Integrated biomechanical model of cells embedded in extracellular matrix

Nature encourages diversity in life forms (morphologies). The study of morphogenesis deals with understanding those processes that arise during the embryonic development of an organism. These processes control the organized spatial distribution of cells, which in turn gives rise to the characteristic form for the organism. Morphogenesis is a multi-scale modeling problem that can be studied at the molecular, cellular, and tissue levels. Here, we study the problem of morphogenesis at the cellular level by introducing an integrated biomechanical model of cells embedded in the extracellular matrix. The fundamental aspects of mechanobiology essential for studying morphogenesis at the cellular level are the cytoskeleton, extracellular matrix (ECM), and cell adhesion. Cells are modeled using tensegrity architecture. Our simulations demonstrate cellular events, such as differentiation, migration, and division using an extended tensegrity architecture that supports dynamic polymerization of the micro-filaments of the cell. Thus, our simulations add further support to the cellular tensegrity model. Viscoelastic behavior of extracellular matrix is modeled by extending one-dimensional mechanical models (by Maxwell and by Voigt) to three dimensions using finite element methods. The cell adhesion is modeled as a general Velcro-type model. We integrated the mechanics and dynamics of cell, ECM, and cell adhesion with a geometric model to create an integrated biomechanical model. In addition, the thesis discusses various computational issues, including generating the finite element mesh, mesh refinement, re-meshing, and solution mapping. As is known from a molecular level perspective, the genetic regulatory network of the organism controls this spatial distribution of cells along with some environmental factors modulating the process. The integrated biomechanical model presented here, besides generating interesting morphologies, can serve as a mesoscopic-scale platform upon which future work can correlate with the underlying genetic network

STRUCTURAL AND MOLECULAR REGULATORS OF EMBRYONIC TISSUE STIFFNESS

Embryonic development involves large scale tissue movements that construct complex three-dimensional tissue structures, governed by basic physical principles. Fine-grained control of mechanical properties and force production is critical to the successful placement of tissues and organs within the embryo. Cell generated forces and passive mechanical properties not only physically construct tissue structures, but may also provide feedback to instruct cell behavior, remodel extracellular matrix, and regulate intercellular adhesions. Early embryos of the frog Xenopus laevis provide a dramatic example of these physical processes with rapidly changing mechanical properties, increasing in elastic modulus by six-fold to 80 Pascal over eight hours as germ layers and the central nervous system are formed. These physical changes coincide with emergence of complex anatomical structures, several rounds of cell division and remodeling of the cytoskeleton. We analogize the mechanics of embryonic tissues to closed-cell foams to predict the influence of tissue architecture, cell size, and cell cortex on bulk tissue mechanics. The Cellular Solids Model (CSM) relates bulk stiffness of a solid-foam to the unit-size of individual cells, their microstructural organization, and their material properties. We confirmed the central assumption of the CSM, that tissue modulus does not depend on embedded structural elements by engineering and mechanically testing a tissue devoid of large coherent 3D structures. To test the role of cell size we generated large cells by arresting the cell cycle and generated small cells by inhibiting a developmentally regulated cell cycle inhibitor. Tissues with lower and higher cell density confirm predictions of the CSM but are only responsible for a modest 20% increase in stiffness from early to late neurulation. To modulate the composition and modulus of the "cell-wall" we enhanced and diminished cortical F-actin cross-linking. We found that levels of crosslinking regulate bulk tissue modulus. Our results indicate that large scale architecture and cell size are not likely to influence the bulk passive mechanical properties of early embryonic or progenitor tissues. Our findings suggest that regulation of F-actin cortical thickness, density, and integrity plays a central role in regulating the physical mechanics of embryonic multicellular tissues

Modélisation et simulation 3D de la morphogenèse

The embryo of the Drosophila Melanogaster undergoes a series of cell movements during its early development. Gastrulation is the process describing the segregation of the future internal tissues into the interior of the developing embryo. Gastrulation starts with the formation of the ventral furrow, a process commonly known as the ventral furrow invagination. During this process, the most ventrally located blastoderm cells flatten and progressively constrict their apical sides until they are wedge shaped. As a result of these cell-shape changes, the blastoderm epithelium first forms an indentation, the ventral furrow, which is then completely internalized. We focus on the study of the mechanisms that drive the invagination. The main questions that gave birth to this thesis are: “What is the role of the apical constriction of the ventral cells in the invagination?” and “Once the ventral cells are internalized, what is the mechanism that drives the ventral closure?” We attempt to answer to these two questions from a biomechanical point of view. For this purpose, a 3D mesh of the embryo of the Drosophila Melanogaster has been created. Based on this mesh, two “a minima” biomechanical models of the Drosophila embryo have been created, a physically based discrete model and a model based on the Finite Element Method. The results of the simulations in both models show that the geometry of the embryo plays a crucial role in the internalization of the ventral cells. The two models efficiently simulate the internalization of the ventral cells but are incapable of reproducing the ventral closure. We hypothesize that the ventral closure can be explained by the interplay of forces developed in the embryo once the internalized ventral cells undergo cell division. We propose an approach to divide elements in a Finite Element Mesh and we integrate it to the Finite Element Model of the Drosophila Melanogaster.L'embryon de la Drosophila Melanogaster subit une série des mouvements cellulaires pendant son développement. La gastrulation est le processus qui décrit la différentiation des futurs tissus à l'intérieur de l'embryon. La gastrulation commence par la formation du sillon ventral, un processus connu sous le nom de “Ventral Furrow Invagination”. Pendant ce processus, les cellules de la blastoderme positionnées dans la région ventrale de l'embryon, aplatissent et contractent leur surface apicale jusqu'à ce qu'elles deviennent prismatiques. Ce changement de forme cellulaire aboutit à un enfoncement au niveau de la région ventrale, le sillon ventral, qui est ensuite totalement intériorisé. Nous focalisons notre étude sur les mécanismes qui conduisent à l'invagination. Les questions principales auxquelles ce travail de thèse essaie de répondre sont: “Quel est le rôle de la contraction apicale des cellules ventrales dans l'invagination?” et “Quel est le mécanisme qui conduit à la clôture ventrale, une fois les cellules ventrales intériorisées?”. Nous essayons de répondre à ces questions d'un point de vue biomécanique. Dans ce but, un maillage 3D de l'embryon de la Drosophila Melanogaster a été créé. Basés sur ce maillage, deux modèles biomécaniques “a minima” de l'embryon de la Drosophila ont été créés: un modèle physique discret et un modèle basé sur la Méthode des Eléments Finis. Les résultats des simulations des deux modèles montrent que la géométrie joue un rôle décisif dans l'intériorisation des cellules ventrales. Les deux modèles ont permis de simuler l'intériorisation des cellules ventrales mais se trouvent incapables de simuler la clôture ventrale. Notre hypothèse est que la clôture ventrale peut s'expliquer par l'intéraction des forces développées à l'intérieur de l'embryon, une fois que les cellules ventrales commencent à proliférer. Nous proposons une méthode pour diviser des éléments dans un maillage d'éléments finis et ensuite nous expliquons l'intégration de cette méthode dans le modèle des Eléments Finis pour l'embryon de la Drosophila Melanogaster