Mathematical models of dorsal closure

Automated profiling of gene function during embryonic development

Systematic functional profiling of the gene set that directs embryonic development is an important challenge. To tackle this challenge, we used 4D imaging of C. elegans embryogenesis to capture the effects of 500 gene knockdowns and developed an automated approach to compare developmental phenotypes. The automated approach quantifies features-including germ layer cell numbers, tissue position, and tissue shape-to generate temporal curves whose parameterization yields numerical phenotypic signatures. In conjunction with a new similarity metric that operates across phenotypic space, these signatures enabled the generation of ranked lists of genes predicted to have similar functions, accessible in the PhenoBank web portal, for ∼25% of essential development genes. The approach identified new gene and pathway relationships in cell fate specification and morphogenesis and highlighted the utilization of specialized energy generation pathways during embryogenesis. Collectively, the effort establishes the foundation for comprehensive analysis of the gene set that builds a multicellular organism.

Gears of life: A primer on the simple machines that shape the embryo

A simple machine is a basic of device that takes mechanical advantage to apply force. Animals and plants self-assemble through the operation of a wide variety of simple machines. Embryos of different species actuate these simple machines to drive the geometric transformations that convert a disordered mass of cells into organized structures with discrete identities and function. These transformations are intrinsically coupled to sequential and overlapping steps of self-organization and self-assembly. The processes of self-organization have been explored through the molecular composition of cells and tissues and their information networks. By contrast, efforts to understand the simple machines underlying self-assembly must integrate molecular composition with the physical principles of mechanics. This primer is concerned with effort to elucidate the operation of these machines, focusing on the "problem" of morphogenesis. Advances in understanding self-assembly will ultimately connect molecular-, subcellular-, cellular- and meso-scale functions of plants and animals and their ability to interact with larger ecologies and environmental influences.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster . During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Significance Statement

During embryogenesis, cells in tissues can undergo significant shape changes. Many epithelial tissues fluidize, i.e. cells exchange neighbors, when the average cell aspect ratio increases above a threshold value, consistent with the standard vertex model. During dorsal closure in Drosophila melanogaster , however, the amnioserosa tissue remains solid even as the average cell aspect ratio increases well above threshold. We introduce perimeter polydispersity and allow the preferred cell perimeters, usually held fixed in vertex models, to decrease linearly with time as seen experimentally. With these extensions to the standard vertex model, we capture experimental observations quantitatively. Our results demonstrate that vertex models can describe the behavior of the amnioserosa in dorsal closure by allowing normally fixed parameters to vary with time.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrink-age of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Super-resolution microscopy reveals actomyosin dynamics in medioapical arrays

Arrays of actin filaments (F-actin) near the apical surface of epithelial cells (medioapical arrays) contribute to apical constriction and morphogenesis throughout phylogeny. Here, super-resolution approaches (grazing incidence structured illumination, GI-SIM and lattice light sheet, LLSM) microscopy resolve individual, fluorescently labeled F-actin and bipolar myosin filaments that drive amnioserosa cell shape changes during dorsal closure in Drosophila. In expanded cells, F-actin and myosin form loose, apically domed meshworks at the plasma membrane. The arrays condense as cells contract, drawing the domes into the plane of the junctional belts. As condensation continues, individual filaments are no longer uniformly apparent. As cells expand, arrays of actomyosin are again resolved - some F-actin turnover likely occurs, but a large fraction of existing filaments rearrange. In morphologically isotropic cells, actin filaments are randomly oriented and during contraction, are drawn together but remain essentially randomly oriented. In anisotropic cells, largely parallel actin filaments are drawn closer to one another. Our images offer unparalleled resolution of F-actin in embryonic tissue show that medioapical arrays are tightly apposed to the plasma membrane, are continuous with meshworks of lamellar F-actin and thereby constitute modified cell cortex. In concert with other tagged array components, super-resolution imaging of live specimens will offer new understanding of cortical architecture and function. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

A Comparative Study of the Role of Formins in Drosophila Embryonic Dorsal Closure

Dorsal closure is a late embryogenesis process required to seal the epidermal hole on the dorsal side of the Drosophila embryo. This process involves the coordination of several forces generated in the epidermal cell layer and in the amnioserosa cells, covering the hole. Ultimately, these forces arise due to cytoskeletal rearrangements that induce changes in cell shape and result in tissue movement. While a number of cytoskeleton regulatory proteins have already been linked to dorsal closure, here we expand this list by demonstrating that four of the six Drosophila formin type actin assembly factors are needed to bring about the proper fusion of the epithelia. An analysis of the morphological and dynamic properties of dorsal closure in formin mutants revealed a differential contribution for each formin, although we found evidence for functional redundancies as well. Therefore, we propose that the four formins promote the formation of several, and only partly identical, actin structures each with a specific role in the mechanics of dorsal closure.

Dynamics of PAR Proteins Explain the Oscillation and Ratcheting Mechanisms in Dorsal Closure

We present a vertex-based model for Drosophila dorsal closure that predicts the mechanics of cell oscillation and contraction from the dynamics of the PAR proteins. Based on experimental observations of how aPKC, Par-6, and Bazooka translocate from the circumference of the apical surface to the medial domain, and how they interact with each other and ultimately regulate the apicomedial actomyosin, we formulate a system of differential equations that captures the key features of dorsal closure, including distinctive behaviors in its early, slow, and fast phases. The oscillation in cell area in the early phase of dorsal closure results from an intracellular negative feedback loop that involves myosin, an actomyosin regulator, aPKC, and Bazooka. In the slow phase, gradual sequestration of apicomedial aPKC by Bazooka clusters causes incomplete disassembly of the actomyosin network over each cycle of oscillation, thus producing a so-called ratchet. The fast phase of rapid cell and tissue contraction arises when medial myosin, no longer antagonized by aPKC, builds up in time and produces sustained contraction. Thus, a minimal set of rules governing the dynamics of the PAR proteins, extracted from experimental observations, can account for all major mechanical outcomes of dorsal closure, including the transitions between its three distinct phases.