Shigeru Kondo

Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation

Turing Model Explained The reaction-diffusion (Turing) model is a theoretical model used to explain self-regulated pattern formation in biology. Although many biologists have heard of this model, a better understanding of the concept would aid its application to many research projects and developmental principles. Kondo and Miura (p. 1616) now review the reaction-diffusion model. Despite the associated mathematics, the basic idea of the Turing model is relatively easy to understand and relates to morphogen gradients. In addition, user-friendly software makes it easy to understand how a whole variety of patterns can be produced by this simple mechanism. 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.

Noise-resistant and synchronized oscillation of the segmentation clock

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.

Interactions between zebrafish pigment cells responsible for the generation of Turing patterns

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 reaction–diffusion 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.

Spot pattern of leopard Danio is caused by mutation in the zebrafish connexin41.8 gene

Leopard, a well‐known zebrafish mutant that has a spotted skin pattern instead of stripes, is a model for the study of pigment patterning. To understand the mechanisms underlying stripe formation, as well as the spot variation observed in leopard, we sought to identify the gene responsible for this phenotype. Using positional cloning, we identified the leopard gene as an orthologue of the mammalian connexin 40 gene. A variety of different leopard alleles, such as leot1, leotq270 and leotw28, show different skin‐pattern phenotypes. In this manuscript we show that the mutation in allele leot1 is a nonsense mutation, whereas alleles leotq270 and leotw28 contain the missense mutations I202F and I31F, respectively. Patch‐clamp experiments of connexin hemichannels demonstrated that the I202F substitution in allele leotq270 disrupted the channel function of connexin41.8. These results demonstrate that mutations in this gene lead to a variety of leopard spot patterns.

Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism

The mechanism by which animal markings are formed is an intriguing problem that has remained unsolved for a long time. One of the most important questions is whether the positional information for the pattern formation is derived from a covert prepattern or an autonomous mechanism. In this study, using the zebrafish as the model system, we attempted to answer this classic question. We ablated the pigment cells in limited areas of zebrafish skin by using laser irradiation, and we observed the regeneration of the pigmentation pattern. Depending on the area ablated, different patterns regenerated in a specific time course. The regenerated patterns and the transition of the stripes during the regeneration process suggest that pattern formation is independent of the prepattern; furthermore, pattern formation occurs by an autonomous mechanism that satisfies the condition of “local self-enhancement and long-range inhibition.” Because the zebrafish is the only striped animal for which detailed molecular genetic studies have been conducted, our finding will facilitate the identification of the molecular and cellular mechanisms that underlie skin pattern formation.

Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate

We present direct evidence of an activator-inhibitor system in the generation of the regularly spaced transverse ridges of the palate. We show that new ridges, called rugae, that are marked by stripes of expression of Shh (encoding Sonic hedgehog), appear at two growth zones where the space between previously laid rugae increases. However, inter-rugal growth is not absolutely required: new stripes of Shh expression still appeared when growth was inhibited. Furthermore, when a ruga was excised, new Shh expression appeared not at the cut edge but as bifurcating stripes branching from the neighboring stripe of Shh expression, diagnostic of a Turing-type reaction-diffusion mechanism. Genetic and inhibitor experiments identified fibroblast growth factor (FGF) and Shh as components of an activator-inhibitor pair in this system. These findings demonstrate a reaction-diffusion mechanism that is likely to be widely relevant in vertebrate development.

Pigment Pattern Formation by Contact-Dependent Depolarization

Cell culture experiments reveal that direct interactions between pigment cells play a key role in skin pattern formation. Although recent experimental studies have suggested that the interactions among the pigment cells play a key role in the skin pattern formation, details of the mechanism remain largely unknown. By using an in vitro cell culture system, we have detected interactions between the two pigment cell types, melanophores and xanthophores, in the zebrafish skin. During primary culture, the melanophore membrane transiently depolarizes when contacted with the dendrites of a xanthophore. This depolarization triggers melanophore migration to avoid further contact with the xanthophores. Cell depolarization and repulsive movement were not observed in pigment cells with the jaguar mutant, which shows defective segregation of melanophores and xanthophores. The depolarization-repulsion of wild-type pigment cells may explain the pigment cell behaviors generating the stripe pattern of zebrafish.

Zebrafish leopard gene as a component of the putative reaction-diffusion system.

It has been suggested, on a theoretical basis, that a reaction-diffusion (RD) mechanism underlies pigment pattern formation in animals, but as yet, there is no molecular evidence for the putative mechanism. Mutations in the zebrafish gene, leopard, change the pattern from stripes to spots. Interestingly each allele gives a characteristic pattern, which varies in spot size, density and connectivity. That mutations in a single gene can generate such a variety of patterns can be understood using a RD model. All the pattern variations of leopard mutants can be generated in a simulation by changing a parameter value that corresponds to the reaction kinetics in a putative RD system. Substituting an intermediate value of the parameter makes the patterns similar to the heterozygous fish. These results suggest that the leopard gene product is a component of the putative RD mechanism.

Pigment cell organization in the hypodermis of zebrafish

Zebrafish have a characteristic horizontal‐stripe pigment pattern made by a specific distribution of three types of pigment cells: melanophores, xanthophores, and iridophores. This pattern is a valuable model to investigate how the spatial patterns form during animal development. Although recent findings suggest that the interactions among the pigment cells play a key role, the particular details of these interactions have not yet been clarified. In this report, we performed transmission electron microscopic study to show the distribution, conformation, and how the cells contact with each other in the hypodermis. We found that the pigment cells form complex but ordered, layered structures in both stripe and interstripe regions. The order of the layered structures is kept strictly all through the hypodermal regions. Our study will provide basic information to investigate the mechanism of pigment pattern formation in zebrafish. Developmental Dynamics 227:497–503, 2003.

Pigment cell distributions in different tissues of the zebrafish, with special reference to the striped pigment pattern.

The orderly pigment pattern of zebrafish (Danio rerio) is a good model system for studying how spatial patterns form in animals. Recent molecular genetic studies have shown that interactions between the pigment cells play major roles in pattern formation. In the present study, we performed comparative transmission electron microscopy of pigment cells, in order to clarify the structural interactions of pigment cells in tissues with and without a striped pattern. In patterned tissues, pigment cells were distributed as a one‐cell‐thick sheet. The layer order of the sheets is always kept strictly. In tissues without a striped pattern, the layer order was often disturbed or the cells were distributed in a scattered, double‐sheeted, or an accumulated pile. Our observations suggest that the underlying mechanism that controls the vertical order of the pigment cells is related to that controlling the stripe pattern. Developmental Dynamics 234:293–300, 2005.