Download PDF

© 2014. Published by The Company of Biologists Ltd | Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
RESEARCH ARTICLE
Spatial gradients of protein-level time delays set the pace of the
traveling segmentation clock waves
ABSTRACT
The vertebrate segmentation clock is a gene expression oscillator
controlling rhythmic segmentation of the vertebral column during
embryonic development. The period of oscillations becomes longer as
cells are displaced along the posterior to anterior axis, which results in
traveling waves of clock gene expression sweeping in the unsegmented
tissue. Although various hypotheses necessitating the inclusion of
additional regulatory genes into the core clock network at different
spatial locations have been proposed, the mechanism underlying
traveling waves has remained elusive. Here, we combined molecularlevel computational modeling and quantitative experimentation to solve
this puzzle. Our model predicts the existence of an increasing gradient of
gene expression time delays along the posterior to anterior direction to
recapitulate spatiotemporal profiles of the traveling segmentation clock
waves in different genetic backgrounds in zebrafish. We validated this
prediction by measuring an increased time delay of oscillatory Her1
protein production along the unsegmented tissue. Our results refuted
the need for spatial expansion of the core feedback loop to explain the
occurrence of traveling waves. Spatial regulation of gene expression
time delays is a novel way of creating dynamic patterns; this is the first
report demonstrating such a control mechanism in any tissue and future
investigations will explore the presence of analogous examples in other
biological systems.
KEY WORDS: Segmentation clock, Oscillation, Traveling wave,
Systems biology, Computational modeling, Gene expression
INTRODUCTION
Vertebral segments differentiate from their embryonic rudiments called
somite segments. Segmentation of somites, namely somitogenesis,
occurs at a species-specific pace during embryonic development.
Somitogenesis is controlled by a gene expression oscillator called
the vertebrate segmentation clock that ‘ticks’ in cells located in the
unsegmented presomitic mesoderm (PSM). The period of the
segmentation clock in cells located at the posterior end of the PSM is
equivalent to the period of somite formation. The period of oscillation
increases as cells are passively displaced closer to the anterior end of the
PSM. The oscillations finally halt as cells bud off as a somite segment
at the anterior end of the tissue. Cells exiting the PSM are arrested in
different states of the oscillation cycle, defining which portion of a
1
Department of Mathematics, Colgate University, Hamilton, NY 13346, USA.
Department of Biology, Colgate University, Hamilton, NY 13346, USA.
Department of Computer Science, Colgate University, Hamilton, NY 13346, USA.
4
Department of Genetics, Albert Einstein College of Medicine, Bronx, NY 10461,
USA.
*These authors contributed equally to this work
2
3
‡
Authors for correspondence ([email protected];
[email protected])
Received 26 April 2014; Accepted 30 August 2014
4158
somite they will form and which set of genes they will express during
differentiation (Pourquié, 2011).
The spatiotemporal dynamics of oscillations create a phase
difference among cells along the PSM. Anterior PSM cells are
retarded in the oscillator phase relative to posterior PSM cells; the
further anterior the cells are located, the greater the retardation is.
This phase difference results in the formation of traveling wave-like
gene expression patterns along the PSM (Fig. 1A), which can be
visualized by in situ hybridization for oscillating mRNAs or realtime imaging of oscillating proteins. The different phases of the
oscillator cycle are mapped out in space as stripes of expression of
the oscillating genes. The number of expression stripes reflects the
number of oscillation cycles by which the anterior cells are lagging
behind posterior cells (Giudicelli et al., 2007; Gomez et al., 2008).
The spatial period profile of the segmentation clock was measured
in zebrafish by utilizing fluorescent in situ hybridization data
(Giudicelli et al., 2007). We have further demonstrated that the
period profile is conserved between zebrafish and corn snake
(Gomez et al., 2008).
The prevailing model in the somitogenesis field states that the
pacemaker mechanism of the segmentation clock is based on an
autoinhibitory transcriptional feedback loop of Her/Hes family
genes (Harima et al., 2013; Jensen et al., 2003; Lewis, 2003; Monk,
2003; Özbudak and Pourquie, 2008). Quantitative data have
become more available in the somitogenesis field in recent years.
Molecular-level models coupled with experimentation have
provided insight into how the dynamics of the segmentation clock
in the posterior PSM cells can be affected in various mutant
conditions (Ay et al., 2013; Hanisch et al., 2013; Özbudak and
Lewis, 2008; Schroter et al., 2012). Although we have a good
understanding of how the oscillator functions in the posterior PSM,
the underlying mechanism that generates the spatiotemporal
traveling waves in the whole PSM has remained elusive.
A few modeling studies addressing the formation of traveling
waves have been carried out (Campanelli and Gedeon, 2010;
Cinquin, 2007; Uriu et al., 2009). Although these studies provided
insight into the system, these models were based on regulatory
assumptions that have been corrected by recent experimental results
(Hanisch et al., 2013; Schroter et al., 2012; Trofka et al., 2012).
Furthermore, these models focused on simulating the system only in
a wild-type background and were therefore largely unconstrained.
More rigorous models can be built by constraining them to explain
the spatiotemporal dynamics of the segmentation clock in all
available genetic backgrounds.
Four broad hypotheses could explain the traveling wave-like gene
expression patterns in the tissue. The first three hypotheses require
the inclusion of new genes into the core clock regulatory network,
whereas the fourth does not have such a restriction: (1) instructive
regulation of clock gene expression by upstream transcription
factors [such as tbx6 (also known as fss and tbx24)] (Brend and
DEVELOPMENT
Ahmet Ay1,2,‡, Jack Holland3, *, Adriana Sperlea3, *, Gnanapackiam Sheela Devakanmalai4, *, Stephan Knierer4, *,
Sebastian Sangervasi1, *, Angel Stevenson4 and Ertuğ rul M. Ö zbudak4,‡
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
Holley, 2009; Gajewski et al., 2003; Holley, 2007; Holley et al.,
2000); (2) inclusion of regionally expressed oscillatory Her family
genes into the core clock network (Cinquin, 2007; Schroter et al.,
2012; Shankaran et al., 2007); (3) inclusion of anterior PSMspecific genes into the core clock network (Holley, 2007); and (4)
spatial variation of biochemical reaction rates of core clock genes
(Uriu et al., 2009).
Here, we built a molecular-level multicellular model to assess the
feasibility of the fourth scenario in generating the traveling waves
throughout the PSM. Our model is able to explain the formation of
traveling waves in wild-type background as in Giudicelli et al.
(2007). The model predicts an increasing gradient of effective
translational time delay along the posterior to anterior direction and
in this way recapitulates the spatiotemporal profile of the traveling
segmentation clock waves in six genetic backgrounds (wild type,
her1−/−, her7−/−, hes6−/−, her7−/−;hes6−/− and notch1a−/−). We
experimentally measured the effective Her1 translational time delay,
which includes translation and nuclear import of proteins, and found
that it increases approximately 4-fold towards the anterior PSM in
zebrafish embryos and confirmed the major prediction of our model.
Our model further predicts how the spatial profiles of period,
amplitude and degree of synchronization of the segmentation clock
vary in all available genetic backgrounds and lays the foundation for
future experimental tests.
segmentation clock is yet to be discovered. We reasoned that these
potential regulators should change the ‘effective’ rates of selected
biochemical reactions along the PSM, without changing the core
clock regulatory network, to set the gradient-like period profile along
the PSM. To determine which reaction rates influence the period most,
we extended our published model (Ay et al., 2013) into 6×10 cells
representing the posteriormost tailbud region. Then, we identified
parameter sets that robustly reproduced roughly 20 different
experimental phenotypes in six different genetic backgrounds as
before (Ay et al., 2013). We then performed a sensitivity analysis at
different positions in the PSM to determine the reaction parameters
whose perturbation influences the oscillation period the most
(Fig. 2A). We found that the most influential parameters are time
delays in the transcription or translation of the her1, her7 or deltaC
genes, the halflives of their three respective mRNAs, and the halflives
of repressor dimers (Fig. 2A). These results echoed the single-cell
analytic solution of Lewis (2003). However, the sensitivity analysis
showed that expression time delays of the deltaC gene also influence
the clock period, in agreement with Herrgen et al. (2010). A further
difference from Lewis (2003) is that halflives of dimer proteins more
strongly affect the period than halflives of monomer proteins
(supplementary material Tables S2 and S3).
RESULTS
Key biochemical reaction rates influencing the period are
determined by sensitivity analysis
We sought to determine the reaction parameters whose spatial
variation could reproduce the measured period profile in wild-type
zebrafish embryos (Giudicelli et al., 2007). We applied increasing
or decreasing gradients to each parameter along the PSM (6×50
cells), similar to Uriu et al. (2009), and assessed whether gradients
of any combinations of influential parameters could match the
period profile with a maximum of 10% error. Our results showed
that, contrary to an earlier model (Uriu et al., 2009), the gradients in
The activities of three signaling pathways generate gradients along the
PSM (Pourquie, 2011). Furthermore, many transcription factors are
expressed along the PSM regionally that could potentially influence
the period of the segmentation clock (Özbudak et al., 2010). How all
these potential regulators join forces to generate traveling waves of the
Traveling segmentation clock waves can be generated only
if the effective time delays increase along the PSM
4159
DEVELOPMENT
Fig. 1. The traveling segmentation clock waves. (A) In one oscillation cycle, the expression profiles ( purple corresponds to higher levels of her1 mRNA)
return back to the original phase, and one somite segments at the anterior end of the PSM. Oscillations of neighboring cells are locally synchronized by
Notch signaling. (B) The regulatory interactions in the zebrafish segmentation clock network. Her1, Her7 and Hes6 proteins can form homo- and heterodimers.
However, only the Her1-Her1 homodimer and the Her7-Hes6 heterodimer repress transcription of her1, her7 and deltaC. Notch signaling activates transcription of
her1 and her7.
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
increasing gradients of transcriptional time delays of her1+her7 or
deltaC or her1+her7+deltaC mRNAs, and translational time delays
of Her1+Her7 or DeltaC or Her1+Her7+DeltaC proteins along the
PSM (Fig. 2B).
Surprisingly, we noticed that a joint increase in the transcriptional
and translational time delays of her1 and her7 mRNA or protein
could slow down oscillations sufficiently; however, the synchrony
in oscillation phases of nearest neighbors is then lost in the anterior
PSM (supplementary material Fig. S3). This is due to the creation of
an imbalance between the time delays of Her genes functioning
intracellularly and that of deltaC functioning intercellularly (see
Discussion).
Of the remaining four different parameter gradients, the triple
transcriptional time delay and triple translational time delay work
with more parameter sets compared with time delays in expression
of the deltaC gene alone (Fig. 2B). The triple time delays provide
robustness into the system. This again reflects the need for balance
between the timings of the intracellular and intercellular feedback
loops.
Fig. 2. Sensitivity analysis. (A) The period of the segmentation clock is
sensitive to eight model parameters: transcriptional time delays of deltaC
(delaymd), her1 (delaymh1) and her7 (delaymh7); translational time delays of
DeltaC (delaypd) and Her1 (delayph1); and degradation rates of her1 (mdh1),
her7 (mdh7) and Her1-Her1 (ddgh1h1). (B) Eight sensitive parameters are used
to create ten parameter groups to be varied from posterior to anterior. The
gradients of six out of ten parameter groups resulted in similar period behavior
to previously measured oscillation period data (Giudicelli et al., 2007). The
distributions of successful numbers of parameter sets (out of 165 tested) for
varying gradients are shown. Triple transcriptional and translational time
delays lead to the highest frequency of parameter sets satisfying the period
condition.
halflives of mRNAs or proteins do not slow down the period
sufficiently along the PSM and cannot accommodate the formation
of two expression stripes. Jointly decreasing gradients of
degradation rates of the two Her genes or of all three oscillating
genes did not change the outcome. These modifications rather
dampened the oscillations in the intermediate PSM (supplementary
material Fig. S1). Furthermore, we experimentally measured
the stability of Her7 protein at different locations along the PSM
(see Materials and Methods). We induced a short pulse of Her7
expression in transgenic embryos (Giudicelli et al., 2007)
and observed that Her7 protein degrades uniformly along the
PSM (supplementary material Fig. S2). This result rules out a
regionalized protein degradation mechanism for generating
traveling waves and confirms the conclusion of our model.
Among all parameter combinations tested, however, there were
six that slowed down the period in a manner similar to that measured
in wild-type zebrafish embryos (Giudicelli et al., 2007). These are
4160
We next simulated the spatiotemporal dynamics of the segmentation
clock in wild-type and five mutant backgrounds using four successful
parameter gradients. For each gradient, the rate changes that give the
highest number of successful parameter sets that fit to the period
observations in wild-type embryos, together with the corresponding
parameter sets, are selected for anterior PSM simulations (Fig. 2). Our
model successfully reproduces the formation of distinct expression
waves in wild-type, hes6−/− and her7−/−;hes6−/− backgrounds
(Fig. 3; supplementary material Figs S4-S6 and Movies 1-6). The
snapshots resemble published in situ hybridization images in these
genetic backgrounds (Fig. 3A) (Schroter et al., 2012).
We and others have recently reported that her1−/− embryos halt
their oscillations earlier in the PSM and manifest only one or two
expression waves at mid-somitogenesis stages; this results in the
formation of one less stripe in the anterior PSM in her1−/− mutants
(Choorapoikayil et al., 2012; Hanisch et al., 2013) compared with
wild-type, hes6−/− and her7−/−;hes6−/− embryos (Schroter et al.,
2012). Our model reproduced this observation successfully (Fig. 3).
We and others have also reported that traveling wave-like
expression patterns are significantly disturbed in her7−/− mutants;
there is also a large variation from embryo to embryo from the same
mutant clutch (Choorapoikayil et al., 2012; Hanisch et al., 2013;
Schroter et al., 2012). Our model nicely recapitulates this
phenotype. Snapshots of the simulation movie show that, within a
given embryo, the traveling wave pattern is disturbed significantly
and the disturbance varies from phase to phase, reflecting the
variation observed in embryos from the same clutch (Fig. 3).
In the Notch pathway mutants, oscillations are desynchronized
and the traveling wave pattern is disturbed. Our simulations readily
reproduce this phenotype. The synchronized traveling wave pattern
of wild-type embryos is lost in notch1a−/− mutants and instead a
salt-and-pepper-like expression profile is observed at each snapshot
(Fig. 3).
Spatial profiles of the period, amplitude and synchronization
scores of the segmentation clock in all genetic backgrounds
are calculated from simulations
We measured how the period, amplitude and synchronization of the
segmentation clock vary in cells located at different positions along
DEVELOPMENT
The model successfully reproduces spatiotemporal
expression of the segmentation clock in wild-type and
mutant backgrounds
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
Fig. 3. her1 mRNA levels in the whole PSM in different genetic
backgrounds under the influence of a Her1-Her7-DeltaC
translational time delay gradient. (A) Snapshots of 6×50 cells
located along the PSM in different genetic backgrounds. Images are
obtained by setting an increasing gradient to the translational time
delay of Her1, Her7 and DeltaC proteins. Traveling waves are readily
generated under these conditions. Darker color corresponds to
higher levels of her1 mRNA. (B) her1 mRNA levels in six cells for the
300 min have been plotted as they travel from the posterior to anterior
PSM in different genetic backgrounds. Period and amplitude
increase in all genetic backgrounds. Early arrest of oscillations in the
her1−/− mutant and loss of synchronization in her7−/− and notch1a−/−
mutants are observed.
The increased gradient of effective translational time delays
of segmentation clock genes underlies the formation of
traveling waves along the PSM
Our model outlined two potential mechanisms to generate
synchronized traveling waves in the PSM: an increasing gradient
of time delays of the transcription or of the translation of oscillating
segmentation clock genes along the PSM (Figs 2–5; supplementary
material Figs S4-S12). Which one of these two possibilities is
utilized to generate the characteristic spatiotemporal dynamics of
the segmentation clock?
We previously measured the transcriptional time delays of her1,
her7 and deltaC genes to be approximately 10-12 min in the anterior
PSM (Giudicelli et al., 2007; Hanisch et al., 2013). However, our
model utilizes the same parameter range for cells located in the
posterior PSM to reproduce phenotypes in all genetic backgrounds.
Therefore, the experimentally measured rates in anterior PSM cells
exactly correspond to those rates necessitated by our model for
posterior PSM cells. These results argue against the possibility of a
significant increase in transcriptional time delays along the PSM.
To determine the spatial variation of the effective protein
production time delay of oscillating genes, we experimentally
measured this rate for Her1 protein by utilizing a transgenic animal
4161
DEVELOPMENT
the PSM (Fig. 4; supplementary material Figs S7-S9). The
parameter sets were selected to match to the Giudicelli et al.
(2007) data in the 0% to 80% length of PSM; therefore, the period
profiles in the wild-type background show the expected increase
along the PSM. Strikingly, the period profiles in individual cells in
all mutants also present similar increases along the PSM
independently of whether synchronized traveling waves can be
observed at the tissue level (Fig. 4A). This prediction of the model
may be tested following the future development of more sensitive
real-time reporters that allow imaging at the posterior PSM (Delaune
et al., 2012).
The amplitude of oscillations in our model mildly increases along
the PSM (Fig. 4B). Such an increase had previously been observed
experimentally at the level of deltaC mRNA (Jiang et al., 2000) and
Her1 protein (Delaune et al., 2012). The synchronization scores
reveal near-perfect synchrony in wild type, hes6−/−, her1−/− and
her7−/−;hes6−/− mutants, reproducing the synchronized traveling
waves in these backgrounds (Fig. 4C). The synchronization score of
notch1a−/− mutants is close to zero, reflecting the absence of cellcoupling in this background. The synchronization score of her7−/−
mutants is very low in the posterior PSM, echoing our previous
results (Ay et al., 2013) (Fig. 4C).
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
of mRNA stripes lies further anteriorly than that of protein stripes,
i.e. while cells located anteriorly have just started to produce
mRNAs, those located posteriorly have already past this phase of
their oscillation cycle and started to make proteins. We measured the
spatial distance between the onset of cytoplasmic mRNA and
nuclear protein stripes. This distance is used to calculate the
effective Her1 translational time delay (see Materials and Methods).
To our initial surprise, we observed that the effective translational
time delay increases 4.4-fold from the intermediate to the anterior
PSM in zebrafish embryos (Fig. 6; supplementary material
Figs S13-S21).
DeltaC translational time delays have previously been measured as
approximately 30 min in anterior PSM (Giudicelli et al., 2007). In our
simulations, the DeltaC translational time delay has been estimated to
be approximately 12 min to satisfy all mutant phenotypes in posterior
PSM. This constitutes a 2.5-fold increase in the translational
time delay of DeltaC protein from posterior PSM to anterior PSM.
We have now measured Her1 translational time delays to have
increased approximately 4.4-fold in the anterior PSM. We performed
new simulations to confirm that non-symmetric increases in the
translational time delays also recapitulate the synchronized traveling
waves in the PSM. We fixed the translational time delay of DeltaC
protein to a 2.5-fold increase from posterior to anterior PSM, and
searched for all the possible Her1 and Her7 translational time delay
gradients that could still match all the available experimental
observations for the segmentation network. We found that a 4- to
9-fold increase in Her1 and Her7 translational time delays in the PSM
reproduce the experimentally observed increase in period (Giudicelli
et al., 2007) (Fig. 6F; supplementary material Figs S14-S16). This
result agrees well with our experimental observations of an increased
Her1 translational time delay in the anterior PSM.
Fig. 4. Spatial profiling of period, amplitude and synchronization scores
along the PSM in all genetic backgrounds under the influence of a Her1Her7-DeltaC translational time delay gradient. (A,B) The period (A) and
amplitude (B) of oscillations are increased as cells traverse from the posterior
to the anterior PSM in all genetic backgrounds. (C) The oscillations are locally
synchronized in wild type, her1−/−, hes6−/− and her7−/−;hes6−/− mutants. The
synchrony is lost in her7−/− and notch1a−/− mutants; however, the synchrony in
her7−/− mutants is increased in the anterior PSM. (A-C) x-axis corresponds to
spatial location in the PSM; y-axis corresponds to the period, amplitude or
synchrony score, which are normalized to corresponding wild-type values in
the posterior PSM.
that expresses Her1-Venus fusion protein (Delaune et al., 2012).
We simultaneously detected the spatial profiles of her1-Venus
mRNA and protein by fluorescent in situ hybridization and
immunohistochemistry along the PSM. The slowdown of
oscillations towards the anterior PSM causes a phase delay in
cells located in the anterior PSM compared with those located in the
posterior PSM. Owing to this phase difference, the anterior domain
4162
We first performed simulations for cells located in the posterior
PSM and trained the model with roughly 20 different phenotypes
obtained in six genetic backgrounds. This narrowed down the
parameter space that can generate all observed phenotypes
simultaneously. Furthermore, we trained our model by matching
the predicted rate of slowdown to the rate experimentally observed
in zebrafish and by requiring the occurrence of two to three traveling
waves in the PSM. Finally, we utilized recently updated information
on the nature of functional repressor dimers in zebrafish. All these
updates collectively reduced the set of parameters whose variation
along the PSM could account for the observed traveling waves; and
these parameters can be experimentally measured.
The results of our simulations argue against previous claims that the
traveling waves are due to a gradient of hes6 transcription along the
PSM (Cinquin, 2007) or gradients of effective halflives of mRNA and
proteins along the PSM (Uriu et al., 2009). Our analysis shows,
moreover, that the traveling waves can be generated without resorting
to assumptions of faster decay of monomers versus dimers and an
order of magnitude longer halflife of hes6 versus her7 (Campanelli
and Gedeon, 2010). Uriu et al. (2009) listed slower mRNA
transcription and Delta protein synthesis in posterior than in anterior
PSM among the possible scenarios explaining the formation of
traveling waves in the PSM. These ideas run counter to our model,
which posits that increased, rather than decreased, time delays in
transcription and translation along the posterior-anterior direction
slow down the oscillations and result in traveling waves.
DEVELOPMENT
DISCUSSION
Constraining mathematical models with quantitative
experimental data restricts the number of potential
mechanisms generating traveling waves in the PSM
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
The time delays in the expression of Her genes that constitute
the intracellular feedback loop and the deltaC gene that forms the
intercellular feedback loop have to be balanced (Herrgen et al.,
2010; Lewis, 2003). Skewing the relationship of this balance
could result in desynchronized oscillations of neighboring cells.
Therefore, the model was not able to reproduce synchronized
oscillations along the PSM by only increasing the time delays of Her
genes (supplementary material Fig. S3). The model shows that
increasing the time delays of three oscillating genes along the PSM
is a more robust mechanism of generating traveling waves in the
tissue (Fig. 2B).
Spatiotemporal profiles of the segmentation clock in various
genetic backgrounds are readily satisfied with the model
The parameter sets that satisfy the requirement of formation of two to
three expression waves in the simulations for wild-type embryos also
reproduce the in situ hybridization profiles that were published in
various mutant conditions (Choorapoikayil et al., 2012; Hanisch
et al., 2013; Jiang et al., 2000; Schroter et al., 2012). Two to three
synchronized traveling waves are obtained in hes6−/− and her7−/−;
hes6−/− mutants as in wild-type embryos (Fig. 3). The simulations
demonstrate formation of one less stripe and the arrest of oscillations
in more posterior locations in her1−/− mutants than in wild-type
embryos (Fig. 3), again matching previous observations. However,
the oscillations arrest at high expression levels in our simulations
rather than at the low expression level that is experimentally
observed. This, we suggest, reflects the fact that our current model
does not account the many additional genes (in addition to her1,
her7, hes6 and deltaC) that are expressed in a patterned manner in the
anterior PSM and/or define the extent of the PSM as a whole. These
additional genes might shut off expression of the clock genes at the
end of the anterior PSM. One candidate for such a role is the ripply1
gene: expression of this gene is restricted to the anterior PSM and it is
crucial for switching off the expression of segmentation clock genes
as cells segment into somites (Kawamura et al., 2005).
The synchronization scores of hes6−/−, her7−/−;hes6−/−, her1−/−
and wild-type embryos are similar along the tissue (Fig. 4C). There
is no synchronization of oscillations in the notch1a−/− mutants
4163
DEVELOPMENT
Fig. 5. Density plots of traveling waves in all genetic
backgrounds under the influence of a Her1-Her7-DeltaC
translational time delay gradient. (A-F) Traveling waves
are observed in wild-type, her1−/−, hes6−/− and her7−/−;
hes6−/− but are blurred in her7−/− and notch1a−/− embryos.
The oscillations in her1−/− mutants arrest at more posterior
locations. The x-axis reflects time (min) and the y-axis maps
spatial locations in the PSM ( posterior is top and anterior
is bottom).
RESEARCH ARTICLE
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
(Fig. 4C). The synchronization score of oscillations is very low in
her7−/− mutants in the posterior PSM (Fig. 4C), which explains why
her7−/− mutants are sensitized and oscillations fail frequently
during the formation of posterior somites in many of the mutant
embryos. However, the synchronization score of her7−/− mutants
recovers appreciably along the PSM, reflecting the formation of
irregular stripes in some of the embryos in a clutch of mutants that
are fixed at different oscillation phases (Hanisch et al., 2013). This
result can be explained by the absence of expression of the hes6
gene in the anterior PSM. Thus, the cells located in the anterior PSM
of her7−/− mutants effectively lack expression of both her7 and
hes6; these cells resemble their counterparts in the her7−/−;hes6−/−
double mutant, with the exception that they experience oscillations
with compromised synchrony when they were in the posterior PSM
before they join the anterior PSM domain. Therefore, the
synchronization score in anterior PSM cells of her7−/− mutants
never recovers to the levels of the wild type, and her7−/−;hes6−/−
mutants and likewise her7−/− mutants never form stripy expression
waves that are as defined and regular as those of her7−/−;hes6−/−
embryos.
In all the genetic backgrounds that we examined, the amplitudes
of oscillations increase towards the anterior end of the PSM. These
results align with previous experimental results indicating that
levels of deltaC mRNA (Jiang et al., 2000) and Her1 protein
(Delaune et al., 2012) increase in a similar way before cells exit
the PSM.
Spatial variation of protein level time delay induces the
traveling waves of clock gene expression
Our previously published experimental measurements of
transcriptional time delays of three genes in the anterior PSM
cells (10-12 min) (Giudicelli et al., 2007; Hanisch et al., 2013) were
4164
as low as postulated by our model for the posterior PSM cells.
Hence, the experimental data argue against a drastic increase in the
transcriptional time delays along the PSM. However, we previously
measured the translational time delay of DeltaC protein in the
anterior PSM and found it to be more than 30 min (Giudicelli et al.,
2007). The experimentally measured value is similar to that
predicted by our model for anterior PSM cells and about 2- to
3-fold greater than that of posterior PSM cells. DeltaC antibody
staining is insufficiently sensitive for the measurement of low levels
of DeltaC protein in the posterior PSM, so that we cannot
experimentally measure the DeltaC translational time delay in
posterior regions. Using a transgenic animal that was generated by
fusing Venus coding sequences to her1 (Delaune et al., 2012), we
now measured the effective translational time delay of Her1 protein
and found this to increase 4.4-fold in cells located in anterior versus
intermediate PSM. Our simulations suggested that respective
increases in the translational time delays of Delta/Her proteins can
recapitulate the formation of synchronized traveling waves along the
PSM (supplementary material Figs S14-S16).
Although we have optimized the parameters in our model for the
zebrafish system, the results of our study are general and can be
extended to other vertebrate organisms. The transcriptional time
delays were first determined in the zebrafish model (Giudicelli et al.,
2007; Hanisch et al., 2013). Recently, this technique has been
adapted to measure the transcriptional time delays in other
vertebrate species (Hoyle and Ish-Horowicz, 2013; Takashima
et al., 2011). It now remains to be determined whether the
spatiotemporal regulation of effective translational time delays,
which has now been discovered in zebrafish, is conserved in other
vertebrate species.
Alternative models were previously put forward to explain the
formation of traveling waves. Expression of clock genes is lost in
DEVELOPMENT
Fig. 6. Effective Her1 translational
time delay increases in the anterior
PSM. (A-C) Fluorescent in situ
hybridization of Tg(her1:her1-Venus)
transgenic embryos with a Venus
antisense probe (A),
immunohistochemistry against Venus
protein (B) and merge of RNA and
protein staining with DAPI
counterstaining (blue) (C). (D) Spatial
profiles of RNA (green) and protein
(red) levels from A-C. Solid lines are
smoothed profiles. The short arrow
indicates d (spatial interval) and the
long arrow indicates S (spatial
wavelength). (E) Effective Her1
protein production time delay is plotted
along normalized PSM length. The
measurements are made from
intermediate to anterior PSM. The
data are binned at equal spatial
distances and the mean (±s.e.m.) is
plotted along the axis. (F) The number
of parameter sets (out of the 165
robust parameter sets satisfying
posterior PSM experimental
conditions) that reproduce period
elongation in the tissue as the effective
protein production time delay for Her
proteins increases at different times
(DeltaC protein production time delay
is set to a 2.5-fold increase along the
full PSM).
the anteriormost PSM in tbx6 mutants (Holley, 2007); distinct cisregulatory elements have been identified to drive expression of the
her1 clock gene specifically in the anterior PSM (Brend and Holley,
2009; Gajewski et al., 2003) and these DNA sequences are bound
by upstream transcription factors (Brend and Holley, 2009). If the
upstream transcription factors create a new negative-feedback loop
and their activities oscillate with a long period in the anterior PSM,
then they could impose a longer oscillation period on Her/Delta
gene expression than the period obtained by the time delays of the
Her autoinhibitory feedback loop in the posterior PSM. A second
alternative mechanism is the spatially tiled expression of various
Her family oscillatory genes in the PSM. Although the expression of
master oscillatory genes (her1, her7 and deltaC) exhibit traveling
waves in the tissue, oscillations of other Her genes are confined to
different spatial locations in the PSM (Shankaran et al., 2007).
Integration of regionally expressed Her genes into the core
regulatory network has been proposed to underlie positionspecific control of the oscillation period (Schroter et al., 2012;
Shankaran et al., 2007). Furthermore, many additional genes are
expressed differentially in the anterior PSM (Holley, 2007;
Özbudak et al., 2010); these genes could potentially regulate
expression of Her/Delta genes in the anterior PSM. All three
alternative models necessitate the integration of additional genes
into the core clock network to generate the traveling segmentation
clock waves. The results of our interdisciplinary approach negate
such a need. Even though different factors regulate the expression of
oscillating clock genes in the anterior PSM, these regional
regulators act permissively for clock gene expression and they do
not expand the core negative-feedback loop.
The molecular mechanism that controls such a spatiotemporal
transition in effective biochemical rates in the segmentation clock is
currently unknown. It is likely to involve gradients of signaling
pathways and genes that are expressed in the anterior PSM and
define its extent and special character. The effective protein-level
time delay that we experimentally measured includes the translation
and intracellular transport of proteins. Regulation of translational
time delay has previously been observed (Buchan and Stansfield,
2007; Lakkaraju et al., 2008). However, the rate of nuclear
trafficking contributes significantly to the period of the circadian
clock (Meyer et al., 2006; Tataroğlu and Schafmeier, 2010). We
previously found that the expression of many genes regulating
intracellular protein transport is downregulated in the anterior
compared with the posterior PSM (Özbudak et al., 2010). The
protein products of some of these genes could modify expression
time delays of the segmentation clock genes in the anterior PSM.
Future quantitative experiments coupled with computational
modeling will reveal the molecular mechanism underlying this
spatial transition.
MATERIALS AND METHODS
Protein time delay measurement
Double fluorescent Venus transcript and protein staining was carried out
with 12- to 14-somite stage Tg(her1:her1-Venus)bk15 (Delaune et al., 2012)
transgenic embryos. Antisense Venus RNA probe was synthesized by
in vitro transcription from linearized plasmids using digoxigenin RNA
labeling mix (Roche). Embryos were incubated jointly with peroxidaseconjugated anti-digoxigenin (Roche, 11207733910; 1/500) and anti-GFP
rabbit IgG fraction (Molecular Probes, A-11122; 1/200) antibodies
overnight. The peroxidase activity was detected using the TSA Plus
Fluorescein system (PerkinElmer). The peroxidase activity was then
quenched with 1% H2O2, followed by extensive washes. Embryos were
incubated with secondary peroxidase-conjugated AffiniPure goat anti-rabbit
IgG antibody (Jackson ImmunoResearch Laboratories, 111-035-144;
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
1/200) and peroxidase activity was detected using the TSA Plus TMR
system (PerkinElmer). Specimens were counterstained with DAPI, flatmounted in 50% glycerol, and imaged with a Zeiss Imager Z2 microscope
equipped with Apotome and Axiovision 4.8 Rel. Fluorescent images were
taken at 1-3 μm serial sections and 2D images were created by projecting all
images taken at different focal planes.
DAPI staining is used to determine the last segmented somite and the
posterior end of the notochord. As Her1 protein is short lived and we carried
out stringent double RNA-protein staining, the protein signal can be
robustly detected only in the nucleus, where proteins are confined in a much
smaller area and the signal is higher than background noise in the
fluorescence channel. The image is warped in Adobe Photoshop to make
the stripes of gene expression appear at right angles to the body axis, and
the notochord is blanked out leaving only PSM tissue to contribute to the
analysis, as in Hanisch et al. (2013). The spatial profiles of mRNA and
protein staining are plotted using the Analyze:Plot Profile tool of ImageJ.
For each point along the axis, we took the total signal summed over the
transverse column of pixels (supplementary material Table S4) and used
Gaussian smoothing (see supplementary methods for explanation and code)
to obtain a smooth graph (Hanisch et al., 2013). By comparing two graphs,
we calculated the spatial interval (d) between the onset of cytoplasmic
mRNA signal and that of the nuclear protein signal for selected stripes in the
anterior and intermediate PSM (Giudicelli et al., 2007; Hanisch et al., 2013).
The spatial profile of the oscillation period, T(x), is obtained from Giudicelli
et al. (2007). The spatial wavelength, S(x), is calculated by the distance
between consecutive peaks or troughs of RNA or protein expression levels.
We converted this spatial distance to a time interval using the following
equation (Giudicelli et al., 2007): tp(x)=30×d(x)×T(x)/S(x). The time
interval corresponds to the effective translational time delay including
translation and nuclear import of proteins (supplementary material
Table S5). Since calculations necessitate two consecutive expression
stripes (Giudicelli et al., 2007), we could not determine the effective
translational time delay in the posterior PSM as the signal of protein staining
is too weak in that region. Data from a set of 65 embryos are pooled together
and binned at equal axis width to determine the spatial profile of proteinlevel time delay in the PSM.
Protein degradation measurement
Tg(hsp70l:HA-her7) (Giudicelli et al., 2007) transgenic embryos at 12- to
14-somite stages were heat shocked in a water bath for 40 min at 37°C,
dechorionated manually, and incubated in embryo media containing
100 μg/ml cycloheximide for 10 min at 28°C. Then, embryos were
collected every 5 min, fixed and stained with a rat monoclonal anti-HA
antibody (Roche, 3F10; 1/500) in combination with Alexa Fluor 647 goat
anti-rat IgG secondary antibody (Life Technologies, A21247; 1/400).
Specimens were counterstained with DAPI, imaged as single sections and
spatial protein profiles were measured as described above. The PSM was
divided into ten equal sections; protein levels were averaged in each
section, normalized to the mean of all sections and plotted.
Deterministic model
We have developed a time-delayed differential equation (DDE) model
consisting of 14 equations with 44 parameters (Ay et al., 2013) (see
supplementary material Table S1). Our model includes her1, her7, hes6
and deltaC genes. Her1, Her7 and Hes6 proteins form six different homoand heterodimers. However, only Her1-Her1 and Her7-Hes6 dimers are able
to repress transcription of the her1, her7, deltaC genes (Fig. 1B). DeltaC
ligand binds to a Notch receptor and results in proteolytic cleavage of the
intracellular domain of Notch protein (NICD). NICD translocates into
the nucleus to activate transcription of her1 and her7. The transcriptional
repressors are assumed to compete with the NICD protein for binding to the
DNA regulatory region to repress transcription of her1 and her7 (Özbudak
and Lewis, 2008). Following Lewis (2003), we do not explicitly write an
equation representing the production of NICD. The translational time delay
of DeltaC effectively incorporates translation and membrane localization of
DeltaC protein, interaction of Delta-Notch proteins, and production and
nuclear localization of NICD. The translational time delays of Her1
and Her7 proteins include the translation and nuclear import of repressor
4165
DEVELOPMENT
RESEARCH ARTICLE
RESEARCH ARTICLE
Spatial modeling
The PSM tissue is represented as a two-dimensional hexagonal grid of
6×50 cells in our simulations. We artificially connected the right- and
leftmost cells in each column, such that each cell has six neighbors, except
for the cells located in the most posterior and anterior columns, which have
four neighbors. The model is simulated for 1200 min in total: (1) we first
simulated only the 6×10 cells forming the posterior PSM for 600 min; (2) to
represent the posterior growth of the PSM, we then added a column of six
cells every 6 min for the next 240 min until the PSM was full; (3) after the
PSM reaches its full size of 6×50 (300) cells, a column of six cells was added
at the posterior end and removed at the anterior end of the PSM in the last
360 min, preserving a fixed PSM size. We set the hes6 mRNA synthesis rate
(msh6) to a biologically relevant parameter range in the posterior PSM (first
ten columns of cells); this rate is linearly interpolated at all intermediate PSM
locations (20 columns of cells), and we finally set this synthesis rate to zero in
the anterior PSM (last 20 columns of cells). Similarly, we varied time delay
and degradation rates suggested by the sensitivity analysis (described below)
from the posterior end of the PSM (eleventh column of cells) to the anterior
end of the PSM (fiftieth column of cells). The reaction rates were set to the
same level (with up to ±5% perturbation) in all cells up to the tenth column
and the rates are increased or decreased linearly until a specified level at the
end of the anterior PSM. Time delays were increased up to tenfold and
degradation rates were decreased down to 1% at the end of anterior PSM.
Pseudo-stochastic simulations
In order to reflect randomness in biochemical reactions of the segmentation
clock network, we carried out pseudo-stochastic simulations of our model.
Randomness has been introduced by allowing each cell to have up to 10%
difference in rates for each biochemical reaction. The parameter values that
have been randomly selected from the biologically relevant ranges have
been perturbed up to ±5% for each cell. This extrinsic noise is kept constant
throughout the lifetimes of cells in the PSM. The perturbed system has been
numerically solved with Euler’s method by incrementing time at every
0.01 min, and updating mRNA and protein levels at each iteration using rate
of changes provided by the model.
Parameter estimation and sensitivity analysis
mRNA and protein decay rates and transcriptional time delays have been
measured previously (Ay et al., 2013; Giudicelli et al., 2007; Hanisch et al.,
2013). However, some of the reaction rates in the segmentation clock
network have not been experimentally measured. In our study, initial
parameter sets were composed of randomly generated parameter values
within biologically relevant ranges. In the posterior PSM simulations, we
employed a global parameter estimation algorithm called stochastic
ranking evolutionary strategy (SRES) to identify the parameter sets that
give the best model fitness to experimental data in wild type and her1−/−,
her7−/−, hes6−/−, her7−/−;hes6−/− and notch1a−/− mutants (supplementary
methods). The SRES method creates superior results in large-scale
biological systems (Fakhouri et al., 2010; Fomekong-Nanfack et al.,
2007; Moles et al., 2003).
To test the impact of different reaction rates on the segmentation clock
period, we employed sensitivity analysis at different spatial points along the
PSM (cell#: 5, 15, 20, 25, 40). The sensitivity analysis was performed using
a local sensitivity analysis technique (supplementary methods) at 165
diversely selected robust parameter sets that satisfy the experimental
conditions in the posterior PSM.
In the anterior PSM simulations, the parameter sets obtained from the
posterior simulations are pruned by comparing the simulated period profiles
of the her1 mRNA in 30 neighboring cells with the experimental period
profile of Giudicelli et al. (2007). For each reaction rate gradient, we selected
parameter sets reproducing the experimental period profile (within ±10%
4166
variation) in 80% of the PSM in more than 24 out of 30 cells. These
parameter sets and specific gradients were used to create spatial movies and
snapshots and to calculate period, amplitude and synchronization profiles.
Analysis of oscillation dynamics
Posterior PSM
The model was run for 600 min in 60 posterior PSM cells, and expression
levels of her1 mRNA were used to calculate oscillation features in the
posterior PSM. The period was calculated as the time difference between
the last two peaks, while amplitude was calculated as the average expression
level difference between the last peak and two flanking troughs. The
synchronization score was calculated as the average of the Pearson
correlation coefficients between each cell and the cell located roughly in
the middle of the posterior PSM.
Whole PSM
After the PSM reached its full size of 300 cells, we followed the next added
five columns of cells (30 cells in total) for 300 min (total time that they spent
in the PSM). For each cell, the peak and troughs of her1 mRNA oscillations
were used to calculate the period and amplitude of oscillations. The period
was calculated as the time difference between two consecutive peaks, and
the amplitude was calculated as the average expression level change between
a peak and two flanking troughs. For a single parameter set, the average of
period and amplitude at eight spatial locations (cell#: 5, 12, 17, 22, 27, 32,
37, 42) was calculated. The synchronization score was measured by finding
the average of the Pearson correlation coefficients between each cell and the
first cell in a given column and this was then averaged over five consecutive
columns of cells. For a single parameter set, the average of synchronization
levels at nine spatial locations (cell#: 5, 10, 15, 20, 25, 30, 35, 40, 45)
was calculated.
Coding
The codes have been implemented in C++ and Python (codes are available
upon request). C++ was used due to its speed and Python was used due to its
ease of use in plotting libraries. The current version of our code can perform
a 1200-min simulation of 300 PSM cells in less than 1 min (on an iMAC
running MAC OSX 10.8.5 with 3.06 GHz Intel Core 2 Duo and 8 GB of
RAM). A parallel version of the code was written using the Message Passing
Interface (MPI) for time-intensive simulations.
Acknowledgements
We thank Sharon Amacher and Emilie Delaune for sharing the Tg(her1:her1bk15
transgenic line and protocols; Julian Lewis, Stuart Newman and Priscilla
Venus)
Van Wynsberghe for critically reading the manuscript; and Spartak Kalinin for
fish care.
Competing interests
The authors declare no competing financial interests.
Author contributions
A.A. and E.M.O. designed the project, built the mathematical model and analyzed
experimental data. A.A., J.H., A. Sperlea and S.S. executed the computational
simulations. G.S.D., S.K., A. Stevenson and E.M.O. performed the experiments.
A.A., J.H., A. Sperlea, G.S.D., S.K., S.S., A. Stevenson and E.M.O. wrote the
manuscript.
Funding
This study was supported by Colgate University NASC Division funds (to A.A.), by an
Alfred P. Sloan Foundation Research Fellowship (to E.M.O.) and by the National
Institutes of Health [1 R01 GM111987 01 to E.M.O.]. Deposited in PMC for release
after 12 months.
Supplementary material
Supplementary material available online at
http://dev.biologists.org/lookup/suppl/doi:10.1242/dev.111930/-/DC1
References
Ay, A., Knierer, S., Sperlea, A., Holland, J. and Ö zbudak, E. M. (2013). Shortlived Her proteins drive robust synchronized oscillations in the zebrafish
segmentation clock. Development 140, 3244-3253.
DEVELOPMENT
proteins, while the transcriptional time delays of her1, her7 and deltaC
mRNAs include transcription, splicing and nuclear-to-cytoplasmic export
of mRNAs. Each equation describes the rate of change of an mRNA, a
monomer protein or a dimer protein. Reaction terms describe the synthesis
and degradation of mRNAs and proteins as well as dimer association,
dissociation and degradation.
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
Brend, T. and Holley, S. A. (2009). Expression of the oscillating gene her1 is directly
regulated by Hairy/Enhancer of Split, T-box, and Suppressor of Hairless proteins
in the zebrafish segmentation clock. Dev. Dyn. 238, 2745-2759.
Buchan, J. R. and Stansfield, I. (2007). Halting a cellular production line:
responses to ribosomal pausing during translation. Biol. Cell 99, 475-487.
Campanelli, M. and Gedeon, T. (2010). Somitogenesis clock-wave initiation
requires differential decay and multiple binding sites for clock protein. PLoS
Comput. Biol. 6, e1000728.
Choorapoikayil, S., Willems, B., Strö hle, P. and Gajewski, M. (2012). Analysis of
her1 and her7 mutants reveals a spatio temporal separation of the somite clock
module. PLoS ONE 7, e39073.
Cinquin, O. (2007). Repressor dimerization in the zebrafish somitogenesis clock.
PLoS Comput. Biol. 3, e32.
Delaune, E. A., François, P., Shih, N. P. and Amacher, S. L. (2012). Single-cellresolution imaging of the impact of notch signaling and mitosis on segmentation
clock dynamics. Dev. Cell 23, 995-1005.
Fakhouri, W. D., Ay, A., Sayal, R., Dresch, J., Dayringer, E. and Arnosti, D. N.
(2010). Deciphering a transcriptional regulatory code: modeling short-range
repression in the Drosophila embryo. Mol. Syst. Biol. 6, 341.
Fomekong-Nanfack, Y., Kaandorp, J. A. and Blom, J. (2007). Efficient parameter
estimation for spatio-temporal models of pattern formation: case study of
Drosophila melanogaster. Bioinformatics 23, 3356-3363.
Gajewski, M., Sieger, D., Alt, B., Leve, C., Hans, S., Wolff, C., Rohr, K. B. and
Tautz, D. (2003). Anterior and posterior waves of cyclic her1 gene expression are
differentially regulated in the presomitic mesoderm of zebrafish. Development
130, 4269-4278.
Giudicelli, F., Ö zbudak, E. M., Wright, G. J. and Lewis, J. (2007). Setting the
tempo in development: an investigation of the zebrafish somite clock mechanism.
PLoS Biol. 5, e150.
Gomez, C., Ö zbudak, E. M., Wunderlich, J., Baumann, D., Lewis, J. and
Pourquié , O. (2008). Control of segment number in vertebrate embryos. Nature
454, 335-339.
Hanisch, A., Holder, M. V., Choorapoikayil, S., Gajewski, M., Ö zbudak, E. M. and
Lewis, J. (2013). The elongation rate of RNA Polymerase II in the zebrafish and its
significance in the somite segmentation clock. Development 140, 444-453.
Harima, Y., Takashima, Y., Ueda, Y., Ohtsuka, T. and Kageyama, R. (2013).
Accelerating the tempo of the segmentation clock by reducing the number of
introns in the Hes7 gene. Cell Rep. 3, 1-7.
Herrgen, L., Ares, S., Morelli, L. G., Schrö ter, C., Jü licher, F. and Oates, A. C.
(2010). Intercellular coupling regulates the period of the segmentation clock. Curr.
Biol. 20, 1244-1253.
Holley, S. A. (2007). The genetics and embryology of zebrafish metamerism. Dev.
Dyn. 236, 1422-1449.
Holley, S. A., Geisler, R. and Nusslein-Volhard, C. (2000). Control of her1
expression during zebrafish somitogenesis by a delta-dependent oscillator and an
independent wave-front activity. Genes Dev. 14, 1678-1690.
Hoyle, N. P. and Ish-Horowicz, D. (2013). Transcript processing and export kinetics
are rate-limiting steps in expressing vertebrate segmentation clock genes. Proc.
Natl. Acad. Sci. USA 110, E4316-E4324.
Development (2014) 141, 4158-4167 doi:10.1242/dev.111930
Jensen, M. H., Sneppen, K. and Tiana, G. (2003). Sustained oscillations and time
delays in gene expression of protein Hes1. FEBS Lett. 541, 176-177.
Jiang, Y.-J., Aerne, B. L., Smithers, L., Haddon, C., Ish-Horowicz, D. and Lewis,
J. (2000). Notch signalling and the synchronization of the somite segmentation
clock. Nature 408, 475-479.
Kawamura, A., Koshida, S., Hijikata, H., Ohbayashi, A., Kondoh, H. and Takada, S.
(2005). Groucho-associated transcriptional repressor ripply1 is required for proper
transition from the presomitic mesoderm to somites. Dev. Cell 9, 735-744.
Lakkaraju, A. K. K., Mary, C., Scherrer, A., Johnson, A. E. and Strub, K. (2008).
SRP keeps polypeptides translocation-competent by slowing translation to match
limiting ER-targeting sites. Cell 133, 440-451.
Lewis, J. (2003). Autoinhibition with transcriptional delay: a simple mechanism for
the zebrafish somitogenesis oscillator. Curr. Biol. 13, 1398-1408.
Meyer, P., Saez, L. and Young, M. W. (2006). PER-TIM interactions in living
Drosophila cells: an interval timer for the circadian clock. Science 311, 226-229.
Moles, C. G., Mendes, P. and Banga, J. R. (2003). Parameter estimation in
biochemical pathways: a comparison of global optimization methods. Genome
Res. 13, 2467-2474.
Monk, N. A. M. (2003). Oscillatory expression of Hes1, p53, and NF-kappaB driven
by transcriptional time delays. Curr. Biol. 13, 1409-1413.
Ö zbudak, E. M. and Lewis, J. (2008). Notch signalling synchronizes the zebrafish
segmentation clock but is not needed to create somite boundaries. PLoS Genet.
4, e15.
Ö zbudak, E. M. and Pourquié , O. (2008). The vertebrate segmentation clock: the
tip of the iceberg. Curr. Opin. Genet. Dev. 18, 317-323.
Ö zbudak, E. M., Tassy, O. and Pourquie, O. (2010). Spatiotemporal
compartmentalization of key physiological processes during muscle precursor
differentiation. Proc. Natl. Acad. Sci. USA 107, 4224-4229.
Pourquié , O. (2011). Vertebrate segmentation: from cyclic gene networks to
scoliosis. Cell 145, 650-663.
Schrö ter, C., Ares, S., Morelli, L. G., Isakova, A., Hens, K., Soroldoni, D.,
Gajewski, M., Jü licher, F., Maerkl, S. J., Deplancke, B. et al. (2012). Topology
and dynamics of the zebrafish segmentation clock core circuit. PLoS Biol. 10,
e1001364.
Shankaran, S. S., Sieger, D., Schrö ter, C., Czepe, C., Pauly, M.-C., Laplante,
M. A., Becker, T. S., Oates, A. C. and Gajewski, M. (2007). Completing the set of
h/E(spl) cyclic genes in zebrafish: her12 and her15 reveal novel modes of
expression and contribute to the segmentation clock. Dev. Biol. 304, 615-632.
Takashima, Y., Ohtsuka, T., Gonzalez, A., Miyachi, H. and Kageyama, R. (2011).
Intronic delay is essential for oscillatory expression in the segmentation clock.
Proc. Natl. Acad. Sci. USA 108, 3300-3305.
Tataroğ lu, O. and Schafmeier, T. (2010). Of switches and hourglasses: regulation
of subcellular traffic in circadian clocks by phosphorylation. EMBO Rep. 11,
927-935.
Trofka, A., Schwendinger-Schreck, J., Brend, T., Pontius, W., Emonet, T. and
Holley, S. A. (2012). The Her7 node modulates the network topology of the
zebrafish segmentation clock via sequestration of the Hes6 hub. Development
139, 940-947.
Uriu, K., Morishita, Y. and Iwasa, Y. (2009). Traveling wave formation in vertebrate
segmentation. J. Theor. Biol. 257, 385-396.
DEVELOPMENT
RESEARCH ARTICLE
4167