SYSTEMS BIOLOGY

Morphogen gradient reconstitutionreveals Hedgehog pathwaydesign principlesPulin Li,1* Joseph S. Markson,1* Sheng Wang,1 Siheng Chen,1

Vipul Vachharajani,1 Michael B. Elowitz1,2†

In developing tissues, cells estimate their spatial position by sensing gradedconcentrations of diffusible signaling proteins called morphogens. Morphogen-sensingpathways exhibit diverse molecular architectures, whose roles in controlling patterningdynamics and precision have been unclear. In this work, combining cell-based in vitrogradient reconstitution, genetic rewiring, and mathematical modeling, we systematicallyanalyzed the distinctive architectural features of the Sonic Hedgehog pathway.We foundthat the combination of double-negative regulatory logic and negative feedback through thePTCH receptor accelerates gradient formation and improves robustness to variation inthe morphogen production rate compared with alternative designs.The ability to isolatemorphogen patterning from concurrent developmental processes and to compare thepatterning behaviors of alternative, rewired pathway architectures offers a powerful wayto understand and engineer multicellular patterning.

During development and regeneration, tis-sue patterning unfolds with astonishingprecision in space and time. Diffusible sig-naling molecules known as morphogensprovide a key patterning mechanism. Mor-

phogens are secreted by sender cells and formconcentration gradients that are interpreted bycognate signaling pathways in receiver cells togenerate distinct cell fate domains (1). Morphogen-sensing pathways have diverse regulatory archi-tectures that actively process intracellular signalsand modulate the abundance of extracellularmorphogens (2, 3). However, the roles of thesefeatures in pattern formation have generally re-mained unclear. To address this gap, we devel-oped a system to reconstitute patterning in cellculture and used it to directly compare the pat-terning behaviors of natural and rewiredmorpho-gen pathways (Fig. 1A).We focused on the Hedgehog (HH) pathway,

a classic long-range morphogen system that isimplicated in developmental diseases and cancer(4). Unlike other morphogen pathways, in whichligands positively activate their receptors, theHH pathway uses a distinctive “double-negative”activationmechanism (Fig. 1B): UnligandedPTCHreceptors suppress intracellular pathway activity,and this suppression is relieved by HH ligandbinding. Furthermore, by sequesteringHH, PTCHreceptors alsomodulate the ligand’s extracellularspatial distribution. The combination of theseintracellular and extracellular activities makesPTCH effectively bifunctional (5). Lastly, HH sig-

naling up-regulates PTCH expression, generatingnegative feedback through both inhibition of in-tracellular signaling and sequestration of extra-cellular ligands (6–8). Despite much work, thefunctional rationale for this pathway architec-ture has largely remained obscure.We reconstituted HH signaling gradients in

NIH 3T3 cells, which transduce HH signals with-out differentiating and do not naturally expressHH ligands (9). We generated an inducible sen-der line by placing the wild-type Sonic Hedgehog(Shh) coding sequence under the control of a4-hydroxytamoxifen (4-OHT)–inducible system(Fig. 1C). We also engineered a receiver cell linecontaining a synthetic construct in which GBS(GLI-binding site) sequences recognized by thedownstream transcription factor GLI drive theexpression of nuclear-localized H2B-Citrine fluo-rescent protein (10, 11). Reporter expression re-sponded to SHH in a dose-dependent mannerand correlated with endogenous SHH pathwaytargets (fig. S1). Diluting sender cells in a 1000-foldexcess of receivers produced radial gradients ofSHH signaling extending from single sendercells, reaching a limiting size of about four orfive cell diameters (80 to 100 mm) over a timespan of 60 hours (Fig. 1D). Additionally, tomimicquasi–one-dimensional contexts, such as limbbuds, neural tubes, and Drosophila wing discs(12), we used a cell culture insert system to platesenders and receivers in adjacent, contiguous re-gions (Fig. 1E). In this configuration, gradientsextendedmore than ~200 mm. These results showthat SHH signaling gradients with sizes com-parable to naturally occurring gradients can begenerated by coculturing synthetic senders andreceivers in vitro.In principle, SHHgradients could form through

diffusion of ligands in the liquid medium orthrough lateral movement of ligands within the

cell layer (as by diffusion in the extracellularmatrix or transport along filopodia) (13–16).To distinguish between these two possibilities,we analyzed gradient formation on a laboratoryrocker, which should disrupt media-based gra-dients. However, rocking had no effect on gra-dients (Fig. 1F). In a second experiment, wecultured senders and receivers on coverslip frag-ments separated by a 30-mmgap. This gap, whichis much shorter than the gradient length, wassufficient to prevent activation of receivers bysenders (Fig. 1G). In contrast, when the cover-slipswere directly adjacent (no gap), the gradientformed normally. Both experiments indicate that,under these conditions, the SHH gradient formspredominantly throughmovement within the celllayer, requiring cell-cell contact or continuousextracellular matrix (17). In addition, cell migra-tion and division have minimal effects on gradientformation owing to their low rates in this context,but they could play more substantial roles innatural contexts (fig. S2, B to D).The ability to reconstitute gradient formation

in cell culture enabled us to explore the functionalimplications of the SHH pathway architecture.We first focused on the unusual double-negativelogic of the core pathway (Fig. 1B) by eliminatingthe feedback on PTCH (table S1) to create a sim-pler, “open-loop” receiver cell line (Fig. 2A). Weknocked out both endogenous Ptch1 alleles andintegrated a copy of Ptch1 under a doxycycline(Dox)–inducible promoter (fig. S3). Coculturingthis open-loop cell line adjacent to sender cellsallowed us to observe the dynamics of open-loopgradient formation across a matrix of SHH andPTCH expression levels (Fig. 2, B to D; fig. S4, Aand B; and movies S1 and S2). Analysis of theresultingmovies revealed that elevating the SHHproduction rate increased gradient amplitudeand extended the length scale, whereas elevatingthe PTCHproduction rate had the opposite effect(Fig. 2D and fig. S4C). Gradient length scale andamplitude specifically depended on the ratio ofSHH and PTCH production rates (Fig. 2E andfig. S4D).To understand this ratiometric behavior, we

constructed a minimal mathematical model ofthe core pathway (fig. S5A). This model assumesthat free PTCH promotes production of the re-pressor form of GLI (GLIR), which in turn in-hibits target gene expression. Binding of PTCHto HH inactivates both proteins, decreasing GLIRproduction.We fit themodel to experimental datafor a range of SHH production rates at a singlePTCH level (fig. S5, B to D, and table S2) (17). Themodel recapitulated ratiometric length-scale andamplitude control across a broad range of PTCHexpression levels (Fig. 2F and fig. S5E). Furtheranalysis revealed that double-negative regulatorylogic is sufficient for ratiometric control (17). Thisbehavior was preserved when additional factors,such as the activating form of GLI, were incor-porated (fig. S6) (18). Together, these resultsshow that control of gradient properties is sharedby both senders (through the SHH productionrate) and receivers (through the PTCH produc-tion rate) in the open-loop configuration.

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1Division of Biology and Biological Engineering, CaliforniaInstitute of Technology, Pasadena, CA 91125, USA. 2HowardHughes Medical Institute and Department of Applied Physics,California Institute of Technology, Pasadena, CA 91125, USA.*These authors contributed equally to this work.†Corresponding author. Email: melowitz@caltech.edu

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Ratiometric control provides robustness tocorrelated changes in SHH and PTCH expres-sion that preserve their ratio, but it implies sen-sitivity to perturbations in these parametersindividually. Deletion of one SHH allele has noobvious phenotype in mice (19). Although it isnot known whether gene dosage directly affectsthe level of secreted SHH, this nevertheless sug-gests that the system may have intrinsic mech-anisms to buffer variations in the morphogenproduction rate.

We hypothesized that negative feedback result-ing from the highly conserved, SHH-dependentup-regulation of PTCH expression could providerobustness to SHH expression level (20–22). Torepresent this feedback in the model, we intro-duced a GLI-dependent PTCH production term,with a single new parameter for feedback strength,defined as the amount of PTCH expression for agiven level of signaling (Fig. 3A and fig. S7). Insimulations, the PTCH feedback had three effects.First, it enhanced the robustness of gradient am-

plitude and length scale to variations in ligandproduction rate (Fig. 3B). Second, it acceleratedthe approach to steady state (Fig. 3C). Third, itpreserved the relatively linear gradient shape asHH production rate increased, whereas the open-loop gradients became increasingly plateau-like(Fig. 3, D and E). Linear profiles have been sug-gested to maximize the extent of the “useful” re-gion for patterningmultiple cell fate domains (23).To understandwhat features of PTCHproduce

these advantageous effects, we considered alternative

Li et al., Science 360, 543–548 (2018) 4 May 2018 2 of 6

Fig. 1. In vitro reconstitution of morphogen signaling gradients.(A) Reconstitution enables quantitative analysis of the spatiotemporalpatterning dynamics, including length scale (ruler) and speed (clock),generated by natural morphogen pathways, as well as by minimal andrewired variants. The sensitivity of circuit variants to perturbations, suchas changes in ligand production, can also be determined. The variouscomponents of the schematic are clarified in the subsequent panels.(B) The distinctive combination of architectural features in the Hedgehog(HH) pathway. (C) Sender and receiver cell lines for reconstituting theSHH signaling gradient in wild-type NIH 3T3 cells. Senders constitutivelyexpressing GAL4 fused to a mutant estrogen receptor (ERT2) andmTurquoise2 (mTurq2) fused to histone 2B (H2B) produce SHH uponinduction with 4-hydroxytamoxifen (4-OHT). An 8×GLI-binding sequence(GBS) driving H2B-Citrine expression reports pathway activity in receivers.

(D and E) Reconstituting SHH signaling gradients in radial and linear geo-metries. Blue and yellow cells (schematic) represent senders and receivers,respectively, and the varying opacity of the yellow shading corresponds to thelevel of intracellular pathway activity. Arrows indicate the direction of gradientpropagation. In the radial gradients [n = 13 (D)], all activation was due to asingle sender cell (blue, near the center of the dashed circle that indicates thegradient’s outer edge). In the linear gradients [n = 7 (E)], the white dashed lineindicates the boundary between sending and receiving fields. (FandG) Ligandtransport requires continuous cell or extracellular matrix contact. In principle,ligand transport could involve bulk diffusion through the medium [upperschematic in (F)] or lateral movement within the cell layer [lower schematic in(F)]. Gradient formation is unaffected by rocking that should disturb bulkdiffusion [n = 8 (F)] and is blocked by a 30-mm gap between senders andreceivers [n = 5 (G)]. Error bars (F) and shading (G), SEM. a.u., arbitrary units.

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feedback schemes mediated by hypotheticalPTCH-like proteins possessing subsets of itsfeatures (Fig. 3A and fig. S7, A and B). Feedbackthrough a protein denoted “I,” possessing onlyPTCH’s intracellular signal inhibition activity,provided amplitude robustness but exacerbatedlength-scale sensitivity (Fig. 3B and figs. S7, Cand D, and S8). On the other hand, feedbackthrough a protein denoted “E,” possessing onlyPTCH’s ligand-binding activity, provided length-scale but not amplitude robustness [consistentwith studies of self-enhanced ligand degradation(21)]. Furthermore, simply coexpressing I and Etogether in a single “uncoupled” model was notsufficient to reproduce the benefits of the PTCHfeedback (Fig. 3, B to E, and fig. S7, C and D). Amodel in which I and E were physically tethered,but where the intracellular activity persisted evenwhen the extracellular domain was bound to lig-and, also did not provide PTCH-like robustness(fig. S9D). Thus, the bifunctional nature of PTCH—

specifically, its ability to switch between intra-cellular inhibition (ligand-free) and extracellularsequestration (ligand-bound) states—is essentialfor the robustness provided by this feedbackmech-anism. The coupling of multiple functions in thesameprotein has similarly been shown to promoterobustness in other biological contexts (24).The differences between PTCH and uncoupled

feedbacks can be understood in terms of theirdivergent responses to high ligand concentra-tions (fig. S8). In both models, high ligand levelscan deplete the extracellular feedback compo-nent (E or PTCH). With the PTCH feedback, thissimultaneously reduces the intracellular activity,which in turn activates the pathway, replenish-ing PTCH and thereby continuing to limit ligandpenetration. In contrast, in the uncoupled model,depletion of E does not directly reduce I; thisresults in a disproportionate accumulation of I,which blocks replenishment of E by suppressingsignaling. In this way, the uncoupled model fails

to keep upwith increasing ligand expression levels.The benefit of the PTCH feedback comparedwith the uncoupled feedback persists even if theI and E feedback strengths are independentlyfine-tuned (fig. S9, A to C). These qualitative dif-ferences among feedback models are preservedin models that incorporate the activator form ofGLI, positive feedback on GLI expression, or tem-poral adaptation through GLI down-regulation(figs. S6 and S10 to S12).To experimentally test the prediction that the

PTCH feedback improves the speed and robust-ness of gradient formation, we designed a syn-thetic feedback (SynFB) pathway in which SHHsignaling up-regulates PTCH1 expression (Fig. 4A).We placed the Tet3G activator under SHH sig-naling control by using an additional copy of theGBS promoter (Fig. 1C and fig. S1A). The SynFBdesign mimics the natural PTCH1 feedbackbut allows continuous modulation of feedbackstrength through Dox concentration, from an

Li et al., Science 360, 543–548 (2018) 4 May 2018 3 of 6

Fig. 2. Open-loop SHH pathway architecture produces gradientssensitive to variations in key parameters. (A) Engineering open-loopreceiver cells. Both Ptch1 alleles in wild-type receivers were deleted andreplaced by ectopic Ptch1 under Tet-3G control, enabling graded tuning ofPTCH1 abundance with doxycycline (Dox), indicated by coexpression ofmCherry (mChr). (B) Time-lapse images of representative radial and linearSHH signaling gradients. Dashed lines are as in Fig. 1. (C) Quantifyingspatiotemporal dynamics of linear signaling gradients. Total fluorescence(upper plot) reflects the time-integrated pathway activity (mean of n = 8).Thetime derivative of Citrine (lower plot) approximates instantaneous pathway

activity over space and time (fig. S1C). (D) Signaling gradient sensitivity tovariations in SHH and PTCH1 production rates (aHH and aPTC, respectively).aHH was increased by varying the sender density (upper panel), whereas aPTCwas increased in the receivers by varying the Dox concentration (lower panel).(E) The ratio of aHH to aPTC determines gradient length scale, defined by thedistance at which the signal drops to 1/e of the amplitude.The aHH/aPTCratio also controls gradient amplitude, defined by the signaling strengthin the cells closest to the boundary (fig. S4D). Error bars, SEM. (F) A simplemodel recapitulates the ratiometric dependence of gradient properties on aHHand aPTC (fig. S5E). Relative aHH is an arbitrary unit.

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open-loop regime to a strong closed-loop regimeexceeding the feedback strength of wild-type 3T3cells (fig. S13, A to C). Movies of gradient forma-tion in the SynFB cell line revealed that the PTCHfeedback accelerated the approach to steady state,made both the amplitude and the length scale ofthe signaling gradient less sensitive to variationsin ligand production rates, and improved thelinearity of the gradient (Fig. 4, B to D; fig. S13,D to F; and movies S3 to S6). Furthermore, themagnitude of improvement increased with thestrength of the feedback (fig. S13D). These resultsare consistent with model predictions.As a further test of the model, we constructed

a cell line incorporating a synthetic intracellularfeedback (Fig. 4E). We substituted a PTCH mu-tant, PTCH1DLoop2, which is unable to bind ligand,for wild-type PTCH1 in SynFB (25) (Fig. 4E and

fig. S14). As predicted by the model, these cellsproduced gradients whose amplitudes were morerobust to ligand production rate and whose lengthscales and shapes were more sensitive (Fig. 4Eand fig. S13F). Together, these results demonstratethat the PTCH feedback architecture has theremarkable capability of both reducing gradi-ent sensitivity to variations in ligand productionrates and accelerating the approach to steadystate, providing a functional rationale for thishighly conserved feature of the HH pathway(6–8).Spatial patterning is an active process inwhich

the dynamics of the morphogen and those of itssignaling pathway are intertwined. Comparedwith analysis of embryos, reconstitution of mor-phogen gradient formation in vitro provides sev-eral advantages: It avoids interference from other

processes and pathways (isolation), permits quan-titative control of key parameters, allows rewiringof regulatory interactions, and facilitates straight-forward analysis of patterning dynamics in spaceand time. In this case, reconstitution revealed howthe distinctive combination of features in theHHpathway provides a compact, elegant design so-lution to the challenge of rapidly generating ro-bust gradients (Fig. 4F and fig. S9C). Future workshould help to extend the bottom-up approachdeveloped here to more complex phenomena byincorporating downstream signal interpretationcircuits (26) and integrating with additional, con-current, morphogenetic patterning processes (27).The HH architecture contrasts sharply with

that of other morphogen pathways, such as BMP(bone morphogenetic protein) or FGF (fibroblastgrowth factor), in which ligands activate receptors,

Fig. 3. Mathematical modeling shows that the PTCH feedbackimproves patterning performance by physically coupling intracellularand extracellular activities. (A) A negative feedback can act intra-cellularly by inhibiting signaling (IC feedback) or extracellularly bysequestering ligand (EC feedback). These functionalities can coexist,implemented either through separate molecules (uncoupled feedback)or through a bifunctional molecule such as PTCH (PTCH feedback).(B) Steady-state gradient length scale and amplitude as a function ofaHH (marker size) for different models. The feedback strengths for the ICand EC models were fine-tuned so that the amplitude or length scale,respectively, matches that of the PTCH feedback at relative aHH =0.0625. Those same feedback strengths were used for the uncoupledmodel, but the qualitative differences between those models hold

across all nonzero feedback strengths (figs. S7, C and D, and S9, A andB). The same feedback strengths were used for (C) to (E). (C) Timeto reach steady state (t) for each model as a function of aHH and l50, theposition at which steady-state signal activity equals 50% of theamplitude. t is the first time point at which signal activity reaches 90%of its steady-state value at l50 (schematic). (D) Amplitude-normalizedsignaling gradient profiles for the open-loop, uncoupled, and PTCHfeedback models at different relative values of aHH (0.0625, 0.25, 0.50,and 1.0) show distinct trends in length scale and shape. (E) Only thePTCH feedback maintains a constant gradient shape with increasingaHH. The shape factor q equals the ratio of the width of the second thirdof the gradient (L2) to the width of the first third of the gradient(L1) (schematic).

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which in turn activate intracellular effectors. These“double-positive” architectures should exhibit adifferent dependence on ligand and receptor levels(17). Compared with the HH pathway, receptorfeedback appears to be less pervasive in these

systems, provoking the question of whether theypossess alternativemechanisms to achieve similarpatterning capabilities, or whether they are opti-mized for distinct spatiotemporal behaviors (28).The approaches developed here should provide

general insights into the performance trade-offsamong differentmorphogen systems and establisha platform for designing synthetic circuits thatgenetically program cells to self-pattern into spa-tially organized tissues.

Li et al., Science 360, 543–548 (2018) 4 May 2018 5 of 6

Fig. 4. The PTCH feedback simultaneously improves gradient speedand robustness. (A) A synthetic PTCH1 feedback loop (red), whosestrength is tunable with Dox, was introduced in Ptch1−/− receiver cellsto generate the PTCH1-SynFB cell line. At 0 ng/ml Dox, the basal activityof the TRE promoter produces sufficient PTCH1 to suppress pathwayactivity in the absence of SHH. (B) Temporal evolution of PTCH1-SynFBsignaling gradients (yellow) with (20 ng/ml Dox) or without (0 ng/ml Dox)PTCH1 feedback. Sender cells (blue) remain throughout the experimentbut are visually obscured by increasing Citrine expression. (C) PTCH1-SynFB accelerates the approach to steady state at l50 (defined in Fig. 3C).(D) Profile of PTCH1-SynFB signaling gradients, with (right; 20 ng/ml Dox)or without (left; 0 ng/ml Dox) PTCH1 feedback, at 42.5 hours after100 nM 4-OHT induction. Gradient profiles are normalized to their own

amplitudes to show differences in length scale (distance at which thedashed line is crossed) and shape. Bar plots show amplitudes (mean ± SEM;n = 7 each). (E) A SynFB circuit was introduced in wild-type receiver cellsto generate the PTCH1-DLoop2-SynFB cell line (left). PTCH1DLoop2 lacksthe HH-binding domain but has the same capability as PTCH to suppressintracellular signaling (fig. S14). This IC feedback circuit enables robustgradient amplitude at the cost of greatly flattened shape and exacerbatedlength-scale sensitivity to aHH (right). (F) Summary of the performance ofdifferent feedback architectures (simulation results). The distinctive, con-served architectural features of the HH pathway combine to enhance thespeed and robustness of signaling gradient formation. Performance ismeasured relative to that of the open-loop model at relative aHH = 0.25, whichhas a value of 1 in each dimension (fig. S9C shows plots at other aHH values).

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ACKNOWLEDGMENTS

We thank J. Briscoe and A. McMahon for DNA constructs and helpfuldiscussion, Y. Antebi for data analysis programs and discussion ofmodeling, J. Bois for advice on model simulation, Z. Singer for cloningERT2-GAL4, F. Tan for suggesting the rocker experiment, and theElowitz laboratory for discussion. We also thank U. Alon, N. Barkai,P. Beachy, A. Eldar, J. Garcia-Ojalvo, L. Goentoro, E. Hui, P. Jordan,B. Shilo, B. Shraiman, and D. Sprinzak for discussion and feedback.Funding:The work was funded by the Howard Hughes Medical Institute(M.B.E.), American Cancer Society Postdoc Fellowship 127270-PF-15-032-01-DDC (P.L.), NICHD (Eunice Kennedy Shriver National Instituteof Child Health and Human Development) Pathway to Independence

Career Award K99HD087532 (P.L.), NIH Ruth Kirschstein NationalResearch Service Award F32 AR067103 (J.S.M.), Institute forCollaborative Biotechnologies contract W911NF-09-D-0001 through theU.S. Army Research Office, and BBSRC (UK Biotechnology andBiological Sciences Research Council)–NSF award 1546197.The RNA-sequencing work was supported by the Millard andMuriel Jacobs Genetics and Genomics Laboratory at the CaliforniaInstitute of Technology. Author contributions: P.L. and M.B.E.conceived the project and designed the experiments. P.L., S.W., andV.V. performed the experiments. P.L., J.S.M., and S.W. analyzed theexperimental data. J.S.M., P.L., and S.C. developed the mathematicalmodels. P.L., J.S.M., and M.B.E. wrote the paper. Competinginterests: The authors declare no competing interests. Data andmaterials availability: Original data, Matlab code, DNA constructs,and cell lines are available upon request.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/360/6388/543/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S14Tables S1 to S4References (29–52)Movies S1 to S6

14 June 2017; accepted 22 March 2018Published online 5 April 201810.1126/science.aao0645

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Morphogen gradient reconstitution reveals Hedgehog pathway design principlesPulin Li, Joseph S. Markson, Sheng Wang, Siheng Chen, Vipul Vachharajani and Michael B. Elowitz

originally published online April 5, 2018DOI: 10.1126/science.aao0645 (6388), 543-548.360Science 

, this issue p. 543Scienceformation and explain the robustness of the system to changes in the rate of morphogen production.signaling through the receptor promotes synthesis of more inhibitory receptor. These characteristics help speed gradientligand binding. PTCH also regulates spatial distribution of the signal by sequestering the HH ligand. Furthermore,

byThe HH morphogen's receptor, Patched (PTCH), sends an inhibitory signal when no ligand is bound, which is relieved tested the effects of unusual properties of Hedgehog (HH) signaling.et al.Through in vitro experiments and modeling, Li

cell localization. Morphogen gradients allow precise and highly reproducible pattern formation during development. To translate insights in developmental biology into medical applications, techniques are needed to ensure correct

How to build a better morphogen gradient

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