Models for the generation and interpretation of gradients

The Midbrain Preisthmus: A Poorly Known Effect of the Isthmic Organizer

This essay reexamines molecular evidence supporting the existence of the 'preisthmus', a caudal midbrain domain present in vertebrates (studied here in the mouse). It is thought to derive from the embryonic m2 mesomere and appears intercalated between the isthmus (caudally) and the inferior colliculus (rostrally). Among a substantial list of gene expression mappings examined from the Allen Developing and Adult Brain Atlases, a number of quite consistent selective positive markers, plus some neatly negative markers, were followed across embryonic stages E11.5, E13.5, E15.5, E18.5, and several postnatal stages up to the adult brain. Both alar and basal subdomains of this transverse territory were explored and illustrated. It is argued that the peculiar molecular and structural profile of the preisthmus is due to its position as rostrally adjacent to the isthmic organizer, where high levels of both FGF8 and WNT1 morphogens must exist at early embryonic stages. Isthmic patterning of the midbrain is discussed in this context. Studies of the effects of the isthmic morphogens usually do not attend to the largely unknown preisthmic complex. The adult alar derivatives of the preisthmus were confirmed to comprise a specific preisthmic sector of the periaqueductal gray, an intermediate stratum represented by the classic cuneiform nucleus, and a superficial stratum containing the subbrachial nucleus. The basal derivatives, occupying a narrow retrorubral domain intercalated between the oculomotor and trochlear motor nuclei, include dopaminergic and serotonergic neurons, as well as a variety of peptidergic neuron types.

Wnt signaling in whole-body regeneration

Regeneration abilities are widespread among animals and select species can restore any body parts removed by wounds that sever the major body axes. This capability of whole-body regeneration as exemplified in flatworm planarians, Acoels, and Cnidarians involves initial responses to injury, the assessment of wound site polarization, determination of missing tissue and programming of blastema fate, and patterned outgrowth to restore axis content and proportionality. Wnt signaling drives many shared and conserved aspects of the biology of whole-body regeneration in the planarian species Schmidtea mediterranea and Dugesia japonica, in the Acoel Hofstenia miamia, and in Cnidarians Hydra and Nematostella. These overlapping mechanisms suggest whole-body regeneration might be an ancestral property across diverse animal taxa.

An Update on the Molecular Mechanism of the Vertebrate Isthmic Organizer Development in the Context of the Neuromeric Model

A crucial event during the development of the central nervous system (CNS) is the early subdivision of the neural tube along its anterior-to-posterior axis to form neuromeres, morphogenetic units separated by transversal constrictions and programed for particular genetic cascades. The narrower portions observed in the developing neural tube are responsible for relevant cellular and molecular processes, such as clonal restrictions, expression of specific regulatory genes, and differential fate specification, as well as inductive activities. In this developmental context, the gradual formation of the midbrain-hindbrain (MH) constriction has been an excellent model to study the specification of two major subdivisions of the CNS containing the mesencephalic and isthmo-cerebellar primordia. This MH boundary is coincident with the common Otx2-(midbrain)/Gbx2-(hindbrain) expressing border. The early interactions between these two pre-specified areas confer positional identities and induce the generation of specific diffusible morphogenes at this interface, in particular FGF8 and WNT1. These signaling pathways are responsible for the gradual histogenetic specifications and cellular identity acquisitions with in the MH domain. This review is focused on the cellular and molecular mechanisms involved in the specification of the midbrain/hindbrain territory and the formation of the isthmic organizer. Emphasis will be placed on the chick/quail chimeric experiments leading to the acquisition of the first fate mapping and experimental data to, in this way, better understand pioneering morphological studies and innovative gain/loss-of-function analysis.

Insights from chemical systems into Turing-type morphogenesis

In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction-diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237, 37-72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction-diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

The pattern of nodal morphogen signaling is shaped by co-receptor expression

Embryos must communicate instructions to their constituent cells over long distances. These instructions are often encoded in the concentration of signals called morphogens. In the textbook view, morphogen molecules diffuse from a localized source to form a concentration gradient, and target cells adopt fates by measuring the local morphogen concentration. However, natural patterning systems often incorporate numerous co-factors and extensive signaling feedback, suggesting that embryos require additional mechanisms to generate signaling patterns. Here, we examine the mechanisms of signaling pattern formation for the mesendoderm inducer Nodal during zebrafish embryogenesis. We find that Nodal signaling activity spans a normal range in the absence of signaling feedback and relay, suggesting that diffusion is sufficient for Nodal gradient formation. We further show that the range of endogenous Nodal ligands is set by the EGF-CFC co-receptor Oep: in the absence of Oep, Nodal activity spreads to form a nearly uniform distribution throughout the embryo. In turn, increasing Oep levels sensitizes cells to Nodal ligands. We recapitulate these experimental results with a computational model in which Oep regulates the diffusive spread of Nodal ligands by setting the rate of capture by target cells. This model predicts, and we confirm in vivo, the surprising observation that a failure to replenish Oep transforms the Nodal signaling gradient into a travelling wave. These results reveal that patterns of Nodal morphogen signaling are shaped by co-receptor-mediated restriction of ligand spread and sensitization of responding cells.

Adhesion as a trigger of droplet polarization in flowing emulsions

Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the response of cohesive cellular assemblies under such stresses. In particular, we use biomimetic emulsions in which the droplets are functionalized in order to exhibit specific droplet-droplet adhesion. We flow these emulsions in microfluidic constrictions and study their response to this forced deformation via confocal microscopy. We find that the distributions of avalanche sizes are conserved between repulsive and adhesive droplets. However, adhesion locally impairs the rupture of droplet-droplet contacts, which in turn pulls on the rearranging droplets. As a result, adhesive droplets are a lot more deformed along the axis of elongation in the constriction. This finding could shed light on the origin of polarization processes during morphogenesis.

Mesoderm patterning by a dynamic gradient of retinoic acid signalling

Retinoic acid (RA), derived from vitamin A, is a major teratogen, clinically recognized in 1983. Identification of its natural presence in the embryo and dissection of its molecular mechanism of action became possible in the animal model with the advent of molecular biology, starting with the cloning of its nuclear receptor. In normal development, the dose of RA is tightly controlled to regulate organ formation. Its production depends on enzymes, which have a dynamic expression profile during embryonic development. As a small molecule, it diffuses rapidly and acts as a morphogen. Here, we review advances in deciphering how endogenously produced RA provides positional information to cells. We compare three mesodermal tissues, the limb, the somites and the heart, and discuss how RA signalling regulates antero-posterior and left-right patterning. A common principle is the establishment of its spatio-temporal dynamics by positive and negative feedback mechanisms and by antagonistic signalling by FGF. However, the response is cell-specific, pointing to the existence of cofactors and effectors, which are as yet incompletely characterized. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.

What are the roles of retinoids, other morphogens, and Hox genes in setting up the vertebrate body axis?

This article is concerned with the roles of retinoids and other known anterior-posterior morphogens in setting up the embryonic vertebrate anterior-posterior axis. The discussion is restricted to the very earliest events in setting up the anterior-posterior axis (from blastula to tailbud stages in Xenopus embryos). In these earliest developmental stages, morphogen concentration gradients are not relevant for setting up this axis. It emerges that at these stages, the core patterning mechanism is timing: BMP-anti BMP mediated time space translation that regulates Hox temporal and spatial collinearities and Hox-Hox auto- and cross- regulation. The known anterior-posterior morphogens and signaling pathways--retinoids, FGF's, Cdx, Wnts, Gdf11 and others--interact with this core mechanism at and after space-time defined "decision points," leading to the separation of distinct axial domains. There are also other roles for signaling pathways. Besides the Hox regulated hindbrain/trunk part of the axis, there is a rostral part (including the anterior part of the head and the extreme anterior domain [EAD]) that appears to be regulated by additional mechanisms. Key aspects of anterior-posterior axial patterning, including: the nature of different phases in early patterning and in the whole process; the specificities of Hox action and of intercellular signaling; and the mechanisms of Hox temporal and spatial collinearities, are discussed in relation to the facts and hypotheses proposed above.

Planarian regeneration as a model of anatomical homeostasis: Recent progress in biophysical and computational approaches

Planarian behavior, physiology, and pattern control offer profound lessons for regenerative medicine, evolutionary biology, morphogenetic engineering, robotics, and unconventional computation. Despite recent advances in the molecular genetics of stem cell differentiation, this model organism's remarkable anatomical homeostasis provokes us with truly fundamental puzzles about the origin of large-scale shape and its relationship to the genome. In this review article, we first highlight several deep mysteries about planarian regeneration in the context of the current paradigm in this field. We then review recent progress in understanding of the physiological control of an endogenous, bioelectric pattern memory that guides regeneration, and how modulating this memory can permanently alter the flatworm's target morphology. Finally, we focus on computational approaches that complement reductive pathway analysis with synthetic, systems-level understanding of morphological decision-making. We analyze existing models of planarian pattern control and highlight recent successes and remaining knowledge gaps in this interdisciplinary frontier field.

Emergence of form in embryogenesis

The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.

Mean-Independent Noise Control of Cell Fates via Intermediate States

Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination.

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Mean-independent noise control allows noise attenuation without affecting the mean

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Intermediate states enable such control through proportional coupling

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This controls spatial gene expression noise without shifting boundary locations

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Specific noise levels are required for successful downstream boundary sharpening

Nodal patterning without Lefty inhibitory feedback is functional but fragile

Developmental signaling pathways often activate their own inhibitors. Such inhibitory feedback has been suggested to restrict the spatial and temporal extent of signaling or mitigate signaling fluctuations, but these models are difficult to rigorously test. Here, we determine whether the ability of the mesendoderm inducer Nodal to activate its inhibitor Lefty is required for development. We find that zebrafish lefty mutants exhibit excess Nodal signaling and increased specification of mesendoderm, resulting in embryonic lethality. Strikingly, development can be fully restored without feedback: Lethal patterning defects in lefty mutants can be rescued by ectopic expression of lefty far from its normal expression domain or by spatially and temporally uniform exposure to a Nodal inhibitor drug. While drug-treated mutants are less tolerant of mild perturbations to Nodal signaling levels than wild type embryos, they can develop into healthy adults. These results indicate that patterning without inhibitory feedback is functional but fragile.

During animal development, a single fertilized cell gives rise to different tissues and organs. This ‘patterning’ process depends on signaling molecules that instruct cells in different positions in the embryo to acquire different identities. To avoid mistakes during patterning, each cell must receive the correct amount of signal at the appropriate time.

In a process called ‘inhibitory feedback’, a signaling molecule instructs cells to produce molecules that block its own signaling. Although inhibitory feedback is widely used during patterning in organisms ranging from sea urchins to mammals, its exact purpose is often not clear. In part this is because feedback is challenging to experimentally manipulate. Removing the inhibitor disrupts feedback, but also increases signaling. Since the effects of broken feedback and increased signaling are intertwined, any resulting developmental defects do not provide information about what feedback specifically does. In order to examine the role of feedback, it is therefore necessary to disconnect the production of the inhibitor from the signaling process.

In developing embryos, a well-known signaling molecule called Nodal instructs cells to become specific types – for example, a heart or gut cell. Nodal also promotes the production of its inhibitor, Lefty. To understand how this feedback system works, Rogers, Lord et al. first removed Lefty from zebrafish embryos. These embryos had excessive levels of Nodal signaling, did not develop correctly, and could not survive. Bathing the embryos in a drug that inhibits Nodal reduced excess signaling and allowed them to develop successfully. In these drug-treated embryos, inhibitor production is disconnected from the signaling process, allowing the role of feedback to be examined. Drug-treated embryos were less able to tolerate fluctuations in Nodal signaling than normal zebrafish embryos, which could compensate for such disturbances by adjusting Lefty levels.

Overall, it appears that inhibitory feedback in this patterning system is important to compensate for alterations in Nodal signaling, but is not essential for development. Understanding the role of inhibitory feedback will be useful for efforts to grow tissues and organs in the laboratory for clinical use. The results presented by Rogers, Lord et al. also suggest the possibility that drug treatments could be developed to help correct birth defects in the womb.

Why we need mechanics to understand animal regeneration

Mechanical forces are an important contributor to cell fate specification and cell migration during embryonic development in animals. Similarities between embryogenesis and regeneration, particularly with regards to pattern formation and large-scale tissue movements, suggest similarly important roles for physical forces during regeneration. While the influence of the mechanical environment on stem cell differentiation in vitro is being actively exploited in the fields of tissue engineering and regenerative medicine, comparatively little is known about the role of stresses and strains acting during animal regeneration. In this review, we summarize published work on the role of physical principles and mechanical forces in animal regeneration. Novel experimental techniques aimed at addressing the role of mechanics in embryogenesis have greatly enhanced our understanding at scales from the subcellular to the macroscopic - we believe the time is ripe for the field of regeneration to similarly leverage the tools of the mechanobiological research community.

Morphogene adsorption as a Turing instability regulator: Theoretical analysis and possible applications in multicellular embryonic systems

The Turing instability in the reaction-diffusion system is a widely recognized mechanism of the morphogen gradient self-organization during the embryonic development. One of the essential conditions for such self-organization is sharp difference in the diffusion rates of the reacting substances (morphogens). In classical models this condition is satisfied only for significantly different values of diffusion coefficients which cannot hold for morphogens of similar molecular size. One of the most realistic explanations of the difference in diffusion rate is the difference between adsorption of morphogens to the extracellular matrix (ECM). Basing on this assumption we develop a novel mathematical model and demonstrate its effectiveness in describing several well-known examples of biological patterning. Our model consisting of three reaction-diffusion equations has the Turing-type instability and includes two elements with equal diffusivity and immobile binding sites as the third reaction substance. The model is an extension of the classical Gierer-Meinhardt two-components model and can be reduced to it under certain conditions. Incorporation of ECM in the model system allows us to validate the model for available experimental parameters. According to our model introduction of binding sites gradient, which is frequently observed in embryonic tissues, allows one to generate more types of different spatial patterns than can be obtained with two-components models. Thus, besides providing an essential condition for the Turing instability for the system of morphogen with close values of the diffusion coefficients, the morphogen adsorption on ECM may be important as a factor that increases the variability of self-organizing structures.

Go ahead, grow a head! A planarian's guide to anterior regeneration

The unique ability of some planarian species to regenerate a head de novo, including a functional brain, provides an experimentally accessible system in which to study the mechanisms underlying regeneration. Here, we summarize the current knowledge on the key steps of planarian head regeneration (head‐versus‐tail decision, anterior pole formation and head patterning) and their molecular and cellular basis. Moreover, instructive properties of the anterior pole as a putative organizer and in coordinating anterior midline formation are discussed. Finally, we highlight that regeneration initiation occurs in a two‐step manner and hypothesize that wound‐induced and existing positional cues interact to detect tissue loss and together determine the appropriate regenerative outcomes.

Visualizing retinoic acid morphogen gradients

Morphogens were originally defined as secreted signaling molecules that diffuse from local sources to form concentration gradients, which specify multiple cell fates. More recently morphogen gradients have been shown to incorporate a range of mechanisms including short-range signal activation, transcriptional/translational feedback, and temporal windows of target gene induction. Many critical cell-cell signals implicated in both embryonic development and disease, such as Wnt, fibroblast growth factor (Fgf), hedgehog (Hh), transforming growth factor beta (TGFb), and retinoic acid (RA), are thought to act as morphogens, but key information on signal propagation and ligand distribution has been lacking for most. The zebrafish provides unique advantages for genetics and imaging to address gradients during early embryonic stages when morphogens help establish major body axes. This has been particularly informative for RA, where RA response elements (RAREs) driving fluorescent reporters as well as Fluorescence Resonance Energy Transfer (FRET) reporters of receptor binding have provided evidence for gradients, as well as regulatory mechanisms that attenuate noise and enhance gradient robustness in vivo. Here we summarize available tools in zebrafish and discuss their utility for studying dynamic regulation of RA morphogen gradients, through combined experimental and computational approaches.

Physiological controls of large-scale patterning in planarian regeneration: a molecular and computational perspective on growth and form

Planaria are complex metazoans that repair damage to their bodies and cease remodeling when a correct anatomy has been achieved. This model system offers a unique opportunity to understand how large-scale anatomical homeostasis emerges from the activities of individual cells. Much progress has been made on the molecular genetics of stem cell activity in planaria. However, recent data also indicate that the global pattern is regulated by physiological circuits composed of ionic and neurotransmitter signaling. Here, we overview the multi-scale problem of understanding pattern regulation in planaria, with specific focus on bioelectric signaling via ion channels and gap junctions (electrical synapses), and computational efforts to extract explanatory models from functional and molecular data on regeneration. We present a perspective that interprets results in this fascinating field using concepts from dynamical systems theory and computational neuroscience. Serving as a tractable nexus between genetic, physiological, and computational approaches to pattern regulation, planarian pattern homeostasis harbors many deep insights for regenerative medicine, evolutionary biology, and engineering.

Positional Information and Pattern Formation

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; however, 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 proposed gradients and details how they are set up. The way in which a signaling gradient regulates differential gene expression in a concentration-dependent manner also raises several technical and quite difficult issues. A key feature of positional information being the basis for pattern formation is that there is no prepattern in the embryo.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

A Temporal Window for Signal Activation Dictates the Dimensions of a Nodal Signaling Domain

Morphogen signaling is critical for the growth and patterning of tissues in embryos and adults, but how morphogen signaling gradients are generated in tissues remains controversial. The morphogen Nodal was proposed to form a long-range signaling gradient via a reaction-diffusion system, on the basis of differential diffusion rates of Nodal and its antagonist Lefty. Here we use a specific zebrafish Nodal biosensor combined with immunofluorescence for phosphorylated Smad2 to demonstrate that endogenous Nodal is unlikely to diffuse over a long range. Instead, short-range Nodal signaling activation in a temporal window is sufficient to determine the dimensions of the Nodal signaling domain. The size of this temporal window is set by the differentially timed production of Nodal and Lefty, which arises mainly from repression of Lefty translation by the microRNA miR-430. Thus, temporal information is transformed into spatial information to define the dimensions of the Nodal signaling domain and, consequently, to specify mesendoderm.

Models for patterning primary embryonic body axes: The role of space and time

Models for the generation and interpretation of spatial patterns are discussed. Crucial for these processes is an intimate link between self-enhancing and antagonistic reactions. For spatial patterning, long-ranging antagonistic reactions are required that restrict the self-enhancing reactions to generate organizing regions. Self-enhancement is also required for a permanent switch-like activation of genes. This self-enhancement is antagonized by the mutual repression of genes, making sure that in a particular cell only one gene of a set of possible genes become activated - a long range inhibition in the 'gene space'. The understanding how the main body axes are initiated becomes more straightforward if the evolutionary ancestral head/brain pattern and the trunk pattern is considered separately. To activate a specific gene at particular concentration of morphogenetic gradient, observations are compatible with a systematic and time-requiring 'promotion' from one gene to the next until the local concentration is insufficient to accomplish a further promotion. The achieved determination is stable against a fading of the morphogen, as required to allow substantial growth. Minor modifications lead to a purely time-dependent activation of genes; both mechanisms are involved to pattern the anteroposterior axis. A mutual activation of cell states that locally exclude each other accounts for many features of the segmental patterning of the trunk. A possible scenario for the evolutionary invention of segmentation is discussed that is based on a reemployment of interactions involved in asexual reproduction.

Inferring regulatory networks from experimental morphological phenotypes: a computational method reverse-engineers planarian regeneration

Transformative applications in biomedicine require the discovery of complex regulatory networks that explain the development and regeneration of anatomical structures, and reveal what external signals will trigger desired changes of large-scale pattern. Despite recent advances in bioinformatics, extracting mechanistic pathway models from experimental morphological data is a key open challenge that has resisted automation. The fundamental difficulty of manually predicting emergent behavior of even simple networks has limited the models invented by human scientists to pathway diagrams that show necessary subunit interactions but do not reveal the dynamics that are sufficient for complex, self-regulating pattern to emerge. To finally bridge the gap between high-resolution genetic data and the ability to understand and control patterning, it is critical to develop computational tools to efficiently extract regulatory pathways from the resultant experimental shape phenotypes. For example, planarian regeneration has been studied for over a century, but despite increasing insight into the pathways that control its stem cells, no constructive, mechanistic model has yet been found by human scientists that explains more than one or two key features of its remarkable ability to regenerate its correct anatomical pattern after drastic perturbations. We present a method to infer the molecular products, topology, and spatial and temporal non-linear dynamics of regulatory networks recapitulating in silico the rich dataset of morphological phenotypes resulting from genetic, surgical, and pharmacological experiments. We demonstrated our approach by inferring complete regulatory networks explaining the outcomes of the main functional regeneration experiments in the planarian literature; By analyzing all the datasets together, our system inferred the first systems-biology comprehensive dynamical model explaining patterning in planarian regeneration. This method provides an automated, highly generalizable framework for identifying the underlying control mechanisms responsible for the dynamic regulation of growth and form.

Developmental and regenerative biology experiments are producing a huge number of morphological phenotypes from functional perturbation experiments. However, existing pathway models do not generally explain the dynamic regulation of anatomical shape due to the difficulty of inferring and testing non-linear regulatory networks responsible for appropriate form, shape, and pattern. We present a method that automates the discovery and testing of regulatory networks explaining morphological outcomes directly from the resultant phenotypes, producing network models as testable hypotheses explaining regeneration data. Our system integrates a formalization of the published results in planarian regeneration, an in silico simulator in which the patterning properties of regulatory networks can be quantitatively tested in a regeneration assay, and a machine learning module that evolves networks whose behavior in this assay optimally matches the database of planarian results. We applied our method to explain the key experiments in planarian regeneration, and discovered the first comprehensive model of anterior-posterior patterning in planaria under surgical, pharmacological, and genetic manipulations. Beyond the planarian data, our approach is readily generalizable to facilitate the discovery of testable regulatory networks in developmental biology and biomedicine, and represents the first developmental model discovered de novo from morphological outcomes by an automated system.

Temporally coordinated signals progressively pattern the anteroposterior and dorsoventral body axes

The vertebrate body plan is established through the precise spatiotemporal coordination of morphogen signaling pathways that pattern the anteroposterior (AP) and dorsoventral (DV) axes. Patterning along the AP axis is directed by posteriorizing signals Wnt, fibroblast growth factor (FGF), Nodal, and retinoic acid (RA), while patterning along the DV axis is directed by bone morphogenetic proteins (BMP) ventralizing signals. This review addresses the current understanding of how Wnt, FGF, RA and BMP pattern distinct AP and DV cell fates during early development and how their signaling mechanisms are coordinated to concomitantly pattern AP and DV tissues.

Scaling and regeneration of self-organized patterns

Biological patterns generated during development and regeneration often scale with organism size. Some organisms, e.g., flatworms, can regenerate a rescaled body plan from tissue fragments of varying sizes. Inspired by these examples, we introduce a generalization of Turing patterns that is self-organized and self-scaling. A feedback loop involving diffusing expander molecules regulates the reaction rates of a Turing system, thereby adjusting pattern length scales proportional to system size. Our model captures essential features of body plan regeneration in flatworms as observed in experiments.

Molecular dissection of segment formation in the developing hindbrain

Although many components of the genetic pathways that provide positional information during embryogenesis have been identified, it remains unclear how these signals are integrated to specify discrete tissue territories. Here, we investigate the molecular mechanisms underlying the formation of one of the hindbrain segments, rhombomere (r) 3, specified by the expression of the gene krox20. Dissecting krox20 transcriptional regulation has identified several input pathways: Hox paralogous 1 (PG1) factors, which both directly activate krox20 and indirectly repress it via Nlz factors, and the molecular components of an Fgf-dependent effector pathway. These different inputs are channelled through a single initiator enhancer element to shape krox20 initial transcriptional response: Hox PG1 and Nlz factors define the anterior-posterior extent of the enhancer's domain of activity, whereas Fgf signalling modulates the magnitude of activity in a spatially uniform manner. Final positioning of r3 boundaries requires interpretation of this initial pattern by a krox20 positive-feedback loop, orchestrated by another enhancer. Overall, this study shows how positional information provided by different patterning mechanisms is integrated through a gene regulatory network involving two cis-acting elements operating on the same gene, thus offering a comprehensive view of the delimitation of a territory.

Moesin and myosin phosphatase confine neutrophil orientation in a chemotactic gradient

Jingsong Xu and colleagues investigate how neutrophils initiate polarized migration toward bacteria or chemoattractants. They find that attractant-induced activation of myosin phosphatase results in the deactivation of moesin at the prospective leading edge and its redistribution to the trailing edge, establishing polarity and directional pseudopod formation.

Neutrophils respond to invading bacteria by adopting a polarized morphology, migrating in the correct direction, and engulfing the bacteria. How neutrophils establish and precisely orient this polarity toward pathogens remains unclear. Here we report that in resting neutrophils, the ERM (ezrin, radixin, and moesin) protein moesin in its active form (phosphorylated and membrane bound) prevented cell polarization by inhibiting the small GTPases Rac, Rho, and Cdc42. Attractant-induced activation of myosin phosphatase deactivated moesin at the prospective leading edge to break symmetry and establish polarity. Subsequent translocation of moesin to the trailing edge confined the formation of a prominent pseudopod directed toward pathogens and prevented secondary pseudopod formation in other directions. Therefore, both moesin-mediated inhibition and its localized deactivation by myosin phosphatase are essential for neutrophil polarization and effective neutrophil tracking of pathogens.

Cytonemes and the dispersion of morphogens

Filopodia are cellular protrusions that have been implicated in many types of mechanosensory activities. Morphogens are signaling proteins that regulate the patterned development of embryos and tissues. Both have long histories that date to the beginnings of cell and developmental biology in the early 20th century, but recent findings tie specialized filopodia called cytonemes to morphogen movement and morphogen signaling. This review explores the conceptual and experimental background for a model of paracrine signaling in which the exchange of morphogens between cells is directed to sites where cytonemes directly link cells that produce morphogens to cells that receive and respond to them.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Development: scaling to size by protease inhibition

The dorsal half of bisected Xenopus laevis embryos can regenerate a well-proportioned organism on a smaller scale. A new study indicates that the removal of ventral tissue generates a steeper Chordin gradient by reducing Sizzled, a secreted inhibitor of Tolloid chordinases.

Morphogenetic action through flux-limited spreading

A central question in biology is how secreted morphogens act to induce different cellular responses within a group of cells in a concentration-dependent manner. Modeling morphogenetic output in multicellular systems has so far employed linear diffusion, which is the normal type of diffusion associated with Brownian processes. However, there is evidence that at least some morphogens, such as Hedgehog (Hh) molecules, may not freely diffuse. Moreover, the mathematical analysis of such models necessarily implies unrealistic instantaneous spreading of morphogen molecules, which are derived from the assumptions of Brownian motion in its continuous formulation. A strict mathematical model considering Fick's diffusion law predicts morphogen exposure of the whole tissue at the same time. Such a strict model thus does not describe true biological patterns, even if similar and attractive patterns appear as results of applying such simple model. To eliminate non-biological behaviors from diffusion models we introduce flux-limited spreading (FLS), which implies a restricted velocity for morphogen propagation and a nonlinear mechanism of transport. Using FLS and focusing on intercellular Hh-Gli signaling, we model a morphogen gradient and highlight the propagation velocity of morphogen particles as a new key biological parameter. This model is then applied to the formation and action of the Sonic Hh (Shh) gradient in the vertebrate embryonic neural tube using our experimental data on Hh spreading in heterologous systems together with published data. Unlike linear diffusion models, FLS modeling predicts concentration fronts and the evolution of gradient dynamics and responses over time. In addition to spreading restrictions by extracellular binding partners, we suggest that the constraints imposed by direct bridges of information transfer such as nanotubes or cytonemes underlie FLS. Indeed, we detect and measure morphogen particle velocity in such cell extensions in different systems.

Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions

The Wnt/β-catenin pathway is involved in the regulation of a multitude of physiological processes by controlling the differential expression of target genes. In certain tissues such as the adult liver, the Wnt/β-catenin pathway can attain different levels of activity due to gradients of Wnt ligands and/or intracellular pathway components like APC. How graded pathway activity is converted into regionally distinct patterns of Wnt/β-catenin target gene expression is largely unknown. Here, we apply a mathematical modeling approach to investigate the impact of different regulatory mechanisms on target gene expression within Wnt or APC concentration gradients. We develop a minimal model of Wnt/β-catenin signal transduction and combine it with various mechanisms of target gene regulation. In particular, the effects of activation, inhibition, and an incoherent feedforward loop (iFFL) are compared. To specify activation kinetics, we analyze experimental data that quantify the response of β-catenin/TCF reporter constructs to different Wnt concentrations, and demonstrate that the induction of these constructs occurs in a cooperative manner with Hill coefficients between 2 and 5. In summary, our study shows that the combination of specific gene regulatory mechanisms with a time-independent gradient of Wnt or APC is sufficient to generate distinct target gene expression patterns as have been experimentally observed in liver. We find that cooperative gene activation in combination with a TCF feedback can establish sharp borders of target gene expression in Wnt or APC gradients. In contrast, the iFFL renders gene expression independent of gradients of the upstream signaling components. Our subsequent analysis of carcinogenic pathway mutations reveals that their impact on gene expression is determined by the gene regulatory mechanism and the APC concentration of the cell in which the mutation occurs.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Dynamics and precision in retinoic acid morphogen gradients

Retinoic acid (RA) regulates many cellular behaviors during embryonic development and adult homeostasis. Like other morphogens, RA forms gradients through the use of localized sources and sinks, feedback, and interactions with other signals; this has been particularly well studied in the context of hindbrain segmentation in vertebrate embryos. Yet, as a small lipophilic molecule derived from a dietary source-vitamin A-RA differs markedly from better-studied polypeptide morphogens in its mechanisms of transport, signaling, and removal. Computational models suggest that the distinctive features of RA gradients make them particularly robust to large perturbations. Such features include combined positive and negative feedback effects via intracellular fatty acid binding proteins and RA-degrading enzymes. Here, we discuss how these features, together with feedback interactions among RA target genes, help enable RA to specify multiple, accurate pattern elements in the developing hindbrain, despite operating in an environment of high cellular and biochemical uncertainty and noise.

Encoding and decoding of positional information in morphogen-dependent patterning

Patterning during organogenesis is fundamentally realized through the interpretation of morphogen gradients by particular types of gene regulatory networks (GRNs). However, as quantitative studies have reported, spatial profiles of morphogen gradients include intra-embryo and inter-embryo variability, which could lead to errors in spatial recognition by cells and variations in patterning. By mathematically modeling the processes of generation and readout of spatial information - information encoding and decoding, by an analogy to computer communication - and maximizing the reproducibility of patterning against noise, the general designs of gradient profiles and their interpretation have been clarified. Furthermore, over the past few years, basic studies on patterning in more dynamic situations, that is, patterning in growing tissues with time-variant gradients, have been initiated. Here we provide an overview of patterning studies, pattern generating GRNs, concepts of information coding design for robust patterning, and patterning in growing tissues.

Comprehensive timeline of mesodermal development in the quail small intestine

BACKGROUND

To generate the mature intestine, splanchnic mesoderm diversifies into six different tissue layers each with multiple cell types through concurrent and complex morphogenetic events. Hindering the progress of research in the field is the lack of a detailed description of the fundamental morphological changes that constitute development of the intestinal mesoderm.

RESULTS

We used immunofluorescence and morphometric analyses of wild-type and Tg(tie1:H2B-eYFP) quail embryos to establish a comprehensive timeline of mesodermal development in the avian intestine. The following landmark features were analyzed from appearance of the intestinal primordium through generation of the definitive structure: radial compartment formation, basement membrane dynamics, mesothelial differentiation, mesenchymal expansion and growth patterns, smooth muscle differentiation, and maturation of the vasculature. In this way, structural relationships between mesodermal components were identified over time.

CONCLUSIONS

This integrated analysis presents a roadmap for investigators and clinicians to evaluate diverse experimental data obtained at individual stages of intestinal development within the longitudinal context of intestinal morphogenesis.

Cellular retinoic acid-binding proteins are essential for hindbrain patterning and signal robustness in zebrafish

The vitamin A derivative retinoic acid (RA) is a morphogen that patterns the anterior-posterior axis of the vertebrate hindbrain. Cellular retinoic acid-binding proteins (Crabps) transport RA within cells to both its nuclear receptors (RARs) and degrading enzymes (Cyp26s). However, mice lacking Crabps are viable, suggesting that Crabp functions are redundant with those of other fatty acid-binding proteins. Here we show that Crabps in zebrafish are essential for posterior patterning of the hindbrain and that they provide a key feedback mechanism that makes signaling robust as they are able to compensate for changes in RA production. Of the four zebrafish Crabps, Crabp2a is uniquely RA inducible and depletion or overexpression of Crabp2a makes embryos hypersensitive to exogenous RA. Computational models confirm that Crabp2a improves robustness within a narrow concentration range that optimizes a 'robustness index', integrating spatial information along the RA morphogen gradient. Exploration of signaling parameters in our models suggests that the ability of Crabp2a to transport RA to Cyp26 enzymes for degradation is a major factor in promoting robustness. These results demonstrate a previously unrecognized requirement for Crabps in RA signaling and hindbrain development, as well as a novel mechanism for stabilizing morphogen gradients despite genetic or environmental fluctuations in morphogen availability.