Robust Generation and Decoding of Morphogen Gradients Naama Barkai1,2 and Ben-Zion Shilo1 1Department of Molecular Genetics, 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 gene 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 gene expression 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 genes, 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; doi: 10.1101/cshperspect.a001990 Cite this article as Cold Spring Harb Perspect Biol 2009;1:a001990 1 N. Barkai and B.-Z. Shilo In the past three decades, many of the com- Drosophila 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 Robustness 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 Bicoid 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 2 Cite this article as Cold Spring Harb Perspect Biol 2009;1:a001990 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