Diffusible Morphogen Research Articles

Anterior-posterior patterning and segmentation of the vertebrate head.

Segmentation of the vertebrate head emerges out of earlier processes that establish the anterior-posterior (A-P) axis. Recent genetic studies and comparisons across species have led to a better understanding of the links between A-P patterning and segmentation. These point to similar signals acting on both head and trunk, such as retinoic acid and fibroblast growth factors. These form interacting networks of diffusible morphogen gradients that pattern both hindbrain rhombomeres and mesodermal somites. New computational models, particularly for retinoic acid, have revealed how morphogen gradients are established and made robust to changes in signaling levels. However, the orientations of these gradients, as well as how they interact to generate segments, differ remarkably between germ layers and body regions. Thus, the vertebrate head is, in part, built through modifications of the same processes that link A-P patterning and segmentation in the trunk, but fundamental differences in how these processes are deployed lend further doubt to the notion that head and trunk segments are homologous.

Activator‐inhibitor dynamics of vertebrate limb pattern formation

The development of the vertebrate limb depends on an interplay of cellular differentiation, pattern formation, and tissue morphogenesis on multiple spatial and temporal scales. While numerous gene products have been described that participate in, and influence, the generation of the limb skeletal pattern, an understanding of the most salient feature of the developing limb--its quasiperiodic arrangement of bones, requires additional organizational principles. We review several such principles, drawing on concepts of physics and chemical dynamics along with molecular genetics and cell biology. First, a "core mechanism" for precartilage mesenchymal condensation is described, based on positive autoregulation of the morphogen transforming growth factor (TGF)-beta, induction of the extracellular matrix (ECM) protein fibronectin, and focal accumulation of cells via haptotaxis. This core mechanism is shown to be part of a local autoactivation-lateral inhibition (LALI) system that ensures that the condensations will be regularly spaced. Next, a "bare-bones" model for limb development is described in which the LALI-core mechanism is placed in a growing geometric framework with predifferentiated "apical," differentiating "active," and irreversibly differentiated "frozen" zones defined by distance from an apical source of a fibroblast growth factor (FGF)-type morphogen. This model is shown to account for classic features of the developing limb, including the proximodistal (PD) emergence over time of increasing numbers of bones. We review earlier and recent work suggesting that the inhibitory component of the LALI system for condensation may not be a diffusible morphogen, and propose an alternative mechanism for lateral inhibition, based on synchronization of oscillations of a Hes mediator of the Notch signaling pathway. Finally, we discuss how viewing development as an interplay between molecular-genetic and dynamic physical processes can provide new insight into the origin of congenital anomalies.

The Turing mechanism in vertebrate limb patterning

In the Review ‘Making digit patterns in the vertebrate limb’ 1 , Cheryll Tickle discusses evidence that the long-standing concept of ‘positional information’ — which was formulated to account for differences in the appearance of distinct skeletal elements — is inadequate to explain the number and arrangement of such elements. As an alternative means for laying out the overall template for the limb skeleton, she briefly mentions an entirely different mechanism of pattern formation: the reaction–diffusion model, which was originally put forward by the mathematician A.M. Turing 2 . As Tickle states, “The series of many unpatterned digits, which develop in the absence of GLI3 function in mouse mutants, is reminiscent of the digit pre-pattern that has been proposed to function in combination with the morphogen gradient [3] . According to this proposal, a series of digit condensations, a pre-pattern, is specified by a wave-like distribution of a morphogen that is generated by a reaction–diffusion mechanism, with the peaks corresponding to the condensations. A gradient of another morphogen … then provides each peak with a positional value and a digit identity. The number of peaks that are generated by the reaction–diffusion mechanism depends on the width of the limb.” The proposal that the limb skeleton is generated by a reaction–diffusion mechanism, with other morphogen gradients having a fine-tuning role, was first made not in the 1989 review 3 that she cites, but a decade previously, in conjunction with a specific model for the production of patterns of pre-cartilage condensation through the inter action of mesenchymal cells with morpho gens and with the extracellular matrix (ECM) 4 . More importantly, Tickle failed to describe research in the ensuing three decades that has seriously considered, tested and elaborated on the role of reaction– diffusion patterning in limb development. This includes a series of papers by Takashi Miura and his colleagues that provided evidence for a reaction–diffusion mechanism over a mechanochemical alternative in an in vitro model for pre-chondrogenic pattern formation 5 , and for the functionality of transforming growth factor-β2 (TGFβ2) as the activator in a reaction–diffusion scheme 6 . Later, it was demonstrated that lateral inhibition of limb pre-cartilage condensation (a necessary component of the reaction–diffusion framework) was induced by ectodermally produced fibroblast growth factors (FGFs) 7 . This was followed by a reaction–diffusion-based mathematical analysis 8 that accounted for the coordinate effects of FGFs in laterally inhibiting and accelerating the rate of appearance of foci of pre-cartilage condensation. Miura and co-workers also showed that the peculiar ‘thick–thin’ morphology of limb skeletal elements that is observed in doublefoot-mutant mice could be understood by assuming that a reaction–diffusion mechanism underlies skeletal patterning 9 . In the original reaction–diffusion-based limb model, the hypothesis that the nondiffusible ECM protein fibronectin mediates pre-cartilage condensation as part of a regulatory circuit that involves diffusible morphogens 4

An Evolutionarily Conserved Mechanism Delimiting SHR Movement Defines a Single Layer of Endodermis in Plants

Intercellular protein movement plays a critical role in animal and plant development. SHORTROOT (SHR) is a moving transcription factor essential for endodermis specification in the Arabidopsis root. Unlike diffusible animal morphogens, which form a gradient across multiple cell layers, SHR movement is limited to essentially one cell layer. However, the molecular mechanism is unknown. We show that SCARECROW (SCR) blocks SHR movement by sequestering it into the nucleus through protein-protein interaction and a safeguard mechanism that relies on a SHR/SCR-dependent positive feedback loop for SCR transcription. Our studies with SHR and SCR homologs from rice suggest that this mechanism is evolutionarily conserved, providing a plausible explanation why nearly all plants have a single layer of endodermis.

An Nkx2-5/Bmp2/Smad1 Negative Feedback Loop Controls Heart Progenitor Specification and Proliferation

During heart development the second heart field (SHF) provides progenitor cells for most cardiomyocytes and expresses the homeodomain factor Nkx2-5. We now show that feedback repression of Bmp2/Smad1 signaling by Nkx2-5 critically regulates SHF proliferation and outflow tract (OFT) morphology. In the cardiac fields of Nkx2-5 mutants, genes controlling cardiac specification (including Bmp2) and maintenance of the progenitor state were upregulated, leading initially to progenitor overspecification, but subsequently to failed SHF proliferation and OFT truncation. In Smad1 mutants, SHF proliferation and deployment to the OFT were increased, while Smad1 deletion in Nkx2-5 mutants rescued SHF proliferation and OFT development. In Nkx2-5 hypomorphic mice, which recapitulate human congenital heart disease (CHD), OFT anomalies were also rescued by Smad1 deletion. Our findings demonstrate that Nkx2-5 orchestrates the transition between periods of cardiac induction, progenitor proliferation, and OFT morphogenesis via a Smad1-dependent negative feedback loop, which may be a frequent molecular target in CHD.

A mechanism for the sharp transition of morphogen gradient interpretation in Xenopus

BackgroundOne way in which positional information is established during embryonic development is through the graded distribution of diffusible morphogens. Unfortunately, little is known about how cells interpret different concentrations of morphogen to activate different genes or how thresholds are generated in a morphogen gradient.ResultsHere we show that the concentration-dependent induction of the T-box transcription factor Brachyury (Xbra) and the homeobox-containing gene Goosecoid (Gsc) by activin in Xenopus can be explained by the dynamics of a simple network consisting of three elements with a mutual negative feedback motif that can function to convert a graded signal (activin) into a binary output (Xbra on and Gsc off, or vice versa). Importantly, such a system can display sharp thresholds. Consistent with the predictions of our model, Xenopus ectodermal cells display a binary response at the single cell level after treatment with activin.ConclusionThis kind of simple network with mutual negative feedback might provide a general mechanism for selective gene activation in response to different levels of a single external signal. It provides a mechanism by which a sharp boundary might be created between domains of different cell types in response to a morphogen gradient.

Transfer of differentiation signal by membrane microvesicles harboring hedgehog morphogens

AbstractHedgehog (Hh) proteins are considered diffusible morphogens that can be membrane anchored, playing an essential role during development. Here we show that Hh morphogens are associated with microvesicles (MVs) shed from the plasma membrane of apoptotic/stimulated T cells. Hh+ MVs induced differentiation of human K562 pluripotent erythroleukemic cells toward megakaryocytic lineage, as testified to by the expression of αIIbβ3 integrin and CD42b and changes in the cell cycle. Blocking Hh pathway with either cyclopamine, neutralizing antibodies, or inhibitors of the protein kinase A pathway resulted in the inhibition of these effects. Activation of Hh signaling by SAG, a synthetic agonist, mimicked effects of Hh+ MVs on K562 cells. Human Hh+ MVs, circulating in vivo or derived from apoptotic/stimulated lymphocytes from healthy and diabetic individuals, elicited K562 cell differentiation, also inhibited by cyclopamine. In addition, Hh+ MV-treated primary human CD34+ cells presented an increase of CD41+CD42– and CD41+CD42+ megakaryocytic populations with an increase of corresponding polyploidy, both being reduced by blockers of the Hh pathway. Because virtually all cell types undergo plasma membrane remodeling when stimulated, derived MVs can therefore be considered true vectors in the transfer of morphogen-borne biologic information to remote responsive cells, and thereby contribute to the maintenance of homeostasis.

From Biochemistry to Morphogenesis in Myxobacteria

Many aspects of metazoan morphogenesis find parallels in the communal behavior of microorganisms. The cellular slime mold D. discoideum has long provided a metaphor for multicellular embryogenesis. However, the spatial patterns in D.d. colonies are generated by an intercellular communication system based on diffusible morphogens, whereas the interactions between embryonic cells are more often mediated by direct cell contact. For this reason, the myxobacteria have emerged as a contending system in which to study spatial pattern formation, for their colony strutures rival those of D.d. in complexity, yet communication between cells in a colony is carried out by direct cell contacts. Here I sketch some of the progress my laboratory has made in modeling the life cycle of these organisms.

Solving the advection-diffusion equations in biological contexts using the cellular Potts model

The cellular Potts model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approximate the Laplacian. Directed spin flips in the CPM handle the advective movement of the fluid particles. A constraint on relative velocities in the fluid explicitly accounts for fluid viscosity. We use the CPM to solve various diffusion examples including multiple instantaneous sources, continuous sources, moving sources, and different boundary geometries and conditions to validate our approximation against analytical and established numerical solutions. We also verify the CPM results for Poiseuille flow and Taylor-Aris dispersion.

Why cavefish are blind

Some fish exist as eyed, surface-dwelling and eyeless, cave-dwelling forms. The developmental processes that cause eye degeneration in different populations of Astyanax cavefish are similar. Although small optic primordia start to form, apoptosis of lens cells triggers developmental arrest and degeneration of the eyes. Degeneration has been linked to reduced expression of the transcription factor Pax6 in the anterior embryonic midline and optic primordia. Recently, Yamamoto and colleagues reported that increased expression of the diffusible morphogen Sonic hedgehog (Shh) at the embryonic midline of cavefish reduces pax6 expression and increases expression of Shh-regulated genes, which might confer selective advantages for life in caves.

Evidence for an Expansion-Based Temporal Shh Gradient in Specifying Vertebrate Digit Identities

The zone of polarizing activity (ZPA) in the posterior limb bud produces Sonic Hedgehog (Shh) protein, which plays a critical role in establishing distinct fates along the anterior-posterior axis. This activity has been modeled as a concentration-dependent response to a diffusible morphogen. Using recombinase base mapping in the mouse, we determine the ultimate fate of the Shh-producing cells. Strikingly, the descendants of the Shh-producing cells encompass all cells in the two most posterior digits and also contribute to the middle digit. Our analysis suggests that, while specification of the anterior digits depends upon differential concentrations of Shh, the length of time of exposure to Shh is critical in the specification of the differences between the most posterior digits. Genetic studies of the effects of limiting accessibility of Shh within the limb support this model, in which the effect of the Shh morphogen is dictated by a temporal as well as a spatial gradient.

Waves and aggregation patterns in myxobacteria.

Under starvation conditions, a population of myxobacteria aggregates to build a fruiting body whose shape is species-specific and within which the cells sporulate. Early in this process, cells often pass through a "ripple phase" characterized by traveling linear, concentric, and spiral waves. These waves are different from the waves observed during slime mold aggregation that depend on diffusible morphogens, because myxobacteria communicate by direct contact. The difference is most dramatic when waves collide: rather than annihilating one another, myxobacterial waves appear to pass through one another unchanged. Under certain conditions, the spacing and location of the nascent fruiting bodies is determined by the wavelength and pattern of the waves. Later in fruiting body development, waves are replaced by streams of cells that circulate around small initial aggregates enlarging and rounding them. Still later, pairs of motile aggregates coalesce to form larger aggregates that develop into fruiting bodies. Here we present a mathematical model that quantitatively explains these wave and aggregation phenomena.

FABRICATION AND FUNCTION OF AMMONITE SEPTA—COMMENT ON LEWY

Lewy (2002) addressed a variety of the muscular-attachment hypothesis for the function of the ammonite septal suture, namely, that of fastening the body to the shell during active prey subjugation. In this way, sutural complexity is an index of how active the ammonite was as a carnivore. He followed Henderson (1984, p. 461) in that complex septa “facilitated the attachment of adductor muscles” (Lewy, 2002, p. 64). Without adding new data, Lewy (2002) discredited not only other functional hypotheses, but also those of fabricational nature, in particular the tie-point model (Seilacher, 1973, 1975) and the viscous-fingering (VF) model (Garcia-Ruiz et al., 1990; Checa and Garcia-Ruiz, 1996). These models are currently the only ones aiming to explain the complex shape of the septal template by means of simple biophysical processes. Additionally, Hammer (1999) explains the formation of septal sutures as the result of morphogen diffusion. Hammer's model has been proposed only on theoretical grounds and has not yet confronted the paleobiological evidence. Therefore, it will not be further examined here. The following comments aim not only to reveal some misconceptions in Lewy's paper concerning the tie-point and VF models but also to stress the need to keep function and fabrication of the ammonite septum separate though related concepts. Other topics covered by Lewy (2002) will not be dealt with here. In Lewy's view, the posterolateral part of the body “formed …

Pattern formation and traveling waves in myxobacteria: theory and modeling.

Recent experiments have provided new quantitative measurements of the rippling phenomenon in fields of developing myxobacteria cells. These measurements have enabled us to develop a mathematical model for the ripple phenomenon on the basis of the biochemistry of the C-signaling system, whereby individuals signal by direct cell contact. The model quantitatively reproduces all of the experimental observations and illustrates how intracellular dynamics, contact-mediated intercellular communication, and cell motility can coordinate to produce collective behavior. This pattern of waves is qualitatively different from that observed in other social organisms, especially Dictyostelium discoideum, which depend on diffusible morphogens.

Is Chordin a morphogen?

Models employing gradients of diffusible morphogens are often invoked to explain regional specification in the early embryo. In these models, a concentration gradient of a secreted factor generates distinct cell fates, based on the differential response of cells to local concentrations of this morphogen. In recent years, there has been a great deal of focus on the factors involved in the dorsoventral patterning of the vertebrate mesoderm and ectoderm. Dorsoventral specification during amphibian gastrulation is regulated by the antagonistic actions of the Bone Morphogenetic Proteins (BMPs) and a number of dorsally expressed inhibitors, including the secreted factor, Chordin. In a recent paper, Blitz and colleagues explore the possibility that Chordin acts as a long-range factor in the amphibian gastrula embryo, to establish a functional gradient of BMP activity.

Stomatal Pore Density

As atmospheric CO 2 concentration increases, the density of stomatal pores on the leaf surface decreases to prevent loss of water during transpiration. An analysis of mutants by Gray et al. reveals that a gene in the plant Arabidposis thaliana called high carbon dioxide ( HIC ) may be responsible for regulating stomatal development in response to CO 2 . HIC , expressed exclusively in guard cells that flank stomatal pores, encodes a putative 3-keto acyl coenzyme A synthase, an enzyme involved in synthesizing long-chain fatty acids that comprise components of the extracellular matrix found at the surface of guard cells. When HIC expression is disrupted, plants can no longer respond to increases in CO 2 . The authors propose that absence of the HIC -encoded enzyme could alter the composition of the extracellular matrix and thus affect diffusion of CO 2 -regulated morphogens that regulate stomatal development. Gray, J.E., Holroyd, G.H., Van der Lee, F.M., Bahrami, A.R., Sijmons, P.C., Woodward, F.I., Schuch, W., and Hetherington, A.M. (2000) The HIC signalling pathway links CO 2 perception to stomatal development. Nature 408 : 713-716. [Online Journal]

Is Chordin a Long-Range- or Short-Range-Acting Factor? Roles for BMP1-Related Metalloproteases in Chordin and BMP4 Autofeedback Loop Regulation

Diffusible morphogen models have been used widely to explain regional specification of tissues and body axes during animal development. The three-signal model for patterning the dorsal–ventral axis of the amphibian embryo proposes, in part, that a factor(s) secreted from Spemann's organizer is responsible for converting lateral marginal zone into more dorsal cell fates. We examine the possibility that chordin, a secreted inhibitor of bone morphogenetic protein (BMP) signaling and candidate “dorsalizing signal,” is a long-range-acting factor. We show that chordin can, when overexpressed, act directly over distances of at least 450 μm in the early Xenopus embryo to create a gradient of BMP signaling. However, since lower levels of chordin can still induce secondary axes and these amounts of chordin act only locally to inhibit a BMP target gene, we suggest that chordin likely acts as a short-range signal in vivo. Furthermore, BMP1, a secreted metalloprotease that cleaves chordin protein in vitro, inhibits chordin's axis-inducing effects, suggesting that BMP1 functions to negatively regulate chordin's action in vivo. A dominant-negative mutant BMP1 blocks the in vitro cleavage of chordin protein by wild-type BMP1 and induces secondary axes when injected ventrally. We argue that BMP1 and Xolloid are probably functionally redundant metalloproteases and may have two roles in the early Xenopus embryo. One role may be to inhibit the action of low-level chordin protein expressed throughout the entire embryo and a possible second role may be to inhibit activation of a juxtacrine cell relay, thereby confining chordin's action to the organizer region preventing chordin from functioning as a long-range-acting factor.

The homeobox gene mirror links EGF signalling to embryonic dorso-ventral axis formation through notch activation.

Recent studies in vertebrates and Drosophila melanogaster have revealed that Fringe-mediated activation of the Notch pathway has a role in patterning cell layers during organogenesis. In these processes, a homeobox-containing transcription factor is responsible for spatially regulating fringe (fng) expression and thus directing activation of the Notch pathway along the fng expression border. Here we show that this may be a general mechanism for patterning epithelial cell layers. At three stages in Drosophila oogenesis, mirror (mirr) and fng have complementary expression patterns in the follicle-cell epithelial layer, and at all three stages loss of mirr enlarges, and ectopic expression of mirr restricts, fng expression, with consequences for follicle-cell patterning. These morphological changes are similar to those caused by Notch mutations. Ectopic expression of mirr in the posterior follicle cells induces a stripe of rhomboid (rho) expression and represses pipe (pip), a gene with a role in the establishment of the dorsal-ventral axis, at a distance. Ectopic Notch activation has a similar long-range effect on pip. Our results suggest that Mirror and Notch induce secretion of diffusible morphogens and we have identified TGF-beta (encoded by dpp) as such a molecule in germarium. We also found that mirr expression in dorsal follicle cells is induced by the EGF-receptor (EGFR) pathway and that mirr then represses pip expression in all but the ventral follicle cells, connecting EGFR activation in the dorsal follicle cells to repression of pip in the dorsal and lateral follicle cells. Our results suggest that the differentiation of ventral follicle cells is not a direct consequence of germline signalling, but depends on long-range signals from dorsal follicle cells, and provide a link between early and late events in Drosophila embryonic dorsal-ventral axis formation.

Reaction-diffusion processes: Application to the morphogenesis of Ammonoid ornamentation

Ammonoid ribs, tubercles, keels and other ornamental features are organized in a great diversity of patterns. From the viewpoint of developmental biology, these patterns can only be understood as the product of a dynamical system controlled by genes but also dependent upon biochemical and mechanical processes. Here, an attempt is made to view the development of ammonoid ornamentation in the light of reaction-diffusion systems, though it is emphasized that diffusion of biochemical morphogens is only one of several possible interpretations of this class of theoretical models. Also, morphogenetical gradients and threshold functions are presented as partial explanations for some specific ornamental patterns.

The Drosophila short gastrulation gene prevents Dpp from autoactivating and suppressing neurogenesis in the neuroectoderm.

The short gastrulation (sog) gene is expressed in broad lateral stripes comprising the neuroectoderm of the Drosophila blastoderm embryo. sog encodes a predicted secreted protein that functions nonautonomously to antagonize the activity of the TGF-beta-like Decapentaplegic (Dpp) signaling pathway in the dorsal region of the embryo. Recently, it has been shown that sog and dpp are functionally equivalent to their respective Xenopus homologs chordin and BMP-4. In this report we provide the first direct evidence that sog plays a local role in the lateral region of the blastoderm embryo to oppose Dpp activity in the neuroectoderm. In the dorsal region, Dpp signaling both suppresses neurogenesis and maintains expression of genes that promote dorsal cell fates (dorsalization). We show that Dpp also can perform both of these functions in the neuroectoderm. In wild-type embryos, the ability of Dpp to induce expression of dorsal markers including itself (autoactivation) in the neuroectoderm is blocked by sog. We propose that Sog protects the neuroectoderm from an invasive positive feedback loop created by Dpp diffusion and autoactivation. We show that the two functions of Dpp signaling, neural suppression and dorsalization, are triggered by distinct thresholds of Dpp activity. Epistasis experiments reveal that all observed sog activity can be accounted for by Sog functioning as a dedicated Dpp antagonist. Finally, we provide evidence that Sog functions as a diffusible morphogen in the blastoderm embryo. These data strongly support the view that the primary phylogenetically conserved function of the Drosophila sog and dpp genes and the homologous Xenopus chordin and BMP-4 genes is to subdivide the primitive embryonic ectoderm into neural versus non-neural domains.