3266 RESEARCH ARTICLE
TECHNIQUES AND RESOURCES
Development 140, 3266-3274 (2013) doi:10.1242/dev.096040
© 2013. Published by The Company of Biologists Ltd
Systematic quantification of developmental phenotypes at
single-cell resolution during embryogenesis
Julia L. Moore, Zhuo Du and Zhirong Bao*
SUMMARY
Current imaging technology provides an experimental platform in which complex developmental processes can be observed at cellular
resolution over an extended time frame. New computational tools are essential to achieve a systems-level understanding of this highcontent information. We have devised a structured approach to systematically analyze complex in vivo phenotypes at cellular
resolution, which divides the task into a panel of statistical measurements of each cell in terms of cell differentiation, proliferation
and morphogenesis, followed by their spatial and temporal organization in groups and the cohesion within the whole specimen. We
demonstrate the approach to C. elegans embryogenesis with in toto imaging and automated cell lineage tracing. We define statistical
distributions of the wild-type developmental behaviors at single-cell resolution based on over 50 embryos, cumulating in over 4000
distinct, developmentally based measurements per embryo. These methods enable statistical quantification of abnormalities in mutant
or RNAi-treated embryos and a rigorous comparison of embryos by testing each measurement for the probability that it would occur
in a wild-type embryo. We demonstrate the power of this structured approach by uncovering quantitative properties including subtle
phenotypes in both wild-type and perturbed embryos, transient behaviors that lead to new insights into gene function and a
previously undetected source of developmental noise and its subsequent correction.
INTRODUCTION
The interpretation of complex in vivo phenotypes is a crucial and
challenging step required to achieve a functional understanding of
molecular networks. Advances in imaging technology offer an
unprecedented opportunity for systems-level studies with high
spatial and temporal resolutions. Using automated image analysis,
dozens to hundreds of measurements can be made to systematically
and objectively extract and analyze complex information. In cell
culture, such methods have enabled systems analysis and large-scale
screens examining cell shapes, division, death and subcellular
textures (Carpenter et al., 2006; Bakal et al., 2007; Neumann et al.,
2010; Danuser, 2011). Meanwhile, 3D time-lapse imaging has
allowed detailed, cellular resolution recording of extensive time
windows of embryogenesis in organisms such as C. elegans
(Schnabel et al., 1997; Bao et al., 2006), Drosophila (McMahon et
al., 2008; Keller et al., 2010; Truong et al., 2011), zebrafish (Keller
et al., 2008; Truong et al., 2011) and mouse (Kwon et al., 2008).
Automated methods are needed to systematically dissect the
intertwined in vivo processes of differentiation, proliferation and
morphogenesis recorded at single-cell resolution (Megason and
Fraser, 2007).
C. elegans has proven to be an effective model for systems-level
analysis of in vivo phenotypes (Kamath et al., 2003; Rual et al.,
2004; Fernandez et al., 2005; Gunsalus et al., 2005; Sönnichsen et
al., 2005; Lehner et al., 2006; Piano et al., 2006; Byrne et al., 2007;
Hunt-Newbury et al., 2007; Liu et al., 2009; Green et al., 2011).
Automated image analysis and data mining methods are emerging
to further facilitate such efforts (Dupuy et al., 2007; Long et al.,
Developmental Biology Program, Sloan-Kettering Institute, New York, NY 10065,
USA.
*Author for correspondence ([email protected])
Accepted 22 May 2013
2009; White et al., 2010; Wählby et al., 2012). Early embryogenesis
of C. elegans, where lineage patterning, gastrulation and extensive
cell-cell signaling occur, is particularly amenable for systematic in
vivo analysis because the entire cell lineage can be traced at minutelevel resolution (Schnabel et al., 1997; Hamahashi et al., 2005; Bao
et al., 2006; Dzyubachyk et al., 2009; Hench et al., 2009; Santella
et al., 2010; Giurumescu et al., 2012). Genome-wide RNAi has been
used to analyze behaviors of individual cells up to the 4-cell stage
(Sönnichsen et al., 2005). Although this analysis was conducted
during development, the effort was mainly focused on cell
biological behaviors regarding different aspects of cell polarity and
the cell cycle. The 46 behaviors were carefully chosen in cellspecific manners to be most biologically informative, but the
manual effort required prohibits propagating the analysis beyond
the 4-cell stage.
We present a structured approach to systematically quantify
complex developmental phenotypes during C. elegans
embryogenesis. We choose a small and uniform set of
measurements per cell that can be automatically applied to any cell
to systematically assay differentiation, proliferation and
morphogenesis in the entire embryo at single-cell resolution. We
have also developed methods to measure the organization of cellular
behaviors at whole-organism and regional levels. We quantify the
range of variability of these behaviors in 53 wild-type embryos to
the 350-cell stage, when the embryo has gone through the first nine
rounds of cell division and completed gastrulation (Sulston et al.,
1983). This cumulates in over 4000 distributions of wild-type
cellular behaviors. These distributions are used to calculate the
probability that a particular quantity observed in a mutant or RNAitreated embryo would be observed in a wild-type embryo. We
demonstrate the power of this structured approach in detecting
subtle phenotypes, transient behaviors and developmental noise and
correction through analyses of wild-type and RNAi-treated
embryos.
DEVELOPMENT
KEY WORDS: Automated phenotyping, Cell migration, Cell tracking, Caenorhabditis elegans
RESEARCH ARTICLE 3267
Systematic phenotyping
Experimental methods
RNAi was administered by feeding as described (Fraser et al., 2000).
Embryos were collected and imaged as previously described (Bao and
Murray, 2011). Nuclei were segmented and tracked as described (Santella
et al., 2010). Automated tracking results were edited by hand as described
previously (Murray and Bao, 2012).
Software to quantify phenotypes was written using MATLAB
(MathWorks). Morphogenesis visualizations were made using POV-Ray
(POV-Ray 3.6, Persistence of Vision team) to generate images containing
the desired shapes.
General framework
The developmental behaviors of each cell are measured, compared with the
wild-type distribution and assigned P-values representing the likelihood
that each measurement would be observed in a wild-type embryo. The
statistics compiled for each cell’s measurements are available in
supplementary material Appendix S1. Measurements in a pal-1(RNAi)
embryo are also provided (supplementary material Appendix S2). The
corresponding P-values for this pal-1(RNAi) embryo are displayed in a chart
to visualize abnormalities (supplementary material Fig. S1). To guard
against false positives as a result of the large number of statistical tests, we
use the Benjamini and Hochberg method (Benjamini and Hochberg, 1995)
on the entire P-value matrix. To be flagged as abnormal, we chose the
arbitrary adjusted P-value cut-off of 0.01, which yields an average of 2.2
false positives per embryo. This cut-off can be tuned based on the subtlety
of the phenotype of interest.
The method discussed here is available as a software package that we
named Dev-scape. The source code is provided as supplementary material
Appendix S3. Additionally, the source code can be downloaded from
SourceForge (http://sourceforge.net/projects/devscape/files). Using Devscape from the source code requires MATLAB. Compiled versions for both
PC and Mac, which allow users to run Dev-scape without access to
MATLAB, are also available from SourceForge. Detailed instructions on
installation and using Dev-scape are provided as part of the download. The
PC version is recommended. Using the source code or the Mac version
requires the user to compile POV-Ray.
When using Dev-scape, a graphical user interface guides users to specify
the input, choose the types of analysis to be performed, and enter parameters
about their data (supplementary material Fig. S2). When the analysis is
completed, an output browser opens to facilitate examination of the results.
The input file is a zip file as outputted by AceTree (Murray and Bao, 2012),
which contains the result of automated cell lineage tracing. All results of
Dev-scape analysis are written to text files to facilitate further analysis of
data and comparison between embryos. A list of the output files is provided
in supplementary material Table S1. Detailed instructions and explanations
are provided when the user downloads Dev-scape.
Differentiation
We use tissue-specific markers to assay cell fate. Each of the five markers
used is a well-studied master transcription factor in determining the
corresponding tissue type (supplementary material Table S2). The reporter
strains have been shown to have stable and reproducible expression that
reliably reflects cell fate in both the wild type and known fate
transformations (Mathies et al., 2003; Murray et al., 2008) (data not shown).
To make a binary classification of each cell as expressing or nonexpressing, we first calculate each cell’s background corrected expression
level at each time point as described (Murray et al., 2008). Next, we
calculate the average expression level of each cell over time and perform a
robust linear regression on all average expression levels using the MATLAB
‘robustfit’ function with weighting parameter ‘fair’ (supplementary material
Fig. S3A). This method fits a line to the background population of nonexpressing cells and identifies the expressing cells as outliers. To accomplish
this, non-expressing cells are interspersed with expressing cells, which is
achieved by ordering cells by lineage identity. Most expressing cells can be
identified by the low weights they are assigned due to their not fitting the
non-expressing line. Cells with positive expression values and a weight
below 0.3 are classified as expressing. Cells that fit the line well are assigned
weights between 0.7 and 1 and classified as not expressing. Many embryos
contain a few cells with borderline expression levels; cells assigned weights
between 0.3 and 0.7 are considered borderline expressing. In general, these
cells are either not expressing or begin expression during the cell’s life. To
differentiate between these two types, we examine the cell’s time series of
expression levels with a Wilcoxon rank-sum test to identify cells with
expression values that increase over time. The series of expression values
is repeatedly split into early and late sections, which serve as separate
distributions for the test. To search for any time point as the initiation of
expression, the split progresses through the cell cycle and a cell is called
expressing if any P-value below 0.001 is found (supplementary material
Fig. S3B). This method is robust to both the number of low expressing cells
and imaging noise that affects the perceived baseline level of expression.
Examining 22 embryos, we found a false-positive rate of 0.02%.
Differentiation results are displayed in a lineage tree to allow users to
compare various wild-type and mutant patterns. Trees can be displayed in
the canonical way with branch length corresponding to time or with a
uniform branch length to separate proliferation and differentiation data
(supplementary material Fig. S3C).
Proliferation
Global clock and normalization of cell cycle lengths
Under normal experimental conditions, wild-type embryos exhibit a linear
global clock in that individual cell cycle lengths in an embryo vary
proportionally to each other (Bao et al., 2008) (supplementary material Fig.
S4A). For each embryo examined, we calculate this clock by performing a
robust linear regression (as above) on the wild-type average cell cycle
lengths versus their length in the given embryo. We examine how well the
linear regression fits the cell cycle lengths using root mean squared
deviation (RMSD). A high RMSD (empirical cut-off of 7) means that the
cell cycle lengths do not vary proportionally to each other. To choose an
empirical RMSD cut-off, we examined the relationship between global
clock linearity and RMSD in 91 embryos that were treated with RNAi for
genes required for embryogenesis. In the case of linear changes of the global
clock, we use the slope from the regression to scale each cell cycle length
in the given embryo. For non-linear changes, we test for the pace of
proliferation slowing down over time. This often occurs when an embryo is
approaching arrest, as represented by cdt-1(RNAi) (supplementary material
Fig. S4A). We look for changes in each lineage group’s proliferation rate
over time by calculating the average cell cycle length for each generation of
cells within a given lineage and measure the ratio between wild-type cells
in consecutive generations. Results of all the calculations discussed above
are outputted into a text file and most are displayed in graphs for the user
to examine (supplementary material Table S1).
Synchrony and organization of proliferation
We cluster cells that divide at roughly the same time into groups based on
the pairwise correlation of each cell’s history of division timing. Each cell’s
history is represented by a vector where each element corresponds to a time
point and is assigned a value representing the proportion of the cell cycle
that the corresponding time point is away from a division. We use the
MATLAB ‘clusterdata’ function to perform single linkage clustering based
on the pairwise correlations.
We examine the synchrony of each wild-type group defined above in
mutants/RNAi. For each cell within a given group, we determine whether
the cell is still in sync with the group as follows. We measure the difference
between the cell’s division time and the average division time of the group.
This difference is then normalized to the cell’s cycle length and compared
with the wild-type distribution of the normalized difference across embryos.
We treat the wild-type distributions as normal because for 83% of the cells
the distribution passes the D’Agostino’s K2 test for normality with an alpha
value of 0.05 (D’Agostino et al., 1990).
Individual cell cycle length
Single cell-cycle length distributions were tested for normality using
D’Agostino’s K2 test, which is suitable for our relatively small sample size
(D’Agostino et al., 1990). We found that 81% of the distributions were
normal with an alpha value of 0.05.
DEVELOPMENT
MATERIALS AND METHODS
Morphogenesis
To properly characterize the spatial variation between embryos, we first
align the embryo according to the body axes then normalize axes to a
standard size. We detect the anterior-posterior axis by finding the largest
axis of variation in cell positions at the final time point of a time-lapse series,
typically with 100 to 350 cells. Because of the mounting technique, the leftright axis in the early embryo is aligned with the z-axis of the image stack
(Bao et al., 2006). We determine the orientation of the left-right axis by
examining the position of the left and right side AB cells at the AB4 stage.
The length of each body axis is determined by finding the minimum and
maximum cell position along that axis; for stability, we use the 99th
percentile minimum and maximum. Each body axis is then linearly scaled
to the wild-type average size compiled from the 53 embryos, normalizing
the position of each cell in the process.
We measure each cell’s average position and displacement based on the
normalized coordinates. Cell position is measured as the three coordinates
(assumed to be independent) in the three body axes, 5 minutes into the cell’s
life. This time point is chosen to capture the position near the beginning of
the cell cycle while avoiding the variation associated with cell divisions due
to cell collisions. Each covariance ellipsoid is calculated using principal
component analysis to identify the directions of variation and the variance
in those directions (supplementary material Fig. S5A). The displacement is
measured as the magnitude of total displacement as well as the displacement
along each axis between a cell’s position at birth and division or death. In
total, we calculate seven quantities describing each cell’s behavior in
embryonic morphogenesis. Each of these distributions was tested for
normality using D’Agostino’s K2 test. On average, 89% of the distributions
passed the test when an alpha value of 0.05 was used.
To identify groups of cells that migrate together, we use mean shift
clustering on the cell positions and displacements, allowing the
identification of cells that are near each other and moving together. We also
quantify the coordination of cell movement by measuring the pairwise
correlation of migration paths for each time point that both members of the
Development 140 (15)
pair are in the embryo (supplementary material Fig. S5B). The correlation
is calculated in each body axis, and then weighted by the amount of
displacement that occurs in that axis and then summed.
To quantify angular movement, we treat the center of the normalized
embryo as the origin. We project all cells onto the center plane bisecting
the dorsal-ventral axis and only examine cells beyond the center two-thirds.
Displacement is calculated over 15-minute windows. Before performing
the paired t-test comparing the correlation between C and non-C periphery
cell movement in wild-type and pal-1 averages, we tested both distributions
for normality using D’Agostino’s K2 test. Both were normally distributed
with P-values of 0.37 and 0.39, respectively.
RESULTS
A statistical strategy to achieve single-cell
phenotypic descriptions
As outlined in Fig. 1, we build upon the histone-fluorescent protein
fusion-based automated segmentation (Santella et al., 2010), cell
tracking (Bao et al., 2006) and lineage tracing (Bao et al., 2006) to
characterize development. We use a collection of tissue-specific
markers to measure differentiation. We characterize proliferation
by measuring the temporal, spatial and lineage-based organization
of cell divisions. To quantify morphogenesis, we measure cell
position, displacement and organization of collective movement.
We also provide visualization tools to aid the understanding of the
phenotypes.
We have not only developed measurements for behaviors of the
whole embryo and coordinated cell groups, but also for each cell.
The key to characterizing the distribution of developmental
behaviors of a given cell is the ability to find the equivalent cells
across embryos. The general approach to this alignment in
Fig. 1. The process of converting time-lapse image
data to a panel of probabilities. (A) Representative
frames from a time series of C. elegans embryogenesis
imaged with histone-fluorescent protein labels. Images
are segmented and cells are tracked. (B) Each cell’s
differentiation, proliferation and morphogenesis are
measured. (C) Measurements are compared with the
wild-type probability distributions to obtain P-values
that represent the probability of a measurement as far
from or further from the mean being present in a wildtype embryo. After adjusting for testing multiple
hypotheses, measurements within the wild-type range
(P>0.01) are shown in white and significantly different
values (P<0.01) are in red (when measurements are
smaller than the mean) and in blue (when
measurements are larger than the mean).
DEVELOPMENT
3268 RESEARCH ARTICLE
developmental biology is anatomy-based registration between
specimens; for example, a particular tissue layer in a particular
organ occupying a particular part of the body. The invariant cell
lineage of C. elegans (Sulston et al., 1983) offers a convenient
approximation of this general rule: because of the stereotypical
orientation of each mitosis, the name of a cell provides the
equivalent information as its anatomical position. This allows us to
automate single-cell analysis through automated cell lineage tracing
without additional computational steps of anatomy-based
registration.
For single-cell measurements, the probability that a value would
be found in a wild-type embryo is calculated by determining the
probability that a measurement this extreme or more extreme would
appear in a wild-type embryo. Repeating this process for each
measurement and each cell leads to the calculation of 4000
statistical quantifications per embryo (supplementary material Fig.
S1). After correcting for multiple tests, this list of the statistical
significance of phenotypes can be readily used to guide in-depth
characterization of in vivo gene function and for comparisons
between embryos to identify related gene functions or construct
functional gene networks. We describe the individual methods
below and provide the technical details of each method in the
Materials and methods.
Differentiation
We use tissue-specific marker expression to assay when cells take
on a fate. With two-color imaging, one color is used to trace the
lineage and the other to assay the expression of a fate marker. We
use markers that are transcription factors expressed in the major
tissue types: gut, hypodermis, muscle, neuron and pharynx. We
examine each cell to determine whether it is expressing the marker
or not. As shown in Fig. 2A,B, this approach provides detailed
dynamics of marker expression in individual cells.
To decide whether a cell expresses the marker, we apply an
embryo-specific binary classification based on marker expression
levels that are found in each segmented nucleus at each time point
RESEARCH ARTICLE 3269
(Murray et al., 2008). The automated classification relies on the fact
that the majority of cells do not express a given fate marker and
performs an iterative multilinear regression to summarize the
background fluorescence level, which can vary widely between
embryos (supplementary material Fig. S3A). Cells with expression
levels significantly higher than the background are classified as
expressing. To better capture expression that is initially low, we use
a Wilcoxon rank-sum test to identify cells with a time-dependent
increase of expression level (supplementary material Fig. S3B)
(Murray et al., 2008). Using these two statistical classifications,
expressing cells match well with known fates (Fig. 2C; see
Materials and methods).
To formulate a wild-type differentiation standard we examine the
consistency of marker expression in multiple wild-type embryos.
Owing to the invariant lineage of C. elegans, fates are also invariant
at the single-cell level and any fluctuation in expression status is
due to marker inconsistency. Because of this fundamental reliability,
and the time-consuming nature of data collection, we examined four
to ten embryos per marker. As the relatively small number of
samples limits the statistical power, we formulated the standard to
include only the consistently expressing and consistently nonexpressing cells among all wild-type embryos. If, for a given
marker, a cell sometimes expresses and sometimes does not in wildtype embryos, neither state can be considered abnormal in a mutant
or RNAi-treated embryo.
To systematically assay cell fate across the lineage, one can use
a panel of selected markers. We selected five well-studied tissue
markers with consistent expression patterns corresponding to the
five major tissue types, namely cnd-1 for neuronal, pha-4 for
pharyngeal and endodermal, nhr-25 for hypodermal, elt-2 for
endodermal and hnd-1 for muscular fate (Mathies et al., 2003;
Murray et al., 2012). Between the five tissue-type markers, 40% of
cells consistently express at least one marker and 100% of cells
consistently do not express at least three markers. This means that
loss of expression can be detected in 40% of cells and a gain of
expression can be detected in all cells.
Fig. 2. Consistent wild-type differentiation
patterns allow the discovery of perturbations
at single-cell resolution. (A) Nuclear expression
of HND-1::GFP in the MS lineage for each time
point. Expression levels in cells marked by asterisks
are shown in B. (B) Expression levels over time
show that HND-1 is transiently expressed in MSxp
cells, but not in MSxa cells. a.u., arbitrary units.
(C) Summaries of expression across different
markers, all at the 350-cell stage. Cells are
represented by vertical lines displayed in lineage
order and color coded by fate marker expression.
Each color represents a combination of markers
being expressed in that cell. The expression of
each marker is observed in separate embryos. The
first row shows markers that are expressed in every
wild-type embryo examined. The second row
shows markers that are expressed in at least 50%
of wild-type embryos. The third row shows
markers that are expressed in one or both of two
pal-1(RNAi) replicates. In the case that only one
replicate is expressing, we display whichever
behavior occurs more commonly in wild-type
embryos. The bottom row shows which of the pal1(RNAi) expression patterns were abnormal.
DEVELOPMENT
Systematic phenotyping
Fig. 3. Analyzing proliferation at multiple scales can uncover a
variety of phenotypes. (A) The number of cells in the embryo over time
reflects the global proliferation rate. Blue represents the wild-type
average plus and minus one standard deviation. Green and red each
represent an RNAi-treated embryo. (B) (Top) The spatial distribution of
cells that divide synchronously. Each synchronous group is marked by a
different color. These groups correspond perfectly with lineage groups.
The embryo is at the start of the AB64 stage, viewed ventrally. (Bottom) A
heat map showing the degree of correlation between cells. The colors
along the axes represent the lineage groups as in the top panel. Division
timing is correlated within lineage groups, but not between them.
(C) Wild-type average cell cycle lengths and standard deviations in the C
lineage, and pal-1(RNAi) cell cycle lengths highlighting statistically
significant deviations (P<0.01). (D) Correlation of the division timing
histories of the C lineage in a wild-type embryo and pal-1(RNAi) embryo.
The wild-type lineage forms two groups separated by cell fates, whereas
all of the pal-1(RNAi) cells are correlated with the wild-type muscle
division timing. hyp, hypodermal; musc, muscle.
To test our approach, we examined the phenotype of pal-1(RNAi).
PAL-1 is the ortholog of Caudal in Drosophila and is a transcription
factor that is required to specify the fate of the posterior lineages,
named C and D, that give rise to muscle and hypodermal cells
(Hunter and Kenyon, 1996). Consistent with the known function of
pal-1, we observed a loss of muscle and disruption of hypodermal
fates in the C and D lineages and no other consistent deviation from
wild type (n=2 embryos per marker; Fig. 2C) (Hunter and Kenyon,
1996; Edgar et al., 2001). PAL-1 also has a redundant role in
specifying the E lineage, which gives rise to endoderm (Maduro et
al., 2005). As expected, pal-1(RNAi) alone does not affect
expression of the endoderm marker elt-2.
Proliferation
We measured proliferation at three levels. First, we examined the
global pace of proliferation by counting the number of cells over
time. To formulate a standard for how closely this number of cells
matches the wild type, we plotted each average wild-type cell cycle
length verses the cell cycle length in the embryo being examined. In
wild-type embryos, this relationship is linear and we refer to the
slope of the line on this plot as the global clock (supplementary
material Fig. S4A) (Bao et al., 2008). The global clock is known to
vary slightly between embryos due to external factors and we detect
Development 140 (15)
intra-embryo global clock changes as a phenotype, such as slowing
toward arrest. pal-1(RNAi) does not lead to a significant change in
the global clock (Fig. 3A; supplementary material Fig. S4A). By
contrast, RNAi against cdt-1, a conserved DNA replication licensing
factor (Zhong et al., 2003), dramatically slows the global clock.
Second, to assay the spatial organization of proliferation, such as
mitotic waves, we examined groups of synchronized divisions. For
de novo detection of these groups, we clustered cells based on
pairwise correlations of their division histories (Fig. 3B;
supplementary material Fig. S4C). In wild-type C. elegans embryos
the clusters correspond to lineage groups, which are known to divide
synchronously, validating the clustering method. We also measured
the synchrony within each of these defined groups by examining
the difference between the group’s average cell division time and
individual cell division times (supplementary material Fig. S4B).
Third, we measured the pace of proliferation in individual cells
in terms of cell cycle length. Across embryos, wild-type single cellcycle length distributions were normal (see Materials and methods)
and had an average percent coefficient of variation of 4.3. This level
of consistency allows small aberrations to be detected as statistically
significant (supplementary material Fig. S4C).
Our sensitive measurements uncovered new phenotypes of pal1 loss of function and insights regarding how this conserved master
transcription factor coordinates proliferation between different
tissue types. Consistent with the knowledge that pal-1(RNAi)
disrupts cell fate only in the C and D lineages (Hunter and Kenyon,
1996; Edgar et al., 2001), we found that pal-1(RNAi) only
consistently affected cell cycle lengths in these two lineages
(P<0.01). D lineage cell cycle length abnormalities are all in the
form of increases in cycle length, appearing in seven out of ten pal1(RNAi) embryos examined. The C lineage abnormalities
comprised both increases and decreases in cell cycle length and
occurred in nine out of ten pal-1(RNAi) embryos (Fig. 3C). In the
C lineage, divisions of the presumptive hypoderm cells become
synchronous with those of the presumptive muscle cells (Fig. 3D;
supplementary material Fig. S4B), and the entire C lineage
proliferates at the same pace as the wild-type muscle cells in the C
lineage. These results indicate that the C lineage has a default
proliferation rate that is independent of pal-1. This default rate is
used in the muscle sublineages but is accelerated by pal-1 in the
hypoderm.
Morphogenesis: measuring cellular position and
migration
To characterize the variation in cell positions, we fit the distribution
of the wild-type position of each cell across 53 wild-type embryos
with a covariance ellipsoid (Fig. 4A; supplementary material
Fig. S5A). Wild-type cell positions are consistent, as ellipsoids
drawn with radii of one standard deviation in each component do
not overlap (supplementary material Movie 1). For cell movement,
we found that the trend of migration is consistent for a given cell
between embryos, but that the path is usually noisy (supplementary
material Fig. S6). To emphasize the movement instead of the noise,
we quantify the amount of displacement. To measure the overall
similarity of an embryo to the wild type, we calculate the RMSD
between average positions and those in the embryo of interest
(Schnabel et al., 2006). We also developed visualization techniques
to allow users to better grasp the 3D cell migration dynamics, which
are difficult to describe (Fig. 4C,F; supplementary material Fig. S5,
Movie 2).
Furthermore, we use two methods to identify groups of cells that
migrate together. The first is a weighted average of the correlation
DEVELOPMENT
3270 RESEARCH ARTICLE
Systematic phenotyping
RESEARCH ARTICLE 3271
Fig. 4. Morphogenesis quantification and visualization
reveals disruption in pal-1(RNAi). (A) Dorsal view of
covariance ellipsoids at the AB32 stage. The long axis of
each ellipsoid is aligned with the direction of most
variation of a cell’s position in 53 wild-type embryos
examined 5 minutes after cell birth. Each radius shows one
standard deviation in one principal component of the cell
position distribution. (B) A pal-1(RNAi) embryo has an
increasing number of cells with abnormal displacement as
development progresses. (C,F) Cell displacement patterns
are shown for wild type and pal-1(RNAi) during the AB64
stage. (D,G) Brown, light blue and dark blue cells are part of
co-migrating groups identified by performing mean shift
clustering on the positions and displacements in C and F.
(E,H) Pairwise correlation coefficients of migration
trajectories within the same embryos show high
correlation in wild type and lack of correlation in pal1(RNAi). A subset of the lineage is shown here; see
supplementary material Fig. S5 for the complete
correlation matrix of the wild-type embryo.
abnormal amount of displacement (Fig. 4B). Many more cells have
an abnormal amount of displacement during AB64 and AB128.
More specifically, the displacement is variably reduced among C8
cells (P<0.01) and the co-migration is diminished (Fig. 4C,F). Two
other co-migrating groups adjacent to C8 (ABplp8 and ABprp8) are
also diminished (Fig. 4H). Given the lineage-specific function of
pal-1, these later migration abnormalities are likely to be secondary
defects. We did not observe the early misplacement of the C
Fig. 5. Angular shift is initiated by C cells. (A) Mid
AB32 shows clockwise motion in peripheral cells in
an individual embryo. Early AB64 shows the
covariance ellipsoids of cell positions over 53 wildtype embryos. Late AB64 shows counterclockwise
motion in the same embryo as in mid AB32. Early
AB128 shows the covariance ellipsoids of cell
positions over the same set of wild-type embryos as
in late AB64. (B) The maximum magnitude of the
average clockwise angular movement (x-axis)
plotted versus counterclockwise angular movement
(y-axis) in wild-type and pal-1(RNAi) embryos.
Average is calculated across C cell and non-C
periphery cell groups in each embryo. Angular
displacement is defined within a plane bisecting the
dorsal-ventral axis. Only cells beyond the center twothirds of the embryo are included (blue and red in A).
(C) One embryo’s average angular displacement in C
cells (red in A) and non-C periphery cells (blue in A)
over time. (D) Time-shifted correlation between C
and non-C periphery cells over a range of temporal
shifts. Lines show average correlation values and
range shows plus and minus one standard deviation.
The wild-type curve shows that moving the non-C
periphery cells back in time relative to the C cells
leads to larger correlation, i.e. comparing C cell
movement to the movement of the non-C periphery
cells 4 minutes later results in the largest correlation.
DEVELOPMENT
of migration along each developmental axis (Fig. 4E,H;
supplementary material Fig. S5B). This allows cells to be grouped
based on the dynamics of their migration. The second is mean shift
clustering based on cell positions and displacements (Fig. 4D,G).
We examined the function of pal-1 in organizing posterior
morphogenesis using the above methods. In pal-1(RNAi),
displacement is largely diminished. This is first detected at the
AB32 stage, with the cell named Cap being the only cell with an
3272 RESEARCH ARTICLE
Development 140 (15)
Fig. 6. Collective migration patterns emerge in RNAi
treatments. (A,B) Each rod represents a cell’s
displacement over a 15-minute period. (A) In an embryo
treated with pie-1(RNAi), cells at the posterior and anterior
extremes of the embryo migrate from left to right and
meet at on the embryo’s right side. (B) An apx-1(RNAi)
embryo shows cells producing a similar pattern to those
in A. (C,D) The P-value chart for cell positions and
movements in A (C) and in B (D). Measurements with
P<0.01 are in red or blue. A-P, anterior-posterior; L-R, leftright; D-V, dorsal-ventral.
Morphogenesis: developmental noise and
correction
The covariance ellipsoid visualization revealed that, at the AB64
stage, many of the ellipsoids are aligned in a circular pattern when
viewed dorsally (Fig. 5A). This pattern of directional variance is
caused by a previously unobserved global cell movement,
producing a rotation about the dorsal-ventral axis in a subset of
embryos. This new rotation is perpendicular to a previously
observed rotation about the long axis of the embryo that occurs one
cell cycle later (Giurumescu et al., 2012). In the subset of embryos
that undergo this rotation, cells move clockwise in a 15-minute time
window beginning a few minutes after the C4 cells are born
(Fig. 5A). This movement exaggerates the angle between the leftright midline and the long axis of the embryo (Pohl and Bao, 2010).
Cells later move counterclockwise, so that by the start of the AB128
stage the exaggerated angle is reduced (Fig. 5A). Measurements of
the angular displacements show that wild-type embryos undergo
varying degrees of this shift and countershift (Fig. 5B).
Based on cell displacements over time, the C4 cells are the first
to move in the initial clockwise shift (supplementary material
Fig. S7). Time-shifted correlations of the angular displacement
curves between C4 and other cells confirmed this observation
(Fig. 5C). The wild-type embryos (n=53) showed a maximal
correlation value around −4 minutes. We then used pal-1(RNAi) to
perturb the C4 cells. In pal-1(RNAi) embryos (n=10) the shiftcountershift was diminished, and there was no significant
correlation between the residual C4 and non-C movements [Fig. 5D;
paired t-test between wild-type and pal-1(RNAi) average correlation
values, P=4×10–7]. The correlation between shift and countershift
magnitudes is also diminished [Pearson’s correlation
coefficient=0.56 in wild type and 0.14 in pal-1(RNAi)]. Taken
together, our analyses suggest that variation in C4 movement leads
to noise and correction in global cell positions.
Morphogenesis: emerging global patterns
We found that novel patterns of whole-embryo collective migrations
can arise in RNAi knockdowns of specific genes (Fig. 6). For
example, in RNAi of pie-1, which encodes a zinc-finger protein
required for germline fate (Mello et al., 1996), bilateral cells in the
ABp lineage form two half-circular flows in opposite directions that
merge at the anterior end of the midline (Fig. 6A). Interestingly,
apx-1(RNAi) produces strikingly similar morphogenetic patterns
(Fig. 6B), which is reflected in the similarity in their P-value
matrices (Fig. 6C,D). As a notch ligand required for fate induction
of ABp in the 4-cell embryo, expression of apx-1 is dependent on
pie-1 (Mango et al., 1994; Mickey et al., 1996). Therefore, it is most
likely that the pattern that emerged in pie-1(RNAi) is a result of
abolishing apx-1 expression.
It has been proposed that cell movement during C. elegans
embryogenesis is governed by systematic pairwise cell-cell
interactions that guide cells to sort among themselves (Bischoff and
Schnabel, 2006; Schnabel et al., 2006). The co-migrating groups
and the new patterns of global organization apparent in the above
experiments can assist investigations of how systematic local
interactions can lead to the emergence of global patterns.
DISCUSSION
We have presented a structured approach to systematically
quantify complex developmental phenotypes at cellular resolution
based on long-term 3D time-lapse imaging. The measurements are
designed to systematically capture three key aspects of
development, namely differentiation, proliferation and
morphogenesis, from single-cell behaviors to local and global
patterns. This leads to over 4000 quantitative measurements in C.
elegans embryogenesis through the first nine of ten total rounds of
cell division. We tested these methods by systematically dissecting
the phenotypes of pal-1(RNAi). In addition to recapitulating the
known phenotypes, our approach detected subtle but significant
changes in individual cells revealing a new function of this
conserved transcription factor in coordinating proliferation
between two tissue types.
DEVELOPMENT
granddaughters and their anterior neighbors (ABarppa/p) that was
reported in the strong loss-of-function allele pal-1(ct224) (Edgar et
al., 2001), probably owing to the weaker penetrance of RNAi.
Our work builds on several studies of C. elegans embryogenesis
at single-cell resolution. Pioneering work using DIC imaging and
manual lineaging documented the nature of the cell movements and
the relatively high level of noise (Schnabel et al., 1997). Relative
positions have also been characterized based on distance and
Voronoi diagrams (Schnabel et al., 2006; Hench et al., 2009), which
we did not address in this study. Based on the same imaging and
cell-tracking platforms used in our study, computational methods
and an extensive collection of transgenic strains have been
developed to quantify single-cell marker expression (Murray et al.,
2008; Murray et al., 2012). Most recently, cell tracking has been
extended late into embryogenesis to quantitatively characterize
highly coordinated cell movement patterns (Giurumescu et al.,
2012). The statistical nature of our study, quantifying not only the
average behaviors but the degree of variation in wild-type
development, is a key addition to these previous studies of singlecell behavior in C. elegans embryogenesis.
Our results demonstrate the value of the structured approach in
characterizing complex developmental processes. In particular, they
show that a small and uniform set of measurements applied to each
cell can effectively capture the key information of complex
developmental processes. Although the invariant cell lineage of C.
elegans plays an important technical role in our study, the
conceptual framework of combining long-term 3D time-lapse
imaging with a small but well-designed set of single-cell
measurements can be applied to more complex organisms with
variable development. As discussed above, this would require
additional techniques of anatomy-based registration between
specimens to identify equivalent cells. An additional consideration
is that in C. elegans each cell is unique so that embryos can be
compared on a cell-by-cell basis. In more complex organisms, the
meaningful level of comparison would be each cell type, which may
comprise multiple and variable numbers of cells that share the same
properties. As shown in our study, clustering of cells based on
single-cell measurements can be an effective approach to define cell
groups with homogeneous behaviors, which can then be compared
across specimens. As studies in developmental biology show,
molecular markers can also be used to facilitate the detection of cell
type to compare phenotypes.
More importantly, our approach enables systems-level analysis
of in vivo development. The measurements constitute a panel of
probabilities that summarizes multiple facets of development and
readily supports quantitative measurement of functional similarity
between genes and the construction of functional gene networks at
single-cell resolution (Gunsalus et al., 2005). Furthermore, high
temporal and spatial resolution allows the detection of transient and
variable behaviors in a large set of embryos. This allowed us to
capture and dissect noise and correction in the morphogenesis of an
organism that is renowned for invariant and stereotypical
development. Much of the current effort in studying developmental
noise and robustness is devoted to molecular studies of gene
expression (Balázsi et al., 2011). Our study suggests that systematic
cell tracking and single-cell analysis will also open doors to study
how noise and its control at the molecular level is transformed into
cellular behaviors and how cellular-level noise and control affects
the assembly of an organism.
Acknowledgements
We thank Christian Pohl, Anthony Santella, Robert Vogel and Jennifer Zallen
for helpful discussions and critical reading of the manuscript; Anthony Santella
for help with software packaging; and members of the Z.B. laboratory for
software testing.
RESEARCH ARTICLE 3273
Funding
J.L.M. was supported by the Tri-Institutional Training Program in
Computational Biology and Medicine. Work in the laboratory of Z.B. is
supported by the National Institutes of Health [grants GM097576 and
HD075602]. Deposited in PMC for release after 12 months.
Competing interests statement
The authors declare no competing financial interests.
Author contributions
J.L.M. and Z.B. developed the method framework and wrote the manuscript.
J.L.M. implemented the framework and created the visualizations. Z.D.
performed experimental data collection and contributed to discussions.
Supplementary material
Supplementary material available online at
http://dev.biologists.org/lookup/suppl/doi:10.1242/dev.096040/-/DC1
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