How animals get their skin patterns: fish pigment pattern as a live Turing wave

Abstract

It is more than fifty years since Alan Turing first presented the reaction-diffusion (RD) model, to account for the mechanism of biological pattern formation. In the paper entitled "The chemical basis of morphogenesis", Turing concluded that spatial patterns autonomously made in the embryo are generated as the stationary wave of the chemical (cellular) reactions. Although this novel idea was paid little attention by experimental biologists, recent experimental data are suggesting that the RD mechanism really functions in some of the course of animal development. Among the phenomena in which involvement of the RD mechanism is suspected, the striped pigment pattern of zebrafish has been highlighted as an ideal model system for the following reasons: the stationary wave made by the RD mechanism stays alive and can be observed only in the fish skin; and in zebrafish, we can utilize genomic information and molecular genetic techniques to clarify the molecular basis of pattern formation. In this review, we summarize recent progresses in the study of zebrafish pigment pattern formation that is uncovering how the RD wave is made and maintained in the skin.

The Dynamics of Turing Patterns for Morphogen-Regulated Growing Domains with Cellular Response Delays

“…Recent models of the development of fish patterning suggest that the Turing mechanism should be considered with different cell types fulfilling the roles of activator and inhibitor rather than diffusible morphogens (Nakamasu et al 2009;Kondo et al 2009). Then the gene expression dynamics considered above are absent and any retardation in the interaction of model constituents arises from the constraints of cellular dynamics, such as the cell cycle.…”

How Does Cellular Contact Affect Differentiation Mediated Pattern Formation?

“…3 are not sufficiently wide to be realistic melanophore stripes. Therefore, although our system is clearly able to produce patterning for other systems which contain narrower stripes, we conclude that a community effect is insufficient in itself as a mechanism for creating stripes and other patterns in zebrafish; permanent and accurate stripe formation requires coupling with a stronger mechanism such as homotypic cellular attraction (Caicedo-Carvajal and Shinbrot 2008;Maderspacher and Nusslein-Volhard 2003), intercellular adhesion (Moreira and Deutsch 2005), or indeed, perhaps something entirely different such as a reaction-diffusion system (see Kondo et al 2009 for a review).…”

A Neurochemical Basis for Phenotypic Differentiation in Alzheimer's Disease? Turing's Morphogens Revisited

“…As originally proposed, Turing's theory eschewed scenarios far from the onset of inhomogeneity and did not explicitly model changing temporal dynamics: these scenarios are clearly apposite to AD and may be more effectively addressed using more recent extensions of the theory, including the incorporation of temporal Hopf instabilities (Kondo et al, 2009; Steyn-Ross et al, 2009, 2013; Kondo, 2016). …”