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Embryonic development is a largely self-organizing process, in which the adult body plan arises from a ball of cells with initially nearly equal potency. The reaction-diffusion theory first proposed by Alan Turing states that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of patterns. The reaction-diffusion theory provides a valuable framework for self-organized pattern formation, but it has been difficult to relate simple two-component models to real biological systems with multiple interacting molecular species. Recent studies have addressed this shortcoming and extended the reaction-diffusion theory to realistic multi-component networks. These efforts have challenged the generality of previous central tenets derived from the analysis of simplified systems and guide the way to a new understanding of self-organizing processes. Here, we discuss the challenges in modeling multi-component reaction-diffusion systems and how these have recently been addressed. We present a synthesis of new pattern formation mechanisms derived from these analyses, and we highlight the significance of reaction-diffusion principles for developmental and synthetic pattern formation., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

The tentacular system of Clytia hemisphaerica medusa (Cnidaria, Hydrozoa) has recently emerged as a promising experimental model to tackle the developmental mechanisms that regulate cell lineage progression in an early-diverging animal phylum. From a population of proximal stem cells, the successive steps of tentacle stinging cell (nematocyte) elaboration, are spatially ordered along a "cellular conveyor belt". Furthermore, the C. hemisphaerica tentacular system exhibits bilateral organisation, with two perpendicular polarity axes (proximo-distal and oral-aboral). We aimed to improve our knowledge of this cellular system by combining RNAseq-based differential gene expression analyses and expression studies of Wnt signalling genes. RNAseq comparisons of gene expression levels were performed (i) between the tentacular system and a control medusa deprived of all tentacles, nematogenic sites and gonads, and (ii) between three samples staggered along the cellular conveyor belt. The behaviour in these differential expression analyses of two reference gene sets (stem cell genes; nematocyte genes), as well as the relative representations of selected gene ontology categories, support the validity of the cellular conveyor belt model. Expression patterns obtained by in situ hybridisation for selected highly differentially expressed genes and for Wnt signalling genes are largely consistent with the results from RNAseq. Wnt signalling genes exhibit complex spatial deployment along both polarity axes of the tentacular system, with the Wnt/β-catenin pathway probably acting along the oral-aboral axis rather than the proximo-distal axis. These findings reinforce the idea that, despite overall radial symmetry, cnidarians have a full potential for elaboration of bilateral structures based on finely orchestrated deployment of an ancient developmental gene toolkit., (Copyright © 2019. Published by Elsevier Inc.)

The reproducibility of embryonic development is remarkable, although molecular processes are intrinsically stochastic at the single-cell level. How the multicellular system resists the inevitable noise to acquire developmental reproducibility constitutes a fundamental question in developmental biology. Toward this end, we focused on vertebrate somitogenesis as a representative system, because somites are repeatedly reproduced within a single embryo whereas such reproducibility is lost in segmentation clock gene-deficient embryos. However, the effect of noise on developmental reproducibility has not been fully investigated, because of the technical difficulty in manipulating the noise intensity in experiments. In this study, we developed a computational model of ERK-mediated somitogenesis, in which bistable ERK activity is regulated by an FGF gradient, cell-cell communication, and the segmentation clock, subject to the intrinsic noise. The model simulation generated our previous in vivo observation that the ERK activity was distributed in a step-like gradient in the presomitic mesoderm, and its boundary was posteriorly shifted by the clock in a stepwise manner, leading to regular somite formation. Here, we showed that this somite regularity was robustly maintained against the noise. Removing the clock from the model predicted that the stepwise shift of the ERK activity occurs at irregular timing with irregular distance owing to the noise, resulting in somite size variation. This model prediction was recently confirmed by live imaging of ERK activity in zebrafish embryos. Through theoretical analysis, we presented a mechanism by which the clock reduces the inherent somite irregularity observed in clock-deficient embryos. Therefore, this study indicates a novel role of the segmentation clock in noise-resistant developmental reproducibility., Competing Interests: The authors have declared that no competing interests exist.

Humans (at least a select few) have long known about the cephalochordate amphioxus, first as something to eat and later as a subject for scientific study. The rate of publication on these animals has waxed and waned several times. The first big surge, in the late nineteenth century, was stimulated by Darwin's evolutionary ideas and by Kowalevsky's embryologic findings suggesting that an amphioxus-like creature might have bridged the gap between the invertebrates and the vertebrates. Interest declined sharply in the early twentieth century and remained low for the next 50 years. An important contributing factor (in addition to inhibition by two world wars and the Great Depression) was the indifference of the new evolutionary synthesis toward broad phylogenetic problems like the origin of the vertebrates. Then, during the 1960s and 1970s, interest in amphioxus resurged, driven especially by increased government support for basic science as well as opportunities presented by electron microscopy. After faltering briefly in the 1980s (electron microscopists were running out of amphioxus tissues to study), a third and still-continuing period of intensive amphioxus research began in the early 1990s, stimulated by the advent of evolutionary developmental biology (evo-devo) and genomics. The volume of studies peaked in 2008 with the publication of the genome of the Florida amphioxus. Since then, although the number of papers per year has dropped somewhat, sequencing of additional genomes and transcriptomes of several species of amphioxus (both in the genus Branchiostoma and in a second genus, Asymmetron) is providing the raw material for addressing the major unanswered question of the relationship between genotype and phenotype.

How periodic patterns are generated is an open question. A number of mechanisms have been proposed--most famously, Turing's reaction-diffusion model. However, many theoretical and experimental studies focus on the Turing mechanism while ignoring other possible mechanisms. Here, we use a general model of periodic patterning to show that different types of mechanism (molecular, cellular, mechanical) can generate qualitatively similar final patterns. Observation of final patterns is therefore not sufficient to favour one mechanism over others. However, we propose that a mathematical approach can help to guide the design of experiments that can distinguish between different mechanisms, and illustrate the potential value of this approach with specific biological examples., (© 2015. Published by The Company of Biologists Ltd.)

In this review we consider Reaction-Diffusion as the archetype of a model in developmental biology. We consider its history in relation to experimental work since it was first proposed in 1952 by Turing and revived in the 1970s by Meinhardt. We then discuss the most recent examples of experiments that address this model, including the challenges that remain in capturing the physico-chemical manifestation of the model mechanism in a real developmental system. Finally we discuss the model's current status and use in the experimental community., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Patterning is an important step in animal development that generates spatially non-uniform gene expression patterns or spatially heterogeneous cellular responses. Patterning is realised by the generation and reading of positional information provided by spatial gradients of morphogens, diffusive chemicals in the extracellular environment. To achieve normal development, accurate patterning that is robust against noise is necessary. Here the authors describe how morphogen gradient formation and gradient interpretation processes are designed to achieve highly reproducible patterning. Furthermore, recent advancements in measurement and imaging techniques have enabled researchers to obtain quantitative dynamic and multi-physical data, not only for chemical events, but also for the geometrical and mechanical properties of cells in vivo. The authors briefly review some recent studies on the effects of such non-chemical events on patterning.

The tenth annual RIKEN Center for Developmental Biology symposium 'Quantitative Developmental Biology' held in March 2012 covered a range of topics from coat colour patterning to the mechanics of morphogenesis. The studies presented shared a common theme in which a combination of physical theory, quantitative analysis and experiment was used to understand a specific cellular process in development. This report highlights these innovative studies and the long-standing questions in developmental biology that they seek to answer.

A schema is proposed by which the three-dimensional structure and temporal development of a biological organism might be encoded and implemented via a genetic "lookup table". In the schema, diffusive morphogen gradients and/or the global concentration of a quickly diffusing signal index sets of kinase genes having promoters with logarithmically diminished affinity for the signal. Specificity of indexing is enhanced via concomitant expression of phosphatases undoing phosphorylation by "neighboring" kinases of greater affinity. Combinations of thus-selected kinases in turn jointly activate, via multiple phosphorylation, a particular enzyme from a virtual, multi-dimensional array thereof, at locations and times specified within the "lookup table". In principle, such a scheme could be employed to specify arbitrary gross anatomy, surface pigmentation, and/or developmental sequencing, extending the burgeoning toolset of the nascent field of synthetic morphology. A model of two-dimensional surface coloration using this scheme is specified, and LabVIEW software for its exploration is described and made available.

The development of an anterior-posterior (AP) polarity is a crucial process that in the mouse has been very difficult to analyse, because it takes place as the embryo implants within the mother. To overcome this obstacle, we have established an in-vitro culture system that allows us to follow the step-wise development of anterior visceral endoderm (AVE), critical for establishing AP polarity. Here we use this system to show that the AVE originates in the implanting blastocyst, but that additional cells subsequently acquire AVE characteristics. These 'older' and 'younger' AVE domains coalesce as the egg cylinder emerges from the blastocyst structure. Importantly, we show that AVE migration is led by cells expressing the highest levels of AVE marker, highlighting that asymmetry within the AVE domain dictates the direction of its migration. Ablation of such leading cells prevents AVE migration, suggesting that these cells are important for correct establishment of the AP axis.

Determination of left-right asymmetry in mouse embryos is achieved by a leftward fluid flow (nodal flow) in the node cavity that is generated by clockwise rotational movement of 200-300 cilia in the node. The precise action of nodal flow and how much flow input is required for the robust read-out of left-right determination remains unknown. Here we show that a local leftward flow generated by as few as two rotating cilia is sufficient to break left-right symmetry. Quantitative analysis of fluid flow and ciliary rotation in the node of mouse embryos shows that left-right asymmetry is already established within a few hours after the onset of rotation by a subset of nodal cilia. Examination of various ciliary mutant mice shows that two rotating cilia are sufficient to initiate left-right asymmetric gene expression. Our results suggest the existence of a highly sensitive system in the node that is able to sense an extremely weak unidirectional flow, and may favour a model in which the flow is sensed as a mechanical force.

In a bilaterally symmetric animal, the midline plays a key role in directing axon growth during wiring of the nervous system. Midline cells provide a variety of guidance cues for growing axons, to which different types of axons respond in different ways and at different times. For some axons, the midline is an intermediate target. They first seek it out, but then move on towards their final targets on the opposite side. For others, the midline is a repulsive barrier that keeps them on their own side of the midline. And for many of these axons the midline provides signals that guide them along specific lateral pathways or up and down the longitudinal axis.

The enormous diversity of extant animal forms is a testament to the power of evolution, and much of this diversity has been achieved through the emergence of novel morphological traits. The origin of novel morphological traits is an extremely important issue in biology, and a frequent source of this novelty is co-option of pre-existing genetic systems for new purposes (Carroll et al., 2008). Appendages, such as limbs, fins and antennae, are structures common to many animal body plans which must have arisen at least once, and probably multiple times, in lineages which lacked appendages. We provide evidence that appendage proximodistal patterning genes are expressed in similar registers in the anterior embryonic neurectoderm of Drosophila melanogaster and Saccoglossus kowalevskii (a hemichordate). These results, in concert with existing expression data from a variety of other animals suggest that a pre-existing genetic system for anteroposterior head patterning was co-opted for patterning of the proximodistal axis of appendages of bilaterian animals., (Copyright (c) 2010 Elsevier Inc. All rights reserved.)

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.

In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.

Patterns are orders embedded in randomness; they may appear in spatial arrangements or in temporal sequences, and each element may appear identical or with variations. Patterns exist in the physical world as well as in living systems. In the biological world, patterns can range from simple to complex, forming the basic building blocks of life. When we see patterns in peacock feathers, leopard spots or zebra stripes, we are fascinated by the order, the variations and the beauty. The process that generates this ordering in the biological world has been termed Pattern Formation. Since Lewis Wolpert promoted this concept four decades ago, scientists from molecular biology, developmental biology, stem cell biology, tissue engineering, theoretical modeling and other disciplines have made remarkable progress towards understanding its underlying mechanisms. We have learned that both molecular processes and physico-chemical principles are important for biological Pattern Formation and as Guest Editors, felt that it is time to review and re-integrate our understanding of this fundamental and fantastic process.

In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming cues and generate spatially heterogeneous patterns. We base our discussion around two well known patterning events that take place in the early embryo: somitogenesis and feather bud formation. We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes.

This article considers the role played by a core set of "dynamical patterning modules" (DPMs) in the origination, development and evolution of complex organisms. These consist of the products of a subset of the genes of what has come to be known as the "developmental-genetic toolkit" in association with physical processes they mobilize. The physical processes are those characteristic of chemically and mechanically excitable mesoscopic systems like cell aggregates: cohesion, viscoelasticity, diffusion, spatiotemporal heterogeneity based on activator-inhibitor interaction, and multistable and oscillatory dynamics. We focus on the emergence of the Metazoa, and show how toolkit gene products and pathways that pre-existed the metazoans acquired novel morphogenetic functions simply by virtue of the change in scale and context inherent to multicellularity. We propose that DPMs, acting singly and in combination with each other, constitute a "pattern language" capable of generating all metazoan body plans and organ forms. This concept implies that the multicellular organisms of the late Precambrian-early Cambrian were phenotypically plastic, fluently exploring morphospace in a fashion decoupled from both function-based selection and genotypic change. The relatively stable developmental trajectories and morphological phenotypes of modern organisms, then, are considered to be products of stabilizing selection. This perspective solves the apparent "molecular homology-analogy paradox," whereby widely divergent modern animal types utilize the same molecular toolkit during development, but it does so by inverting the neo-Darwinian principle that phenotypic disparity was generated over long periods of time in concert with, and in proportion to genotypic change.

Basic research in pattern formation is concerned with the generation of phenotypes and tissues. It can therefore lead to new tools for medical research. These include phenotypic screening assays, applications in tissue engineering, as well as general advances in biomedical knowledge. Our aim here is to discuss this emerging field with special reference to tools based on zebrafish developmental biology. We describe phenotypic screening assays being developed in our own and other labs. Our assays involve: (i) systemic or local administration of a test compound or drug to zebrafish in vivo; (ii) the subsequent detection or "readout" of a defined phenotypic change. A positive readout may result from binding of the test compound to a molecular target involved in a developmental pathway. We present preliminary data on assays for compounds that modulate skeletal patterning, bone turnover, immune responses, inflammation and early-life stress. The assays use live zebrafish embryos and larvae as well as adult fish undergoing caudal fin regeneration. We describe proof-of-concept studies on the localised targeting of compounds into regeneration blastemas using microcarriers. Zebrafish are cheaper to maintain than rodents, produce large numbers of transparent eggs, and some zebrafish assays could be scaled-up into medium and high throughput screens. However, advances in automation and imaging are required. Zebrafish cannot replace mammalian models in the drug development pipeline. Nevertheless, they can provide a cost-effective bridge between cell-based assays and mammalian whole-organism models.

Patterns are orders embedded in randomness. They may appear as spatial arrangements or temporal series, and the elements may appear identical or with variations. Patterns exist in the physical world as well as in living systems. In the biological world, patterns can range from simple to complex, forming the basic building blocks of life. The process which generates this ordering in the biological world was termed pattern formation. Since Wolpert promoted this concept four decades ago, scientists from molecular biology, developmental biology, stem cell biology, tissue engineering, theoretical modeling and other disciplines have made remarkable progress towards understanding its mechanisms. It is time to review and re-integrate our understanding. Here, we explore the origin of pattern formation, how the genetic code is translated into biological form, and how complex phenotypes are selected over evolutionary time. We present four topics: Principles, Evolution, Development, and Stem Cells and Regeneration. We have interviewed several leaders in the field to gain insight into how their research and the field of pattern formation have shaped each other. We have learned that both molecular process and physico-chemical principles are important for biological pattern formation. New understanding will emerge through integration of the analytical approach of molecular-genetic manipulation and the systemic approach of model simulation. We regret that we could not include every major investigator in the field, but hope that this Special Issue of the Int. J. Dev. Biol. represents a sample of our knowledge of pattern formation today, which will help to stimulate more research on this fundamental process.

The control of hair growth in the adult mammalian coat is a fascinating topic which has just begun to be explored with molecular genetic tools. Complex hair cycle domains and regenerative hair waves are present in normal adult (> 2 month) mice, but more apparent in mutants with cyclic alopecia phenotypes. Each hair cycle domain consists of initiation site(s), a propagating wave and boundaries. By analyzing the dynamics of hair growth, time required for regeneration after plucking, in situ hybridization and reporter activity, we showed that there is oscillation of intra-follicular Wnt signaling which is synchronous with hair cycling, and there is oscillation of dermal bone morphogenetic protein (BMP) signaling which is asynchronous with hair cycling. The interactions of these two rhythms lead to the recognition of refractory and competent phases in the telogen, and autonomous and propagating phases in the anagen. Boundaries form when propagating anagen waves reach follicles which are in refractory telogen. Experiments showed that Krt14-Nog mice have shortened refractory telogen and simplified wave dynamics. Krt14-Nog skin grafts exhibit non-autonomous interactions with surrounding host skin. Implantation of BMP coated beads into competent telogen skin prevents hair wave propagation around the bead. Thus, we have developed a new molecular understanding of the classic early concepts of inhibitory "chalone", suggesting that stem cells within the hair follicle micro-environment, or other organs, are subject to a higher level of macro-environmental regulation. Such a novel understanding has important implications in the field of regenerative medicine. The unexpected links with Bmp2 expression in subcutaneous adipocytes has implications for systems biology and Evo-Devo.

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 developing limb is a major model for pattern formation in vertebrate embryos. Many of the seminal discoveries of the mechanisms involved in patterning have been made using chick embryos because of the ease of manipulating their developing limbs. More recently, the molecular basis of limb pattern formation has been increasingly uncovered and now, with the availability of genomic resources, the genetic approaches available are even more powerful. Nevertheless, since the limb is ultimately built of cells, gene action must ultimately be translated into cell behaviour and a major challenge will be to integrate genetics with molecular and cellular biology. In this review, we will first outline the stages in limb development, the major interacting signalling pathways that pattern the limb and the molecules involved. We will describe fate maps of the developing limb, and discuss what is known about cellular activities including proliferation, death, adhesiveness, communication and migration during the patterning process. Finally we will explore how these cell activities produce form.

Differentiation of the Drosophila compound eye from the eye imaginal disc is a progressive process: columns of cells successively differentiate in a posterior to anterior sequence, clusters of cells form at regularly spaced intervals within each column, and individual photoreceptors differentiate in a defined order within each cluster. The progression of differentiation across the eye disc is driven by a positive autoregulatory loop of expression of the secreted molecule Hedgehog, which is temporally delayed by the intercalation of a second signal, Spitz. Hedgehog refines the spatial position at which each column initiates its differentiation by inducing secondary signals that act over different ranges to control the expression of positive and negative regulators. The position of clusters within each column is controlled by secreted inhibitory signals from clusters in the preceding column, and a single founder neuron, R8, is singled out within each cluster by Notch-mediated lateral inhibition. R8 then sequentially recruits surrounding cells to differentiate by producing a short-range signal, Spitz, which induces a secondary short-range signal, Delta. Intrinsic transcription factors act in combination with these two signals to produce cell-type diversity within the ommatidium. The Hedgehog and Spitz signals are transported along the photoreceptor axons and reused within the brain as long-range and local cues to trigger the differentiation and assembly of target neurons.

One of the major goals in evolutionary developmental biology is to understand the relationship between gene regulatory networks and the diverse morphologies and their functionalities. Are the diversities solely triggered by random events, or are they inevitable outcomes of an interplay between evolving gene networks and natural selection? Segmentation in arthropod embryogenesis represents a well-known example of body plan diversity. Striped patterns of gene expression that lead to the future body segments appear simultaneously or sequentially in long and short germ-band development, respectively. Moreover, a combination of both is found in intermediate germ-band development. Regulatory genes relevant for stripe formation are evolutionarily conserved among arthropods, therefore the differences in the observed traits are thought to have originated from how the genes are wired. To reveal the basic differences in the network structure, we have numerically evolved hundreds of gene regulatory networks that produce striped patterns of gene expression. By analyzing the topologies of the generated networks, we show that the characteristics of stripe formation in long and short germ-band development are determined by Feed-Forward Loops (FFLs) and negative Feed-Back Loops (FBLs) respectively, and those of intermediate germ-band development are determined by the interconnections between FFL and negative FBL. Network architectures, gene expression patterns and knockout responses exhibited by the artificially evolved networks agree with those reported in the fly Drosophila melanogaster and the beetle Tribolium castaneum. For other arthropod species, principal network architectures that remain largely unknown are predicted. Our results suggest that the emergence of the three modes of body segmentation in arthropods is an inherent property of the evolving networks.

I started my scientific carer by investigating the development of the digestive tract in the laboratory of a well-known embryologist, Etienne Wolff, then professor at the Collège de France. My animal model was the chick embryo. The investigations that I pursued on liver development together with serendipity, led me to devise a cell-marking technique based on the construction of chimeric embryos between two closely related species of birds, the Japanese quail (Coturnix coturnix japonica) and the chick (Gallus gallus). The possibility to follow the migration and fate of the cells throughout development from early embryonic stages up to hatching and even after birth, was a breakthrough in developmental biology of higher vertebrates. This article describes some of scientific achievements based on the use of this technique in my laboratory during the last 38 years.

How left-right (LR) asymmetry emerges during development has been a classic problem in the field of developmental biology, but it is only since the 1990s that molecular and genetic approaches have become possible. Since current progress in LR patterning has been summarized in several other reviews, I would like to briefly describe how this topic developed in the early days and what remains to be solved. In particular, two breakthroughs in the mid to late 1990s made major contributions to recent progress. Despite the rapid progress, there remain many challenging issues that need to be addressed in future.

Somitic and head mesoderm contribute to cartilage and bone and deliver the entire skeletal musculature. Studies on avian somite patterning and cell differentiation led to the view that these processes depend solely on cues from surrounding tissues. However, evidence is accumulating that some developmental decisions depend on information within the somitic tissue itself. Moreover, recent studies established that head and somitic mesoderm, though delivering the same tissue types, are set up to follow their own, distinct developmental programmes. With a particular focus on the chicken embryo, we review the current understanding of how extrinsic signalling, operating in a framework of intrinsically regulated constraints, controls paraxial mesoderm patterning and cell differentiation., ((c) 2007 Wiley-Liss, Inc.)

Identification of gene products that function in some specific process of interest is a common goal in developmental biology. Although use of drug compounds to probe biological systems has a very long history in teratology and toxicology, systematic hierarchical drug screening has not been capitalized upon by the developmental biology community. This "chemical genetics" approach can greatly benefit the study of embryonic and regenerative systems, and we have formalized a strategy for using known pharmacological compounds to implicate specific molecular candidates in any chosen biological phenomenon. Taking advantage of a hierarchical structure that can be imposed on drug reagents in a number of fields such as ion transport, neurotransmitter function, metabolism, and cytoskeleton, any assay can be carried out as a binary search algorithm. This inverse drug screen methodology is much more efficient than exhaustive testing of large numbers of drugs, and reveals the identity of a manageable number of specific molecular candidates that can then be validated and targeted using more expensive and specific molecular reagents. Here, we describe the process of this loss-of-function screen and illustrate its use in uncovering novel bioelectrical and serotonergic mechanisms in embryonic patterning. This technique is an inexpensive and rapid complement to existing molecular screening strategies. Moreover, it is applicable to maternal proteins, and model species in which traditional genetic screens are not feasible, significantly extending the opportunities to identify key endogenous players in biological processes.

The aim of the present review is to provide a comprehensive explanation of Turing reaction-diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction-diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction-diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.

The widely held notion of an independent evolutionary origin of invertebrate and vertebrate brains is based on classical phylogenetic, neuroanatomical and embryological data. The interpretation of these data in favour of a polyphyletic origin of animals brains is currently being challenged by three fundamental findings that derive from comparative molecular, genetic and developmental analyses. First, modern molecular systematics indicates that none of the extant animals correspond to evolutionary intermediates between the protostomes and the deuterostomes, thus making it impossible to deduce the morphological organization of the ancestral bilaterian or its brain from living species. Second, recent molecular genetic evidence for the body axis inversion hypothesis now supports the idea that the basic body plan of vertebrates and invertebrates is similar but inverted, suggesting that the ventral nerve chord of protostome invertebrates is homologous to the dorsal nerve cord of deuterostome chordates. Third, a developmental genetic analysis of the molecular control elements involved in early embryonic brain patterning is uncovering the existence of structurally and functionally homologous genes that have comparable and interchangeable functions in key aspects of brain development in invertebrate and vertebrate model systems. All three of these findings are compatible with the hypothesis of a monophyletic origin of the bilaterian brain. Here we review these findings and consider their significance and implications for current thinking on the evolutionary origin of bilaterian brains. We also preview the impact of comparative functional genomic analyses on our understanding of brain evolution.

The relationship between theoretical and experimental approaches to the problem of pattern generation during embryonic development has often been uneasy. This stems at least in part from the different emphases that have typically been used in the two approaches. The spectacular success of modern genetic techniques in uncovering developmental mechanisms has led to a widespread belief that theory is no longer very relevant. However, recent examples of data-driven modelling point to new roles for theoretical approaches in exploring important issues such as the robustness and evolution of pattern-forming mechanisms.

During vertebrate embryonic development, the organs of the chest and abdomen, heart, lung and gastrointestinal tract, acquire characteristic asymmetric positions with respect to the left-right body axis. In the beginning of the 20th century Hans Spemann and his co-workers described manipulations of amphibian embryos which resulted in inversion of organ laterality in a predictable manner. Hedwig Wilhelmi concluded from these experiments that determinants on the left side of the embryo specify laterality, and Meyer postulated that a mediator should transfer this positional information to the forming heart. In this review we discuss the classical experiments in the light of recent advances in the molecular understanding of left-right development, with a focus on the mediator role of the homeobox gene Pitx2.