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Tissue elongation is a fundamental morphogenetic process to construct complex embryonic structures. In zebrafish, somites rapidly elongate in both dorsal and ventral directions, transforming from a cuboidal to a V-shape within a few hours of development. Despite its significance, the cellular behaviors that directly lead to somite elongation have not been examined at single-cell resolution. Here, we describe the motion and shapes of all cells composing the dorsal half of the somite in three-dimensional space using lightsheet microscopy. We identified two types of cell movements-in horizontal and dorsal directions-that occur simultaneously within individual cells, creating a complex, twisted flow of cells during somite elongation. Chemical inhibition of Sdf1 signaling disrupted the collective movement in both directions and inhibited somite elongation, suggesting that Sdf1 signaling is crucial for this cell flow. Furthermore, three-dimensional computational modeling suggested that horizontal cell rotation accelerates the perpendicular elongation of the somite along the dorsoventral axis. Together, our study offers novel insights into the role of collective cell migration in tissue morphogenesis, which proceeds dynamically in the three-dimensional space of the embryo.

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Tiling patterns are observed in many biological structures. The compound eye is an interesting example of tiling and is often constructed by hexagonal arrays of ommatidia, the optical unit of the compound eye. Hexagonal tiling may be common due to mechanical restrictions such as structural robustness, minimal boundary length, and space-filling efficiency. However, some insects exhibit tetragonal facets.1-4 Some aquatic crustaceans, such as shrimp and lobsters, have evolved with tetragonal facets.5-8 Mantis shrimp is an insightful example as its compound eye has a tetragonal midband region sandwiched between hexagonal hemispheres.9,10 This casts doubt on the naive explanation that hexagonal tiles recur in nature because of their mechanical stability. Similarly, tetragonal tiling patterns are also observed in some Drosophila small-eye mutants, whereas the wild-type eyes are hexagonal, suggesting that the ommatidial tiling is not simply explained by such mechanical restrictions. If so, how are the hexagonal and tetragonal patterns controlled during development? Here, we demonstrate that geometrical tessellation determines the ommatidial tiling patterns. In small-eye mutants, the hexagonal pattern is transformed into a tetragonal pattern as the relative positions of neighboring ommatidia are stretched along the dorsal-ventral axis. We propose that the regular distribution of ommatidia and their uniform growth collectively play an essential role in the establishment of tetragonal and hexagonal tiling patterns in compound eyes.

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The human hand can detect both form and texture information of a contact surface. The detection of skin displacement (sustained stimulus) and changes in skin displacement (transient stimulus) are thought to be mediated in different tactile channels; however, tactile form perception may use both types of information. Here, we studied whether both the temporal frequency and the temporal coherency information of tactile stimuli encoded in sensory neurons could be used to recognize the form of contact surfaces. We used the fishbone tactile illusion (FTI), a known tactile phenomenon, as a probe for tactile form perception in humans. This illusion typically occurs with a surface geometry that has a smooth bar and coarse textures in its adjacent areas. When stroking the central bar back and forth with a fingertip, a human observer perceives a hollow surface geometry even though the bar is physically flat. We used a passive high-density pin matrix to extract only the vertical information of the contact surface, suppressing tangential displacement from surface rubbing. Participants in the psychological experiment reported indented surface geometry by tracing over the FTI textures with pin matrices of the different spatial densities (1.0 and 2.0 mm pin intervals). Human participants reported that the relative magnitude of perceived surface indentation steeply decreased when pins in the adjacent areas vibrated in synchrony. To address possible mechanisms for tactile form perception in the FTI, we developed a computational model of sensory neurons to estimate temporal patterns of action potentials from tactile receptive fields. Our computational data suggest that (1) the temporal asynchrony of sensory neuron responses is correlated with the relative magnitude of perceived surface indentation and (2) the spatiotemporal change of displacements in tactile stimuli are correlated with the asynchrony of simulated sensory neuron responses for the fishbone surface patterns. Based on these results, we propose that both the frequency and the asynchrony of temporal activity in sensory neurons could produce tactile form perception.

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One of the fundamental processes in morphogenesis is dome formation, but many of the mechanisms involved are unexplored. Previous in vitro studies showed that an osmotic gradient is the driving factor of dome formation. However, these investigations were performed without extracellular matrix (ECM), which provides structural support to morphogenesis. With the use of ECM, we observed that basal hypertonic stress induced stable domes in vitro that have not been seen in previous studies. These domes developed as a result of ECM swelling via aquaporin water transport activity. Based on computer simulation, uneven swelling, with a positive feedback between cell stretching and enhanced water transport, was a cause of dome formation. These results indicate that osmotic gradients induce dome morphogenesis via both enhanced water transport activity and subsequent ECM swelling.

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The external organs of holometabolous insects are generated through two consecutive processes: the development of imaginal primordia and their subsequent transformation into the adult structures. During the latter process, many different phenomena at the cellular level (e.g. cell shape changes, cell migration, folding and unfolding of epithelial sheets) contribute to the drastic changes observed in size and shape. Because of this complexity, the logic behind the formation of the 3D structure of adult external organs remains largely unknown. In this report, we investigated the metamorphosis of the horn in the Japanese rhinoceros beetle Trypoxylus dichotomus. The horn primordia is essentially a 2D epithelial cell sheet with dense furrows. We experimentally unfolded these furrows using three different methods and found that the furrow pattern solely determines the 3D horn structure, indicating that horn formation in beetles occurs by two distinct processes: formation of the furrows and subsequently unfolding them. We postulate that this developmental simplicity offers an inherent advantage to understanding the principles that guide 3D morphogenesis in insects.

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Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. van Iterson (Mathematische und mikroskopisch - anatomische Studien über Blattstellungen nebst Betrachtungen über den Schalenbau der Miliolinen, Verlag von Gustav Fischer, Jena, 1907) suggested a centric model representing ideal phyllotactic patterns as disk packings of Bernoulli spiral lattices and presented a phase diagram now called Van Iterson's diagram explaining the bifurcation processes of their combinatorial structures. Geometrical properties on disk packings were shown by Rothen & Koch (J. Phys France, 50(13), 1603-1621, 1989). In contrast, as another centric model, we organized a mathematical framework of Voronoi tilings of Bernoulli spiral lattices and showed mathematically that the phase diagram of a Voronoi tiling is graph-theoretically dual to Van Iterson's diagram. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices.

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Individual cells migrate toward the direction of the cell polarity generated by interior or exterior factors. Under situations without guides such as chemoattractants, they migrate randomly. On the other hand, it has been observed that cell groups lead to systematic collective cell migrations. For example, Dictyostelium discoideum and Madin-Darby canine kidney (epithelial) cells exhibit typical collective cell migration patterns such as uniformly directional migration and rotational migration. In particular, it has been suggested from experimental investigations that rotational migrations are intimately related to morphogenesis of organs and tissues in several species. Thus, it is conjectured that collective cell migrations are controlled by universal mechanisms of cells. In this paper, we review actual experimental data related to collective cell migrations on dishes and show that our self-propelled particle model based on the cell polarity can accurately represent actual migration behaviors. Furthermore, we show that collective cell migration modes observed in our model are robust.

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