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Robust Generation and Decoding of Morphogen Gradients

Naama Barkai1,2 and Ben-Zion Shilo1

1Department of Molecular , Weizmann Institute of Science, Rehovot 76100, Israel 2Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel Correspondence: [email protected]

Morphogen gradients playa key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific “shuttling” mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.

n order for a uniform field of cells to differen- these general features of morphogen-based Itiate into a reproducible pattern of organs and patterning are universal, the range and form tissues, cells need to receive information about of the morphogen profile, and the pattern of their position within the field. During develop- induced target , vary significantly depend- ment, positional information is often conveyed ing on the tissue setting and the signaling by spatial gradients of morphogens (Wolpert pathways used. 1989). In the presence of such gradients, cells The formation of a morphogen gradient is a are subject to different levels of morphogen, dynamic process, influenced by the kinetics of depending on their positions within the field, morphogen production, diffusion, and degra- and activate, accordingly, one of several gene dation. These processes are tightly controlled expression cassettes. The quantitative shape through intricate networks of positive and of the morphogen gradient is critical for pat- negative feedback loops, which shape the gradi- terning, with cell-fate boundaries established ent and enhance its reproducibility between in- at specific concentration thresholds. Although dividual embryos and developmental contexts.

Editors: James Briscoe, Peter Lawrence, and Jean-Paul Vincent Additional Perspectives on Generation and Interpretation of Morphogen Gradients available at www.cshperspectives.org Copyright # 2009 Cold Spring Harbor Laboratory Press; all rights reserved. Advanced Online Article. Cite this article as Cold Spring Harb Perspect Biol doi: 10.1101/cshperspect.a001990

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N. Barkai and B.-Z. Shilo

In the past three decades, many of the com- wing imaginal disc (Teleman et al. ponents comprising the morphogen signaling 2001). Quantitative properties of such morpho- cascades have been identified and sorted into gen profiles are relatively well understood. In pathways, enabling one to start addressing the absence of feedbacks, the steady-state gradi- seminal questions regarding their functionality: ent is exponential, M e2x/l. The decay length How is it that morphogen signaling is reprodu- (scale) of the profile is defined by the mor- cible from one embryo to the next, despite fluc- phogen diffusion coefficient (D) andp itsffiffiffiffiffiffiffi typical tuations in the levels of signaling components, degradation time (a) such that l ¼ Da, and temperature differences, variations in size, or its overall level is proportional to the morpho- unequal distribution of components between gen production rate. daughter cells? Are there underlying mechan- Within this canonical paradigm, the sensi- isms that assure a reproducible response? Are tivity to changes in morphogen production these mechanisms conserved across species, rate is easily derived (Eldar et al. 2003). The similar to the signaling pathways they control? shift in cell-fate boundaries, dx, upon modulat- In this review, we outline insights we ing the morphogen production rate by some gained by quantitatively analyzing the process factor h, is proportional to the morphogen of morphogen gradient formation. We focus decay length l: on mechanisms that buffer morphogen pro- files against fluctuations in gene dosage, and dx ¼ l ln(h): (1) describe general means by which such buffering is enhanced. These mechanisms include self- This means that all thresholds are shifted by enhanced morphogen degradation and pre- the precise same amount, independently of steady-state decoding. In addition, we describe their position in the unperturbed system. a more specific “shuttling” mechanism that Thus, a single length scale, l, controls both is used to generate a sharp and robust profile the spread of the morphogen (its decay across of a morphogen activity from a source that is the field) and the sensitivity of patterning to broadly produced. We discuss the implication perturbations in morphogen production rate. of the shuttling mechanism for the ability of and dynamic range are thus inher- embryos to adjust their pattern with size. ently linked: The system can be readily made Finally, we consider the transformation of the less sensitive by reducing the decay length l˙, smooth gradient profile into sharp borders of but this will inevitably limit the spread of gene expression in the signal-receiving cells. the gradient. A gradient that spreads over most of the field requires l to be of the order of field size, and consequently will be highly CANONICAL PARADIGM OF MORPHOGEN sensitive to fluctuations in morphogen pro- GRADIENT FORMATION: INTERPLAY duction rate. BETWEEN DYNAMIC RANGE AND ROBUSTNESS The canonical model of morphogen gradient UNCOUPLING THE INTERPLAY: formation assumes that morphogen is secret- “SELF-ENHANCED DEGRADATION” ed from a localized source, and spreads across ENHANCES ROBUSTNESS WITHOUT LIMITING THE DYNAMIC RANGE OF THE the tissue while being degraded. The result- MORPHOGEN GRADIENT ing concentration gradient peaks at the source and decays gradually away from it. This The distribution of morphogens is typically general paradigm applies to a number of well- shaped by feedback loops. Morphogen signal- studied systems, including the gradient ing regulates the abundance or activity of in the early Drosophila embryo (Driever genes coding for receptors, heparan sulfate and Nu¨sslein-Volhard 1988b) and the Dpp, proteoglycans (HSPGs) or other regulatory Hedgehog, and Wingless gradients in the proteins, and a feedback loop is established

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Robust Generation and Decoding

when these molecules regulate the diffusion, other positions is independent of the rate by degradation, or production of the morphogen which morphogen is produced. Consequently, (Akiyama et al. 2008; Chen and Struhl 1996; if we shift the perturbed profile (corresponding Tsuda et al. 1999). In principle, such feedbacks to the system with modified production rate) by could buffer the morphogen gradient against just a bit along the position-axis, such that it genetic and environmental perturbations. will coincide with the nonperturbed profile at To explore the types of feedback that will just one point (e.g., the origin of the original uncouple the interplay between robustness system), the two profiles must coincide also and dynamic range, it is instructive to examine at all other points. This is because the two more closely the factors that control these two profiles (unperturbed and perturbed profiles properties in a general morphogen system in shifted x-coordinate) are now defined by (Eldar et al. 2003). Consider first the sensitivity precisely the same dynamic equations and the of the steady-state profile to changes in mor- same boundary conditions. A consequence of phogen production rate (Fig. 1). Morphogen this simple analysis is that all threshold positions production is localized to the origin (x ¼ 0), are shifted by the same amount, independent of and as such defines the boundary conditions their absolute position along the position-axis. for morphogen dynamics. Importantly, the We have noted this property when discuss- dynamics (diffusion and degradation) in all ing the properties of the exponential profile

A B 1 100 Wild type 0.8 Reduced production

0.6 10–1 0.4 Morphogen Morphogen 0.2

0 10–2 01234 01234 Position Position C D 1 100

0.8

0.6 10–1 0.4 Morphogen Morphogen 0.2

0 10–2 0123 0123 Position (shifted coordinates) Position (shifted coordinates) Figure 1. Shift morphogen in profile following perturbation in morphogen production rate. (A–B) Steady-state morphogen profiles. Shown is the steady-state profile of two models, differing only in the rate by which the morphogen is produced. In both models, the morphogen degrades linearly, with the same degradation rate, and diffuses with the same diffusion coefficient. The perturbed profile (green line) corresponds to morphogen that is produced at half the rate by which wild-type morphogen is produced (black line). The profiles are shown in linear scale (A) and log scale (B). The red arrow denotes the shift in profile. (C–D) The two steady-state morphogen profiles are related through a shift in the position coordinates. The perturbed profile is plotted in a new coordinate frame, obtained by shifting the original coordinates along the x-axis (defining new_x ¼ old_x þ D, with D as some fixed value). In these coordinates, the perturbed profile coincides with the wild-type profile (dashed gray line, plotted in the original coordinate system). The profiles are shown in linear scale (C) and log scale (D).

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N. Barkai and B.-Z. Shilo

(Equation 1, previously). The present discus- example, enhances the uptake and degradation sion concludes that this property holds more of Hh (Incardona et al. 2000), leading to generally for steady-state morphogen profiles, enhanced Hh degradation in the vicinity of its even in the presence of feedbacks (provided source. Specifically in the Drosophila wing that the profile decays sufficiently and rapidly imaginal disc, Hh is produced in the posterior across the field [Eldar et al. 2003]). compartment and signals to the adjacent cells Moreover, it is clear from the above anal- in the anteriorcompartment, which, in response, ysis that the shift in the morphogen profile induce Ptc expression (Chen and Struhl 1996). depends only on the rate by which morphogen This induction of Ptc results in increased profile decays close to the source (boundary). sequestering and degradation of Hh by the Robustness thus depends only on the dynamics receiving cells (Tabata and Kornberg 1994), properties close to the source. In contrast, thus likely increasing the robustness to fluctu- the spread of the gradient is a function of the ations in the level of Hh. Similarly, in the average decay of the profile throughout the zebrafish embryo, (RA) is pro- field. The case of no-feedback (exponential duced posterior to the hindbrain, and generates profile) is unique in the sense that the gradient a posterior-to-anterior gradient that specifies is defined by a single decay length (l). Hence, rhombomere location. RA signaling leads to in- the decay length in the vicinity of the source duction of cyp26a, a cytochrome p450 enzyme (which controls robustness) is the same as the that oxidizes RA to promote its removal from decay length everywhere, coupling robustness the tissue, thus generating an RA gradient that and dynamic range. is robust to fluctuations in RA synthesis Feedback regulation can result in a mor- (White et al. 2007). phogen profile that decays at multiple length scales, and can thus break the interplay PRE-STEADY-STATE DECODING between robustness and dynamic range (Eldar et al. 2003). A multitude of length scales is Most analyses of morphogen patterning assume achieved, for example, when morphogen signal- that the fate of the responding cells is deter- ing enhances morphogen degradation. In such mined by the morphogen gradient after the a case, morphogen decays rapidly close to the gradient had reached its steady state. However, source (where morphogen levels are highest) developmental processes often occur rapidly, but decays at a slower rate further away from and it is not clear whether the profile can con- the source (where morphogen levels are verge to its steady state within the restricted lower). Robustness is thus improved without time frame available. Moreover, temporal aver- comprising the dynamic range. The resulting aging throughout the kinetics is also possible gradient is not exponential. Rather, it is better and was shown to apply, e.g., in the readout of approximated by a power-law S(x) 1/xm. the morphogen gradient in The same uncoupling can be obtained also the vertebrate central nervous system (Dessaud if morphogen signaling alters the (local) diffu- et al. 2007). We also realized that feedbacks, sion coefficient (e.g., by modulating the level which shape morphogen gradients through of HSPG), such that diffusion becomes regulation of transcription or translation, are smaller in regions of high morphogen signaling lengthy, and might not be possible to use (Bollenbach et al. 2005). during rapid early development. Several theo- The robustness mechanism described above retical studies suggested that the morphogen is general, and does not depend on the precise signal might be read (decoded) before the means by which morphogen signaling impacts profile had reached its steady state (Gursky on morphogen degradation or diffusion. Self- et al. 2004; Mizutani et al. 2005; Saha and enhanced degradation was described in sev- Schaffer 2006). This motivated us to examine eral developmental contexts. The induction of whether the time at which the gradient is transcription by Hh signaling, for being decoded affects the sensitivity of the

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Robust Generation and Decoding

profile-to-morphogen production rate (Berg- because of its more rapid decay away from mann et al. 2007). the source. The mathematical formula describing the pre-steady-state morphogen profile is some- what more complex than that describing the PRE-STEADY-STATE DECODING OF steady-state distribution, precluding meaning- THE BICOID MORPHOGEN PROVIDES ful analytical manipulation. Still, the sensitivity QUANTITATIVE EXPLANATIONS TO A NUMBER OF UNRESOLVED PROPERTIES OF of the pre-steady-state profile to changes in THIS PATTERNING SYSTEM morphogen production rate can be predicted using straightforward numerical integration One of the best-studied examples of molecular (Bergmann et al. 2007). Two features that dis- gradients is that of Bicoid (Bcd), a maternally tinguish the pre-steady-state profile were encoded that plays a described. First, the shift in profile following a pivotal role in patterning the early Drosophila change in morphogen production rate is not embryo (reviewed in Ephrussi and Johnston uniform. Rather, thresholds positioned differ- 2004). Visualization of the graded Bcd dis- ently across the field shift to different extents tribution along the anterior–posterior axis of (Fig. 2). This is in contrast to the uniform the embryo provided the first experimental shift expected of the steady-state profile, as dis- demonstration that molecular gradients exist cussed previously. The reason for this difference (Driever and Nu¨sslein-Volhard 1988a,b). Bcd is that the morphogen profile does not converge induces the expression of different target to its steady state at a uniform rate everywhere. genes (termed “gap genes”) in a concentration- Rather, positions that are close to the source dependent manner, leading to their expres- converge rapidly, whereas positions that are sion in distinct spatial domains along the further away take a longer time to converge. anterior–posterior axis (Driever et al. 1989a; Consequently, at any point in time, different Driever and Nu¨sslein-Volhard 1989; Driever positions will be at different stages of their et al. 1989b; Johnston and Nu¨sslein-Volhard dynamics, and this will affect the shift in their 1992; Struhl et al. 1989). The pattern of gap position when morphogen production rate is gene expression is subsequently refined through perturbed. the cross-regulatory interactions between the A second interesting aspect is that, for most gap genes themselves, which, similar to Bcd, threshold positions, the sensitivity to morpho- function as transcription factors (Rivera- gen production rate is in fact lower when decod- Pomar and Ja¨ckle 1996). ing is performed before steady state has been Consistent with Bcd functioning as a reached (Bergmann et al. 2007). The reason morphogen, changes in the dosage of maternal for this smaller shift in the pre-steady-state Bcd cause a shift in the expression domains gradient has to do with differences in the of Bcd-target genes such as hunchback (hb). decay profile. Thus, although the steady-state Reducing Bcd dosage leads to an anterior profile decays exponentially, the rate by which shift, whereas increasing its dosage shifts the the pre-steady-state profile converges to this expression domains posteriorly. Surprisingly, limiting exponential pattern increases with however, several studies noted that the observed the distance from the source. Consequently, shifts are significantly smaller than expected before the steady state, the local steepness of by the simple morphogen model (Driever and the gradient increases with the distance from Nu¨sslein-Volhard 1988a; Houchmandzadeh the source. This increased steepness decreases et al. 2002). For example, in embryos derived the shift in threshold position upon a change from mothers bearing only one functional in morphogen production rate. It should be allele of bcd, the Hb expression domain shifts noted, however, that although this increased by only 7% embryo length (EL), about half steepness enhances robustness, it also com- of what is expected theoretically. These anoma- promises the dynamic range of the profile lous shifts in cell fates were recognized over two

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AB1 100 t = 0.1t 0.8 t = 0.3t t = 1t 0.6 t = 3t 10–2 t = 10t 0.4 Morphogen

0.2

0 10–4

C 100 D dx dx

dx dx –2 10 dx Morphogen

dx

10–4

1x bcd vs wt EF4x bcd vs wt 12

10

8

6 Shift ? x (%) 4

2

0 Anterior PosteriorAnterior Posterior (source) (source) Figure 2. Pre-steady-state decoding. (A, B) Temporal evolution of morphogen profile: The morphogen profiles at different time points, as indicated, are shown using either absolute levels (A) or normalized by their maximum at x ¼ 0(B). The morphogen degrades linearly at a rate f ¼ t21. Morphogen production began at time t ¼ 0. Time is in units of morphogen degradation time t.(C, D) Change in morphogen profile following reduction in production rate: The wild-type morphogen profile is compared with a perturbed profile, corresponding to morphogen that is produced twofold slower. dx denotes the shift between the wild-type and the perturbed profiles. Note the uniform shift for the steady-state profile (C), compared with the position-dependent shift for the pre-steady-state profile (D), where the shift decreases further away from the morphogen source. (E, F) Shifts in morphogen profile following reduction in production rate: Shown are the shifts in threshold positions following twofold reduction (E) or enhancement (F) in morphogen-production rate. The shifts are shown as a function of the position of the threshold in the unperturbed system, with the different lines corresponding to different pre-steady-state profiles, obtained following the initiation of morphogen production, at the indicated times. Symbols correspond to simulation of the full gap-gene system, as described in Bergmann et al. 2007.

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Robust Generation and Decoding

decades ago, in the early analysis of the Bcd gra- which were shown to be strongly position- dient (Driever and Nu¨sslein-Volhard 1988a), dependent (Bergmann et al. 2007): Anterior and were further emphasized by recent quanti- gap genes display a relatively high sensitivity tative measurements (Houchmandzadeh et al. to changes in Bcd dosage, whereas those that 2002). are expressed more posteriorly display a lower The simple morphogen model was further sensitivity. As discussed above, this position- challenged by several observations that seemed dependent shift is a signature of a pre-steady- to decouple the hb-expression domain from state decoding. the Bcd gradient. First, it was shown that Pre-steady-state decoding provides a parsi- changes in temperature alter the Bcd gradient monious explanation to other apparent mys- but do not influence the hb-expression domain teries characterizing the relationship between (Houchmandzadeh et al. 2002; Lucchetta et al. Hb and Bcd (Bergmann et al. 2007; Bergmann 2005). An additional difficulty was raised when et al. 2008). First and foremost, the measured the stochastic fluctuations in the binding shifts in Hb expression domain are fully of Bcd to gene promoters were considered explained by the corresponding changes in (Gregor et al. 2007a; Gregor et al. 2007b). It Bcd dosage. Second, at early times, greater dis- was argued, based on physical considerations, tances separate the nuclei, increasing the differ- that this noise is too high to allow distinc- ence in Bcd dosage between neighboring tion between the Bcd levels at two neighbor- nuclei, and limiting the impact of stochastic ing nuclei at the border of the hb-expression fluctuations. Finally, it was shown that Hb domain. Again, it was proposed that a novel, profile scales with the natural variations in yet to be determined mechanism is used embryo size whereas the Bcd profile does for ensuring the high precision by which the not (Driever and Nu¨sslein-Volhard 1988a; hb-expression domain is defined, as seen Houchmandzadeh et al. 2002). This, again, can experimentally. be explained by the pre-steady-state theory, We revisited these issues, and in particular under the additional assumption that Bcd tran- the anomalous shift in gap-gene expression smits rapidly between nucleus and cytoplasm domains, by examining the basic assump- (Gregor et al. 2007b). In such a case, the pre- tions leading to the apparent inconsistencies steady-state profile (defining Hb expression between the measured and the predicted shifts domain) scales with embryo size, whereas (Bergmann et al. 2007). In previous studies, the late, steady-state profile of Bcd does not the expected shifts in Hb expression domains (Bergmann et al. 2007). following a change in Bcd dosage were calcu- Experiments analyzing the Bcd gradient lated using Equation 1. This equation requires were reported recently (Gregor et al. 2007b), two parameters: l, the decay length of the but their interpretation is under debate morphogen, and h, the relative change in Bcd (Bergmann et al. 2008). Three different ap- dosage. Both parameters can be readily esti- proaches for measuring the Bcd diffusion mated: l is deduced from the measured Bcd coefficient gave a consistently low value of D profile, whereas h is well approximated by the 0.3 mm2/s (Gregor et al. 2007b). Considering change in the number of maternal copies of the relevant time scale in which patterning takes bcd. We noted, however, that the use of place (90 min following egg lay), and the Equation 1 is justified only if the profile had scale of the Bcd gradient (100 microns), reached its steady state. As we discussed pre- this diffusion coefficient is clearly inconsistent viously, the expected shifts are different if the with the steady-state assumption. In fact, even Bcd profile is decoded early, before reaching for pre-steady-state decoding, this low diffusion its steady state. A first indication that the entails a high production of the Bcd protein in steady-state assumption might not hold here order to allow for sufficient accumulation of was provided by the shifts in gap-gene ex- Bcd at mid-embryo, which enables the determi- pression domains upon change in Bcd dosage, nation of Hb transcription at early times.

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Interestingly, direct measurements of nuclear dorsal domain into several distinct regions of Bcd-GFP distribution in early embryos did gene expression. reveal a stable pattern as early as stage 10–11. The protein components involved in this This apparent contradiction might be recon- patterning system, as well as the interaction ciled by further analysis, which showed that between them, are well described. Still, the the total level of Bcd does in fact continue function of this patterning network depends to accumulate in embryos (Bergmann et al. on the quantitative values of the kinetic 2008). This analysis suggested that the overall parameters. In fact, changing the parameter profile has not yet reached its steady state, in values might not only alter the quantitative accordance with the pre-steady-state hypoth- dynamics, but also lead to a qualitatively differ- esis. Further clarification of these issues will ent mechanism for gradient formation. For require measuring the Bicoid degradation example, if only some of the proteins or com- time, and the time of gap genes determination plexes are allowed to diffuse, a gradient will be by the Bcd gradient, which are not yet available. established by a mechanism that is distinct from the case where all protein species are allowed to diffuse. The values of these kinetic NONCANONICAL GRADIENT FORMATION: parameters are largely unknown. How then ESTABLISHING A SHARP DISTRIBUTION can modeling assist in our understanding of FROM A SHALLOW SOURCE the patterning mechanism? Our discussion so far has focused on the canon- Our working hypothesis is that evolution ical model of morphogen gradient formation, favors a robust network design. Specifically, we which assumes that morphogen is secreted by assumed that the networks that function in a localized source, and diffuses to create a gradi- nature display minimal sensitivity to fluctu- ent that peaks at the source (Fig. 3A). Although ations in gene dosage or kinetic parameters. this model is applicable to many systems, other Because the subspace of robust networks is typi- cases exist where morphogen is in fact produced cally small, identifying a robust topology can in a broad domain but its activity is sub- predict the patterning mechanism, which can sequently restricted to a narrow area that is then be verified experimentally. well within its domain of expression (Fig. 3B). The best way to describe the function of Properties of gradients created by this paradigm a patterning network for an arbitrary set of are significantly less understood. parameters is to formulate a general enough The dorsoventral (DV) axis of the early model, and derive an analytical solution for Drosophila embryo is patterned by a graded the concentrations of the different molecular activity of the bone-morphogenetic protein species. Such an analytical solution, however, (BMP) (Ferguson and Anderson 1992). This is typically difficult to obtain, in particular for system provides a well-studied example for the the noncanonical paradigm for morphogen noncanonical strategy for morphogen gradient gradient formation, where several diffusing formation. Two BMP ligands (Screw and Dpp) and interacting species cooperate in establishing participate in this patterning, and both are the gradient. A numerical screen provides an broadly expressed: Dpp is produced in the alternative approach. The idea here is to start dorsal domain whereas Screw is produced from a general (“liberal”) model that is restricted throughout the embryo (reviewed by Raftery only by the known network topology, and to and Sutherland 1999). The key asymmetry solve this model systematically over a wide leading to the formation of a BMP-activation range of parameters. Each parameter choice gradient is the of the BMP inhibitor, consists of a particular “network.” The consis- Short gastrulation (Sog), from the neuroecto- tency of each network with experimental derm regions flanking the dorsal domain evidence or some other requirement (e.g., (Srinivasan et al. 2002). The resulting activation robustness) is then evaluated, and the properties gradient is sharp enough to subdivide the of the “consistent” networks are characterized.

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Robust Generation and Decoding

1 1 A Canonical model B Noncanonical 0.8 0.8 model

0.6 0.6

0.4 0.4 Activation level 0.2 Activation level 0.2 Activator InhibitorActivator Inhibitor 0 0 –1 –0.5 0 0.5 1 –1 –0.5 0 0.5 1 Position Position C D Inhibitor Inhibitor Total Total morphogen morphogen Concentration Concentration Activation Activation

D L V D L V

EFInhibition Shuttling

wt wt BMP activity BMP activity

Normalized position Normalized position G H Free inhibitor Robustness to change 2 in inhibitor dosage Complex 102 1.5

Wild type 1 1 10

Concentration 0.5 100 0 Activator concentration –1.5 –1 –0.5 0 0.5 1 1.5 –1.5 –1 –0.5 0 0.5 11.5 Position Position I Robustness to change 103 in activator dosage

102

101

100 Activator concentration –1.5 –1 –0.5 0 0.5 1 1.5 Position

Figure 3. Shuttling versus inhibition-based mechanism for gradient formation. (A) Canonical model for morphogen gradient formation: Morphogen is produced from a local source. Diffusion and degradation of the morphogen across the field leads to a concentration gradient that picks at the source and decays away from it. (B) Noncanonical model for morphogen gradient formation: Morphogen is produced in a broad domain but its activity is subsequently restricted to a narrow area that is well within its domain of expression. Restricted activity could be because of, e.g., an inhibitor secreted from the adjacent domains. (Continued)

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SHUTTLING MECHANISM: GENERATING A An alternative, shuttling-based mechanism SHARP AND ROBUST GRADIENT was also proposed (Holley et al. 1996), and was found to be implemented by the second We analyzed the BMP patterning network in class of networks (Fig. 3D). Here, the inhibitor Drosophila using the numerical screen approach Sog functions to physically translocate the BMP (Eldar et al. 2002). The results of this screen molecules to the dorsal region. The activation revealed two distinct mechanisms that can be used for establishing an activation gradient. gradient now reflects mostly the graded redistri- The first class of networks achieved patterning bution of the BMP molecules themselves, and by relying strictly on the inhibition of BMP by not the inhibition of their activity by graded its inhibitor Sog. Within this inhibition-based Sog. Shuttling is obtained when BMP diffuses mechanism (Fig. 3C), the inhibitor Sog diffuses primarily when bound by Sog. This binding into a region of uniform BMP, where it is also is also assumed to facilitate the degradation of cleaved by a protease (Tolloid). A gradient of Sog by its protease, Tolloid. Conversely, free inhibition is generated, leading to an inverse BMP does not readily diffuse, thus accumulat- activation gradient. This mechanism does not ing in the dorsal-most region where the levels require the redistribution of BMP molecules of free Sog are low. This lack of diffusion of themselves. Rather, BMP may still be uniformly Dpp could result, for example, from its rapid distributed, but its activity is now graded be- binding to receptors or to components of the cause of the graded distribution of its inhibitor. extracellular environment.

Figure 3. (Continued). (C) Inhibition-based patterning mechanism: A schematic representation of the inhibition-based mechanism. An inhibition gradient is generated through the localized secretion of an inhibitor and its degradation by a uniform protease. This inhibition gradient is established over a field of an activator. The activator may be uniformly distributed. Note that positive feedback of BMP expression may eventually result in graded BMP expression as well, but this is not required for the generation of the gradient itself, and does not constitute a main aspect of the patterning mechanism. The figure is based on the paradigm of early Xenopus patterning, with D, L, and V standing for dorsal, lateral, and ventral regions of the embryo, respectively. Inhibitor is shown in gray, activator in black, and the total activator (free and in complex with the inhibitor) in dashed black. (D) Shuttling-based patterning mechanism: A schematic representation of the shuttling-based mechanism. Patterning here relies mostly on the physical translocation of the BMP ligands to the ventral region. The activation gradient thus arises primarily from the graded distribution of the BMP ligands themselves. Effective shuttling requires that the binding of to the inhibitor greatly facilitates its diffusion, and that the free ligand is released by cleavage of the complex. Notations are the same as those in A.(E) Inhibition-based profile does not scale: Shown is a typical profile of BMP activation within the inhibition-based model. The profile was solved twice: first for parameters simulating wild-type embryos and second for dorsal-half embryos (same parameters, but embryo’s size halved). The profiles are shown in scaled coordinates. Note the different profiles corresponding to the wild-type versus half embryo. (F) Scaling of shuttling-based profile: A typical profile of BMP activation within the shuttling-based model. The profile was solved twice: First for parameters simulating wild-type embryos and second for dorsal-half embryos (same parameters, but embryo’s size halved). The profiles are shown in scaled coordinates. Note the accurate scaling of the profiles corresponding to the wild-type versus half embryo. (G–I) Robustness of shuttling-based mechanism. (G) Inhibitor profile is not robust: The profile of the inhibitor is not robust to dosage of the inhibitor or the protease. In fact, changing the inhibitor dosage causes a proportional change in its spatial profile, as is shown in the figure. (H ) Robustness of the activation profile to the levels of inhibitor: The activation profile is robust to changes in inhibitor or protease because of the fact that the level of inhibitor-activator complex, which is uniform throughout the field and functions as a global integrator, is also altered in proportion to the change in the inhibitor dosage. Because the free activator does not diffuse, its level at any point in space is given by the ratio between the complex and free inhibitor, which is independent of the inhibitor or protease dosages. (I) Robustness of the activation profile to the levels of activator: The activation profile is also robust to the total level of activator. This, again, is because of the fact that the free activator does not diffuse. Lack of diffusion allows the storage of any excess activator in the dorsal-most region, where no inhibitor is present.

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Robust Generation and Decoding

As expected, both mechanisms can establish on environmental factors (e.g., nutrition and a graded BMP activation profile. The mecha- temperature) or specific genetic polymor- nisms differ substantially, however, in the phisms. The must be adjusted to sharpness of the resulting profile and also in these size fluctuations to maintain proper its robustness. Gradients established by the proportions between the different tissues or inhibition-based mechanism are relatively shal- organs. How this scaling of pattern with size is low, and are highly sensitive to the dosages of achieved mechanistically is largely unknown. the inhibitor, activator, or protease. In contrast, The ability of embryos to scale pattern with the shuttling-based mechanism defines a much size was emphasized most dramatically in two sharper profile, and this profile is robust to classical experiments performed by Hans changes in gene dosage (Eldar et al. 2002; Spemmann at the beginning of the century Meinhardt and Roth 2002). The mechanisms (reviewed in De Robertis 2006). The first exper- ensuring the robustness of the activation iment showed that dorsal-half embryos grow to profile to the dosage of the inhibitor or the pro- generate a complete and well-proportioned tease, and to the dosage of the activator itself, embryo, albeit smaller in size. The second are explained in Figure 3G,H, respectively. experiment shows that transplanting a dorsal The finding that the shuttling-based mecha- group of cells from one embryo to the ventral nism confers a significantly higher robustness side of a second embryo generates a twinned led us to propose that this mechanism operates tadpole. Here also, both axes are well- in Drosophila. This prediction was confirmed proportioned and include dorsal, lateral, and experimentally in the Drosophila embryo ventral tissues. The precision of scaling, and (Eldar et al. 2002; Mizutani et al. 2005; Shimmi the lack of compensatory growth, was further et al. 2005; Wang and Ferguson 2005) (review illustrated in subsequent quantitative exper- by O’Connor et al. 2006) and was subsequently iments (Cooke 1981). also shown to be used for patterning the What is the mechanistic basis for scaling? embryonic DV axis in short-germ insects (van One of our motivations in addressing this der Zee et al. 2006). question was the fact that the patterning Notably, this strategy for creating a pattern network involved is largely homologous to the is particularly useful for early embryos, where network that patterns the dorsal region of distinct yet broad zygotic gene expression the early Drosophila embryo, discussed above domains are defined, but a highly restricted (De Robertis and Kuroda 2004; Holley and source for morphogen production has not Ferguson 1997). In fact, in all bilatera, DV pat- been generated yet. The physical concentration terning of the early embryo involves a graded of ligand by shuttling molecules provided BMP activation profile, although in vertebrates by adjacent tissues can thus generate a sharp the positions are inverted with respect to and robust morphogen profile, even in the Drosophila, i.e., maximal activation by BMP absence of a restricted morphogen expression takes place at the ventral side. Other com- source. ponents of the patterning network are also conserved. For example, the key asymmetry in generating the BMP activation gradient in SHUTTLING OF BMP LIGANDS IN amphibians relies on the localized secretion of XENOPUS: IMPLICATION FOR THE a BMP inhibitor (including Chordin, homol- SCALING OF PATTERN WITH SIZE ogous to Sog), which is produced at the dorsal So far, we focused on the property of robustness, region by cells of the “Spemman organizer” defined as the quantitative ability to buffer fluc- (De Robertis and Kuroda 2004). An important tuations in gene dosage or kinetic rate con- difference between the Drosophila and ver- stants. The embryo, however, faces additional tebrate systems, however, is the use of a unique sources of variability, most notably fluctuations BMP ligand in vertebrates, Admp (Reversade in size. Embryo size can differ greatly, depending and De Robertis 2005), which is repressed by

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N. Barkai and B.-Z. Shilo

BMP signaling and accordingly is expressed demarcated by sharp borders. This poses a together with the BMP inhibitor Chordin in challenge for the responding cells: how to the dorsal region, where pathway activation is sense small differences in morphogen activation lowest. profile, and execute one of several alternative Using a numeric screen for networks that gene expression programs, accordingly. Coop- support scaling, we identified again the shutting erative binding to the regulatory region of the mechanism.This mechanism provided a simple, responding target gene provides one solution, quantitative explanation for the capacity of the and is used, for example, in the responses Xenopus embryo to scale pattern with size to the early Bicoid or Dorsal gradients in (Ben-Zvi et al. 2008). The key for scaling was Drosophila embryos (Jiang and Levine 1993; the shuttling of two types of BMP ligands, a Struhl et al. 1989). The degree of cooperativity canonical one (BMP) and noncanonical one determines the sharpness of the response, and (Admp), both of which compete for binding the binding affinity dictates the position of to the inhibitor Chordin. This competition the borders of expression with respect to the allows for a range of possible activation profiles, source of the gradient. depending on the relative amount of the two We sought alternative mechanisms for ligands in the system. The precise activation generating threshold responses. The ETS- profile can thus be controlled by modulating transcription factor Pointed executes most of the levels of the two BMP ligands. Importantly, the transcriptional responses following EGF these levels are in fact controlled through feed- activation in Drosophila (Gabay et al. back loops. In particular, Admp expression is 1996). Different Pointed isoforms are acti- repressed by the BMP pathway. This repression vated at the transcriptional or posttranscrip- provides an effective means for measuring the tional level, by MAP kinase phosphorylation. size of the embryo and adjusting the morphogen In parallel, the repressor ETS-domain protein profile accordingly. Yan is phophorylated by MAP kinase, leading More precisely, note that the repression of to its nuclear export and degradation. The Admp by BMP signaling functions to “pin” the sharp border of Yan degradation, which is magnitude of BMPactivation at the dorsal-most well within the domain of graded activation side to a precise value, defined by the threshold of the EGF receptor (Fig. 4), prompted us to at which Admp expression is repressed. Once examine the mechanism in detail. this boundary level of the activation gradient Goldbeter and Koshland have suggested had been determined, the rest of the gradient that sharp borders can be defined by a mecha- will follow, resulting in a robust scaling of the nism they coined “zero order ultrasensitivity” morphogen profile (both length scale and (Goldbeter and Koshland 1981; Goldbeter amplitude) with embryo size. Intriguingly, and Wolpert 1990). This mechanism considers we find that this scaling mechanism functions a reversible reaction in which substrate is, for through an effective implementation of an example, phosphorylated and dephosphory- integral-feedback controller, a key concept in lated, and assumes that the substrate is in engineering (Barkai and Ben-Zvi 2009). excess, allowing both reactions to occur at zero order (saturation). Under these conditions, the rate of reactions is practically independent GRADIENT INTERPRETATION: USING of the concentration of the substrate. All SHALLOW GRADIENTS TO DEFINE substrate will thus accumulate as one of the SHARP ACTIVATION BORDERS forms, depending simply on the difference Because the distribution of a morphogen is in the rates of the forward and backward governed by diffusion processes, its profile is reactions. Because the rates of the reactions smooth, decaying gradually between adjacent depend on the concentration of the modifying cells. This continuous distribution is converted and de-modifying enzymes, this system is ultra- to well-defined domains of gene expression, sensitive to small changes in the concentrations

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Robust Generation and Decoding

AB

dpERK Yan

CD E1 MAPK*

a YYp Yan Yanp dp d

E2 Phosphatase Figure 4. Generating threshold responses by zero-order ultrasensitivity. (A) In awild-type embryo (stage 10), the activating ligand Spi emanates from the ventral midline (arrowhead), triggering EGF receptor in the adjacent cells, and leading to graded activation of MAP kinase that is detected with dpERK antibodies (red). (B) Within the domain of MAP kinase activation (dashed white line), the degradation pattern of Yan (green, full line) at the same stage shows a much more restricted and sharp response. (C) A classical zero-order hypersensitivity model, showing the reversible conversion of a substrate between two states, and the dependence of the final product only on the difference between the rate of opposing enzymatic reactions. (D) In the case of the Yan degradation network, in addition to phosphorylation by MAP kinase (MAPK) and dephosphorylation by unknown proteases, aspects such as synthesis and degradation have to be considered. Similar to the classical model, a switchlike behavior is generated when the substrate is in excess with respect to the dissociation constants for the two opposing enzymes.

of these enzymes, being able to respond to small transcription factors can be achieved by this changes in these concentrations in a switchlike mechanism. manner (Fig. 4). In accordance with this model, we were able CONCLUDING REMARKS to show that the degradation of Yan follows zero-order kinetics (Melen et al. 2005). An The studies described in this review represent elevation in the level of Yan did not alter the our initial foray to address patterning by mor- position of the threshold, but led to an increase phogens in a quantitative and computational in the time to reach steady state, which was manner. This analysis is enlightening, as the directly proportional to the excess level of Yan cells sense not only the presence or absence of that was produced. This mechanism provides the morphogen, but elicit a variety of responses several advantages. First, it generates a sharp that are highly dependent on the level of acti- threshold. Second, the same kinase-activity vation by the morphogen. Most importantly, gradient could generate distinct thresholds for beyond the quantitative analysis of the response, different transcription factors, depending on our approach examines the mechanisms the affinity. Finally, in a noisy and fluctuating that buffer fluctuations to allow a reproducible environment, having a large substrate pool, output. The feature of robustness imposes con- which is completely phosphorylated or non- straints on the emerging solutions, and guides phosphorylated, may buffer against temporal us toward the biologically relevant mechanisms. fluctuations in activity, as well as against From what we have learned so far, are noise. It will be interesting to determine if there any generalities we can draw on regarding sharp thresholds of activated (phosphorylated) the mechanisms that provide robustness? First,

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N. Barkai and B.-Z. Shilo

these mechanisms are not absolute, but only Chen Y,Struhl G. 1996. Dual roles for patched in sequester- minimize the effects of fluctuations. Second, ing and transducing Hedgehog. Cell 87: 553–563. Cooke J. 1981. Scale of body pattern adjusts to available cell diverse strategies seem to be used, and are number in amphibian embryos. Nature 290: 775–778. adapted to each of the systems. In the case of De Robertis EM. 2006. Spemann’s organizer and self- ligand-induced degradation, the morphogen regulation in amphibian embryos. Nat Rev Mol Cell distribution close to the source is uncoupled Biol 7: 296–302. from its distribution away from the source. De Robertis EM, Kuroda H. 2004. Dorsal-ventral patterning and neural induction in Xenopus embryos. Annu Rev Cell For the Bicoid gradient, early decoding Dev Biol 20: 285–308. before steady state may minimize fluctuations. 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Robust Generation and Decoding of Morphogen Gradients

Naama Barkai and Ben-Zion Shilo

Cold Spring Harb Perspect Biol published online August 5, 2009

Subject Collection Generation and Interpretation of Morphogen Gradients

Regulation of Organ Growth by Morphogen Gradients in Planarian Regeneration and Gradients Homeostasis Gerald Schwank and Konrad Basler Teresa Adell, Francesc Cebrià and Emili Saló Signaling Gradients during Paraxial Mesoderm Shaping Morphogen Gradients by Proteoglycans Development Dong Yan and Xinhua Lin Alexander Aulehla and Olivier Pourquié Morphogen Gradient Formation Forming Patterns in Development without Ortrud Wartlick, Anna Kicheva and Marcos Morphogen Gradients: Scattered Differentiation González-Gaitán and Sorting Out Robert R. Kay and Christopher R.L. Thompson Nodal Morphogens Robust Generation and Decoding of Morphogen Alexander F. Schier Gradients Naama Barkai and Ben-Zion Shilo Gradients and the Specification of Planar Polarity Models for the Generation and Interpretation of in the Insect Cuticle Gradients David Strutt Hans Meinhardt Vertebrate : Moving from Graded Dorsal and Differential Gene Regulation in Classical Morphogen Gradients to an Integrated the Drosophila Embryo 4-Dimensional Patterning System Gregory T. Reeves and Angelike Stathopoulos Jean-Denis Bénazet and Rolf Zeller Establishing and Interpreting Graded Sonic Chemical Gradients and Chemotropism in Yeast Hedgehog Signaling during Vertebrate Neural Robert A. Arkowitz Tube Patterning: The Role of Negative Feedback Vanessa Ribes and James Briscoe Systems Biology of the Self-regulating Gradients in the Brain: The Control of the Morphogenetic Gradient of the Xenopus Gastrula Development of Form and Function in the Jean-Louis Plouhinec and E. M. De Robertis Cerebral Cortex Stephen N. Sansom and Frederick J. Livesey

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