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

Asai, Rihito; Taguchi, Emiko; Kume, Yukari; Saito, Mayumi; Kondo, Shigeru

doi:10.1016/s0925-4773(99)00211-7

Cited by 124 publications

(134 citation statements)

References 14 publications

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“…Note the transition of the stripes by changing the ␦ u (or ␦ v ) from O to A (or I ). Quantitatively, the same results were obtained even if we used different reaction terms (Shoji et al, 2002;for example, f(u,v) [Kondo and Asai, 1995;Asai et al, 1999]) or a different form of anisotropy (for example, D ϭ 1 ϩ ␦ cos 2 , ϭ u or v, as proposed by Kobayashi, 1993).…”

Section: Discussionsupporting

confidence: 67%

“…To show that the result of the simulation is not specific to a particular equation, but rather to the general property of the RD pattern, we used three different forms of reaction terms that satisfy the Turing conditions (e.g., Murray, 1989) and form stripes in a two-dimensional field. The equations we tested are the models of activator-depleted substrate type (Gierer and Meinhardt, 1972), linear type with saturation (Kondo and Asai, 1995;Asai et al, 1999), and activator-inhibitor type (Gierer and Meinhardt, 1972). Because we obtained basically the same results from all of these models, only the results from the activator-depleted substrate type model are shown below.…”

Section: Reaction-diffusion Modelmentioning

confidence: 99%

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Origin of directionality in the fish stripe pattern

Shoji

Mochizuki

Iwasa

et al. 2003

Developmental Dynamics

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The formation of stripe patterns in animal skin has been explained by the reaction-diffusion (RD) system, a hypothetical chemical reaction proposed by A. Turing. Although animal stripes usually have directionality, the RD model alone cannot explain how the direction is specified. To investigate the mechanism regulating the direction of stripes, we studied stripe pattern formation in two species of Genicanthus during sexual conversion. These species share almost identical morphologic properties, except for their stripe direction. In both species, spots transiently arise at random positions and then combine and rearrange to form directional stripes. Computational analysis has shown that diffusion anisotropy is very effective at specifying the direction of stripes formed by the RD system. Model simulations reproduce the transient dynamics of directional pattern formation observed in fish as well as the resulting stripes. In cases where the magnitude and direction of diffusion anisotropy of the substances are identical, the resulting stripes are not directional. However, if they differ, stripes become directional. As only a small difference in anisotropy is required for this effect, any kind of structure with directional conformation might cause a marked change in stripe direction. Scales are the most likely candidate structure for generating anisotropic interactions in skin. Developmental Dynamics 226:627-633, 2003.

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Section: Discussionsupporting

confidence: 67%

Section: Reaction-diffusion Modelmentioning

confidence: 99%

Origin of directionality in the fish stripe pattern

Shoji

Mochizuki

Iwasa

et al. 2003

Developmental Dynamics

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“…This mechanism implies that R8s are chosen earlier than previously thought, during the initial process of induction. Unlike previous scenarios (8,9), the switch and template mechanism predicts that genetically identical tissue can readily sustain different patterns depending on initial conditions, as we verify experimentally.…”

supporting

confidence: 49%

A dynamical model of ommatidial crystal formation

Lubensky¹,

Pennington

Shraiman

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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The crystalline photoreceptor lattice in the Drosophila eye is a paradigm for pattern formation during development. During eye development, activation of proneural genes at a moving front adds new columns to a regular lattice of R8 photoreceptors. We present a mathematical model of the governing activator-inhibitor system, which indicates that the dynamics of positive induction play a central role in the selection of certain cells as R8s. The "switch and template" patterning mechanism we observe is mathematically very different from the well-known Turing instability. Unlike a standard lateral inhibition model, our picture implies that R8s are defined before the appearance of the complete group of proneural cells. The model reproduces the full time course of proneural gene expression and accounts for specific features of the refinement of proneural groups that had resisted explanation. It moreover predicts that perturbing the normal template can lead to eyes containing stripes of R8 cells. We observed these stripes experimentally after manipulation of the Notch and scabrous genes. Our results suggest an alternative to the generally assumed mode of operation for lateral inhibition during development; more generally, they hint at a broader role for bistable switches in the initial establishment of patterns as well as in their maintenance.imaginal disc | neural fate specification R egular patterns of cell fate appear widely in biology, and it has long been a major challenge to explain how such de novo patterning occurs during development. The R8 photoreceptor lattice in the Drosophila melanogaster eye is a particularly striking example. The adult Drosophila eye comprises ∼750 ommatidia, each composed of photoreceptors and support cells, packed in a crystalline array (1). These ommatidia are founded by R8 photoreceptors, whose orderly alignment takes shape in the wake of the morphogenetic furrow (MF) that moves from posterior to anterior across the eye imaginal disc during the third larval instar ( Fig. 1) (2). The emergence of a solitary R8 from within a proneural group of competent cells has parallels in many examples of neural and neuronal fate specification (3,4). This selection of a neural precursor through lateral inhibition is generally believed to involve an instability whereby feedback loops reinforce random fluctuations to choose one among a collection of equivalent cells (5-7). Here, we present a mathematical model of R8 selection and spacing that suggests a different scenario. This model turns out to generate patterns through a "switch and template" mechanism at whose heart is a cell-autonomous, bistable switch that takes one state in the R8s and another in the surrounding, undifferentiated cells. Whether a cell switches from undifferentiated to R8 depends primarily on the balance between inductive and inhibitory signals emanating from more mature cells to its posterior; direct inhibitory interactions among neighboring cells play a secondary role, preventing the appearance of superfluous R8s after the ini...

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“…For example, a wide range of mutant strains of zebrafish have been identified that exhibit altered pigmentation patterns. In the case of mutations of one gene in particular, the leopard gene, it is possible to match the observed allelic sequence by smoothly varying a parameter in a Turing-type model (19). This lends further support to the notion that a self-organizing process is at work in this system.…”

Section: If Morphogens Cued Cell Differentiation Then Natural Pattersupporting

confidence: 54%

How the mouse got its stripes

Maini

2003

Proc. Natl. Acad. Sci. U.S.A.

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

Cited by 124 publications

References 14 publications

Origin of directionality in the fish stripe pattern

Origin of directionality in the fish stripe pattern

A dynamical model of ommatidial crystal formation

How the mouse got its stripes

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