Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients

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Science  01 Aug 2014:
Vol. 345, Issue 6196, pp. 566-570
DOI: 10.1126/science.1252960

How do fingers know where to grow?

Most researchers today believe that each finger forms because of its unique position within the early limb bud. However, 30 years ago, developmental biologists proposed that the arrangement of fingers followed the Turing pattern, a self-organizing process during early embryo development. Raspopovic et al. provide evidence to support a Turing mechanism (see the Perspective by Zuniga and Zeller). They reveal that Bmp and Wnt signaling pathways, together with the gene Sox9, form a Turing network. The authors used this network to generate a computer model capable of accurately reproducing the patterns that cells follow as the embryo grows fingers.

Science, this issue p. 566; see also p. 516


During limb development, digits emerge from the undifferentiated mesenchymal tissue that constitutes the limb bud. It has been proposed that this process is controlled by a self-organizing Turing mechanism, whereby diffusible molecules interact to produce a periodic pattern of digital and interdigital fates. However, the identities of the molecules remain unknown. By combining experiments and modeling, we reveal evidence that a Turing network implemented by Bmp, Sox9, and Wnt drives digit specification. We develop a realistic two-dimensional simulation of digit patterning and show that this network, when modulated by morphogen gradients, recapitulates the expression patterns of Sox9 in the wild type and in perturbation experiments. Our systems biology approach reveals how a combination of growth, morphogen gradients, and a self-organizing Turing network can achieve robust and reproducible pattern formation.

Digits form in a periodic pattern that alternates digital and interdigital fates along the anterior-posterior (AP) axis of the limb bud. Traditionally, this pattern has been explained by a positional information model (1) based on an AP gradient of Sonic hedgehog (Shh) (2, 3). However, embryonic and genetic manipulations (4, 5) have shown that digit patterning is independent of Shh and may be instead controlled by a self-organizing mechanism. Over three decades ago, it was proposed that such a mechanism could be a Turing system (6, 7), in which a diffusible activator and inhibitor (8) interact and self-organize to form the periodic digit pattern. Recent work has strengthened this hypothesis (9); however, two important questions remain to be addressed.

First, although a number of mathematical Turing models have been proposed to explain the periodic digit pattern (10, 11), no computer simulation has been able to correctly reproduce the expression patterns of digit markers over time and space. Second, the diffusible molecules that implement the Turing network have not yet been identified. Transforming growth factor–β (TGF-β) molecules were proposed as activators in a Turing system (12, 13), but the corresponding diffusible inhibitor could not be found. The galectins CG-1A and CG-8 have also been proposed as Turing molecules in the chick (14) but are not believed to play a similar role in mammals (15). More recently, bone morphogenetic proteins (BMPs) and their receptors have been proposed to form a Turing network (10), but this model assumed that the BMP receptors can diffuse through tissue, for which there is no evidence.

To identify the molecules that control digit specification, it is crucial to distinguish the genes involved in early digit patterning from downstream differentiation factors. We therefore analyzed the expression of the earliest known skeletal marker Sox9 (16) and identified embryonic day 11.5 (E11.5) as the earliest stage that shows a periodic digital pattern (Fig. 1A). We also performed micromass cultures with E11.5 Sox9-EGFP (enhanced green fluorescent protein) limb autopods (17) and found that cells create a periodic Sox9 pattern by 15 hours, faster than previously reported (18), with dynamics reminiscent of a two-dimensional (2D) Turing simulation (Fig. 1B and movie S1). We observed that the periodic pattern formed even when the culture was initiated with Sox9 or Sox9+ cells sorted by fluorescence-activated cell sorting (FACS) (Fig. 1, B and C, and movies S2 and S3), confirming that Sox9 is dynamically regulated by a self-organizing patterning mechanism.

Fig. 1 The Sox9 periodic digit pattern.

(A) Top: Sox9 expression patterns (red) from E11 to E12 (limb shape in green). Bottom: Anterior-posterior (AP) profiles (dashed line above) highlight the progressive appearance of the Sox9 periodic pattern, first visible at E11.5; arrowheads indicate digit 4. Limb orientation in all figures: distal to the right, posterior to the bottom. (B) First row: time course of micromass culture with Sox9-EGFP autopod cells; a periodic pattern emerges by 15 hours. Second and third rows: When cultures are initiated with Sox9 or Sox9+ cells obtained by FACS sorting, they still form a periodic pattern by up-regulating or down-regulating Sox9 depending on the position (single cells highlighted by red and green circles). (C) Sox9-EGFP intensities of the tracked cells over time. (D) The two simplest models that can form a Turing pattern. In the Activator-Inhibitor model, an autocatalytic activator (A) promotes its own inhibitor (I), resulting in in-phase periodic patterns. In the Substrate-Depletion model, an activator (A) activates itself by depleting its own substrate (S), resulting in out-of-phase periodic patterns.

When Sox9 is knocked out, all the genes that reflect a digital or interdigital pattern (e.g., Bmp2, Chordin, Noggin) lose their normal periodic expression (19), suggesting that Sox9 itself is part of the Turing network rather than a downstream differentiation marker. The two simplest Gierer-Meinhardt topologies (8), the activator-inhibitor and the substrate-depletion model (Fig. 1D), predict that the diffusible molecules of the Turing network should have periodic patterns that are either in-phase or out-of-phase, respectively. We therefore performed a microarray analysis to identify genes related to the major developmental signaling pathways that were differentially expressed between Sox9+ and Sox9 FACS-sorted cells. On the basis of both the number of genes and fold-change magnitude, the pathways that were most strongly represented were WNT, BMP, and FGF (fibroblast growth factor) (fig. S1). We performed a second level of screening by whole-mount in situ hybridization (WMISH) to check which genes were genuinely expressed in-phase or out-of-phase with Sox9 (fig. S1). The analysis revealed in-phase and out-of-phase expression patterns for genes in the BMP and WNT pathways, but not for the FGF pathway. Specifically, Bmp2 showed a pattern that is out-of phase with Sox9 at all stages of digit patterning (Fig. 2A and fig. S1). None of the WNT ligands were differentially expressed, but target genes (e.g., Axin2 and Lef1) were expressed in Sox9 cells at E12 (fig. S1). This is consistent with the observation that WNT ligands produced in the ectoderm repress Sox9 and chondrogenesis (20, 21). Indeed, knockout of β-catenin in the limb results in the expansion of Sox9 toward the ectoderm, whereas β-catenin gain-of-function results in Sox9 down-regulation (22, 23).

Fig. 2 Sox9 is out of phase with BMP and WNT.

(A) Time course of Bmp2 expression, Sox9-EGFP fluorescence (Sox9), BMP signaling (pSMAD), and WNT signaling activity (act-βcat). Digit 4 (white arrowhead) appears first (E10.5), followed by digit 3 and then 2 (see Sox9). Bmp2 and act-βcat are out-of-phase with Sox9, whereas pSMAD is in-phase (see also fig. S2). (B) Top: Graphs show the progressive patterning along the AP axis measured from the images above. Black arrowheads point to digit 4. Bottom: A 1D simulation of the BSW model produces a Sox9 pattern that is out-of-phase with Bmp and Wnt, as shown in the experimental data above. (C) Network topology and equations of the BSW model.

For a direct analysis of BMP, WNT, and FGF signaling activity, we performed immunohistochemistry for phosphorylated Smad1/5/8 (pSMAD), nonphosphorylated active β-catenin (act-βcat), and phosphorylated extracellular signal–regulated kinase (pERK) on serial cryosections of Sox9-EGFP limbs. This allowed us to correlate the activity of the three pathways with the spatial dynamics of digit patterning. We found that BMP signaling (pSMAD) is high in the digits and correlates with Sox9-EGFP (Fig. 2A and fig. S2), supporting the positive effect of BMP signaling on Sox9 (2426) and its importance for digit patterning (27). In contrast to pSMAD, WNT signaling (act-βcat) is high in the interdigital regions and has a pattern that is out-of-phase with Sox9 at all stages (Fig. 2A and fig. S2). This close spatial correspondence supports Wnt/β-catenin involvement in the Turing mechanism and is consistent with the repression of Sox9 by Wnt/β-catenin (21, 22). Finally, FGF signaling (pERK) shows no periodic pattern but only the expected proximo-distal (PD) gradient, which is highest under the apical ectodermal ridge (AER) (fig. S2). Indeed, Fgf has previously been proposed as a modulator of the digit wavelength (9) rather than being part of the Turing network.

From the spatial relationships between these molecular patterns (Fig. 2B), we hypothesized that the Turing network that controls digit patterning is a three-node model implemented by Sox9, Bmp, and Wnt. Of the possible regulatory interactions between these three nodes, two are clear from the literature: the positive influence of BMP signaling on Sox9 (2426) and the inhibition of Sox9 by WNT signaling (2123). With these two interactions fixed, we performed a linear stability analysis for a three-component reaction-diffusion system (see supplementary text 2.2 and 2.3). Among all possible cases, we identified the topology shown in Fig. 2C (the Bmp-Sox9-Wnt, or BSW, model) as the simplest and most robust Turing network that can self-organize to produce a periodic pattern in which Sox9 is out-of-phase with both Bmp expression and Wnt signaling activity (Fig. 2B).

When simulated in 2D, the BSW model produces a pattern of randomly oriented stripes reminiscent of the pattern formed in micromass culture (fig. S3). The next challenge was to show that the model can reproduce the time course of Sox9 expression in a realistic simulation of limb development. Because Turing patterns are influenced by growth and shape changes of the underlying tissue (28, 29), we used a 2D growth model derived from clonal fate-mapping experiments (30). Within this tissue-movement map, the BSW network generated a stripy pattern that tended to orient along the PD axis (Fig. 3A, movie S4, and supplementary text 2.9.1). Next, because digit patterning appears to be relatively independent from the rest of the skeleton (9, 24, 27, 31), we chose to modulate the BSW model to generate the Turing instability only in the digital region defined by Hoxd13 expression (Fig. 3B, movie S5, and supplementary text 2.9.2). This naturally promoted the sequential appearance of PD-oriented stripes and greatly reduced the variability of the pattern across different simulation runs (supplementary text 2.9.2); however, digit bifurcations occurred after E12 (Fig. 3B). We previously showed that distal Hox genes and FGF signaling jointly modulate the wavelength (digit width) to specify digit number and avoid bifurcations (9). When we combined modulation by FGF signaling (Fig. 3C and movie S6) and Hoxd13 (Fig. 3D), the model robustly produced Sox9 patterns that recapitulated the Sox9 expression in wild-type limbs (Fig. 3, E and F; fig. S4; supplementary text 2.9.4 and 2.12; and movies S7 and S8).

Fig. 3 Realistic computer simulation of digit patterning.

(A) When the BSW model was simulated inside an experimental limb growth map (left), Sox9 (red) formed a pattern with randomly oriented stripes biased along the PD axis (right). (B) Experimental Hoxd13 expression was mapped into the growing model (left, heat-color map: blue = 0 and red = 1). With the Hoxd13 modulation, the model creates a digit-like pattern (right), which eventually shows digit bifurcation (arrowhead). (C) Fgf expression in the AER was mapped into the model (solid line for Fgf8, dashed line for Fgf4-9-17) and used to simulate an Fgf signaling gradient (left, heat-color map: blue = 0 and red = 1). With the Fgf modulation, the model predicted a radially oriented Sox9 pattern with bigger wavelength toward the distal tip (right). (D) When Fgf and Hoxd13 jointly modulate the parameters k4 and k7, the system shifts (dashed arrow) into the Turing space (gray region). (E) The simulated Sox9 pattern recapitulates the main features of (F) the experimental Sox9 expression in the digits, outlined by the white dotted lines. Arrowheads mark the late appearance of digits 5 and 1.

Finally, we used E11.5 Sox9-EGFP limb cultures (fig. S5) to test predictions from the computer model and to verify the Turing network. Reducing Bmp signaling in the simulation (from E11.5 onward) predicted a loss of digital Sox9 expression (Fig. 4A and movie S9) similar to the result of inhibiting BMP signaling in limb culture (Fig. 4B). Conversely, reducing Wnt signaling in the model predicted that all digits should expand until they merge into a continuous domain of Sox9 expression (Fig. 4A and movie S10). The same dynamics were observed when WNT signaling was inhibited in vitro (Fig. 4B). Our results reveal that upon abrogation of Wnt/β-catenin signaling, Sox9 expands not only in the subectodermal mesenchyme (23) but also into the interdigital regions (Fig. 4C), proving that Wnt/β-catenin signaling is a necessary component of the periodic digital patterning process. The model also predicted that in all cases, Bmp expression should be opposite to that of Sox9, and we observed the same for Bmp2 expression in the experiments (Fig. 4D). A further series of experiments, in which we implanted protein-soaked beads into the limb bud mesenchyme (fig. S6), also confirmed the predictions of the model and allowed us to hypothesize that the primary ligands are BMP2 and WNT3 (supplementary text 2.11.5 and movies S11 to S14).

Fig. 4 Model predictions and experimental perturbations.

(A) Sox9 patterns (red) predicted by the BSW model in different perturbations. Bmp inhibition causes loss of digital expression (second row), whereas Wnt inhibition predicts gradual loss of interdigits (third row). (B) Experimental manipulation of E11.5 limb buds in Sox9-EGFP limb culture confirmed the model predictions. Addition of the BMP signaling inhibitor LDN caused a loss of digital Sox9-EGFP (second row), whereas addition of the WNT inhibitor IWP2 caused the opposite result: Each digit expanded until complete fusion (third row). (C) Transverse sections show that WNT inhibition (+IWP2) induces expansion of Sox9-EGFP in the interdigital tissue (not only under the ectoderm). (D) The BSW model predicts that distal Bmp should be up-regulated and down-regulated in Bmp or Wnt signaling inhibition, respectively; the same behavior was observed for Bmp2 expression in culture. (E) The model predicts progressively larger and fewer digits when both pathways are inhibited simultaneously (bottom row). Similar results are obtained by adding LDN and IWP2 simultaneously with progressively higher concentrations (low, medium, high) (upper row).

Because inhibiting Bmp caused a loss of digits, whereas inhibiting Wnt caused a loss of interdigits, we explored whether the simultaneous inhibition of both pathways could balance out and instead cause an alteration of the pattern. The computer simulation predicted that a combination of both drugs would increase the digit period (the effective wavelength), resulting in an oligodactyly phenotype with fewer digits (Fig. 4E and supplementary text 2.11.4). Application of both drugs to the limb bud culture confirmed this prediction, showing that the digit period becomes larger as the concentrations of both drugs increase (Fig. 4E and fig. S7). This supports both our BSW model and the general concept of a Turing-type process, because the new pattern was not just a down-regulation or up-regulation of Sox9 but a genuine rearrangement of the already initiated periodic digital pattern.

Our study reveals the main feedbacks involved in digit patterning; however, other regulatory pathways may be involved to confer extra redundancy or robustness to the system. We propose that Wnt/β-catenin is essential for digit patterning and in particular for repressing Sox9 in the interdigital regions. This suggests a possible mechanistic link between molecular patterning and mesenchymal condensations, as Wnt/β-catenin signaling may prevent the formation of β-catenin–cadherin complexes, which otherwise promote tighter cell adhesion (32). Finally, our model suggests a correlation between three separate functions of FGF signaling: control of growth (33), promotion of distal PD markers as Hoxd13 (34), and promotion of larger digit wavelength (9). Taken together, this suggests that any FGF-driven change in limb bud size would naturally be accompanied by a change in PD digit length (Hoxd13 domain) and in AP digit width (Turing wavelength) (fig. S8 and supplementary text 2.9.4), thereby implementing a perfect strategy for scale invariance.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S8

References (3587)

Movies S1 to S14

References and Notes

  1. Acknowledgments: The Sox9-EGFP mouse line was kindly provided by H. Akiyama and P. Jay. The mRNA probe for Bmp2 was kindly provided by C. Pujades. We thank R. Zeller for the Smad4 mutant limbs; A. R. Moreno for in situs of Fgf4, 8 and Twist1; and D. Barcena for the help with the micromass cultures. J.S. was supported by CRG and ICREA, L.R. by Ministerio de Economía y Competitividad (MINECO) BFU2010-16428, and Centro de Excelencia Severo Ochoa, SEV-2012-0208, and L.M. by the CRG; J.R. was funded by a Ph.D. Fellowship from the Fundaçao para a Ciencia e Tecnologia. Confocal microscopy was done in the CRG Advanced Light Microscopy Unit, and FACS and microarrays in the CRG Core Facilities. The microarray data discussed in this publication are accessible through Gene Expression Omnibus series accession number GSE58158.
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