The reaction-diffusion system is one of the most studied nonlinear mechanisms that generate spatially periodic structures autonomous. On the basis of many mathematical studies using computer simulations, it is assumed that animal skin patterns are the most typical examples of the Turing pattern (stationary periodic pattern produced by the reaction-diffusion system). However, the mechanism underlying pattern formation remains unknown because the molecular or cellular basis of the phenomenon has yet to be identified. In this study, we identified the interaction network between the pigment cells of zebrafish, and showed that this interaction network possesses the properties necessary to form the Turing pattern. When the pigment cells in a restricted region were killed with laser treatment, new pigment cells developed to regenerate the striped pattern. We also found that the development and survival of the cells were influenced by the positioning of the surrounding cells. When melanophores and xanthophores were located at adjacent positions, these cells excluded one another. However, melanophores required a mass of xanthophores distributed in a more distant region for both differentiation and survival. Interestingly, the local effect of these cells is opposite to that of their effects long range. This relationship satisfies the necessary conditions required for stable pattern formation in the reactiondiffusion model. Simulation calculations for the deduced network generated wild-type pigment patterns as well as other mutant patterns. Our findings here allow further investigation of Turing pattern formation within the context of cell biology.nonlinear system ͉ pattern formation ͉ reaction-diffusion ͉ stripes T he reaction-diffusion system is one of the most studied and well-known nonlinear mechanisms that are able to generate spatially periodic structures. In the original article, Turing (1) presented the idea that the periodic structures generated by the reaction-diffusion mechanism may provide correct positional information that is used in the course of animal development. On the basis of many mathematical studies using computer simulations (2-5), animal coat pattern is assumed to be the most typical example of the Turing pattern. However, the mechanism underlying pattern formation remains unknown because the molecular or cellular basis of the phenomenon has yet to be identified. Recently, the zebrafish (Danio rerio), a small fish with distinctive stripes on the body trunk and fins, was selected as one of the model animals for molecular genetic research (6). Studies using this model animal have made it possible to uncover the basic mechanism that generates the Turing pattern in biological systems.The stripes of zebrafish are composed of a mosaic-like arrangement of 3 types of pigment cells: melanophores, xanthophores, and iridophores (7). Evidence from recent molecular and genetic studies (8-10) on the altered patterns of mutant fish has suggested that the interaction between the melanophores (black) and xanthophor...

Creating vascular networks in tissues is crucial for tissue engineering. Although recent studies have demonstrated the formation of vessel-like structures in a tissue model, long-term culture is still challenging due to the lack of active perfusion in vascular networks. Here, we present a method to create a three-dimensional cellular spheroid with a perfusable vascular network in a microfluidic device. By the definition of the cellular interaction between human lung fibroblasts (hLFs) in a spheroid and human umbilical vein endothelial cells (HUVECs) in microchannels, angiogenic sprouts were induced from microchannels toward the spheroid; the sprouts reached the vessel-like structures in a spheroid to form a continuous lumen. We demonstrated that the vascular network could administer biological substances to the interior of the spheroid. As cell density in the spheroid is similar to that of a tissue, the perfusable vasculature model opens up new possibilities for a long-term tissue culture in vitro.

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves.

Summary:The leaves of some plant species are able to change their morphology in response to environmental conditions. This phenomenon is termed heterophylly. Various aquatic plants exhibit drastic changes in leaf shape in response to submerged aquatic conditions. Heterophyllic variation ranges from mere modification of leaf width to drastic alteration in the outline of leaves and is interpreted as an adaptation to aquatic habitats. Although this phenomenon is widely observed among angiosperms, there is limited information on the regulation of heterophyllic switch in leaf development. Here, we have reviewed existing knowledge on leaf development and heterophylly and have introduced Neobeckia aquatica as an emerging model to elucidate the mechanisms underlying heterophylly.

The cytoskeleton is a network of crosslinked, semiflexible filaments, and it has been suggested that it has properties of a glassy state. Here we employ optical-trap-based microrheology to apply forces to a model cytoskeleton and measure the high-bandwidth response at an anterior point. Simulating the highly nonlinear and anisotropic stress-strain propagation assuming affinity, we found that theoretical predictions for the quasistatic response of semiflexible polymers are only realized at high frequencies inaccessible to conventional rheometers. We give a theoretical basis for determining the frequency when both affinity and quasistaticity are valid, and we discuss with experimental evidence that the relaxations at lower frequencies can be characterized by the experimentally obtained nonaffinity parameter.

A spheroid (a multicellular aggregate) is regarded as a good model of living tissues in the human body. Despite the significant advancement in the spheroid cultures, a perfusable vascular network in the spheroids remains a critical challenge for long-term culture required to maintain and develop their functions, such as protein expressions and morphogenesis. The protocol presents a novel method to integrate a perfusable vascular network within the spheroid in a microfluidic device. To induce a perfusable vascular network in the spheroid, angiogenic sprouts connected to microchannels were guided to the spheroid by utilizing angiogenic factors from human lung fibroblasts cultured in the spheroid. The angiogenic sprouts reached the spheroid, merged with the endothelial cells co-cultured in the spheroid, and formed a continuous vascular network. The vascular network could perfuse the interior of the spheroid without any leakage. The constructed vascular network may be further used as a route for supply of nutrients and removal of waste products, mimicking blood circulation in vivo. The method provides a new platform in spheroid culture toward better recapitulation of living tissues.

When different growth speeds along axes of a divaricating leaf were introduced into our previous model, robust and directed asymmetries were reproduced. The differences in growth speed could be predicted from the distributions of leaf segments in actual leaves. Developmental Dynamics 246:981-991, 2017. © 2017 Wiley Periodicals, Inc.

Different diffusivities among interacting substances actualize the potential instability of a system. When these elicited instabilities manifest as forms of spatial periodicity, they are called Turing patterns. Simulations using general reaction-diffusion (RD) models demonstrate that pigment patterns on the body trunk of growing fish follow a Turing pattern. Laser ablation experiments performed on zebrafish reveal apparent interactions among pigment cells, which allow for a three-component RD model to be derived. However, the underlying molecular mechanisms responsible for Turing pattern formation in this system remain unknown. A zebrafish mutant with a spotted pattern was found to have a defect in Connexin41.8 (Cx41.8) which, together with Cx39.4, exists in pigment cells and controls pattern formation. Here, molecular-level evidence derived from connexin analyses is linked to the interactions among pigment cells described in previous RD modeling. Channels on pigment cells are generalized as “gates,” and the effects of respective gates were deduced. The model uses partial differential equations (PDEs) to enable numerical and mathematical analyses of characteristics observed in the experiments. Furthermore, the improved PDE model, including nonlinear reaction terms, enables the consideration of the behavior of components realistically.