The development of a multicellular organism, such as a human or an animal, begins with the fertilization of an egg cell. Thereupon the organism grows by repeated cell divisions until the adult size is reached and growth stops. Although it is known that intrinsic mechanisms determine the final size of developing organs and organisms, the basic principles of growth control are still poorly understood. However, there is strong evidence that certain morphogens, which are a special class of signaling molecules, act as growth factors and play a key role in growth control. In this work, growth control is studied from a mainly theoretical viewpoint. A discrete vertex model describing the organization of cells by a network of polygons is used, including a description of the cell cycle and a description of dynamical morphogen distributions. Self-organized growth is studied by introducing growth rules that govern cell divisions based on the local morphogen level. This discrete description is complemented by a continuum theory to gain further insight into the dynamics of self-organized growth processes. The theoretical description is applied to the developing wing of the fruit fly Drosophila melanogaster. In the developing wing, which is an epithelium consisting of single-layered cell sheets, the morphogen Decapentaplegic (Dpp) acts as a key growth factor. Experimental data shows that the Dpp distribution is dynamic and adapts to the size of the developing wing. Two mechanisms that rely on a regulatory molecule species and lead to such a dynamic behaviour of the Dpp distribution are studied. Several growth rules are tested and the resulting growth behaviour is quantitatively compared to experimental data of the developing wing. A particular growth rule, that triggers a cell division when the local morphogen level has increased by a certain relative amount, is found to be consistent with experimental observations under normal and several perturbed conditions. It is shown that mechanical stresses that arise due to spatial growth inhomogeneities can have a stabilizing effect on the growth process.

The development of a multicellular organism, such as a human or an animal, begins with the fertilization of an egg cell. Thereupon the organism grows by repeated cell divisions until the adult size is reached and growth stops. Although it is known that intrinsic mechanisms determine the final size of developing organs and organisms, the basic principles of growth control are still poorly understood. However, there is strong evidence that certain morphogens, which are a special class of signaling molecules, act as growth factors and play a key role in growth control. In this work, growth control is studied from a mainly theoretical viewpoint. A discrete vertex model describing the organization of cells by a network of polygons is used, including a description of the cell cycle and a description of dynamical morphogen distributions. Self-organized growth is studied by introducing growth rules that govern cell divisions based on the local morphogen level. This discrete description is complemented by a continuum theory to gain further insight into the dynamics of self-organized growth processes. The theoretical description is applied to the developing wing of the fruit fly Drosophila melanogaster. In the developing wing, which is an epithelium consisting of single-layered cell sheets, the morphogen Decapentaplegic (Dpp) acts as a key growth factor. Experimental data shows that the Dpp distribution is dynamic and adapts to the size of the developing wing. Two mechanisms that rely on a regulatory molecule species and lead to such a dynamic behaviour of the Dpp distribution are studied. Several growth rules are tested and the resulting growth behaviour is quantitatively compared to experimental data of the developing wing. A particular growth rule, that triggers a cell division when the local morphogen level has increased by a certain relative amount, is found to be consistent with experimental observations under normal and several perturbed conditions. It is shown that mechanical stresses that arise due to spatial growth inhomogeneities can have a stabilizing effect on the growth process.

During development of tissues, cells collectively organize to form complex patterns and morphologies. A general feature of many developing epithelia is their distinct organization into cellular compartments of different cell lineages. The interfaces between these compartments, called compartment boundaries, maintain straight and sharp morphologies. The interfaces play key roles in tissue development and pattern formation. An important model system to study the morphology of compartment boundaries during development is the wing disc of the fruit fly. Two compartment boundaries exist in the fly wing disc, the anteroposterior (AP) boundary and the dorsoventral (DV) boundary. A crucial question is how compartment boundaries are shaped and remain stable during growth. In this work, we discuss the dynamics and mechanisms of compartment boundaries in developing epithelia. We analyze the general features of interfacial phenomena in coarse- grained models of passive and active fluids. We introduce a continuum description of tissues with two cell types. This model allows us to study the propagation of interfaces due to the interplay of cell dynamics and tissue mechanics. We also use a vertex model to describe cellular compartments in growing epithelia. The vertex model accounts for cell mechanics and describes a 2D picture of tissues where the network of adherens junctions characterizes cell shapes. We use this model to study the general physical mechanisms by which compartment boundaries are shaped. We quantify the stresses in the cellular network and discuss how cell mechanics and growth influence the stress profile. With the help of the anisotropic stress profile near the interfaces we calculate the interfacial tension. We show that cell area pressure, cell proliferation rate, orientation of cell division, cell elongation created by external stress, and cell bond tension all have distinct effects on the morphology of interfaces during tissue growth. Furthermore, we investigate how much different mechanisms contribute to the effective interfacial tension. We study the mechanisms shaping the DV boundary in wing imaginal disc at different stages during the development. We analyze the images of wing discs to quantify the roughness of the DV boundary and average cell elongation in its vicinity. We quantify increased cell bond tension along the boundary and analyze the role of localized reduction in cell proliferation on the morphology of the DV boundary. We use experimentally determined values for cell bond tension, cell elongation and bias in orientation of cell division in simulations of tissue growth in order to reproduce the main features of the time-evolution of the DV boundary shape.

During development of tissues, cells collectively organize to form complex patterns and morphologies. A general feature of many developing epithelia is their distinct organization into cellular compartments of different cell lineages. The interfaces between these compartments, called compartment boundaries, maintain straight and sharp morphologies. The interfaces play key roles in tissue development and pattern formation. An important model system to study the morphology of compartment boundaries during development is the wing disc of the fruit fly. Two compartment boundaries exist in the fly wing disc, the anteroposterior (AP) boundary and the dorsoventral (DV) boundary. A crucial question is how compartment boundaries are shaped and remain stable during growth. In this work, we discuss the dynamics and mechanisms of compartment boundaries in developing epithelia. We analyze the general features of interfacial phenomena in coarse- grained models of passive and active fluids. We introduce a continuum description of tissues with two cell types. This model allows us to study the propagation of interfaces due to the interplay of cell dynamics and tissue mechanics. We also use a vertex model to describe cellular compartments in growing epithelia. The vertex model accounts for cell mechanics and describes a 2D picture of tissues where the network of adherens junctions characterizes cell shapes. We use this model to study the general physical mechanisms by which compartment boundaries are shaped. We quantify the stresses in the cellular network and discuss how cell mechanics and growth influence the stress profile. With the help of the anisotropic stress profile near the interfaces we calculate the interfacial tension. We show that cell area pressure, cell proliferation rate, orientation of cell division, cell elongation created by external stress, and cell bond tension all have distinct effects on the morphology of interfaces during tissue growth. Furthermore, we investigate how much different mechanisms contribute to the effective interfacial tension. We study the mechanisms shaping the DV boundary in wing imaginal disc at different stages during the development. We analyze the images of wing discs to quantify the roughness of the DV boundary and average cell elongation in its vicinity. We quantify increased cell bond tension along the boundary and analyze the role of localized reduction in cell proliferation on the morphology of the DV boundary. We use experimentally determined values for cell bond tension, cell elongation and bias in orientation of cell division in simulations of tissue growth in order to reproduce the main features of the time-evolution of the DV boundary shape.