Turing patterns in development: what about the horse part?

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For many years Turing patterns  the repetitive patterns which Alan Turing proved could arise from simple diffusing and interacting factors  have remained an interesting theoretical possibility, rather than a central concern of the developmental biology community. Recently however, this has started to change, with an increasing number of studies combining both experimental and theoretical work to reveal how Turing models may underlie a variety of patterning or morphogenetic processes. We review here the recent developments in this field across a wide range of model systems.

Introduction

For a long time it has been recognized that two fundamentally different mechanisms exist for creating spatially-organised patterns in multicellular systems. The more prominent theory during the last few decades has been that of positional information, as described by Lewis Wolpert over 40 years ago [1]. The most familiar form of this theory involves a diffusible molecule which is produced asymmetrically and thus creates a spatial concentration gradient. Each position along this gradient has a unique concentration, thus giving cells direct access to information about where they are in the field, and to make the appropriate cell fate choices. The alternative theory was first proposed 27 years earlier, by Alan Turing [2]. In this model two chemical species can react with each other and diffuse through the tissue (hence the common name of reaction–diffusion model). If the reaction and diffusion constants are set just right (e.g. A is an activator of both species, I is an inhibitor of both species and I diffuses faster than A) then an initially homogeneous concentration can spontaneously break the uniform state and form periodic patterns  peaks and valleys of concentration  which in 2D may take the form of spots or stripes, such as the coat pattern of leopards or zebras (depending on the parameter values). A critical difference of this mechanism compared to a positional information gradient is that each position in space does not have a unique concentration. Thus cells with the maximal ‘peak’ concentration have no way to distinguish which peak they are in  they do not have unambiguous positional information (Figure 1).

In most cases, the two theories are not considered to be alternative explanations for the same patterning task. The Wolpert model is mostly relevant to regionalization (e.g. positioning the head at one end of the embryo, and the tail at the other), while Turing mechanisms are most relevant to repetitive, periodic patterns (such as the zebra's stripes). However, the theories were for a long time seen as competing against each other  at least for their conceptual importance to the field of developmental biology  and Turing's model generally seemed to lose out [3]. Interestingly, even Turing himself apparently had doubts about the importance of his model. Regarding the zebra he allegedly exclaimed ‘Well the stripes are easy, but what about the horse part?’ [4]. This has been interpreted in at least two different ways. Firstly, as an acknowledgement that animal coat patterns are often considered less important to developmental biology than morphogenesis. Secondly, that Turing patterns, although elegant are rather simple  just a repetitive sequence of alternative states (on, off, on, off, etc.)  whereas building the ‘horse part’ of the zebra, with it's body plan, internal organs and skeletal arrangement, must require much more complicated and sophisticated patterning processes.

However, the last decade has seen a gradual but steady revival in the interest in Turing's model  especially in projects that have combined mathematical modeling with experimental approaches. Excitingly, new studies are increasingly countering Turing's own doubts about the relevance to morphogenesis  more examples are emerging in which the Turing mechanism may control the structural arrangement of an organ's tissues, such as branching patterns in lung development and digital pattern in limb development (described towards the end of this review). It is particularly fitting this year to review some of the key systems for which evidence is accumulating  firstly because of the recent crop of papers on this topic (12 papers over the last 2 years), and secondly because 2012 is the centenary of Alan Turing's birth.

Section snippets

Left-right asymmetry

Several studies in zebrafish, frog and mouse [5, 6] have revealed that left-right asymmetry in early bilaterian embryos is governed mainly by two diffusible proteins of the Tgf-family: Nodal and Lefty. The first is a ligand that signals through the receptor Alk4 and EGF-CFC co-receptors, and the second is a molecule that inhibits Nodal signaling by sequestration and competitive binding to its co-receptor. Many functional experiments had confirmed that these two proteins fulfill the requirements

Patterns in the skin  feathers

The patterning of skin appendages (such as hair follicles and feathers) are natural systems to consider a Turing model as they involve the positioning of repetitive, evenly-spaced structures (Figure 2b). The first molecular evidence for a reaction–diffusion in skin appendage patterning proposed that Sonic Hedgehog (SHH) and a member of the Fibroblast Growth Factor family (Fgf4) acted as activators of feather primordia, and that the Bone Morphogenetic Proteins (Bmp2 and Bmp4) acted as inhibitors

Patterns in the skin  hair follicles

The other main skin appendage for which a reaction–diffusion system was proposed is hair follicle specification (Figure 2c). This was first hypothesised in the early eighties [20, 21], however molecular evidence only started to emerge 3 decades later. In 2006 a study in mice proposed that Wnts and their inhibitors Dkks were the Turing molecules responsible for follicular patterning [22]. A Wnt signaling lacZ reporter revealed that signaling was active on the developing hair follicle. Moreover,

Patterns in the skin  fish stripes

Ironically, one of the originally proposed Turing systems has been revealed by more recent work, not to be a strict molecular reaction–diffusion system. In 1995 a pioneering study by Kondo and Asai demonstrated Turing-type spatio-temporal dynamics of a in a natural biological system  the stripes formed by the arrangement of pigmented scales on fish [26]. The dynamic rearrangement of the fish stripes after some parts were laser-ablated showed a striking concordance with numerical simulations of a

Lung branching

Another system proposed to operate by reaction–diffusion is lung branching [32], but only recently has a Turing model been developed that describes it [33]. This model is based on the interaction between two signaling molecules expressed in the lung bud tip: Fgf10 and Shh (Figure 2d). Fgf10 is produced at high levels only in the mesenchyme and diffuses to stimulate growth. In addition, Fgf10 signaling promotes the expression of Shh, which in turn inhibits the expression of Fgf10. An

Ruggae

Another recent study has revealed a Turing system in an unexpected tissue  the ridges which form on the roof of the mammalian palate, called ruggael [34]. In mouse, the specification of new ruggae happens as the palate grows, and experimental removal of a stripe induces new stripes protruding out perpendicular from the remaining stripes (Figure 2e). Similar to the stripe ablation in zebrafish, the behaviour of the system thus fits with two-dimensional simulations of a Turing model. It was also

Digital patterning

Polydactyly  the development of extra digits  is a relatively common abnormality during limb development, both for humans and in mouse mutants. Already many years ago, this observation lead to the hypothesis that a Turing mechanism may be the underlying patterning mechanism [35]. However, one key prediction of a Turing model had not been clearly documented until recently. Although many previous polydactylies contain multiple normal-sized digits, which may result from the development of an

Conclusions

One of the most important questions in the field is the identity of the Turing molecules. Evidence exists in most of the examples described above for some of the key molecules. However, multiple questions remain, even for those that have been relatively well-studied: Given that many developmental systems exhibit widespread redundancy in their regulatory networks, can simple 2-species systems accurately represent the underlying mechanism? Moreover, are there principles underlying the pairs of

References and recommended reading

Papers of particular interest, published within the period of review, have been highlighted as:

  • • of special interest

  • •• of outstanding interest

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