Fluorescently Labeled DNA Oligonucleotides Allow Visualization of Individual Diffraction-Limited bcd RNP Complexes

To examine bcd mRNA distribution in fixed embryos, we adapted a fluorescent in situ hybridization (FISH) protocol [24] using a set of 48 20-mer DNA oligonucleotides complementary to the bcd open reading frame (Table S1) directly conjugated to AlexaFluor fluorophores [25]. This approach has been used previously to detect single mRNA molecules in mammalian cell culture and C. elegans embryos [25]. By employing directly labeled oligonucleotides as probes, we bypassed the use of antibodies and enzymes for detection [26]–[28], and thus minimized nonspecific background, nonlinear signal response, variable tissue penetration by reagents, or other potential difficulties associated with quantification of conventional FISH signal [29]. Using standard laser scanning confocal microscopy, we can readily detect the anterior localization of bcd mRNA at low magnification (Figure S1) and distinguish individual bcd RNP complexes in high resolution images (Figures 1 and 2).

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Figure 1. Visualization of discrete bcd mRNA particles with fluorescently labeled oligonucleotides.

(A–G) Confocal slices through the midsagittal plane at the anterior (A) and posterior (G) of a wild-type embryo during nuclear cycle (n.c.) 4. Copper-shaded boxes in (A) and (G) indicate regions shown in magnified views (B–F); top row, near embryo surface; lower row, center views; arrowheads indicate selected dimly fluorescent particles. (G inset) Low magnification image of whole embryo (mRNA in green, DNA in blue), boxed regions are shown in (A) and (G). (H) Six sequential confocal z-slices beginning 0.8 µm below (leftmost panel) and ending 1.2 µm above (rightmost panel) the image shown in (C); lower panel in (C) is identical to third panel from the left in (H). Arrows: bright particles appearing on five slices. Arrowheads: weak particles appearing on three slices. (I–K) Confocal slices of the same embryo imaged ∼5 µm beneath cortical surface. (J) Magnified views of selected regions indicated by six shaded boxes in (I) and (K). Here and in Figure 2, posterior regions containing particles were deliberately chosen for zoomed views; however, the majority of the posterior does not contain detectable particles. Scale bars: 25 µm (A), 2 µm (B, H).

https://doi.org/10.1371/journal.pbio.1000596.g001

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Figure 2. bcd mRNA particles surrounding surface nuclei during syncytial blastoderm stages.

(A–F) n.c. 11 embryo near the midsagittal plane at the anterior (A) and posterior (F). Shaded boxes indicate magnified views (B–E) corresponding to cortex (upper) or core (lower); arrowheads indicate selected faint particles. (F inset) Low magnification image of whole embryo (mRNA in green, DNA in blue), boxes indicate regions shown in (A) and (F). (G–L) Same embryo imaged at the nuclear layer. (H–K) Selected z-slices of boxed regions indicated in (G) and (L) showing apical (upper panels) and basal (lower panels) planes surrounding the nuclear layer (middle panels). Arrowheads indicate selected dimly fluorescent particles. Scale bars: 25 µm (A), 2 µm (B).

https://doi.org/10.1371/journal.pbio.1000596.g002

To obtain the complete three-dimensional (3d) structure of bcd mRNA distribution, we generated high resolution confocal stacks at high magnification, such that a spatial unit voxel represents a volume of 75 nm×75 nm×420 nm. These stacks span the entire left or right half of each embryo from the midsagittal plane to the embryo surface, representative of the entire embryo due to left-right symmetry. Figures 1 and 2 show typical images of embryos labeled during interphase 4 and interphase 11, respectively. Corresponding 3d stacks are provided in Movies S1 and S2. Images taken at the anterior of labeled embryos reveal readily identifiable individual bcd RNP particles above background noise (Figures 1A–E and 2A–D), whereas the embryo posterior is essentially devoid of bcd mRNA particles (Figures 1F–G and 2E–F). Individual particles appear on multiple neighboring z-slices (Figure 1H), owing to the objective's spatially extended point spread function (PSF).

To obtain counts of discrete bcd mRNA particles, their localization, and fluorescence intensities, we designed custom image analysis software to determine the spatial positions, radii, and fluorescence intensities of bcd mRNA particles (see Materials and Methods). As illustrated in Figure S2, the analysis algorithm discriminates between overlapping particles which densely populate the anterior and readily detects dim particles. A large majority of detected bcd particles are circular in shape (Figure 3A), confirming that the algorithm resolves closely neighboring particles. The particles have a spatial extent of about 3 pixels on average, corresponding to a physical distance of ∼200 nm (Figure 3B). This is identical to the PSF in the confocal slices (Figure S3), indicating that the particles are smaller than the diffraction limit of our microscopy. The extended PSF dictates that each mRNA particle must be detected simultaneously on consecutive z-slices, and the algorithm uses this property to discriminate true particles from local background noise (see Materials and Methods). We identified an optimal threshold for distinguishing between candidate particles and random fluorescence fluctuations by examining posterior stacks which contain few particles (see Materials and Methods and Figure S4). As additional controls, we examined background fluorescence in cleavage stage embryos processed without any probes (Figure S5A–C) or exposed to probes against the purely zygotically expressed gene giant (Figure S5D–F). Both show a low level of fluorescent signal, but no detected particles. These controls allow us to exclude falsely identified particles.

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Figure 3. Quantification of diffraction-limited bcd mRNA particles.

Individual particles identified in anterior stacks of 32 embryos hybridized with fluorescently labeled bcd oligonucleotides ranging from n.c. 4 to n.c. 14 (see color code in legend). (A) bcd particle eccentricity e calculated as the ratio of the difference of the major and minor particle axes (r_x and r_y) to their sum; e = 0 and e = 0.3 correspond to r_x/r_y = 1 (perfectly circular) and r_x/r_y = 2, respectively. Shown is the probability distribution of e across all identified particles. (B) Probability distribution of bcd particle diameters d with a mean of 3.05±0.10 pxl and a standard deviation of 0.42±0.05 pxl (1 pixel = 75.7 nm). (C) Distribution of bcd particle intensities (note log units on x-axis). (D) Average bcd particle intensity as a function of distance along the AP axis in fractional egg length x/L. (E) Distribution of fluorescence intensities in bcd mRNA particles along the AP axis; error bars are standard deviations across embryos (note difference from total bcd particle distribution in Figure S4). (F) Cumulative distribution of bcd mRNA fluorescence intensity (cumulative plot of (E)).

https://doi.org/10.1371/journal.pbio.1000596.g003

bcd particles coalesce in vivo during bcd mRNA anterior localization in late oogenesis, and subsequently disperse upon egg activation [18],[30],[31], suggesting that bcd RNPs may remain at least partially intact in fertilized embryos. The fluorescent intensities of particles observed by our method span about a 10-fold range (Figure 3C). This broad distribution suggests the presence of multiple bcd mRNAs in a single detected particle, consistent with previous biochemical and fluorescence microscopy observations [32]–[34]. bcd mRNA is not degraded until the onset of cellularization at n.c. 14 [3]. Therefore, it is highly likely that the broad intensity distribution reflects variation in the number of RNAs per particle. Fluorescence variability is reflected in the axial (z) diameter of particles: we observe that bright particles occupy up to 5 z-slices, whereas dim particles are detectable above noise level in fewer slices (Figure 1H). Our ability to distinguish discrete particles affords an unprecedented quantitative view of mRNA particles and allows us to separate their dynamics from the ultimate dynamics of Bcd protein.

bcd RNP Complexes Form a Short Anterior Gradient at All Times, With <1% of bcd Present in the Posterior 60% of the Egg

To quantify the spatial distributions of bcd mRNA, we examined embryos ranging from n.c. 3 to n.c. 14. During all stages of development, bcd particles are found in a graded distribution peaking at around 7% egg length (EL, as measured from the anterior pole) and leveling off at nearly zero particle density by 40% EL (Figure S6). Confocal images taken at both early cleavage (Figure 1) and blastoderm (n.c. 11, Figure 2, and n.c. 13, Figure S7) stages reveal a higher density of bcd particles in anterior compared to posterior regions. Moreover, anteriorly localized particles are brighter than those toward the posterior (Figure 3D). The higher density of brighter anterior particles results in a sharp, steep gradient of total bcd mRNA distribution within the anterior third of the embryo (Figure 3E). At all times, 90% or more of total bcd mRNA is found within the anterior 20% of the embryo (Figure 3F), as previously reported [35]. The quantitative difference between Figures 3E and S4A arises from both the increased number and intensity of anterior particles.

Although the majority of mRNA particles are detected in the anterior 20%, we nevertheless observe faint discrete particles scattered along the entire AP axis. During both cleavage and blastoderm, very few or no particles are detected in the posterior embryo core (Figures 1F–G, 2E–F, S7E–F). Conversely, a small number of particles exhibiting weak fluorescence sparsely populate the posterior surface (Figures 1I–K, 2G–L, S7I–L). A handful of particles can be detected even at almost 100% EL near the posterior pole (Figure 2K–L). Thus, we can document even the small fraction of particles that either fail to localize during oogenesis or which are transported an unusually large distance away from the anterior cortex after egg activation. To our knowledge, bcd RNP complexes have not been detected in the posterior of wild-type embryos. These observations demonstrate the exquisite sensitivity of our method to the presence of dimly fluorescent bcd mRNA particles. However, we emphasize that the particles found in the entire posterior 60% of the embryo constitute less than 1% of the total bcd mRNA (Figure 3F). These particles are uniformly dimly fluorescent (Figure 3D) and are found at a sparse density which does not change significantly during development. Translation of bcd mRNA is repressed by Nanos activity [36], silencing posteriorly localized bcd mRNA. Based on these observations, the fraction of bcd mRNA present in the posterior 60% of the embryo likely contributes only negligibly to protein gradient formation.

bcd RNP Complexes Translocate from the Embryo Core to the Cortex Concomitant with Nuclear Expansion

Previous studies have demonstrated that egg activation triggers release of bcd mRNA from its initial tight localization at the anterior egg cortex, resulting in a posterior dispersion of bcd mRNA within 25 min at 25°C [30]. This corresponds to the interphase of n.c. 3 (Figure S8), by which time bcd mRNA has already reached its most posterior extent, where it remains from n.c. 4 through 6 (Figure 3E and 3F). The AP particle distribution at n.c. 4 therefore results from this early release of bcd mRNA from the cortex. Prior to and during n.c. 6, 97% of all bcd mRNA is found in the anterior 20% (Figure 3F), with the remainder forming a gradient which drops to nearly zero before 40% EL.

In midsagittal planes at n.c. 4, regions near the embryo surface contain fewer particles than the center of the embryo (compare upper and lower panels in Figure 1B–D). Consistent with this, confocal planes taken near the embryo surface contain fewer particles compared to the same AP position at the midsagittal plane (compare Figure 1A and 1I). Therefore, much of bcd mRNA is not near the cortex but is found in the embryo interior (Figures 1A, S1A–B, S8), as observed previously [5]. In low magnification images, we often observe mRNA localization in a wedge or cone-shaped distribution jutting in toward the interior core of the embryo in midsagittal planes (Figures S8, S9A–D), suggesting the presence of uncharacterized structures along which bcd mRNA particles might translocate upon egg activation. The observation that particles do not progress further into the posterior after n.c. 3 supports the idea that bcd mRNA is tethered to underlying cytoskeletal structure(s) throughout embryogenesis [32] and is not free to diffuse.

We observed a marked change in bcd mRNA spatial localization after interphase 6. As the nuclei undergo expansion toward the axial poles beginning at the sixth mitosis and continuing at n.c. 7, bcd mRNA moves ahead of the expanding nuclei (Figures 4A, S1C–E). bcd mRNA progresses to the cortex during nuclear cortical migration between n.c. 8 to 10, such that in midsagittal planes at n.c. 11, bcd mRNA is highly enriched near the embryo cortex, with the majority of fluorescence found within about 25 µm of the embryo surface (Figures 2A–G, 4A). This enrichment is also apparent in z-slices collected at the cortical nuclear layer (Figures 2G–L, 4B, S7G–L). Compared to earlier cycles, bright bcd particles are now present on the surface at a greater distance from the anterior pole (compare Figure 1I to Figure 2G). Thus, with the nuclei penetrating the cloud of bcd mRNA during their cortical migration, by the start of the syncytial blastoderm stage, bcd mRNA fluorescence resembles a cup covering the anterior end of the embryo (Figure S9E–H), which remains in place through n.c. 14 (Figures 3E, 3F, S1F–G, and S6).

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Figure 4. bcd mRNA particle dynamics, disassembly, and stability.

All panels are generated on same data set as in Figure 3, with identical color labeling for different nuclear cycles. (A) bcd particle density as a function of fractional distance from the cortex d/L (d is the red line in inset of partial image of DAPI stained embryo) in a single midsagittal plane. (B) Probability distribution of bcd particle intensities along the z-axis within a confocal stack (error bars are standard deviations across embryos). (C) Absolute number of bcd particles as a function of n.c. Each dot corresponds to total number count in full anterior stack of an individual embryo (stack encompasses left or right embryo-half; due to left-right symmetry, the full embryo contains twice the number of particles indicated). Black squares and error bars correspond to averages and standard deviations across embryos at a given n.c., respectively (black line is a guide to the eye). Note the sharp drop during n.c. 14 (time point corresponds to 15 min after the end of mitosis 13; the actual average particle count below 50). (D) Average total bcd particle intensity as a function of n.c. (black squares; error bars are standard deviations across embryos in a given n.c.). In color, for individual embryos, mean bcd particle intensity as a function of n.c. (green scale on right).

https://doi.org/10.1371/journal.pbio.1000596.g004

Concomitant with bcd particle translocation from core to cortex, we observe a mild posterior shift of the bcd mRNA distribution along the AP axis by the onset of the blastoderm stage at n.c. 10 (Figures 3E, 3F, and S6), as previously observed [5]. Embryos at all blastoderm stages appear similar, with bcd mRNA particles surrounding the nuclei on both the basal and apical surfaces (compare n.c. 11 in Figure 2 and n.c. 13 in Figure S7). Despite dynamic cortical relocalization, more than 90% of bcd is found in the anterior 20% of the embryo (Figure 3F), with the remaining 10% falling to zero particle density by 40% EL.

bcd mRNA Particles Disassemble During Cortical Translocation, But bcd mRNA Is Not Degraded Until the Onset of Cellularization

Concomitant with the particle relocalization, the distribution of fluorescence intensities shifts from bright to dim spot intensities (Figure 3C), and the number of detected particles tends to increase with developmental age from about 70,000 per embryo in cycles prior to n.c. 7, to about 110,000 particles in blastodermal stages (Figure 4C). Despite these changes, the total fluorescent signal from bcd mRNA remains constant across all developmental times through early n.c. 14 (Figure 4D), arguing that our method is capable of detecting the constant maternal bcd mRNA pool. Given previous work indicating the presence of multiple bcd mRNA molecules per particle [32]–[34], these observations indicate that such particles disassemble during their relocalization to the cortex and suggest that mRNA degradation likely plays little role in particle dissolution.

bcd RNA is degraded with other maternal mRNAs at the midblastula transition during n.c. 14; prior to this time, no degradation of bcd mRNA occurs [4],[37]. To contrast bcd mRNA particle disassembly with mRNA degradation, we documented the loss of bcd mRNA during n.c. 14 (Figure 5), which spans about 1 h at 25°C. During this time, wholesale zygotic gene expression is activated, maternal mRNAs are degraded, and cellular membranes form between the cortically positioned nuclei. We gauged the approximate age of fixed embryos in n.c. 14 on the presence of the cellularization front and the morphology of nuclei which elongate during cellularization. Immediately following the 13^th mitosis, embryos exhibit particles with intensity and spatial distributions similar to the earlier blastoderm stages (Figure 5A, 5D, 5G). During the next ∼10 min, the cell surface protrudes above each nucleus and membrane invagination begins [38],[39], during which we observe a dramatic reduction in overall fluorescence and a sharp decrease in the number of particles and fluorescence of particles in all regions of the embryo (Figure 5B, 5E, 5H, 5J–L). As nuclei undergo elongation, bcd mRNA is almost completely lost, and we detect only a handful of dim particles in the anterior, usually at the cortical or lateral surfaces between nuclei (Figure 5F, 5L). At this time, the total particle count has dropped to essentially zero (see the final data point on x-axis in Figure 4D). Thus, degradation of bcd can be readily distinguished from the separate earlier event of particle dissolution.

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Figure 5. Uniform bcd mRNA particle degradation at the onset of cellularization.

Each row shows an embryo during early (0–5 min, top row), mid- (5–10 min, middle row), or late (10–20 min, bottom row) n.c. 14 (times are approximate after mitosis 13). (A–C) Anterior midsagittal views. Boxed regions are magnified in (D–F). (G–O) Images of nuclear layer at embryo cortex; (G–I), anterior; (M–O), posterior; (J–L) magnified views of boxed regions apical (top panels) and basal (bottom panels) to nuclei (middle panels). Arrowheads indicate selected faint particles. Box in (F) highlights a cluster of particles. Scale bars: 25 µm (A), 5 µm (B), and 2 µm (J).

https://doi.org/10.1371/journal.pbio.1000596.g005

In summary, we have observed that bcd mRNPs behave dynamically in the embryo: after fertilization, bcd mRNA establishes a wedge-shaped distribution, which is subsequently reformed into a cup-shaped geometry during n.c. 6–10 (Figure S9), followed by mRNA decay at the onset of cellularization. Despite these dynamic rearrangements, more than 99% of all mRNA particles occupy the anterior 40% of the egg at all times. These findings demonstrate that an exponentially graded protein distribution, which is detectable as far as the posterior 85% of the egg [8],[9],[40], can be established only if the protein moves away from the anterior source.

Nuclei Begin Accumulating Bcd Within 45 Min of Egg Deposition

Understanding the degree to which a graded mRNA source influences the formation of the Bcd protein gradient requires a comparison of mRNA and protein dynamics. Live imaging of transgenic embryos suggests that nuclear Bcd-GFP levels approach a nearly stable concentration gradient during the 10^th interphase, approximately 80–90 min AED [9]. Gradient formation must occur prior to this time; however, no previous study has quantified Bcd distributions in living cleavage stage embryos, due to challenges to optical measurements created by the greater opacity and autofluorescence of presyncytial embryos. To minimize these complications, we devised a specific fixation protocol (see Materials and Methods), which preserves GFP fluorescence of Bcd-GFP expressing embryos, allowing us to detect and measure nuclear Bcd-GFP with conventional confocal microscopy (Figure 6).

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Figure 6. Bicoid gradient formation.

Presyncytial blastoderm stage (A–D) and syncytial stage (E–I) embryos expressing Bcd-GFP. Images are maximum-projections of confocal stacks to display nuclei residing in several focal planes (A–D) or midsagittal confocal slices (E–I, 7 µm thick sections). Nuclear cycle (nc) is indicated. DAPI staining shown (A′–C′) to indicate positions of nuclei. Scale bar: 50 µm. Arrowheads in (A) show nuclear Bcd-GFP in n.c. 6, i.e. the earliest nuclear Bcd-GFP detected in any examined embryo.

https://doi.org/10.1371/journal.pbio.1000596.g006

The earliest time at which we can detect nuclear Bcd-GFP is about 45 min AED, when Bcd-GFP begins to accumulate in the most anteriorly positioned nuclei during the first 2 min of the sixth interphase (Figure 6A), coinciding with the expansion of nuclei into the cloud of bcd mRNA and with the onset of bcd mRNA relocalization. We detect Bcd-GFP fluorescence above background autofluorescence in nuclei positioned within the anterior third of the embryo when the nuclei extend from about 25% to 60% EL (Figure 6A). In contrast, during interphase 5 nuclear Bcd-GFP appeared no greater than background (Figure S10; n = 12 embryos), showing that Bcd-GFP has not accumulated to high enough levels for visualization in nuclei. Tissue autofluorescence may preclude detection of lower levels of nuclear localized Bcd-GFP; therefore, Bcd-GFP accumulation begins during n.c. 6 at the latest. Delayed nuclear accumulation would be consistent with previous work suggesting that the translation rate of bcd may be relatively low during the first hour of development before polyadenylation of bcd mRNA [41].

The Nuclear Bcd Gradient Forms During n.c. 6–10, Is Stable During n.c. 11–13, and Decays Thereafter

Between the sixth mitosis and interphase 10, nuclei migrate toward the egg cortex as an expanding, elliptical shell, while continuing to accumulate Bcd-GFP (Figure 6A–D). A gradient of nuclear Bcd-GFP can be readily distinguished within the anterior third of the embryo from n.c. 7 and 8 (Figure 6B, C). By n.c. 9, Bcd-GFP is apparent in nuclei throughout the anterior half of the embryo (Figure 6D), demonstrating the continued heightening of Bcd-GFP levels along the AP axis. The nuclei arrive at the egg cortex and form the syncytial blastoderm upon completing the ninth mitosis. From n.c. 10 onward, the Bcd-GFP gradient is evident in single confocal slices of the midsagittal plane (Figure 6E–I), reminiscent of images of Bcd-GFP obtained previously by live imaging [9].

To quantify the Bcd gradient at these early stages, we extracted nuclear fluorescence intensities from embryos expressing both Bcd-GFP and Histone-RFP. The latter provides a nominally uniform fluorescence signal in all nuclei and serves as a reference to normalize Bcd-GFP values at different optical depths in the sample (see Materials and Methods). Corrected nuclear Bcd-GFP gradients between n.c. 6 and n.c. 11 show that at all positions along the AP axis, nuclear Bcd-GFP rises continuously (Figure 7A and 7C). The shape of the gradient, however, does not change (see slopes on log-linear inset to Figure 7A), whereas its amplitude continues to rise and increases by a factor of ∼3 over the course of n.c. 6–11. The embryo-wide increase in Bcd-GFP is abruptly halted along the entire AP axis at n.c. 11–12, by which time nuclei have attained Bcd concentrations >90% of their maximal values. Therefore, the nuclear gradient forms over approximately 50 min between n.c. 6 and n.c. 11. During n.c. 11 and 12 nuclear Bcd-GFP concentration remains within ∼95% of its maximum along the whole AP extent. After n.c. 12, nuclear concentrations drop, starting at the anterior; by n.c. 13, values in the anterior 20% of the embryo are approximately 80%–90% of their maxima at n.c. 12. At the beginning of n.c. 14, all positions along the AP axis decay to around 70%–85% of the maximum (Figure 8D). Despite this decrease in nuclear Bcd, the total amount of Bcd protein still rises through n.c. 13 (Figure S11) [9], consistent with continued protein production until mRNA degradation.

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Figure 7. Bcd gradient dynamics.

(A–B) Mean attenuation-corrected nuclear Bcd-GFP gradients as a function of relative position along the AP axis extracted from 35 embryos expressing Bcd-GFP fixed in n.c. 6 to n.c. 14; each dot corresponds to an individual nucleus (see Materials and Methods for image analysis procedures); color indicates nuclear cycle (see legend). Insets show log-linear plots of same data; slopes of fitted lines indicate a length constant of ∼0.15 EL from n.c. 8 onward. From n.c. 10 onward, GFP intensities for cortically localized dorsal nuclei only are shown for clarity. (C–D) Same data as in (A–B) but plotted as a function of developmental time (nuclear cycles) with copper shading indicating AP position as fraction of EL. (C) Nuclear GFP intensities as a function of time. Lines connect binned means of 50 equally spaced intervals along the AP axis. (D) Binned means normalized to the maximum attained in each bin during development, plotted as a function of time.

https://doi.org/10.1371/journal.pbio.1000596.g007

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Figure 8. Bcd-GFP gradients in fixed and living embryos.

Living Bcd-GFP (A–B) and Histone-RFP embryos (C–D) were imaged at blastoderm stages using confocal microscopy. Embryos were fixed within 3 min of live imaging, then subsequently re-imaged under the same microscopy settings (midsagittal slices of the same embryo at n.c. 13 are shown live in (A, C) and fixed in (B, D)). (E–F) Mean nuclear fluorescence intensities in living (red) and fixed (blue) embryos expressing Bcd-GFP (E) and Histone-RFP (F) as a function of position along AP axis. (G) Live and fixed Bcd-GFP gradients rescaled by 3-fold. (H) Scatter plot of fixed (x-axis) and 3-fold rescaled live (y-axis) mean intensities in equally spaced bins along the AP axis in embryos expressing Bcd fusions to GFP, Venus, or RFP. Dashed line indicates 1-to-1 correspondence. Error bars for Bcd-GFP are standard deviations within each bin. To plot curves on the same axes, values were normalized to maximum.

https://doi.org/10.1371/journal.pbio.1000596.g008

These observations of gradient dynamics differ sharply from the bcd mRNA distribution, which at no time resembles an exponentially decreasing gradient reaching to >75% EL, such as observed for Bcd-GFP from n.c. 9 onward. Bcd-GFP is visible in nuclei positioned at 50% EL and beyond from n.c. 8 onward, yet at these positions we observe essentially no mRNA particles. Instead, the protein gradient can only be accounted for if protein moves towards the posterior from anteriorly localized mRNA.

Delayed GFP Maturation Can Account for Apparent Discrepancy Between Gradients in Fixed and Live Tissue and Provides Further Evidence for Cytoplasmic Protein Movement

By live imaging, nuclear Bcd-GFP levels appear relatively stable after the 10^th mitosis [9], in contrast to our observations in fixed tissue. Additionally, we observe that the decay length of fixed gradients is approximately 0.15 EL (Figure 8A inset), compared to a decay length of around 0.2 EL in live embryos [9]. These differences do not result from the use of different microscopy methods (Figure S12) and therefore must arise from the fixation procedure.

To determine the effect of fixation on Bcd-GFP fluorescence, we imaged living Bcd-GFP and Histone-RFP embryos at blastoderm stages, then fixed the embryos within 3 min of live imaging, and subsequently re-imaged under the same microscopy settings (Figure 8A–D). We found that fixation increases the overall brightness by about 3-fold (Figure 8E–F), possibly as a result of increased transparency of fixed material mounted in a glycerol-based medium. However, rescaling live or fixed Bcd-GFP gradients by a factor of 3 reveals qualitatively different gradient shapes in the anterior 25% of the egg, wherein fixed gradients exhibit an additional increase in relative intensity (Figure 8G). This remaining difference could be accounted for if newly synthesized Bcd-GFP is not immediately visible but becomes fluorescent after fixation. This phenomenon can be attributed to the well-known process of GFP maturation ([42] and refs therein). To test whether delayed maturation can affect the appearance of Bcd gradients detected by fluorescent protein fusions, we imaged transgenic embryos expressing protein fusions of Bcd with either the rapidly maturing GFP derivative Venus [43] or the more slowly maturing mRFP [44]. We found that after 3-fold rescaling, live and fixed Bcd-Venus gradients exhibited similar appearances, consistent with the rapid attainment of fluorescence by Venus (Figures 8H, S13A–C). In contrast, rescaled live Bcd-mRFP gradients showed poor correspondence with fixed gradients along the majority of the AP axis (Figures 8H, S13D–F). This result supports the view that delayed maturation can alter the appearance of the Bcd protein gradient. In addition, by incorporating delayed maturation into a simulation of gradient formation (see below), we could qualitatively recapture the stable nuclear gradients observed in live embryos at late blastoderm (Figure S14). We note that previous work has determined that gradients of equivalent shape are observed upon quantification of GFP fluorescence and anti-GFP immunostaining in the same embryo [45]. Moreover, the distribution of Bcd protein detected by anti-Bcd antibodies does not differ between wild-type and embryos in which Bcd-GFP is the only source of Bcd protein [8].

A maturation-based explanation supports the idea of protein movement away from anterior mRNA. With delayed maturation, immature fluorescent protein synthesized at the anterior would tend to attain fluorescence while en route toward the posterior. As a result, in a live embryo, the fraction of immature eGFP would be higher in the anterior than the posterior, and allowing additional time for eGFP to attain fluorescence would then disproportionately increase anterior fluorescence compared to posterior, as we observe by fixation.

A Spatially Distributed Source Is Necessary to Account for Observed Protein Gradient Dynamics

Diffusion represents a simple plausible mechanism of protein transport away from the anterior mRNA source, and diffusion-based models such as the SDD model provide a straightforward mathematical framework for describing gradient establishment. Previous modeling efforts have treated the site of synthesis either as an anteriorly localized point source [9],[46]–[49] or as conjectured anterior domains [11],[50]–[53]. Having characterized the actual distribution of bcd RNA, we asked whether that distribution is a necessary component of gradient establishment by performing numerical reaction-diffusion simulations of gradient formation. We compared our measured nuclear gradients to protein distributions predicted to arise from either a realistic mRNA distribution or an anterior point source. We find that the combination of a non-monotonic time course for nuclear gradient amplitude (Figure 7D) and a relatively stable length constant between n.c. 8 and 14 (Figure 7B) precludes a classical SDD-type model in which the biophysical parameters of translation rate S, degradation rate τ, and diffusion D are kept constant at all times. Therefore, to reproduce the measured nuclear concentrations, our simulations utilized an “extended SDD” model which allowed some subset of these parameters to change in time (see Materials and Methods).

Using the measured bcd mRNA distribution for the source, we found excellent fits between predicted and observed nuclear protein gradients from n.c. 7 to n.c. 14 (Figure 9A–B), as determined by a χ²-error measure (Figure S15). Conversely, if the model assumes a point-source geometry at the anterior of the embryo, an equivalent search through the parameter space of extended SDD models fails to adequately reproduce our observed Bcd protein data (Figure 9C). In particular, at early time points, the point source causes anterior protein levels to rise inappropriately high to attain a good overall fit. Additionally, the disperse source allows the model to better predict the late decrease in gradient amplitude. Indeed, estimates of total protein based on available measurements suggest that total Bcd decreases between n.c. 13 and n.c. 14 despite the doubling of nuclei (Figure S11). Simultaneously with the global decrease in protein levels, we see a degradation of disperse mRNA. Our simulation can account for the observed drop in protein distribution only if we use the realistic mRNA geometry during this decay period, rather than a point source (Figure 9B, C). These numeric results demonstrate that realistic mRNA distributions significantly outperform the point source geometry in reproducing the observed protein gradient dynamics.

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Figure 9. Extended SDD models with realistic 3d geometry and source distribution.

(A) A well-fitting model with parameters as in Figure S10: solid lines are measured Bcd protein gradients from n.c. 7 (dark blue) to n.c. 14 (red); dashed line come from a single model fit. (B) Log-log plot of the measurement versus the model prediction at different developmental times (colors as in (A)); dashed black line corresponds to perfect overlap. (C) The best-fitting model when an mRNA point source at the anterior pole is assumed. Despite having the same freedom to pick the model parameters as in (B), the best-found model for the point source deviates from the data substantially.

https://doi.org/10.1371/journal.pbio.1000596.g009

A Sensitive FISH Method Captures Global bcd mRNA Particle Dynamics

Our method enabled us to quantify the global bcd mRNA particle distribution as a function of developmental time. The detection of dim particles even in the far posterior of the embryo demonstrates the improved sensitivity of our protocol. In addition, the high degree of spatial resolution allows us to document the characteristics of individual particles over developmental time. The method is sufficiently sensitive that we can successfully discriminate mRNA degradation at n.c. 14 from particle dissolution by the beginning of blastoderm stages.

Until n.c. 7, we see intensity distributions clearly separated from the noise peak (Figure S4), yielding robust estimates of particle counts with very low deviations (∼10%) across embryos (Figure 4C). As the particles disassemble after n.c. 10, the weakest particles (possibly single bcd mRNA molecules) move closer to the detection threshold, which could, in principle, lead to a significant number of missed particles. Therefore our counting results for late embryos should be strictly interpreted as lower bounds on the actual number of particles in late embryos. However, the fact that the total particle light is approximately conserved (Figure 4D), and that we can clearly identify an explicit mRNA degradation event during n.c. 14, strongly argue for the possibility that even in later embryos we are in fact recovering most of the particles and their cumulative intensity.

The biological mechanism(s) mediating mRNA particle movement during embryogenesis are as yet unknown. Previous work has shown that the reorganization of the cortical actin cytoskeleton upon egg activation allows the dispersion of bcd away from the oocyte cortex [30]. Whether endogenous bcd particles continue to localize with other cytoskeletal elements, such as microtubules, during embryogenesis is unknown, although in vitro synthesized mRNA containing the bcd 3′ UTR localization signal associates with microtubules when injected into embryos [32]. Redistribution of bcd RNP binding sites on microtubules might provide a method of scaling mRNA spatial distribution with different egg sizes. Such scaling could then potentially influence the observed scaling of the protein gradient [21].

It is interesting that bcd particles containing more mRNAs tend to be localized closer to the anterior than weakly fluorescent particles. Possibly, brighter bcd RNP complexes possess greater numbers of protein components required for establishment and/or maintenance of anterior localization, such as Staufen [5]. A greater content of Staufen (or other factors) would then lead to a greater probability of maintenance at the anterior. If so, then the slight posterior shift we observe may be linked to particle dissolution: as particles dissociate during development, they lose some fraction of localization components and tend to move posteriorly.

We observed weakly fluorescent particles in the posterior at all nuclear cycles. Such particles likely represent bcd RNA which failed to localize to the anterior during oogenesis, although we cannot formally rule out that such RNAs were in fact initially correctly localized and became posterior later. The fraction of bcd mRNA in the posterior 60% is near zero and thus contributes only negligibly to the protein gradient. Nevertheless, the embryo possesses a failsafe mechanism of suppressing bcd translation via Nanos activity in the posterior [36]. Such a failsafe might buffer the effects of environmental or genetic conditions that result in mislocalization of bcd.

The Spatial Distribution of bcd mRNA Cannot Account for Protein Gradient Dynamics

Our observations of bcd mRNA are similar to the originally observed, steeply graded mRNA distributions of St. Johnston et al. [5]. In contrast, our results do not fully agree with a recent study which suggested that posteriorly directed bcd mRNA movement at the cortex accounts for the gradient of Bcd protein [19]. Our analysis is partially consistent with their findings: during early cleavages, bcd mRNA on the embryo surface does not extend far beyond ∼5% EL (Figure 2I–J), whereas surface particles are relatively dense even at 15% EL during syncytial stages (Figure 3A, 3C, 3G). However, the latter change is the result of bulk particle movement from the interior to the embryo surface. Such movement would not have been detected in the study by Spirov et al. [19], which did not succeed in labeling internally localized bcd mRNA in either early cleavage stage embryos or unfertilized eggs (Figures 2A–C, 6A–C of Spirov et al. 2009 [19]). This is reflected in the apparent increase in total mRNA fluorescence observed in that study between n.c. 3 and 10, a behavior impossible for strictly maternally supplied transcripts, but consistent with the arrival of previously undetected internal bcd mRNA at the embryo cortex. Since the amount of mRNA falls to nearly zero too close to the anterior to account for the presence of Bcd-GFP in nuclei at nearly 70% EL, we conclude that the spatial distributions of bcd mRNA and protein are at no point in time rescaled versions of each other. As we note above, Bcd-GFP is evident in nuclei positioned at 50% EL and beyond beginning at n.c. 8, yet at these positions, the mRNA concentration is essentially zero. Similarly, Bcd-GFP is retained in yolk nuclei after bcd mRNA has relocalized cortically (Figures 6E–I, S16). Furthermore, if we suppose that Bcd is unstable so that the local concentration of bcd mRNA dictates protein concentration (as proposed recently [19]), then the amount of mRNA at, e.g., 20% EL during n.c. 7 should be the same as the amount of mRNA at 50% EL at n.c. 11, given that nuclear Bcd-GFP concentrations are approximately the same in those locations at those times; however, this is not what we observe.

Modeling Implicates bcd mRNA Distribution in Protein Gradient Dynamics

Our observations present a revised description of protein gradient dynamics in which along the entire AP axis, nuclear Bcd concentrations reach their maximum values by n.c. 11. Previous work cited the difficulties of a simple SDD-based model of gradient formation given the apparent slow diffusion coefficient D of Bcd-GFP (∼0.3 µm²/s) as measured in the blastoderm cytoplasm by photobleaching [9]. More recent measurements by fluorescence correlation spectroscopy have estimated D≈7 µm²/s, which in principle would be rapid enough to establish a stable gradient prior to n.c. 9 [22],[23]. The observations presented here, however, indicate that nuclear Bcd-GFP continues evolving beyond that point in a non-monotonic manner. Taken together with recent work suggesting that nuclei function as passive absorbers of local Bcd [40], these results would appear to preclude a classical SDD model with constant parameters in which the Bcd distribution reaches a stable state.

Simple extensions of SDD provide the mathematical framework within which to model protein movements from disperse sources. While such minimally extended models do not explicitly include the role of nuclei and non-diffusive modes of protein transport that might play an important role [51], they nevertheless allowed us to discover parameter sets that successfully predict the observed protein gradient when incorporating the observed, disperse mRNA sources; in contrast, the best fit parameters utilizing only an anterior point source do not match data as well. This result can be understood by noting that while the protein gradient beyond the AP extent of its mRNA source is not influenced much by the geometry of the source, the same does not hold for the anterior part of protein gradient that overlaps with mRNA.

We note that our measurements are limited to nuclei and that we do not explicitly account for cytoplasmic Bcd-GFP. Using currently available estimates [9], it is likely that total nuclear and cytoplasmic Bcd-GFP continue rising through n.c. 13 (Figure S11). We also note that n.c. 13 and 14 exhibit extended interphases, during which nuclear diameter increases and Bcd-GFP concentrations fall as a result [9]. These changes in Bcd levels both during and between interphases pose a challenge to understanding the transcriptional readout of Bcd concentrations. The well-documented dependence of Bcd target gene expression on Bcd levels implies that the readout process must be insensitive to such global changes in nuclear Bcd concentration. The nature of the underlying readout process, and how it achieves the observed reproducibility and accuracy of transcriptional regulation, will be the subject of future experiments.

FISH of Drosophila Embryos

OregonR embryos were fixed as described [26] in 10% paraformaldehyde and stored in methanol. We performed fluorescent in situ hybridization as described [25], using AlexaFluor 514-conjugated probes complementary to the bcd open reading frame diluted in a solution of 35% formamide, 2× SCC, 0.1% Tween-20. Embryos were mounted in Aqua-Poly/Mount (Polysciences). For high resolution imaging, we used a 100× HCX PL APO CS NA 1.46 oil immersion objective on a Leica SP5 laser-scanning confocal microscope with 514 nm excitation wavelength at 2048×2048 pixels (linear dimension of 75.7 nm) and z-spacing of 420 nm, and obtained one anterior and one posterior stack of each embryo. Low resolution images of the midsagittal plane were taken with a 20× HC PL APO NA 0.7 oil immersion objective at 1024×500 pixels.

FISH Image Analysis

To correct for drift of the microscope stage in the xy-plane, we first realigned the z-slices by starting at the midsaggital plane (z = 0) and shifted successive slices such that the pixel-wise cross-correlation in raw intensity between slice z and z+1 was maximized. To normalize for changes in optical medium with depth z, we selected 10⁵ small image patches from each posterior z-slice, computed the mean and variance in raw intensity from each patch, and fit a linear relation between the two; if noise in the image were purely uncorrelated Poisson shot noise, the slope would yield a conversion factor between the raw microscope signal and the photon counts. We then normalized every z-slice by this factor, which changed slowly and systematically with z. Neither realignment nor normalization crucially affect our reported results.

We next filtered each z-slice by a balanced circular difference-of-Gaussians filter with center radius size of 1.5 pixels and surround size 2.5 pixels, roughly matched to the size of single bcd mRNA particle, and found the local maxima in the filtered images that exceed the detection threshold. These are candidate particles. If the detection threshold is too low, the number of candidate particles in the posterior stack rapidly increases due to false detections of noise and autofluorescence, as shown in Figure S4 (red line). We pick for the threshold a value just above this rapid increase and find that after normalization, a single threshold value can be chosen for all embryos.

Each candidate particle is then processed in turn: starting with the brightest unprocessed candidate C in the z-stack, successive nearby z-slices are examined for other candidates that appear at the same x-y location due to the axially extended PSF of the microscope (Figure S3); these candidates are considered as shadows of C, not independent particles. By identifying candidates and their shadows on successive planes, we find that the average light intensity profile of the mRNA particle in the axial (z) direction is approximately Gaussian, with decay length of about 1 slice. Given our detection and microscopy settings, we therefore expect to observe 1–2 shadows for each true mRNA particle. Next, we proceed by fitting the light intensity of each candidate particle as a 2D elliptical Gaussian profile plus constant background (Figure S2). In detail, we clip 9×9 pixel patches centered on the candidate and fit a light intensity model I(x,y) = offset+amplitude * Gaussian(x−x_c, y−y_c, r_x, r_y, theta), where x_c and y_c are the light intensity center coordinates, r_x and r_y are orthogonal ellipse axes, with r_x inclined by angle theta to the horizontal. If within the 9×9 patch other candidates are identified, we clip out a larger patch and simultaneously fit all nearby candidates to properly resolve their radii and amplitudes (Figure S2). Each candidate particle in the list has thus been concisely described by parameters (x_c, y_c, r_x, r_y, offset, amplitude, number of shadows).

Since the threshold is set as low as possible to capture all mRNA signal, the candidates might include false positive detections. To eliminate these, we require that (i) r_x, r_y be above 0.7 and below 2.5 pixels, (ii) the amplitude to exceed the background offset, and (iii) the number of shadows be at least 1. Detection threshold and number of shadows are the most stringent criteria (Figure S4, blue and cyan lines), while (i), (ii) are far less restrictive. Candidates passing these criteria are considered as mRNA particles, which exhibit stereotyped, circular shape (Figure 3A–B); their intensity is proportional to amplitude * r_x * r_y. We find a very good linear correspondence between the intensity and difference-of-Gaussians filter value for each particle, and the results are robust to the choice of either of these intensity measures as the thresholded variable. Figures 3C and 4C–D report the statistics of particle counts and intensities (distributions are normalized to unit area).

To extract the spatial distributions, we must translate the x_c, y_c location of each particle detected at 100× into the projection along AP axis. Using image manipulation, we register the 20× and 100× images of midsaggital plane and extract automatically the coordinates of the AP axis, of length L, from 20× images. This allows us to compute for each particle its x/L relative coordinate, and to construct distributions in Figure 3D–F. In 4A we similarly compute the density of mRNA particles per unit area in midsaggital plane in thin slices parallel to embryo surface at depth d/L.

Protein Gradient Quantification

Embryos from yw egfp-bcd; His2Av-mRFP1; bcd^E1 females (obtained by crossing [9],[54]) were fixed in 6.7% paraformaldehyde and the vitelline membrane removed by hand. DAPI-stained embryos were mounted in Aqua-Poly/Mount and imaged using a 20× HC PL APO Gly 0.7 NA objective on a Leica SP5 laser-scanning microscope with excitation wavelengths of 405 nm (DAPI), 488 nm (eGFP), and 561 nm (mRFP). Image stacks were obtained at 2048×2048 pixels (linear dimension 445 nm) with z interval of 3.5 µm spanning approximately 75% of embryo z-thickness. Custom software employed smoothened DAPI and RFP images to identify nuclei by thresholding in individual z slices, as well as embryo edges [11], resulting in 3d nuclear masks. For embryos at blastoderm stages, a watershed was applied to separate closely spaced objects. 3d masks were checked in parallel with GFP, RFP, and DAPI images to ensure detected objects consisted only of nuclei; inappropriate objects were discarded and each independent set of connected pixels was designated a nucleus. The mean GFP and RFP pixel intensities and centroid position for each nucleus were calculated. Histone-GFP and Histone-RFP mean nuclear intensities attenuate at similar rate as function of depth beneath the embryo surface. Assuming that all nuclei contain the same DNA content and therefore the same concentration of Histone-RFP, we used the attenuation in mean RFP intensity to apply a corrective factor to nuclei (as performed previously using anti-Histone antibodies [55]). We calculated autofluorescent background by comparing to OregonR embryos, observing that nuclei at 85%–95% EL in Bcd-GFP expressing embryos contain the same mean GFP intensity as fixed OregonR embryos imaged under the same conditions. In all plots except Figure 8E–F, we show attenuation corrected, background subtracted mean nuclear Bcd-GFP values.

For the experiment in Figure 8 and Figure S13, after live imaging, embryos were immediately transferred to fixative, processed, and imaged as described above. Embryos were handled individually to ensure we could match live and fixed images to the same embryo. Live and fixed images were taken under identical conditions.

Simulations of Bcd Gradient Establishment

We performed numerical reaction-diffusion simulations of the extended SDD model on a 3d 10 µm grid. We adopted the embryo geometry from the BDTNP map [56], which represented our solution domain with no-flux boundary conditions. In the interior, we solved(1)where is the concentration of Bcd protein, and D, τ, and ρ are (nominally time-dependent) diffusion, degradation, and synthesis rates. The source ρ was taken to be a collection of measured bcd mRNA particle intensities; the positions of the particles were readjusted to undo the axial compression caused by the imaging protocol. We kept the source geometry unchanged for nuclear cycles for which we do not have explicit measurements. The total source strength was kept constant according to the observed constant total intensity with developmental time (Figure 4D). We extracted the temporal snapshots after time increments of 8 min each for n.c. 1 to 9, 9 min for n.c. 10, 10 min for n.c. 11, 12 min for n.c. 12, and 20 min for n.c. 13 and 14. The obtained concentration profiles were projected along the AP axis. As the units of measurement are arbitrary, the simulation gradients were rescaled with a single scale parameter to match as closely as possible the measurements for n.c. 7–12; the goodness of fit was defined as(2)Thus, models that have small match the data better. We then asked how closely we can reproduce the observed gradients (without any assumption about the gradient equilibration and without any reference to previously measured D and τ parameters) within the classic SDD model, where D, τ are constant and ρ is given by the measurement, assuming continuous translation from the source. As expected from the non-monotonic temporal dependence of the gradient amplitude reported in Figure 7D, no combination of parameters for the classic SDD model fits the data well.

The most straightforward extension of the SDD model is to allow some subset of translation rate, degradation rate τ, and diffusion constant D parameters to vary in time. To guide our exploration of such extended SDD models, we first noted that protein gradients at different times are rescaled versions of each other, i.e. the length scale is approximately constant from n.c. 8 onwards (relative change is less than 10% from n.c. 8 till n.c. 14), while the gradient amplitude increases by ∼3-fold from n.c. 8 to the time it reaches its peak in n.c. 12, and decreases to about 3/4 of the value in n.c. 14. Simultaneously satisfying both constraints, i.e. preserving the decay length and properly scaling the gradient amplitude as a function of time, is challenging in the framework of such extended SDD models. Decrease in gradient amplitude at later times can be generated in models in which the source turns off at n.c. 12, but if diffusion still remains active, the gradients are very flat at low x/L, inconsistent with the data. Models in which the decrease in gradient amplitude after n.c. 12 is generated by turning on degradation later yield gradients that match the data reasonably at low x/L, but do not preserve the exponential profile with a conserved decay constant across developmental time; even models in which degradation is present during the whole developmental time, but can accelerate to a higher value in blastoderm stages, do not fit the data well. Furthermore, to account for low gradient amplitudes at n.c. 7 and 8, the source needs to be turned on late, i.e. for most of the models around n.c. 5 or 6.

With these observations in mind we carried out an exhaustive search for D, τ, and the start and end of bcd mRNA translation, to find the set of parameters minimizing error (Figure S15); the source term is set to 0 before the start and after the end of translation. A well-fitting model could only be found if additionally the diffusion constant was allowed to change during developmental time. The best match to our data is obtained for models where (i) the source is active only during n.c. 6–12, (ii) degradation is essentially constant with τ∼100–140 min, and, (iii) the diffusion constant (initially set to D∼3 µm²/s) decreases sharply to 0 at n.c. 11–12 (Figure 9C–D) (a decrease to a small value, e.g. 0.3 µm²/s, instead of 0 yields an even better fit). The of this model is approximately one half of the classic SDD with realistic source.

To assess the effects of the source geometry on the protein gradients, we replaced our measured source by a point source localized at the anterior pole, and repeated the parameter search by varying D, τ, and the start and stop times for translation. The best fit in this scenario deviates substantially from the measured gradients (Figure 9D), mostly because simulations tend to overestimate the steepness of the gradient close to x/L = 0. The of this model is 2 times larger than the best extended SDD model with a realistic source.

To assess the effects of GFP maturation (Figure S14), in equation (1) represented immature Bcd-GFP and we used an additional reaction-diffusion equation for the mature species without the source (ρ) term, but including a conversion term from the immature to mature species with rate k.

We emphasize that we employ these simulations for the express purpose of exploring the potential of disparate mRNA geometries to impact protein gradient formation. Our simulations represent coarse-grained descriptions of all processes that might impact protein production, stability, and diffusion. Multiple events could influence protein movement, such as advective transport, nuclear import/export dynamics, and/or changes in numbers or affinities of Bcd binding sites [9],[48],[51],[53],[57],[58]. As such, our model does not distinguish between these, and thus it does not explicitly support the notion that Bcd movement occurs only via thermally driven random molecular motion.

Likewise, within our model, protein production and stability are bound by two assumptions: first, that translation occurs from particles in proportion to their measured fluorescence intensities; and second, that nuclear Bcd-GFP gradients at all times reflect rescaled versions of the underlying cytoplasmic gradient [9],[40]. Because we observe nuclear accumulation of Bcd-GFP beginning at n.c. 6, it is unsurprising that we obtained better fits in simulations where protein production does not begin immediately upon fertilization (Figure S15). However, absent additional data between n.c. 1 and 5, we cannot advocate that translation of bcd mRNA necessarily begins at a later time point, although this would be consistent with previous proposals [41].

Similarly, at late blastoderm, simulating an apparent gradient decay while preserving the gradient shape requires that both production and effective diffusion decrease (see Materials and Methods, Figure S15). However, we do not conclude that either production or diffusion actually slow over time, as our model does not explicitly incorporate any mechanisms that could in principle affect the distribution of protein among nuclei (e.g., the geometric increase in the number of nuclei, Bcd trapping within local nuclear neighborhoods [51],[53], or the possibility that the nuclear-cytoplasmic ratio of Bcd in an equilibrated nucleus could change over time).