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Supplemental Information

Figure S1. Making of the spatio-temporal profile from time-lapse imaging of

Hes7-UbLuc. (A) The filmstrips of representative pictures corresponding to phases I, II and III are shown above. (B) Spatiotemporal profiles of Hes7 and NICD, which were produced based on the time-lapse imaging (A) and Fig. 1A-C,G-I,M-O.

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Figure S2. Importance of oscillators in the PSM for making segmental structures. (A-C)

Time-lapse imaging of Hes7 expression with Hes7-UbLuc reporter mice in the control (A, n = 5), Lfng KO (B, n = 6) and Hes7 KO embryos (C, n = 6). (D-F) Uncx4.1 expression detected by in situ hybridization in the control (D, n = 4), Lfng KO (E, n = 3)

and Hes7 KO embryos (F, n = 3). (G) The signal intensities on the yellow line in A-C were quantified. A.I. is the arbitrary index reflecting the intensities of average values in each position. Note that in Lfng KO embryos, the period did not seem to change,

compared to control embryos, although the amplitude was severely affected. In Hes7 KO mice, signals were slightly changed, but this was probably due to difference in penetration of luciferin during explant cultures.

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Figure S3. Making of the spatiotemporal profiles of Hes7 and pERK immunostaining

and Dusp-UbSLR reporter expression. (A) Representative results of immunostaining for Hes7. Note that segmentation (arrow) occurred between 3 and 4 when the Hes7 expression in S−1 disappeared. (B) Immunostaining for Hes7 was performed with 77

wild-type embryos at E10.5. Hes7 expression is shown in black bars, and the tail positions are indicated by open (Hes7−) or closed (Hes7+) circles. The numbers on the

horizontal axis correspond to those in (A). (C) Immunostaining for pERK was

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performed with 16 wild-type embryos at E10.5. The length of the pERK expression domain was measured and divided by the whole PSM length. Immunostaining of Hes7 was also performed with the same embryos, and the sequence of alignment was decided

by comparing each Hes7 expression pattern (B). The numbers 5, 6, 7 and 8 on the horizontal axis correspond to the samples of Fig. 2A/Fig. 3E, Fig. 2D/Fig. 3A, Fig. 2G/Fig. 3C and Fig. 1M-R, respectively. The numbers 1-4 are the same as in (B). (D)

Schematic representation of the spatiotemporal profiles of Hes7 and pERK. (E-H) Time-lapse imaging of the Dusp4-UbSLR reporter expression in explant cultures. The reporter expression reached S−2 and regressed periodically in the control (E, n = 5).

The reporter expression regressed at the end of phase III when segmentation occurred (the segmentation is indicated by yellow bars in E). This expression pattern is very similar to the pERK expression pattern (C,D), suggesting that Dusp4-UbSLR is a good

reporter for pERK expression. In Hes7 KO embryos, the Dusp4-UbSLR reporter expression regressed steadily (F, n = 3). In explants treated with the Fgf inhibitor SU5402 (30µM), the Dusp4-UbSLR reporter expression totally disappeared (G, n = 2).

In explants treated with the Dusp inhibitor BCI (2µM), the Dusp4-UbSLR reporter

expression regressed steadily (H, n = 3).

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Figure S4. Schematic representation of spatiotemporal patterns of pERK (blue) and

Mesp2 (green) expression in the wild type (A) and Hes7 KO mice (B) (See Fig. 4A,B). In the control, pERK expression displays an on-off pattern, and Mesp2 expression is initiated periodically in the whole S−1 region after pERK expression is down-regulated.

Then, Mesp2 expression is gradually reduced to the rostral region of S−1. By contrast,

in Hes7 KO mice, pERK expression steadily regressed posteriorly, and Mesp2 expression also steadily regressed in the anterior PSM after Fgf/ERK signaling became

off. Thus, Mesp2 expression is not periodic in Hes7 KO mice, indicating that the onset of Mesp2 expression occurs at different time between the anterior and posterior cells even in the same prospective somites. A black dot indicates the caudal end of the PSM

at each time point. The PSM grows caudally (downward).

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Mathematical modeling 1. Period of Hes7 protein oscillations

In the PSM reference frame (Morelli et al., 2009), the PSM is fixed and cells move towards the somite. In this framework, the rate of phase change is given by,

φj'(t) = ωj(t) + (v / (yj+1-yj)) (φj+1(t)-φj(t))

with φj, yj and ωj, the phase, position and frequency, respectively, of the j-th oscillator,

and v the velocity of growth. If we plug in the derivative definition, redefine the

frequency as a period, and rearrange it, we get

[φj(t+Δt)-φj(t)] = Δt/Tj(t) + (Δt v / [yj+1-yj]) [φj+1(t)-φj(t)],

where Tj(t) is the period of the j-th oscillator at time t. This equation is similar to the material derivative used to estimate the oscillation period in a previous work (Giudicelli

et al., 2007). A significant difference is that here the velocity of the cells does not depend on the position. The term [φj+1(t)-φj(t)] corresponds to the observed phase change

in the PSM and can be estimated from the gene expression data. The expression patterns

in the PSM repeat with a periodicity equal to the segmentation period TSeg , so that the phase change [φj(t+Δt)-φj(t)] in every PSM point is equal to Δt/TSeg. The time step is chosen as Δt=[yj+1-yj]/v. By solving Tj(t), we get an expression,

Ti(t) = {1/TSeg - v / [yj+1-yj] [φj+1(t)-φj(t)]})-1 (1)

that can be used to estimate the period of the j-th oscillator when moving positions along the PSM. For the spatiotemporal profile, we used the expression patterns of Hes7

introns in 56 embryos (Niwa et al., 2007). These data were smoothed by fitting it to two

polynomial functions, one for the upper border and the other for the bottom border (Fig. S5A).

Then, we used equation (1) to calculate the period in different positions along

the PSM. We found a good fitting with a second degree polynomial function Ti(t) = t2 + 1 (Fig. S5B).

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A

B

Figure S5. Estimation of the period of Hes7 oscillation in the PSM. (A) The spatio -temporal plot of intronic Hes7 expression was first smoothened by fitting it to two

polynomial curves in the upper and bottom boundary (Niwa et al. 2007). The dots show the upper and bottom limits of intronic Hes7 expression domains, while the continuous line shows the fitted dots. (B) We have calculated the oscillation period at different

PSM positions. Fitting of these periods to a 2nd degree polynomial function results in a period function coefficients Ti(t) = t2 + 1. The x-axis was normalized to L/v, which is the time needed by a cell to cross the PSM L at velocity v. The posterior-anterior PSM

direction is oriented from bottom to top in (A) and from left to right in (B).

2. Waves of Hes7 protein expression

In the somite reference, the somites are fixed and cells grow posteriorly. The phase is given by,

with θi, and xi the phase and position of the i-th oscillator, v the velocity of growth and

TSeg the segmentation period. In the right-hand side, the first summand gives the

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non-constant phase increase after entering the PSM, the second summand gives the constant phase increase after entering the PSM, and the third summand gives the initial phase of the first cell. The oscillatory expression of Hes7 protein is h7j(t) = (1 + sin(2πθj(t)))/2. The increasing period is modeled with the previously estimated function

T(t) = t2 + 1 (Fig. S6).

Figure S6. Computer simulations of Hes7 expression patterns in the PSM for the period

distribution shown in Figure S4B. The posterior PSM is oriented to the left.

3 Simulation of other genes

In addition to Hes7 protein (p), we included four Boolean variables, Mesp2 (m2), NICD (ni), Tbx6 (t6) and pERK (er) in a model, which is based on the interaction network

(Fig. S7). The dynamical model is represented as, eri(t) = TRUE If S0 + 3*S+v*t < xi Or

S0 ≤ Position(h7-on-off-border) ≤ (S0+3*S+v*t)

And Position(h7-on-off-border) < xi

FALSE Else

m2i(t+Δt) = TRUE If t6i(t) And ni(t) And Not eri(t),

FALSE Else; ni(t+Δt) = TRUE If h7i(t) < 0.5,

FALSE Else; t6i(t+Δt) = TRUE If yi ≥ S0 + v*t

FALSE Else

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Figure S7. Interaction network of the gene products in this work. The Fgf8 gradient and the oscillating Hes7 protein

are input functions to pERK, NICD and Mesp2 products. The new somite becomes defined by the repression of Tbx6 protein

by Mesp2 in the anterior PSM. Green and red arrows stand for positive and negative functions, respectively.

The state of pERK (er) and Tbx6 (t6) depends on spatial variables. The equation of pERK states, that the variable is ON in the cells posteriorly to the S-3 region or in more

anterior cells of the ON-OFF phase border of Hes7 protein expression. In the case of Tbx6, the variable is ON posteriorly to the S0 domain. Mesp2 and NICD states depend on the states of other genes. The parameters are the PSM length L = 1, the segmentation

period TSeg = 1, the growth velocity v = S/TSeg, the somite size S = L/6, the simulation time step Δt = 0.1, the simulation position step Δx = Δt*v. The initial somite border is at

x = 0, the S0 somite border at S0 = S and the tail bud at L. The Boolean functions

depend on continuous or Boolean variables. We found that the simulation of this model could reproduce the observed patterns (Fig. S8). In this model, Mesp2 expression is initiated in the whole S−1 region.

To evaluate whether the increase of the period of Hes7 oscillations is important, we carried out a mutant simulation where the Hes7 protein oscillation

showed almost no period change along the PSM (1.1-fold increase, whereas in the control, there is twofold increase in the period). In this simulation, the Mesp2 domain is not progressively restricted anteriorly (Fig. S9).

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A

B

C

D

Figure S8. Four different phases of a wild-type simulation. (A) Phase I shows the posterior pERK and anterior Mesp2 domain separated by the domain of Hes7 protein.

(B) Phase II shows the anterior Mesp2 domain that is shrinking, the posterior pERK domain that is expanding separated by the domain of Hes7 protein. (C) Phase III shows the absence of anterior Mesp2 because a very anterior pERK domain and two patterns

of Hes7 protein. (D) Phase I shifted by one oscillation cycle (cf. A). The posterior PSM is oriented to the right.

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A

B

C

D

Figure S9. Four different phases of a wild-type simulation. In a mutant simulation, where the Hes7 protein oscillation showed almost no period change along the PSM

(1.1-fold increase, whereas in the control, there is twofold increase in the period), the Mesp2 domain is not progressively restricted anteriorly

References Giudicelli, F., Ozbudak, 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.

Morelli, L.G., Ares, S., Herrgen, L., Schröter, C., Jülicher, F., and Oates, A.C. (2009). Delayed coupling theory of vertebrate segmentation. HFSP J. 3, 55-66.

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Niwa, Y., Masamizu, Y., Liu, T., Nakayama, R., Deng, C.X., and Kageyama, R. (2007). The initiation and propagation of Hes7 oscillation are cooperatively regulated by Fgf

and notch signaling in the somite segmentation clock. Dev. Cell 13, 298-304.

Movie legends Movie S1. Time-lapse imaging of Hes7-UbLuc reporter in E10.5 wild type mice.

Luminescence images in yellow (left) and bright field images (right) are shown. Movie was used to generate spatio-temporal profile in Fig. S2A.

Movie S2. Time-lapse imaging of Hes7-UbLuc reporter in E10.5 Lfng-null mice. Luminescence images in yellow (left) and bright field images (right) are shown. Movie was used to generate spatio-temporal profile in Fig. S2B.

Movie S3. Time-lapse imaging of Hes7-UbLuc reporter in E10.5 Hes7-null mice. Luminescence images in yellow (left) and bright field images (right) are shown. Movie

was used to generate spatio-temporal profile in Fig. S2C. Movie S4. Time-lapse imaging of Mesp2-UbELuc (green) and Dusp4-UbSLR (red)

reporters in E10.5 wild type mice. Luminescence images (left) and bright field images (right) are shown. Movie was used to generate filmstrip in Fig. 3G.