The epithelial polarity genes frazzled and GUK-holder adjust morphogen gradients to coordinate changes in cell position with cell fate specification

Morphogenetic gradients specify distinct cell populations within tissues. Originally, morphogens were conceived as substances that act on a static field of cells, yet cells usually move during development. Thus, the way cell fates are defined in moving cells remains a significant and largely unsolved problem. Here, we investigated this issue using spatial referencing of cells and 3D spatial statistics in the Drosophila blastoderm to reveal how cell density responds to morphogenetic activity. We show that the morphogen decapentaplegic (DPP) attracts cells towards its peak levels in the dorsal midline, whereas dorsal (DL) stalls them ventrally. We identified frazzled and GUK-holder as the downstream effectors regulated by these morphogens that constrict cells and provide the mechanical force necessary to draw cells dorsally. Surprisingly, GUKH and FRA modulate the DL and DPP gradient levels and this regulation creates a very precise mechanism of coordinating cell movement and fate specification.


Introduction
The "French Flag model" of positional information is a central model in developmental biology that explains how cell fates are specified within broad regions of developing embryos, limbs, and other organs. In this model, cells are thought to interpret threshold levels of a morphogen according to their spatial position and acquire distinct fates through the activation of specific gene expression programs [1][2][3][4]. Despite its immense power to explain diverse phenomena such as embryonic axial patterning and segregation of different neuronal populations in the nervous system, a major simplification is frequently overlooked in this model. Namely, it is assumed that morphogen thresholds reach and modify a static cell population. However, this condition is seldom if ever met in most developmental contexts, which generally involve a dynamic displacement of cells at the same time they read the instructive thresholds that determine their fates. Here, we sought to understand how tissues coordinate cell movements with cell fate specification during pattern formation. and late cellularization stages defined by initial and fully extended membrane invagination on the ventral side, respectively. Images obtained from these stages were then segmented to obtain the centroids of each nucleus, and the 3D cell features were imported into geographic information system (GIS) to generate average cell density heatmaps for the dorsal and ventral regions and to analyze the data with spatial statistics. In addition to heatmaps and hot/cold spot maps, we also tested for differences in cell count numbers (see Methods).
Our results show that at the cellularization onset, there is already a slightly higher number of dorsal cells than ventral cells (Fig 1A). These differences are established prior to cellularization by the DL gradient as evidenced by the fact that embryos without nuclear DL have equal cell densities in the ventral and dorsal sides at the beginning of cellularization (Fig 1C and 1D). In agreement with previous reports [9,12], by the end of cellularization, the asymmetric pattern of high density of cells within the dorsal region versus low density in the ventral region becomes evident in density heatmaps of late stage embryos (Fig 1B and 1D).
Since the total cell number in the embryo remains constant during cellularization [20,21] and apoptosis is absent during this stage [22], the emergence of a dorsal region of high cell density reflects the movement of cells towards the dorsal midline [9]. To visualize these movements, we analyzed time-lapse videos of live embryos expressing the cell membrane protein E-Cadherin/Shotgun-GFP (E-CAD/Shg-GFP) [23] as well as E-CAD in fixed embryos throughout cellularization (Fig 1D). The data obtained with E-CAD-GFP agree with previous analyses using Histone-GFP [9], but since E-CAD-GFP labels cell contours, our analyses rule out the possibility of nuclear movement within cells and reveal that the cell movements involve cell constriction with no evident intercalation between cells (S1 Video). We measured the segmented surface areas of individual dorsal cells expressing E-CAD-GFP in time-lapse images (S2 Video and S1 Fig) and from dorsal and ventral cells of same fixed embryos at 3 distinct stages (Fig 1E and 1F). These results show that the apical surface of dorsal cells becomes constricted and tightened as cells move dorsally, resulting in a significant decrease in cell size from early to mid and to late stage. In contrast, cells located in the ventral side of the embryo do not constrict over time ( Fig 1F). Thus, these experiments confirm the stereotyped cell movements from the lateral regions and poles towards the dorsal midline center, resulting in an increase in cell density on the dorsal surface of the embryo compared to the ventral surface.

DL regulates cell movements indirectly through DPP
From the data presented above and previous reports, it is clear that cells are attracted to the dorsal region and their density increases in this region over time. To a large extent, this pattern of cell clustering is the mirror image of the DL gradient, which decreases continuously towards the dorsal side. In addition, the asymmetric dorsal clustering of cells was shown to be abrogated in embryos with no nuclear DL [9]. However, if DL regulated this dorsal-bound cell movement directly, then this would imply that it does so by creating cell repulsion. In this case, we should expect repulsion to reach its maximum in the ventral region where the levels of DL peak. Nevertheless, in this region, the cell movement is virtually inexistent [9]. Thus, DL cannot be the morphogen that directly governs these cell movements, but rather it must do so indirectly through repression of another morphogen that attracts cells dorsally. The natural candidate to exert this activity is DPP, which meets the requirements of being repressed ventrally by DL and achieving peak levels in the dorsal midline, the site where cells are attracted to.
To understand the relationship between cell clustering and the DL and DPP gradients, we tested the effects caused by the removal of DL and DPP individually and simultaneously. First, we analyzed embryos without the DL gradient using the maternal mutation gastrulation defective (gd), which prevents the processing of Spätzle and the activation of Toll. In those embryos, the DL gradient is not formed because DL is absent from the nuclei. In addition, the DPP gradient is not formed because the relief of DL repression allows DPP to expand across the DV axis as can be seen by the ubiquitous activation of its target rho ( Fig 1G). As expected, we observe a high cellular density across the D/V axis within the center region of these embryos (Fig 1B, 1G and 1H) [9]. The anterior and posterior poles have a low density as in the wild type, indicating that the movements controlled by the A/P coordinates are maintained, but these anterior/posterior-most cells move towards the center of the embryo without noticeable dorso-ventral differences (i.e., the directionality to the dorsal midline is lost in gd embryos). Next, to test if this cellular density packing stems from the indirect ubiquitous activation of DPP, we removed DPP from embryos without DL gradient (note loss of rho activation in Fig  1G). In contrast to the loss of DL only, embryos without DL and DPP gradients have a much lower cell density across the D/V axis (Fig 1G and 1H). Thus, DPP is required for cell clustering. To further test the ability of DPP to attract cells, we analyzed embryos without DL and DPP gradients expressing DPP orthogonally by using the even-skipped stripe 2-dpp (st2-dpp) construct [24]. These experiments show that DPP expressed in this position activates ectopically its target gene rho and indeed attracts cells to the center of the embryo across its entire circumference (Fig 1G and 1H).
Several other pieces of evidence unambiguously demonstrate that DPP attracts cells. First, the cell density in the dorsal region never increases over time in embryos without DPP (Fig  2A-2C). Second, this phenotype can be rescued by the addition of st2-dpp. The rescued embryos have a broad area of high cell density on the dorsal surface beyond the sites of dpp RNA expression and rho activation ( Fig 2D). Third, cell counts along the A/P axis of these embryos show a higher cell density anteriorly than posteriorly, showing a reorganization in the cell density along the A/P axis in response to the localized ectopic DPP source (Fig 2E and  2F). Finally, Getis-Ord Gi � spatial statistics show that while wild-type embryos have large hot spots in the central dorsal region flanked by cold spots in the poles (Fig 2G), the hot and cold spots are smaller in dpp embryos and there is an increase in randomly distributed cells (Fig 2GAU : PleasenotethatFig2HiscitedinthesentenceFinally; Getis À OrdGi � spatialstatisticsshowtha ). The expression of st2-dpp reverts this phenotype similar to the wild type, with hot spots shifted more anteriorly (Fig 2GAU : PleasenotethatFig2IiscitedinthesentenceTheexpressionofst2 À ).
A genome-wide search identifies GUK-holder and frazzled as candidate genes to regulate cell movements The results above show that DPP attracts cells dorsally and DL stalls them ventrally by excluding DPP expression. However, since DL encodes a transcription factor and DPP encodes a secreted signaling protein, these cell movements must be enabled by downstream genes. To identify these effectors, we searched for genes likely to respond to DL and/or DPP gradients and that encode proteins with a role consistent with the regulation of cell movement. We screened the Drosophila genome for genes with similar developmental expression patterns to the DPP receptor thickveins using the existing modENCODE mRNAseq development database. Out of 101 genes identified, we selected those with predicted functions in cell migration, cell adhesion, and/or cytoskeleton regulation, as well as asymmetric expression along the D/V axis (see Methods for details). This search led to the identification of 2 genes, frazzled (fra) and GUK-holder (gukh). Both genes have been implicated in migration in various developmental contexts but were not previously associated to either DPP or DL, and their early embryonic functions are unknown. fra is the Drosophila homolog of Deleted in Colorectal Cancer gene (DCC) and encodes a protein belonging to the immunoglobulin subfamily that functions as the receptor of Netrin [25]. FRA/DCC was previously implicated in glial and axonal migration, and migration of various cell types including cardiac, salivary gland, and mesenchymal cells in Drosophila [25][26][27][28][29][30]. gukh encodes a protein with a SCAR-WAVE domain predicted to act on the nucleation of actin filaments [31]. In addition, GUKH physically interacts with membrane-associated guanylate kinases (MAGUKs), such as DISCS LARGE (DLG) [31][32][33] and is required for the correct subcellular localization of the planar cell polarity proteins DLG and Scribble (SCRIB) [31,34]. In Danio rerio, its ortholog has been shown to regulate cell migration during craniofacial development [35]. Furthermore, the human orthologue of GUKH, the Nance-Horan syndrome gene (NHS), nucleates actin filaments [36]. Noteworthy, emerging work link both fra and gukh to epithelial polarity functions, morphogenesis, and regulation of adherens junctions along the cell apico-basal axis [29,34,[37][38][39].

DPP and DL regulate gukh expression and DL regulates fra expression
We next tested if gukh and fra are regulated by DL and/or DPP. gukh RNA is strongly expressed in 2 lateral stripes in the ventral neuroectoderm, in the mesoderm, and in a thin stripe within the dorsal midline as revealed by sensitive fluorescent in situ hybridization (Figs 3A, 3C, S2A and S2B). Our results show that both DPP and DL are required to activate gukh in the dorsal and ventral regions, respectively. This regulation is evident in dpp-mutants where the expression of gukh in the dorsal midline is lost (Fig 3A and 3B; note the presence and absence of gukh nascent transcripts in high magnification boxes) and restored by the expression of st2-dpp (S2C and S2D Fig). Furthermore, in gd 7 mutant embryos that cause the loss of nuclear DL and the activation of DPP signaling, the dorsal stripe of gukh expression expands . Representative heatmap on right shows ftz stripes (black dots). (C) Cell number differences between ventral and dorsal sides in dpp-at early and late stages. (D) Cell density heatmaps of the dorsal surface of late stage dpp-embryos ectopically expressing dpp (st2-dpp) (gray dots, stripe position). Black dots in representative heatmap show rho-expressing cells. (E) Selected regions for cell counts using ftz as an A/P landmark for nearby (st-2) and distant (st-6~7) regions from ectopic dpp. (F) Cell counts in late-stage wild type and dpp-and dpp-, st2-dpp embryos. Note that st2-dpp expression increases the density of cells in ftz stripe 2 and reduces the density of cells between stripes 6 and 7 compared to wild type. Error bars, standard deviation. N.S., not significant. Asterisks, threshold values based on p-values ( �� p < 0.01) calculated with two-tail Mann-Whitney test (different stages in C; genotype comparisons in F) or two-tailed Wilcoxon signed-rank test (st-2 and st-6~7 comparisons of same genotypes in F). (G) Hot spot analysis of dorsal surface of wild type, dpp and dpp, st2-dpp embryos. Legend on left side indicates color-code for confidence intervals of hot spots (red shades) and cold spots (blue shades), and nonsignificant regions (NS, yellow). Scale bars, 60 μm (D and E, top) and 20 μm (E, bottom). Metadata for the graphs shown in C and F can be found at Supporting information S1 Metadata. A/P, antero-posterior; DPP, decapentaplegic; FTZ, fushi tarazu; ST2, even skipped stripe 2.
https://doi.org/10.1371/journal.pbio.3002021.g002 throughout the embryo circumference ( Fig 3D). Evidence that gukh is also activated by DL was obtained using Tl r4 , a mutation that maintains uniform levels of nuclear DL around the entire embryo circumference [16,40]. In these embryos, the gukh ventral expression domain is expanded around their entire circumference ( Fig 3E). Finally, gukh expression is completely lost in gd 7 , dpp-embryos that lack both DL and DPP ( Fig 3F). In contrast to the expression of GUKH that appears in discrete positions, fra RNAs are distributed in a dorsal to ventral gradient ( Fig 3G) that is not regulated by DPP (S2E-S2H Fig) but generated by a dosage-dependent repression by DL. This can be best demonstrated by quantifying the levels of fra in embryos without nuclear DL (gd 7 embryos) ( Fig 3H) or intermediate ( Fig 3I) and high levels of nuclear DL (Fig 3J) (i.e., using moderate and strong dominant mutations of Tl). Indeed, the intensity levels of fra RNA obtained in mutants that do not express DL or express DL uniformly at a single level, reproduce discrete points of the curve of decaying fra levels from dorsal to ventral regions in normal embryos (Fig 3K).

fra and gukh are required for stereotyped cell movements
We next asked if the response of fra and gukh to the D/V gradients of DL and/or DPP is required for the stereotyped cell movements in the embryo. To address this issue, we analyzed cell density heatmaps and hot/cold spots of the null mutants fra 3 and gukh L1 . The heatmaps show that the cell density decreases in the dorsal region of mutant embryos and increases in the ventral region ( Fig 3L). These findings are confirmed by direct cell counts that yield a significantly lower D/V cell count differences in fra and gukh embryos compared to the wild type ( Fig 3M). The hot spot analyses in the dorsal region can still identify hot spot clusters in the mutants, and those are established with less cell numbers ( Fig 3N). Noteworthy, we observe the emergence of cell density hot spots within the ventral midline of mutant embryos ( Fig 3N). This finding contrasts to wild-type embryos, which typically show random cell distribution in the ventral region, and occasionally have few hot spots in more lateral regions but not in the ventral midline ( Fig 3N). Finally, density heatmaps in the lateral region of the embryo corresponding to the neuroectoderm show a higher cell density in fra 3 and gukh L1 than the wild type (S3 Fig), in agreement with a decreased attraction of lateral cells to the dorsal region. Taken together, these results show that fra and gukh are required for the stereotyped cell movements in the blastoderm.

The cell movement towards the dorsal side of embryos deploys changes in cell area that are regulated by FRA and GUKH
Our results show that there is a noticeable decrease in the size of dorsal cells from early to late stage ( Fig 1D and 1E). We also observe that in late stage, dorsal cells are on average 34% smaller than ventral cells (Fig 4A-4D). Since the shape of these cells often approximates a regular hexagon (Figs 1D and 4A), a single dorsal row that shrinks 34% of its area could dislodge 20% of the diameter of a ventral cell or 24% of a dorsal cell. Thus, the constriction of 5 cell rows can roughly pull 1 cell diameter of ventral-sized cells. To test whether the expression of fra and gukh in dorsal cells are required to constrict and pull lateral cells dorsally, we analyzed if mutants for these genes changed the area of dorsal cells. These experiments reveal that dorsal cells of fra mutants are 26% larger than wild-type dorsal cells, whereas gukh dorsal cells are almost 40% larger than the wild type ( Fig 4D). Thus, we conclude both fra and gukh are required for the constriction of dorsal cells.

FRA increases the levels of E-CAD in adherens junctions and GUKH increases F-Actin bundles
While quantifying the cellular areas of fra and gukh mutants, we noticed that E-CAD at spot adherens junctions (SAJs) appeared much weaker, ill-defined, and with gaps in fra mutants, indicating that fra is required for maintaining correct E-CAD levels and the integrity of the SAJs (Fig 4F-4G). In contrast, E-CAD levels at the membrane do not appear to change in gukh mutants, though there is more diffuse signal within the cells compared to the wild type, as well as abnormal SAJs with fewer interruptions than those seen in fra mutants ( Fig 4H). In segmented images of E-CAD in the mutants, we note the presence of cells with jagged membranes and fused cells, as opposed to the smooth contours of well-separated cells in the wild type. These differences can be quantified by measuring the circularity of cell contours in fra and gukh mutants and wild-type embryos (red and green outlines in Fig 4I-4K). The SAJs are apical constrictions containing E-CAD with catenin among other proteins that interact with actin and regulate cell adhesion and signaling [41][42][43]. Our analyses also revealed that like FRA, E-CAD is more abundant dorsally than ventrally and its expression is greatly reduced in the ventral presumptive mesoderm (Fig 4E and 4F) [44]. This asymmetry of E-CAD is regulated directly or indirectly by DL since dorsalized embryos that lack nuclear DL have high E-CAD levels, and ventralized embryos with ubiquitous nuclear DL have low E-CAD levels (S3 Fig). Previous work on wound healing also found that E-CAD is either directly or indirectly regulated by DL [45]. However, in the case shown here, at least part of this regulation is indirect and mediated by FRA because in the absence of fra, the levels of E-CAD throughout the embryo drop to levels found in the ventral region (Figs 4E, 4G and S4). This similar distribution of E-CAD and FRA is consistent with the fact that E-CAD was also identified in our genomic screening for targets of DPP and/or DL. In agreement with these results, we show that both FRA and E-CAD co-localize at SAJs (Figs 4L-4Q and S5). In addition, we show that E-CAD regulation is independent from DPP (S6A Fig). Together, these data indicate that FRA is necessary to maintain high levels of E-CAD at the membrane.
SinceAU : Pleasenotethatemoreevidentboudsedataissubjectedtoananalysisofcellboudnariesplainsneu GUKH is required for apical cell constriction and its protein contains the SCAR--WAVE domain implicated in the nucleation of actin in filaments [31,46,47], we asked if the distribution of filamentous actin (F-Actin) in the cell perimeter was affected in gukh mutants. These analyses show that the loss of GUKH reduces the thickness of the actin bundles localized right below the cell membranes (S7 Fig). Consistent with this result, we show that dpp mutants, which lack gukh expression in the dorsal midline (Fig 3B), also have thinner actin bundles in the dorsal region (S6B Fig). Thus, from these experiments, we conclude that GUKH constricts cells by increasing Factin. The ability of GUKH to regulate cell area appears to be highly conserved since proteins of the SCAR/WAVE family regulate cell morphology from plants to humans by promoting actin filament nucleation [46,47]. For example, the gukh human ortholog NHS was shown to maintain cells constricted, and its removal leads to a cell spreading phenotype [36].

Cell movement is required for the proper formation of gene expression domains
Thus far, our results reveal how DL and DPP gradients regulate organized cell movements through 2 effector genes that modify cell shape and adhesion, gukh and fra. However, it is unclear if the cell movement generated by these proteins is required for the proper separation of the embryonic layers in different gene expression domains. To address this issue, we analyzed whether fra and gukh embryos affect the expression domains of 6 D/V genes involved in ectodermal, neuroectodermal, and mesodermal cell specification. Our results show that the gukh stained with E-CAD. The low levels of E-CAD in the mutants result in less cells with high circularity (red outlines) and more cells with lower circularity (green outlines) compared to the wild type. FRA-GFP (L, O, green) and E-CAD (M, P, red) in dorsal cells shown in sagittal (L and M) and apical-lateral surface views (O, P). (N, Q) Signal co-localization in merged images (arrows) (see also S4 Fig). Scale bar, 10 μm. Metadata for the graph shown in D can be found at Supporting information S1 Metadata. E-CAD, E-Cadherin; FRA, frazzled; GUKH, guk-holder;.
https://doi.org/10.1371/journal.pbio.3002021.g004 changes in cell density profiles in these mutants affect the specification of all 3 D/V layers ( Fig 5A). In the dorsal region, we note that within the nested domains of race and rho, race decreases in size and rho is expanded (Fig 5A and 5B). In the neuroectoderm, the muscle segment homeodomain (msh) [48] domain is expanded and misshapen in fra 3 and gukh L1 , whereas the lateral and ventral domains marked by ind [49] and ventral nervous defective (vnd) [50,51] are reduced in fra 3 (Fig 5A, 5C and 5D). Finally, in the mesoderm, the sna domain is expanded in fra 3 but reduced in gukh L1 (Fig 5A and 5E). Thus, these results show that the formation of cell density patterns is essential for the correct embryonic patterning.

The stereotyped cell movements define the precise gradient thresholds required for the separation of gene expression domains
The finding above implies that the gradients of DPP and/or DL must be affected in fra and gukh mutants. To directly test this prediction, we first analyzed the distribution of nuclear DL levels in fra and gukh mutants ( Fig 6A). These experiments show that the increase in ventral cell density seen in the heatmaps of both mutants ( Fig 3L) involves a broader domain of visible nuclear DL in fra and an apparent lower intensity in the midline of both mutants compared to the wild type ( Fig  6A). To determine the shape of the DL gradient, we quantified the levels of nuclear DL in these mutants ( Fig 6B). These analyses reveal that the DL gradient in fra and gukh mutants has a pronounced flattened peak in the ventral midline compared to the wild type ( Fig 6B). In the regions with lower DL levels (where standard deviations of signal intensities overlap, Fig 6B), we note that DL signal appear fuzzier in fra than in the wild type ( Fig 6A). This fuzziness suggested that the gradient decays more gradually in fra, which could explain the expansion of the sna domain, and the normalized gradients confirm this expectation (S8 Fig). Since SNA is a negative regulator of neuroectodermal genes, including vnd, the invasion of SNA into the neuroectoderm explains why part of the vnd expression in the neuroectoderm is eliminated in fra (Fig 5A and 5D) [16,[52][53][54][55][56]. In contrast, gukh mutants do not have an expansion in SNA and vnd and ind are not affected ( Fig  5A and 5D). Thus, from these experiments, we conclude that the movements of cells exiting from the ventral region in the wild type affects how the DL gradient is laid out.  These experiments suggest that lateral cells of fra and gukh mutants are more dorsalized due to the reduction in DL levels, which could explain the ectodermal expansion of rho into more lateral regions (Fig 5A). However, if this were the case, the reduction of nuclear DL in the mutants should increase the exposure of msh to the repressive activity of DPP and cause a retraction of msh domain [57,58]. Nevertheless, what we see in both mutants is exactly the opposite, which is a significant expansion of msh domain dorsally (Fig 5A and 5C). This result unmistakably shows that in these 2 mutants, DPP reaches the neuroectoderm below the threshold necessary to repress the dorsal boundary of msh [58], and therefore, the DPP gradient must be also affected. To confirm this expectation, we analyzed the expression of phosphorylated-Mothers Against DPP (p-MAD), which accumulates in the nucleus in response to DPP [59][60][61]. We measured nuclear pMAD levels at late cellularization stage, when the DPP gradient becomes stable and nuclear pMAD levels are high and report peak levels of DPP activation within a narrow stripe of dorsal-most cells [60,[62][63][64]. These experiments show that pMAD levels drop dramatically in fra and gukh mutants (Fig 6A and 6C), which is consistent with the reduction in the race domain of both mutants (Fig 5A and 5B). Thus, in these mutants, DPP does not reach its peak levels dorsally and collapses forming a flattened gradient that spreads more laterally as revealed by the expansion of rho (Figs 5A, 6A and 6C), and reaches the neuroectoderm at lower levels than normal as seen by the expansion of msh. Together, these results reveal an unexpected relationship between cell movement and the formation DPP and DL gradients. Namely, that the thresholds of gene activation or repression elicited by the DPP and DL gradients are tightly coordinated with the movement of cells. In other words, the correct gradient thresholds are only achieved when the cells are moving in defined trajectories in response to these gradients.

FRA and GUKH are required for defining the separation of juxtaposed expression domains
The experiments above show that GUKH and FRA regulate the fate and position of cells by changing the way gradients and thresholds are spread in space. However, it is unclear if in addition, the movement of these cells is required to fine tune borders of gene expression. To address this issue, we analyzed a particular group of cells bordering the mesoderm and neuroectoderm. At this position, single minded (sim) is expressed in a single row of mesectodermal cells forming a straight line [65], which depends on the sharp sna boundary for precise localization of Notch signaling activation [66][67][68][69]. If the formation of a straight line of sim-expressing cells depends on a highly coordinated exiting of cells from the mesoderm, then halting the exiting of cells should disorganize the line of sim-expressing cells. The analysis of the mesodermal boundary in fra and gukh mutants shows that the sna border becomes jagged (S9 Fig), whereas the sim expression has gaps and abnormal clusters containing 2 rows of sim-expressing cells (Fig 6D). We conclude that FRA and GUKH are required to maintain sharp boundaries and prevent the intrusion of neighboring cell fates from different expression domains. In sum, our data support a model whereby morphogens control organized cell movements, which are essential for the correct placement of cell fates and for maintaining shapes of the gradients themselves.

Discussion
It has been well established that morphogens instruct cells about their fates within tissues by activating and repressing genes at different threshold levels and eliciting local cross-regulation among target genes that help separate domains of gene expression. Extensive evidence shows that morphogens can act over relatively long distances, yet cells can be separated into different genetic programs even when located within few cell diameters apart. If fate separation within neighboring cells per se is remarkable, even more surprising is that morphogens achieve this level of precision while cells are in motion. Indeed, it is difficult to understand how a system of coordinates that seems utterly dependent on protein dispersion can instruct cells in motion with such high level of precision. Our results support a new model that integrates gradient activity and cell position, which we refer to as model of Dynamic Adjustment of Movement with Morphogenetic Activity (DynaMMA, Fig 7) and discuss below.
Current models of DV patterning draw from the considerable effort put forth to explain fate specification and position through mathematical models that test different scenarios involving variables such as dispersion of ligands, production, and degradation rates of pathway components and time (reviewed in [70]). Since these models usually assume that cell fields are static, the variations in the shape of a gradient and gene responses are frequently interpreted in the realm of the dynamics of the components of a pathway, not cells and their spatial positions over time (Fig 7A). The gradient of DL, for example, is generated by the graded activation of Tl receptor in response to a cascade that activates its ligand Spätzle in the perivitelline space. Tl activation causes the degradation of cactus allowing free DL to translocate into the nucleus (reviewed in [71]). In contrast, our results reveal an additional mechanism that is key to the formation of this gradient which is the exiting of cells from the ventral region and their passing through progressively lower levels of active Tl. The cells that remain in the ventral-most region of the embryo are expected to experience an increase in nuclear DL levels due to a decreased

PLOS BIOLOGY
competition among nuclei that receive DL. Indeed, it has been shown the DL gradient is sensitive to nuclear density and quickly increases in amplitude during early cellularization stage [72][73][74][75]. fra and gukh mutants clearly lack this increase in amplitude, which can be explained by the increased competition for DL nuclear transport caused by the more densely packed nuclei in the ventral region of these mutants compared to the wild type. The change in nuclear DL gradient caused by the exit of ventral cells towards the dorsal region appears to be an important mechanism that ties DL and DPP to a single coordinate system similar to a tug of war where DPP is on one end pulling cells and DL on the other resisting to this pulling force. This system allows for assigning cells with nuclear DL to specific positions in response to DPP levels, and in these positions, cells acquire fates that depend on both DL and DPP. Since DPP can modulate the exiting of ventral cells from the mesoderm and how much these cells move in and away from the zone of Tl activation, DPP ultimately can regulate the levels of nuclear DL, not transcriptionally, but by cell attraction. This exquisitely simple mechanism of cell-cell interaction is potentially capable of creating very precise variations in target gene expression that are based on the thresholds of 2 morphogens in a single position. With this view in mind, it is inevitable to conclude that cell movement does not pose a hindrance to fate specification, but indeed is the very way of achieving maximal precision in determining the position of cells and their fate (Fig 7B).

Peak levels of DPP are regulated by cell density
Whereas ventrally the DL gradient can be readjusted by the exit of ventral cells to more lateral regions, dorsally, the shape of the DPP gradient appears to be regulated by the attraction of cells by DPP to the site where its signaling peaks. This is best illustrated by the collapse of peak levels of DPP and the narrowing of the pMAD stripe in gukh and fra. Since FRA and GUKH are part of a complex of proteins involved in cell adhesion, it seems clear that the normal sudden sharpening of the pMAD stripe depends on these cell contacts (Fig 7B). In particular, the adherens junctions, which have high levels of E-CAD and make strong contacts in the presence of high levels of FRA. Consistent with these observations, FRA co-localizes with E-CAD and the loss of FRA alone eliminates the asymmetric localization of E-CAD along the D/V axis (Figs 4G and S3). Thus, the dorsal-to-ventral gradient of FRA elicits a gradient of E-CAD and these gradients appear to be essential in determining the range of peak DPP levels. The mechanism by which FRA increases E-CAD levels is unknown and needs to be investigated further, but it seems likely that FRA normally might prevent a default degradation of E-CAD. There are at least 3 reasons to believe that the presence of FRA might regulate the degradation of E-CAD. First, it has been shown that cells exposed to high levels of DPP/BMP usually have low levels of E-CAD and high mobility [76,77], which is exactly the opposite of what we have shown in embryos where dorsal cells have high levels of DPP, E-CAD, and FRA. Second, the high levels of E-CAD where DPP peaks can be abolished by removing the FRA receptor alone (Fig 4G). Third, mutants without FRA have low E-CAD levels throughout the embryo comparable to ventral regions without FRA (S3 Fig). Consistent with these observations, it has been reported that human E-CAD is cleaved by Presenilin-1 (PS1), which serves the purpose of disassembling AJs [78]. This is achieved by the binding of PS1 to the GGG binding site in human E-CAD and the cleaving of E-CAD at a γ secretase-like site right at the transmembrane domain on the cytoplasmic side. In Drosophila, we note that E-CAD and FRA have the PS1 binding site (1376GGG1378 in E-CAD and 1328GGG1330 in FRA) and the γ secretase-like site. Thus, FRA appears to have the necessary sequences to compete with E-CAD for the binding to PS1 and in this way reduce E-CAD degradation. Since FRA is regulated by DL and not DPP, FRA becomes expressed where the high levels of DPP would normally lead to a decrease in E-CAD. Such mechanism allows for keeping high levels of DPP signaling without the adverse effects of disassembling cell contacts.
Previous studies have found an association between DPP signaling and E-CAD and suggest that this type of signaling might be recurrently used during development. For example, in the stem cell niche of the Drosophila testis, the DPP receptor TKV appears to be guided to the apical region of cells by E-CAD and in this way the signaling is concentrated in a particular region [79]. Similarly, during retinal development, TKV is required for the integrity of cell junctions containing E-CAD and the specification of pigment cells [80]. In addition, the overexpression of E-CAD causes up-regulation of the Punt ortholog TFG-β Receptor II and increases TGF-β signaling in vitro. Finally, E-CAD binds directly to this type II receptor in a complex that includes the type I receptor [81]. Together, these data suggest that FRA might be required to increase the levels of E-CAD and cell tightening, which in turn guides TKV to achieve high levels of DPP signaling. In this view, the lower levels of pMAD in gukh and fra mutants may be explained by the decrease in cell clustering observed in these mutants (Figs 6C and 7). The role of asymmetric DV cell densities for the formation of peak levels of DL and DPP gradients can be summarized as follows. In the ventral embryonic region, a low cell density is essential to decrease the competition of DL to enter the nuclei, whereas in the dorsal region, a high cell density achieved via cell constriction with tight F-actin bundles and E-CAD membrane localization may contribute to a higher concentration of TKV receptors and DPP peak levels ( Fig  7B). Consistent with the possibility that E-CAD is required to generate the peak levels of DPP required to pull cells and create a normal DL gradient, we note that the loss of e-cad causes the expansion of rho and retraction of vnd and sna (S10 Fig) that are defects reminiscent of a lower-than-normal DL gradient.

Dynamic cell interactions are essential for a self-correcting system that organizes tissues and adjusts supply with demand
Polarized gradients in which 1 morphogen antagonizes the other are frequently deployed to establish a series of cell fates within a field of moving cells. Movement is not the exception, but the rule. These facts suggest that after 50 years of the French Flag Model or the French Flag Problem as originally stated [1,4], there is enough evidence that the field of cells that is instructed to differentiate participates in the way this instruction is delivered. Lewis Wolpert, the proponent of the French Flag Model concedes that the current view of morphogen needs additional alternatives that include cell interactions [2]. In a recent work, it was shown that the formation of neural cell fates in the vertebrate neural tube depends on a differential distribution of cadherins established by the Sonic Hedgehog gradient, providing patterning robustness despite cell movements and noisy morphogen signals [82]. Here, we show that cells change their positions in a coordinated fashion in response to morphogenetic gradients. Additionally, cells subjected to the instructive activity of one morphogen can be allocated to different positions by a second morphogen, and in this way, create a continuum of cell fates. Finally, we show that the integrity of this system regulates the shapes of the gradients and therefore how much of the morphogen is delivered. Thus, the separation of different embryonic tissues requires a system that coordinates the levels of morphogen with the position of cells and gene expression.

Confocal microscopy
Embryos were mounted in SlowFade Gold Antifade with added glass beads (Polyscience, 150 to 210 microns, Cat. #05483) to prevent flattening and enable rolling of embryos into desired position. Images were acquired with Zeiss LSM700 confocal microscope Z-stacks using a Plan-Apochromat 20×/0.3 M27, EC Neofluar 40×/1.3 Oil M27 or Plan-Apochromat 63×/1.40 oil M27 objective lenses. Laser power and gain were adjusted within the dynamic range with no signal saturation. For nuclei segmentation of entire embryo surfaces and signal intensity quantifications, Z-stacks of about 30 slides for the embryo dorsal surface and 40 slices for ventral surface were obtained at 1.5 μm Z-step, line average 2, 1.58 μs speed, 1,024 × 1,024 pixels, 12 bits, and 20× objective lens. D/V orientation of embryos was defined by the gene expression patterns of rho, sna, and ind; A/P markers used were ftz and eve [49,54,[85][86][87]. Ventralized (Tl mutants) and dorsalized embryos (gd mutants) do not show a patterned gene expression along the D/V axis. However, the geometry of embryo (shorter dorsal side and longer ventral side) and location of pole cells at a more dorsal region are preserved and were used for orienting the embryos. Imaging for segmentation of cell surfaces and measuring of cell size and E-CAD signal intensity in fra and wild-type embryos was done with 40× oil objective lens at 0.8 μm Zstep with settings above. For measurements of intensity levels of pMAD and DL, images were collected with 12 bits (pMAD) and 16 bits (DL). Line average 4 and 3.16 μs speed were used for some figure panels to improve visualization.

Time-lapse imaging
Embryos expressing shg/e-cad-GFP constructs were collected at 3 to 4 h after being laid on a grape plate and transferred to a double-sided tape and dechorionated by hand using a needle. The dechorionated embryo was placed on a coverslip covered with Heptane glue and inverted on a gas permeable Lumox culture dish (Greiner) covered with Halocarbon oil. Time-lapse imaging was initiated right before cellularization for about 1 to 1.5 h of duration. Z-stacks were set up for 3-min intervals. After imaging, embryos were unmounted, transferred to a slide with halocarbon oil, placed inside a humid chamber, and allowed to develop at 25˚C. Videos from embryos that hatched to the first instar larva stage were used for analysis.

Image segmentation of nuclei and cell density spatial analyses
Z-stacks confocal images of nuclei stained with Hoechst or DAPI were segmented using Fiji software version 1.49s. For segmentation of the embryo dorsal surface, the first 20 slices from the confocal Z-stacks were used from embryos of all genotypes. For the ventral side, the first 25 slices for gd 7 , gd 7 ;dpp-and gd 7 ;dpp-st2-dpp embryos and the first 35 slices for embryos of all other genotypes were used. Accuracy of segmentation confirmed with manual nuclei counts was between 90% and 100%. The last few slices of the confocal Z-stacks containing the embryo periphery were discarded, since this region is not segmented reliably [88]. The Z-stack subsets were processed using a "median 3D filter" with x, y, z radius set to 2.0, "gaussian 3D filter" with x, y, z radius set to 1, and "unsharp mask" filter (1.4 radius and 0.7 mask weight for the embryo dorsal surface images; 1.2 and 0.6 for ventral surface images). For dorsal side images of wild-type embryos, an additional "maximum 3D" filter with x, y, z radius 1.0 was applied to improve segmentation in areas with high nuclei densities. All images were filtered 1 last time using sharpen process. The processed images were segmented using the 3D iterative threshold segmentation available in the 3D plugin package [89,90]. The minimum volume was set at 15 μm for ventral and dorsal embryo surfaces and the maximum volume was set at 190 μm for dorsal surface and 200 μm for ventral surface. "Criteria method" was set as "volume," "threshold method" was set as "kmeans," "value method" was set at 100, "minimum threshold" was set as default, and "filtering box" was selected. After segmentation, 3D object counter was used to obtain centroids of segmented nuclei and their x, y, z coordinates. In order to identify most cells with least background noise, a threshold value between 40 and 100 was selected in the 3D object counter window depending on the embryo image. To obtain the signal intensity of some of the markers (e.g., ftz, dpp, and rho) within corresponding expressing nuclei objects, we used the option redirect to original confocal image in the 3D object counter settings. Next, the resulting.csv files containing the centroid x, y, z coordinates were imported into Esri Arc-Map software to generate the density heatmaps and contour plots. First, a surface mask was created using the "aggregate points" function using an aggregation distance 30. Next, the heatmaps were generated using "kernel density" function and the symbology applied was a "stretched" color-map with high/low values set as 0.0105 and 0.002. The contour plots were set with an interval of 0.0005. For creating average heatmaps of embryos of same genotype, 4 coordinates of points (i.e., anterior and posterior poles, and lateral-most points at the center of the embryo) were matched into the same location across different embryos using "add control points" function in "georeferencing" tool. The average heatmap was then generated using the "raster calculator" under "Map algebra" in "spatial analysis" tools. The symbology applied and contour plot settings used were the same as above.

Cell counts and statistical analyses
For comparing cell counts at the dorsal and ventral midline regions, Matlab was used to identify the centroid of the projected confocal Z-stack of ventral and dorsal embryo surfaces and to crop a rectangle of 300 × 100 pixels (156.14 × 52.04 μm). The number of nuclei from this rectangle was recorded. The two-tailed Mann-Whitney test was used to test whether dorsal-ventral cell number differences varied among embryos of different genotypes. The two-tailed Wilcoxon signed-rank test was used to test whether cell numbers varied from dorsal to ventral within embryos of the same genotype. For cell counts of st2-dpp expressing embryos, regions of interest of 100 × 100 pixels (52.05 × 52.05 μm) were cropped from stripe 2 ftz region and in between stripes 6 and 7 along the dorsal midline using Matlab. The cell numbers within these regions of interest were obtained and compared using a two-tailed Wilcoxon signed-rank test. For D/V gene expression domain analyses, two-tailed Mann-Whitney test was used to compare cell counts. In all cases, we used a p-value of 0.05 to reject the null hypothesis and accept the alternative hypothesis that the 2 compared data sets are significantly different with a 95% confidence interval.

Spatial statistics for hot spot analyses
To identify statistically significant cell clusters of high and low density versus nonsignificant randomly distributed cells, Getis-Ordi G � spatial statistic was applied to nuclei centroids of dorsal and ventral embryo surfaces using Esri ArcPro or ArcMap software. The centroids were split using a grid system of size 20 and the "hot spot analysis" tool was used with a fixed distance band of 50 for the denser dorsal embryo surface and 120 for the less dense ventral surface. Grids identified as hot spots are labeled according to their confidence intervals (dark red, 99%; red, 95%, light red, 90%) and the same for cold spots (dark blue, 99%; blue, 95%; light blue, 90%). Nonsignificant grids (NS) with randomly distributed cells are labeled in yellow.

fra and gukh identification in genomic in silico screenings
Three main criteria were established to identify our candidate genes. First, a genome-wide search was conducted to select genes with similar expression pattern to the DPP receptor thickveins throughout development. This search was done using the mRNAseq data from "modEN-CODE Temporal Expression Data" [91], deposited in Flybase database (Flybase release FB2014_03May, Dmel 5.57, available in Flybase archives). Second, out of 101 genes identified in this search, we selected those genes with previously described or predicted functions related to cell migration, cell adhesion, or cytoskeleton regulation. Finally, we selected genes with asymmetric expression patterns along the D/V axis according to the expression pattern database maintained by the Berkeley Drosophila Genome Project [92,93]. gukh was the first hit on the list of genes with developmental expression pattern similar to tkv with a 93.66% of similarity; fra was the sixth hit with 89.84% of similarity. Both genes fit the other 2 criteria established.

fra RNA and E-CAD dorso-ventral signal intensity analysis
Individual embryos stained with fra antisense probe or anti-E-CAD antibody were imaged on the dorsal, lateral, and ventral sides using the confocal settings described above. The Z-stacks from ventral, dorsal, and lateral surfaces were projected in 2D using maximum intensity projection and the average intensity level and standard deviation from a region of 50 × 50 pixels (26.03 × 26.03 μm) was obtained using Fiji software. Intensity levels of fra RNA were measured from 5 D/V locations and were fit to a Gaussian curve using vnd as a D/V marker. The measurement of E-CAD intensity was obtained from the centermost region of dorsal, lateral, and ventral projected images and a linear fit was performed. Curve fittings were performed using OriginLab or Excel software.

Measurement of pMAD and DL gradients
The DL gradient was measured and normalized according to [94]. Briefly, embryos stained with anti-DL antibody and sog RNA (used as a D/V marker) were hand-sliced using a 26G 3/ 8-inch needle at approximately 35% and 65% AP positions to obtain cross-sections of the trunk region [95]. The cross-sections were flipped up and imaged using the same confocal settings for all genotypes (see description of confocal settings above). A small circle of approximately 10 μm 2 was selected within the 30 ventral-most nuclei and the DL average signal intensity levels were obtained in Fiji. The pMAD gradient was measured in the 18 dorsal-most cells of the embryo. Confocal Z-stacks were projected using maximum intensity 2D projection and a region of interest of 10.4 μm 2 was cropped inside each of the 18 nuclei and the pMAD signal intensity level was obtained using Fiji software. A Gaussian curve fit for pMAD and DL gradients were obtained using OriginLab or Excel software. Measurements of E-CAD intensity levels in small regions from one side of cell across the other side, spanning the membranes and intracellular regions. E-CAD intensity levels in the membrane are lower in the mutants compared to the wild type but more intense within the intracellular regions than in the wild type. This pattern is consistent with a more diffuse staining of E-CAD within the cell and less localized signal at the membrane. Error bars, standard deviation. Sample size n = 9. Metadata for the graphs shown in A and B can be found at Supporting information S1 Metadata.