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

Multicellular Systems Biology of Development

Embryonic development depends on the precise coordination of cell fate specification, patterning and morphogenesis. Although great strides have been made in the molecular understanding of each of these processes, how their interplay governs the formation of complex tissues remains poorly understood. New techniques for experimental manipulation and image quantification enable the study of development in unprecedented detail, resulting in new hypotheses on the interactions between known components. By expressing these hypotheses in terms of rules and equations, computational modeling and simulation allows one to test their consistency against experimental data. However, new computational methods are required to represent and integrate the network of interactions between gene regulation, signaling and biomechanics that extend over the molecular, cellular and tissue scales. In this thesis, I present a framework that facilitates computational modeling of multiscale multicellular systems and apply it to investigate pancreatic development and the formation of vascular networks. This framework is based on the integration of discrete cell-based models with continuous models for intracellular regulation and intercellular signaling. Specifically, gene regulatory networks are represented by differential equations to analyze cell fate regulation; interactions and distributions of signaling molecules are modeled by reaction-diffusion systems to study pattern formation; and cell-cell interactions are represented in cell-based models to investigate morphogenetic processes. A cell-centered approach is adopted that facilitates the integration of processes across the scales and simultaneously constrains model complexity. The computational methods that are required for this modeling framework have been implemented in the software platform Morpheus. This modeling and simulation environment enables the development, execution and analysis of multi-scale models of multicellular systems. These models are represented in a new domain-specific markup language that separates the biological model from the computational methods and facilitates model storage and exchange. Together with a user-friendly graphical interface, Morpheus enables computational modeling of complex developmental processes without programming and thereby widens its accessibility for biologists. To demonstrate the applicability of the framework to problems in developmental biology, two case studies are presented that address different aspects of the interplay between cell fate specification, patterning and morphogenesis. In the first, I focus on the interplay between cell fate stability and intercellular signaling. Specifically, two studies are presented that investigate how mechanisms of cell-cell communication affect cell fate regulation and spatial patterning in the pancreatic epithelium. Using bifurcation analysis and simulations of spatially coupled differential equations, it is shown that intercellular communication results in a multistability of gene expression states that can explain the scattered spatial distribution and low cell type ratio of nascent islet cells. Moreover, model analysis shows that disruption of intercellular communication induces a transition between gene expression states that can explain observations of in vitro transdifferentiation from adult acinar cells into new islet cells. These results emphasize the role of the multicellular context in cell fate regulation during development and may be used to optimize protocols for cellular reprogramming. The second case study focuses on the feedback between patterning and morphogenesis in the context of the formation of vascular networks. Integrating a cell-based model of endothelial chemotaxis with a reaction-diffusion model representing signaling molecules and extracellular matrix, it is shown that vascular network patterns with realistic morphometry can arise when signaling factors are retained by cell-modified matrix molecules. Through the validation of this model using in vitro assays, quantitative estimates are obtained for kinetic parameters that, when used in quantitative model simulations, confirm the formation of vascular networks under measured biophysical conditions. These results demonstrate the key role of the extracellular matrix in providing spatial guidance cues, a fact that may be exploited to enhance vascularization of engineered tissues. Together, the modeling framework, software platform and case studies presented in this thesis demonstrate how cell-centered computational modeling of multi-scale and multicellular systems provide powerful tools to help disentangle the complex interplay between cell fate specification, patterning and morphogenesis during embryonic development

Multiscale analysis of pattern formation via intercellular signalling

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier \emph{et al.} (Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, \emph{J. Theor. Biol.}, 183, 1996, 429--446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis

Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its usability for modeling complex developmental phenomena by examining four fundamental examples of tissue morphogenesis: (i) cell sorting, (ii) cyst formation, (iii) tube morphogenesis in kidney development, and (iv) blood vessel formation. The review provides an introduction for biologists for starting simulation analysis using the CPM framework

Toward a quantitative understanding of the Wnt/beta-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

A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue

Angiogenesis, the formation of new blood vessel networks from existing capillary or post-capillary venules, is an intrinsically multiscale process occurring in several physio-pathological conditions. In particular, hypoxic tissue cells activate downstream cascades culminating in the secretion of a wide range of angiogenic factors, including VEGF isoforms. Such diffusive chemicals activate the endothelial cells (ECs) forming the external walls of the nearby vessels that chemotactically migrate toward the hypoxic areas of the tissue as multicellular sprouts. A functional network eventually emerges by further branching and anastomosis processes. We here propose a CPM-based approach reproducing selected features of the angiogenic progression necessary for the reoxygenation of a hypoxic tissue. Our model is able to span the different scale involved in the angiogenic progression as it incorporates reaction-diffusion equations for the description of the evolution of microenvironmental variables in a discrete mesoscopic cellular Potts model (CPM) that reproduces the dynamics of the vascular cells. A key feature of this work is the explicit phenotypic differentiation of the ECs themselves, distinguished in quiescent, stalk and tip. The simulation results allow identifying a set of key mechanisms underlying tissue vascularization. Further, we provide evidence that the nascent pattern is characterized by precise topological properties. Finally, we link abnormal sprouting angiogenesis with alteration in selected cell behavior