A facilitated diffusion mechanism establishes the Drosophila Dorsal gradient

In a developing organism, tissues are patterned by long-range signaling enacted through morphogen concentration gradients, which carry the positional information necessary to control gene expression in a spatially dependent manner. The mechanisms by which morphogen concentration gradients form has been an area of intense study (Wartlick et al., 2009; Smith, 2009; Matsuda et al., 2016; Müller et al., 2013; Christian, 2012; Guerrero and Kornberg, 2014). For example, in the Drosophila wing disc, there are conflicting theories for Dpp gradient formation, including receptor-mediated transcytosis, (restricted) diffusion and cytonemes (Entchev et al., 2000; Lander et al., 2002; Schwank et al., 2011; Matsuda et al., 2016; Belenkaya et al., 2004; Roy et al., 2014). In the Drosophila syncytial blastoderm, the anterior-posterior (AP) Bicoid gradient, perhaps the most well-studied morphogen gradient system, has long been thought to develop through a mechanism of diffusion from a spatially localized source (Driever and Nüsslein-Volhard, 1988; Houchmandzadeh et al., 2002; Gregor et al., 2005, 2007; Little et al., 2011). More recently, it has been proposed that the Bicoid gradient develops largely from a bicoid mRNA gradient, which itself developed through active transport (Spirov et al., 2009; Fahmy et al., 2014; Ali-Murthy and Kornberg, 2016).

During the same stages in which Bicoid patterns the AP axis, the maternally provided transcription factor Dorsal (Dl), which is natively found as a homodimer (Govind et al., 1992; Isoda et al., 1992; Whalen and Steward, 1993; Drier et al., 2000), also acts as a morphogen to regulate the spatial patterns of >50 genes along the dorsal-ventral (DV) axis (Reeves and Stathopoulos, 2009; Moussian and Roth, 2005; Chopra and Levine, 2009). Both dl mRNA and Dl protein are maternally deposited into the embryo, and Dl protein is initially uniformly distributed around the DV axis (Steward et al., 1988; Roth et al., 1989). During nuclear cycle (nc)10, when the nuclei migrate to the periphery of the syncytial blastoderm, a nuclear concentration gradient of Dl develops, with high concentrations in the ventral nuclei, graded levels in ventral-lateral (VL) nuclei, and basal levels in the nuclei on the dorsal half of the embryo (Roth et al., 1989; Liberman et al., 2009; Reeves et al., 2012). In the ventral 20% of the embryo, the highest levels of Dl are achieved, and, as a result, high threshold genes, such as twist (twi) and snail (sna) are activated, which are required to specify the future mesoderm (Stathopoulos and Levine, 2002; Reeves and Stathopoulos, 2009; Chopra and Levine, 2009). Intermediate threshold genes, such as vnd and rhomboid, are expressed in VL domains, and low threshold genes, such as sog and dpp, have boundaries at ∼50% of the way around the DV axis.

The mechanisms by which the Dl nuclear concentration gradient develops are well known, partly because Dl is one of three Drosophila homologs of NF-κB. At the single nucleus/cell level, Dl is sequestered to the cytoplasm in an inactive complex with the IκB homolog Cactus (Cact). On the ventral side of the embryo, signaling through the Toll receptor results in the degradation of Cact, freeing Dl to enter the nucleus, where it regulates transcription (Belvin et al., 1995; Bergmann et al., 1996; Reach et al., 1996; Whalen and Steward, 1993). cact mutant embryos still develop a shallow Dl gradient (Bergmann et al., 1996; Roth et al., 1991; Cardoso et al., 2017), probably due to a weak bias in Dl nuclear import from Toll signaling (Drier et al., 1999, 2000). The weakly polarized DV axis in the absence of Cact activity can also be seen in the Dl target gene expression domains, which are altered, but retain some DV polarity (Roth et al., 1991; Cardoso et al., 2017).

Cytoplasmic sequestration of Dl by Cact, combined with a ventral-to-dorsal gradient of Toll signaling, is sufficient to develop a gradient of nuclear Dl concentration, and is evidently the primary driving force for the formation of spatial asymmetry in Dl nuclear concentration. However, taken alone, this mechanism would result in a local depletion of Dl from the cytoplasm surrounding the ventral nuclei to create a counter-gradient in cytoplasmic Dl (Roth et al., 1989) (Fig. 1A). This paradigm is implicitly accepted, and has been depicted many times in the literature (e.g. in Haskel-Ittah et al., 2012; Rushlow and Shvartsman, 2012). However, this paradigm is in contrast to recent observations that nuclear+cytoplasmic levels of Dl fluorescence accumulate on the ventral side of the embryo over time (Reeves et al., 2012) (Fig. 1B). It is important to note that fluorescence measurements of Dl likely do not distinguish between free Dl and bound Dl (Dl/Cact complex). The mechanism by which this ventral accumulation of total Dl (defined henceforth as the sum of local nuclear+cytoplasmic levels of bound+free Dl) takes place remains unknown, as does the question of whether accumulation is necessary for proper gene expression patterning and the fitness of the embryo.

One possible mechanism is that the hypothesized counter-gradient in cytoplasmic Dl, mentioned above, might drive free Dl to diffuse to the ventral side. However, this is unlikely to be the case, as the predominant Dl-containing species on the dorsal side of the embryo should be Dl/Cact complex, not free Dl. Therefore, we propose that the ventral accumulation of total Dl occurs by a facilitated diffusion, or ‘shuttling’ mechanism via Dl/Cact complex (Shilo et al., 2013). According to this mechanism, a carrier molecule (Cact) helps to shuttle the morphogen up its concentration gradient so that it may accumulate in one location. In the Dl/Cact system, the shuttling hypothesis states that a dorsal-to-ventral concentration gradient of cytoplasmic Dl/Cact complex develops as the result of Toll-mediated degradation of Cact, which in turn results in ventrally directed flux of Dl (Fig. 1C).

The shuttling mechanism has been previously described and is responsible for gradient formation in the Dpp/BMP signaling pathway (Ben-Zvi et al., 2008; Eldar et al., 2002; Holley et al., 1996; Marqués et al., 1997; Mizutani et al., 2005; Shimmi et al., 2005; Wang and Ferguson, 2005; Ashe and Levine, 1999; Dorfman and Shilo, 2001; Umulis et al., 2006). It has also been suggested for the formation of the Spätzle gradient upstream of Toll signaling (Haskel-Ittah et al., 2012). It should be noted that the Dl/Cact system has each of the four features required for shuttling to occur in the embryo (Fig. 1D) (Shilo et al., 2013): (1) the primary molecule (Dl) binds to a ‘carrier’ molecule (Cact) that protects it from capture/degradation; (2) the primary/carrier complex is diffusible on a global scale (shown in this study); (3) the complex is broken in a spatially dependent manner (through Toll signaling on the ventral side of the embryo); and (4) when free of the carrier, the primary molecule is captured (in this case, by the nuclei) or degraded.

The main analysis in this paper was performed using a combination of computational model predictions and experimental validation to support the shuttling hypothesis. To this end, we first demonstrated that Dl diffuses globally throughout the embryo, so that each of the four criteria above are met for the Dl/Cact system. Next, we used a simplified version of previously published computational models (O'Connell and Reeves, 2015; Kanodia et al., 2009; Ambrosi et al., 2014) to predict the outcome of experiments in which shuttling is compromised by lowering Dl diffusion: depending on the severity of the perturbation, the Dl gradient widened, became flat on top, or split into two peaks (i.e. there was no longer a single peak at the ventral midline). Through careful analysis of BAC-recombineered, GFP-tagged Dl constructs, which slow the mobility of Dl, we validated the predicted outcomes of the shuttling hypothesis. The same three phenotypes are also seen in embryos from dl heterozygous mothers, in embryos with a widened Toll domain, and in embryos with an ectopically expressed, AP Dl gradient (Liberman et al., 2009; Roth and Schüpbach, 1994; Huang et al., 1997). To account for these phenotypes, we extended our simplified model to take into account the possibility that active Toll receptors are limiting in the VL regions of the Toll domain. The extended Toll saturation model successfully explained the phenotypes in those three sets of embryos. We experimentally validated the Toll saturation assumption by showing that the single, curved Dl gradient peak is restored in dl heterozygotes by lowering the maternal Toll dosage, as well as in embryos with a wide Toll domain, by increasing the dosage of Dl.

Our data show that shuttling does occur, and that it is necessary when maternal dl levels are compromised. Although dl heterozygous mothers in an otherwise wild-type background are not sterile, we showed that embryos from mothers carrying a single copy of dl-GFP and zero endogenous copies of dl are nonviable, owing to severe shuttling-based defects in the Dl gradient and the consequent failure to express sna in a sufficient number of ventral cells. The data are less clear as to whether shuttling is necessary for embryonic fitness when maternal dl levels are not compromised (Roth et al., 1991; Cardoso et al., 2017). Even so, we argue that the data, on balance, favor the necessity of the shuttling mechanism in wild-type embryos. We conclude that, in addition to its primary role of regulating Dl entry into the nucleus, Cact performs a secondary, but important, role in Dl gradient formation: shuttling Dl to the ventral side to form the mature gradient.

Initially, Dl is uniformly distributed along the DV axis of the developing embryo (Roth et al., 1989) (Fig. 1E,G); during nc 11-14, it accumulates on the ventral side (Fig. 1F,G). This observation is consistent with previously published fluorescent images of anti-Dl immunostaining in fixed embryos and in images of Dl-GFP fluorescence in live embryos (Kanodia et al., 2009; Reeves and Stathopoulos, 2009; Liberman et al., 2009; Reeves et al., 2012). In particular, live imaging of a Dl-Venus construct in optical cross sections showed that, even during mitosis, when the nuclear concentration gradient is abolished, there is a bias of total Dl on the ventral side (Reeves et al., 2012). To measure this bias, we imaged and quantified cross sections of fixed younger (nc 9-10) embryos (Fig. 1E) and compared their total Dl distribution to similar quantifications of older (nc 13-14) embryos (Fig. 1F). We found that, in younger embryos, total Dl was distributed evenly throughout the embryo, while older embryos displayed a total Dl gradient with a strong ventral peak, similar to quantifications of the Dl nuclear concentration gradient (Fig. 1G).

The mechanism for this overall polarization of total Dl in the embryo could stem from net flux of Dl to the ventral side of the embryo. Previous work showed that, on short time scales (seconds), the free diffusion of Dl-GFP is rapid enough that nucleocytoplasmic compartments (the regions surrounding a single nucleus) appear well mixed, while there are barriers to movement between neighboring nucleocytoplasmic compartments (Delotto et al., 2007). On the other hand, on longer time scales (minutes), exchange between nucleocytoplasmic compartments is possible, which we consider behaves like diffusion on coarse length scales. To confirm the global movement of Dl throughout the embryo (hereafter referred to simply as diffusion), we used a photoactivatable GFP (paGFP) tag (Patterson and Lippincott-Schwartz, 2002), and noticed that Dl appears in regions of the embryo >7-10 nuclei away from the site of paGFP activation over a time span of 90 min (Fig. 1H,I; Fig. S1), during which the activation region was under near-constant photoactivation (see Materials and Methods). The distance over which activated Dl can spread appears to depend on the region of the embryo. When activated near the ventral midline, Dl-paGFP moves from its location of activation and fills adjacent nuclei, extending ∼6-7 nuclei away (Fig. 1H,H′; Movie 1). When activated on the dorsal side of the embryo, Dl-paGFP can eventually be seen in all nuclei in view, and shows a typical pattern of exclusion from nuclei in more dorsal regions and moderate uptake into the nuclei in more lateral regions (Fig. 1I,I′; Movie 2). The difference in mobility is likely to be caused by nuclear capture of free Dl on the ventral side. In any case, our observation of global movement of Dl within the embryo provides the final, previously unconfirmed, physical process necessary for shuttling to occur.

To determine whether the four biophysical processes outlined in the Introduction are sufficient to drive the accumulation of Dl on the ventral side of the embryo, we analyzed a simplified model of Dl/Cact/Toll interactions in the early embryo (Fig. 2A). Our model included partial differential equations for four species: nuclear Dl, cytoplasmic Dl, cytoplasmic Cact, and cytoplasmic Dl/Cact complex (see Materials and Methods). These equations describe the processes of Dl/Cact binding (k_bind); the production (V_cact; not shown in Fig. 2A) and degradation of Cact (k_deg); the nuclear import/export of Dl (k_in, k_out); the Toll-mediated dissociation of the Dl/Cact complex (k_diss); and the intercompartmental movement of cytoplasmic species (D; Fig. 2A). The catalytic activity of Toll signaling was modeled phenomenologically by allowing k_diss to be a function of x: k_diss(x)=k_diss,0 exp (−0.5x²/φ²), where β models the strength of Toll signaling and φ is a parameter that controls the spatial extent of Toll signaling.

We quantitatively defined shuttling as the scenario in which there is a net flux of Dl-containing species to the ventral 33% of the embryo (see Materials and Methods). We simulated 10⁵ randomly chosen data sets from among reasonable allowed variations in parameter values (see Supplementary Materials and Methods) and examined under what conditions shuttling would occur. We found that the diffusivity of the Dl/Cact complex (D_DC) must be greater than the effective diffusivity of free Dl for shuttling to occur. In our simplified model, nuclear and cytoplasmic Dl are assumed to be in equilibrium, which makes the effective diffusivity of Dl D^eff_Dl=D_Dl/(1+K_eq), where K_eq=k_in/k_out (see Supplementary Materials and Methods for more details). In other words, shuttling occurs when D_DC/D^eff_Dl >1 (Fig. 2B). This is relatively unsurprising, as the Dl/Cact complex must be able to diffuse toward the ventral midline more efficiently than free Dl can diffuse away. Furthermore, difference in diffusivities between the free activator and the inhibitory complex has previously been shown to be a hallmark of a shuttling system (Eldar et al., 2002). The equilibrium constant for nuclear import also plays an important role because nuclear capture of free, cytoplasmic Dl must be sufficiently strong to prevent Dl from diffusing back to the dorsal side of the embryo (Fig. 1D). See Supplementary Materials and Methods for more details.

Further analysis of our model showed that the mechanism of facilitated diffusion can be tested by slowing diffusion of the Dl/Cact complex. The model predicts that different instances in a hallmark series of phenotypes will be observed, depending on the severity of the perturbation. In order of increasing strength of perturbation: the Dl gradient widens, becomes flat on top, or splits into two peaks (Fig. 2C,D). These predictions and the shuttling phenomenon itself arise naturally out of biophysical processes known to occur in the embryo: global movement, binding of Dl and Cact, Toll-mediated destruction of the Dl/Cact complex on the ventral side, and nuclear capture of free Dl. Indeed, previous models of the Dl gradient, which included these processes, also exhibit shuttling, even when it was not considered in the models (Fig. S2, Supplementary Materials and Methods) (Kanodia et al., 2009; Ambrosi et al., 2014; O'Connell and Reeves, 2015). In particular, in previous work using a model of the Dl/Cact system, the authors found that increasing the diffusion rate caused the gradient to sharpen (Ambrosi et al., 2014), which is the same prediction detailed here (Fig. 2C,D). We analyzed the model presented in that study, and show that this result arose because shuttling was indeed occurring in that model, even though the authors did not intend it to be (Fig. S2).

Our approach to slowing the diffusion of the Dl/Cact complex was to tag Dl with a bulky protein domain. Multiple versions of Dl tagged with GFP variants have been made to study Dl gradient dynamics in living embryos (Delotto et al., 2007; Reeves et al., 2012); in two instances, GFP tags caused the Dl gradient to expand as predicted by the shuttling mechanism (Fig. 2C,D). Previous work has shown that tagging Dl with a monomeric Venus (Dl-mVenus) causes the Dl gradient to widen, while a GFP tag causes a much greater widening (Liberman et al., 2009; Reeves et al., 2012). We surmised that the difference between these scenarios is that Venus is an obligate monomer, whereas the GFP construct weakly dimerizes (Zacharias et al., 2002).

However, as these observations were comparing GFP to mVenus, we wished to investigate further by minimizing differences between the monomeric and dimeric GFP variants. Therefore, we constructed a transgenic fly line carrying a BAC-recombineered Dl tagged with monomeric GFP (Dl-mGFP; see Materials and Methods). The weak dimerization of GFP can be abolished by the A206K mutation, so that GFP^A206K is an obligate monomer (Zacharias et al., 2002). Together with a wild-type fly line and a line carrying the Dl tagged with a GFP that weakly dimerizes (Dl-dGFP) (Reeves et al., 2012), this created an ‘allelic series’ of Dl constructs with progressively decreasing mobility. If the shuttling hypothesis is correct, we would expect that lowering the mobility would widen the gradient. First, we measured the gradient width in fixed wild-type embryos using an antibody against Dl and found the width parameter, σ, to be 0.147±0.002 (mean±s.e.m. here and elsewhere) (Fig. 3; Fig. S3A; see Supplementary Materials and Methods for a description of the width parameter) (Liberman et al., 2009; Reeves et al., 2012; Garcia et al., 2013).

Next, we investigated the Dl-mGFP embryos. These embryos are from dl, dl-mGFP/+ mothers (one copy of Dl-mGFP, one functional copy of endogenous Dl). Because Dl naturally self-associates (Govind et al., 1992; Isoda et al., 1992; Whalen and Steward, 1993; Drier et al., 2000), three species of Dl dimer would exist in these embryos: Dl:Dl, Dl:Dl-mGFP and Dl-mGFP:Dl-mGFP. Therefore, the effective, overall mobility of Dl in these embryos would be slightly lower than in wild type. As predicted by the shuttling hypothesis, these Dl-mGFP embryos have gradients slightly wider than wild type (σ=0.184±0.005; P=10⁻⁷; Fig. 3).

Third, we investigated whether the Dl-dGFP embryos would have even wider gradients than the Dl-mGFP embryos. Therefore, we analyzed the gradient in embryos from mothers carrying one copy of dl-dGFP (Reeves et al., 2012) and heterozygous null for endogenous dl (genotype dl/+; dl-dGFP/+). In these embryos, heterodimers of endogenous Dl and Dl-dGFP might form weak interactions with similar heterodimers, which would result in larger groups of heterodimers with slower mobility. The situation is further exacerbated if the dimer happens to be a homodimer of Dl-dGFP, which should account for ∼25% of the Dl dimer species. We found that the Dl gradient in these embryos widened significantly as compared to wild type (σ=0.207±0.007; P=2×10⁻⁹; Fig. 3).

Finally, we analyzed embryos completely lacking endogenous Dl and with two copies of Dl-dGFP (maternal genotype: dl; dl-dGFP). In these embryos, 100% of the Dl molecules are fused to dGFP, so that every Dl-containing dimer has the ability to weakly interact with two other Dl-dGFP dimers. As predicted by the shuttling hypothesis, the Dl gradients in these embryos were also widened compared to wild type (σ=0.228±0.008; P=10⁻¹²; Fig. 3). Moreover, the ‘allelic series’ behaved as predicted: embryos with progressively less mobile Dl had progressively wider gradients.

To further test the predicted phenotype of slowing diffusion, we also examined embryos with Venus-tagged Dl (Reeves et al., 2012), β-galactosidase-tagged Dl (Govind et al., 1996) and β-galactosidase-tagged Cact (Fernandez et al., 2001). In each of these cases, the phenotype expected from the shuttling hypothesis was found (Supplementary Materials and Methods, Fig. S3B,C).

The length scale of a concentration gradient can be altered by changing the rate of capture (in this case, by the nuclei) in addition to diffusion. Therefore, we used a combination of photobleaching experiments, to measure the import and export rate of Dl-dGFP and Dl-mGFP, and modeling, to show that only perturbing diffusion, and not nuclear import/export, results in a shuttling-based phenotype (Fig. S3D-O, Movie 3, Supplementary Materials and Methods).

In embryos from mothers heterozygous null for Dl (hereafter referred to as dl/+ embryos), the shape of the gradient becomes slightly wider and flatter, sometimes to the point of generating a double peak (Fig. 4A-D; note especially in Fig. 4B the local minimum at the ventral midline and local maxima elsewhere) (Liberman et al., 2009; Ambrosi et al., 2014). This phenotype bears striking resemblance to the model predictions for lowering diffusion (Fig. 2C,D); therefore, we investigated whether the shuttling mechanism could possibly explain the phenotype in dl/+ embryos. However, model simulations showed that reducing the dl dosage could not significantly change the width or the shape of the Dl gradient, much less result in a double peak (Ambrosi et al., 2014) (Fig. S4A-D).

One mechanism that could explain this phenotype is saturation of active Toll receptors. If the domain of active Toll signaling is graded in space (Haskel-Ittah et al., 2012; Rahimi et al., 2016), active Toll receptors should be limiting at the domain edge. If active Toll saturation is sufficiently extensive in wild-type embryos, then the formation of a smooth peak is the result of sufficient numbers of Dl/Cact complexes bypassing the saturated Toll regime and arriving at the ventral midline (Fig. 4E). However, in dl/+ embryos, less Dl implies fewer Dl/Cact complex molecules will arrive at the ventral midline (Fig. 4F), resulting in a wider, flatter and sometimes split peak of nuclear Dl. However, previous models did not account for this possibility because the rate of Toll-mediated Cact degradation was assumed to be proportional to the concentration of Dl/Cact, creating a potentially unlimited sink, even at the edges of the active Toll domain (O'Connell and Reeves, 2015; Kanodia et al., 2009; Ambrosi et al., 2014). Therefore, we extended our simplified mathematical model (Fig. 2A) to account for the possibility that active Toll receptors numbers are limiting (Fig. 4G; see Materials and Methods). In the remainder of this paper, we use this extended model. When active Toll receptors are saturable, simulated dl/+ embryos have widened, flattened gradients (Fig. S4E,F).

To experimentally test whether active Toll receptors are limiting, we compared Dl gradients in wild-type embryos and dl/+ embryos with those from dl/+; Tl/+ mothers (hereafter dl/+; Tl/+ embryos). In dl/+; Tl/+ embryos, reducing the Toll dosage should partially ‘rescue’ the saturation of the active Toll receptor, and thus result in a smoother Dl gradient peak at the ventral midline. We found that the profile of total Dl in these embryos is, on average, more smoothly peaked (Fig. 4H; Fig. S4G-I). To determine whether the gradient peaks are different in dl/+ versus double-heterozygote embryos, we calculated two measures of peak shape: location of peak (Fig. 4I,J) and intensity of the peak at the ventral midline (Fig. 4I,K). In both cases, the dl/+ embryos were statistically different from the dl/+; Tl/+ embryos, which validates our hypothesis that active Toll receptors are limiting.

Our model also predicts that simultaneously lowering both dosage and mobility would have a combined effect on the severity of the shuttling phenotype. To test this hypothesis experimentally, we investigated embryos from mothers that carry a single copy of dl-dGFP and no endogenous dl (dl; dl-dGFP/+). In our and previous studies, this genotype is observed to be female sterile; two copies of dl-dGFP are necessary to rescue the mutant (Liberman et al., 2009; Reeves et al., 2012). We found that dl; dl-dGFP/+ embryos have highly widened gradients (σ=0.219±0.009), with severe flat-top/mild double-peaked phenotypes (Fig. 4D and Fig. 5A,B). However, it should be noted that σ is a less accurate measure of the width when the gradient is not bell shaped.

Because the peak shape is severely perturbed in dl; dl-dGFP/+ embryos, we surmised that gene expression could be disrupted, which might explain why dl; dl-dGFP/+ females are sterile. Therefore, we analyzed sna expression in dl; dl-dGFP/+ embryos (n=33) and found that these embryos either lacked sna expression entirely (16/33), had sna expression too faint to quantify above background (5/33), or expressed sna in a very narrow domain (Figs 5B-E; Fig. S5), confirming our hypothesis that the double perturbation results in a breakdown of the typically robust patterning system. By contrast, embryos from dl; dl-dGFP mothers have normal sna expression (Fig. 5C,E), which shows that Dl-dGFP retains transcriptional function. Furthermore, embryos from dl; dl-mVenus/+ mothers, which have a less severe shuttling defect than dl; dl-dGFP/+ embryos, have robust sna expression (Fig. S5C,D) and are viable (our observations and Reeves et al., 2012). This result suggests that shuttling is indeed exacerbated in these embryos and that this shuttling defect is responsible for the female sterility.

The shuttling hypothesis predicts that severe widening of the active Toll domain results in a split Dl gradient (Fig. S6A,B). As the extent of the Toll domain is controlled by Gurken/EGFR signaling during oogenesis (Sen et al., 1998; Schüpbach, 1987), we analyzed embryos from mothers carrying a hypomorphic EGFR allele (Egfr^t1) (Roth and Schüpbach, 1994). We found that embryos from mothers heterozygous for this allele have significantly widened Dl gradients, and most (10/12) embryos from homozygous mothers have gradients so wide that the peak splits (Fig. 6A-D). This result is consistent with previous reports that various gurken and Egfr mutations generate a duplicated Dl gradient as measured by Dl staining, Twist staining, and sites of ventral furrow formation (Roth and Schüpbach, 1994), which are not readily explained in the absence of a shuttling phenomenon (Meinhardt, 2004; Moussian and Roth, 2005; Haskel-Ittah et al., 2012).

A model with Toll saturation predicts that the split peak can be alleviated either by decreasing the levels of active Toll receptors or by increasing the dosage of maternal dl (Fig. S6C-F). We chose to test the possibility by examining embryos from mothers carrying one (Egfr^t1; dl^RC/+) or two (Egfr^t1; dl^RC) extra copies of a Dl rescue construct (Reeves et al., 2012) in the Egfr^t1 background. These embryos have three or four copies of full-length Dl, respectively. We found that, as our model predicts, increasing the dosage of maternal dl reduces the severity of the split-peak phenotype (Fig. 6E; Fig. S6G-I), providing further evidence for active Toll receptor saturation.

It has been suggested that a shuttling phenomenon also occurs through the processing of Spätzle (Spz), the ligand for Toll signaling (Haskel-Ittah et al., 2012), which might explain some of the phenotypes described here. To determine whether the hallmark phenotypes of shuttling could occur without assistance from the protease cascade or Spz processing, we expressed a constitutively active form of Toll (Toll^10b) at the anterior pole of the developing embryo using the bicoid (bcd) 3′ UTR and the bcd promoter, similar to previously performed experiments using the stronger Hsp83 promoter (Huang et al., 1997). Embryos from mothers carrying this construct (bcd>Toll^10b: bcd 3′ UTR) have an AP Dl gradient in addition to the native DV gradient. Naïvely, one may expect that the existence of two gradients of active Toll signaling would result in higher concentrations of nuclear Dl where the two overlap. By contrast, the shuttling hypothesis predicts that Dl nuclear concentration would be depleted in the region where both gradient tails overlap, as the two competing Dl/Cact sinks cause Cact to shuttle Dl toward both the anterior pole and the ventral midline (Fig. 7A-C). This prediction is borne out in experiments, as these embryos show a decreased intensity of the Dl gradient near the region of overlap. Furthermore, 64% (9/14) of these embryos show a visible narrowing of the sna expression domain at ∼30% egg length, consistent with previously published data (Fig. 7B,C) (Huang et al., 1997). Our results show domain narrowing rather than a gap as previously reported, owing to the weaker bcd promoter.

Our modeling results further support that the shuttling mechanism is responsible for this phenomenon (Fig. 7C). We expanded our model system from a one-dimensional array of nuclear compartments to a two-dimensional array, and added a second Toll signaling domain perpendicular to the first (Supplementary Materials and Methods). Our simulation results show that the overlap between the AP and DV Toll domains creates a low point in nuclear Dl concentration, similar to our experimental results. We then approximated a threshold for sna expression based on the DV Dl gradient, and found that the local minimum in Dl concentration results in reduced or abolished sna expression in that region (Fig. 7C′).

We also examined embryos from mothers carrying a homozygous mutation in gastrulation defective (gd⁷), which eliminates the endogenous ventral-to-dorsal gradient. Swapping the bcd promoter for the stronger Hsp83 promoter (Hsp83>Toll^10b: bcd 3′ UTR construct; Huang et al., 1997), we were able to create a wider Dl gradient at the anterior pole. Half of these embryos (7/16) show two peaks of Dl (Fig. 7D-E); furthermore, they have a double peak of sna (Trisnadi et al., 2013). To determine whether this double-peak phenomenon was a result of the embryo's geometry at the pole, we analyzed embryos with an AP Dl gradient initiated by the weaker bcd promoter. These embryos showed no such double-peak effect (Fig. S7). These results further support our shuttling hypothesis as the Dl gradient progresses from narrow (weak promoter) to double peak (strong promoter), much as it does in the native DV system when the Toll domain expands.

In this study, we investigated the embryo-scale formation of the Dl morphogen gradient in the early Drosophila embryo. Based on our model and experimental verification, we conclude that establishment of peak levels of the Dl gradient is aided by a facilitated diffusion, or shuttling mechanism, in which Dl/Cact complex diffuses towards the ventral midline, where Cact is degraded. Lowering the diffusivity of either Dl or Cact widens the gradient rather than the narrowing that one might expect from a morphogen gradient established by (nonfacilitated) diffusion. The shuttling mechanism explains why Dl tagged with a weakly dimerizing GFP widens the gradient more than one tagged with monomeric GFP (Reeves et al., 2012), and also explains the related observation that one copy of Dl tagged with monomeric GFP variants complements loss of endogenous Dl while one copy of Dl-dGFP does not (Liberman et al., 2009; Reeves et al., 2012). Similarly, this mechanism makes sense of the observation that Dl tagged with β-galactosidase, which forms tetramers, is antimorphic (Govind et al., 1992), as the Dl moieties in tetramers of Dl-βgal dimerize with endogenous Dl to disrupt the formation of the endogenous Dl gradient.

When the Toll gradient is greatly expanded, as in embryos from Egfr^t1 mothers (Roth and Schüpbach, 1994), the domains of saturated Toll receptors move further from the ventral midline, resulting in a split peak. This split-peak phenomenon has also been observed in the Dl gradient in abnormally large embryos (Garcia et al., 2013). This specific phenotype could be explained by the shuttling of the Toll ligand Spz (Haskel-Ittah et al., 2012); however, we observed the same phenomenon in embryos with an ectopic AP Dl gradient established by constitutively active Toll. In both cases, ventrally (anteriorly) diffusing Dl/Cact complex does not reach the ventral midline (anterior pole) before being dissociated, leaving the ventral (anterior)-most nuclei somewhat devoid of Dl. A similar mechanism, in which the removal rate of BMP ligands surpasses the rate of BMP flux to the dorsal midline, has been suggested to explain the computationally predicted split-peak phenotype for the BMP system in the early embryo (Umulis et al., 2006).

We further propose that active Toll receptors are saturated in the edges of the Toll domain in wild-type embryos; this saturation is not essential to the shuttling mechanism per se, though it is necessary for the mechanism to explain phenotypes associated with changing the dose of maternal dl. Under wild-type conditions, a significant flux of Dl/Cact complex can bypass the saturated active Toll receptors in the edges of the Toll domain, which results in the accumulation of a smooth, intense peak of Dl signaling at the ventral midline of the embryo. However, in dl/+ embryos, there is not enough Dl/Cact complex to saturate active Toll receptors in the tails of the gradient, leading to less accumulation of Dl at the ventral midline (Liberman et al., 2009). We have verified this assumption of active Toll saturation in dl/+; Tl/+ and Egfr^t1; dl^RC embryos.

The shuttling mechanism requires four biophysical processes: (1) Dl binding to Cact; (2) Dl/Cact complex readily diffusing through the embryo; (3) Toll signaling acting as a sink for Dl/Cact complex; and (4) Cact protecting Dl from entering the nuclei. As our experiments with Dl-paGFP show that Dl does indeed move globally through the embryo, it is now clear that Dl/Cact shuttling naturally arises in the early embryo. Indeed, our previous Dl/Cact model (O'Connell and Reeves, 2015) did not explicitly have shuttling ‘programmed in’, but instead it was a natural consequence of the model equations. In the same way, shuttling naturally emerges in previous models of the Dl gradient without the authors' explicit intention (Ambrosi et al., 2014; Kanodia et al., 2009).

Given the natural emergence of the shuttling mechanism from the topology of the known Dl/Cact interactions, one may ask whether the mechanism operates at a relevant level in the fly embryo. In the Dpp system, formation of peak levels of Dpp signaling requires the BMP antagonist Sog, which binds to Dpp and facilitates its diffusion to the dorsal midline of the early embryo. Loss of zygotic Sog function results in loss of both the highest levels of Dpp signal as well as the expression of genes that require those peak levels (Ashe and Levine, 1999; Zusman et al., 1988; Rushlow et al., 2001). Cact serves as the analog to Sog in the Dl/Cact system. A seminal study of Cact showed that loss of Cact function results in an expansion of the domain of cells expressing twi, a gene that requires peak levels of nuclear Dl (Roth et al., 1991), suggesting that there is no need for shuttling of Dl through Cact to form the peak levels of the Dl gradient. By contrast, a recent quantitative study, which analyzed embryos with varying levels of compromised cact function, could support the possibility that shuttling is necessary for embryonic fitness (Cardoso et al., 2017). Embryos with stronger loss of cact function have progressively flatter Dl gradients with lower peak values and progressively narrower domains of sna, which, like twi, requires peak levels of Dl (Cardoso et al., 2017). Curiously, the same study suggests a third role for Cact in establishing the Dl gradient: Cact fragments that result from Toll-independent degradation potentiate Dl signaling, which might explain most, if not all, their cact mutant phenotypes. Even so, the authors maintain the position that the shuttling mechanism could be necessary for the formation of peak Dl levels. Further work should be done to continue to dissect novel roles Cact might have in Dl gradient formation.

Regardless of the conflicting data from cact mutant embryos, the data presented here from the dl; dl-dGFP/+ embryos show that, at minimum, the shuttling mechanism is required for formation of peak levels of the Dl gradient (and the consequent sna expression) when Dl levels are compromised. Given the data presented here, the literature data explained by the shuttling hypothesis, and the fact that all biological processes required for shuttling are known to be present in the embryo, we suggest that Cact serves a dual role in establishing the Dl nuclear gradient: preventing nuclear translocation of Dl and shuttling of Dl.

yw flies were used as wild type. dl-paGFP, dl-mGFP and dl-dVenus were created by BAC recombineering. For live imaging, flies carrying dl-paGFP were crossed to flies carrying H2A-RFP on the second chromosome (BS# 23651). dl/+ flies were created by cleaning up dl¹ via two homologous recombinations with yw to generate dl^1.2.5. cact/+; cact-full lacZ 25 flies were obtained from David Stein (Janelia Research Campus, Ashburn, VA, USA) (Fernandez et al., 2001). dl-lacZ flies were obtained from Govind et al. (1992). dl-dGFP and dl-mVenus flies and the original BACs used to create them were obtained from Angela Stathopoulos (California Institute of Technology, Pasadena, CA, USA). dl-mGFP,dl^1.2.5 flies were created by homologous recombination. Presence of dl-mGFP was confirmed by w⁺. Presence of dl^1.2.5 was confirmed via sequencing by GENEWIZ. Egfr^t1/CyO flies were obtained from the Bloomington Drosophila Stock Center (# 2079). Flies carrying the bcd>Toll^10b: bcd 3′UTR construct were obtained from Angela Stathopoulos. The plasmid carrying FRT-stop-FRT Hsp83>Toll^10b: bcd 3′UTR was also obtained from Angela Stathopoulos. To remove the FRT-stop-FRT cassette, we crossed flies carrying this construct into a line carrying hsFLP on the X chromosome (BS# 8862). To remove the native DV Dl gradient, flies carrying the Toll^10b: bcd 3′UTR construct were crossed into a gd⁷ background. See Supplementary Materials and Methods for more details. dl/+; Tl/+ fly lines resulted from crossing the dl^1.2.5/+ fly line with Tl^rv18/+ (BS# 30913).

We followed Protocol 3 of the NCI at Frederick Recombineering website (http://ncifrederick.cancer.gov/research/brb/recombineeringinformation.aspx) to generate dl-paGFP, dl-mGFP and dl-dVenus in pACMAN (Venken et al., 2006). A proofreading Q5 DNA polymerase (New England Biolabs) was used to amplify sequences at a high level of authenticity. Using a GalK selection protocol (Warming et al., 2005), single amino acid mutations were introduced at residue 206 in previously established BACs (Reeves et al., 2012) to generate dl-mGFP (A206K) and dl-dVenus (K206A). dl-paGFP was created by adding the open reading frame of paGFP (Addgene plasmid #11911) (Patterson and Lippincott-Schwartz, 2002) in frame to the 3′ end of the dl open reading frame in a dl rescue construct (Reeves et al., 2012) in pACMAN (Venken et al., 2006) using a 6x-Gly linker. See Table S1 for a list of primers used.

All embryos were aged to 2-4 h, except for ‘young’ yw embryos, which were aged to 0-2 h, then fixed in 37% formaldehyde according to standard protocols (Kosman et al., 2004). A combination fluorescent in situ hybridization/fluorescent immunostaining was performed according to standard protocols (Kosman et al., 2004). Briefly, fixed embryos were washed in Tween/PBS buffer, then hybridized with a digoxigenin-conjugated anti-sense sna probe at 55°C overnight. The embryos were then washed and incubated with primary antibodies at 4°C overnight. Next, the embryos were washed and incubated for 1-2 h with fluorescent secondary antibodies at room temperature. The embryos were then washed and stored in 70% glycerol at −20°C. Embryos were imaged within one month of completing the protocol. See Supplementary Materials and Methods for more details, including suppliers and dilutions of antibodies.

Embryos were cross-sectioned and mounted in 70% glycerol as described previously (Carrell and Reeves, 2015). Briefly, a razor blade was used to remove the anterior and posterior thirds of the embryo, leaving a cross section ∼200 µm long by 200 µm in diameter. These sections were then oriented such that the cut sides became the top and bottom. They were imaged at 20× magnification on a Zeiss LSM 710 microscope. Fifteen z-slices 1.5 µm apart were analyzed. Embryos with an AP Dorsal gradient were mounted laterally in 70% glycerol using one piece of double-sided tape (weak bcd promoter) or two pieces of double-sided tape (strong Hsp83 promoter). Images were taken at 2.5 µm intervals from just above the top of the embryo to the depth at which the embryo reached maximal size in the xy plane, which was assumed to be the midsagittal section. Stacks ranged from 15 to 25 slices.

Images of embryo cross sections were analyzed using previously derived code (Trisnadi et al., 2013). Briefly, the border of the embryo was found computationally, then the nuclei were segmented using a local thresholding protocol. The intensity of Dl in each segmented nucleus was calculated as the ratio between the intensity in the Dl channel divided by the intensity in the nuclear channel (Damle et al., 2006; Liberman et al., 2009). The intensity of mRNA expression and total Dl were calculated as average intensity within an annulus ∼18 μm wide around the perimeter of the embryo. A description of the image analysis of whole-mount embryos can be found in the Supplementary Materials and Methods and in Jermusyk et al. (2016).

All Dl gradients were fit to a Gaussian, and these fits were used to determine the width parameter, σ, and to normalize the Dl gradients. An r² goodness of fit was calculated for each embryo, and if this fell below 0.80, the measurement was discarded. Widths of sna domains were found by fitting the sna intensity curves to canonical profiles. For further explanation of these two procedures, see the Supplementary Materials and Methods. All replicates were biological.

Statistical significance was calculated using two-tailed homoscedastic t-tests. For 80% power, minimum sample size was calculated to be <10 embryos for our measurements of the Dl gradient width.

Embryos were dechorionated by hand or for 30 s in 100% bleach. They were then mounted laterally on a slide coated with heptane glue. Deionized water was used as a mounting medium. Two pieces of double-sided tape were used to attach the coverslip. Images were taken using a 40× water immersion objective on an LSM 710 confocal microscope. Activation box: 9000 pixels (300×30 μm); number of activation passes (number of times the laser activates the region in a single cycle): 10; rest time (the length of rest time between cycles): 15 s; number of cycles: 40. Each activation session lasted ∼25 min and was followed by imaging the entire depth of the embryo. Each embryo underwent five activation sessions. Laser power was 3% for embryos activated near the ventral midline, and 2.5% for embryos activated near the dorsal midline. A 405 nm laser was used for activation and a 488 nm laser was used for excitation of the activated GFP.

To simplify analysis and interpretation, we simulated 100 min of development with 51 nuclei positioned along a linear (x) axis and ignore mitosis and nuclear division. The active Toll gradient was modeled phenomenologically in space as k_diss(x)=k_diss,0exp (−0.5x²/φ²) (Ambrosi et al., 2014; Kanodia et al., 2009; O'Connell and Reeves, 2015). In the Toll saturation model (Figs 4–7), activated Toll receptors were allowed to saturate (Fig. 4G), which altered the Dl/Cact complex dissociation term to a Michaelis–Menten-like saturable function (see Supplementary Materials and Methods). In other words, the final term in Eqns 2-4 became k_dissC_DC/(K_R+C_DC), where K_R is a Michaelis constant for Toll saturation. For more details on the model formulation, see Supplementary Materials and Methods.

To ensure our results were not the result of oversimplification, we also formulated a more complete (full) model of Dl/Cact/Toll interactions, which is an extension to the model found in O'Connell and Reeves (2015). This full model (see Supplementary Materials and Methods) consists of differential equations for three species distributed between two compartments: nuclear Dl, cytoplasmic Dl, nuclear Cact, cytoplasmic Cact, nuclear Dl/Cact complex, and cytoplasmic Dl/Cact complex, plus an equation for free active Toll receptor and one for active Toll receptor bound to Dl/Cact complex. It takes into account the mitosis and interphase associated with nc 10-14 and the possibility that Cact and Dl/Cact complex could be present in the nucleus. During mitosis, the nucleus becomes undefined, and the contents of each nucleus mix with those of the surrounding cytoplasm. At the end of mitosis, the nucleus reforms, and the concentration of Dl, Cact and Dl/Cact inside the nucleus is initialized as equal to their respective concentrations in the cytoplasm, and each species can enter and exit the nucleus. All cytoplasmic species can move between adjacent cytoplasmic compartments during interphase and mitosis.

The production rate of activated Toll receptors was modeled phenomenologically. The eight differential equations were nondimensionalized, resulting in a model with 20 free parameters. Optimization was performed in MATLAB (MathWorks) using an evolutionary optimization algorithm with stochastic ranking (Runarsson and Yao, 2000, 2005), yielding 114 parameter sets that were generally consistent with the spatiotemporal data published by Reeves et al. (2012). Further detail on model equations and analysis can be found in the Supplementary Materials and Methods.

We also analyzed two previous models of Dl/Cact interactions, which each have the processes necessary for shuttling, to investigate whether these processes together are sufficient for shuttling (Kanodia et al., 2009; Ambrosi et al., 2014). See Supplementary Materials and Methods for more details.

We thank Angela Stathopoulos and Leslie Dunipace for provision of Dl-dGFP and Dl-mVenus flies and BACs, bcd>Toll^10b: bcd 3′ UTR flies, and the DNA used to generate Hsp83>Toll^10b: bcd 3′ UTR flies. We are grateful to ImmunoReagents for providing goat anti-biotin antibody, Alex Thomas for generating the sna-biotin probe, Parv Gondalia for generating the sna-FITC probe, David Stein for providing the cact-lacZ fly line, and Shubba Govind for providing the dl-lacZ flies.