Dynamics of the Dorsal morphogen gradientJitendra S. Kanodiaa, Richa Rikhyb, Yoosik Kima, Viktor K. Lundc, Robert DeLottoc, Jennifer Lippincott-Schwartzb,1,and Stanislav Y. Shvartsmana,1

aDepartment of Chemical Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Washington Road, Princeton, NJ 08544;bCell Biology and Metabolism Branch, NIH, Building 32, 18 Library Drive, Bethesda, MD 20892; and cDepartment of Molecular Biology, University ofCopenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen, Denmark

Contributed by Jennifer Lippincott-Schwartz, October 28, 2009 (sent for review September 6, 2009)

The dorsoventral (DV) patterning of the Drosophila embryo dependson the nuclear localization gradient of Dorsal (Dl), a protein related tothe mammalian NF-�B transcription factors. Current understanding ofhow the Dl gradient works has been derived from studies of itstranscriptional interpretation, but the gradient itself has not beenquantified. In particular, it is not known whether the Dl gradient isstable or dynamic during the DV patterning of the embryo. To addressthis question, we developed a mathematical model of the Dl gradientand constrained its parameters by experimental data. Based on ourcomputational analysis, we predict that the Dl gradient is dynamicand, to a first approximation, can be described as a concentrationprofile with increasing amplitude and constant shape. These time-dependent properties of the Dl gradient are different from those ofthe Bicoid and MAPK phosphorylation gradients, which pattern theanterior and terminal regions of the embryo. Specifically, the gradientof the nuclear levels of Bicoid is stable, whereas the pattern of MAPKphosphorylation changes in both shape and amplitude. We attributethese striking differences in the dynamics of maternal morphogengradients to the differences in the initial conditions and chemistries ofthe anterior, DV, and terminal systems.

computational modeling � Drosophila � systems biology �parameter estimation

A tissue patterned by morphogen gradients can change itstranscriptional state, grow, or deform either in response to the

gradients or independently of them (1–3). When these changes aremuch slower than the dynamics of the gradient, a tissue responds toa stable signal. Transcriptional interpretation of such signals canrely on differences in the expression thresholds of target genes withrespect to the spatially distributed repressors or activators (2, 4). Adifferent strategy for signal interpretation is required when theformation of positional information becomes intertwined with thedynamics of the patterned system (2, 5). Here, we suggest thatthe dorsoventral (DV) patterning of the Drosophila embryo oper-ates in this regime.

The DV patterning of the Drosophila embryo depends on thenuclear localization gradient of Dorsal (Dl), a protein related to theNF-�B family of transcription factors (6–10). Transcriptional in-terpretation of the Dl gradient depends on the differences in theaffinities of the Dl binding sites in the Dl-target genes and severalgene expression and signaling cascades initiated by Dl (6, 11, 12).A ventral-to-dorsal occupancy gradient of the Toll cell surfacereceptor provides the activating signal for the DV patterning (13).In the absence of this signal, Dl is sequestered in the cytoplasm, incomplex with an inhibitory protein I-�B, called Cactus (Cact) inDrosophila. In response to Toll signaling, the Dl–Cact complexdissociates, Cact is degraded, and Dl enters the nucleus to controlgene expression. In the current model of DV patterning, positionalinformation is established by the spatial pattern of Toll occupancy(13, 14).

The Dl gradient forms during the last five nuclear divisions in asyncytical blastoderm, a single cell with multiple nuclei (15).Because nuclei can be viewed as competing with Cact for Dl, anincrease in the number of nuclei can influence the Dl gradient, butwhether or not this happens is currently unknown. Dl undergoesrapid nucleocytoplasmic shuttling with a nuclear residence time of

several minutes (16). Nuclei change in volume and undergo fivesynchronous divisions (15, 17). To explore how these processescontribute to the formation of the Dl gradient, we formulated amathematical model that accounts for the nuclear import andexport of Dl, its interaction with Cact, and the dynamics of nucleardensity and volumes in the syncytial blastoderm. Based on thecomputational analysis of this model and a number of our model-based experiments, we argue that the Dl gradient is dynamic and,to a first approximation, can be described as a spatial pattern withconstant shape and increasing amplitude.

ResultsAt the outset of this work, the only quantitative information aboutthe spatial distribution of nuclear Dl could be found in the study byZinzen et al. (18), who had characterized the DV pattern of nuclearDl at a single time point. The domains of the Dl-target genes beginto form several nuclear cycles before cellularization, and it isimportant to determine whether these genes respond to a constantor time-dependent signal. This question has been prompted byrecent studies of the anterior-posterior (AP), DV, and terminalsystems. First, the nuclear levels of Bcd, a morphogen that specifiesthe anterior structures of the embryo, are stable throughout the lastfive syncytial nuclear divisions. Bcd undergoes nucleocytoplasmicshuttling on the time scale of several minutes. After mitosis, thenuclear levels of Bcd drop to zero, but are then rapidly reestablishedto the premitosis level. Thus, with the exception of a rapid transientassociated with nuclear divisions, a particular point in the embryois exposed to a constant level of nuclear Bcd, which is distributedin a spatial pattern with constant shape and amplitude. In contrast,the pattern of phosphorylated ERK/MAPK (dpERK), which spec-ifies the terminal regions of the embryo, changes in both shape andamplitude. Over the five last nuclear divisions in the syncytialblastoderm, the nuclear levels of dpERK increase at the poles anddecrease in the midbody of the embryo.

We asked whether the spatial pattern of nuclear localization ofDl is stable, similar to the pattern of Bcd, or dynamic, similar to thepattern of dpERK. Answering this question requires quantitativecharacterization of the nuclear levels of Dl along the DV axis andat multiple time points. Here, this goal is achieved using a combi-nation of quantitative imaging and mathematical modeling of thebiophysical processes associated with the DV patterning of theembryo. Our experimental and computational results reveal thatthe DV pattern of nuclear Dl behaves differently from both the Bcdand dpERK gradients. Similar to Bcd, the shape of the DV patternof nuclear Dl has approximately constant shape, but the amplitudeof this pattern increases with time.

To visualize the DV distribution of nuclear Dl, we used atransgenic line where one endogenous copy of dl was replaced by

Author contributions: J.S.K., R.R., Y.K., R.D., J.L.-S., and S.Y.S. designed research; J.S.K., R.R.,Y.K., and S.Y.S. performed research; J.S.K., R.R., Y.K., V.K.L., J.L.-S., and S.Y.S. analyzed data;and J.S.K., J.L.-S., and S.Y.S. wrote the paper.

The authors declare no conflict of interest.

1To whom correspondence may be addressed. E-mail: jlippin@helix.nih.gov orstas@princeton.edu.

This article contains supporting information online at www.pnas.org/cgi/content/full/0912395106/DCSupplemental.

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a dl-gfp transgene (see Materials and Methods). Several controlexperiments were done to test whether the Dl gradient, quantifiedfrom the GFP signal in this line is close to the Dl gradient obtainedby quantifying the wild-type �-Dl antibody stainings. First, fixedembryos were stained with �-Dl and �-GFP antibodies and thefluorescent intensities of the nuclear �-Dl and �-GFP stainingswere compared with each other (Fig. 1 A–D). As shown in Fig. 1D,there is a strong linear correlation between the intensities of the�-Dl and �-GFP antibody stainings. Thus, except for the differencesin the background levels, the DV pattern of nuclear Dl obtained onthe basis of the GFP staining is proportional to the pattern that isbased on the �-Dl antibody staining. Because the �-Dl antibodydetects both endogenous and GFP-tagged Dl, whereas the �-GFPantibody detects only GFP-tagged Dl, the linear correlation sug-gests that the GFP tag does not significantly interfere with thenormal processes of Dl transport and interactions. As an additionalcontrol experiment, we used the �-Dl antibody and stained thewild-type embryos together with embryos with one wild-type andone GFP-tagged copy of dl (Fig. 1E). Comparison of the nuclear Dlgradients in the wild-type and transgenic embryos (Fig. 1F) indi-cates that they are very close to each other. Thus, the line with onewild-type and one GFP-tagged dl can be used to monitor thedynamics of the Dl gradient in live imaging experiments.

To follow the dynamics of the DV pattern of nuclear Dl, we usedthe ‘‘end on’’ imaging technique (19), where embryos are mountedwith their AP axis perpendicular to the horizontal surface, enablingthe imaging along the DV axis of the embryo. The space–time plotof nuclear Dl extracted from a live-imaging experiment with �130time points between cycles 11 and 14 is shown in Fig. 2A. Thegradient of nuclear Dl is very dynamic. Concentration of nuclear Dlincreases during interphase, which is followed by a drop to a low

value during mitosis and a subsequent increase during the next cycle(Fig. 2 A and B).

One of the main sources of variability in the end-on imaging ofthe Dl gradient is introduced by the movement of nuclei in and outof the focal plane, both during interphase and between differentnuclear division cycles. The inherent dynamics of the arrangementof the nuclei induces large variability in the profiles of the Dlgradients along the DV axis. This effect, which is particularlysignificant during the earlier nuclear division cycles, makes thequantitative analysis of the Dl gradients during these cycles ex-tremely challenging. At the same time, the arrangement of nucleiis much more regular during cycle 14, when they are tightly packedunder the plasma membrane. Thus, we use cycle-14 data from fourseparate live imaging experiments to extract the DV pattern ofnuclear Dl at a fixed time point: �15 min into cycle 14 (Fig. 2C).To characterize the dynamics of the DV pattern of nuclear Dl at theprevious time points, we use the data in Fig. 2C as a quantitativeconstraint for the mathematical model that accounts for the dy-namics of Dl/Cact interactions and nuclear divisions.

The objective of our model is to characterize the dynamics of theDV pattern of nuclear Dl during the last five syncytial cell cycles.We model the syncytium as a periodic arrangement of cuboidalcompartments, each of which contains a single spherical nucleusand an associated cytoplasmic region (Fig. 3A). Dl, Cact, andDl–Cact complex diffuse rapidly within each of the compartmentsand undergo slow exchange with the neighboring compartments.The kinetic part of our model is a subset of reactions included in themore detailed models of the mammalian NF-�B system (Fig. 3B)(20). The association of Dl and Cact is modeled as a second-orderreaction with a spatially uniform rate constant. The dissociation ofthe Dl–Cact complex is modeled as a first-order process with a rateconstant that depends on the DV position, reflecting a DV patternof Toll activation. We assume that this pattern remains constantduring the entire patterning process. The rates of the nuclear importand export of Dl depend on the surface area of the nucleus. Finally,we assume free Cact is produced at a constant rate and degradedin a first-order reaction.

Within each nuclear cycle nuclear radius increases (17). As aconsequence of this change, nuclear and cytoplasmic concentra-tions are affected by both the chemical processes and volumechanges. At specific time intervals that correspond to the detailedmeasurements of Foe and Alberts (15), nuclei divide. During

Fig. 1. Validation of the Dl-GFP transgenic line using imaging of fixed embryos.(A and B) End-on imaging of transgenic embryos costained with �-Dl (A) and�-GFP (B) antibodies. In A, C, and E the cross-sections of the embryos are orientedwith the dorsal side up, and cycle-14 embryos are shown (XY scale is 150 microns).(C) Comparing the normalized gradients of �-Dl (red) and �-GFP (green) intensitylevels in six embryos. (D) Plot of �-Dl intensity vs. �-GFP intensity in six embryos.(E) End-on imaging of the wild-type embryos stained with �-Dl antibodies. (F)Comparing the normalized gradients of �-Dl intensity levels in eight wild-typeembryos (blue) and six transgenic embryos (red).

Fig. 2. Live imaging of the Dl gradient. (A) An interpolated surface plot of thenuclear Dl-GFP levels along the DV axis at �130 time points during nucleardivisioncycles11–14. (B)DynamicsofthenuclearDl levelat theventral-mostpointof the embryo. (C) The average gradient (line) at 15 min in cycle 14 obtained fromfour live-imaging experiments (dots).

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mitoses, the content of each nucleus is instantaneously redistributedin the corresponding cytoplasmic region. After mitosis, the nuclearenvelope reforms, and the number of syncytial compartmentsdoubles. The model for doubling of compartments is shown in Fig.3C; more details can be found in SI Appendix ( Fig. S1).

The dynamics of the model depend on nine dimensionlessparameters that characterize the spatial pattern of Toll activation,the rates of nuclear import and export of Dl, the relative amountsof total Dl and Cact, the rates at which the species move betweenthe adjacent cytoplasmic compartments, and the formation anddegradation rates of the Dl–Cact complex (see SI Appendix, TableS1). Given these parameters, numerical solution of the modelpredicts the spatial patterns of Dl, Cact, and Dl–Cact complexduring nuclear cycles 10–14. Although the exact values of modelparameters are largely unknown, they can be constrained by theavailable experimental data. Specifically, it is known that the Dllevels are mainly nuclear/cytoplasmic at the most ventral/dorsalpoints, respectively and that the levels of Cact at the dorsal side ofthe embryo are higher than those at the ventral side (2–4, 14). Basedon the results of the live imaging studies, we required that theventral-most level of nuclear Dl increases monotonically within theinterphase of cycle 14 and that this level reaches 90% of its finalvalue in �15 min (16). Finally, we used the spatial pattern of nuclearDl at �15 min in cycle 14 (Fig. 2C), based on the quantification ofthe GFP autofluorescence from our live imaging experiments. Thisinformation does not define the parameters of our model uniquely.Rather, it constrains them to a ‘‘cloud,’’ or ensemble, in the

nine-dimensional space of parameters. Each point in this ensemble,i.e., a particular parameter vector, can be used to predict theproperties of the DV system that cannot be readily measuredexperimentally. In particular, we are interested in the dynamics ofnuclear Dl levels at all times from nuclear cycle 10 to cycle 14 andalong the entire DV axis.

Thus, we start with a relatively small amount of experimentaldata on the DV pattern of nuclear Dl at a specific time point duringthe cycle 14, identify an ensemble of parameter vectors that satisfythese constraints, and then use this ensemble to predict the Dlgradient at all times. A similar approach has been successfully usedto make model-based statistical predictions about the dynamics ofother cell signaling systems (21). To identify parameter sets thatsatisfy the experimentally based constraints for our model, we useda stochastic evolutionary optimization technique (22). The Dlgradient dynamics predicted for one particular parameter vector ispresented in Fig. 4A that shows a surface plot that represents thedynamics of nuclear Dl at all times and all positions along the DVaxis. Fig. 4B shows a comparison of the nuclear Dl gradientsreached at the end of all nuclear cycles, and Fig. 4C shows thedynamics of the nuclear Dl level at the ventral-most point. Afterobtaining a large set of acceptable parameters (�40,000), we usedthe resulting ensemble as the basis for statistical analysis of the Dlgradients predicted by the model.

As a first step in the statistical analysis of model predictions, weused the identified ensemble to calculate a distribution function forthe ratio of the amplitudes of the Dl gradients at the end of nuclearcycles 14 and 10 (A14/A10; Fig. 5Ai). We chose this metric based onthe previous analysis of the gradients of dpERK, which patterns theterminal regions of the embryo, and the Bcd gradient, whichpatterns the AP axis (17, 23). For the nuclear Bcd gradient, whichis stable during cycles 10 and 14, A14/A10 � 1. For the dpERKgradient, however, A14/A10 � 1, which reflects a pattern that isamplified at the poles. The distribution function for the ratio of themaxima of the spatial patterns of nuclear Dl at cycles 14 and 10 hasa single peak at �1.5 (Fig. 5Aii). Upon further examination, wefound that approximately two-thirds of the parameter sets predicta continuous increase in the ventral levels of nuclear Dl at the endof each cycle (from cycle 10 to 14; Fig. 5Aii Lower Inset). Theremaining parameter sets predict multiple combinations of increaseand decrease in nuclear Dl level from one cycle to another (Fig. 5AiiUpper Inset).

To test whether the amplitudes of the Dl gradients changemonotonically between subsequent nuclear cycles, embryos ex-pressing the histone-GFP transgene, which marks the nuclei, werestained using the �-Dl antibody. In this case, we used lateral imagesof embryos and located the peak of the gradient in each image (seeMaterials and Methods). Using a previously developed image pro-cessing approach (23), we assigned each embryo to one of the fourtemporal classes, corresponding to the nuclear cycles 11, 12, 13, and14. For each group, we measured the amplitude of the gradient atthe ventral-most point in the embryo (Fig. 5B). We analyzed theresulting dataset using a linear regression model and found a strongcorrelation (P � 0.001) between the age of the embryo (i.e., thenuclear division cycle) and the amplitude of the gradient (Fig. 5B).Based on these results, we conclude that the amplitude of the Dlgradient is an increasing function of the number of nuclei. Based onthis, we restricted the further statistical analysis to those membersof the identified ensemble of parameter sets that satisfied thisadditional constraint (�67% of the parameter vectors in theoriginal ensemble).

Focusing on these remaining two-thirds of parameter sets, weexamined how the shape of the Dl gradient changes from onenuclear cycle to another. We constructed a distribution function forthe change in the half-width of the gradients from cycles 10 to 14(Fig. 5C). Strikingly, we found that this distribution function has apeak at 0.05 and corresponds to the half-width change of at most15%, which implies that the shape of the gradient is only weakly

Fig. 3. Mathematical modeling of reaction and transport processes in thesyncytium. (A) (i) Schematic of the DV cross-section of the embryo. (ii) Model ofthe syncytium, with compartments arranged in a spatially periodically manner.(B) Reaction and transport processes within a single compartment of the syncy-tium. (C) Model for division of syncytial compartments. The cuboids divide in away such that the height (w) of compartment remains the same while the length(l) and width (b) reduce by a factor of �2. Thus, the volume of the compartmenthalves, but the surface area shared by the two compartments reduces by �2.

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affected by nuclear divisions. We have also confirmed that the sameis true for other nuclear cycles. In fact, the Dl gradients at the endof the five nuclear cycles can be collapsed into one shape by simplerescaling (Fig. 5D). To a first approximation, the DV distributionof nuclear Dl can be viewed as a pattern with constant shape andincreasing amplitude. In addition to characterizing how the ampli-tude of the gradient changes from one nuclear cycle to another, wefound that all points along the DV axes are exposed to a mono-tonically increasing level of Dl within each nuclear cycle. Thus,based on the statistical analysis of the gradients predicted by themodel, we conclude that the nuclear levels of Dl are monotonicallyincreasing in time during the interphase of syncytial nuclear divi-sions; after mitosis, they are reestablished, reaching a value that itis higher than in the previous cycle.

DiscussionThe DV patterning of the Drosophila embryo by the Dl gradientis arguably the best-studied morphogenetic patterning event (6,11, 24, 25). Multiple genes controlled by Dl were identified, andsequence-specific patterns of their transcriptional regulationhave become progressively understood. At the same time, thespatial distribution of Dl and its dynamics have not been directlycharacterized. Both of these pieces of information are essentialfor quantitative understanding of the DV patterning. For in-stance, the relative arrangement of the expression domains of theDl target genes has been interpreted within the framework ofthermodynamic models (18, 25). A key assumption of suchmodels is that the input ‘‘seen’’ by the regulatory regions of theDl target genes is stable, but whether or not this is the case isunknown. Given the fact that the Dl undergoes nucleocytoplas-mic shuttling in a medium with increasing number of nuclei, theanswer to the question about the stability of the nuclear levels ofDl is far from obvious. Here, we answer this question based on

the imaging experiments with fixed and live embryos, mathe-matical modeling, and computational analysis.

Each of these approaches has its relative advantages and limi-tations. Experiments with fixed embryos have limited temporalresolution and cannot follow the dynamics of the gradient withinthe same embryo. We have used imaging of fixed embryos to testthe applicability of the Dl-GFP transgene and characterize how theventral-most levels of nuclear Dl change from one nuclear cycle tothe next. In contrast to experiments with fixed embryos, liveimaging provides a dynamic view of the Dl pattern as a function oftime. At the same time, high-resolution images are typically col-lected from a single optical section, and quantitative analysis of theDl dynamics is compounded by the dynamics of nuclear rearrange-ments. We have used live imaging to quantify the spatial pattern ofDl at a specific time point when the arrangement of nuclei is stable.This information provides one of the inputs for our mathematicalmodel, which is clearly an approximation of processes in the realembryo. We assumed that the spatial pattern of Toll occupancy andthe total amount of Dl in the embryo remain constant and used asimple geometric model to describe the syncytial embryo. As moredata become available, our model can be extended to describe theseadditional effects. For example, including the Dl-dependent syn-thesis of Cact can explain why the shape of the Dl gradient isdynamic during the DV patterning in other insects (26, 27).Nevertheless, by capturing what we believe are the essential featuresof the Dl gradient and its interaction with the dynamics of thesyncytium, our model provides a basis for more complex mathe-matical models that are essential for understanding the DV pat-terning in the wild-type and mutant backgrounds and exploring theevolvability of the DV patterning system (24, 28).

Based on the computational analysis of this model, we argue thatthe Dl morphogen is distributed in a dynamic pattern with increas-ing amplitude and constant shape. These dynamics are differentfrom the dynamics of Bcd and MAPK phosphorylation gradients,

Fig. 4. Computational modeling of the Dl gradient. (A) The spatiotemporal pattern of nuclear Dl obtained by numerical solution of the model equations for oneparticular set of parameters. (B) The gradient of nuclear Dl at the end of interphase for each cycle from cycles 10 to 14. The time point at which these gradients areextracted is color-coded and marked by arrows in A. The dotted curve represents the averaged experimental gradient of nuclear Dl at 15 min in cycle 14. (C) Dynamicsof the nuclear Dl level at the ventral-most point.

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which are formed in the same medium and at the same time as theDl gradient (29). Specifically, neither the shape nor the amplitudeof the nuclear levels of Bcd are affected by changes in the numberof nuclei. The two-peaked pattern of dpERK, however, changes inboth shape and amplitude.

What is the origin of these striking differences between thedynamics of the three gradients? The terminal and DV gradientsare initiated only when nuclei have reached the plasma membraneand respond to signals from the activated cell surface receptors. Atthe same time, the functional Bcd gradient is already established atthis stage (30). Thus, the stability of the nuclear Bcd gradient duringthe last five nuclear divisions can be due to the fact that this gradientstarts to form earlier and is not affected by nuclei, which sampleonly a small fraction of total Bcd at any given point along the APaxis (17, 31). Another key factor is the difference in the ‘‘chemis-tries’’ of Bcd, Dl, and dpERK molecules. We have previouslyproposed that Bcd is not degraded on the time scale relevant for theformation of the gradient (31). In contrast, the molecules thatpattern the DV and terminal regions are reactive: Dl interacts withCact and dpERK is dephosphorylated. Both of these processes canbe affected by changes in nuclear density. Why, then, does the samechange in nuclear density lead to different changes in the Dl anddpERK gradients?

We attribute the fact that amplification of the dpERK levels isrestricted to the poles, whereas the nuclear Dl levels increaseeverywhere, to the different spatial extents of the sources thatactivate the DV and terminal systems. Our recent experimentssuggest that the occupancy of the Torso receptor, which activatesMAPK, is sharply localized to the poles and that the formation ofthe dpERK gradient relies on the diffusion of activated MAPKto the midbody regions (23, 32). By decreasing the distance to whichthe dpERK molecule can diffuse before being trapped or dephos-phorylated, an increase in the nuclear density can prevent thelateral transport of dpERK to the midbody regions and amplify itslevel at the poles. However, we argue that a significant fraction ofnuclei along the DV axis are exposed to appreciable levels of Tollsignaling. As a consequence, lateral movement of the intracellularsignaling components is less important for the DV patterning thanfor patterning of the terminal system, which agrees with the imagingexperiments that revealed a slow Dl exchange between the adjacentcytoplasmic regions (16).

Understanding how a dynamic Dl gradient specifies multiplegene expression boundaries along the DV axis requires quantitativestudies of the dynamics of other patterning signals in the earlyembryo (18, 33–37). As an example, we discuss the expression ofgenes that are expressed in the ventral and lateral regions of theembryo. Consider the regulation of sog, a gene repressed in the

Fig. 5. Statistical analysis of model predictions. (A) (i) Schematic of nuclear Dl gradients at cycles 10 and 14; the lines correspond to the amplitude of the gradient (A10

and A14) and the width of the gradient at half-peak amplitude (w10 and w14). (ii) Distribution of the ratio of the amplitudes of nuclear Dl gradient at cycles 14 and 10,computed on the basis of the ensemble of parameter vectors. Approximately one-third of parameter sets predict multiple combinations of increase and decrease innuclear Dl level at the end of each cycle (Upper Inset), while the other two-thirds of the parameter sets predict an ordered increase in nuclear Dl level from one cycleto another (Lower Inset). (B) Experimental results for the amplitude of nuclear Dl gradients at the ventral-most point of the embryo for cycles 11–14. (C) Model-baseddistribution function of the changes in the half-widths (width of gradient at half-peak amplitude) of the Dl gradients, cycles 14 to 10; half-width is defined in Ai). Thedistribution shows a peak at 0.05, indicating that the half-width remains almost constant. (D) The Dl gradient has constant shape and increasing amplitude. (i) NuclearDl at different cycles. (ii) Nuclear Dl gradient at different cycles with its amplitude normalized to one at the ventral-most end.

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prospective mesoderm and expressed in more lateral regions. It ispossible that the ventral boundary of this pattern is stabilized by thefeed-forward loop that is induced by Dl and relies on the positiveautoregulation of Twist, a high threshold target of Dl (18). If thisnetwork operates in a bistable regime, then its output, and hencethe ventral boundary of sog, can be stable even with increasing levelsof Dl. The dorsal boundary, however, depends on the joint regu-lation of sog by both Dl and Zelda, a maternally provided activatorof early zygotic transcription (38, 39). We speculate that the dorsalboundary of the sog pattern is stabilized by the combined effect ofthe temporally increasing levels of spatially distributed Dl anddecreasing levels of spatially uniform Zelda. Thus, increasing levelsof nuclear Dl can be important for the dynamic expression ofDl-target genes. Direct tests of this prediction can rely on thecombined experimental, modeling, and computational strategydescribed in this work.

Materials and MethodsFly Lines. Dorsal mutants dl1 and dl4 were obtained from the Bloomington StockCenter at the Indiana University and crossed with the dl-GFP/TM3 line. Liveimaging was performed with embryos of the genotype dl1/�;p[w�-dl-GFP]/�.

Antibody Staining and Live Imaging. Embryos were dechorionated in bleach for1 min and then washed in 0.7% NaCl containing 0.05% Triton X-100. They werethen treated with heptane for 30 s and fixed in a 1:1 mixture of heptane/4%paraformadehyde in PBS for 20 min at room temperature. After fresh heptanewas added, embryos were devitelinized in equal volumes of methanol and storedinmethanolat�20 °C.For immunostaining,embryoswererehydratedfor10minin PBS with 0.3% Triton X-100 (PBT) and blocked for 1 h with 2% BSA in PBT atroom temperature; this was followed by a 2-h incubation with the primaryantibody. The primary antibodies used were mouse anti-Dorsal 7A4 (Develop-mental Studies Hybridoma Bank at the University of Iowa) at 1:50 and rabbit

anti-GFP (Molecular Probes) at 1:1,500. Embryos were washed in PBT and subse-quently stained with fluorescently coupled secondary antibodies (MolecularProbes). For end-on imaging, embryos were mounted on their posterior pole andimaged as described (19).

Embryos were imaged at �70 �m from the posterior pole, at a position wherethe diameter of the embryo was �140–150 �m. Control embryos for secondarybackground, wild-type embryos, and dl1;GFP-dorsal embryos were immuno-stained on the same day and imaged under the same settings of the confocalmicroscope. For quantification, small regions of interest were drawn in the nucleimarked by Hoechst dye (Molecular Probes) using the software Image J. Averagefluorescence intensity with corresponding positions of nuclei was obtained foranti-Dl and anti-GFP. The gradients were normalized between zero and one bysubtracting the minimum intensity measurement within a nucleus and thendividing the entire gradient by the maximum intensity.

Live imaging was performed with dl1 heterozygous embryos expressing GFP-dorsal (dl1/�;p[w�-GFP-dorsal]/�) to match the wild-type dl copy number. Flieswere allowed to lay embryos for 1 h at 25 °C on grape juice agar plates. Embryoswere dechorionated and mounted on their posterior pole in Lab Tek chamberscoated with silane (40), immersed in PBS, and imaged on an LSM 510 confocalmicroscope. Imaging was performed at �70 �m from the posterior pole. Quan-tification was performed with Image J.

For lateral imaging of fixed embryos, they were dechorionated for 1 min in100% bleach, fixed for 20 min by gentle shaking on a nutator, and devitellinizedby vigorous 1-min shaking in a mixture of heptane and methanol. Next, embryoswere quickly rehydrated and transferred to the blocking and antibody steps ofthe protocol. All further processing was done with 0.02% PBS-Triton X-100 as thediluting solution. Dl antibody (Developmental Hybridoma Bank) was used in1:100 dilution, and goat anti-mouse Alexa Fluor 546 antibody (Invitrogen; 1:500dilution) was used as a secondary antibody. Imaging was done on a Zeiss LSM510confocal microscope, with a Zeiss 20� (NA 0.6) A-plan objective.

ACKNOWLEDGMENTS. We thank Tsuyoshi Hirashima for help with image pro-cessing; Dmitry Papatsenko, Christine Rushlow, Ruth Steward, and Mike Levinefor helpful discussions; and Christine Sample, Miriam Osterfield, Alistair Boetti-ger, and Lily Cheung Chang for critical reading of the manuscript.

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21712 � www.pnas.org�cgi�doi�10.1073�pnas.0912395106 Kanodia et al.

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