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Constructing a Quantitative Spatio-temporal Atlas of Gene

Expression in the Drosophila Blastoderm

Charless C. Fowlkes1,2,, Cris L. Luengo Hendriks1,3, Soile V. E. Keränen1,4, Gunther H. Weber1,5,

Oliver Rübel1,5, Min-Yu Huang1,5, Sohail Chatoor1,3, Angela H. DePace1,4, Lisa Simirenko1,4, Clara

Henriquez1,4, Amy Beaton4, Richard Weiszmann4, Susan Celniker1,3, Bernd Hamann1,5, David W.

Knowles1,3, Mark D. Biggin1,4, Michael B. Eisen1,4*, Jitendra Malik1,6*

1 Berkeley Drosophila Transcription Network Project 2 School of Information and Computer Science, University of California, Irvine, CA 92697, USA 3 Life Sciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA 4 Genomics Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA 5 Institute for Data Analysis and Visualization (IDAV) and Department of Computer Science, University of California, Davis, CA 95616, USA 6 Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA * Corresponding Authors Email: mbeisen@lbl.gov, Phone: 510-486-5214, Fax: 786-549-0137 Email: malik@cs.berkeley.edu, Phone: 510-642-7597, Fax: 510-642-5775

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SUMMARY To fully understand animal transcription networks, it is essential to accurately measure the spatial

and temporal expression patterns of transcription factors and their targets. We describe a registration

technique that takes image-based data from hundreds of Drosophila blastoderm embryos, each co-

stained for a reference gene and one of a set of genes of interest, and builds a model VirtualEmbryo.

This model captures in a common framework the average expression patterns for many genes in

spite of significant variation in morphology and expression between individual embryos. We

establish the method’s accuracy by showing that relationships between a pair of genes’ expression

inferred from the model are nearly identical to those measured in embryos co-stained for the pair.

We present a VirtualEmbryo containing data for 95 genes at six time cohorts. We show that known

regulatory interactions within the network can be recovered from this dataset and predict hundreds

of new interactions.

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INTRODUCTION The output of animal transcription networks are dynamic, three-dimensional patterns of gene

expression. The expression level of each gene can vary radically between neighboring cells and

these intricate spatial variations play a major role in determining animal body plans. It is a grand

challenge to decipher the transcriptional information encoded in animal genomes to the point where

we can model and predict such patterns. Developing techniques that accurately characterize and

analyze gene expression patterns in the context of changing morphology is a critical step towards

this goal.

Spatial patterns of protein and mRNA expression are being systematically recorded and catalogued

by various approaches over a range of spatial and temporal resolutions in several animal systems,

e.g., Drosophila (Simin et al., 2002; Tomancak et al., 2002; Myasnikova et al., 2001; Tomancak et

al, 2007), Xenopus (Pollet et al., 2005), zebrafish (Kudoh et al., 2001), the ascidian Ciona

intestinalis (Imai et al., 2006; Tassy et al., 2006), mouse embryos (Neidhardt et al., 2000; Visel et

al., 2004), and mouse brains (Carson et al., 2005; Davidson et al., 1997; Gong et al., 2003, Lein et

al., 2007). These data sets, however, do not provide a comprehensive quantitative description of

gene expression in a whole developing embryo at the spatio-temporal resolution needed for detailed

computational modeling of animal transcription networks in three dimensions. For example, in situ

datasets constructed from images of alkaline phosphatase-based probes have provided only

qualitative, 2D descriptions of gene expression patterns that lack cellular resolution and critical

morphological detail (e.g., Tomancak et al., 2002) Kumar et al., 2002; Peng et al., 2006). Perhaps

the most comprehensive and automated expression atlas construction efforts to date are of mouse

brain (Carson et al., 2005; Davidson et al., 1997; Gong et al., 2003, Lein et al., 2007) imaged via

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serial sectioning and registered using anatomical features. These techniques, however, currently

yield relatively low temporal and spatial resolution (along the sectioning axis) and limited

quantitation of gene expression.

To address the need for highly quantitative spatial expression data, we have developed methods,

based on fluorescence microscopy, that measure relative concentrations of gene products in three

dimensions over an entire Drosophila blastoderm embryo at the resolution of individual cells

(Luengo Hendriks et al., 2006; Keränen et al., 2006) along with tools for interactively visualizing

such data (Rübel et al., 2006; Weber et al., 2007). These methods have already revealed previously

unknown features of blastoderm gene expression and morphology, such as an intricate, dynamic

pattern of nuclear densities that change over time along both body axes (Luengo Hendriks et al.,

2006; Keränen et al., 2006). These results illustrate the importance of, and were dependent upon,

capturing data for the whole embryo at cellular resolution.

A serious difficulty encountered in all current strategies for quantitating spatially resolved gene

expression is that it is not possible to label the expression of more than a few gene products in a

given animal or tissue (e.g., Kosman et al., 2004; Levsky et al., 2002). Yet, even simple portions of

animal transcription networks can comprise tens of regulators and hundreds of target genes (e.g.,

Stathopoulos et al., 2002; Liang and Biggin, 1998; Oliveri and Davidson, 2004). A single cis-

regulatory module (CRM) may often be bound by five, ten or even more co-localized regulators

(see e.g., Yuh et al., 2001). Therefore, to analyze how spatial and temporal changes in transcription

factors correlate with changes in expression of their targets, it will be necessary to simultaneously

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compare the expression levels of many more gene products than is possible with conventional

microscopy.

In this paper, we present a computational technique that overcomes this limitation by compositing

independent expression measurements made from images of hundreds of different embryos into a

common spatio-temporal atlas in which the average expression patterns of many gene products can

be studied simultaneously. Our technique involves two key components, outlined in Figure 1.

The first is a spatial registration algorithm that uses a reference gene expression pattern common to

all labeled embryos to help identify equivalent corresponding cells or nuclei across images of

multiple embryos at the same stage of development. The resulting correspondences are used to map

expression measurements for other genes, whose expression was labeled in only a subset of

embryos, onto a common model.

The second component is a dynamical morphological template that specifies the average locations

of cells or nuclei over time, providing temporal correspondences between nuclei in embryos imaged

at different developmental time points (Figure 1). This morphological template consists of an

average number of nuclei whose three-dimensional (3D) motions track changes in the average

blastoderm shape and nuclear packing density between each of six temporal cohorts during the 50

minutes prior to gastrulation (Fowlkes and Malik, 2006; Keränen et al., 2006).

Once correspondences have been established among embryos within and between cohorts,

expression measurements are combined into a single composite model, termed a VirtualEmbryo,

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which describes the average patterns of expression for many genes at multiple time points (Figure

1).

In developing our method, we measured significant geometric variability between individual

embryos at the same developmental stage both in their size, shape, number and positions of nuclei

and in the locations of gene expression patterns. We show that our registration methods correctly

take this geometric variation into account by quantitatively analyzing the relationship between pairs

of genes, a measure which is independent of the exact spatial location of cells. We find that the

relationship between a pair of genes’ expression in individual embyos co-stained for the pair is

similar to the average co-expression recorded in the model, thus demonstrating that the

VirtualEmbryo accurately describes average patterns of gene expression present in individual

embryos. Finally, to establish the utility of this comprehensive, quantitative spatial expression data,

we carry out a statistical analysis for a set of 17 regulatory factors and 95 target genes which is able

to recover many known regulatory interactions from the literature and predicts many new ones.

RESULTS

Data acquisition pipeline

Our previously established pipeline was used to obtain quantitative measurements of gene

expression in individual embryos (Luengo Hendriks et al., 2006). Briefly, embryos were fixed and

fluorescently stained to label the mRNA expression patterns of two genes and nuclear DNA. One of

the genes labeled was either eve or ftz, which were used as fiduciary markers for subsequent spatial

registration. Embryos were manually staged into one of six temporal cohorts based on the extent of

cell membrane invagination (e.g., stage 5:0-3% membrane invagination) and imaged by two-photon

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microscopy. Using the DNA marker, the location and extent of each blastoderm nucleus was

automatically determined and its location was recorded along with expression levels of the two

genes in the nucleus and surrounding cytoplasm.

The resulting data structure, which we call a PointCloud, contains 3D coordinates of the center of

mass of each nucleus, average fluorescence within each nucleus and the surrounding cytoplasm,

estimates of nuclear and cytoplasmic volumes, neighborhood relationships between nuclei, and

experimental meta-data associated with a given embryo. This provides a compact representation of

the image data for each embryo that is readily amenable to further computational analysis, while

faithfully capturing the blastoderm morphology and gene expression patterns measured.

PointClouds were generated for 1822 embryos, including data for 95 genes over the 50 minutes

prior to the onset of gastrulation.

Spatial registration

Analysis of the PointCloud data suggests that even embryos at approximately the same

developmental stage vary quite significantly in their size, shape, number and distribution of nuclei,

and in the relative spatial locations of gene expression patterns (e.g., Figure 2). This geometric

variability in the data describing individuals must include true biological variations among embryos

as well as measurement errors and physical deformations introduced by our methods.

For example, the PointCloud data showed that the embryos imaged ranged in overall egg-length

from 301µm to 502µm (mean=398µm, std dev=29.4µm). Although some of this size variation

certainly results from the fixation, staining and mounting procedures the embryos were subjected to,

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much of it likely represents true biological variation since egg length and blastoderm surface area

showed a marked correlation with the total number of peripheral nuclei (r = 0.62 and r=0.64, Figure

2A,B). While our counts of nuclear number (which exclude yolk nuclei and pole cells) are also

subject to some small error on the order of a few percent (Luengo Hendriks et al, 2006), these errors

are too small to explain the measured variation and should not correlate with egg length or surface

area. Thus significant biological variation in the shapes of individual embryos must exist prior to

any experimental manipulation. Indeed, the variation in embryo size we measured is comparable to

reports for embryos that have not been fixed and stained (Warren, 1924; Azevedo et al, 1996) and

our automated counts of nuclei number are comparable to those derived from manual counting of

nuclei in a few embryos (Zalokar and Erk, 1976; Turner and Mahowald, 1976). Although a

correlation between embryo size and nuclei number among members of a population has not been

noted previously, our observation is consistent with the results of embryo ligation experiments,

which have shown that nuclear divisions are controlled by local nuclear densities (reviewed by

Edgar et al, 1986). Thus, our PointCloud data can be used to detect many aspects of biological

variation which have not been realistically measurable before.

Such large geometric variation makes comparing gene expression among individuals non-trivial, as

some technique more sophisticated than simply overlaying embryos is required to identify

equivalent corresponding cells in different embryos. Unlike the adult animal, the blastoderm lacks

distinctive morphological features that identify particular cells or tissues. Instead, nuclei are

primarily distinguished by the expression levels of transcription factors and other regulators that

control development, including the genes whose expression we measured. Therefore, our spatial

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registration method seeks to identify corresponding nuclei in different embryos which have similar

gene expression profiles.

Broadly, our spatial registration method works as follows. We first use data from all PointClouds in

each temporal cohort to build a morphological template with a fixed number of nuclei arranged to

match the average measured nuclear distribution and mean embryo shape. The template also

specifies the mean locations of the ftz and eve marker gene expression boundaries (Figure 1). We

compute a smooth deformation of each individual PointCloud to warp both the extracted marker

gene boundaries and the overall PointCloud shape into alignment with the template (see Figure 3).

For each nucleus, a best match in the template is identified, establishing correspondences for all

cells across all embryos in the cohort. Once detailed correspondences among embryos have been

found, estimates of the average locations of marker genes specified in the template are refined and

the spatial registration process repeated until further iterations provide no significant changes in the

correspondence. We now describe this process in more detail (see also Experimental Procedures).

An initial estimate of the deformation required to bring PointClouds of a given cohort into register

with the template was computed by automatically identifying the anterior-posterior (A-P) axis and

scaling the PointClouds to the average egg length for that cohort. To establish the dorsal-ventral (D-

V) orientation, the location of the ventral midline was judged by eye using gene expression and

morphological markers. While this coarse alignment step did bring the reference genes into closer

alignment by factoring out gross variations in overall embryo size, significant differences remained

in the locations of expression patterns, as well as residual differences in PointCloud shape and the

distribution of nuclei. For example, Figure 2C, D shows the standard deviation in the A-P locations

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of ftz expression boundaries before and after scaling embryos to the average egg length. Measuring

expression boundaries with respect to egg length removes up to half the apparent variability in some

stripe boundary locations but standard deviations after scaling are still near 30% the average stripe

width.

To determine correspondences in a way that factors out this remaining non-rigid geometric

variation, we carried out a fine registration step in which the embryos in each temporal cohort were

registered onto the morphological template using the boundaries of either ftz or eve expression

domains. These two markers provided high contrast boundaries (up to four-fold change in

fluorescence between neighboring nuclei) whose locations were easy to extract by identifying

maxima of the gradient magnitude along the blastoderm surface. At a given coordinate around the

embryo’s D-V circumference, these genes provide 14 well-defined A-P locations spaced along the

trunk region (Figures 1 and 3). To match stripe boundaries extracted from each PointCloud to the

template, we performed an alignment using dynamic programming along the A-P axis at each of 40

D-V circumference coordinates spread uniformly around the circumference of the embryo. This

matching allowed for the possibility of missing edge points or falsely detected edges arising from

non-specific staining (see Experimental Procedures).

After matching points along stripe boundaries were identified, a non-rigid 3D coordinate

transformation, or warp, was computed that brought the corresponding points into alignment with

the template (Figure 3). We represented this coordinate transformation using a non-parametric

deformation model, the regularized thin-plate spline (TPS) (Duchon, 1977; Meinguet, 1979;

Wahba, 1990). The TPS is the higher-dimensional generalization of the cubic spline and has been

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shown effective for modeling variation in biological forms (Bookstein, 1989). We found that in

practice, the TPS yielded quantifiably better registration results than other splines we tested (see

Experimental Procedures). Once all PointClouds had been warped into alignment with the template,

each nucleus in the morphological template is assigned to the nearest PointCloud nucleus. This

many-to-one matching, which allows multiple nuclei in the template to correspond to the same

detected nucleus, is appropriate since the total number of nuclei varies across embryos. Averaging

the marker gene expression measurements from individuals onto the template gives an improved

estimate of the template stripe boundary locations. The entire process of deriving correspondences

was repeated using this improved template until no further significant change was observed between

iterations.

The warping of individual PointClouds during fine registration not only establishes more accurate

correspondences between cells, but also provides an estimate of the geometric variation among

PointClouds, excluding that component due to isotropic variation in size (which was removed by

coarse alignment). Supplementary Figure 1 shows example deformations required to bring

individual PointClouds into alignment with the template during fine registration. Supplementary

Figure 2 shows a principal components analysis (Mardia et al., 1979) of these spatial deformations.

The figure indicates the directions along which nuclei were displaced relative to the average shape

but the magnitude of the displacement has been greatly magnified for the purposes of visualization.

The dominant mode of this geometric variation, which explained more than 45% of the variance in

displacement fields for all cohorts, was an anisotropic “bulging” about the blastoderm center. We

also measured overall shifts along the A-P axis in the location of the trunk domain specified by the

marker genes (8% of variance), curving of the embryo axis (6% of variance), and more subtle

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variations in the asymmetry between anterior and posterior ends and dorsal and ventral sides of the

PointClouds (Supplementary Figure 2, rows 2, 3, 4).

Temporal correspondence

To track the temporal dynamics of gene expression, it is necessary to estimate correspondences

between the nuclei in successive temporal cohorts. While there are no nuclear divisions during the

50 minute period spanned by our cohorts, we previously showed using both fixed and live embryo

data that there are changes in the locations of both nuclei and gene expression patterns (Keränen et

al., 2006). Careful measurements of several genes, including eve and ftz, showed that expression

pattern domains move relative to the lattice of nuclei, and thus our marker gene boundaries cannot

be used to identify corresponding nuclei over time (Keränen et al., 2006). Furthermore, based on

nuclear tracking in live imaging and nuclear density measurements from fixed material, we found

that, as well as moving basally and elongating, nuclei flow from the anterior and posterior poles

towards the dorsal surface (Keränen et al., 2006). Previous models of the Drosophila blastoderm

have tacitly assumed that a unique spatial coordinate identifies the same cellular/nuclear location at

different times (e.g. Jaeger et. al. 2004; Lucchetta et. al. 2005; Lott et. al. 2007). Our results clearly

indicated this assumption is not valid as localized contractions or expansions of the blastoderm

surface mean some nuclei consistently travel as far as three cell diameters during stage 5 (Keränen

et al., 2006).

In order to take these nuclear movements into account in establishing correspondences across cohort

templates, we developed a method to infer nuclear movements from fixed material (Fowlkes and

Malik, 2006). The average embryo shape and nuclear density pattern from each cohort was used to

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constrain a numerical model that predicted the direction and distance each nucleus needed to move

through space to account for the measured changes in density and shape between cohorts. Based on

the behavior of nuclei observed in live imaging (Keränen et al., 2006), our model assumed that

nuclear movements were smooth and small, and that the total number of nuclei was conserved. The

resulting morphological template time-series, which specified the locations of 6078 nuclei for each

of the six temporal cohorts, was used for spatially registering and compositing expression data as

described above. This provided the needed correspondences between nuclei at different time points

(Figure 1).

Compositing expression levels

Before averaging expression levels for each gene onto the morphological template, it was necessary

to put fluorescence measurements from different embryos onto a common scale. While our data

does provide an accurate measure of relative mRNA expression levels of a gene between cells

within an individual embryo (Luengo Hendriks et al., 2006), our fixation, and staining methods

result in variation in the absolute fluorescence between different embryos. In particular, the

absolute degree of fluorescence varied significantly across embryos stained in different batches,

presumably due to variable reaction time and efficiency and other experimental artifacts.

To mitigate this error, we normalized mRNA expression levels for each gene across multiple

batches by assuming that the total expression level of a gene was the same between embryos in the

same cohort, and that the fluorescence levels measured in different batches were related by a single

multiplicative factor. Once expression levels were normalized, we averaged peak expression levels

for each gene across all embryos within each temporal cohort in order to estimate the degree of total

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up- or down-regulation between cohorts (see Experimental Procedures). As Supplemental Figure 3

shows, the relative temporal changes in averaged fluorescence levels measured for each gene were

reasonably consistent across staining batches. These expression time-courses matched general

expectations based on other data, suggesting that absolute differences in fluorescence provide a

useful estimate of relative changes in expression levels between cohorts.

To remove any remaining differences in the quantitation of each gene between embryos within a

cohort, we chose a scale and offset for each embryo that minimized the average standard deviation

in expression between embryos, subject to the constraint that the maximum average expression level

matched the estimated time course. The scaled expression data for each gene from each PointCloud

was then transferred to the corresponding nuclei in the appropriate cohort template and averaged

together.

The atlas

The result of registration and compositing is a VirtualEmbryo that describes the average dynamics

of gene expression and morphology in the blastoderm. Figure 4 shows example lateral views of the

final average expression patterns recorded in the VirtualEmbryo for several genes displayed in

cylindrical projection. This “unrolling” of the blastoderm surface allows one to see the entire

pattern of expression laid flat. As the embryos are approximately bilaterally symmetric, we show

only the left side from dorsal midline to ventral midline. Supplementary Figure 3 shows the

complete set of mRNA patterns for 95 different genes estimated from 1822 embryos and over 11

million cells. The genes analyzed include many of the known early acting transcription factors that

specify patterning prior to gastrulation in Drosophila. For 23 of these factors, we have combined

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mRNA data from 25 or more embryos spanning the entire 50 minutes leading up to gastrulation.

For the remaining 72 genes, which are known or putative targets of these early transcription factors,

we have collected mRNA data from a smaller number of embryos falling primarily in the three

temporal cohorts just prior to gastrulation.

In addition to the average description present in the VirtualEmbryo, we also provide the individual

raw PointClouds, files recording the nuclear correspondences identified between each individual

PointCloud and the VirtualEmbryo, and associated meta-data. We refer to this comprehensive

dataset as a “gene expression atlas”. Our VirtualEmbryo and the initial atlas release are publicly

available through a web-based interface hosted at http://bdtnp.lbl.gov/. [[For purposes of review,

we have enclosed a pdf file containing screen shots of this part of our website as it will appear when

our work is published. A previous release containing of a smaller set of individual PointClouds is

currently available for viewing at the link given. ]]

Evaluating registration quality

It is nearly impossible to judge by eye if the correspondence between nuclei in two different

embryos is “correct” as most blastoderm nuclei lack any identifying morphological features. Since

our method for determining correspondences is based on finding equivalent nuclei using gene

expression data, one objective criterion we have used to evaluate the accuracy of our registration is

to measure the extent to which nuclei from different individuals identified as corresponding have

similar expression profiles. A second evaluation criterion is to ask how accurately the mean

expression data in the VirtualEmbryo quantitatively captures the relationships between

transcriptional regulator and target gene expression patterns as measured in individual embryos co-

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stained for the target and the regulator. This evaluation speaks directly to the utility of the

VirtualEmbryo for modeling transcriptional regulation.

Registration decreases the apparent variation between PointClouds.

In principle, a perfect registration method would remove all of the differences between individuals

that are attributable to geometric variation. Any remaining variation would then constitute measured

expression differences between otherwise equivalent cells. Such non-geometric variability could

arise from measurement error or from genuine regulatory variability, such as stochasticity in the

response of targets to their regulators (see e.g., Gregor et al., 2007). Quantifying non-geometric

variability is important as it limits the degree to which any registration method can possibly reduce

the apparent expression variation among embryos. Although the true amount of regulatory

variability between embryos is uncertain, below we describe an experimentally derived upper-

bound and measure how close our registration results are to achieving this limit.

First we examined the effect of registration on the apparent variation in expression levels for

reference and non reference genes. Figure 5A,B shows the mean and standard deviation in

expression levels at a given time point (stage 5: 50-75%) for three different genes along a lateral A-

P strip (n=100, 25, and 8 embryos for ftz, slp1 and gt respectively). For comparison, the variation in

expression is plotted when nuclear correspondences have been determined by coarse alignment

alone, i.e., assuming nuclei at the same relative spatial location along the A-P axis correspond

(Figure 5A). We quantified the apparent inter-embryo variation in expression for each gene in a

cohort by averaging the standard deviation across all corresponding nuclei in each PointCloud

containing data for the gene (Figure 5A,B, top right of each panel; Supplemental Table 1). The

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apparent inter-embryo variation is lower when correspondences are derived from fine registration

rather than coarse alignment alone. Furthermore, after fine registration our estimates of the average

patterns become less “blurry” and more like those observed in individual embryos, particularly for

highly modulated pair-rule patterns (e.g., ftz and slp1).

The decrease in apparent variability of our registration marker (here ftz) suggests that our fine

registration accurately identified corresponding ftz boundaries and warped them into alignment.

More importantly, the apparent inter-embryo variation also decreased for “held out” expression

patterns (e.g., slp1 and gt) which were not used during the fine registration process. This indicates

that our deformation model (TPS warping) makes good predictions about how all nuclei should be

shifted based only on how the nuclei near ftz or eve boundaries are shifted. This holds true both for

trunk patterns that are close to the marker expression stripes (e.g., slp1) and for cephalic patterns

(e.g., anterior gt) that are relatively far from the registration marker. Supplementary Table 1 shows

the change in apparent variability between coarse alignment and fine registration for 23 early

factors. The decrease in variation holds true for most of these genes and time-points. One general

exception is D-V patterning genes, suggesting that the precise locations of D-V expression

boundaries are fairly uncorrelated with our A-P registration markers. Interestingly, the importance

of fine registration generally increases as patterns become more sharply localized over the course of

stage 5.

Expression relationships are similar in co-stained embryos and registered PointClouds

While the above analysis shows that fine registration yields better correspondences than coarse

alignment alone, it does not address what fraction of the remaining variation in expression between

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individuals after fine registration is due to remaining geometric variability and what fraction is

attributable to non-geometric causes. To experimentally establish a baseline on the non-geometric

variability measured among embryos, we directly estimated the relation in expression levels

between pairs of genes in individual embryos co-stained for both genes. This measurement is

invariant to spatial deformations of the individual embryos so any variability measured in the co-

expression across co-stained embryos must arise from non-geometric sources. We can directly

compare the variability in this relation to that inferred by registering data from pairs of embryos

where each embryo was stained for only one of the two genes in order to judge how much

geometric variability remains after registration. The average co-expression relationship estimated

from directly co-stained embryos also provides a “gold standard” against which we can compare the

average co-expression recorded in the VirtualEmbryo inferred from the registered pairs.

Figure 5C shows the relation in expression levels of eve and gt within a three cell wide lateral strip

at the anterior boundary of eve stripe 2 in embryos co-stained for both eve and gt. Each point in the

plot gives the joint expression level measured in a single nucleus from one of 44 embryos at stage

5:9-75%. It is known that gt plays a key role in determining the anterior boundary of eve stripe 2.

This regulatory relationship is revealed in the tight anti-correlation between the two genes’

expression in this part of the embryo (Figure 5C). The blue curve in Figure 5D shows the average

relation between the two factors estimated by binning nuclei based on the level of gt expression and

then computing the average level of eve for each bin. The variability in the relation between the two

genes was quantified by computing the standard deviation for eve expression in each bin. We

measured a maximum standard deviation of 0.21 (relative to a maximal eve expression of 1). This

measure of local variability is comparable in magnitude to similar measurements made on the

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relation of bcd and hb (Gregor et al., 2007). Because this variation is measured within individual

embryos, it cannot be due to geometric variation and thus is not removable by our registration

method. Instead, this variation is likely due to some combination of variability in the regulation of

eve by gt, spatial variations in other unmeasured regulatory factors that also influence eve

expression, and error in our measurements of mRNA concentrations.

Having set an upper bound for non-geometric variation, we then used the co-stained embryo data to

quantify the effect of geometric variation between embryos on the apparent relationships between

regulator and target expression in coarsely registered embryos. Pairs of co-stained embryos were

selected at random and the level of eve in one nucleus was compared to the level of gt in a nucleus

at a corresponding spatial location in the other embryo. The red curve in Figure 5D shows that the

resulting estimate of co-expression in coarsely aligned embryos is significantly different from that

derived from individual co-stained nuclei. Furthermore the apparent variability in the level of eve

as a function of gt is significantly larger. In contrast, if we sample pairs of nuclei from different

embryos that were identified as corresponding by the fine registration process (in this case using

eve as the reference gene) the resulting curve (green in Figure 5D) is very similar to the direct co-

stain curve and has a similarly small apparent variability. This implies that while the exact location

of eve stripe two varies significantly from one embryo to the next (we measured similar variability

to that reported for ftz in Figure 2) the pattern of gt is shifted in a correlated manner. Supplemental

Table 1, which specifies the change in the apparent variability of individual genes before and after

fine registration, thus characterizes the extent to which expression patterns of individual genes are

correlated with those of our registration markers.

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Since most genes are spatially correlated with our registration marker in individuals, this suggests

that the composite VirtualEmbryo data should accurately capture average regulatory relationships

between individual genes as well as between each gene and the registration marker. We verified

this experimentally as displayed in Figure 5E, which shows the co-expression levels for eve and gt

estimated from a VirtualEmbryo constructed using embryos stained for either eve and ftz or gt and

ftz. In this experiment, embryos were registered using ftz as the marker gene and pairs of

corresponding nuclei from different embryos were used to estimate the level of eve as a function of

gt. As the green curve in Figure 5E shows, even though gt and eve are never observed in the same

embryo, the mean functional relationship inferred from the virtual co-expression measurements is

quite close to that inferred from co-stained embryos. The resulting average estimate deviates from

the co-stain estimate by less than 7% of the maximum expression level and has a maximum

standard deviation of 0.30. In contrast, using only coarse alignment to register these same embryos

yields an average relation with a different shape (red curve, Figure 5D) and larger variability (max

std dev = 0.36). Further analysis suggests our estimates of the variability after registration may be

quite conservative (see Experimental Procedures).

In summary, the results of testing our two evaluation criteria suggest that the registration process

successfully factors out a large fraction of the geometric sources of variability, leaving an average

estimate of expression which is quite close to that measured in individual embryos.

Inferring regulatory interactions from spatio-temporal expression data

One of our chief motivations for developing the blastoderm expression atlas is to help determine

which transcription factors regulate which target genes. It has generally been shown that the

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expression patterns of regulators frequently correlate, at least in some portion of an animal, with

those of their target genes. For example, the anti-correlation of gt expression with eve expression

across the anterior border of eve stripe 2 described previously (Fig. 5). In principle, it ought to be

possible to infer regulatory relationships by searching for such correlations. It is unlikely that the

resulting inferences will always be correct, and cannot be taken on their own to indicate that a

transcription factor directly binds and regulates a target gene. They should, however, provide a

significant constraint on possible models for the network, which when combined with other classes

of data such as genome-wide in vivo binding data and in vitro DNA specificity data, will lead to a

deeper understanding of how combinations of factors act together to generate specific

transcriptional outputs.

To demonstrate the utility of the composite expression atlas for inferring regulatory interactions, we

performed a regression analysis to predict regulatory interactions based solely on the spatial

expression data. Since the major transcriptional regulators in the Drosophila blastoderm are known,

we searched for a subset of these potential regulators whose combination best predicted the spatio-

temporal dynamics of each of the 95 genes whose expression we have recorded. Let M(x,t) be the

level of mRNA transcription of a given target in a blastoderm nucleus x at time t and P(x,t) be a

vector where the ith entry specifies the protein concentration of the ith potential regulator. We

sought to identify a set of regulators P and a function F that predicted the target expression M as a

function of the regulator concentrations for all nuclei and cohorts, i.e. M = F(P) for all x,t.

We used a generic form for F consisting of a sigmoid applied to a linear combination of the protein

concentrations (with weighting vector a) and a constant offset b. This linear model was explicitly

22

choosen to be as simple as possible, e.g., ignoring complexities such as possible heteromeric

interactions between transcription factors. To fit the parameters a and b to our observed data, we

performed least squares minimization over all nuclei at all time points for which we had data and

characterized the goodness of fit for each target (see Experimental Procedures).

Because the individual components of blastoderm expression patterns (e.g. each stripe) are often

controlled by distinct cis-regulatory modules (CRMs) (e.g. Fujioka et. al. 1999), we automatically

segmented each target output pattern into individual expression domains and fit each such “module”

independently, assuming that expression elsewhere was zero. This let us use a simple form for the

regulatory function F while still allowing, say KR to repress eve stripe 5 but activate eve stripe 3.

Even for this simple linear model, there are still a large number of potential regulators, which may

result in overfitting. In preliminary experiments, models fit using the complete set of regulators

typically assigned small weights to a large number of factors, limiting their explanatory power. In

contrast, the presence or absence of even a single regulator in vivo has been shown to often have

dramatic effects on the patterns of target genes (see e.g. Carroll 1989; Clyde 2006). Thus, to make

fits more interpretable, we restricted the model space by only considering those weighting vectors a

with 6 or fewer non-zero entries. We selected the best 6 regulators from a pool of 17 early acting

transcription factors by exhaustive feature selection, choosing that set of 6 regulators which best

predicted the each target pattern (largest R2 ).

Because protein expression patterns differ both spatially and temporally from mRNA expression

patterns, we added additional PointCloud data to the atlas from 302 embryos stained with antibodies

23

to BCD, HB, GT, or KR proteins (see Experimental Procedures). Expression patterns for these

proteins are shown in Supplemental Figure 5. Since we lacked protein data for the remaining 13

early transcription factors, we approximated their protein patterns by the distribution of their mRNA

with a fixed temporal delay of two cohorts (roughly 16 minutes), i.e. )16,(),( !" txMtxPii

. For

those strictly zygotic factors for which we measured both mRNA and protein expression data, we

have found that this temporal delay of the mRNA pattern gave the closest match to the gene’s

protein pattern (e.g., Luengo et al, 2006). In addition, using this two cohort delay to approximate

protein patterns yielded the best average quality fit across all genes on held out data in our

regression analysis.

Figure 6 A and B shows the correlation coefficients of each of 17 regulators (columns) determined

by the fitting process for each target eve and gt stripe (rows). Green indicates predicted activators,

red indicates repressors, and black indicates unused regulators (zero entries). Supplemental Figure 6

shows similar fits for all 238 “modules” for the 95 genes in the atlas and Figure 6C summarizes the

distribution of R2 values for all modules.

Broadly speaking, the R2 goodness-of-fit values demonstrate that we can fit much of the expression

data quite well with our relatively simple linear model. Of the 238 modules, 202 (85%) were fit with

an R2 value of 0.5 or greater. This suggests that this small set of 17 regulators contain enough

spatial information to generate the wide variety of cell expression profiles that are apparent by the

end of stage 5.

24

In addition, the regression analysis contains many correct predictions. For example, the analysis

correctly predicts HB as an activator of eve stripe 2 and KR, KNI and GT as repressors (Small et al,

1992; Arnosti et al, 1996). Similarly, for gt stripe 5 the analysis correctly predicts repression by HB

and Huckebein (Eldon and Pirrotta, 1991). Interestingly, the analysis predicts regulation of A-P

target genes by D-V regulators. For example the gt stripes clearly have a D-V pattern which is

picked out by the regression (regulation by SNA and BRK).

Not surprisingly, this model also has some clear failures. For example, BCD does not appear as an

activator in many cases, including for one of its best characterized targets, eve stripe 2. This is not

too surprising since the method will tend to pick regulators whose protein expression changes

sharply near boundaries of the target pattern, while BCD has a graded expression pattern. Another

limitation is that the expression “modules” that we automatically identified may not correspond to

the output of distinct CRMs. For example in eve, stripes 4 and 6 are both controlled by the same

regulators acting via a single CRM and stripes 3 and 7 both by another CRM (Clyde 2003). This

may in part explain the relatively poor quality of fits in Figure 6A to these stripes. The addition of

such known biological information to the model, as well as addition features, such as cooperative or

competitive interactions between pairs of factors acting on CRMs, will no doubt allow even more

precise fits to target expression patterns.

Finally, the comparison of the prediction’s of the regression analysis to results in the literature

underlines the well known difficulty in correctly divining regulatory interactions within this

complex network. For example, our analysis predicts SLP as a regulator of several gt stripes and yet

in slp loss of function mutant embryos, gt expression is not affected (Eldon and Pirrotta, 1991).

25

Such loss of function genetic experiments, however, cannot rule out the possibility of functionally

redundant regulatory interactions, as revealed in other cases by more detailed experiments (e.g.

Laney and Biggin, 1996; Manoukian and Krause, 1992; Walter et al, 1994), and thus cannot

disprove predictions of our regression analysis. This and other complexities of the system suggest

that picking apart network interactions will require careful consideration of multiple datasets.

DISCUSSION

Our work establishes the first spatio-temporal quantitative atlas of gene expression and morphology

for a whole embryo at cellular resolution. By using registration to bring quantitative gene expression

data for many genes into a common spatio-temporal frame, our work opens the way for quantitative

analyses of the large networks of interactions between developmental regulators and their targets.

Our initial regression study demonstrates the utility of this dataset for such analyses. The

correspondences established between cells in different embryos also provide a unique tool for

exploring variations in morphology and gene expression between individuals, beyond those already

noted in this paper. We anticipate that the composite VirtualEmbryo expression and

correspondence data derived here will allow novel insights into many aspects of the system-level

biology of developmental regulatory networks.

Accuracy of Registration

In general, registration techniques are designed to establish correspondences by factoring out a

certain class of variations between individuals (typically geometric variation in size and shape etc.)

while maintaining other variations of interest. Characterizing the performance of a particular

algorithm, however, is conceptually difficult since the actual nature of the variations under study is

26

seldom known in advance. Our analysis suggests that the registration method presented here comes

close to separating geometric variability from the regulatory variability with which promoters in

different cells respond to similar concentrations of transcription factors, at least to within the

accuracy afforded by our measurement techniques. Factoring out geometric variability will be

important in isolating and characterizing differences in regulatory mechanisms, both within and

between closely related species.

From a practical perspective, our results suggest that our registration procedure yields a

VirtualEmbryo containing average expression data that is nearly as accurate as could be obtained

from averaging directly co-stained embryos, and is thus sufficient for many types of analyses of

regulatory interactions. It is worth noting that in a high-throughput setting, our method is far more

efficient than direct staining. To measure pair-wise interactions between N genes directly requires

imaging on the order of N2 embryos, stained for each possible pair of genes. In contrast our method

only requires staining and imaging N embryos.

We feel confident that the registration methods outlined here can be extend to later developmental

stages as well as other organisms with segmented body plan architectures (e.g., vertebrates). We

have also explored a more generic technique, “shape context matching” (Fowlkes et. al., 2005),

which is applicable to general patterns of expression. Although the blastoderm has a very simple

morphology, it exhibits the key challenges in building cellular resolution expression atlases:

biological and experimentally induced variability across animals, temporal changes in morphology

and gene expression, and ambiguity in cell identity. In later developmental stages that have complex

morphologies, the locations of nuclei and cell membranes provide far more information about the

27

identity of a particular cell (unlike the fairly homogeneous blastoderm). In these cases,

morphological features will likely be more useful in constraining the correspondence step. On the

other hand, deformation models used for registration will have to be more flexible and localized to

track complicated anatomical structures (e.g., legs or gut).

Variation between individuals

By identifying corresponding cells, our method allows the direct comparison of the locations and

expression profiles of homologous cells in different individuals. This provides a novel tool for

understanding biological variability arising from genetic, environmental and stochastic sources

within a population. Indeed, as a natural outcome of the development of our registration method, we

have already measured several important aspects of variation between individual blastoderm

embryos. Although some of the variation measured must represent experimental error, as discussed

earlier, a significant percent of the measured differences clearly reflect real biological differences

between embryos.

For example, we have estimated a quantitative upper-bound on the degree of regulatory variability

in the relationship between gt and its repression of the target CRM eve stripe 2. The values we

measure are largely consistent with the earlier work of Gregor et al. who made a similar estimate for

the variability in HB concentration as a function of BCD (Gregor et al., 2007).

We have also provided analogous upper-bounds on the degree of geometric variability. In particular,

we discovered there is a significant correlation between the number of nuclei and size of the

embryo. Although this has not previously been reported, it is consistent with earlier results from

28

embryo ligation experiments suggesting that the number of nuclei and nuclear divisions is

determined by some mechanism that senses, in different parts of the embryo, local nuclear densities

(Edgar et al, 1986). It is also consistent with the result of manipulation experiments in echinoderm

and vertebrate embryos that suggest the ratio of cytoplasm to nuclear material regulates the number

of cells at the mid-blastula transition (reviewed by Edgar et al, 1986). Our extensive measurements

imply that even among wild type embryos that have not been experimentally manipulated, even

modest quantitative changes in egg size likely influence locally the number of nuclear

divisions/nuclear loss events.

This novel decomposition of variability into geometric and regulatory components highlights the

importance of registration methods not only as a technical tool for compositing data but also as a

fundamental approach to understanding and describing the accuracy with which developmental

regulatory systems function.

Predicting regulatory interactions from comprehensive spatio-temporal expression data

The closest work to ours is that of (Myasnikova et al., 2001) and (Spirov et al., 2002) who

registered spatial profiles of protein concentrations along the A-P axis of the Drosophila blastoderm

using images of the lateral surface of embryos which had been flattened before imaging. While their

data only provides a 1D picture that largely disregards the blastoderm morphology, it has been

widely adopted for use in modeling pattern formation due to its quantitative nature (see e.g.,

Janssens et al., 2006; Perkins et al., 2006; Alves et al. 2006; Ludwig et al., 2005; Aegerter-Wilmsen

et al., 2005). Our approach expands this quantitative picture of pattern formation with an explicit

29

description of changing morphology and comprehensive coverage of many more spatially patterned

genes, in full 3D.

We have demonstrated a technique for analyzing such 3D spatio-temporal expression data in order

to uncover regulatory relationships between transcription factors and their targets. While our model

of regulation is intentionally quite simple, it is capable of explaining many target patterns quite well

with only a few regulators (as witnessed by high R2 values for most of the targets). We are also able

to recover many interactions proposed in the literature. While our model does not capture many

potential subtleties of regulation such as co-operative or competitive interactions between multiple

bound factors, post-transcriptional and translational control mechanisms, phosphorylation, etc.,

clearly it could be extended and made more accurate by including these processes (see also e.g.,

Clyde 2003; Struffi 2004; Rivera-Pomar 1996; Ronchi 1993; Simpson-Brose 1994).

Our long-term goal is to construct high fidelity VirtualEmbryos containing protein and mRNA

expression data thousands of genes with the quantitative accuracy necessary to provide firm

grounding for a new generation of pattern formation models that take into account features such as

3D diffusion and transport, nuclear movement, and interaction between A-P and D-V patterning

systems. The availability of accurate 3D quantitative data at cellular resolution should provide far

more constraints on potential models of the regulatory structures underlying animal development.

A visualization tool

One of the challenges of complex quantitative datasets is the difficulty of exploring them. In our

case, the data represent dynamic 3D information for many genes, which is fundamentally difficult to

30

visualize all at once. Since many biologists lack the mathematical and computational skills needed

to work directly with the data files provided, the BDTNP has built a comprehensive set of tools for

interactive visualization and analysis of the atlas, called PointCloudXplore, that run on Windows,

OS X, or UNIX operating systems (Rübel et al., 2006; Frankel, 2007). These tools allow the user to

explore VirtualEmbryo expression data using a simple graphical interface.

For example, the entire surface of the VirtualEmbryo can be viewed in cylindrical projection with

colored surface plots whose height represents gene expression levels (Figure 7). This allows the

expression of several selected genes from one or more stages to be compared across all cells of the

embryo at once. Abstract visualizations are also available that allow gene expression profiles for

specified groups of cells to be compared using 2D and 3D scatter plots (see Supplemental Figure 7),

parallel coordinates, cluster analysis, and bar graphs (Rübel et al., 2006; Rübel, Weber, Huang,

DePace, Fowlkes, Luengo Hendriks, Keränen, Hagen, Bethel, Eisen, Knowles, Biggin, and

Hamann, unpublished data). This tool has been instrumental in informing the development of our

methods and in some of the discoveries made to date. Its availability greatly extends the utility of

our gene expression atlas. [[If the reviewers wish, we can make a version of PCX and the

VirtualEmbryo available to them]]

EXPERIMENTAL PROCEDURES

Imaging individual embryos

Individual embryos were fixed and fluorescently stained to label the mRNA and/or protein

expression patterns of two genes and nuclear DNA, mounted on microscope slides and imaged

31

using protocols in (Luengo Hendriks et al., 2006). Additional antisense RNA probes were

generated from PCR-products of cDNAs in Drosophila Gene Collection I and Drosophila Gold

Collection (for the list of used probes, see the online database). For protein stains, the primary rabbit

antibodies against BCD, KR, and GT were generated by BDTNP, the guinea pig antibodies against

HB and KR were gift from J. Reinitz. The primary antibodies were detected using Alexa546-,

Alexa555-, or Alexa610-conjugated secondary antibodies (Molecular probes, 1:500). Embryos were

usually stained for either eve or ftz and one of the other 93 genes shown in Supplemental Figure 3.

Photomultiplier gains were set so that all the pixels of interest fell within the 12 bit dynamic range.

These settings were recorded and later used to recover the absolute fluorescence level using a

calibrated power-law fit.

Expression values in the PointClouds were corrected for attenuation using a modified version of the

method described in (Luengo Hendriks et al., 2006). The mean intensity of the DNA stain within

the nucleus was assumed to be constant for all nuclei, but to account for different attenuation at

different wavelengths, an offset was computed for the DNA intensity that made the background of

the mRNA expression pattern equal to that DNA intensity (up to a scaling). The corrected

expression levels were then computed by dividing the measured mRNA intensity by the offset DNA

intensity.

Spatial registration

For each temporal cohort, we used the template consisting of eve or ftz stripe boundary points

sampled on a cylindrical grid at each of the 14 stripe boundaries and 40 points uniformly spread in

angle around the D-V axis. We extracted edges of each reference gene pattern in cylindrical

32

coordinates by finding local maxima in the response of an anisotropic Gaussian derivative filter

which was elongated by a factor of three along the D-V direction. At a fixed threshold, this filter

typically detected all the stripe boundaries but also yielded some outliers and an occasional missed

detection due to variability in the staining.

To deal robustly with these errors, we performed an optimization along each of the 40 A-P strips to

match the 14 points in our template with the edges in the PointCloud. This 1D alignment between

the template coordinates and the detected edges was carried out using dynamic programming on a

cost function that depended on the polarity of the edge being matched (whether it is the anterior or

posterior edge of a stripe) and the total displacement necessary to align the model along the strip.

While this enforced consistency of matches along the A-P axis (e.g., two stripes in a template

cannot be matched to the same stripe in the embryo), neighboring A-P strips could still be

inconsistent. Before estimating a warping, we performed a post-processing step using a global

quadratic cost to prune matches that were inconsistent with their neighbors in either the A-P or D-V

directions.

Let m be a matching that specifies for the ith point, located at it in our template, the corresponding

boundary point, )(im detected at location )(ims in an individual embryo. We evaluate the cost:

!"

"""=

jji

jjmiim

i

tt

tstsmQ

2

2)()( )()(

)(

and drop those points i for which iQ exceeds a fixed threshold. We also use the total quadratic cost,

!i

iQ , to evaluate whether a reasonable match was found. A large total cost is indicative of an

33

embryo with a poorly defined marker gene expression pattern. In such cases, the algorithm

automatically defaults to using the coarse alignment.

Modeling deformations

We would like to find a smooth warping 33: !"!u which maps our set of detected boundary

points{ }...,, )3()2()1( mmmsss to their respective targets{ }...,,

321ttt . We treat each coordinate of the

function ),,( 321 uuuu = separately, and solve for the regularized multivariate spline that minimizes

the functional:

dxxxx

xutsuuJ

lkj lkj

i

j

j

i

jm

ii ! "!=

##

$

%

&&

'

(

)))

)+*=

3

1,,

23

2)( )()()( +

Although iu is infinite-dimensional, the optimal solution can be specified in closed form with

coefficients given by the solution of a compact system of linear equations (Wahba, 1990).

The regularized TPS provides a free parameter! that trades off the fidelity of the warping u at the

marker points with the smoothness of the interpolation throughout the remainder of the embryo.

We set this parameter by cross-validation, choosing the value that minimized the apparent inter-

embryo variability on non-marker genes. We also used this same validation technique to compare

TPS to other deformation models. For example, we found that TPS removed 10-20% more

variability than Gaussian radial basis function (RBF) splines at the optimal parameter settings.

Aligning expression levels

We used embryos from different developmental time points that were fixed and hybridized in a

single batch in order to estimate the temporal progression of the 99th percentile expression level.

34

When more than one hybridization was available for a given gene, we estimated a scale parameter

for each batch in order to minimize the squared error relative to the mean. Since the absolute

expression level between different genes is not calibrated in a meaningful way, we scaled

expression so that the maximum average expression recorded for each gene over the entire time

interval was 1.0. These scaled measurements were smoothed using Gaussian process regression

(Rasmussen and Williams, 2006) to yield the smoothed expression time courses plotted as dotted

lines in Supplementary Figure 3. We used a squared exponential covariance function with

characteristic length scale of 3 cohorts (roughly 30 minutes) and independent noise model with

standard deviation of 0.3. Once the max expression level for each gene and cohort was estimated, a

gain and offset was chosen for each embryo that minimized the variability within the cohort while

matching the time course max. As noted by (Gregor et al., 2007) these optimal gains and offsets

can be computed by singular value decomposition.

Bounding geometric variability remaining after registration.

One possible concern with this three-way analysis is that the measurement error could be correlated

with batches of embryos used in the experiment. For example, if the co-stained batch happened to

have higher variability due to measurement error than the registered batch, the level of variability

measured in co-stained embryos would no longer be a lower bound on level of apparent variability

in registered embryos. We measured the average standard deviation after registration for each of

the three batches and found values of 0.116/0.0806 for the eve/gt co-stain, 0.177/0.137 for eve/ftz,

and 0.129/0.142 for ftz/gt. Since the single gene variability within the co-stained batch was

significantly lower for both eve (0.116 < 0.177) and gt (0.0806< 0.142) we conclude that our

estimates of the geometric variability remaining after registration are potentially quite conservative.

35

Fitting regulatory functions

In our experiments, we used a generic form for F consisting of a sigmoid applied to a linear

combination of the protein concentrations (with weighting vector a) and a constant offset b,

bPaT

e

baPF+

+=1

1),|(

The sigmoid provides a saturating, non-linear response that constrains the transcription rate to lie

between 0 and a maximum (scaled to 1) and can be motivated in part from thermodynamic

considerations (Mjolsness 2007, Bintu et. al. 2005). The parameter vector a determines the

steepness of the response while b sets the offset at which transcription reaches half of the maximum

value (normalized to 1). We also considered a similar model for F which included quadratic terms

(products of all pairs of protein concentrations). While such a model is inherently more flexible,

thus providing higher quality fits (not shown) and explicitly captures non-linear interactions

between factors, it results in a far greater number of parameters that are significantly more difficult

to interpret. For example, the response of a target may be non-monotonic with respect to the

concentration of an individual regulator. For this reason, we used the more parsimonious linear

model in the experiments described here.

36

To fit the parameters a and b to our observed data, we perform least squares minimization over all

nuclei at all time points for which we have data

2

,)),|),((),(min! "=

j

jjjjiba

batxPFtxMC

We characterized the goodness of fit for each target using )(

12

MVar

CR != which measures the

extent to which the model explains the variance in expression across measured nuclei and time

points.

37

REFERENCES

Aegerter-Wilmsen, T., Aegerterb, C., Bisselinga, T. (2005). Model for the robust establishment of

precise proportions in the early Drosophila embryo. J. Theor. Biol., 234, 13-19.

Alves F, Dilao R. (2006) Modeling segmental patterning in Drosophila: Maternal and gap genes.

J Theor Biol. 241(2):342-59.

Arnosti DN, Barolo S, Levine M, Small S (1996) The eve stripe 2 enhancer employs multiple

modes of transcriptional synergy. Development (Cambridge, England) 122(1): 205-214.

Azevedo, R., French, V., Partridge, L. (1996). Thermal evolution of egg size in Drosophila

Melanogaster. Evolution. 50, 2338-2345.

Bintu, L., Buchler, N. E., Garcia, H. G., Gerland, U. Hwa, T., Kondev, J. and Phillips, R. (2004)

Transcriptional regulation by the numbers: models. Curr Opin Genetics Dev 15(2): 116-124

Bookstein, F.L., (1989). Principal Warps: Thin-Plate Splines and Decomposition of Deformations.

IEEE Trans. Pattern Analysis and Machine Intelligence, 11(6), 567-585.

Carson, J.P., Ju, T., Lu, H.C., Thaller, C., Xu, M., Pallas, S.L., Crair, M.C., Warren, J., Chiu, W.,

Eichele, G. (2005). A Digital Atlas to Characterize the Mouse Brain Transcriptome. PLoS

Computational Biology 1(4), e41.

38

Christiansen, J., Yang, Y., Venkataraman, S., Richardson, L., Stevenson, P., Burton, N., Baldock,

R., Davidson, D. (2006). EMAGE: a spatial database of gene expression patterns during mouse

embryo development. Nucleic Acids Res. 34, D637-41.

Davidson, D., Bard, J., Brune, R., Burger, A., Dubreuil, C., Hill, W., Kaufman, M., Quinn, J., Stark,

M., Baldock, R. (1997). The mouse atlas and graphical gene-expression database. Seminars in Cell

& Developmental Biology 8(5), 509-517.

Duchon, J. (1977). Splines Minimizing Rotation-Invariant Semi-Norms in Sobolev Spaces. In

Constructive Theory of Functions of Several Variables, W. Schempp and K. Zeller, eds. (Berlin:

Springer-Verlag), 85-100.

Edgar, B.A., Kiehle, C.P., Schubiger, G. (1986). Cell cycle control by the nucleo-cytoplasmic ratio

in early Drosophila development. Cell. 44(2), 365-72.

Eldon, E.D. and Pirrotta, V. (1991) Interaction of the Drosophila gap gene giant with maternal and

zygotic pattern-forming genes. Development 111, 367-378.

Fowlkes, C. C., Luengo Hendriks, C.L., Keränen, S. V. E., Biggin, M.D., Knowles, D.W., Sudar,

D., Malik, J. (2006). Registering Drosophila Embryos at Cellular Resolution to Build a

Quantitative 3D Atlas of Gene Expression Patterns and Morphology. Proc. of CSB 2005 Workshop

on BioImage Data Minning and Informatics, Palo Alto, CA.

39

Fowlkes, C. C., Malik, J. (2006). Inferring nuclear movements from fixed material. Report no.

UCB/EECS-2006-142. EECS Department: University of California, Berkeley.

(http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-142.pdf)

Frankel, F. (2007). Expressing Genes, American Scientist 95, 69-71.

Fujioka M, Emi-Sarker Y, Yusibova GL, Goto T, Jaynes JB. (1999) Analysis of an even-skipped

rescue transgene reveals both composite and discrete neuronal and early blastoderm enhancers, and

multi-stripe positioning by gap gene repressor gradients. Development. 126(11):2527-38.

Gregor, T., Tank, D.W., Wieschaus, E.F., and Bialek, W. (2007). Probing the limits to positional

information. Cell 130(1), 153-164.

Gong, S., Zheng, C., Doughty, M.L., Losos, K., Didkovsky, N., Schambra, U.B., Nowak, N.J.,

Joyner, A., Leblanc, G., Hatten, M.E., Heintz, N. (2003). A gene expression atlas of the central

nervous system based on bacterial artificial chromosomes. Nature 425, 917-925.

Imai, K. S., Levine, M., Satoh, N., Satou, Y. (2006). Regulatory blueprint for a chordate embryo.

Science 312 (5777), 1183-7.

Janssens. H., Hou, S., Jaeger, J., Kim, A., Myasnikova, E., Sharp, D., Reinitz, J. (2006).

Quantitative and predictive modeling of transcriptional control of the Drosophila melanogaster even

skipped gene. Nat. Genetics, 38, 1159-65.

40

Jaeger J, Surkova S, Blagov M, Janssens H, Kosman D, Kozlov KN, Manu, Myasnikova E,

Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J. (2004) Dynamic control of positional

information in the early Drosophila embryo. Nature 430(6997):368-71.

Keränen, S. V. E., Fowlkes, C. C., Luengo Hendriks, C. L., Sudar, D., Knowles, D. W., Malik, J.,

and Biggin, M. D. (2006). 3D morphology and gene expression in the Drosophila blastoderm at

cellular resolution II: dynamics. Genome Biology 7, R124

Kudoh, T., Tsang, M., Hukriede, N.A., Chen, X., Dedekian, M., Clarke, C.J., Kiang, A., Schultz, S.,

Epstein, J., Toyama, R., Dawid, I. (2001) A gene expression screen in zebrafish embryogenesis.

Genome Res. 11, 1979-1987

Kosman, D., Mizutani, C. M., Lemons, D., Cox, W. G., McGinnis, W., Bier, E. (2004). Multiplex

Detection of RNA Expression in Drosophila Embryos. Science 305, 846-846

Kumar, S., Jayaraman, K., Panchanathan, S., Gurunathan, R., Marti-Subirana, A., Newfeld, S.

(2002) BEST: a novel computational approach for comparing gene expression patterns from early

stages of Drosophila melanogaster development. Genetics, 162 (4), 2037-47.

Laney, J.D. and Biggin, M.D. (1996) Redundant control of Ultrabithorax by zeste involves functional

levels of zeste binding at the Ultrabithorax promoter. Development 122, 2303-2311.

41

Lein, E.S., Hawrylycz, M.J., Ao, N., Ayres, M., Bensigner, A., Bernard, A., Boe, A.F., Boguski,

M.S., Brockway, K.S., Byrnes, E.J., et al. (2007). Genome-wide atlas of gene expression in the

adult mouse brain. Nature 445, 168-176.

Levsky, J.M., Shenoy, S.M., Pezo, R.C., Singer, R.H. (2002). Single-Cell Gene Expression

Profiling. Science 297, 836-840.

Liang, Z., Biggin, M.D. (1998). Eve and ftz regulate a wide array of genes in blastoderm embryos:

the selector homeoproteins directly or indirectly regulate most genes in Drosophila. Development

125(22), 4471-82.

Lott SE, Kreitman M, Palsson A, Alekseeva E, Ludwig MZ. (2007) Canalization of segmentation

and its evolution in Drosophila. Proc Natl Acad Sci U S A. 104(26):10926-31.

Lucchetta EM, Lee JH, Fu LA, Patel NH, Ismagilov RF. (2005) Dynamics of Drosophila embryonic

patterning network perturbed in space and time using microfluidics. Nature 434(7037):1134-8.

Ludwig, M., Palsson, A., Alekseeva, E., Bergman, C., Nathan, J., Kreitman, M. (2005). Functional

Evolution of a cis-Regulatory Module. PLoS Bio. 3(4), 588-598.

Luengo Hendriks, C. L. , Keränen, S. V. E. , Fowlkes, C. C., Simirenko, L., Weber, G. H.,

Henriquez, C., Kaszuba, D. W., Hamann, B., Eisen, M. B., Malik, J., Sudar, D., Biggin, M. D., and

42

Knowles, D. W. (2006). 3D morphology and gene expression in the Drosophila blastoderm at

cellular resolution I: data acquisition pipeline. Genome Biology, 7, R123.

Manoukian, A. S., and Krause, H. M. 1992. Concentration-dependent activities of the even-skipped

protein in Drosophila embryos. Genes & Dev. 6: 1740-1751.

Mardia, K., Kent, J., Bibby, J. (1979) Multivariate Analysis (London: Academic Press)

Meinguet, J. (1979). Multivariate Interpolation at Arbitrary Points made Simple. J. Applied Math.

Physics (ZAMP) 5, 439-468.

Mjolsness, E. (2007). On cooperative quasi-equilibrium models of transcriptional regulation. J

Bioinform Comput Biol. 5(2B):467-90.

Myasnikova, E., Samsanova, A., Kozlov, K., Samsonova, M., Reinitz, J. (2001). Registration of the

expression patterns of Drosophila segmentation genes by two independent methods. Bioinformatics

17(1), 3-12.

Neidhardt, L., Gasca, S., Wertz, K., Obermayr, F., Worpenberg, S., Lehrach, H., Herrmann, B.G.

(2000). Large-scale screen for genes controlling mammalian embryogenesis, using high-throughput

gene expression analysis in mouse embryos. Mech Dev 98, 77-94.

43

Oliveri, P., Davidson, E.H. (2004). Gene regulatory network controlling embryonic specification in

the sea urchin. Curr Opin Genet Dev. 14(4), 351-60.

Peng, H., Long, F., Eisen, M., Myers, E. (2006). Clustering gene expression patterns of fly embryos.

Proc. IEEE 2006 International Symposium on Biomedical Imaging (ISBI 2006), 1144-1147.

Perkins TJ, Jaeger J, Reinitz J, Glass L (2006) Reverse Engineering the Gap Gene Network of

Drosophila melanogaster . PLoS Comput Biol 2(5): e51

Pollet, N., Muncke, N., Verbeek, B., Li, Y., Fenger, U., Delius, H., Niehrs, C. (2005). An atlas of

differential gene expression during early Xenopus embryogenesis. Mech Dev. 122(3), 365-439.

Rasmusen, C., Williams, C. (2006). Gaussian Processes for Machine Learning. (Boston: MIT

Press).

RiverA-Pomar R, Niessing D, Schmidt-Ott U, Gehring WJ, Jackle H. (1996) RNA binding and

translational suppression by bicoid. Nature. 379(6567):746-9.

Ronchi E, Treisman J, Dostatni N, Struhl G, Desplan C. (1993) Down-regulation of the Drosophila

morphogen bicoid by the torso receptor-mediated signal transduction cascade. Cell. 74(2):347-55.

Rübel, O., Weber, G.H., Keränen, S.V.E., Fowlkes, C.C., Luengo Hendriks, C.L., Shah, N.Y.,

Biggin, M.D., Hagen, H., Knowles, D.W., Malik, J., Sudar, D., Hamann, B. (2006).

44

PointCloudXplore: Visual analysis of 3D gene expression data using physical views and parallel

coordinates. In B.C. Santos, T. Ertl and K. Joy (eds.), Data Visualization 2006 (Proceedings of the

Eurographics/IEEE-VGTC Symposium on Visualization, Lisbon, Portugal, May 2006).

Simin, K., Scuderi, A., Reamey, J., Dunn, D., Weiss, R., Metherall, J.E., Letsou, A. (2002).

Profiling patterned transcripts in Drosophila embryos. Genome Res. 12, 1040-47.

Simpson-Brose M, Treisman J, Desplan C. (1994) Synergy between the hunchback and bicoid

morphogens is required for anterior patterning in Drosophila. Cell. 78(5):855-65.

Small S, Blair A, Levine M (1992) Regulation of even-skipped stripe 2 in the Drosophila embryo.

The EMBO journal 11(11): 4047-4057.

Spirov, A., Kazansky, A., Timakin, D., Reinitz, J. (2002). Reconstruction of the Dynamics of

Drosophila Genes Expression from Sets of Images Sharing a Common Pattern. Real-Time Imaging

8, 507-518.

Stathopoulos, A., van Drenth, M., Erives, A., Markstein, M., Levine, M. (2002). Whole-genome

analysis of dorsal-ventral patterning in the Drosophila embryo. Cell. 111(5), 687-701.

Struffi P, Corado M, Kulkarni M, Arnosti DN. (2004) Quantitative contributions of CtBP-dependent

and -independent repression activities of Knirps. Development. 131(10):2419-29.

45

Tassy, O., Daian, F., Hudson, C., Bertrand, V., Lemaire, P. (2006). A quantitative approach to the

study of cell shapes and interactions during early chordate embryogenesis. Current Biol. 16, 345-58.

Tomancak, P., Beaton, A., Weiszmann, R., Kwan, E., Shu, S., Lewis, S.E., Richards, S., Ashburner,

M., Hartenstein, V., Celniker, S.E., Rubin, G.M. (2002). Systematic determination of patterns of

gene expression during Drosophila embryogenesis. Genome Biol. 3(12), R88, 1-14.

Tomancak, P., Berman, B. P., Beaton, A., Weiszmann, R., Kwan, E., Hartenstein, V., Celniker, S.

E., Rubin, G. M. (2007) Global analysis of patterns of gene expression during Drosophila

embryogenesis. Genome Biol. 8(7), R145

Turner, F.R., and Mahowald, A.P. (1976) Scanning Electron Microscopy of Drosophila

Embryogenesis. Developmental Biol. 50, 95-108.

Visel, A., Thaller, C., Eichele, G. (2004). GenePaint.org: An atlas of gene expression patterns in the

mouse embryo. Nucleic Acids Res. 32, D552-D556.

Wahba, G. (1990). Spline Models for Observational Data. SIAM.

Walter, J., Dever, C., and Biggin, M.D. (1994) Two homeodomain proteins bind with similar

specificity to a wide range of DNA sites in Drosophila embryos. Genes and Dev. 8, 1678-1692

Warren, DC. (1924). Inheritance of Egg Size in Drosophila Melanogaster. Genetics 9(1), 41-69

46

Weber, GH, Rübel, O., Huang, M-Y., DePace, A.H., Fowlkes, C. C., Keränen, S.V.E., Luengo

Hendriks, C.L., Hagen, H., Knowles, D.W., Malik, J., Biggin, M. D., and Hamann, B. Visual

exploration of three-dimensional gene expression using physical views and linked abstract views, to

appear in: IEEE Transactions on Computational Biology and Bioinformatics, to appear

Yuh, C.H., Bolouri, H., Davidson, E.H. (2001). Cis-regulatory logic in the endo16 gene: switching

from a specification to a differentiation mode of control. Development 128(5), 617-29

Zalokar, M., Erk, I. (1976) Division and Migration of Nuclei during Early Embryogenesis of

Drosophila melanogaster. J. Micro. Biol. Cellularie 25, 97-106

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ACKNOWLEDGEMENTS This work is part of a broader collaboration by the BDTNP. We are grateful for the frequent advice,

support, criticisms, and enthusiasm of its members. We thank Thomas Gregor and William Bialek

for insightful discussions. Work conducted by the BDTNP is funded by a grant from NIGMS and

NHGRI, GM704403, at Lawrence Berkeley National Laboratory under Department of Energy

contract DE-AC02-05CH11231.

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FIGURE LEGENDS

Figure 1. Data from hundreds of individually imaged embryos is averaged into a composite

VirtualEmbryo. Top: Each individual embryo is stained for nuclei, a common marker gene (red)

and a gene of interest (second color). Center: Within each temporal cohort, the marker gene is used

to guide spatial registration on to a morphological template; temporal correspondences between

cohorts are provided by a model of typical nuclear movements. Bottom: Once correspondences

across embryos have been established, expression measurements are averaged and composited to

create a model VirtualEmbryo in which the expression of many genes can be compared.

Figure 2. Variations in blastoderm size, number of nuclei, and gene expression stripe locations

between embryos. Panels A and B show scatter plots in which embryo length (A) and surface area

(B) are both correlated with the number of nuclei (y axis), demonstrated here with a linear fit (red

line). Because experimental errors in nuclear count should not correlate with errors in determining

surface area or egg length, these correlations likely represent true biological variability among

embryos. Panels C and D show the variability in the location of ftz gene expression stripe locations

before (C) and after (D) embryos are scaled to the average cohort egg length just prior to

gastrulation (stage 5:75-100% cell membrane invagination). The plots are orthographic projections

in which the anterior of the embryo is to the left, the dorsal midline to the top and the center of mass

of the embryo is at the origin. Each line specifies the average stripe boundary location with error

bars showing one standard deviation in the A-P coordinate. Prior to scaling embryos to a common

length, standard deviations for ftz stripe locations are as large as 11.1µm, or 62% of the average ftz

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stripe width. After scaling by egg length the variation is reduced but is still significant (std dev up

to 5.4µm, or 30% of average stripe width).

Figure 3. Fine registration and compositing expression values. A marker gene expression pattern

(red) is used to identify corresponding nuclei in different embryos and perform fine spatial

registration. Each individual PointCloud is warped to bring extracted marker gene boundaries (red

lines) into alignment with a standard morphological template (black lines). Individual per-nucleus

measurements (here both red and green) are then composited onto the template to produce an

estimate of average expression.

Figure 4. Examples of average temporal patterns of mRNA expression recorded in the

VirtualEmbryo for several gap (kni,gt,hb) and pair-rule (eve,ftz,slp1) genes. Temporal cohorts,

staged by percent membrane invagination, are arranged from left to right with each row

corresponding to a different gene. Each rectangle shows a lateral view of the blastoderm in a half

cylindrical projection with dorsal at top, anterior to the left (see also Figure 7).

Figure 5. Fine registration removes additional measured inter-embryo geometric variability

and produces average regulatory relationships comparable to those measured in individual

co-stained embryos.. The mean and standard deviations for anterior-posterior expression profiles

taken from a lateral strip before (Panel A) and after (Panel B) fine registration for three genes: ftz

(n=100), slp1 (n=25) and gt (n=8). The inter-embryo variability decreases significantly with fine

registration, both for the marker gene (ftz) but also for “held out” expression patterns (slp,gt). Inset

numbers for each gene give the standard deviation averaged over the entire embryo. Panel C shows

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the co-expression of gt and eve near the dorsal surface along the anterior edge of eve stripe 2 in

embryos co-stained for eve and gt (n=47). Panel D shows the regulatory effect of gt on eve (2)

inferred from co-stained (blue curve) embryos binning nuclei based on the expression level of gt

and computing the mean and standard deviation of eve expression for each bin. The red and green

curves show the regulatory relation estimated by sampling pairs of nuclei in similar spatial locations

after coarse alignment (red) and fine registration based on eve (green). Panel E shows the

regulatory effect inferred from nuclei in different batches of embryos stained for either eve (n=35)

or gt (n=28) which were identified as corresponding based on coarse alignment (red) or fine

registration (green) using ftz. The co-stain estimate (blue curve) is repeated for comparison. The

inferred relation based on registered embryos is quite close to the true co-expression measured in

co-stained embryos. The variation in the regulatory relation across embryos in the virtual co-

expression estimate is significantly smaller than the coarse registration and comes closer to the

lower bound set by the level of variability quantified in individuals.

Figure 6. Regulatory relationships inferred from composite spatio-temporal expression data.

Panel A shows the coefficients of each of 17 regulators (columns) determined by fitting each target

eve stripe (rows). Each row contains only 6 non-zero entries corresponding to the selected regulators

for that target. Green indicates activation, red indicates repression, black indicates no interaction.

The right most column indicates the constant offset b. Quality of fit (R2 ) values are specified in

brackets. Panel B shows the coefficients for the individual components of the gap gene gt, ordered

by A-P location. Panel C shows the distribution of R2 fit values for all “modules” in the atlas (see

Supplementary Figure 6).

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Figure 7. PointCloudXplore allows visualization of quantitative 3D expression data.

Expression of the gap genes fkh, gt, hb, kni, and Kr is shown for the stage 5: 4-8% cohort. Panel A

shows a 3D model of the blastoderm surface (anterior left, dorsal down) with each nucleus colored

according to the expression level of the 5 genes. Panel B shows a cylindrical projection of the entire

blastoderm (anterior left, ventral center, dorsal upper and lower edges). The heights of each surface

plot indicate the average expression level of the gene recorded at that point on the VirtualEmbryo,

making readily visible the quantitative changes in expression of these gap genes along both the A-P

and D-V axes.