Morphogen transport

For more than a century, gradients of signaling molecules have been proposed to direct the formation of tissues during embryogenesis (Morgan, 1901; Turing, 1952; Stumpf, 1966; Wolpert, 1969; Crick, 1970) (reviewed by Rogers and Schier, 2011). The idea of such signaling gradients emerged following observations that some cells can induce the formation of structures in neighboring tissues. This led to the hypothesis that signaling molecules, termed morphogens, are produced at a localized source and disperse in the target tissue. The resulting morphogen concentration gradient dictates the expression of different sets of genes and leads to tissue patterning and morphogenesis. Morphogens act over different distances (tens to hundreds of micrometers) and different times (hours to days) in different developmental contexts, from patterning wing precursors in flies to inducing and patterning germ layers in vertebrate embryos (reviewed by Rogers and Schier, 2011). However, neither the non-autonomous function of morphogens nor their graded distributions and different signaling ranges directly implicate a specific transport mechanism.

Several models have been proposed to explain how morphogens move from their source to target tissues. Here, we analyze recent studies and models of morphogen transport and discuss whether there is a dominant mode of movement. Current transport models can be broadly grouped into: (1) extracellular diffusion-based mechanisms; and (2) cell-based mechanisms, in which morphogens move through cells or along cellular extensions. We first lay out three diffusion-based models for extracellular morphogen transport (free, hindered and facilitated diffusion) and two cell-based mechanisms (transcytosis and cytoneme-mediated transport). We use mathematical modeling and the classic analogy of a ‘drunken sailor’ to illustrate the principles behind each model. Next, we analyze recent experiments that have examined morphogen movement and discuss evidence for and against each transport model, focusing on the morphogens Nodal, fibroblast growth factor (FGF) and Decapentaplegic (Dpp). Based on this analysis, we hypothesize that most of the available data are consistent with diffusion models, in which hindrance due to tortuosity and binding interactions is often considerable. We end by suggesting future research directions to resolve the current debates regarding morphogen transport.

Morphogens move from the site where they are produced (the source) through complex environments, leading to the formation of a morphogen gradient in the target tissue (Fig. 1A). Models of morphogen transport therefore frequently involve complex mathematical descriptions that include several coupled partial differential equations. In simplified terms, these models can be illustrated by the ‘drunken sailor’ analogy (Fig. 1) (Pearson, 1905a; Pearson, 1905b; Rayleigh, 1905; Stewart, 2001). In this analogy, a ship (source) loaded with drunken sailors (morphogen molecules) arrives at the harbor of a city (target tissue). The path of a disembarking drunken sailor moving into the city illustrates the random walk of each molecule as it moves through the target tissue (Fig. 1B, inset). Each drunken sailor walks with a certain average step size and moves in a random direction with each step. This analogy reflects the diffusive behavior of molecules as they bounce off each other and change direction.

Various models explaining the transport of morphogens can thus be described in terms of the drunken sailor analogy. In the following sections, we discuss five major models: (1) free diffusion, i.e. drunken sailors performing purely random walks (Fig. 1B); (2) tortuosity- and binding-mediated hindered diffusion, i.e. drunken sailors walking around buildings (Fig. 1C) and visiting pubs (Fig. 1D); (3) facilitated diffusion, i.e. drunken sailors prevented from visiting pubs by police officers (Fig. 1E,F); (4) transcytosis, i.e. drunken sailors walking through buildings (Fig. 1G); and (5) directed transport via filopodial extensions called cytonemes, i.e. drunken sailors transported through subway tunnels (Fig. 1H).

In the simplest case of morphogen dispersal, molecules move by ‘free diffusion’ (see Glossary, Box 1) from the source to the target tissue. In the drunken sailor analogy, each sailor performs a random walk (Fig. 1B, inset). The dynamics of dispersal can be described by the diffusion coefficient D. However, free diffusion is not sufficient for gradient formation: if sailors simply moved by free diffusion, they would eventually be distributed evenly in the city [i.e. a nearly uniform distribution of morphogen molecules would be seen in the target tissue (Wartlick et al., 2009)]. For a gradient to form, some drunken sailors need to disappear along the way; a sailor might die (i.e. the morphogen is degraded) or he may enter and remain in a building (i.e. the morphogen is permanently trapped by a cell). Both events remove sailors/molecules from the mobile pool and are therefore referred to as ‘clearance’ (see Glossary, Box 1). The combination of drunken sailors constantly disembarking from the ship (production), moving through the city (diffusion) and disappearing (clearance) along the way results in the graded distribution of sailors in the city over time (Fig. 1B) (Crick, 1970; Lander et al., 2002; Wartlick et al., 2009; Yu et al., 2009; Zhou et al., 2012). For a detailed mathematical model of free diffusion, see Fig. 2A.

The free diffusion model makes four major predictions. First, morphogens move by extracellular diffusion. Second, morphogens have a high free ‘diffusivity’ (see Glossary, Box 1) that is described by the Einstein-Stokes relationship (Berg, 1993; Müller and Schier, 2011). The diffusion coefficient should thus be close to theoretical predictions based on the size of the morphogen and the properties of its environment. Third, to allow for gradient formation, morphogen clearance is fast relative to diffusion (Yu et al., 2009; Zhou et al., 2012). Clearance could be achieved by rapid degradation, in which case the molecules have a short lifetime, or by rapid permanent immobilization on or in target cells. In the latter case, the fraction of freely moving molecules is small because most morphogen molecules are permanently trapped (Fig. 2A). Fourth, gradient formation kinetics are rapid; the gradient shape is established early and does not change (Fig. 2C). By contrast, the amplitude of the gradient increases if the immobilized molecules have a long lifetime (Fig. 2A).

In a related model of morphogen transport, ‘hindered diffusion’ (see Glossary, Box 1), the extracellular diffusion of molecules is hindered by obstacles (tortuosity-mediated hindrance) and by transient binding interactions (binding-mediated hindrance). Relating back to the drunken sailor analogy, each sailor walks through the streets of a city around buildings and transiently enters and leaves pubs along the way. Similar to the free diffusion model, morphogens undergo random walks but walks are restricted by cells and interrupted by extracellular binding interactions.

Tissues are often densely packed with cells. In contrast to the free diffusion model, which posits that geometric effects from cells on diffusion are negligible or that movement occurs outside of the cell field, hindered diffusion postulates that cell packing, and hence tortuosity (see Box 2), strongly influences the movement of extracellular molecules. Extracellular morphogens must go around cells and this reduces their overall dispersal (Nicholson and Syková, 1998; Rusakov and Kullmann, 1998; Nicholson, 2001; Tao and Nicholson, 2004; Thorne and Nicholson, 2006; Thorne et al., 2008). In the drunken sailor analogy, sailors perform random walks in a region containing buildings, not in a large empty lot (Fig. 1C). Although the local movements and step sizes of the sailors are identical in both scenarios, it will take sailors, on average, longer to travel a given distance in the packed region (see Box 2). Thus, in a cellular environment, the ‘local’ extracellular diffusion coefficient (or ‘local diffusivity’, see Glossary, Box 1) is similar to free diffusivity, whereas the ‘effective diffusion’ (see Glossary, Box 1) coefficient (or ‘global diffusivity’) is reduced.

In addition to geometric hindrance mediated by cellular obstacles, morphogen movement might be further hindered by transient binding to extracellular molecules, such as morphogen receptors or extracellular matrix components (Crank, 1979; Lander et al., 2002; Baeg et al., 2004; Belenkaya et al., 2004; Han et al., 2004; Lin, 2004; Han et al., 2005; Callejo et al., 2006; Hufnagel et al., 2006; Thorne et al., 2008; Wang et al., 2008; Miura et al., 2009; Yan and Lin, 2009; Müller and Schier, 2011; Müller et al., 2012; Sawala et al., 2012). In the drunken sailor analogy, sailors frequently linger in pubs along the way (Fig. 1D). The local ‘speed’ of sailors moving between pubs is the same as in the free diffusion model, but their residence time in pubs reduces their global ‘speed’ of moving through the city. Thus, binding-mediated hindrance of morphogens will reduce the effective diffusion coefficient. For a detailed mathematical model of binding-mediated hindered diffusion, see Fig. 2B.

The key predictions of the binding-mediated hindered diffusion model are as follows. First, morphogens move through extracellular diffusion. Second, the effective diffusion coefficient is lower than the free diffusion coefficient because morphogens transiently bind to extracellular immobilized molecules (‘diffusion regulators’, see Glossary, Box 1). Third, the number of freely moving molecules is expected to be small because most morphogen molecules would be bound to diffusion regulators at any given point in time (Fig. 2B). Fourth, in contrast to the free diffusion model, the clearance of morphogen does not need to be rapid; because global diffusion is slow, gradients can form even when mobile molecules are long-lived. Fifth, gradient shape evolves more slowly over time than in the free diffusion model due to slower overall dispersal of the morphogen (Fig. 2C). As in the free diffusion model, the amplitude of the gradient increases over time if the cleared molecules have a long lifetime (Fig. 2B).

Notably, the free and hindered diffusion models can eventually lead to the same ‘steady state’ (see Glossary, Box 1) morphogen gradient (Fig. 2A,B), but the kinetics of gradient formation are different (Fig. 2C). This distinction is particularly relevant in rapidly developing systems in which gradients might be interpreted quickly or might not reach steady state.

Models based on ‘facilitated diffusion’ (see Glossary, Box 1) are an extension of hindered diffusion models, in which morphogen movement is enhanced by interactions with ‘positive’ diffusion regulators that release the hindrance exerted by ‘negative’ diffusion regulators. In this scenario, the morphogen is largely immobile until bound to a positive diffusion regulator that enhances its mobility. Immobility can be caused by binding to an immobilized diffusion regulator until binding to a mobile diffusion regulator interferes with the former interaction and allows morphogen molecules to move over longer distances. In the drunken sailor analogy, a sailor visits pubs (negative diffusion regulators; Fig. 1E) until a police officer (positive diffusion regulator) escorts the sailor and prevents further pub visits (Fig. 1F). In this analogy, the drunken sailor is largely immobile and can move over longer distances only when escorted by a police officer.

Shuttling is a special case of facilitated diffusion, in which the ‘shuttles’, not the morphogens, are generated from a localized source (Holley et al., 1996; Eldar et al., 2002; Mizutani et al., 2005; Shimmi et al., 2005; van der Zee et al., 2006; Ben-Zvi et al., 2008; Wang et al., 2008; Ben-Zvi et al., 2011; Haskel-Ittah et al., 2012; Matsuda and Shimmi, 2012; Sawala et al., 2012). The association of morphogen molecules with shuttles results in the formation of a morphogen gradient from an initially broad or even uniform morphogen distribution (Fig. 1E,F). Shuttling involves repeated rounds of: (1) morphogen binding to the shuttle; (2) rapid diffusion of the morphogen-shuttle complex; (3) destruction of the shuttle; and (4) immobilization of the morphogen. When the shuttle molecules are produced at a localized source, morphogens near the source bind shuttle molecules and diffuse away. As morphogen-shuttle complexes diffuse, the shuttles are degraded and morphogen is immobilized. Far from the shuttle source, morphogen molecules accumulate because they are less likely to encounter shuttles and cannot move sufficiently in the absence of shuttles. Eventually, few morphogen molecules are found near the shuttle source but are instead concentrated at a distance. This process generates a sharp gradient from an initially uniform morphogen distribution (Fig. 1E,F).

The facilitated diffusion model has three main predictions. First, in the default state extracellular morphogens are immobilized or significantly hindered in their mobility. Second, competition between the shuttle and the immobilized diffusion regulator releases and mobilizes the morphogen. Third, a localized source of shuttles can generate a morphogen gradient from an initially uniform morphogen distribution.

As an alternative to extracellular diffusion-based mechanisms (see Box 3 for a discussion of perceived weaknesses of diffusive transport mechanisms), it has been proposed that morphogens are transported via cell-based mechanisms: through cells (transcytosis) or along cellular extensions (cytonemes; see below).

In the transcytosis model, signaling molecules bind to the cell surface, resulting in their cellular uptake by endocytosis. Upon exocytosis the signal is released again from the cell. By undergoing multiple rounds of cellular uptake and release, the molecules become dispersed in the target tissue (Dierick and Bejsovec, 1998; González-Gaitán and Jäckle, 1999; Entchev et al., 2000; Kruse et al., 2004; Bollenbach et al., 2005; Bollenbach et al., 2007; Gallet et al., 2008; Kicheva et al., 2012b). In terms of the drunken sailor analogy, the molecules do not move around the buildings but through the buildings (Fig. 1G). Since the drunken sailors still move by random walks, this process reflects a diffusive behavior, but in contrast to the mechanism discussed earlier it is intracellular.

The key predictions of the transcytosis model are as follows. First, the morphogen is taken up and released by cells. Second, the effective diffusion coefficient is small because morphogen transport relies on the relatively slow processes of cellular uptake and release. Third, the number of freely moving molecules is expected to be small because most morphogen molecules are bound to transport vehicles at any given point in time. Fourth, gradients can form even when mobile molecules are long-lived because global diffusion is slow. Fifth, gradient shape evolves slowly over time due to slower overall dispersal of the morphogen, similar to the hindered diffusion model.

As another alternative to extracellular diffusion-based mechanisms, directed delivery mechanisms have been postulated to disperse morphogens (Deuchar, 1970; Miller et al., 1995; Ramírez-Weber and Kornberg, 1999; Ramírez-Weber and Kornberg, 2000; Kerszberg and Wolpert, 2007; Kornberg and Guha, 2007; Wolpert, 2009; Roy and Kornberg, 2011; Kornberg, 2012). One such mechanism is the use of filopodial structures to mediate morphogen transport. There is precedence that such cellular extensions serve to explore the environment, to detect distant signals or to present information to other cells (see Box 4) (Gustafson, 1964; Gustafson and Wolpert, 1967; Karp and Solursh, 1985; Bentley and Toroian-Raymond, 1986; Locke, 1987; Miller et al., 1995; Jacinto et al., 2000; Vasioukhin et al., 2000; Milán et al., 2001; Renaud and Simpson, 2001; Sato and Kornberg, 2002; Wolf et al., 2002; De Joussineau et al., 2003; Rørth, 2003; Gallo and Letourneau, 2004; Yuste and Bonhoeffer, 2004; Lehmann et al., 2005; Demontis and Dahmann, 2007; Kress et al., 2007; Cohen et al., 2010; Swaney et al., 2010; Callejo et al., 2011; Cohen et al., 2011; Inaba et al., 2012; Peng et al., 2012; Rojas-Ríos et al., 2012; Vitriol and Zheng, 2012). The cytoneme model builds on these observations and postulates that long dynamic filopodia-like structures known as cytonemes project from target cells and contact morphogen-producing cells. Morphogens are handed over to and transported along cytonemes to form a concentration gradient (Ramírez-Weber and Kornberg, 1999; Ramírez-Weber and Kornberg, 2000; Sato and Kornberg, 2002; Hsiung et al., 2005; Kornberg and Guha, 2007; Roy and Kornberg, 2011; Kornberg, 2012), akin to drunken sailors taking a subway to their destination (Fig. 1H).

The cytoneme-mediated transport model has four central predictions. First, morphogens do not diffuse extracellularly but are transferred at local contacts between source and target cells. Second, morphogens are transported by cytonemes through the target field. Third, cytonemes extending from target cells orient towards the signaling source over distances that are comparable to the morphogen signaling range. Fourth, because cytonemes must orient towards morphogen sources, morphogen receptors are required for sensing the source and establishing successful contacts.

In recent years, imaging studies and biophysical measurements (see Box 5 and Box 6) have been used to investigate the transport mechanisms of various morphogens, including Nodal, FGF and Dpp, as well as Bicoid (see Box 7). Although these studies have provided some insight into the mechanisms underlying morphogen transport, they have also led to disparate conclusions. For example, several distinct morphogen transport mechanisms have been suggested for gradient formation by Dpp in Drosophila melanogaster wing precursors; evidence has been presented for free diffusion, hindered diffusion, transcytosis and cytoneme-mediated transport (Ramírez-Weber and Kornberg, 1999; Hsiung et al., 2005; Kicheva et al., 2007; Roy et al., 2011; Schwank et al., 2011; Wartlick et al., 2011; Zhou et al., 2012). In the following sections, we discuss the experimental evidence that has been put forward to explain the transport of Nodal, FGF and Dpp.

The Nodal/Lefty morphogen system patterns the germ layers during early embryogenesis over a period of a few hours and the left-right axis during later stages of vertebrate development (reviewed by Schier, 2009). A common theme in these different contexts is that Nodal and its inhibitor Lefty act over different ranges (see Box 8): Nodal activates signaling close to the source, whereas Lefty inhibits Nodal signaling far from the source (Fig. 3A). Recent studies, discussed below, have begun to uncover some of the features of Nodal and Lefty and their modes of transport.

The subcellular localization of morphogens can be an important indicator of what transport process might be at work. For example, if most of the morphogen molecules are found outside cells, it becomes less likely that a concentration gradient is established by movement through cells (e.g. by transcytosis). Nodal and Lefty are members of the transforming growth factor β (TGFβ) superfamily and have signal sequences required for secretion (Zhou et al., 1993; Meno et al., 1996; Beck et al., 2002; Sakuma et al., 2002; Le Good et al., 2005; Jing et al., 2006; Blanchet et al., 2008; Tian et al., 2008; Marjoram and Wright, 2011; Müller et al., 2012). Fusion of the signal sequence-containing N-terminal domains of Nodal and other morphogens to GFP causes secretion of GFP (Entchev et al., 2000; Yu et al., 2009; Müller et al., 2012). Furthermore, western blot analyses reveal efficient secretion of ectopic Nodal-GFP and Lefty-GFP into the extracellular space in zebrafish embryos, and in vivo imaging shows extracellular localization of Nodal-GFP and Lefty-GFP (Müller et al., 2012). These results support the idea that Nodal and Lefty are secreted and mainly extracellular.

The finding that Nodal and Lefty are predominantly extracellular suggests that they move around cells. As discussed above, cells can act as obstacles that increase the path length of molecules diffusing in the extracellular space (see Box 2). As a result, the global effective diffusion coefficient of a population of molecules moving through a tissue should be lower than the local diffusivity within a small extracellular volume. This idea can be tested by studying the movement of secreted GFP using techniques that compare local diffusivity with global effective diffusivity. As described in Box 5 and Box 6, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) can measure local and global diffusivity, respectively. FCS experiments for secreted GFP in zebrafish embryos yielded a local extracellular diffusion coefficient of ∼90 μm²/s, which is about double the effective diffusion coefficient of ∼40 μm²/s measured by FRAP (Yu et al., 2009; Müller et al., 2012). This is consistent with the 50-70% tortuosity-dependent reduction in diffusivity predicted by porous media theory (Nicholson and Syková, 1998; Rusakov and Kullmann, 1998; Nicholson, 2001; Tao and Nicholson, 2004) and observed in densely packed tissues (Thorne and Nicholson, 2006). These results suggest that the tissue architecture of zebrafish embryos can hinder the movement of extracellular morphogens. Interestingly, similar to secreted GFP, FCS and FRAP experiments showed that the local diffusivity of Lefty-GFP (∼40 μm²/s) is only about twice its effective diffusivity (∼20 μm²/s) (Table 1). These results suggest that the diffusion of secreted GFP and Lefty-GFP is mostly hindered by cell packing but not by binding to extracellular diffusion regulators.

Strikingly, Nodal-GFP has a similar local diffusivity to Lefty-GFP (∼40 μm²/s) but a ∼90% lower effective diffusivity (∼2 μm²/s; Table 1) (Müller et al., 2012). Since secreted GFP, Nodal-GFP and Lefty-GFP move in the same tissue and experience the same tortuosity, additional factors must further decrease the effective diffusivity of Nodal-GFP.

One possibility is that Nodal might transiently bind to immobilized extracellular diffusion regulators (Fig. 3B), which would decrease its effective diffusivity (Crank, 1979; Dowd et al., 1999; Miura et al., 2009; Müller et al., 2012), whereas Lefty does not bind to such regulators and thus moves relatively freely through the tissue (Fig. 3C). The hindered diffusion of Nodal morphogens is not only supported by the low effective diffusion coefficient of Nodal, but also by several additional observations. First, measurements of the extracellular clearance of fluorescent Nodal in zebrafish embryos show a long extracellular half-life of ∼100 minutes (Müller et al., 2012), inconsistent with the short half-lives predicted by some forms of the free diffusion model (assuming that extracellular clearance represents clearance of the mobile fraction). Second, nested FRAP experiments (see Box 6) support the hindered diffusion model for Nodal transport. These experiments compare the recovery of fluorescence after photobleaching in two windows: one that encompasses the entire bleached domain, and a smaller one nested within the bleached domain. As predicted by hindered diffusion models, recovery of Nodal-GFP in the smaller window is delayed compared with the large window (Müller et al., 2012). This result is inconsistent with free diffusion models, which predict a very small, experimentally undetectable delay in nested FRAP experiments. Third, the shape of the Nodal gradient is consistent with the measured clearance rate and effective diffusion coefficient and supports the hindered diffusion model (Müller et al., 2012). Given the slow clearance and fast local diffusivity of Nodal, gradients formed by free diffusion would be too flat to account for the observed gradient.

The endogenous Nodal gradient has not yet been analyzed, and the identity of potential extracellular Nodal diffusion regulators is currently unknown, but all available data support the predictions from the hindered diffusion model: extracellular morphogen location, high local mobility, low global effective mobility, slow clearance of mobile proteins, a recovery delay in nested FRAP experiments, and a gradient shape consistent with these biophysical measurements.

FGFs are signals with diverse roles in development and homeostasis. Recent biophysical measurements in living zebrafish embryos (Yu et al., 2009; Nowak et al., 2011) and in cultured mammary fibroblasts (Duchesne et al., 2012) have provided insights into the movement of FGFs (FGF2 and FGF8 in particular) from the nano- to the microscopic scale and together support the model of hindered diffusion for FGF morphogen transport.

FGF8 patterns the dorsal-ventral and animal-vegetal axes during zebrafish embryogenesis over a period of a few hours. FGF8 is produced at a localized source and is thought to form a gradient by diffusion and endocytosis-mediated clearance (Scholpp and Brand, 2004; Yu et al., 2009). Fluorescently labeled FGF8 molecules have a local extracellular diffusion coefficient of ∼50-80 μm²/s as determined by FCS (Table 1) (Yu et al., 2009; Nowak et al., 2011) but an effective diffusion coefficient of ∼2 μm²/s as measured in FRAP experiments (see Box 6). Thus, just like Nodal, FGF8 has a high local diffusivity but a low global effective diffusivity, consistent with the predictions of hindered diffusion models.

The evolution of the extracellular FGF8 gradient provides additional support for hindered diffusion. The gradient shape slowly emerges over time and approaches steady state only after 3 to 4 hours (Fig. 4A) (Yu et al., 2009). The slow emergence of gradient shape is consistent with the hindered diffusion model (Fig. 4B) but not with the free diffusion model (Fig. 4C).

What might hinder the movement of FGFs? Heparan sulfate proteoglycans (HSPGs) are excellent candidate diffusion regulators. FGFs are known to interact with the long sugar chains attached to HSPG core proteins (Dowd et al., 1999; Makarenkova et al., 2009; Miura et al., 2009). Disrupting the interactions between HSPGs and FGF2, for example, leads to a dramatically increased FGF2 diffusion coefficient, suggesting that HSPGs might act as negative regulators of FGF2 diffusion (Dowd et al., 1999). Indeed, mathematical modeling of hindered diffusion with fast reversible binding kinetics reproduces experimental observations of FGF2 movement (Dowd et al., 1999).

Recent single-particle tracking approaches have provided a more detailed view of how HSPGs affect the movement of FGF2 (Duchesne et al., 2012). FGF2 molecules cluster in an HSPG-dependent manner in the extracellular matrix. FGF2 spends most of its time in confined motion bound to HSPG-dependent clusters, but FGF2 molecules are not permanently trapped and can diffuse after leaving a cluster. These results support a central tenet of the hindered diffusion model: at any given time the majority of morphogen molecules is reversibly bound to diffusion regulators.

A role for HSPGs as diffusion regulators is also supported by in vivo studies of FGF8 in zebrafish, although single molecule imaging has not yet been achieved in this context. First, a higher fraction of FGF8-GFP is mobile when HSPG sugar chains are destroyed by injection of heparinase I into the extracellular space (Yu et al., 2009). Second, FGF8-GFP has a higher effective diffusion coefficient in embryos injected extracellularly with heparin, which is thought to compete with endogenous HSPGs for FGF8 binding (Fig. 4D). Third, the largely membrane-localized FGF8-GFP signal becomes more diffuse in the extracellular space upon heparin injection, suggesting that this treatment interrupts interactions with diffusion regulators that retain FGF8-GFP at the cell surface (Fig. 4D).

In summary, recent studies of FGF2 and FGF8 transport suggest the following scenario for hindered diffusion. FGF is secreted from source cells but rapidly binds to HSPGs on the cell surface and in the extracellular matrix. FGF molecules are released from HSPGs after a certain residence time and either diffuse and bind to another HSPG molecule or move away from the cell surface to diffuse freely. In this scenario, most of the FGF molecules are bound to HSPGs and are therefore concentrated at the cell surface, whereas a smaller fraction of freely mobile FGF molecules is found far from cell surfaces. Thus, the diffusion of the morphogen punctuated by binding to HSPGs accounts for the formation of the FGF gradient.

Dpp is a secreted TGFβ superfamily member and a homolog of vertebrate bone morphogenetic proteins (BMPs) (Panganiban et al., 1990a; Panganiban et al., 1990b; Lecuit et al., 1996; Nellen et al., 1996; Lecuit and Cohen, 1998; Entchev et al., 2000; Teleman and Cohen, 2000; Gibson et al., 2002; Belenkaya et al., 2004; Kruse et al., 2004; Kicheva et al., 2007; Schwank et al., 2011; Zhou et al., 2012). A Dpp gradient forms from a localized source and patterns the wing imaginal disc [an epithelial wing precursor tissue that is initially flat and later develops a slight curvature and multiple folds (Sui et al., 2012)] over several days during the larval stages of Drosophila development (Entchev et al., 2000; Teleman and Cohen, 2000). Movement of fluorescently labeled Dpp has been directly observed in explanted Drosophila wing discs, and multiple transport models have been proposed to explain Dpp gradient formation. Here, we discuss whether Dpp in the wing disc disperses by free or hindered diffusion, by transcytosis, or by cytoneme-mediated transport. We also discuss evidence that Dpp moves by facilitated diffusion during early embryogenesis.

Dpp is present intracellularly and extracellularly, but the relative levels in different locations are under debate (Entchev et al., 2000; Teleman and Cohen, 2000; Belenkaya et al., 2004; Schwank et al., 2011). Several lines of evidence suggest that Dpp is largely extracellular. For example, incubation of intact wing discs with proteinase K leads to the digestion of most of the mature Dpp-GFP (Teleman and Cohen, 2000). This suggests that Dpp is accessible extracellularly, although it could be argued that proteinase K might be internalized by endocytosis and thus might also degrade intracellular Dpp. Additional support for extracellular localization comes from incubation of dpp-GFP-expressing wing discs with anti-GFP antibodies, resulting in extensive extracellular labeling of Dpp-GFP (Belenkaya et al., 2004; Kruse et al., 2004; Schwank et al., 2011). Although these experiments are consistent with extracellular localization of Dpp-GFP, they do not indicate whether this fraction of Dpp is mobile, as required in extracellular diffusion models. Conversely, it is unclear whether intracellular Dpp is released, as required in transcytosis models, or if Dpp is transferred to and transported by cellular extensions, as proposed in the cytoneme model.

FCS and pair-correlation function (pCF) microscopy analyses (see Box 5) indicate that a fraction of fluorescently labeled Dpp moves with a local diffusion coefficient of ∼20 μm²/s in the extracellular space (Zhou et al., 2012). These measurements support extracellular diffusion models, but do not distinguish between free and hindered diffusion. Similarly, currently available data on the kinetics of gradient formation (Entchev et al., 2000; Teleman and Cohen, 2000) cannot distinguish between free and hindered diffusion mechanisms (Fig. 5A-C).

As discussed above, a key prediction of the free diffusion model is rapid morphogen clearance: in order to form a gradient, freely diffusing Dpp would have to be cleared rapidly from the mobile pool, with a half-life of less than 15 seconds (Zhou et al., 2012). The clearance rate of Dpp has not been measured experimentally (Kicheva et al., 2012b), but such low half-lives could result from rapid and irreversible binding to receptors or other immobilized extracellular molecules (Lander et al., 2002). Alternatively, high rates of cellular uptake could rapidly clear Dpp, but this scenario is somewhat less likely as ligand internalization in other systems can take several minutes (Lander et al., 2002).

As a consequence of rapid clearance, only a very small fraction of Dpp-GFP would be mobile extracellularly (Fig. 2A). Consistent with this idea, pulse-labeled Dpp was not observed to move in fluorescence spreading after photoconversion (FSAP) experiments (see Box 6; Fig. 5D) (Zhou et al., 2012). The FSAP experiments support the free diffusion model for Dpp transport, but they are also consistent with the hindered diffusion model when trapping by cellular uptake or permanent immobilization is taken into account (see Fig. 5D-F for details).

The key prediction of the hindered diffusion model is that global diffusivity should be significantly decreased by tortuosity and transient binding. Based on FRAP experiments, Dpp-GFP has been suggested to have a low global effective diffusivity of ∼0.1 μm²/s in the wing disc (Table 1) (Kicheva et al., 2007). A ∼95% lower effective diffusion coefficient (Wartlick et al., 2011) was proposed in the smaller haltere imaginal disc (a precursor of a small wing-like organ required for balancing), possibly owing to a higher concentration of diffusion regulators in this tissue (Crickmore and Mann, 2006; de Navas et al., 2006; Crickmore and Mann, 2007; Makhijani et al., 2007). However, these conclusions have been questioned by recent experiments (Zhou et al., 2012) that suggest that the kinetics of Dpp-GFP fluorescence recovery are dominated not by diffusion but by the rates of trapping and degradation of the low levels of highly mobile Dpp (Fig. 5G).

Whether the slow recovery kinetics of Dpp-GFP are due to hindered diffusion or free diffusion can be distinguished in nested FRAP experiments (Fig. 5G; see Box 6). In the free diffusion model, low levels of mobile molecules would rapidly move into the bleached window and fill it almost uniformly. Trapping of mobile molecules would lead to homogeneous changes in fluorescence increases in the bleached window along the gradient over time. By contrast, hindered diffusion predicts that mobile molecules move slowly into the bleached window, causing fluorescence recovery in the outer window prior to the inner window. Thus, hindered diffusion predicts a delay in recovery in the inner window, whereas free diffusion predicts that the recovery in both windows should be experimentally indistinguishable at early times. Such experiments would distinguish between hindered and free diffusion models, but, surprisingly, different groups have obtained conflicting results from nested FRAP experiments (Kicheva et al., 2007; Zhou et al., 2012).

Similar to the hindered diffusion model of FGF transport discussed above, transient binding of Dpp to HSPGs might slow the diffusion of Dpp (Panganiban et al., 1990a; Fujise et al., 2003; Belenkaya et al., 2004; Han et al., 2004; Takei et al., 2004; Akiyama et al., 2008; Dejima et al., 2011). Reduced levels of Dpp are observed in HSPG-deficient tissues (Fujise et al., 2003; Belenkaya et al., 2004; Han et al., 2004; Takei et al., 2004; Akiyama et al., 2008), and increased levels of HSPGs in the source result in a much steeper Dpp gradient (Fujise et al., 2003). Thus, HSPGs may act as Dpp diffusion regulators that retard Dpp movement through the tissue.

It has been argued that “gradient formation based on passive diffusion is incompatible with the [...] geometries of the biological systems that use morphogen gradients to regulate their growth and patterning” (Roy and Kornberg, 2011) and that diffusion “is an unlikely mechanism to move morphogens for long distances in the plane of the epithelium if it cannot prevent them from moving even a short distance out of the plane” (Kornberg and Guha, 2007). In the context of Dpp gradient formation in the Drosophila wing disc, this concern implies that Dpp movement must be restricted to the plane of the epithelium and that extracellular diffusion cannot retain Dpp (see Box 3 for other perceived weaknesses of diffusion-based models). Instead, cell-based dispersal mechanisms, such as transcytosis and cytonemes (discussed below), would be needed to restrict Dpp movement to the plane of the epithelium.

The wing disc is an epithelial sheet (the disc proper) that is covered apically by a fluid-filled space, similar to the geometry shown in Fig. 2A. Intuitively, it might seem that as morphogen is secreted and moves away from the source, it would be lost into the fluid-filled space (Kornberg, 2012). This perception is incorrect: binding interactions can prevent morphogen loss and retain the majority of molecules within the plane, even if movement is not restricted to the plane. To use the drunken sailor analogy, sailors can encounter a strip of pubs (epithelium) located near an open field (fluid-filled space; Fig. 6A). The sailors’ movement is not restricted to the strip, but sailors linger in pubs and are thus hindered in their movement. As a consequence, most of the sailors are found inside pubs over time rather than in the open field. Analogously, a gradient of sailors can form when there is a local source of sailors (Fig. 6B,C).

This model is supported by simulations showing that the combination of (1) localized morphogen production, (2) diffusion in both the disc proper and the fluid-filled space and (3) binding and clearance in the disc proper results in the formation of a morphogen gradient within the plane of the disc proper (Fig. 2A,B). A low-level gradient also forms in the fluid-filled space due to the ‘absorptive’ effect of binding in the disc proper. Far away from the disc proper, morphogen molecules are almost uniformly distributed, but the distributions in the fluid-filled space are largely irrelevant because morphogen concentrations are very low and morphogen receptors are only present in the disc proper. Importantly, the majority of molecules is bound to the disc proper in a graded fashion. Thus, long-range gradients in the plane of an epithelium can form by diffusion despite unrestricted movement both within and outside of the plane.

Transcytosis has been suggested as a transport mechanism for Dpp and several other morphogens (Dierick and Bejsovec, 1998; Entchev et al., 2000; Kruse et al., 2004; Bollenbach et al., 2007; Gallet et al., 2008). Specific evidence in support of transcytosis comes from experiments that interfere with endocytosis and the Dpp receptor Tkv: Dpp-GFP accumulates extracellularly around clones lacking Tkv, and clones that cannot perform endocytosis exhibit transiently decreased levels of Dpp within and behind the clones (Entchev et al., 2000). Furthermore, global but transient inhibition of endocytosis can prevent observable Dpp-GFP spreading, which is rescued when endocytosis is restored (Kicheva et al., 2007). These findings support the idea that receptor-mediated endocytosis is necessary for Dpp movement. However, this conclusion has been undermined by the suggestion that tkv mutant clones are likely to be abnormal (Schwank et al., 2011). Indeed, tkv mutant clones are normally eliminated due to the activity of the transcription factor Brinker, and Dpp can move through receptor-free regions that are mutant for both tkv and brinker (Schwank et al., 2011). These results suggest that receptor-mediated endocytosis does not play a role in Dpp movement. It is still conceivable, however, that receptor-independent modes of internalization (e.g. fluid phase uptake or internalization stimulated by an alternative membrane-bound binding partner) mediate transcytosis.

Additional evidence against transcytosis is the lack of detectable spreading of Dpp during the FSAP experiments described above (Zhou et al., 2012) (Fig. 5D), despite the postulation that a significant fraction of intracellular Dpp should move during transcytosis. Finally, the key prediction of the transcytosis model, i.e. repeated cellular uptake and release, has not been observed for any morphogen.

It is well established that filopodia-like processes can mediate signaling between distant cells (see Box 4), but it has been suggested that these structures are also required for morphogen transport and gradient formation. For example, filopodia in cultured mammalian cells can transport signals to the cell body (Lidke et al., 2004; Lidke et al., 2005). Filopodia-like extensions called cytonemes emanate from target cells in the Drosophila wing disc and project to the Dpp source (Ramírez-Weber and Kornberg, 1999; Hsiung et al., 2005; Roy et al., 2011). It has been proposed that Dpp is transferred to and delivered along cytonemes, leading to Dpp gradient formation (Roy et al., 2011). There are clear connections between cytonemes and Dpp signaling: cytoneme formation requires Dpp signaling; ectopic sources of Dpp can orient cytonemes; and vesicles containing Dpp receptors (Tkv) have been observed along the length of cytonemes (Fig. 7). These observations support a role for Dpp in cytoneme formation and polarity, but it is unclear whether cytonemes are involved in Dpp gradient formation. For example, it is not known whether Dpp is associated with and transported by wing disc cytonemes (Hsiung et al., 2005; Demontis and Dahmann, 2007), and there is no evidence that cytonemes are required for Dpp gradient formation.

How might the role of cytonemes in gradient formation be tested? One possibility is to block or reduce cytoneme formation and determine whether a gradient can still form. Such an experiment has become feasible by the observation that uniform Dpp induces stumpy, disoriented cytonemes (Fig. 7B) (Ramírez-Weber and Kornberg, 1999; Hsiung et al., 2005; Roy et al., 2011). If cytonemes are required for gradient formation, uniform expression of unlabeled Dpp should not only block the formation of long cytonemes but also preclude gradient formation (or significantly decrease the gradient length scale) of Dpp-GFP expressed from the endogenous Dpp source (Fig. 7C). This experiment has not yet been performed in Drosophila, but in zebrafish embryos Nodal-GFP gradients form properly even when unlabeled Nodal is ubiquitously expressed (Müller et al., 2012).

Dpp patterns not only the larval wing disc, but also the dorsal-ventral axis during early embryogenesis. In this context, dpp RNA is expressed dorsolaterally in a broad domain, but Dpp protein forms a sharp gradient that peaks dorsally (Fig. 8A). It is thought that this gradient forms by the shuttling of Dpp molecules towards the dorsal side. In contrast to transport models in which morphogens are expressed from a localized source, shuttling allows the formation of a gradient in the absence of a localized morphogen source.

Dpp movement in the early embryo is hindered by strong binding to cell surface-associated collagen (Wang et al., 2008; Sawala et al., 2012). Dpp can be released from collagen and mobilized by binding to a secreted Short gastrulation (Sog) complex (the shuttle). The Tolloid protease cleaves Sog and releases Dpp from this complex on the dorsal side of the embryo. Dpp is thought to then reassociate with immobile collagen. Because Sog is expressed in a more ventral domain than Dpp, repeated rounds of complex formation, rapid diffusion and Sog cleavage lead to the accumulation of Dpp on the dorsal side of the embryo (Fig. 8A; Fig. 1E,F). Strikingly, Dpp-GFP expressed in a stripe perpendicular to its endogenous expression domain is also redistributed to the dorsal side, strongly supporting the shuttling model (Wang and Ferguson, 2005).

A similar mechanism might act in BMP-Chordin signaling in frogs (Reversade and De Robertis, 2005; Ben-Zvi et al., 2008; Francois et al., 2009). Moreover, a variation on the shuttling theme, in which a localized source of shuttling molecules is generated by self-organization, has recently been described for the Spätzle morphogen system (Haskel-Ittah et al., 2012), which patterns the dorsal-ventral axis in Drosophila before the onset of the Dpp patterning system (see Fig. 8B,C for details). Despite the elegance of the shuttling model, direct visualization and biophysical measurements of Dpp/BMP or Spätzle diffusion and shuttling are not yet available (see Box 9 for biophysical evidence for shuttling of other cell fate determinants).

The morphogen concept was conceived more than a century ago, and the distribution of a morphogen (Bicoid, see Box 7) within an embryo was first visualized 25 years ago (reviewed by Rogers and Schier, 2011). Over the last ten years, biophysical research has started to explore the dynamics of morphogen movement and gradient formation to reveal potential modes of morphogen transport. Our analysis of the currently available data leads us to favor diffusion-based models of morphogen transport: morphogens move through tissues by diffusion that is slowed down by tortuosity and hindered (and in some cases facilitated) by transient binding to extracellular molecules.

Future research will address the following questions. Does a universal morphogen transport mechanism exist, or do morphogens use unique dispersal strategies depending on developmental context (Kornberg, 2012)? Why do signaling ranges differ widely between morphogens and tissue contexts [including the apical and basal surfaces of the same epithelium (Ayers et al., 2010)]? How is morphogen movement affected by the growth and morphogenesis of target tissues? What factors regulate morphogen movement and signaling range? What does the environment through which morphogens move look like, and how does that environment affect dispersal? What are the nanometer to micrometer scale transport mechanisms that together lead to macroscopic gradient formation (Müller and Schier, 2011)?

Answers to these questions might be found using quantitative imaging and modeling techniques, such as single-plane illumination microscopy FCS (SPIM-FCS) (Sankaran et al., 2010; Wohland et al., 2010; Capoulade et al., 2011), single-particle tracking (Duchesne et al., 2012) and multi-scale modeling approaches (Kavousanakis et al., 2010; Sample and Shvartsman, 2010; Daniels et al., 2012), to analyze transport over different time and length scales (Grimm et al., 2010). Such approaches will help to reveal more clearly how morphogen gradients form during development.

We thank Markus Affolter, Konrad Basler, James Briscoe, Edwin Ferguson, James Gagnon, Marcos González-Gaitán, Fisun Hamaratoglu-Dion, Ben Jordan, Thomas Kornberg, Arthur Lander, Andrea Pauli and David Schoppik for helpful comments and discussions.