Models for the generation and interpretation of gradients

Turing's theory of morphogenesis of 1952 and the subsequent discovery of the crucial role of local self-enhancement and long-range inhibition

In his pioneering work, Alan Turing showed that de novo pattern formation is possible if two substances interact that differ in their diffusion range. Since then, we have shown that pattern formation is possible if, and only if, a self-enhancing reaction is coupled with an antagonistic process of longer range. Knowing this crucial condition has enabled us to include nonlinear interactions, which are required to design molecularly realistic interactions. Different reaction schemes and their relation to Turing's proposal are discussed and compared with more recent observations on the molecular-genetic level. The antagonistic reaction may be accomplished by an inhibitor that is produced in the activated region or by a depletion of a component that is used up during the self-enhancing reaction. The autocatalysis may be realized by an inhibition of an inhibition. Activating molecules can be processed into molecules that have an inhibiting function; patterning of the Wnt pathway is proposed to depend on such a mechanism. Three-component systems, as discussed in Turing's paper, are shown to play a major role in the generation of highly dynamic patterns that never reach a stable state.

The Tale of the Three Brothers - Shh, Wnt, and Fgf during Development of the Thalamus

The thalamic complex is an essential part of the brain that requires a combination of specialized activities to attain its final complexity. In the following review we will describe the induction process of the mid-diencephalic organizer (MDO) where three different signaling pathways merge: Wnt, Shh, and Fgf. Here, we dissect the function of each signaling pathway in the thalamus in chronological order of their appearance. First we describe the Wnt mediated induction of the MDO and compartition of the caudal forebrain, then the Shh mediated determination of proneural gene expression before discussing recent progress in characterizing Fgf function during thalamus development. Then, we focus on transcription factors, which are regulated by these pathways and which play a pivotal role in neurogenesis in the thalamus. The three signaling pathways act together in a strictly regulated chronology to orchestrate the development of the entire thalamus.

Modeling planarian regeneration: a primer for reverse-engineering the worm

A mechanistic understanding of robust self-assembly and repair capabilities of complex systems would have enormous implications for basic evolutionary developmental biology as well as for transformative applications in regenerative biomedicine and the engineering of highly fault-tolerant cybernetic systems. Molecular biologists are working to identify the pathways underlying the remarkable regenerative abilities of model species that perfectly regenerate limbs, brains, and other complex body parts. However, a profound disconnect remains between the deluge of high-resolution genetic and protein data on pathways required for regeneration, and the desired spatial, algorithmic models that show how self-monitoring and growth control arise from the synthesis of cellular activities. This barrier to progress in the understanding of morphogenetic controls may be breached by powerful techniques from the computational sciences-using non-traditional modeling approaches to reverse-engineer systems such as planaria: flatworms with a complex bodyplan and nervous system that are able to regenerate any body part after traumatic injury. Currently, the involvement of experts from outside of molecular genetics is hampered by the specialist literature of molecular developmental biology: impactful collaborations across such different fields require that review literature be available that presents the key functional capabilities of important biological model systems while abstracting away from the often irrelevant and confusing details of specific genes and proteins. To facilitate modeling efforts by computer scientists, physicists, engineers, and mathematicians, we present a different kind of review of planarian regeneration. Focusing on the main patterning properties of this system, we review what is known about the signal exchanges that occur during regenerative repair in planaria and the cellular mechanisms that are thought to underlie them. By establishing an engineering-like style for reviews of the molecular developmental biology of biomedically important model systems, significant fresh insights and quantitative computational models will be developed by new collaborations between biology and the information sciences.

Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system

Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients revealed that Nodals have a shorter range than Lefty proteins. Pulse-labeling analysis indicated that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays revealed that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning.

Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain

Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co-express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

The interplay between morphogens and tissue growth

Morphogens are conserved, secreted signalling molecules that regulate the size, shape and patterning of animal tissues and organs. Recent experimental evidence has emphasized the fundamental role of tissue growth in expanding the expression domains of morphogens and their target genes, in generating morphogen gradients and in modulating the response of cells to morphogens. Moreover, the classic view of how morphogens, particularly through their concentration gradient, regulate tissue size during development has been revisited recently. In this review, we discuss how morphogens and tissue growth affect each other, and we attempt to integrate genetic and molecular evidence from vertebrate and invertebrate model systems to put forward the idea that the interaction between growth and morphogens is a general feature of highly proliferative tissues.

Systems control of BMP morphogen flow in vertebrate embryos

Embryonic morphogenetic programs coordinate cell behavior to ensure robust pattern formation. Having identified components of those programs by molecular genetics, developmental biology is now borrowing concepts and tools from systems biology to decode their regulatory logic. Dorsal-ventral (D-V) patterning of the frog gastrula by Bone Morphogenetic Proteins (BMPs) is one of the best studied examples of a self-regulating embryonic patterning system. Embryological analyses and mathematical modeling are revealing that the BMP activity gradient is maintained by a directed flow of BMP ligands towards the ventral side. Pattern robustness is ensured through feedback control of the levels of extracellular BMP pathway modulators that adjust the flow to the dimensions of the embryonic field.

Color-pattern analysis of eyespots in butterfly wings: a critical examination of morphogen gradient models

Butterfly wing color patterns consist of many color-pattern elements such as eyespots. It is believed that eyespot patterns are determined by a concentration gradient of a single morphogen species released by diffusion from the prospective eyespot focus in conjunction with multiple thresholds in signal-receiving cells. As alternatives to this single-morphogen model, more flexible multiple-morphogen model and induction model can be proposed. However, the relevance of these conceptual models to actual eyespots has not been examined systematically. Here, representative eyespots from nymphalid butterflies were analyzed morphologically to determine if they are consistent with these models. Measurement of ring widths of serial eyespots from a single wing surface showed that the proportion of each ring in an eyespot is quite different among homologous rings of serial eyespots of different sizes. In asymmetric eyespots, each ring is distorted to varying degrees. In extreme cases, only a portion of rings is expressed remotely from the focus. Similarly, there are many eyespots where only certain rings are deleted, added, or expanded. In an unusual case, the central area of an eyespot is composed of multiple "miniature eyespots," but the overall macroscopic eyespot structure is maintained. These results indicate that each eyespot ring has independence and flexibility to a certain degree, which is less consistent with the single-morphogen model. Considering a "periodic eyespot", which has repeats of a set of rings, damage-induced eyespots in mutants, and a scale-size distribution pattern in an eyespot, the induction model is the least incompatible with the actual eyespot diversity.

Morphogen gradients: from generation to interpretation

Morphogens are long-range signaling molecules that pattern developing tissues in a concentration-dependent manner. The graded activity of morphogens within tissues exposes cells to different signal levels and leads to region-specific transcriptional responses and cell fates. In its simplest incarnation, a morphogen signal forms a gradient by diffusion from a local source and clearance in surrounding tissues. Responding cells often transduce morphogen levels in a linear fashion, which results in the graded activation of transcriptional effectors. The concentration-dependent expression of morphogen target genes is achieved by their different binding affinities for transcriptional effectors as well as inputs from other transcriptional regulators. Morphogen distribution and interpretation are the result of complex interactions between the morphogen and responding tissues. The response to a morphogen is dependent not simply on morphogen concentration but also on the duration of morphogen exposure and the state of the target cells. In this review, we describe the morphogen concept and discuss the mechanisms that underlie the generation, modulation, and interpretation of morphogen gradients.

Coordination of cell differentiation and migration in mathematical models of caudal embryonic axis extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation.

Early planarian brain regeneration is independent of blastema polarity mediated by the Wnt/β-catenin pathway

Analysis of anteroposterior (AP) axis specification in regenerating planarian flatworms has shown that Wnt/β-catenin signaling is required for posterior specification and that the FGF-like receptor molecule nou-darake (ndk) may be involved in restricting brain regeneration to anterior regions. The relationship between re-establishment of AP identity and correct morphogenesis of the brain is, however, still poorly understood. Here we report the characterization of two axin paralogs in the planarian Schmidtea mediterranea. Although Axins are well known negative regulators of Wnt/β-catenin signaling, no role in AP specification has previously been reported for axin genes in planarians. We show that silencing of Smed-axin genes by RNA interference (RNAi) results in two-tailed planarians, a phenotype previously reported after silencing of Smed-APC-1, another β-catenin inhibitor. More strikingly, we show for the first time that while early brain formation at anterior wounds remains unaffected, subsequent development of the brain is blocked in the two-tailed planarians generated after silencing of Smed-axin genes and Smed-APC-1. These findings suggest that the mechanisms underlying early brain formation can be uncoupled from the specification of AP identity by the Wnt/β-catenin pathway. Finally, the posterior expansion of the brain observed following Smed-ndk RNAi is enhanced by silencing Smed-APC-1, revealing an indirect relationship between the FGFR/Ndk and Wnt/β-catenin signaling systems in establishing the posterior limits of brain differentiation.

Positional information and patterning revisited

The concept of positional information proposes that cells acquire positional values as in a coordinate system, which they interpret by developing in particular ways to give rise to spatial patterns. Some of the best evidence for positional information comes from regeneration experiments, and the patterning of the leg and antenna in Drosophila and the vertebrate limb. Central problems are how positional information is set up, how it is recorded, and then how it is interpreted by the cells. A number of models have been proposed for the setting up of positional gradients, and most are based on diffusion of a morphogen and its interactions with extracellular molecules. It is argued that diffusion may not be reliable mechanism. There are also mechanisms based on timing. There is no good evidence for the quantitative aspects of any of the gradients and details how they are set up. The way in which a signalling gradient regulates differential gene expression in a concentration-dependent manner also raises several mechanistic issues.

Axial patterning in hydra

Morphogen gradients play an important role in pattern formation during early stages of embryonic development in many bilaterians. In an adult hydra, axial patterning processes are constantly active because of the tissue dynamics in the adult. These processes include an organizer region in the head, which continuously produces and transmits two signals that are distributed in gradients down the body column. One signal sets up and maintains the head activation gradient, which is a morphogenetic gradient. This gradient confers the capacity of head formation on tissue of the body column, which takes place during bud formation, hydra's mode of asexual reproduction, as well as during head regeneration following bisection of the animal anywhere along the body column. The other signal sets up the head inhibition gradient, which prevents head formation, thereby restricting bud formation to the lower part of the body column in an adult hydra. Little is known about the molecular basis of the two gradients. In contrast, the canonical Wnt pathway plays a central role in setting up and maintaining the head organizer.