of two reciprocally regulated RPE gene clusters, across four species including the human genome. These TREs were then used to construct transcriptional regulatory network models of the two RPE gene clusters. The validity of these models was then tested using RT-PCR to detect differential expression of the corresponding TF mRNAs during RPE differentiation in both undifferentiated and differentiated ARPE-19 and primary chicken RPE cell cultures. RESULTS: The computational analysis resulted in the successful identification of specific transcription response elements (TREs) and their cognate TFs that are candidates for serving as nodes in a transcriptional regulatory network regulating EMT in RPE cells. The models predicted TFs whose differential expression during RPE EMT was successfully verified by reverse transcriptase polymerase chain reaction (RT-PCR) analysis, including Oct-1, hepatocyte nuclear factor 1 (HNF-1), similar to mothers against decapentaplegic 3 (SMAD3), transcription factor E (TFE), core binding factor, erythroid transcription factor-1 (GATA-1), interferon regulatory factor-1 (IRF), natural killer homeobox 3A (NKX3A), Sterol regulatory element binding protein-1 (SREBP-1), and lymphocyte enhancer factor-1 (LEF-1). CONCLUSIONS: These studies successfully applied computational modeling and biochemical verification to identify biologically relevant transcription factors that are likely to regulate RPE cell phenotype and pathological changes in RPE in response to diseases or trauma. These TFs may provide potential therapeutic targets for the prevention and treatment of ocular proliferative disorders such as PVR

Mechanochemical Regulation of Epithelial Tissue Remodeling: A Multiscale Computational Model of the Epithelial-Mesenchymal Transition Program

Epithelial-mesenchymal transition (EMT) regulates the cellular processes of migration, growth, and proliferation - as well as the collective cellular process of tissue remodeling - in response to mechanical and chemical stimuli in the cellular microenvironment. Cells of the epithelium form cell-cell junctions with adjacent cells to function as a barrier between the body and its environment. By distributing localized stress throughout the tissue, this mechanical coupling between cells maintains tensional homeostasis in epithelial tissue structures and provides positional information for regulating cellular processes. Whereas in vitro and in vivo models fail to capture the complex interconnectedness of EMT-associated signaling networks, previous computational models have succinctly reproduced components of the EMT program. In this work, we have developed a computational framework to evaluate the mechanochemical signaling dynamics of EMT at the molecular, cellular, and tissue scale. First, we established a model of cell-matrix and cell-cell feedback for predicting mechanical force distributions within an epithelial monolayer. These findings suggest that tensional homeostasis is the result of cytoskeletal stress distribution across cell-cell junctions, which organizes otherwise migratory cells into a stable epithelial monolayer. However, differences in phenotype-specific cell characteristics led to discrepancies in the experimental and computational observations. To better understand the role of mechanical cell-cell feedback in regulating EMT-dependent cellular processes, we introduce an EMT gene regulatory network of key epithelial and mesenchymal markers, E-cadherin and N-cadherin, coupled to a mechanically-sensitive intracellular signaling cascade. Together these signaling networks integrate mechanical cell-cell feedback with EMT-associated gene regulation. Using this approach, we demonstrate that the phenotype-specific properties collectively account for discrepancies in the computational and experimental observations. Additionally, mechanical cell-cell feedback suppresses the EMT program, which is reflected in the gene expression of the heterogeneous cell population. Together, these findings advance our understanding of the complex interplay in cell-cell and cell-matrix feedback during EMT of both normal physiological processes as well as disease progression

A cell-based model of Nematostella vectensis gastrulation including bottle cell formation, invagination and zippering

AbstractThe gastrulation of Nematostella vectensis, the starlet sea anemone, is morphologically simple yet involves many conserved cell behaviors such as apical constriction, invagination, bottle cell formation, cell migration and zippering found during gastrulation in a wide range of more morphologically complex animals.In this article we study Nematostella gastrulation using a combination of morphometrics and computational modeling. Through this analysis we frame gastrulation as a non-trivial problem, in which two distinct cell domains must change shape to match each other geometrically, while maintaining the integrity of the embryo. Using a detailed cell-based model capable of representing arbitrary cell-shapes such as bottle cells, as well as filopodia, localized adhesion and constriction, we are able to simulate gastrulation and associate emergent macroscopic changes in embryo shape to individual cell behaviors.We have developed a number of testable hypotheses based on the model. First, we hypothesize that the blastomeres need to be stiffer at their apical ends, relative to the rest of the cell perimeter, in order to be able to hold their wedge shape and the dimensions of the blastula, regardless of whether the blastula is sealed or leaky. We also postulate that bottle cells are a consequence of cell strain and low cell–cell adhesion, and can be produced within an epithelium even without apical constriction. Finally, we postulate that apical constriction, filopodia and de-epithelialization are necessary and sufficient for gastrulation based on parameter variation studies