Modelling planar cell polarity in Drosophila melanogaster

During development, polarity is a common feature of many cell types. One example is the polarisation of whole fields of epithelial cells within the plane of the epithelium, a phenomenon called planar cell polarity (PCP). It is widespread in nature and plays important roles in development and physiology. Prominent examples include the epithelial cells of external structures of insects like the fruit fly Drosophila melanogaster, polarised tissue morphogenesis in vertebrates and sensory hair cells in the vertebrate ear. In this work we focus on the wing and the abdomen of Drosophila, where PCP becomes obvious in the alignment of hairs and bristles. The underlying dynamics are not fully understood yet, but two distinct protein networks centred around the transmembrane proteins Frizzled and Dachsous, respectively, have been shown to play essential roles. We will present and analyse five models for different aspects of the process of planar cell polarisation. The first two models assess the nature of PCP in a generic setting, ensuring that the results are valid for whole classes of PCP models. Models three and four are existing more complex models that include detailed assumptions about the underlying protein interactions of the Frizzled system in the Drosophila wing. Model five considers the Dachsous system in the Drosophila abdomen. We describe the features of the different types of mechanisms and determine the conditions under which they can yield polarity. All five models can establish wild-type polarity for a wide range of parameter values. We find, however, that for model one, three and four an inhomogeneous pattern exists for the same parameter values as the polarised state. Therefore, in these cases either specific initial conditions, which are unlikely in nature, or a global bias are necessary to ensure correct polarisation. Furthermore, we present the effects of clonal clusters of cells on the polarity of the surrounding cells in our models and relate them to the phenotypes observed in experiments. Model one and five show the largest discrepance between the numerical and the experimental results. We discuss the biological relevance of these findings and indicate outstanding questions

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion

Is a persistent global bias necessary for the establishment of planar cell polarity?

Planar cell polarity (PCP)–the coordinated polarisation of a whole field of cells within the plane of a tissue–relies on the interaction of three modules: a global module that couples individual cellular polarity to the tissue axis, a local module that aligns the axis of polarisation of neighbouring cells, and a readout module that directs the correct outgrowth of PCP-regulated structures such as hairs and bristles. While much is known about the molecular components that are required for PCP, the functional details of–and interactions between–the modules remain unclear. In this work, we perform a mathematical and computational analysis of two previously proposed computational models of the local module (Amonlirdviman et al., Science, 307, 2005; Le Garrec et al., Dev. Dyn., 235, 2006). Both models can reproduce wild-type and mutant phenotypes of PCP observed in the Drosophila wing under the assumption that a tissue-wide polarity cue from the global module persists throughout the development of PCP. We demonstrate that both models can also generate tissue-level PCP when provided with only a transient initial polarity cue. However, in these models such transient cues are not sufficient to ensure robustness of the resulting cellular polarisation

Endocytic and Recycling Endosomes Modulate Cell Shape Changes and Tissue Behaviour during Morphogenesis in Drosophila

During development tissue deformations are essential for the generation of organs and to provide the final form of an organism. These deformations rely on the coordination of individual cell behaviours which have their origin in the modulation of subcellular activities. Here we explore the role endocytosis and recycling on tissue deformations that occur during dorsal closure of the Drosophila embryo. During this process the AS contracts and the epidermis elongates in a coordinated fashion, leading to the closure of a discontinuity in the dorsal epidermis of the Drosophila embryo. We used dominant negative forms of Rab5 and Rab11 to monitor the impact on tissue morphogenesis of altering endocytosis and recycling at the level of single cells. We found different requirements for endocytosis (Rab5) and recycling (Rab11) in dorsal closure, furthermore we found that the two processes are differentially used in the two tissues. Endocytosis is required in the AS to remove membrane during apical constriction, but is not essential in the epidermis. Recycling is required in the AS at early stages and in the epidermis for cell elongation, suggesting a role in membrane addition during these processes. We propose that the modulation of the balance between endocytosis and recycling can regulate cellular morphology and tissue deformations during morphogenesis

Modelling planar cell polarity in Drosophila melanogaster

During development, polarity is a common feature of many cell types. One example is the polarisation of whole fields of epithelial cells within the plane of the epithelium, a phenomenon called planar cell polarity (PCP). It is widespread in nature and plays important roles in development and physiology. Prominent examples include the epithelial cells of external structures of insects like the fruit fly Drosophila melanogaster, polarised tissue morphogenesis in vertebrates and sensory hair cells in the vertebrate ear. In this work we focus on the wing and the abdomen of Drosophila, where PCP becomes obvious in the alignment of hairs and bristles. The underlying dynamics are not fully understood yet, but two distinct protein networks centred around the transmembrane proteins Frizzled and Dachsous, respectively, have been shown to play essential roles. We will present and analyse five models for different aspects of the process of planar cell polarisation. The first two models assess the nature of PCP in a generic setting, ensuring that the results are valid for whole classes of PCP models. Models three and four are existing more complex models that include detailed assumptions about the underlying protein interactions of the Frizzled system in the Drosophila wing. Model five considers the Dachsous system in the Drosophila abdomen. We describe the features of the different types of mechanisms and determine the conditions under which they can yield polarity. All five models can establish wild-type polarity for a wide range of parameter values. We find, however, that for model one, three and four an inhomogeneous pattern exists for the same parameter values as the polarised state. Therefore, in these cases either specific initial conditions, which are unlikely in nature, or a global bias are necessary to ensure correct polarisation. Furthermore, we present the effects of clonal clusters of cells on the polarity of the surrounding cells in our models and relate them to the phenotypes observed in experiments. Model one and five show the largest discrepance between the numerical and the experimental results. We discuss the biological relevance of these findings and indicate outstanding questions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion

Integrative approaches to morphogenesis: Lessons from dorsal closure

Although developmental biology has been dominated by the genetic analysis of embryonic development, in recent years genetic tools have been combined with new approaches such as imaging of live processes, automated and quantitative image analysis, mechanical perturbation and mathematical modeling, to study the principles underlying the formation of organisms. Here we focus on recent work carried out on Dorsal Closure, a morphogenetic process during Drosophila embryogenesis, to illustrate how this multidisciplinary approach is yielding new and unexpected insights into how cells organize themselves through the activity of their molecular components to give rise to the stereotyped and macroscopic movements observed during development. © 2010 Wiley-Liss, Inc.Biotechnology and Biological Sciences Research Council; ‘Ramón y Cajal’ fellowship; Engineering and Physical Sciences Research Council (EPSRC)Peer Reviewe