Spatial patterning of contractility by a self-organized mechanogen activity gradient underlies Drosophila gastrulation

Abstract

During development cell deformations are spatially organized, however, how cellular mechanics is spatially controlled is unclear. Spatial control of cell identity often determines local cellular mechanics in a two-tiered mechanism. Theoretical studies also proposed that molecular gradients, so called “mechanogens”, spatially control mechanics. We report evidence of a similar mechanism required for Drosophila gastrulation. We show that the GPCR ligand Fog, expressed in the posterior endoderm, diffuses and acts in a concentration-dependent manner to activate actomyosin contractility at a distance during a wave of tissue invagination. While Fog is uniformly distributed in the extracellular space, it forms a surface-bound gradient that recruits Myosin-II via receptor oligomerization. This activity gradient self-renews as the wave propagates and is shaped by both receptor endocytosis and modulation of GPCR signalling by integrins upon adhesion to the vitelline membrane. This exemplifies how chemical, mechanical and geometrical cues underly the emergence of a self-organized mechanogen activity gradient.

During morphogenesis patterned contractility drives tissue shape changes. Here they show that GPCR signaling and integrin activation give rise to a dynamically translocating gradient of contractility required for a self-organized wave of tissue invagination.

Introduction

Embryonic development entails the spatial and temporal control of both cell fate determination to generate different cell types¹ and of cell mechanics to generate tissue shapes during morphogenesis^2–4. Classically, the latter is considered to be a consequence of the former. For instance, the vertebrate nervous system is first specified in the dorsal region of the ectoderm and subsequently shaped into the neural tube. Similarly, the Drosophila mesoderm is first specified in the ventral part of the embryos, and then invaginates.

Typically, spatial patterning in a field of cells involves morphogens, i.e., diffusing molecules⁵ that form concentration gradients⁶ and impart positional information within tissues⁷. Morphogens are produced from a source, from where they diffuse, and are degraded within the target tissue, thereby producing exponential gradients^8,9. Receiving cells interpret the positional information imparted by morphogen gradients by activating the expression of different genes at different morphogen concentration thresholds. This mechanism partitions the field of receiving cells into discrete domains with different cell identities^10,11. For example, the morphogens Shh, BMP and Wnt specify the identity of different neuron progenitors in the vertebrate neural tube through the expression of different combinations of transcription factors¹². In Drosophila, the morphogen Dorsal specifies mesoderm identity on the ventral side of embryos via the expression of the transcription factors Twist and Snail^13,14. Within this framework, the specification of cell identities directs downstream morphogenetic processes through the expression of molecular effectors that regulate cell mechanics, such as cell contractility, cell motility and cell adhesion^4,15. For example, the differential expression of adhesion molecules downstream of the Shh morphogen controls sorting of neural progenitors in the zebrafish neural tube¹⁶. In the Drosophila ventral mesoderm, the transcription factors Twist and Snail, in response to the morphogen Dorsal, induce the expression of Fog, a GPCR ligand that leads to the apical activation of the small GTPase Rho1, the kinase Rok and non-muscle Myosin-II (MyoII)^17–21. This induces cell-autonomous apical constriction and culminates with the invagination of the mesoderm in the ventral part of the embryos. Thus, morphogens direct morphogenesis via a two-tiered mechanism whereby the spatial control of cell identities determines downstream local cellular mechanics.

By analogy to the concept of morphogens, theoretical studies^22,23 proposed that so-called “mechanogens”, i.e., “external diffusible biomolecules”, may form spatial gradients that “influence mechanical properties, such as cell-cell adhesion and cellular contractility (and therefore, cell shape), and create spatial gradients in cell structure in a tissue”²³. Recent studies reported that classical morphogens can also function as mechanogens by regulating collective tissue mechanical properties without specifying cell fates. For instance, a gradient of Nodal in Zebrafish specifies mesendoderm invagination by two mechanisms: (1) triggering a motility-driven unjamming transition in protrusive leader cells able to autonomously internalize, and (2) promoting adhesion to their immediate followers, which results in a collective and ordered mode of internalization²⁴. Similarly, in the developing feather buds, the morphogens BMP and FGF define two adjacent domains with different supracellular mechanical properties, a rigid elastic core and an active fluid-like margin, that drive mesenchymal budding²⁵. In both cases, the morphogens Nodal and BMP can be considered to act as mechanogens as they tune collective, supracellular mechanical properties; however, they most likely do it indirectly via transcriptional regulation of target genes. Instead, mechanogens have been proposed to form chemical gradients that directly regulate cell mechanics (e.g., cell contractility) without the intermediary of gene transcription²².

Here, we demonstrate that the GPCR ligand Fog, a signaling molecule directly controlling cellular contractility, in addition to its autocrine function in the Drosophila posterior midgut anlage, it diffuses away from its zone of production and acts in a concentration-dependent manner to control a gradient of MyoII activation during the propagation of a wave of tissue invagination. We show that, although Fog is homogenously distributed in the extracellular perivitelline fluid, it forms a multicellular scale activity gradient on the cell surface that constantly renews and propagates towards the anterior as the wave propagates. We propose that the Fog activity gradient patterns contractility in a manner similar to a mechanogen.

Results

GPCR signaling is required in the propagation zone for MyoII activation

The morphogenesis of the Drosophila posterior endoderm begins with MyoII-dependent apical constriction in the posterior-most region of the embryo, the endoderm primordium. Here, the terminal transcription factors Hückebein and Tailless²⁶ control the localized expression and secretion of the ligand Fog, which activates tissue autonomous recruitment of MyoII apically and tissue bending^17,27,28. This induces a polarized flow towards the embryo dorsal-anterior due to the high curvature of the tissue in this region²⁹ (Fig. 1a, b). This initial flow and tissue bending triggers a wave of MyoII activation and tissue invagination that propagates anteriorly within the dorsal epithelium across a region denominated “wave propagation zone (PZ)” (Fig. 1a, c). Wave propagation does not depend on sustained gene transcription and is driven by a self-replicating cycle of 3D cell deformation²⁸ where cells anterior to the furrow undergo in a sequence: (1) contact with the vitelline membrane (VM), (2) integrin-mediated adhesion, (3) MyoII activation, and (4) detachment from the VM due to contractility in the furrow³⁰, as they get closer to the invaginating front (Fig. 1c). During the wave, MyoII is initially recruited at low levels in cells distant from the furrow upon their contact with the vitelline membrane. Then, when cells get closer to the furrow, MyoII recruitment rapidly increases via positive feedback, where integrins promote MyoII recruitment, which in turn stabilizes focal complexes in contact with the VM³⁰. Previous studies²⁸ ruled out that the propagation of MyoII activation solely reflects the movement of the diffusion front of an expanding gradient of the ligand Fog away from the endoderm primordium. However, the requirement for Fog-GPCR signaling in the activation of MyoII in cells of the PZ was not directly tested. Furthermore, since in the absence of integrins (KO of the integrin α-PS3, also known as Scab), MyoII activation, which remains pulsatile at low levels, is not completely abolished during wave propagation³⁰, other factors, such as Fog-GPCR signaling, could be involved.

Fig. 1. MyoII activation in the PZ requires GPCR signaling.

a Endoderm invagination during Drosophila gastrulation. Gray: the domain of hkb expression, green: MyoII contractility. b MyoII activation by Fog/GPCR signaling in the primordium. c 3D cycle of cell deformation during wave propagation. Green arrows: MyoII contractility, blue arrows: compressive forces, orange: integrin-dependent adhesion. Black arrows: Feedback amplification between adhesion and MyoII recruitment, VM vitelline membrane. d Time-lapse of the posterior endoderm invagination in a WT and a Gα^−/− hkb-Gα embryo. Yellow solid and dashed lines: anterior limits of the primordium and the PZ, respectively. Orange dashed line: VM. White arrows: invagination depth measured in (g). Time 0 is 22 min prior to cell divisions (see Methods). Purple: the regions of Gα is expression. e Representative cells in the primordium. Yellow: cell contours. f Apical cell area and MyoII mean intensity over time in cells of the primordium. n = 30 cells from five embryos each. g Depth of the primordium invagination at T = 8 min. n = 4 embryos each. P = 0.17, two-sided unpaired t-test with Welch’s correction. h Cumulated number of cell rows recruiting MyoII over time. Time 0 is the onset of MyoII recruitment in the first cell of the PZ for each embryo. n = 4 embryos for control and 7 for Gα^−/− hkb-Gα. i High-resolution time-lapse of MyoII recruitment in the PZ. White solid and dashed lines: representative cells tracked over time. White arrows: high-level recruitment of MyoII before cell detachment. j MyoII mean intensity over time in cells of the PZ. Time 0 for each cell is when the cell area is maximum (see Methods). Inset: blow-up of the dashed box. k MyoII maximum integrated intensity in cells of the PZ. ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. l Average junctional distance from the VM over time in cells of the PZ. n = 75 cells from 4 embryos each in (j, k). n = 75 and 34 cells in WT and Gα^−/−hkb-Gα from four embryos each in (l). m Kymographs along the AP-axis of E-cadherin junctions in representative cells. A anterior, P posterior, D dorsal, V ventral. Data in (g, k) are mean ± s.d., in (f, h, j, l) are mean ± s.e.m.

The small GTPase Gα_12/13 Concertina (hereafter Gα) is known to transduce Fog-GPCR signaling that activates medio-apical MyoII contractility and tissue invagination in the endoderm and mesoderm primordia^17,21,31,32. In the absence of Gα (null mutants Gα^−/−), invagination of the endoderm primordium, which triggers the subsequent wave propagation, is blocked²⁸. Thus, to test the role of Fog-GPCR signaling in cells of the PZ, we rescued Gα activity in Gα^−/− embryos only in the primordium to be able to induce its invagination. To this end, we expressed a WT form of Gα using a hückebein (hkb) promoter, which drives expression specifically in the posterior endoderm primordium and not in the neighboring PZ^32,33, in Gα^−/− embryos (Gα^−/−hkb-Gα hereafter). We visualized cell contours with E-cadherin::GFP and MyoII recruitment with MyoII Regulatory Light Chain MRLC::mCherry. As expected, in Gα^−/−hkb-Gα embryos, cells in the primordium recruited apical MyoII and constricted apically (Fig. 1d–f, Supplementary Fig. 1a, and Supplementary Movies 1, 2). This led to the formation of an initial invagination with kinetics similar to those in WT embryos (Fig. 1d side views and 1 g), indicating a functional rescue of Gα activity in the primordium. However, despite a normal invagination of the endoderm primordium, in Gα^−/−hkb-Gα embryos, the subsequent wave propagation (Fig. 1h–i) and the dorsal-anterior movement of the posterior endoderm (Supplementary Fig. 1b, c and Supplementary Movie 3) were severely affected. Indeed, MyoII propagation occurred on average only in 2.5 ± 0.06 (mean ± s.e.m.) rows of cells compared to an average of 7.1 ± 0.3 (mean ± s.e.m.) cells in WT embryos (Fig. 1h). Beyond the first two cells at the border with the endoderm primordium, in the PZ of Gα^−/−hkb-Gα, MyoII was not recruited at all (Fig.1i–k and Supplementary Movie 4). As a result, non-contractile cells joined the furrow, which blocked detachment from the VM of more anterior cells once they reached the edge of the invaginating furrow (Fig. 1i, l, m).

Together, we conclude that Gα signaling in cells of the PZ is required to activate MyoII and sustain wave propagation.

Fog diffusion from the primordium is necessary for MyoII activation in the propagation zone

In Drosophila, Gα signaling inducing MyoII-dependent tissue invagination is activated by the secreted GPCR ligand Fog^17,27. We thus considered that Fog might be the ligand activating Gα signaling in the PZ. Consistent with this possibility, Fog protein was detected by immunohistochemistry in the PZ²⁸. In the posterior endoderm, fog is expressed zygotically at high levels only in the primordium region^17,28, but maternally deposited fog transcripts have been detected at low levels everywhere in the embryo¹⁷ and could give rise to Fog detected in the PZ. To test the roles of these two possible sources of Fog, we generated embryos where fog is expressed only zygotically in the endoderm primordium. To this end, we blocked both maternal and zygotic endogenous expression by injection of dsRNAs against fog (fog RNAi)^28,34 and restored fog expression only in the endoderm primordium using an RNAi-resistant fog transgene expressed under the hkb promoter (hereafter hkb-fog_res) (Fig. 2a and Supplementary Fig. 2a). Contrary to the expression of an RNAi-sensitive hkb-fog transgene (hkb-fog_sen hereafter), expression of hkb-fog_res in fog RNAi embryos rescued the invagination and the dorsal-anterior movement of the posterior endoderm (Fig. 2d top and middle, Supplementary Fig. 2b–e, and Supplementary Movies 5, 6), indicating that fog_res is indeed resistant to RNAi. Notably, hkb-fog_res rescued apical MyoII recruitment, cell apical constriction and tissue invagination in the endoderm primordium, which were defective in hkb-fog_sen embryos (Fig. 2d–g and Supplementary Movies 5, 7). Furthermore, hkb-fog_res also rescued the propagation of MyoII in fog RNAi embryos. Propagation of MyoII in these embryos spanned on average 5.3 ± 0.2 (mean ± s.e.m.) cells (Fig. 2h) while it was completely blocked in hkb-fog_sen embryos injected with fog dsRNAs (Fig. 2d). Moreover, in hkb-fog_res embryos injected with fog dsRNAs the levels of MyoII were almost as high as in hkb-fog_res embryos injected with water (Fig. 2i, j and Supplementary Movie 8), showing that fog expression in the endoderm primordium is sufficient to rescue endoderm invagination and wave propagation in fog RNAi embryos. We conclude that Fog produced in the endoderm primordium acts non-autonomously in the PZ to activate GPCR-dependent MyoII activation there.

Fig. 2. Fog production from the primordium and its dispersion into the PZ are necessary for MyoII activation.

a, b Cross-section of the dorsal epithelium with the expression of an RNAi-resistant diffusible (a) and membrane-tethered version (b) of Fog under the hkb promoter. Red stars: Fog, shaded cells: endoderm primordium where the hkb promoter is active. c Illustration of the membrane-tethered Fog fusion protein (Fog-VSV-GΔ1–421). VSV-G full-length is shown for comparison. d Time-lapse of the posterior endoderm invagination in embryos injected with fog RNAi and expressing under the hkb promoter an RNAi-sensitive (hkb-fog_sen, top), an RNAi-resistant (hkb-fog_res, middle) or an RNAi-resistant version of Fog tethered to the plasma membrane (hkb-fog_VSV-G, bottom). Yellow solid and dashed lines: anterior limits of the primordium and the PZ, respectively. Orange dashed line: VM. White arrows: invagination depth measured in (f). e Representative cells in the primordium. Yellow: cell contours. f Depth of the primordium invagination at T = 5 min. n = 5 embryos for hkb-fog_sen and eight embryos for both hkb-fog_res and hkb-fog_VSV-G. **P = 0.0033 (hkb-fog_sen vs hkb-fog_res), **P = 0.0015 (hkb-fog_sen vs hkb-fog_VSV-G) and NS, P = 0.4159 (hkb-fog_res vs hkb-fog_VSV-G) with two-sided unpaired t-test with Welch’s correction. g Apical cell area and MyoII mean intensity over time in cells of the primordium. n = 30 cells from five embryos each. h Cumulated number of cell rows recruiting MyoII over time. Time 0 is the onset of MyoII recruitment in the first cell of the PZ for each embryo. n = 6 and 7 embryos in hkb-fog_res and hkb-fog_VSV-G, respectively. i High-resolution time lapses of MyoII recruitment in the PZ. White solid and dashed lines: representative cells tracked over time. White arrows: high-level recruitment of MyoII before cell detachment. j Maximum MyoII integrated intensity in cells of the PZ. **P = 0.0056 and ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. k Average junctional distance from the VM over time in cells of the PZ. n = 75 cells from three embryos each in (j, k). Data in (f, j) are mean±s.d. and in (g, h, k) are mean ± s.e.m.

Next, we investigated the mechanism by which Fog acts at a distance in the PZ. Fog is a large (100 kDa), secreted molecule and previous reports did not convincingly determine whether Fog acts in a paracrine manner^17,27,35. In light of the non-autonomous rescue of MyoII recruitment in the PZ reported above, we hypothesized that Fog produced and secreted in the primordium might diffuse into the PZ to activate MyoII. To test this, we sought to inhibit Fog dispersal from its source of production (Fig. 2b). We constructed a membrane-tethered version of Fog by fusing the entire fog coding sequence with a truncated form (Δ1–421, see methods for details) of the vesicular stomatitis virus (VSV) G protein, a type-II transmembrane protein (Fig. 2c), and tested its ability to disperse from a localized production source. We expressed Fog-VSV-GΔ1–421 (Fog_VSV-G hereafter) in stripes in the embryo using the wingless-Gal4 driver (Supplementary Fig. 3a) and visualized it with an anti-Fog antibody³⁶. Contrary to a WT version of Fog that was detected also into the neighboring non-expressing tissue, Fog_VSV-G was only observed within the producing cells (Supplementary Fig. 3b, c). To test the ability of Fog_VSV-G to activate MyoII, we overexpressed it homogeneously in the embryo during gastrulation. The resulting MyoII pattern with low-level recruitment in the entire dorsal epithelium and strong MyoII apical recruitment in the endoderm primordium and the PZ²⁸, was similar to that of an overexpressed WT Fog (Supplementary Fig. 3d, e and Supplementary Movie 9). This confirmed that Fog_VSV-G, although unable to diffuse, is able to activate GPCR signaling and MyoII contractility cell-autonomously in the embryo. We next used this tool to test whether Fog produced in the primordium diffuses to the PZ to activate MyoII there. We expressed an RNAi-resistant version of Fog_VSV-G, in the primordium (using the hkb promoter) in embryos injected with fog dsRNA to remove endogenous maternal and zygotic Fog (hereafter referred to as hkb-fog_VSV-G, Fig. 2b). In hkb-fog_VSV-G embryos, cell apical constriction and endoderm primordium invagination were similar to hkb-fog_res (Fig. 2d–g and Supplementary Movies 5, 7). However, the subsequent anterior movement of the endoderm was blocked (Supplementary Fig. 2f, g and Supplementary Movie 6) as was wave propagation (Fig. 2d, h, on average only 1.7 ± 0.1 (mean ± s.e.m.) cells). Indeed, in hkb-fog_VSV-G embryos, MyoII was not recruited apically in cells of the PZ beyond the first 1–2 cell rows (Fig. 2i, j and Supplementary Movie 8), and cells did not detach from the VM (Fig. 2k).

Altogether, we conclude that Fog produced in the primordium diffuses into the zone of wave propagation, where it is required to activate apical MyoII contractility and cell detachment. Our findings demonstrate that Fog acts in a tissue non-autonomous manner during wave propagation.

Fog production and uptake tune an exponential gradient of MyoII

Since Fog diffuses from the primordium to activate MyoII at a distance, we next explored the spatial dynamics of Fog activity. During wave propagation, apical MyoII is graded in a restricted domain of 2–3 cell rows over ~30–40 µm from the advancing furrow, with high MyoII levels in cells just anterior to the furrow and lower levels more anteriorly³⁰. We considered the possibility that Fog diffusion from the primordium and degradation or removal in the receptive field may set the amplitude and range of this graded pattern of MyoII in a manner similar to morphogen activity gradients^9,37. We found that at each moment in time, as the invaginating furrow moves towards the anterior, the spatial distribution of apical MyoII mean intensity in front of the furrow fits a one-phase exponential decay curve with an average length-scale (λ) of 3.18 ± 0.29 (mean±s.e.m.) μm. (Fig. 3a–c and Supplementary Fig. 4a, see Methods). The shape of the activity gradient of morphogens typically depends on (1) the rate of morphogen production at the source, (2) the rate of its removal in the target tissue, and (3) its diffusion coefficient. We tested whether similar mechanisms also control the gradient of MyoII in the PZ. To this end, we first increased Fog production in the primordium (the source) by expressing two additional copies of a WT form of Fog using the hkb promoter. This increased both the amplitude in front of the invaginating furrow (at x = 0 µm, WT: 11.55 ± 0.10 A.U and hkb-fog 32.59 ± 0.32 A.U (mean ± s.e.m.)) and the range of the gradient (WT: 27.08 ± 5.72 µm, hkb-fog: greater than 38.01 ± 1.92 µm (mean ± s.e.m.), see methods) as expected of a concentration gradient that defines the activation profile of MyoII (Fig. 3d, e and Supplementary Movie 10). Interestingly, the length scale of the exponential MyoII gradient also increased (Fig. 3f, WT: 3.18 ± 0.29 μm and hkb-fog: 5.26 ± 0.58 μm, (mean ± s.e.m.)), suggesting that diffusion or degradation/removal of Fog may depend on Fog concentration. Next, we tested whether the spatial gradient of MyoII also depends on Fog removal within the PZ. Since Fog binding to its GPCR induces endocytosis of the receptor-ligand complex³⁸, we sought to interfere with Fog removal by blocking GPCR endocytosis. Gprk2, a kinase that promotes GPCR endocytosis upon ligand binding^39,40, is the only GRK known to interfere with Fog signaling and endocytosis in the embryo^36,38. Knock-down of Gprk2 by RNAi (gprk2 RNAi) resulted in an increase in the amplitude (Control: 9.72 ± 0.08 A.U and gprk2 RNAi: 14.25 ± 0.14 A.U (mean ± s.e.m.)), the range (Control: 20.86 ± 5,72 µm and gprk2 RNAi: greater than 33.59 ± 2.5 µm (mean ± s.e.m.)) and length-scale (Control: 2.96 ± 0.45 μm and gprk2 RNAi: 5.48 ± 0.58 μm (mean ± s.e.m.)) of the exponential MyoII profile (Fig. 3g–i and Supplementary Movie 11) similar to hkb-fog, indicating that Fog removal/endocytosis also tunes the MyoII gradient.

Fig. 3. An exponential gradient of MyoII in the PZ is tuned by GPCR endocytosis and Fog production in the primordium.

a High-resolution micrograph of MyoII in the PZ in a WT embryo. b Spatial profile of MyoII mean intensity in the PZ in four WT embryos along with their fit with a single exponential decay function (red dashed line). n = 4 embryos. c Spatial profile of MyoII mean intensity at different time points from a single WT embryo. Orange dashed lines: fit with a single exponential decay function. R² coefficient of determination. d Left: High-resolution micrograph of MyoII in the PZ in WT (top) and embryos with increased Fog expression in the primordium (hkb-fog, bottom). Right: Temporal averaging of MyoII intensity in the referential of the moving invagination (see Methods). e Spatial profile of MyoII mean intensity in the PZ. Dashed horizontal line: recruitment threshold for MyoII. Bottom inset: zoomed view of the dashed box. Top inset: normalized spatial intensity profiles. f Decay length scale of the MyoII intensity spatial profile in individual embryos. **P = 0.0089, two-sided unpaired t-test with Welch’s correction. g–i Identical set of images and quantification as described in (d–f) for control (top) and embryos uniformly expressing shRNA against Gprk2 (gprk2 RNAi, bottom). **P = 0.0051, two-sided unpaired t-test with Welch’s correction. e, f n = 4 embryos (WT) and 9 embryos (hkb-fog). h, i n = 5 embryos (Control) and 9 embryos (gprk2 RNAi). Data in (f, i) are mean ± s.d. and in (b, c, e, h) are mean ± s.e.m.

Thus, Fog produced in the endoderm primordium sets an exponential gradient of MyoII in the PZ by diffusion/degradation. Furthermore, since we find that the shape of this gradient is not perturbed when gene transcription was blocked with α-amanitin (Supplementary Fig. 4b–d), Fog acts non transcriptionally in the PZ. These findings suggest that Fog might act as a mechanogen directly controlling cellular contractility^22,23. It is worth noting that this exponential gradient, whose maximum is located at the edge of the tissue invagination, is not static but translocates anteriorly as the wave of invagination propagates to the anterior.

Fog is uniformly distributed in the extracellular space

Since Fog regulates the gradient of MyoII in the PZ, we next tested whether Fog also forms a concentration gradient there (Fig. 4a). Immunohistochemistry (IHC) against Fog in fixed embryos revealed a concentration gradient of cellular Fog protein in the PZ, although shallower than that of MyoII (Fig. 4b, c), consistent with the integrin-dependent amplification of MyoII activation closer to the invaginating furrow³⁰. This concentration gradient may reflect intracellular or surface-bound Fog since the soluble extracellular fraction is washed away during fixation and permeabilization. To visualize the entire pool of Fog protein in living embryos (extracellular and intracellular), we engineered an endogenous Fog::SYFP2 protein fusion at the fog locus using CRISPR/Cas9 (referred to as Fog::YFP, Supplementary Fig. 5a). Fog::YFP homozygote flies were viable and their embryos showed no defects in gastrulation (Supplementary Fig. 5b, c and Supplementary Movie 12). Furthermore, IHC to detect Fog::YFP with antibodies anti-GFP (to visualize the YFP tag) and anti-Fog (to visualize the Fog portion of the fusion protein) showed (1) a localization consistent with that of the known endogenous protein in both the endoderm primordium (subapical vesicular accumulation, Supplementary Fig. 5d) and the PZ (shallow apical gradient, Fig. 4d, e) and (2) a high degree of co-localization between the two detection methods. Altogether these results indicate that Fog::YFP is functional and correctly localized. In particular, they also suggest that Fog::YFP is not cleaved in the embryo despite the presence of three putative protein cleavage sites in the Fog protein sequence¹⁷. To further test this latter possibility, we measured the diffusion coefficient (D) of Fog::YFP in the extracellular space using fluorescence correlation spectroscopy (FCS). Within the extracellular space between the VM and the invaginated posterior endoderm (Fig. 4f), Fog::YFP exhibited significantly slower diffusion dynamics than secreted GFP (Fig. 4g and Supplementary Fig. 6a) at comparable excitation power. To circumvent artifacts induced by photophysical effects, we interpolated the values of D obtained from FCS measurements at different excitation powers (Fig. 4h and Supplementary Fig. 6b). We thereby obtained for Fog::YFP a D of 55 μm²s⁻¹, as predicted for a globular 127 kDa protein diffusing in an aqueous fluid and for a secreted version of GFP a significantly higher D = 87 μm²s⁻¹ (sec::GFP, 27 kDa, Fig. 4h, see Methods). Thus, Fog::YFP is a good Fog reporter in vivo and we used it to image Fog distribution during wave propagation.

Fig. 4. Fog::YFP does not form a concentration gradient in the extracellular space.

a Hypothesis that the MyoII gradient (green) in the PZ depends on a concentration gradient of Fog (red stars) diffusing from the primordium. b IHC of Fog and MyoII during wave propagation. c Spatial intensity profiles of Fog and MyoII from IHC. n = 3 embryos. d IHC of Fog revealed with an anti-GFP and an anti-Fog antibody in the PZ of WT and Fog::YFP embryos. e Spatial profiles of GFP and Fog intensities from IHC in the indicated conditions. n = 3 embryos. f An embryo prepared for FCS measurements. Invagination: the FCS spot was placed in the extracellular space within the invaginating furrow. g Average diffusion coefficients of Fog::YFP and sec::GFP obtained by fitting a one-component diffusion model to FCS autocorrelation functions (ACFs) of measurements acquired at comparable effective excitation of YFP and GFP fluorophores at 514 nm. n = 9 for Fog::YFP and 8 for sec::GFP from three embryos each. Corresponding average ACFs are shown in Supplementary Fig. 6a. ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. h Diffusion coefficients of Fog::YFP and sec::GFP from ACFs acquired at different laser powers. To cope with increased noise at low laser powers, ACFs acquired in multiple embryos were averaged per laser power (lp) and the average ACF fitted (Fog::YFP: 9 ACFs per lp in n = 3 embryos, sec::GFP: 6/9/9/8 ACFs at lp 0.25/0.5/1/2 µW in n = 3/4/4/4 embryos). Symbols: mean values, error bars: 95% confidence intervals. Solid lines: linear regression of D with laser power. The interpolation to zero excitation power (dashed lines) provides estimates for diffusion coefficients not biased by photophysical artifacts (in the box). i Distribution of Fog::YFP (top) and sec::GFP (bottom) just below the vitelline membrane during wave propagation. Orange arrowhead: the invagination front. j Spatial profile of the ratio of mean intensities between Fog::YFP and sec::GFP. The yellow dashed line indicates a constant ratio. 0 μm indicates invagination front. n = 12 ratios from four embryos. k Spatial mean intensity profiles of indicated markers. In (j, k) n = 3 embryos. Data in (g) are mean ± s.d and data in (c, e, i, j, k) are mean ± s.e.m.

In contrast to our expectations and the fact that intracellular Fog forms a gradient, we observed that Fog::YFP was present in the extracellular perivitelline space at uniform concentration (Supplementary Movie 13). The distribution of Fog::YFP across the region of wave propagation was similar to that of sec::GFP, which reflects the available space between the apical surface of cells and the VM (Fig. 4i–k and Supplementary Movies 14, 15). Thus, endogenous Fog::YFP is uniformly distributed in the extracellular perivitelline space during wave propagation. This does not depend on the presence of a maternal protein pool since a similar distribution was observed also when Fog::YFP was expressed only zygotically with a hkb promoter (Supplementary Fig. 5e–g and Supplementary Movie 16).

We conclude that extracellular Fog does not exhibit a concentration gradient in the PZ. Yet, intracellular Fog and its signaling (MyoII activation) are restricted to a dynamic domain of few cells anterior to the advancing furrow. This argues that Fog dependent signaling is organized at the cell surface in a dynamic spatial gradient, as the tissue invagination wave propagates anteriorly.

GPCR endocytosis tunes a gradient of cell-surface bound Fog and receptor oligomerization

This led us to investigate how a gradient of MyoII activation emerges in the PZ in spite of uniform extracellular Fog in the vitelline fluid. To test this, we analyzed the diffusion dynamics of Fog at the apical surface of cells in the PZ using FCS (Fig. 5a). In contrast to our measurements in the extracellular space within the posterior invagination, in the PZ we observed two populations of Fog, characterized by two distinct diffusion coefficients (Fig. 5b, c and Supplementary Fig. 6c–e). A large fraction of Fog (84% of the total pool) displayed an average diffusion coefficient D of 51 ± 2 (mean ± s.e.m.) μm²s⁻¹ (D_fast), similar to that measured in the posterior invagination and indicative of free diffusion (Fig. 5c). A minor fraction of Fog (16% of the total pool) showed much slower diffusion dynamics, with an average D of 1.6 ± 0.2 (mean±s.e.m.) μm²s⁻¹ (D_slow). This presumably corresponds to ligands bound to or interacting with the apical plasma membrane of cells, since it was undetectable in measurements within the extracellular space performed inside the invagination (Fig. 5b). Interestingly, the average diffusion coefficient of the Fog receptor Smog::GFP (0.54 ± 0.04 (mean ± s.e.m.) μm²s⁻¹) at the apical cell surface in the PZ measured by FCS was in the same range, but nonetheless significantly lower than D_slow of Fog (Fig. 5d). This suggests that the slow-diffusing fraction of Fog (Fog_slow) could correspond to ligands transiently bound to their receptor in the PZ. To further test this, we sought to increase the half-life of the receptor at the surface by inhibiting GPCR endocytosis (gprk2 RNAi) and measured Fog_slow in the PZ. We found that in gprk2 RNAi embryos the Fog_slow fraction increased to 30 ± 15% (mean ± s.e.m.) of the total pool from 16 ± 1% (mean ± s.e.m.) in WT, consistent with the idea that Fog_slow is receptor-bound on the surface of cells in the PZ (Fig. 5b, d). We next examined whether Fog_slow forms a spatial gradient in the PZ. We found that in WT embryos Fog_slow was higher close to the invagination (0–20 µm) than further away (20–70 µm, Fig. 5e, h) and that a spatial gradient with a negative slope could be detected within each embryo (Fig. 5g, average gradient slope: −1.9 × 10⁻³ ± 1.7 × 10⁻³ μm⁻¹ (mean ± s.d.), p = 3.4 × 10⁻³ of being negative by chance). Furthermore, blocking GPCR endocytosis not only globally increased Fog_slow (Fig. 5f, h) but also significantly reduced the average slope of its gradient, which was now not different from 0 (Fig. 5g, average gradient slope: 6.5 × 10⁻⁴ ± 2.6 × 10⁻³ μm⁻¹ (mean ± s.d.), p = 0.42 of being different from 0 by chance). These results are consistent with the observed higher levels of MyoII and its expanded gradient in gprk2 RNAi embryos and suggest that the Fog activity gradient might emerge from a gradient of ligand-receptor binding within the PZ.

Fig. 5. Slowly diffusing Fog::YFP forms a gradient at the apical cell surface in the PZ.

a An embryo prepared for FCS measurements. Invagination: FCS spot placed in the extracellular space within the invaginating furrow. Propagation zone (PZ): FCS spot placed on the cell apical surface or at junctions during wave propagation. b Fraction of slow-diffusing (Fog_slow) and fast-diffusing (Fog_fast) pools of Fog::YFP obtained from two-component FCS analysis. Fog_fast + Fog_slow = 1. n (measurements) = 19 from 11 embryos (invagination, Fog::YFP), 93 from 11 embryos (PZ, Fog::YFP + water) and 72 from 12 embryos (PZ, Fog::YFP + gprk2 RNAi). ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. c Diffusion coefficient (D) of Fog::YFP in the invagination (white area) or in the PZ (gray area). n (measurements) = 19 for the invagination, and 93 for both D_slow and D_fast from eight embryos each. NS, P = 0.4253, ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. d D of Fog_slow and Smog::GFP in the PZ in the indicated conditions. n (measurements) = 108 from six embryos (Smog::GFP + water), 93 from eight embryos (Fog::YFP + water) and 84 from 12 embryos (Fog::YFP + gprk2 RNAi). NS, P = 0.1464, ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. e, f Fraction of Fog_slow at different distances from the invaginating furrow during wave propagation in water (e, n = 79 measurements from 10 embryos) and gprk2 RNAi (f n = 80 measurements from 13 embryos) injected embryos. g Slopes of the Fog_slow gradient in the PZ in individual embryos in the indicated conditions. n = 10 embryos (Water, ## is P = 0.0034, one-sided one-sample t-test with a hypothetical mean of zero) and 11 embryos (gprk2 RNAi, NS is P = 0.4194, two-sided one-sample t-test with a hypothetical mean of zero). *P = 0.0145, two-sided unpaired t-test with Welch’s correction. Dashed gray line: flat gradient. h Fraction of Fog_slow for the indicated bins of distance in water (n = 33 measurements in 0–20 µm bin and 46 measurements in 20–70 µm bin from ten embryos, **P = 0.0084, two-sided unpaired t-test with Welch’s correction) and gprk2 RNAi (n = 29 measurements in 0–20 µm bin and 51 measurements in 20–70 µm bin from 13 embryos, NS, P = 0.1988, two-sided unpaired t-test with Welch’s correction) injected embryos. Data were mean ± s.d.

Next, we sought to measure Fog receptor activation within the PZ to see if that also formed a gradient as predicted from the distribution of Fog_slow. GPCR ligand binding and activation is known to induce receptor clustering (oligomerization)^38,41,42, which can be measured by FCS³⁸. Using FCS, we measured the per-particle brightness, which reflects the degree of molecular oligomerization (see Methods), of Smog::GFP on the cell apical surface in the PZ. Consistent with previous studies³⁸, we found that the molecular brightness of Smog::GFP decreased upon depletion of the ligand Fog (Fig. 6a) and increased upon depletion of Gprk2 (Fig. 6b) without changing its diffusion coefficient and only slightly affecting its total concentration (Supplementary Fig. 7a–c). We next compared molecular brightness of Smog::GFP with that of the known trimeric protein VSV-G::GFP and found that the brightness of VSV-G::GFP was significantly higher than that of Smog::GFP in both the PZ (Fig. 6a, b) and the lateral ectoderm (Supplementary Fig. 7d). Furthermore, since VSV-G::GFP brightness was not affected by neither Fog nor Gprk2 depletion (Fig. 6a, b), these results confirmed that the observed effects on Smog::GFP are receptor specific and that its oligomerization is a proxy for GPCR activation.

Fig. 6. Smog::GFP oligomers form a gradient at the apical cell surface in the PZ.

a, b Smog::GFP (blue) and VSV-G::GFP (gray) molecular brightness at the cell apical surface in the PZ in the indicated conditions. In a, n (measurements) = 31 from eight embryos (Smog::GFP + water), 49 from ten embryos (Smog::GFP + fog RNAi), 38 from five embryos (VSV-G::GFP + water) and 47 from six embryos (VSV-G::GFP + fogRNAi). NS, P = 0.3970, ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. In b, n (measurements) = 99 from 14 embryos (Smog::GFP + water), 98 from 20 embryos (Smog::GFP + gprk2RNAi), 68 from five embryos (VSV-G::GFP + water) and 62 from eight embryos (VSV-G::GFP + gprk2 RNAi). NS, P = 0.4772 (VSV-G::GFP + water vs VSV-G::GFP + gprk2 RNAi), NS, P = 0.8437 (Smog::GFP + gprk2 RNAi vs VSV-G::GFP + gprk2 RNAi), ****P < 0.0001, two-sided unpaired t-test with Welch’s correction. c Estimated fraction of monomers and higher-order oligomers of Smog::GFP at the cell apical surface in the PZ in the indicated conditions. p_f fluorescence probability (see Methods). d, e Apical Smog::GFP molecular brightness at different distances from the invaginating furrow in water (d, n = 122 measurements from 14 embryos) and gprk2 RNAi (e, n = 91 measurements from 20 embryos) injected embryos. Dashed gray lines: estimated brightness of a scenario with 100% monomers (bottom line) and 100% trimers (top line). f Slopes of the apical Smog::GFP brightness gradient in the PZ in individual embryos in the indicated conditions. n = 14 embryos (Water, # is P = 0.043, one-sided one-sample t-test with a hypothetical mean of zero) and 13 embryos (gprk2 RNAi, NS is P = 0.1584, two-sided one-sample t-test with a hypothetical mean of zero). *P = 0.0346, two-sided unpaired t-test with Welch’s correction. Dashed gray line: flat gradient. g Apical Smog::GFP molecular brightness for the indicated bins of distance in water (n = 28 measurements in 0–20 µm bin and 74 measurements in 20–70 µm bin from 14 embryos, **P = 0.0088, two-sided unpaired t-test with Welch’s correction) and gprk2 RNAi (n = 37 measurements in 0–20 µm bin and 43 measurements in 20–70 µm bin from 20 embryos, NS, P = 0.3901, two-sided unpaired t-test with Welch’s correction) injected embryos. Data were mean ± s.d.

The comparison of molecular brightness with VSV-G::GFP also suggests that, in the simplest scenario, Smog::GFP is present as a mixture of dimers and monomers in WT embryos (molecular brightness lower than VSV-G::GFP), while oligomerization increases upon blocking receptor endocytosis (similar brightness as the trimeric protein VSV-G::GFP, Fig. 6b) and decreases in the absence of the ligand Fog during wave propagation (Fig. 6a). Since our data indicate that Smog::GFP exists as monomers and higher-order oligomers (dimers, trimers, etc.), we next estimated the fraction of oligomers from the measured brightness, assuming a linear dependence of the brightness on the number of protomers (see methods). Since only the average brightness can be directly extracted from FCS measurements, the exact type of oligomeric species cannot be determined. Nevertheless, for a particular model, i.e., a two-species mixture of monomers and oligomers, the fraction of monomers and oligomers can be estimated (see Methods). We calculated these numbers for several possible scenarios (monomers with either dimers, trimers or tetramers) in WT, fog and gprk2 RNAi embryos taking previously reported photophysical properties of GFP⁴³ into account (Fig. 6c and Supplementary Fig. 7e). Depleting the ligand Fog by RNAi reduced the probability of higher-order oligomer formation for Smog::GFP by ~8 folds, i.e., from ~68% dimers in WT embryos to less than 8% in fog RNAi embryos (Fig. 6c and Supplementary Fig. 7e). Conversely, blocking receptor endocytosis significantly increased oligomer formation by ~21% when considering the couple dimers/monomers (from 79 to 100%, Fig. 6c and Supplementary Fig. 7e) or by ~55% when considering the couple trimers/monomers (from 21 to 76%, Fig. 6c and Supplementary Fig. 7e). To test whether Smog::GFP oligomers are distributed in a gradient in the PZ, we measured Smog::GFP brightness on the apical cell surface and at lateral junctions as a function of the distance from the invaginating furrow in the PZ (Fig. 6d–g and Supplementary Fig. 7f–i). In WT embryos we found higher Smog::GFP brightness closer to the invagination (0–20 μm) than at larger distances (20–70 μm, Fig. 6d, g and Supplementary Fig. 7f, i), and spatial gradients with negative slopes within each embryo on the apical surface and similar, although less significant, trends at junctions (Fig. 6f, average gradient slope: −7.8 × 10⁻² ± 4.2 × 10⁻²kHz μm⁻¹ (mean ± s.d.) and p = 0.04 of being negative by chance in the apical region and Supplementary Fig. 7h, average gradient slope −5.0 × 10^-2 ± 2.6 × 10^-2 kHz μm⁻¹ (mean ± s.d.) and p = 0.06 of being negative by chance in the junctional region). gprk2 RNAi reduced this spatial difference by increasing Smog::GFP brightness both close and at a distance from the invagination (Fig. 6e, g and Supplementary Fig. 7g, i) and significantly changed the average slope of the gradients observed within each embryo, which were now not different from 0 or even slightly positive (Fig. 6f, average gradient slope: 1.0 × 10⁻¹ ± 0.24 kHz μm⁻¹ (mean ± s.d.) and p = 0.16 of being different from 0 by chance in the apical region and Supplementary Fig. 7h, gradient slope: 2.4×10⁻¹ ± 0.29 kHz μm⁻¹ (mean ± s.d.) and p = 0.06 of being different from 0 by chance in the junctional region), indicating that the gradient of Smog::GFP oligomerization depends on GPCR endocytosis. Importantly, this spatial dependence of oligomerization was specific to Smog::GFP, as no gradient was observed for VSV-G::GFP (Supplementary Fig. 7j–n, gradient slope: 1.0 × 10⁻² ± 0.35 kHz μm⁻¹ (mean ± s.d.) in the apical region with p = 0.66 of being different from 0 by chance and 5.3 × 10⁻² ± 0.1 kHz μm⁻¹ (mean ± s.d.) in the junctional region and p = 0.24 of being different from 0 by chance).

Altogether, our data indicate that Fog binding to the cell apical surface induces a gradient of receptor activation and oligomerization, which is tuned by receptor endocytosis.

Integrin activation by contact with the vitelline membrane tunes the Fog activity gradient

The gradient of GPCR activation and oligomerization tunes the multicellular spatial pattern of MyoII activation during wave propagation. Integrins, which are activated when cells of the PZ contact the VM, are also involved in MyoII activation^28,30. We showed earlier that the αPS3 integrin Scab amplifies MyoII levels in a positive feedback mechanism³⁰. Consistent with this, in αPS3 null mutants (αPS3^−/−), MyoII was recruited at much lower levels than in WT embryos, although higher than those observed in the absence of Gα signaling (Supplementary Fig. 8a, b). Moreover, in these mutants, MyoII recruitment in the PZ still followed an exponential gradient with a range similar to WT, albeit with lower amplitude, which led to an increased length scale compared to WT embryos (Fig. 7a–d and Supplementary Fig. 8c–e, and Supplementary Movie 17). This suggests that amplification of MyoII activation by integrins is not uniform in the PZ, as the gradient length scale should not change with a uniform amplification by a constant factor. This led us to address whether integrins only amplify MyoII activation in the cell near the edge of invagination front, as previously suggested³⁰, or whether they also have a role in regulating the spatial range of the multicellular Fog/GPCR activity gradient. Since amplitude, range and length scale of the gradient are increased significantly when GPCR endocytosis is inhibited in gprk2 RNAi embryos (Fig. 3g–i and Supplementary Movie 11), we tested whether integrins are required for this effect and thus for the process of gradient formation by acting everywhere in the field where Fog and GPCR signaling can be active. Strikingly, removing integrins in embryos depleted for Gprk2 (gprk2RNAi + αPS3^−/−) dramatically reduced both the levels and the range of MyoII to levels similar to those of the knock-out of integrins (αPS3^−/−, Fig. 7a–d, Supplementary Fig. 8c, and Supplementary Movie 17). These results show that integrins are required for both the expanded gradient and the higher levels of MyoII observed following the hyperactivation of Fog-GPCR signaling. Additionally, it shows that blocking endocytosis has no impact on the shape of the gradient if integrins are absent. We conclude that integrins are part of the multicellular gradient formation mechanism and do not simply amplify MyoII activation in the cell near the invagination front. Next, we tested whether integrins directly promote oligomerization of GPCR and thus MyoII recruitment as part of the gradient formation mechanism. We measured the molecular brightness of Smog::GFP by FCS in the PZ of embryos depleted of the αPS3 integrin Scab by RNAi (αPS3 RNAi), and we found that this was not decreased compared to WT embryos (Supplementary Fig. 8f), contrary to what would be expected if integrins promoted Smog oligomerization. Smog::GFP molecular brightness was instead increased in the PZ compared to WT, suggesting that in the absence of integrins, Smog::GFP oligomers are no longer active (decreased MyoII levels, despite higher molecular clustering). We conclude that integrins do not directly promote GPCR clustering as part of the gradient formation mechanism, but rather they act as co-factors for GPCR oligomer signaling.

Fig. 7. Integrin activation upon contact with the VM define range and activity of the Fog signaling gradient.

a High-resolution micrographs of MyoII in the PZ in control (Water), integrins mutant (Water+αPS3^−/−), and gprk2 RNAi injections in WT (gprk2 RNAi) or integrin mutants (gprk2 RNAi+αPS3^−/−) embryos. b MyoII mean intensity spatial profiles in the indicated conditions. Inset: blow-up of the dashed boxed region. c, d Amplitude (c) and range (d) of the MyoII gradients. n = 12 embryos (Water), 8 embryos (gprk2 RNAi), 9 embryos (water+αPS3^−/−) and 6 embryos (gprk2 RNAi+αPS3^−/−). In c, *P = 0.0177, ****P < 0.0001 and NS P = 0.3239, two-sided unpaired t-test with Welch’s correction. In d, *P = 0.0204, **P = 0.0029, NS P = 0.2973 (water + αPS3^−/− vs gprk2RNAi + αPS3^−/−) and NS, P = 0.1476 (water vs αPS3^−/−), two-sided unpaired t-test with Welch’s correction. e Top left, micrograph of MyoII (green) and βPS integrin (white) in embryos injected with dextran to label the extracellular space (magenta). Other images, temporal average projections of the indicated markers in the referential of the moving invagination. White dashed line: limit of the contact with the VM. f Normalized spatial profiles of the mean intensity of MyoII (black), βPS::GFP (red), and dextran (blue). Black and red dashed lines: range of MyoII and βPS::GFP recruitment, respectively. n = 9 embryos. g Range of MyoII and βPS::GFP recruitment in individual embryos. n = 8 embryos each. NS is P = 0.0911, two-sided unpaired t-test with Welch’s correction. h Left: High-resolution micrographs of MyoII and βPS::GFP in the PZ in the indicated conditions. Center and right: Temporal average projection of MyoII and βPS::GFP. Dashed line: limit of the contact with the VM. n = 6 embryos (Water) and 11 embryos (gprk2 RNAi). i, j Mean intensity spatial profiles of βPS (i) and MyoII (j) in the PZ. n = 6 embryos (water) and 11 embryos (gprk2 RNAi). k–n Amplitude (k, l) and range (m, n) of MyoII/βPS recruitment in individual embryos. n = 7 embryos (water) and 14 embryos (gprk2 RNAi). In k, *P = 0.0353, l, *P = 0.0285, m, ***P = 0.0006, n, *P = 0.0381, two-sided unpaired t-test with Welch’s correction. o Model of the self-organized gradient of MyoII during wave propagation from extracellular Fog acting as a mechanogen. Integrin complexes (orange) indicate the zone of contact of the tissue with the vitelline membrane (VM). Data in c, d, g, k, l, m, n are mean ± s.d. Data in b, f, i, j are mean ± s.e.m.

Integrins accumulate and form bright puncta in the PZ upon apical cell contact with the overlying vitelline membrane. The range of this contact might thus contribute to determining the range of the gradient of MyoII and GPCR signaling. Consistent with this idea, integrin puncta, visualized with the endogenously GFP-tagged βPS integrin Myospheroid (βPS::GFP hereafter), accumulated at highest levels close to the invaginating furrow and decreased more anteriorly forming a gradient with a range identical to that of MyoII activation in the PZ (Fig. 7e–g and Supplementary Fig. 8g). This integrin gradient formed within the region of contact of the tissue with the VM, as revealed by the exclusion of dextran injected in the perivitelline space from the region where βPS::GFP forms bright puncta (Fig. 7e–g). Furthermore, the depletion of Gprk2 increased the amplitude and the range of the gradient of βPS::GFP (Fig. 7h–n and Supplementary Movie 18) as well as the range of tissue contact with the VM (monitored by the exclusion of dextran and by the distance of E-cad junction from the VM, Supplementary Fig. 8h–l and Supplementary Movie 19), suggesting that the increased range of the MyoII gradient observed in these mutants stems from a larger zone of contact with the VM in front of the invaginating furrow.

Together, we conclude that during wave propagation, MyoII is activated where integrins are in contact with the VM and that the range of the exponential gradient of MyoII during wave propagation depends on the contact of the tissue with the VM in a manner that involves integrin activation and their cross-talk with Fog-GPCR signaling.

Discussion

Cell and tissue mechanics must be regulated in space and time to drive tissue morphogenesis. The mechanisms of such regulation remain poorly understood. Here, we report how a traveling and constantly renewing gradient of cell contractility, essential for the propagation of a wave of tissue invagination during Drosophila embryo gastrulation, is set up in a self-organized manner. The mechanism entails long-range and concentration-dependent signaling of a diffusing ligand (Fog) of a GPCR (Smog), tissue geometry (i.e., the contact with the vitelline membrane), and mechanochemical feedback between GPCR, integrins and actomyosin contractility. This is consistent with a hypothesis referred to as a mechanogen^22,23 where, by analogy to morphogens that spatially organize cell identities transcriptionally, diffusible molecules directly pattern, through activity gradients, mechanical properties (e.g., contractility) in fields of cells. However, different from that hypothesis, the activity gradient reported here is not hierarchically controlled by the concentration gradient of the ligand Fog itself. Rather, it emerges from the mutual interactions between the different events involved in wave propagation, namely Fog diffusion, GPCR oligomerization and endocytosis, tissue deformation and contact with the vitelline membrane, integrin activation and MyoII recruitment.

The mechanogen hypothesis contrasts with classical mechanisms where mechanical regulation is organized in two tiers and effected downstream of the spatial patterning of cell identities via transcriptional regulation. For instance, in Drosophila embryos, the morphogen Dorsal activates a transcriptional program governed by the transcription factors Twist and Snail, which define the mesodermal identity of ventral cells, and in turn activate the expression of the GPCR ligand Fog to induce their tissue autonomous apical constriction and tissue invagination. Here, we show that Fog also acts tissue non-autonomously to control a gradient of MyoII required for a wave of tissue invagination driving the morphogenesis of the posterior endoderm. The shape of this gradient matters for the dynamics of tissue invagination as shown by the fact that increasing the amplitude and the range of MyoII activation (e.g., hkb-fog or gprk2 RNAi, Fig. 3) decreases the speed of the wave of invagination, due to the increased adhesion to the vitelline membrane and the reduced de-adhesion rate³⁰. Specifically, we demonstrate that Fog produced zygotically in the posterior endoderm primordium, not only drives cell-autonomous apical constriction and invagination, but it also diffuses in the extracellular perivitelline space to control an exponential gradient of apical MyoII more anteriorly in cells of the PZ. Thus, while Fog has long been proposed to act as a switch factor to locally convert a genetic pattern into a pattern of cortical mechanics driving tissue dynamics, we demonstrate that it is also able to diffuse and pattern cortical mechanics at a distance in the zone of wave propagation. Notably, this is consistent with previous reports excluding the possibility that the wave propagation of MyoII recruitment towards the anterior solely reflects the expansion of a non-steady-state gradient of the ligand Fog diffusing away from the endoderm primordium²⁸. If this were the case, the expansion rate of the gradient would decay over time. Instead, the speed of propagation and the amplitude of the MyoII gradient in front of the invaginating furrow are constant. Therefore, the wave of MyoII recruitment reflects a steady-state activity gradient of the ligand Fog that is constantly renewed as it travels anteriorly across the tissue. Similar to morphogens, we show that the amplitude and the range of Fog activity (MyoII recruitment) depend on the rate of ligand production at the source (the primordium) and the rate of its clearance by endocytosis in the target tissue. Thus, since Fog diffuses from a localized source and directly tunes tissue mechanical properties (actomyosin contractility) in a concentration-dependent and transcription-independent manner, it shows features of a mechanogen^22,23. Strikingly, however, the activity pattern of Fog does not reflect its protein distribution in the extracellular space, where it is distributed uniformly. Yet, we found that Fog forms a gradient of cell surface-bound ligand (Fig. 5e) associated with a gradient of receptor oligomerization (Fig. 6d), both regulated by GPCR endocytosis (Figs. 5f, 6e). Finally, our data suggest that integrins shape the Fog-GPCR activity gradient during wave propagation by acting as co-factors for GPCR signaling. We find that in the absence of integrins blocking GPCR endocytosis (gprk2 RNAi), no longer expands the Fog activity gradient and MyoII recruitment, indicating that integrins are required for robust Fog-GPCR signaling. Furthermore, since we find that integrins do not directly promote GPCR clustering, we suggest that integrins might act as co-factors increasing GPCR signaling, potentially by promoting the binding of GPCRs to downstream molecular effectors. The reported function of integrins in setting up the Fog activity gradient is interesting because, during wave propagation, integrins are activated by the initial posterior tissue invagination, which brings more anterior cells in contact with the vitelline membrane. Within this region of contact, integrins form a gradient due to a positive feedback regulation with MyoII recruitment³⁰. The amplitude and the length scale of the biochemical gradient that recruits MyoII during wave propagation require feedback regulation by integrins, which itself rests on the geometry of tissue invagination and interaction with the vitelline membrane. Such feedback loops tune the length scale of the mechanogen gradient reported here. Thus, the Fog activity gradient is not governed by a concentration gradient of the ligand Fog in the extracellular space. Rather, the gradient emerges from the contact with the vitelline membrane through the mutual interactions between Fog-GPCR signaling, tissue deformations, integrins, and MyoII recruitment, which, in a repeated cycle, self-renew the activity gradient as the wave sweeps through the tissue.

The self-organized Fog activity gradient is constantly renewed over time. This feature allows the gradient to maintain a constant amplitude and range over time as it translocates with the moving front of tissue invagination towards the embryo's anterior. In contrast, a gradient deterministically controlled by a hierarchical mechanism (e.g. by the concentration gradient of a factor, e.g. a receptor or a co-factor/co-receptor, at the beginning of the invagination process) would not display such a feature and its amplitude and range would progressively decrease over time as the furrow moves anteriorly within the embryo, away from the source and down the initial concentration gradient. Notably, this is also true when de novo transcription is blocked, which rules out that expression of putative factors propagates as a wave to shape the gradient and rather suggests that their activation would have to be part of the mechanism of gradient formation. The factors (e.g., a receptor or a co-factor/co-receptor) could be expressed in a fixed but broad enough domain to encompass the whole PZ, and some specific event would potentiate its activity, for instance, the contact with the VM. Interestingly, this is what happens for integrins. Once expressed in the PZ before induction of wave propagation, integrin transcription is no longer required, and integrin activity is potentiated/activated by the contact to the VM, which itself propagates as a wave.

It also important to note that because of the wave nature of the process, any cell within the field of the gradient moves towards the invagination front and experiences a temporal increase in MyoII recruitment (Fig. 1j and Supplementary Fig. 8b). In other words, the spatial nature of the gradient in the referential of the embryo is inherently associated with a temporal “maturation” of cell signaling in the referential of the cells. Therefore, the mechanogen gradient reported here is coupled to a temporal integration process that involves GPCR activation by Fog and integrins (Fig. 7o).

The Fog activity gradient self-organizes at the cell surface while Fog is at a uniform concentration in the vitelline fluid. Since tissue deformation during the wave of invagination is expected to cause hydrodynamic flow in the vitelline fluid, which could disturb extracellular fluid gradients, the ability to self-organize a Fog surface activity gradient at the cell surface via receptor endocytosis and integrins may be an adaptive mechanism to ensure robust gradient formation.

Our study presents some limitations. The exact mechanism of the Fog activity gradient formation is not fully elucidated. Our data indicate that in contact with the vitelline membrane, a functional interaction between integrins and ligand-bound GPCR might shape a gradient with integrins acting as co-factors for GPCR signaling. However, the precise molecular basis of this functional interaction remains to be investigated. Furthermore, it is also possible that the Fog activity gradient might require post-translational modification (PTM) and/or an extracellular regulation of Fog protein activity by proteins capable of binding and/or activating/inactivating Fog or its receptor at the cell surface. The formation of a Dpp morphogen gradient in the vitelline space requires binding to its inhibitor Sog and the protease Tld that enables Dpp activity in a narrower dorsal domain than where Dpp is expressed and diffuses^44,45. Similarly, PTM of the zygotic fraction of Fog protein may explain its higher activity compared to the maternal pool. The maternal pool is more abundant (Supplementary Fig. 5g), yet it does not rescue a zygotic fog null mutant¹⁷ and an extracellular inhibitor or an enzyme modifying Fog PTMs may spatially restrict Fog activity and thereby be part of the gradient formation mechanism^46–49.

Altogether, this work exemplifies the rich modalities of spatial patterning of cell and tissue mechanics during development independent of gene transcriptional regulation. It will be especially intriguing to consider in the future how mechanical patterning by biochemical signaling may depend on the mechanical and geometric properties of the tissues where this is taking place.

Methods

Fly strains and genetics

The following mutant alleles and insertions were used cta^RC10(gift from Leptin lab), pUASt-fog¹² [ref. ²⁷], pUASp-sec::eGFP [ref. ⁴⁶], hkb-fog [ref. ^32,33], pUAS-gprk2shRNA (Bloomington stock #35326), scb^KO [ref. ³⁰], ubi-VSV-G::GFP [Ref. ³⁸], sqh-smogC::GFP (long ORF of the RC isoform of Smog, chromosome 3 [ref. ³⁸]) were described earlier. hkb-Gα, hkb-fog_res, pUASt-fog_VSV-G, hkb-fog_VSV-G, and fog::SYFP2^KIN were generated in this study (see below). Live-cell imaging of MRLC, spaghetti squash (sqh, Genebank ID: AY122159) in Drosophila was carried out using a sqh-Sqh::mCherry transgene inserted either on chromosome 2 (at the VK18 site, located at 53B2 [ref. ²⁸] or a previously generated insertion [ref. ¹⁸]) or on chromosome 3 (VK27 site located at 89E11 [ref. ⁴⁷]). Live imaging of E-cadherin (shg in Drosophila, FlyBase ID:FBgn0003391) and of the main beta integrin βPS (myospheroid (mys), in Drosophila FlyBase ID: FBgn0004657) was carried out with EGFP knock-in alleles at the locus generated by homologous recombination, respectively E-cad::EGFP^KIN [ref. ⁴⁸] and mys::EGFP^KIN [ref. ⁴⁹].

For the expression of Fog in stripes (Supplementary Fig. 3b, c), virgin females ; ; wg-Gal4 were crossed to males ; ; pUASt-fog¹² or ; ; UAS-fog_VSV-G and the F1 progeny (embryos) was analyzed. For the homogeneous overexpression of Fog (Supplementary Fig. 3e), virgin females ; 67-Gal4, E-cad::EGFP^Kin, sqh-Sqh::mCherry were crossed with males ; pUASt-fog¹²; or ; ; pUASt-fog_VSV-G and the F1 progeny was analysed. The presence of the UAS transgene was assessed based on the phenotype. 67-Gal4 (mat α4-GAL-VP16) is ubiquitous and maternally supplied.

For the expression of shRNA against G protein-coupled receptor kinase 2 (gprk2, FlyBase ID: FBgn0261988), F1 progeny was analzyed from females ; 67-Gal4, E-cad::EGFP^KIN, sqh-Sqh::Cherry/+; pUAS-gprk2shRNA/+ crossed to males ; ; pUAS-Gprk2shRNA.

For homogenous expression of secreted GFP (sec::GFP), females ; 67-Gal4/+; UAS-sec::GFP/+ were crossed to males ; ; UAS-sec::GFP and F1 progeny was analzyed. All fly constructs and genetics are listed below (Table 1).

Table 1.

List of the Drosophila stocks and genetic crosses used in each figure panel

Cross or genotype	Figure
;E-cad::EGFPKIN, sqh-Sqh::mCherry (insertion at VK18 site);	Fig. 1d–m, Supplementary Fig. 1a–c, Fig. 3a–f, Supplementary Fig. 4a–d, Fig. 4b, c, Supplementary Fig. 8a, b, f
Females;ctaRC10,E-cad::EGFPKIN,sqh-Sqh::mCherry;hkb-cta x males;ctaRC10,Ecad::EGFPKIN, sqh-Sqh::mCherry; hkb-cta	Fig. 1d–m, Supplementary Fig. 1a–c, Supplementary Fig. 8a, b
;E-cad::EGFPKIN, sqh-Sqh::mCherry; hkb-fogsen	Fig. 2d, f, Supplementary Fig. 2a–c, Fig. 3d–f
;hkb-fogres,E-cad::EGFPKIN, sqh-Sqh::mCherry;	Fig. 2d–k, Supplementary Fig. 2a, d, e
;hkb-fogVSV-G,E-cad::EGFPKIN,sqh-Sqh::mCherry;	Fig. 2d–k, Supplementary Fig. 2f, g
females;;wg-Gal4 x males;UAS-fog12;	Supplementary Fig. 3b, c
females ;67-Gal4,E-cad::EGFPKIN,sqh-Sqh::mCherry; x males; pUASt-fog12;	Supplementary Fig. 3e
females;;wg-Gal4 x males;;UAS-fogVSV-G	Supplementary Fig. 3b, c
females ;67-Gal4,E-cad::EGFPKIN,sqh-Sqh::mCherry x males;;UAS-fogVSV-G	Supplementary Fig. 3e
females y-w-/+ ;67-Gal4,E-cad::EGFPKIN,sqh-Sqh::Cherry/+ x males y-w-;;	Fig. 3g–i, Supplementary Fig. 8k, l
females ;67-Gal4,E-cad::EGFPKIN,sqh-Sqh::Cherry/+;pUAS-Gprk2shRNA /+ x males;;pUAS-gprk2shRNA;	Fig. 3g–i, Supplementary Fig. 8k, l
w1118	Fig. 4d, e, Supplementary Fig. 5b–d
fog::SYFP2KIN;;	Fig. 4d, e, g–k, Supplementary Fig. 5a–g, Fig. 5b–h, Supplementary Fig. 5a–e
females ;67-Gal4/+;UAS-sec::GFP/+ x males;;UAS-sec::GFP	Fig. 4g–k, Supplementary Fig. 6a, Supplementary Fig. 8h–j
;;hkb-Fog::SYFP2	Fig. 4e–g
;;sqh-SmogC::GFP	Fig. 5d, i–o, Supplementary Fig. 7a–i
;;ubi-VSV-G::GFP	Fig. 6a, b, Supplementary Fig. 7a–d, 7j–m
females;E-cad::EGFPKIN,sqh-Sqh::Cherry/CyOYFP; x males;E-cad::EGFPKIN,sqh-Sqh::Cherry	Fig. 7a–d, Supplementary Fig. 8c–e
;scbKO,E-cad::EGFPKIN,sqh-Sqh::mCherry/CyOYFP;	Fig. 7a–d, Supplementary Fig. 8a–e
mys::EGFPKIN;;sqh-Sqh::mCherry	Fig. 7e–n, Supplementary Fig. 8g

Constructs and transgenesis

hkb-Gα

We re-built the plasmid containing hkb-fog from ref. ³³. This plasmid contains the sequence from nucleotide −2498 bp upstream of the ATG to the ATG itself of the hkb gene upstream of an hsp70 basal promoter and the cDNA of the complete fog-RB mRNA (NM_001038771.3). hkb-Gα was cloned into a pCasper5 transformation vector containing an attB site for PhiC31-mediated transgenesis. The pCasper5-attB backbone was purified after EcoRI digest of pRB14 (Addgene 52522, a pCasper5-attB_Cas9 plasmid from Klaus Foerstemann⁵⁰). The final plasmid was called the C5-hkb-Fog plasmid. To build hkb-Gα, the fog ORF in the C5-hkb-Fog plasmid was replaced with the Gα ORF (cta, NM_001273767.1).

hkb-fog_res

To build a fog mRNA resistant to the dsRNA (fog_res) under the control of the hkb promoter, the sequence of fog-RB mRNA targeted by the injected dsRNAs (861 bp: from 24 bp before the ATG to 834 bp after the ATG) in the C5-hkb-Fog plasmid was modified every 4 to 8 bp using codon redundancy to generate the same aminoacidic sequence (see Supplementary Fig. 2a, detailed sequence available in Supplementary Table 1).

hkb-fog_VSV-G

Membrane-tethered Fog was built by cloning a truncated version of type-I transmembrane protein VSV-G (vesicular stomatitis virus-G protein, Genebank NP 041715, amino acids E422-R508, ACK77584) at the C-terminus of the fog ORF (U03717.1). The C5-hkb-Fog plasmid was modified by inserting a DNA fragment containing 2xHA tags surrounded by two SGGGGS flexible linkers plus the truncated VSV-G before the stop codon of fog ORF. For transgenesis, hkb-fog_VSV-G was inserted into the attP2 landing site (Chr3, 68A4) and hkb-fog_res into the attP40 landing site (Chr2, 25C6).

scab^ko allele

A KO-attP founder line was generated by CRISPR/Cas9 gene editing as previously described in ref. ³⁰. Briefly, the entire ORF and a part of the UTRs were deleted (from −281 nucleotide to +8670 nucleotide from ATG of scab-RB, FlyBase ID: FBtr0087369) and replaced by an attP-3xP3-RFP selection marker cassette containing: forward attP (49 bp) and a floxed 3xP3-RFP eye selection marker which was flipped out by Cre recombinase in a second step. The deletion was verified by genomic PCR and Sanger sequencing. This “KO-attP founder” allele is a null allele of scab. Flies are not homozygous viable and are maintained over CyOdYFP balancer.

fog::SYFP2^KIN

We used SYFP2⁵¹ to generate endogenously tagged Fog. SYFP2 was used for tagging because it is reported to be a very rapidly maturing monomer⁵¹. Endogenous fog tagged to SYFP2 (fog::SYFP2^KIN) was generated by CRISPR/Cas9 gene editing (Wellgenetics Fly Genome Editing Service, Taipei, Taiwan), using a donor vector containing in sequence (Supplementary Fig. 5a): (1) the 5’-fog homology arm, (2) a 2xHA tags flanked by two SGGGGS flexible linkers, (3) the SYFP2 inserted before the TAA stop codon of the fog gene, (4) a PiggyBac DsRed eye marker screening cassette, composed of 3xP3- selection cassette⁵² flanked by the 5’ and 3’ PiggyBac terminal repeats, and cloned just after the TAA stop codon, and (5) the 3’-fog homology arm. Following eye color selection to identify successful gene editing, the 3xP3-DsRed cassette was flipped out by PiggyBac Transposase, generating a fog allele (fog::SYFP2^KIN) encoding a Fog::YFP fusion protein at the endogenous locus. The fog::SYFP2^KIN allele is homozygously viable and shows no defects in germband extension (Supplementary Fig. 5b, c). Correct gene editing was verified by genomic PCR and Sanger sequencing.

FASTA sequences of all plasmids are available upon request.

Sample preparation and embryo microinjections

Flies were kept in cages at 25 °C except for experiments using the UAS-GAL4 system (wg-Gal4 and 67-Gal4) in which they were kept at 18 °C. Embryos were prepared as previously described⁵³. Briefly, they were collected using apple cider plates smeared with yeast paste and transferred to a mesh basket, rinsed with water, dechorionated with 2.6% bleach for 90 s, and then rinsed copiously with water before transferring them back to clean agar. For live imaging, embryos were staged and selected (early stages of cellularization) under a dissection microscope and were aligned with the dorsal side facing up. They were then transferred to a glass coverslip coated with homemade glue. A drop of Halocarbon 200 Oil (Polysciences) was placed on the embryos to avoid drying during imaging. For microinjections, embryos were similarly harvested from agar plates, where flies were allowed to lay for 0.5–1 h. Embryos were then rinsed, dechorionated and aligned on coverslips coated with homemade glue. Following a brief desiccation period, embryos were covered with halocarbon oil and were injected with dsRNAs, RNase-free water or chemical inhibitors. The embryos were kept at 22 °C until live imaging. All injections in this study were performed on the lateral side at 50–80% egg length from the posterior.

dsRNAs preparation and drug injections

dsRNA probes directed against fog^28,34,54 (CG9559, Genebank ID: NM_078714), gprk2³⁸ (CG17998, Genebank ID: NM_057519), and scab^28,30 (CG8095, Genebank ID: BT021944) were generated from PCR products containing the T7 promoter sequence (TAATACGACTCACTATAGGG) fused to 18–21 nucleotides specific to each target gene.

The fog dsRNA probe is 861 bp in length and corresponds to nucleotides 1546–2406 of the fog transcript. The gprk2 dsRNA probe is 529 bp long and targets nucleotides 659–1187 within the 5′ UTR of the gprk2-RA transcript. The scab dsRNA probe targets nucleotides 2652–3101 (450 bp) of the scab-RB coding region. Gel-purified PCR products served as templates for in vitro transcription using T7 polymerase (Ribomax, Promega, P1300). Resulting dsRNAs were purified with Sure-Clean Plus (Bioline, BIO-37047) and diluted in RNase-free water to final concentrations of 5–30 μM for fog, 5 μM for gprk2 and 10 μM for scab. Microinjections with dsRNAs were carried out as described in the sample preparation section above. The sequence of the primers used to generate the dsRNA probes are listed in Table 2.

Table 2.

Nucleotide sequences of primers used to generate dsRNA probes

Targeted gene	Annotation ID (Flybase)	Primer name	Primer sequence
fog	CG9559	Fog-T7-S1-F	5’-TAATACGACTCACTATAGGGAAGCGATCGATCGGTCCCGAG-3’
fog	CG9559	Fog-T7-AS1-R	5’-TAATACGACTCACTATAGGGCACAAGGCCATCGTGCTCCTGA-3’
gprk2	CG17998	T7-GPRK2-123F	5’- TAATACGACTCACTATAGGGTTCCAACCAGCCGAAACTCACAG-3’
gprk2	CG17998	T7-GPRK2-629R	5’- TAATACGACTCACTATAGGGCTCTCGCTTTCAAGTAGACCGTA −3’
scab	CG8095	T7-scab-cod-F1	5’-TAATACGACTCACTATAGGGGCTCCACTGCCATTATACCGAT-3'
scab	CG8095	T7-scab-cod-R1	5’-TAATACGACTCACTATAGGGCTCGCATCTCGGCTCGGACA-3'

The annealing sequence, downstream of the T7 promoter, is in bold.

Dextran injections (Fig. 7e and Supplementary Fig. 8g) were performed using dextran 647, 10,000 MW, anionic, fixable from Thermo Fischer Scientific (D22914) at a concentration of 1 mg/mL. Embryos were injected in the perivitelline space at stage 6–7 directly on the microscope and imaged a few minutes later to ensure dextran equilibration in the perivitelline fluid.

α-Amanitin was injected at a concertation of 500 mg/ml at stage 7 directly on the microscope about 2–3 min before imaging.

Live imaging

Live imaging of embryos was performed at stage 7 in the dorsal-posterior region for 12–50 min at room temperature (21–22 °C), depending on the experiment. Dual color time-lapse imaging for EGFP and mCherry was performed using simultaneous acquisition on a spinning disc confocal (CSU-X1, Yokogawa) Nikon Eclipse Ti inverted microscope equipped with two cameras (Rolera EM-C², Q-Imaging or Kinetix22, Photometrics) distributed by Roper and using a 40X/1.25NA Apo water-immersion or a 100X/1.45NA Plan Apo oil-immersion objectives from Nikon, depending on the experiment. Live imaging was performed by simultaneously exciting with 491-nm (EGFP) and 561-nm (mCherry) lasers, using a dichroic mirror to collect emission signals on two cameras. For live imaging with 40X magnification, a z-series of 33 planes (spacing 0.8μm) spanning about 26.4 μm from the apex of cells in the PZ was acquired with a frame rate of 1 stack every 20 s. For live imaging of E-cad and MyoII with 100X magnification, a z-series of ten planes spanning 5μm (spacing 0.5 μm) was acquired with a frame rate of 1 stack every 5 s. Live imaging of sec::GFP in Fig. 4h was performed with 100X magnification, a z-series of ten planes spanning 5 μm (spacing 0.5 μm) below the vitelline membrane and with a frame rate of 1 stack every 5 s. Live imaging of βPS and MyoII was performed with 100X magnification. Z-series of two planes spanning 1 μm (spacing 0.5 μm) just below the vitelline membrane were acquired with a frame rate of 1 stack every 4 s. Similar settings were used to image sec::GFP in Supplementary Fig. 8h.

Live imaging of endogenous Fog::YFP and hkb-Fog::YFP was performed with a Zeiss 880 confocal microscope using a 40X/1.2NA water-immersion or 63X/1.4 NA oil objective. GaAsP hybrid detectors were utilized with a 514-nm excitation laser. Z-stacks of 4–5 planes (spacing 0.5 μm) spanning about 2–2.5 μm just below the vitelline membrane were acquired every 15–90 s for 15–45min.

Imaging conditions (line averaging, camera exposure time, laser power, etc.) were optimized and kept constant during the experiment performed at room temperature (22 °C). Laser powers were measured with a power meter at the back aperture of the objectives for every imaging session.

For brightfield imaging in Supplementary Figs. 1b, 2b, d, f, 5b, embryos were prepared and immobilized for imaging as described above. Brightfield time-lapse images were collected on a Zeiss Axiovert 200 M inverted microscope using a 20X/0.75NA objective and a programmable motorized stage to record different positions over time (Mark&Find module from Zeiss). The system was controlled by AxioVision software (Zeiss). Time-lapse data in WT or injected embryos were performed over 300 min with a frame rate of one image every 1 min.

Antibody staining

Embryos were fixed and permeabilized with 3.7% formaldehyde for 20 min, the vitelline membrane was removed by shaking in heptane/methanol, and then embryos were stained according to standard procedures⁵⁵. The Fog protein was detected with a rabbit antibody (1:1000, a gift from ref. ³⁶), sqh-MRLC::mCherry was detected with a rat antibody (1:1000, anti-RFP, Chromotek, Catalog no. 5f8), and Fog::YFP was detected with a chicken antibody (1:1000, anti-GFP, Aveslabs, Catalog no. GFP-1020). The Fog antibody was pre-adsorbed by incubating overnight at 4 °C with fixed y^-w^- embryos less than 1h old. Patched was detected with a mouse antibody (1:100, Drosophila Ptc (apa1) from DSHB, Catalog no. AB_528441). Secondary antibodies used were donkey anti-rabbit Alexa Fluor 568 (1:500, Thermo Fischer Scientific, Catalog no. A10042), donkey anti-rat Alexa Fluor 568 (1:500, Thermo Fischer Scientific, Catalog no. A78946), donkey anti-chicken Alexa Fluor 488 IgY (1:500, Thermo Fisher Scientific, Catalog no. 703 545 155), donkey anti-mouse Alexa Fluor 647 (1:500, Thermo Fisher Scientific, Catalog no. A32787). Stained embryos were mounted in Aqua-Polymount (Polysciences) and imaged with a Zeiss 880 confocal microscope using a C-Apochromat 63X/1.4 NA oil immersion objective. Image stacks with a spacing of 0.5 μm were collected, and maximum projections of three to seven planes were analysed.

Image processing, segmentation, and cell tracking

All image manipulation and processing were performed using ImageJ (version 2.140/1.54 f).

To generate the top views of 40X image stacks, image projections of selected z-planes around the cell apex were performed as previously described²⁸ using a custom procedure exploiting the Stack Focuser plugin (M. Umorin). The procedure restricts the projection to a narrow set of z-planes surrounding the apical surface, improving both outline definition and signal-to-noise compared with standard maximum-intensity projections. Briefly, the macro applies the stack focuser plugin with a 30-pixel (∼6 μm) kernel to locally identify the apical plane based on the E-cadherin::GFP signal. Subsequently, four z-planes for E-cadherin and seven for MyoII centered on this plane are projected as maximum-intensity projections. The resulting 2D-projected cells were then tracked either manually (by manually drawing ROIs) or automatically (Tissue Analyzer⁵⁶) to measure mean intensity and cell apical area.

Side views from 40X image stacks along the posterior-anterior axis (Figs. 1d, 2d) were generated by a single line re-slice of the hyper-stacks across the dorsal midline. The side views were then smoothened with a Gaussian blur of two pixels (0.15 μm) for representation.

For 100X image stacks, maximum-intensity projections were used for measurements of fluorescence intensity and cell segmentation. Before projection, z-stacks were rotated, cropped and smoothened with a mean filter of kernel 0.5 pixels (0.04 μm) to increase the signal-to-noise (SNR). The 2D-projected stacks were then segmented, and cells were tracked as previously described⁵⁴ using Ilastik (v.1.4) and Tissue Analyzer⁵⁶. In brief, cell outlines were visualized using E-cadherin::GFP. The 2D projections were band-pass filtered using cutoff frequencies of 1 μm (low-pass) and 8 μm (high-pass), after which they were processed with Ilastik to produce outline probability maps. Initial segmentation was carried out on these Ilastik predictions, followed by manual corrections on the original images. Final segmentation and cell tracking were then completed using Tissue Analyzer.

Side views from 100X (Supplementary Fig. 8k) image stacks were generated by re-slicing a rectangle ROI (6-μm wide) across the dorsal midline on images smoothened with a mean blur of one pixel (0.08 μm).

The distance of E-cad from the vitelline membrane (Figs. 1l, 2k and Supplementary Fig. 8l) was measured on height map images that carried the information of the plane where E-cad junctions were most in focus in the stack. These height map images were generated from E-cad hyper-stacks using the Stack Focuser plugin with a kernel of 11 pixels (0.88 μm). Height map images of E-cad were generated for all time points, and a mask based on E-cad intensity in 2D max projections was applied to mask out regions where E-cad junctions were not present.

Kymographs for E-cad::GFP (Fig. 1m) along the posterior-anterior axis were obtained with a method similar to the generation of side views but using maximum-intensity projection time series as an input for re-slicing. Kymographs are obtained using a single line of line width of 20 pixels (1.6 μm) across the medio-apical region of the cell.

Data analysis

Measurement of posterior endoderm displacement from brightfield imaging (Supplementary Figs. 1c, 2c, e, g, 5c)

The extent of posterior endoderm displacement during gastrulation was measured from brightfield movies for 60 min after the time when the cellularization front reaches the basal side of the nuclei on the dorsal side of the embryo (time 0). The cumulated displacement was measured by manually tracking the posterior edge of the invagination and by calculating the cumulative traveled distance of this point, $\mathrm{I}=\sqrt{{\left(\mathrm{x}-{\mathrm{x}}_0\right)}^2+{\left(\mathrm{y}-{\mathrm{y}}_0\right)}^2}$, where (x₀,y₀) is its position at time 0. This was normalized to the maximum embryo length (L) measured as the distance between the anterior-most and posterior-most points of the embryo. Normalized posterior endoderm (PE) displacement = l/L.

Measurements of fluorescence intensity and cell shape

Measurements of fluorescence intensity and cell shape parameters were extracted using ImageJ and further analyzed with Matlab (R2022b, including curve fitting toolbox, image processing toolbox, statistics and machine learning toolbox). For all intensity measurements, local background intensities were subtracted as previously described²⁸. Briefly, background intensities were removed by first masking out the structures of interest, like high and low intensity MyoII clusters or integrin puncta and then subtracting the remaining signal. Images were preprocessed with the “background subtraction” tool from ImageJ using a: radius of ~4 μm (50 pixels) for MyoII and of ~0.4 μm (five pixels) for βPS to minimize uneven illumination across the field of view. Masks were generated using manually defined intensity thresholds applied to these preprocessed images. The residual background images were then smoothed with a Gaussian blur with a radius ~0.3–0.6 μm (4–8 pixels) prior to subtraction.

For measurements of the mean intensity of MyoII and apical area in 40X images (Figs. 1f, 2g), fluorescence intensity and apical surface area were measured on stack-focused projections of 40X image stacks. Individual cells were manually tracked by drawing ROIs (about 6 cells per embryo). The mean gray value and area were measured using ImageJ.

For measurements of the mean/integrated intensity of MyoII in 100X images (Figs. 1j, k, 2j and Supplementary Fig. 8b), fluorescence intensities were measured on standard maximum-intensity projections for 100X image stacks. For individual cell measurements, mean and integrated intensities were measured within a region of interest (ROI) obtained by automated segmentation and tracking, and then shrunken by 10 pixels to remove junctional signals. Cell tracking was performed based on the E-cad signal in maximum-intensity projections of E-cad. Time traces of MyoII and cell apical area in individual cells were registered based on the time when the apical area reached a maximum. This time is defined as time 0 in Figs. 1j, l, 2k and Supplementary Fig. 8b.

Measurements of the invagination depth (Figs. 1g, 2f)

To measure the invagination depth, a straight line was manually drawn in side views from the deepest point of the apical surface of the invagination to the overlying vitelline membrane. The distance measured at 8 min (for Fig. 1g) or at 5 min (for Fig. 2f) was plotted for the indicated conditions. Time 0 is defined by synchronizing embryos relative to the time of onset of cell divisions in the dorsal posterior (see embryo synchronization below).

Manual measurement of the number of cell rows recruiting MyoII during wave propagation (Figs. 1h, 2h)

To measure the propagation of the MyoII wave, we manually recorded the time of MyoII recruitment in cells of the PZ along 3–4 rows of cells parallel to the anterior-posterior axis in each embryo. For each embryo, a mean value was obtained by averaging the 3–4 rows and different embryos were averaged to obtain plots in Figs. 1h, 2h. Time 0 is defined as the time of MyoII recruitment in the first cell in the PZ for each embryo.

Space-intensity plot (Figs. 3b, c, e, f, h, i,4c,e, j, k, 7b, f, i, j and Supplementary Figs. 3c, 4a, c, d, 5f, g, 8d, e, g, i)

In Supplementary Fig. 3c, space-intensity plots were measured from still images. First, a maximum-intensity projection of four planes (2 μm) was obtained. The Ptc signal was used as a proxy to define the posterior boundary of the wgGal4 driven-Fog expression domain. The mean intensity of Fog along three lines with a thickness of 100 pixels (9 μm each) was measured from this posterior boundary (0 μm) and plotted as a function of the distance along the AP-axis. The plots obtained were normalized (using min-max normalization) for representation.

In Fig. 4c, space-intensity plots were measured from still images. The mean intensity of Fog and MyoII was measured on maximum intensity projections of four planes (2 μm), and an average background (across three embryos) was subtracted. The resultant mean intensity was plotted across the distance from the invagination along the AP-axis. To control that the observed profiles do not depend on a confocal sectioning effect, image stacks with the same z-settings were acquired using the 405 nm laser line to capture embryo autofluorescence (gray background profile). Intensity profiles of the autofluorescence were measured to ensure that this value was constant. For Fig. 4e, the mean intensity of GFP and Fog was plotted similarly to Fig. 4c, without background subtraction.

In Fig. 3b, c, e, h and Supplementary Figs. 4a, c, 7b, f, i, j, 8d, g space-intensity plots were measured from registered time series where the position of the invagination front was kept constant. For this, the position of the front of the invagination was tracked manually over time using the ImageJ plugin (Manual tracking, https://imagej.nih.gov/ij/plugins/track/track.html). Each individual time point was then translated to keep the invagination front always in the same position. Then, an average intensity projection over time of the registered time series of MyoII was performed after background intensity subtraction (as shown in Figs. 3d (right), 3g (right), 7e (right), 7h (middle and right) and Supplementary Fig. 8). Additionally, the junctional MyoII signal was removed before the time average projection using a mask based on E-cad intensity above a threshold. The mean intensity of MyoII was then measured in each embryo using three-line profiles (200-pixel, 16 μm wide each) along the AP-axis of the embryo on the dorsal side. For each embryo, data were averaged across the three-line profiles and plotted against the distance from the front of the invagination along the AP-axis (shown as embryo profiles in Fig. 3b and Supplementary Fig. 4a).

The value R² in Fig. 3b, c and Supplementary Fig. 8d quantifies the goodness of fit in GraphPad Prism. R² (a fraction between 0.0 and 1.0) compares the fit of the one-phase exponential decay model to the fit of a horizontal line through the mean of all values on the Y-axis. R² is computed as a ratio of the sum of the squares of distances of the points from the best-fit curve determined by the fitting of the one-phase exponential decay model (SSresiduals) normalized to the sum of squares of the distances of the points from a horizontal line through the mean of all Y values (SStotal). R² is calculated using the equation: R² = 1.0 – (SSresiduals/SStotal). An R² value close to 1.0 indicates a good fit of the experimental data. In Fig. 3c and Supplementary Fig. 4a we fitted an exponential decay model to the intensity profiles of individual embryos (Supplementary Fig. 4a) or individual time points within a single embryo (Fig.3c). In Supplementary Fig. 8d, the exponential decay model was fitted to the intensity profiles from all the measured embryos (fit to the embryo profiles derived by averaging the three-line profiles measured in each embryo).

For quantification of the length-scale (Fig. 3f, i and Supplementary Figs. 4d, 8e), the mean intensity profiles from individual embryos were fitted with a one-phase decay exponential Y = (Y₀ - a) × e^(-x/λ) + a, where Y0 is the measured intensity value at X = 0, a is the plateau intensity value at X → ∞ and λ is the decay length. Decay length across all measured embryos is represented as mean ± s.d.

In Fig. 4k and Supplementary Figs. 5g, 7f (dextran), 8g, space-intensity profiles were also measured from registered time series relative to the position of the invaginating front. Here, average projections over time of maximum intensity projections were obtained without local background subtraction. Average time projections were then used to measure the intensity using three-line profiles of 100-pixel (9 μm) line width along the AP-axis of the embryo at the dorsal side.

In Fig. 4j and Supplementary Fig. 5f, ratios of each line profile from one condition to all line profiles of the other condition were calculated. The average of all measured ratios was plotted against the distance from the front of the invagination.

In Fig. 7f and Supplementary Fig. 8g, i, the normalization is a max-min normalization.

Amplitude and range of MyoII and βPS (Figs. 3e, h, 7c, d, g, k–n and Supplementary Fig. 8j)

For the amplitude, descriptive statistics of the space-intensity profiles of each embryo were obtained in GraphPad Prism, and the maximum values for each embryo were plotted in Fig. 7b, i, j.

For the data in Fig. 7 and Supplementary Fig. 8, the range was estimated as follows. The mean intensity and standard deviation (s.d.) of MyoII and βPS were measured in the region of very low/no recruitment at the embryo anterior of control embryos (the region from 50 to 60 μm anterior to the invagination front). An average of the values corresponding to 3 s.d. above the mean for each control embryo was used as a global threshold of intensity to define recruitment for all conditions. The x-axis values of the point where the intensity profiles overcame this threshold were plotted as the range of activation for each embryo. For Fig. 7c, g, each embryo intensity profile was smoothened (80–90 neighbors on each size to average and 0th order of the smoothing polynomial) in GraphPad Prism before thresholding to achieve a precise value of the range. For Supplementary Fig. 8j, a threshold of 10% of the normalized intensity was used to define a region of contact with the vitelline membrane.

For the data in Fig. 3 (Fig. 3e, h), the activation threshold was defined as the mean + 3 s.d. estimated from the average curves of the controls in the region from 35 to 40 μm anterior to the invagination front, since the measurements did not cover a larger region. This global threshold (indicated by the dotted lines in Fig. 3e, h) was used to estimate the range in individual embryos for all conditions as above. Since the measurements did not cover regions beyond 40 μm anterior to the invagination front, in the text, we indicated the lower limit of the possible range of MyoII activation for the mutant conditions.

Embryo synchronization

Synchronization was performed to compare mutant to wild-type embryos and to register them in developmental time before data pooling and averaging.

For brightfield movies (Supplementary Figs. 1, 2, 5b, c), time 0 is defined as the time when the cellularization front reaches the basal side of the nuclei on the dorsal side of the embryos.

For 40X time lapses, synchronization is based on the time of onset of cell divisions in the dorsal-posterior ectoderm. This phenomenon is independent of the morphogenesis of the posterior endoderm. Time 0 is defined as 22 min (for Fig. 1d, f) and 19 min (for Fig. 2g, h) prior to the first cell division in an embryo to coincide with the onset of MyoII recruitment in the primordium for control embryos.

For experiments in fixed samples, embryos were staged manually based on similarity with events observed in time-lapse experiments.

Fluorescence correlation spectroscopy (FCS)

Data acquisition

FCS measurements were performed at room temperature (22 °C) on an inverted Zeiss LSM880 system (Carl Zeiss, Oberkochen, Germany) using a Plan-Apochromat 100x, 1.4NA DIC M27 oil-immersion objective. Fluorescence was excited with the 488 nm (Smog::GFP, VSV-G::GFP) or 514 nm (Fog::YFP, sec::GFP) line of an Argon laser in spot mode. Fluorescence was detected in the range of 491–700 and 516–700 nm (for measurements in Figs. 4g, h, 5b–h and Supplementary Fig. 6a–e) or 491–558 nm (for measurements performed in Fig. 6a, b, d–g and Supplementary Figs. 7a–d, f–n, 8f) on a 32 channel GaAsP array detector operating in photon counting mode, with a pinhole set to one airy unit. Prior to FCS measurements and at embryonic stages preceding wave propagation, the vitelline membrane was pre-bleached to reduce autofluorescence background in the measurements. For this, the apical-most plane of the embryo (containing the vitelline membrane) was scanned in full field-of-view and continuous scan mode (scan speed 6) for 4 min with the 488 nm line at a power of ca. 15 µW or for 1.5 min with the 514 nm line at ca. 5 µW. Laser powers were measured at the exit of the objective. Four to five FCS measurements per embryo were then acquired within the extracellular space of the invaginating furrow at an approximate depth of 5–10 µm below the vitelline membrane (spot I) during wave propagation. In addition, up to ten measurements per embryo were performed at the apical surface of cells in the propagation zone (spot PZ), in a focal plane ~0.1 μm below the vitelline membrane. Each FCS trace was acquired for 30–60 s with a time resolution of 1.23 µs, at 0.2–2 µW excitation laser power for Fog::YFP (0.25 µW in Fig. 4g for Fog::YFP) and 0.2–6 µW for sec::GFP (2 µW in Fig. 4g for sec::GFP) and Smog::GFP/ VSV-G::GFP. This power range was selected to evaluate the potential bias in the estimated diffusion coefficients by light-induced photophysical transitions of the fluorophores (see below)^57,58. For oligomerization measurements of Smog::GFP and VSV-G::GFP, additional measurements of the residual autofluorescence background were performed in yw embryos, i.e., embryos not expressing any fluorescent construct, on the same day.

Data analysis

FCS measurements were manually exported as TIFF files using the ZEN software (Zen Black 2.3 SP1 FP3), imported and analyzed using custom-written MATLAB (The MathWorks, Natick, MA, USA; version R2020a) code^43,59–61. To correct for signal decrease due to photobleaching, a two-component exponential function, f(t), was fitted to the raw fluorescence time series $F^{raw}\left(t\right)$ and the following correction formula⁶¹ was applied, resulting in the corrected time series $F^{corr}\left(t\right)$:

$$F^{corr}\left(t\right)=\frac{F^{raw}\left(t\right)}{\sqrt{f\left(t\right)/f\left(0\right)}}+f\left(0\right)\left(1-\sqrt{f\left(t\right)/\left(\right)f\left(0\right)}\right).$$

For the analysis of Smog and VSV-G in cells of the PZ, an additional correction was applied to remove residual background from the vitelline membrane. To this end, background intensity time traces acquired in multiple pre-bleached yw embryos were averaged, and a two-component exponential fit was fitted to the average intensity time trace. The obtained fit function was then subtracted from the intensity time trace of each individual measurement acquired in the actual sample, i.e., embryos expressing Smog::GFP or VSV-G::GFP. Due to local variations in the background intensity, this correction procedure occasionally led to very low or even slightly negative intensity values, inducing high noise, particularly in the brightness readout. We therefore removed all measurements with average intensities below 10 kHz after background subtraction (typically 10–20% of measurements at maximum). Generally, background correction by subtraction is valid in the case of a non-correlated background, which we confirmed by FCS analysis of the background measurements (as also shown in ref. ³⁸). Note that the applied correction scheme accounts, on average, for temporal decay of the background intensity due to photobleaching. In fact, intensity time traces of Smog::GFP or VSV-G::GFP did not show substantial photobleaching after background subtraction.

From the resulting intensity time trace F(t), the autocorrelation function (ACF) was calculated as follows, using a multiple tau algorithm:

$$G\left(\tau \right)=\frac{{⟨\delta F\left(t\right)\delta F\left(t+\tau \right)⟩}_t}{{⟨F\left(t\right)⟩}_t^2},$$

where $\delta F\left(t\right)=F\left(t\right)-{⟨F\left(t\right)⟩}_t$.

To avoid artefacts caused by rarely occurring long-term instabilities, ACFs were calculated segment-wise (5–10 segments) and then averaged. Segments showing clear distortions were manually removed from the analysis⁶². In addition, the first segment was always removed since it was occasionally corrupted by residual intensity changes due to temporal variations of background photobleaching that were not properly captured by the average background correction⁶³.

For measurements inside the invagination (spot I), a model for three-dimensional diffusion and Gaussian confocal volume geometry was fitted to the average ACFs⁵⁹:

$${G\left(\tau \right)}_{1comp}=\frac{1}{N}\left(1+\frac{T}{1-T}{e}^{-\frac{\tau }{{\tau }_b}}\right){\left(1+\frac{\tau }{{\tau }_d}\right)}^{-1}{\left(1+\frac{\tau }{{\tau }_d{S}^2}\right)}^{-1/2},$$

Here, N denotes the particle number, ${\tau }_d$ the diffusion time, T is the fraction of fluorophores undergoing photophysical transitions with an average time constant ${\tau }_b$ (see details below), and S is the structure parameter. From the diffusion time, the diffusion coefficient D was determined by $D=\frac{{\omega }_0^2}{4{\tau }_d}$. The waist ω₀ was calibrated from FCS measurements of Alexa Fluor® 488 (Thermo Fisher Scientific, Waltham, MA, USA) dissolved in water at 20 nM, using the previously determined diffusion coefficient of $D_{AF488}=435\frac{{\mu m}^2}{s}$ (ref. ⁶³). Calibration measurements were performed at ca. 1 µW (at 488 nm) or 10 µW laser power (to compensate for suboptimal excitation of AF488 at 514 nm) and 2 µm depth to minimize aberrations. The structure parameter was fixed to the average value determined in calibration measurements, typically around 6.

Under the assumption of an aqueous environment and globular protein conformation, the relative diffusion dynamics of two proteins (i.e., diffusion coefficients D₁ and D₂) of different size (i.e. of molecular weights MW₁ and MW₂) diffusing freely in 3D can be estimated using the Stokes-Einstein relation, $D=\frac{k_{B}T}{6\pi \eta R}$ (with $k_B$ denoting the Boltzmann’s constant, T the temperature and $\eta$ the viscosity of the solvent, and R the proteins hydrodynamic radius) and the fact that the hydrodynamic radius approximately scales with the cubic root of the molecular weight (for proteins of similar mass density). Thus, $\frac{D_1}{D_2}=\sqrt[3]{\frac{{MW}_2}{{MW}_1}}$. Using secreted GFP (molecular weight of ca. 27 kDa) as a ruler, it is thus expected that Fog::YFP (molecular weight of ca. 127 kDa) diffuses about 1.7 times slower than secreted GFP. With careful analysis of photophysical effects (see details below), a relative ratio of 1.6 was obtained with the determined diffusion coefficients of 55 µm²/s for Fog::YFP and 87 µm²/s for sec::GFP in the invagination.

For measurements in the propagation zone (spot PZ), a two-component diffusion fit model was applied:

$${G\left(\tau \right)}_{2comp}=\frac{1}{N}{G}_b\left(\tau \right){\left(1-F_2\right)\left(1+\frac{\tau }{{{\tau }_d}_1}\right)}^{-1}{\left(1+\frac{\tau }{{{\tau }_d}_1{S}^2}\right)}^{-\frac{1}{2}}+F_2{\left(1+\frac{\tau }{{{\tau }_d}_2}\right)}^{-1},$$

where $G_b\left(\tau \right)$ denotes the photophysics term, $G_b\left(\tau \right)=\left(1+\frac{T}{1-T}{e}^{-\frac{\tau }{{\tau }_b}}\right)$, and F₂ the fraction of the second component. The first component is attributed to particles diffusing freely in 3D and the second component to diffusion in a 2D plane⁶⁴, corresponding to particles that diffuse extracellularly in the space between the vitelline membrane and the apical cell surface but potentially bind to receptors in the apical membrane resulting in (transient) 2D diffusion, a behavior that has often been observed for extracellularly diffusing morphogens^60,65,66. For measurements of membrane-bound proteins, i.e., Smog and VSV-G, the 2D diffusion term corresponds to molecular diffusion in the apical membrane, while the 3D diffusion term corresponds to intracellular background, as previously discussed³⁸.

To minimize the number of free fit parameters, a single photophysics term was included in the ACF fit models given above. However, the fluorescent protein tags, GFP and SYFP2, utilized in this study exhibit multiple (at least two) photophysical transitions^57,58,62,67: (1) triplet state transitions occurring on the µs time scale, (2) (light-induced) flickering occurring on the 10−100-µs time scale. Thus, estimates of fast diffusion dynamics characterized by fluctuations on similar time scales might be biased. Indeed, fitting ACFs with maximal time resolution (fit routine 1) resulted in photophysics time constants of ca. 1 µs and illumination intensity-dependent diffusion coefficients (see Fig. 4h and Supplementary Fig. 6b). To obtain unbiased diffusion coefficients, the values were interpolated to zero illumination power, according to a previous study⁶⁷. To cope with low signal-to-noise ratio of individual ACFs in this analysis, ACFs of several measurements acquired at the same power in multiple embryos were first averaged and the 3D diffusion model fitted to the average ACF (Supplementary Fig. 6a). This was particularly crucial for sec::GFP, which is ca. sevenfold less efficiently excited as Fog::YFP at the same 514 nm laser power. A comparison of the diffusion coefficients obtained by fitting individual ACFs at comparable effective excitation (i.e., 0.25 µW for Fog::YFP vs. 2 µW for sec::GFP) is shown in Fig. 4g.

Measurements in the propagation zone (spot PZ) had to be performed at higher excitation power (i.e., 1–2 µW) to maximize signal-to-noise ratio and minimize acquisition time with respect to the movement of the propagating wave. To minimize bias in estimating the fast-diffusing component, an alternative fit routine was applied (fit routine 2, Supplementary Fig. 6b), in which fitting was restricted to lag times larger than 5 µs. For measurements of Fog::YFP inside the invagination (spot I), the photophysics term then converged to time constants of 30–80 µs with a fraction of 8% at the lowest and 30% at the highest laser power. The resulting diffusion coefficients were almost independent of excitation power, showing that this fit model captures well the flickering contribution and hence minimizes the bias in the estimated diffusion dynamics (Supplementary Fig. 6b). The second fit routine was therefore applied to analyze all measurements performed in the propagation zone (spot PZ). From the determined particle number N, the protein concentration c was estimated, $c=\frac{N}{V_{eff}}=\frac{N}{{\pi }^{3/2}{\omega }_0^{3}S}$, where $V_{eff}={\pi }^{3/2}{\omega }_0^{3}S$ is the effective detection volume. It should be noted that for measurements of Fog diffusing in the propagation zone, this formula and the applied FCS fit model provide an approximation because the physical space in which molecules diffuse extracellularly is confined by the vitelline membrane at the top and the apical cell surface at the bottom.

In Fig. 5c, in the invagination, D was measured by fitting ACFs with a one-component diffusion model (as in Supplementary Fig. 6c), in the PZ the diffusion coefficients of the slow- and fast-diffusing fractions (D_slow and D_fast) of Fog::YFP were obtained by fitting ACFs with a two-component diffusion model (as in Supplementary Fig. 6e).

For oligomerization measurements of the membrane proteins Smog and VSV-G, the two-component fit was dominated by the 2D diffusion term, corresponding to a fraction of 60–80% of molecules and diffusion times of ca. 5−100 ms. The 3D diffusion term converged to faster diffusion times of few hundred µs to few ms. The photophysics term converged to decay times of ca. 5–50 µs.

Molecular brightness measurements using FCS

The molecular brightness was quantified from the average fluorescence intensity and the particle number determined from the FCS analysis, $B=\frac{I}{N}$. For a mixture of a monomeric species (brightness B₁) and an oligomeric species (i.e., n-mers, brightness B_n = nB₁), the average brightness is calculated as follows, $B=\frac{{f_{n}B}_n^2+{\left(1-f_n\right)B}_1^2}{f_n{B}_n+\left({1-f}_n\right)B_1}$, where f_n is the relative fraction of the oligomeric species and f₁ = 1-f_n the monomeric fraction⁴³. Inverting this equation allows computing the oligomeric fraction, $f_n=\frac{B_1^2-B{\cdot B}_1}{B{\cdot B}_n-B\cdot B_1-B_n^2+B_1^2}.$ Previous studies have reported that fluorescent protein properties strongly affect brightness-based oligomerization measurements. In particular, dark fluorophore states have to be taken into account, which can effectively be modeled with a single parameter, the fluorescence probability p_f⁴³. For an n-mer, the brightness B_n in the equation for the oligomer fraction is then calculated as follows, $B_n\left(p_f\right)=$ $\frac{{\sum }_{i=1}^n\left(\begin{array}{c}\hfill n\hfill \\ \hfill i\hfill \end{array}\right)p_f^i{\left(1-p_f\right)}^{n-i}{\left(i{B}_1\right)}^2}{{\sum }_{i=1}^n\left(\begin{array}{c}\hfill n\hfill \\ \hfill i\hfill \end{array}\right)p_f^i{\left(1-p_f\right)}^{n-i}\left(i{B}_1\right)}$, assuming that all fluorescent protein subunits are independent and in a fluorescent state with a probability p_f.

In our analysis, we first calculated the brightness of monomeric GFP assuming that VSV-G::GFP is exclusively present as trimers and then used this value to calculate the oligomer fraction for a putative monomer-oligomer mixture of Smog::GFP, given the experimentally determined average brightness B. We calculated oligomer fractions for p_f = 1 (i.e., absence of dark GFP states, since they have not been characterized in Drosophila embryos yet) and p_f = 0.7 (i.e., the value that has been previously measured for GFP in mammalian cells⁴³).

Gradient analysis using FCS

FCS measurements were performed at the apical cell surface at increasing distances from the moving invagination. Before each measurement, a confocal image capturing the position of the invagination front and the anterior part of the embryo was acquired where the position of the FCS spot was marked. In the analysis, the position of the invagination front was manually determined in the image. Then, FCS and image metadata were extracted (using custom-written MATLAB code) to determine the distance of the FCS spot from the invagination for each FCS measurement. Estimates for the relative fractions (F_fast and F_slow) of fast and slow-diffusing components and molecular brightness values resulting from FCS analysis were pooled for several measurements in each embryo and across multiple embryos. These values were then plotted as a function of distance from the invagination.

Calculation of gradient slopes (Fig. 5g, n and Supplementary Fig. 7h, l,m)

Measurements at different distances from the invagination within individual embryos were fitted with a simple linear regression from 0 to 70 µm from the invagination using the linear regression model in GraphPad Prism. The best-fit values of the slope of each individual embryo were then plotted in the dot plots in Fig. 5g, n and Supplementary Fig. 7h, l, m. Their mean ± s.d is reported in the main text.

Statistics

For all experiments, data points from different cells, measurements or embryos from at least two independent experiments were pooled to estimate the plotted mean, s.d., and s.e.m.

In order to determine whether the two datasets were significantly different, a two-sided unpaired t-test was performed using GraphPad Prism. It was assumed that the datasets are sampled from Gaussian populations but have unequal variances (Welch’s correction). In Fig. 5h, n and Supplementary Fig. 7h, l, m, a two-sided one-sample t-test was carried out to compare the sample mean to a hypothetical mean of zero. For the control sample (water) in 5h, n, and Supplementary Fig. 7h the test was one sided to the hypothesis that mean of the distribution is below 0. The test assumes sampling from a gaussian distribution. No statistical method was used to predetermine the sample size. The experiments were not randomized, and the investigators were not blinded to allocation during experiments and outcome assessment. The experimental procedure did not allow identifying the sex of the embryos at the time of the experiment.

Repeatability

All measurements were performed in 3–9 embryos. In experiments involving living embryos, we considered each embryo as an independent experiment. In immunostainings, independent experiments correspond to distinct staining procedures. Representative images, which are shown in Figs. 1–7 and Supplementary Figs. 1–8 were repeated at least twice and up to more than ten times. The experiments in Figs. 1e, m, 2e were repeated independently for four embryos in both conditions with similar results. The experiment in Supplementary Fig. 5d was repeated independently for 5 embryos in both conditions with similar results.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

C.C. and T.L. conceived and co-supervised the study. G.M., C.C., and T.L. planned the experiments with help from V.D.-E. for the planning of the FCS experiments. G.M. performed all the experiments and quantifications except for those in Fig. 7e–j and Supplementary Figs. 3e, 4b–d, 8f–j, which were performed by C.C. V.D.-E. analyzed and quantified all the FCS data. J.M.P. and E.D.S. designed and generated all the molecular constructs with the help of G.M. All authors discussed the data. G.M. and C.C. prepared the figures. G.M., C.C., and T.L. wrote the paper with help from V.D.-E. for the discussion of the FCS results. All authors made comments.

Peer review

Peer review information

Nature Communications thanks Rita Mateus, Nicoletta Petridou, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

In reason of the large size of the raw image dataset, the data supporting the findings of this study and material are available on request from the corresponding authors (T.L and C.C.). Source data are provided with this paper.

Code availability

The custom code used to process images, perform measurements and analyse the FCS data is available on GitHub at https://github.com/ValDunsing/pointFCS.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-68418-z.