Caenorhabditis elegans Gastrulation: A Model for Understanding How Cells Polarize, Change Shape, and Journey Toward the Center of an Embryo

Gastrulation is fundamental to the development of multicellular animals. Along with neurulation, gastrulation is one of the major processes of morphogenesis in which cells or whole tissues move from the surface of an embryo to its interior. Cell internalization mechanisms that have been discovered to date in Caenorhabditis elegans gastrulation bear some similarity to internalization mechanisms of other systems including Drosophila, Xenopus, and mouse, suggesting that ancient and conserved mechanisms internalize cells in diverse organisms. C. elegans gastrulation occurs at an early stage, beginning when the embryo is composed of just 26 cells, suggesting some promise for connecting the rich array of developmental mechanisms that establish polarity and pattern in embryos to the force-producing mechanisms that change cell shapes and move cells interiorly. Here, we review our current understanding of C. elegans gastrulation mechanisms. We address how cells determine which direction is the interior and polarize with respect to that direction, how cells change shape by apical constriction and internalize, and how the embryo specifies which cells will internalize and when. We summarize future prospects for using this system to discover some of the general principles by which animal cells change shape and internalize during development.

A fast and simple algorithm for calculating flow accumulation matrices from raster digital elevation models

<p><strong>Abstract.</strong> Flow accumulation is an essential input for many hydrological and topographic analyses such as stream channel extraction, stream channel ordering and sub-watershed delineation. Flow accumulation matrices can be derived directly from DEMs and general have O(NlogN) time complexity (Arge, 2003; Bai et al., 2015). It is more common to derive the flow accumulation matrix from a flow direction matrix. This study focuses on calculating the flow accumulation matrix from the flow direction matrix that is derived using the single-flow D8 method (Barnes et al., 2014; Garbrecht &amp; Martz, 1997; Nardi et al., 2008; O'Callaghan &amp; Mark, 1984). In this study, we find give an overview of algorithms for flow accumulation calculation that have O(N) time complexity. These algorithms include algorithms are based on the concept of the number of input drainage paths (Wang et al.2011, Jiang et al. 2013), the algorithm based on the basin tree indices (Su et al. 2015), and the recursive algorithm (Choi, 2012; Freeman, 1991).</p><p>We propose a fast and simple algorithm to calculate the flow accumulation matrix. Compared with the existing algorithms that have O(N) time complexity, our algorithm runs faster and generally requires less memory. Our algorithm is also simple to implement. In our algorithm, we define three types of cells within a flow direction matrix: source cells, interior cells and intersection cells. A source cell does not have neighboring cells that drain to it and its NIDP value is zero. An interior cell has only one neighboring cell that drains to it and its NIDP value is one. An intersection cell has more than one neighboring cell that drains to it and its NIDP value is greater than one. The proposed algorithm initializes the flow accumulation matrix with the value of one. Our algorithm first calculates the NIDP matrix from the flow direction matrix. The algorithm then traverses each cell within the flow direction matrix row by row and column by column, similar to the traversal algorithm. When a source cell <i>c</i> is encountered, the algorithm traces all downstream cells of <i>c</i> until it encounters an intersection cell <i>i</i>. During the tracing, the accumulation value of a cell is added to the accumulation value of its immediate downstream cell. An interior cell has only one neighboring cell that drains to it and its final accumulation value is obtained when the tracing is done. The accumulation value of the intersection cell i is updated from this drainage path. However, cell <i>i</i> has other unvisited neighboring cells that drain to it and its final accumulation value cannot be obtained after this round of tracing. The algorithm decreases the NIDP value of <i>i</i> by one. Cell <i>i</i> is visited again when other drainage paths that pass through it are traced. When all of the drainage paths that pass through it are traced, cell <i>i</i> is treated as an interior cell and the final accumulation value of <i>i</i> is obtained correctly and the last tracing process can continue the tracing after cell <i>i</i> is treated as an interior cell. A worked example of the proposed algorithm is shown in Figure 1.</p><p>The five flow accumulation algorithms with O(N) time complexity, including Wang’s algorithm, Jiang’s algorithm, the BTI-based algorithm, the recursive algorithm and our proposed algorithm, are implemented in C++. The 3-m LiDAR-based DEMs of thirty counties in the state of Minnesota, USA, are downloaded from the FTP site operated by the Minnesota Geospatial Information Office. The first 30 counties in Minnesota in alphabetic order are chosen for the experiments to avoid selection bias. We use the algorithm proposed by Wang and Liu (2006) to fill the depressions and derive the flow direction matrices for all tested counties. The running times on the Windows system are listed in Figure 2.The average running times per 100 million cells are 14.42 seconds for Wang’s algorithm, 15.90 seconds for Jiang’salgorithm, 18.95 seconds for the BTI-based algorithm, 10.87 seconds for the recursive algorithm, and 5.26 seconds forour proposed algorithm. Our algorithm runs the fastest for all tested DEM. The speed-up ratios of our proposedalgorithm over the second fastest algorithm is about 51%.</p>

Progressive tensile damage simulation and strength analysis of three-dimensional braided composites based on three unit-cells models

In order to explore the micro-failure mechanism and predict tensile strength of three-dimensional braided composites, the three unit-cells models, namely interior cell, surface cell and corner cell, are established to simulate progressive damage of these materials. Macro model is firstly created and divided into three kinds of unit cells by their periodical distributions. A criterion is approached to determine damage and its pattern of each element, and stiffness degradation is implemented for the damaged elements with geometric damage theory. Periodical boundary conditions are applied on the models to calculate micro-stress and damage propagation is simulated with the increase of load. Each type of damage and its percentage is obtained by simulation and micro-failure mechanism is analyzed. Furthermore, the tensile strengths are predicted from calculated stress–strain curves. From simulation, composites with large braiding angle have more complicated micro-failure mechanism than composites with small braiding angle. It is also observed that there are more damages in surface cell than in interior cell and the damage types in the surface cell are various. The predicted results on the three unit-cells models agree well with the experimental data and are more accurate than only using an interior-cell model.

Finite element analyses on bending fatigue of three-dimesional five-directional braided composite T-beam with mixed unit-cell model

This paper reports the bending fatigue behavior of three-dimensional five-directional braided T-shaped composite from finite element analyses and experimental characterizations. The braided composite microstructure was divided into five types of unit cell models, that is, interior cell, surface cell, corner cell, interior cell in joint region, and corner cell in joint region. A user-defined material subroutine was developed to characterize the unit cells properties, damage accumulation, and failure criterion of the T-beam under different stress levels. The stiffness degradation curves and bending displacement curves were obtained from the finite element analysis to show the three stages of fatigue developments, that is, matrix cracks, interface debonding, and fiber breaking. The stress and strain concentration areas were found in the middle of the flange and the web of the T-beam composites. The high strength reinforced fibers are recommended to add in the middle of the flange and the web for improving the bending fatigue resistance. And also, we hope the mixed unit-cell model could be extended to the other braided composite structures under quasi-static or cyclic loadings.

Design Optimization of Honeycomb Core Sandwich Panels for Maximum Sound Transmission Loss

This study focuses on sound transmission frequency response through honeycomb core sandwich panels with in-plane orientation. Specifically, an optimization technique has been presented to determine the honeycomb unit cell geometric parameters that maximize the sound transmission loss (STL) through a sandwich panel, while maintaining constraints of constant mass and overall dimensions of panel length and height. The vibration characteristics and STL response of a sandwich panel are parameterized in terms of four honeycomb unit cell independent geometric parameters; two side lengths, cell wall thickness, and interior cell wall angle. With constraints of constant mass and overall dimensions, relationships are determined such that the number of independent variables needed to define the honeycomb cell and panel geometry is reduced to three; the integer number of unit cells in the longitudinal direction of the core, number of unit cells in the height direction, and interior cell wall angle. The optimization procedure is implemented by linking a structural acoustic finite-element (FE) model of the panel, with modefrontier, a general purpose optimization software. Optimum designs are obtained in representative frequency ranges within the resonance region of the STL response. Optimized honeycomb geometric solutions show at least 20% increase in STL response compared to standard hexagonal honeycomb core panels. It is found that the STL response is not only affected by the cell wall angle, but strongly depends also on the number of unit cells in the horizontal and vertical direction.