The Turing, or reaction-diffusion (RD), model is one of the best-known theoretical models used to explain self-regulated pattern formation in the developing animal embryo. Although its real-world relevance was long debated, a number of compelling examples have gradually alleviated much of the skepticism surrounding the model. The RD model can generate a wide variety of spatial patterns, and mathematical studies have revealed the kinds of interactions required for each, giving this model the potential for application as an experimental working hypothesis in a wide variety of morphological phenomena. In this review, we describe the essence of this theory for experimental biologists unfamiliar with the model, using examples from experimental studies in which the RD model is effectively incorporated.

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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...

Periodic somite segmentation in vertebrate embryos is controlled by the 'segmentation clock', which consists of numerous cellular oscillators. Although the properties of a single oscillator, driven by a hairy negative-feedback loop, have been investigated, the system-level properties of the segmentation clock remain largely unknown. To explore these characteristics, we have examined the response of a normally oscillating clock in zebrafish to experimental stimuli using in vivo mosaic experiments and mathematical simulation. We demonstrate that the segmentation clock behaves as a coupled oscillator, by showing that Notch-dependent intercellular communication, the activity of which is regulated by the internal hairy oscillator, couples neighbouring cells to facilitate synchronized oscillation. Furthermore, the oscillation phase of individual oscillators fluctuates due to developmental noise such as stochastic gene expression and active cell proliferation. The intercellular coupling was found to have a crucial role in minimizing the effects of this noise to maintain coherent oscillation.