Dynamics of the Dorsal Morphogen Gradient

Dynamics of the Dorsal morphogen gradient

Jitendra 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 of Copenhagen, 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 depends several minutes (16). Nuclei change in volume and undergo five on the nuclear localization gradient of Dorsal (Dl), a protein related to synchronous divisions (15, 17). To explore how these processes the mammalian NF-␬B transcription factors. Current understanding of contribute to the formation of the Dl gradient, we formulated a how the Dl gradient works has been derived from studies of its mathematical model that accounts for the nuclear import and transcriptional interpretation, but the gradient itself has not been export of Dl, its interaction with Cact, and the dynamics of nuclear quantified. In particular, it is not known whether the Dl gradient is density and volumes in the syncytial blastoderm. Based on the stable or dynamic during the DV patterning of the embryo. To address computational analysis of this model and a number of our model- this question, we developed a mathematical model of the Dl gradient based experiments, we argue that the Dl gradient is dynamic and, and constrained its parameters by experimental data. Based on our to a first approximation, can be described as a spatial pattern with computational analysis, we predict that the Dl gradient is dynamic constant shape and increasing amplitude. and, to a first approximation, can be described as a concentration profile with increasing amplitude and constant shape. These time- Results dependent properties of the Dl gradient are different from those of At the outset of this work, the only quantitative information about the Bicoid and MAPK phosphorylation gradients, which pattern the the spatial distribution of nuclear Dl could be found in the study by anterior and terminal regions of the embryo. Specifically, the gradient Zinzen et al. (18), who had characterized the DV pattern of nuclear of the nuclear levels of Bicoid is stable, whereas the pattern of MAPK Dl at a single time point. The domains of the Dl-target genes begin phosphorylation changes in both shape and amplitude. We attribute to form several nuclear cycles before cellularization, and it is these striking differences in the dynamics of maternal morphogen important to determine whether these genes respond to a constant gradients to the differences in the initial conditions and chemistries of or time-dependent signal. This question has been prompted by the anterior, DV, and terminal systems. recent studies of the anterior-posterior (AP), DV, and terminal systems. First, the nuclear levels of Bcd, a morphogen that specifies computational modeling ͉ Drosophila ͉ systems biology ͉ the anterior structures of the embryo, are stable throughout the last parameter estimation five syncytial nuclear divisions. Bcd undergoes nucleocytoplasmic

shuttling on the time scale of several minutes. After mitosis, the BIOLOGY nuclear levels of Bcd drop to zero, but are then rapidly reestablished tissue patterned by morphogen gradients can change its DEVELOPMENTAL Atranscriptional state, grow, or deform either in response to the to the premitosis level. Thus, with the exception of a rapid transient gradients or independently of them (1–3). When these changes are associated with nuclear divisions, a particular point in the embryo much slower than the dynamics of the gradient, a tissue responds to is exposed to a constant level of nuclear Bcd, which is distributed a stable signal. Transcriptional interpretation of such signals can in a spatial pattern with constant shape and amplitude. In contrast, rely on differences in the expression thresholds of target genes with the pattern of phosphorylated ERK/MAPK (dpERK), which spec- respect to the spatially distributed repressors or activators (2, 4). A ifies the terminal regions of the embryo, changes in both shape and different strategy for signal interpretation is required when the amplitude. Over the five last nuclear divisions in the syncytial formation of positional information becomes intertwined with the blastoderm, the nuclear levels of dpERK increase at the poles and dynamics of the patterned system (2, 5). Here, we suggest that decrease in the midbody of the embryo. the dorsoventral (DV) patterning of the Drosophila embryo oper- We asked whether the spatial pattern of nuclear localization of ates in this regime. Dl is stable, similar to the pattern of Bcd, or dynamic, similar to the The DV patterning of the Drosophila embryo depends on the pattern of dpERK. Answering this question requires quantitative nuclear localization gradient of Dorsal (Dl), a protein related to the characterization of the nuclear levels of Dl along the DV axis and NF-␬B family of transcription factors (6–10). Transcriptional in- at multiple time points. Here, this goal is achieved using a combi- terpretation of the Dl gradient depends on the differences in the nation of quantitative imaging and mathematical modeling of the affinities of the Dl binding sites in the Dl-target genes and several biophysical processes associated with the DV patterning of the gene expression and signaling cascades initiated by Dl (6, 11, 12). embryo. Our experimental and computational results reveal that A ventral-to-dorsal occupancy gradient of the Toll cell surface the DV pattern of nuclear Dl behaves differently from both the Bcd receptor provides the activating signal for the DV patterning (13). and dpERK gradients. Similar to Bcd, the shape of the DV pattern In the absence of this signal, Dl is sequestered in the cytoplasm, in of nuclear Dl has approximately constant shape, but the amplitude complex with an inhibitory protein I-␬B, called Cactus (Cact) in of this pattern increases with time. Drosophila. In response to Toll signaling, the Dl–Cact complex To visualize the DV distribution of nuclear Dl, we used a dissociates, Cact is degraded, and Dl enters the nucleus to control transgenic line where one endogenous copy of dl was replaced by gene expression. In the current model of DV patterning, positional information is established by the spatial pattern of Toll occupancy 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., (13, 14). 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; The Dl gradient forms during the last five nuclear divisions in a and J.S.K., J.L.-S., and S.Y.S. wrote the paper. syncytical blastoderm, a single cell with multiple nuclei (15). The authors declare no conﬂict of interest. Because nuclei can be viewed as competing with Cact for Dl, an 1To whom correspondence may be addressed. E-mail: [email protected] or increase in the number of nuclei can influence the Dl gradient, but [email protected]. whether or not this happens is currently unknown. Dl undergoes This article contains supporting information online at www.pnas.org/cgi/content/full/ rapid nucleocytoplasmic shuttling with a nuclear residence time of 0912395106/DCSupplemental.

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0912395106 PNAS ͉ December 22, 2009 ͉ vol. 106 ͉ no. 51 ͉ 21707–21712 Downloaded by guest on September 25, 2021 Fig. 2. Live imaging of the Dl gradient. (A) An interpolated surface plot of the nuclear Dl-GFP levels along the DV axis at Ϸ130 time points during nuclear division cycles 11–14. (B) Dynamics of the nuclear Dl level at the ventral-most point of the embryo. (C) The average gradient (line) at 15 min in cycle 14 obtained from four live-imaging experiments (dots).

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 value during mitosis and a subsequent increase during the next cycle ␣-GFP (B) antibodies. In A, C, and E the cross-sections of the embryos are oriented (Fig. 2 A and B). with the dorsal side up, and cycle-14 embryos are shown (XY scale is 150 microns). One of the main sources of variability in the end-on imaging of (C) Comparing the normalized gradients of ␣-Dl (red) and ␣-GFP (green) intensity the Dl gradient is introduced by the movement of nuclei in and out levels in six embryos. (D) Plot of ␣-Dl intensity vs. ␣-GFP intensity in six embryos. of the focal plane, both during interphase and between different ␣ (E) End-on imaging of the wild-type embryos stained with -Dl antibodies. (F) nuclear division cycles. The inherent dynamics of the arrangement Comparing the normalized gradients of ␣-Dl intensity levels in eight wild-type embryos (blue) and six transgenic embryos (red). of the nuclei induces large variability in the profiles of the Dl gradients along the DV axis. This effect, which is particularly significant during the earlier nuclear division cycles, makes the quantitative analysis of the Dl gradients during these cycles ex- a dl-gfp transgene (see Materials and Methods). Several control tremely challenging. At the same time, the arrangement of nuclei experiments were done to test whether the Dl gradient, quantified is much more regular during cycle 14, when they are tightly packed from the GFP signal in this line is close to the Dl gradient obtained ␣ under the plasma membrane. Thus, we use cycle-14 data from four by quantifying the wild-type -Dl antibody stainings. First, fixed separate live imaging experiments to extract the DV pattern of ␣ ␣ embryos were stained with -Dl and -GFP antibodies and the nuclear Dl at a fixed time point: Ϸ15 min into cycle 14 (Fig. 2C). ␣ ␣ fluorescent intensities of the nuclear -Dl and -GFP stainings To characterize the dynamics of the DV pattern of nuclear Dl at the were compared with each other (Fig. 1 A–D). As shown in Fig. 1D, previous time points, we use the data in Fig. 2C as a quantitative there is a strong linear correlation between the intensities of the constraint for the mathematical model that accounts for the dy- ␣-Dl and ␣-GFP antibody stainings. Thus, except for the differences namics of Dl/Cact interactions and nuclear divisions. in the background levels, the DV pattern of nuclear Dl obtained on The objective of our model is to characterize the dynamics of the the basis of the GFP staining is proportional to the pattern that is DV pattern of nuclear Dl during the last five syncytial cell cycles. based on the ␣-Dl antibody staining. Because the ␣-Dl antibody We model the syncytium as a periodic arrangement of cuboidal detects both endogenous and GFP-tagged Dl, whereas the ␣-GFP compartments, each of which contains a single spherical nucleus antibody detects only GFP-tagged Dl, the linear correlation sug- and an associated cytoplasmic region (Fig. 3A). Dl, Cact, and gests that the GFP tag does not significantly interfere with the Dl–Cact complex diffuse rapidly within each of the compartments normal processes of Dl transport and interactions. As an additional and undergo slow exchange with the neighboring compartments. control experiment, we used the ␣-Dl antibody and stained the The kinetic part of our model is a subset of reactions included in the ␬ wild-type embryos together with embryos with one wild-type and more detailed models of the mammalian NF- B system (Fig. 3B) one GFP-tagged copy of dl (Fig. 1E). Comparison of the nuclear Dl (20). The association of Dl and Cact is modeled as a second-order reaction with a spatially uniform rate constant. The dissociation of gradients in the wild-type and transgenic embryos (Fig. 1F) indi- the Dl–Cact complex is modeled as a first-order process with a rate cates that they are very close to each other. Thus, the line with one constant that depends on the DV position, reflecting a DV pattern dl wild-type and one GFP-tagged can be used to monitor the of Toll activation. We assume that this pattern remains constant dynamics of the Dl gradient in live imaging experiments. during the entire patterning process. The rates of the nuclear import To follow the dynamics of the DV pattern of nuclear Dl, we used and export of Dl depend on the surface area of the nucleus. Finally, the ‘‘end on’’ imaging technique (19), where embryos are mounted we assume free Cact is produced at a constant rate and degraded with their AP axis perpendicular to the horizontal surface, enabling in a first-order reaction. the imaging along the DV axis of the embryo. The space–time plot Within each nuclear cycle nuclear radius increases (17). As a of nuclear Dl extracted from a live-imaging experiment with Ͼ130 consequence of this change, nuclear and cytoplasmic concentra- time points between cycles 11 and 14 is shown in Fig. 2A. The tions are affected by both the chemical processes and volume gradient of nuclear Dl is very dynamic. Concentration of nuclear Dl changes. At specific time intervals that correspond to the detailed increases during interphase, which is followed by a drop to a low measurements of Foe and Alberts (15), nuclei divide. During

21708 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0912395106 Kanodia et al. Downloaded by guest on September 25, 2021 nine-dimensional space of parameters. Each point in this ensemble, i.e., a particular parameter vector, can be used to predict the properties of the DV system that cannot be readily measured experimentally. In particular, we are interested in the dynamics of nuclear Dl levels at all times from nuclear cycle 10 to cycle 14 and along the entire DV axis. Thus, we start with a relatively small amount of experimental data on the DV pattern of nuclear Dl at a specific time point during the cycle 14, identify an ensemble of parameter vectors that satisfy these constraints, and then use this ensemble to predict the Dl gradient at all times. A similar approach has been successfully used to make model-based statistical predictions about the dynamics of other cell signaling systems (21). To identify parameter sets that satisfy the experimentally based constraints for our model, we used a stochastic evolutionary optimization technique (22). The Dl gradient dynamics predicted for one particular parameter vector is presented in Fig. 4A that shows a surface plot that represents the dynamics of nuclear Dl at all times and all positions along the DV axis. Fig. 4B shows a comparison of the nuclear Dl gradients reached at the end of all nuclear cycles, and Fig. 4C shows the dynamics of the nuclear Dl level at the ventral-most point. After obtaining a large set of acceptable parameters (Ϸ40,000), we used the resulting ensemble as the basis for statistical analysis of the Dl gradients predicted by the model. As a first step in the statistical analysis of model predictions, we used the identified ensemble to calculate a distribution function for the ratio of the amplitudes of the Dl gradients at the end of nuclear cycles 14 and 10 (A14/A10;Fig.5Ai). We chose this metric based on the previous analysis of the gradients of dpERK, which patterns the terminal regions of the embryo, and the Bcd gradient, which patterns the AP axis (17, 23). For the nuclear Bcd gradient, which is stable during cycles 10 and 14, A14/A10 Ϸ 1. For the dpERK Fig. 3. Mathematical modeling of reaction and transport processes in the gradient, however, A14/A10 Ͼ 1, which reflects a pattern that is syncytium. (A)(i) Schematic of the DV cross-section of the embryo. (ii) Model of amplified at the poles. The distribution function for the ratio of the

the syncytium, with compartments arranged in a spatially periodically manner. maxima of the spatial patterns of nuclear Dl at cycles 14 and 10 has BIOLOGY (B) Reaction and transport processes within a single compartment of the syncy- a single peak at Ϸ1.5 (Fig. 5Aii). Upon further examination, we DEVELOPMENTAL tium. (C) Model for division of syncytial compartments. The cuboids divide in a way such that the height (w) of compartment remains the same while the length found that approximately two-thirds of the parameter sets predict (l) and width (b) reduce by a factor of ͌2. Thus, the volume of the compartment a continuous increase in the ventral levels of nuclear Dl at the end halves, but the surface area shared by the two compartments reduces by ͌2. of each cycle (from cycle 10 to 14; Fig. 5Aii Lower Inset). The remaining parameter sets predict multiple combinations of increase and decrease in nuclear Dl level from one cycle to another (Fig. 5Aii mitoses, the content of each nucleus is instantaneously redistributed Upper Inset). in the corresponding cytoplasmic region. After mitosis, the nuclear To test whether the amplitudes of the Dl gradients change envelope reforms, and the number of syncytial compartments monotonically between subsequent nuclear cycles, embryos ex- doubles. The model for doubling of compartments is shown in Fig. pressing the histone-GFP transgene, which marks the nuclei, were 3C; more details can be found in SI Appendix ( Fig. S1). stained using the ␣-Dl antibody. In this case, we used lateral images The dynamics of the model depend on nine dimensionless of embryos and located the peak of the gradient in each image (see parameters that characterize the spatial pattern of Toll activation, Materials and Methods). Using a previously developed image pro- the rates of nuclear import and export of Dl, the relative amounts cessing approach (23), we assigned each embryo to one of the four of total Dl and Cact, the rates at which the species move between temporal classes, corresponding to the nuclear cycles 11, 12, 13, and the adjacent cytoplasmic compartments, and the formation and 14. For each group, we measured the amplitude of the gradient at degradation rates of the Dl–Cact complex (see SI Appendix, Table the ventral-most point in the embryo (Fig. 5B). We analyzed the S1). Given these parameters, numerical solution of the model resulting dataset using a linear regression model and found a strong predicts the spatial patterns of Dl, Cact, and Dl–Cact complex correlation (P Ͻ 0.001) between the age of the embryo (i.e., the during nuclear cycles 10–14. Although the exact values of model nuclear division cycle) and the amplitude of the gradient (Fig. 5B). parameters are largely unknown, they can be constrained by the Based on these results, we conclude that the amplitude of the Dl available experimental data. Specifically, it is known that the Dl gradient is an increasing function of the number of nuclei. Based on levels are mainly nuclear/cytoplasmic at the most ventral/dorsal this, we restricted the further statistical analysis to those members points, respectively and that the levels of Cact at the dorsal side of of the identified ensemble of parameter sets that satisfied this the embryo are higher than those at the ventral side (2–4, 14). Based additional constraint (Ϸ67% of the parameter vectors in the on the results of the live imaging studies, we required that the original ensemble). ventral-most level of nuclear Dl increases monotonically within the Focusing on these remaining two-thirds of parameter sets, we interphase of cycle 14 and that this level reaches 90% of its final examined how the shape of the Dl gradient changes from one value in Ͻ15 min (16). Finally, we used the spatial pattern of nuclear nuclear cycle to another. We constructed a distribution function for Dl at Ϸ15 min in cycle 14 (Fig. 2C), based on the quantification of the change in the half-width of the gradients from cycles 10 to 14 the GFP autofluorescence from our live imaging experiments. This (Fig. 5C). Strikingly, we found that this distribution function has a information does not define the parameters of our model uniquely. peak at 0.05 and corresponds to the half-width change of at most Rather, it constrains them to a ‘‘cloud,’’ or ensemble, in the 15%, which implies that the shape of the gradient is only weakly

Kanodia et al. PNAS ͉ December 22, 2009 ͉ vol. 106 ͉ no. 51 ͉ 21709 Downloaded by guest on September 25, 2021 Fig. 4. Computational modeling of the Dl gradient. (A) The spatiotemporal pattern of nuclear Dl obtained by numerical solution of the model equations for one particular 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 are extracted 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) Dynamics of the nuclear Dl level at the ventral-most point.

affected by nuclear divisions. We have also confirmed that the same the imaging experiments with fixed and live embryos, mathe- is true for other nuclear cycles. In fact, the Dl gradients at the end matical modeling, and computational analysis. of the five nuclear cycles can be collapsed into one shape by simple Each of these approaches has its relative advantages and limi- rescaling (Fig. 5D). To a first approximation, the DV distribution tations. Experiments with fixed embryos have limited temporal of nuclear Dl can be viewed as a pattern with constant shape and resolution and cannot follow the dynamics of the gradient within increasing amplitude. In addition to characterizing how the ampli- the same embryo. We have used imaging of fixed embryos to test tude of the gradient changes from one nuclear cycle to another, we the applicability of the Dl-GFP transgene and characterize how the found that all points along the DV axes are exposed to a mono- ventral-most levels of nuclear Dl change from one nuclear cycle to tonically increasing level of Dl within each nuclear cycle. Thus, the next. In contrast to experiments with fixed embryos, live based on the statistical analysis of the gradients predicted by the imaging provides a dynamic view of the Dl pattern as a function of model, we conclude that the nuclear levels of Dl are monotonically time. At the same time, high-resolution images are typically col- increasing in time during the interphase of syncytial nuclear divi- lected from a single optical section, and quantitative analysis of the sions; after mitosis, they are reestablished, reaching a value that it Dl dynamics is compounded by the dynamics of nuclear rearrange- is higher than in the previous cycle. ments. We have used live imaging to quantify the spatial pattern of Dl at a specific time point when the arrangement of nuclei is stable. Discussion This information provides one of the inputs for our mathematical model, which is clearly an approximation of processes in the real The DV patterning of the Drosophila embryo by the Dl gradient embryo. We assumed that the spatial pattern of Toll occupancy and is arguably the best-studied morphogenetic patterning event (6, the total amount of Dl in the embryo remain constant and used a 11, 24, 25). Multiple genes controlled by Dl were identified, and simple geometric model to describe the syncytial embryo. As more sequence-specific patterns of their transcriptional regulation data become available, our model can be extended to describe these have become progressively understood. At the same time, the additional effects. For example, including the Dl-dependent syn- spatial distribution of Dl and its dynamics have not been directly thesis of Cact can explain why the shape of the Dl gradient is characterized. Both of these pieces of information are essential dynamic during the DV patterning in other insects (26, 27). for quantitative understanding of the DV patterning. For in- Nevertheless, by capturing what we believe are the essential features stance, the relative arrangement of the expression domains of the of the Dl gradient and its interaction with the dynamics of the Dl target genes has been interpreted within the framework of syncytium, our model provides a basis for more complex mathe- thermodynamic models (18, 25). A key assumption of such matical models that are essential for understanding the DV pat- models is that the input ‘‘seen’’ by the regulatory regions of the terning in the wild-type and mutant backgrounds and exploring the Dl target genes is stable, but whether or not this is the case is evolvability of the DV patterning system (24, 28). unknown. Given the fact that the Dl undergoes nucleocytoplas- Based on the computational analysis of this model, we argue that mic shuttling in a medium with increasing number of nuclei, the the Dl morphogen is distributed in a dynamic pattern with increas- answer to the question about the stability of the nuclear levels of ing amplitude and constant shape. These dynamics are different Dl is far from obvious. Here, we answer this question based on from the dynamics of Bcd and MAPK phosphorylation gradients,

21710 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0912395106 Kanodia et al. Downloaded by guest on September 25, 2021 BIOLOGY 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 DEVELOPMENTAL 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 in nuclear 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 cycle to 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-based distribution 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). The distribution 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) Nuclear Dl at different cycles. (ii) Nuclear Dl gradient at different cycles with its amplitude normalized to one at the ventral-most end.

which are formed in the same medium and at the same time as the We attribute the fact that amplification of the dpERK levels is Dl gradient (29). Specifically, neither the shape nor the amplitude restricted to the poles, whereas the nuclear Dl levels increase of the nuclear levels of Bcd are affected by changes in the number everywhere, to the different spatial extents of the sources that of nuclei. The two-peaked pattern of dpERK, however, changes in activate the DV and terminal systems. Our recent experiments both shape and amplitude. suggest that the occupancy of the Torso receptor, which activates What is the origin of these striking differences between the MAPK, is sharply localized to the poles and that the formation of dynamics of the three gradients? The terminal and DV gradients the dpERK gradient relies on the diffusion of activated MAPK are initiated only when nuclei have reached the plasma membrane to the midbody regions (23, 32). By decreasing the distance to which and respond to signals from the activated cell surface receptors. At the dpERK molecule can diffuse before being trapped or dephos- the same time, the functional Bcd gradient is already established at phorylated, an increase in the nuclear density can prevent the lateral transport of dpERK to the midbody regions and amplify its this stage (30). Thus, the stability of the nuclear Bcd gradient during level at the poles. However, we argue that a significant fraction of the last five nuclear divisions can be due to the fact that this gradient nuclei along the DV axis are exposed to appreciable levels of Toll starts to form earlier and is not affected by nuclei, which sample signaling. As a consequence, lateral movement of the intracellular only a small fraction of total Bcd at any given point along the AP signaling components is less important for the DV patterning than axis (17, 31). Another key factor is the difference in the ‘‘chemis- for patterning of the terminal system, which agrees with the imaging tries’’ of Bcd, Dl, and dpERK molecules. We have previously experiments that revealed a slow Dl exchange between the adjacent proposed that Bcd is not degraded on the time scale relevant for the cytoplasmic regions (16). formation of the gradient (31). In contrast, the molecules that Understanding how a dynamic Dl gradient specifies multiple pattern the DV and terminal regions are reactive: Dl interacts with gene expression boundaries along the DV axis requires quantitative Cact and dpERK is dephosphorylated. Both of these processes can studies of the dynamics of other patterning signals in the early be affected by changes in nuclear density. Why, then, does the same embryo (18, 33–37). As an example, we discuss the expression of change in nuclear density lead to different changes in the Dl and genes that are expressed in the ventral and lateral regions of the dpERK gradients? embryo. Consider the regulation of sog, a gene repressed in the

Kanodia et al. PNAS ͉ December 22, 2009 ͉ vol. 106 ͉ no. 51 ͉ 21711 Downloaded by guest on September 25, 2021 prospective mesoderm and expressed in more lateral regions. It is anti-GFP (Molecular Probes) at 1:1,500. Embryos were washed in PBT and subse- possible that the ventral boundary of this pattern is stabilized by the quently stained with fluorescently coupled secondary antibodies (Molecular feed-forward loop that is induced by Dl and relies on the positive Probes). For end-on imaging, embryos were mounted on their posterior pole and autoregulation of Twist, a high threshold target of Dl (18). If this imaged as described (19). Embryos were imaged at Ϸ70 ␮m from the posterior pole, at a position where network operates in a bistable regime, then its output, and hence the diameter of the embryo was Ϸ140–150 ␮m. Control embryos for secondary the ventral boundary of sog, can be stable even with increasing levels background, wild-type embryos, and dl1;GFP-dorsal embryos were immuno- of Dl. The dorsal boundary, however, depends on the joint regu- stained on the same day and imaged under the same settings of the confocal lation of sog by both Dl and Zelda, a maternally provided activator microscope. For quantification, small regions of interest were drawn in the nuclei of early zygotic transcription (38, 39). We speculate that the dorsal marked by Hoechst dye (Molecular Probes) using the software Image J. Average boundary of the sog pattern is stabilized by the combined effect of fluorescence intensity with corresponding positions of nuclei was obtained for the temporally increasing levels of spatially distributed Dl and anti-Dl and anti-GFP. The gradients were normalized between zero and one by subtracting the minimum intensity measurement within a nucleus and then decreasing levels of spatially uniform Zelda. Thus, increasing levels dividing the entire gradient by the maximum intensity. of nuclear Dl can be important for the dynamic expression of Live imaging was performed with dl1 heterozygous embryos expressing GFP- Dl-target genes. Direct tests of this prediction can rely on the dorsal (dl1/ϩ;p[wϩ-GFP-dorsal]/ϩ) to match the wild-type dl copy number. Flies combined experimental, modeling, and computational strategy were allowed to lay embryos for1hat25°Congrape juice agar plates. Embryos described in this work. were dechorionated and mounted on their posterior pole in Lab Tek chambers coated with silane (40), immersed in PBS, and imaged on an LSM 510 confocal Materials and Methods microscope. Imaging was performed at Ϸ70 ␮m from the posterior pole. Quan- tification was performed with Image J. Fly Lines. Dorsal mutants dl1 and dl4 were obtained from the Bloomington Stock For lateral imaging of fixed embryos, they were dechorionated for 1 min in Center at the Indiana University and crossed with the dl-GFP/TM3 line. Live 100% bleach, fixed for 20 min by gentle shaking on a nutator, and devitellinized imaging was performed with embryos of the genotype dl1/ϩ;p[wϩ-dl-GFP]/ϩ. by vigorous 1-min shaking in a mixture of heptane and methanol. Next, embryos were quickly rehydrated and transferred to the blocking and antibody steps of Antibody Staining and Live Imaging. Embryos were dechorionated in bleach for the protocol. All further processing was done with 0.02% PBS-Triton X-100 as the 1 min and then washed in 0.7% NaCl containing 0.05% Triton X-100. They were diluting solution. Dl antibody (Developmental Hybridoma Bank) was used in then treated with heptane for 30 s and fixed in a 1:1 mixture of heptane/4% 1:100 dilution, and goat anti-mouse Alexa Fluor 546 antibody (Invitrogen; 1:500 paraformadehyde in PBS for 20 min at room temperature. After fresh heptane dilution) was used as a secondary antibody. Imaging was done on a Zeiss LSM510 was added, embryos were devitelinized in equal volumes of methanol and stored confocal microscope, with a Zeiss 20ϫ (NA 0.6) A-plan objective. in methanol at Ϫ20 °C. For immunostaining, embryos were rehydrated for 10 min in PBS with 0.3% Triton X-100 (PBT) and blocked for 1 h with 2% BSA in PBT at ACKNOWLEDGMENTS. We thank Tsuyoshi Hirashima for help with image pro- room temperature; this was followed by a 2-h incubation with the primary cessing; Dmitry Papatsenko, Christine Rushlow, Ruth Steward, and Mike Levine antibody. The primary antibodies used were mouse anti-Dorsal 7A4 (Develop- for helpful discussions; and Christine Sample, Miriam Osterfield, Alistair Boetti- mental Studies Hybridoma Bank at the University of Iowa) at 1:50 and rabbit ger, and Lily Cheung Chang for critical reading of the manuscript.

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