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# Synchrony Dynamics During Initiation, Failure, and Rescue of the Segmentation Clock

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Science  28 Sep 2007:
Vol. 317, Issue 5846, pp. 1911-1915
DOI: 10.1126/science.1142538

## Abstract

The “segmentation clock” is thought to coordinate sequential segmentation of the body axis in vertebrate embryos. This clock comprises a multicellular genetic network of synchronized oscillators, coupled by intercellular Delta-Notch signaling. How this synchrony is established and how its loss determines the position of segmentation defects in Delta and Notch mutants are unknown. We analyzed the clock's synchrony dynamics by varying strength and timing of Notch coupling in zebra-fish embryos with techniques for quantitative perturbation of gene function. We developed a physical theory based on coupled phase oscillators explaining the observed onset and rescue of segmentation defects, the clock's robustness against developmental noise, and a critical point beyond which synchrony decays. We conclude that synchrony among these genetic oscillators can be established by simultaneous initiation and self-organization and that the segmentation defect position is determined by the difference between coupling strength and noise.

The periodic and sequential segmentation of the vertebrate embryo along its anterior-posterior axis into blocks of cells called somites, the precursors of axial bone and muscle, is thought to be driven by the segmentation clock (Fig. 1A) (1, 2). This clock comprises a multicellular genetic network of oscillators located within the posterior mesoderm (Fig. 1B) (3, 4). Delta-Notch signaling has been proposed (3, 5) to couple these oscillators (Fig. 1C) such that they are spatiotemporally synchronized despite the presence of noise. Desynchronization over developmental time (5) could explain the zebrafish Delta-Notch mutant phenotypes (610) in which only the first 6 to 10 anterior segments form correctly (11); alternatively, genetic differences in anterior and posterior patterning might set the positions of these segmentation defects (11, 12). A physical theory that accounts for these defect positions based on desynchronization dynamics and Delta-Notch signaling strength is lacking, and how this clock is started and attains initial synchrony is also unknown.

If desynchronization is the cause of Delta-Notch mutant phenotypes, such a decay process should be inducible throughout somitogenesis. We delivered saturating doses of N-[N-(3,5-difluorophenacetyl-L-alanyl)]-S-phenylglycine t-butyl ester (DAPT) to wild-type (WT) embryos at hourly intervals (13). DAPT binds to and blocks the intramembrane protease required for cleavage of the Notch intracellular domain in response to Delta binding the receptor's extracellular domain (Fig. 1D) (14). We quantified the resulting organismal phenotype with the anterior limit of defects (ALD) (Fig. 1E), that is, the number of the anterior-most defective segment (15), which, averaged over an embryo population, is characteristic for each mutant (11, 15) and is indicated by the myotome boundary marker cb1045 (16). The ALD of fixed embryos translated into the developmental time, t, of the first misformed segment boundary (Fig. 1F) because segments formed at a linear rate $Math$(1) with segment number S, segmentation rate α = 2.5 ± 0.25 hour–1, and offset μ =25±3(N =6 embryos) (mean ± uncertainty = 2 SEM and 95% confidence unless stated otherwise). DAPT delivered before t0 = 5.8 ± 0.5 hours caused a constant ALD of S/ALD = 5.2 ± 0.18 (N = 31), whereas later delivery shifted the ALD posteriorly (Fig. 1, E and F). These data are consistent with a decay process underlying the Delta-Notch mutant phenotype, and, assuming near-instantaneous action of DAPT treatment, t0 would mark the beginning of this process with a decay time of 6.5 hours.

Furthermore, if desynchronization is the cause of Delta-Notch phenotypes, this decay time should be modifiable. We blocked Notch signaling before t0 in WT and des+/– (notch1a heterozygote mutant) (7), varying (i) DAPT concentrations to reduce Notch activation and (ii) antisense morpholino (MO) amounts to reduce translation of notch1a mRNA (Fig. 1D) (7, 13). Both treatments for quantitative perturbation of gene function gave consistent results (Fig. 2, A and B): The ALD shifted posteriorly with lower treatment levels, and curves for des+/– and WT shifted along the treatment axis, requiring about half the amount of treatment in des+/– to achieve the same effect as WT, suggesting a 0.5-fold difference in signaling. Saturating MO amounts caused an ALD consistent with des–/–, S/ALD = 7.63± 0.12 (N = 108) (11), whereas saturated DAPT concentrations caused lower ALDs, as above (Fig. 1, E and F), potentially because of DAPT targeting additional Notch receptors (17). Consequently, intercellular Delta-Notch signaling here is not simply a qualitative on-or-off switch; instead it can transmit smoothly graded quantitative signals, and this signal strength sets the decay time.

We sought a physical theory describing the dynamics of synchrony in the segmentation clock that predicts the first defective segment boundary SALD (=ALD) from the treatment level, n. We consider the segmentation clock as a population of identical, mutually coupled phase oscillators in the presence of noise (13, 18), thereby neglecting the spatial aspects of cyclic gene wave patterns (2, 4) and the biochemical details and amplitudes of the postulated cell-autonomous Her-feedback oscillators (19). We then described the synchrony among oscillating cells in mean-field approximation (Fig. 2C) (13) by an order parameter Z, with Z =0 and Z = 1 for none and perfect synchrony, respectively (18). Below the threshold Zc, proper segment formation fails (Fig. 2D). The dynamics of Z approximate an exponential (18) starting at t0 $Math$(2) with the time constant $Math$(3) determined by the antagonistic influence of the total noise experienced by the clock, 2σ2, and coupling among cells, ϵ.2σ2 comprises environmental sources, like temperature fluctuations; intracellular sources, like cell division (35); and intercellular sources, like relative cell movements in the PSM mixing cells from regions with different phases (5). ϵ depends linearly on activated Notch protein level, p $Math$(4) where A accounts for potential additional coupling pathways. The sign of λ then determines whether synchrony decays or builds up, depending on whether noise or coupling dominates, respectively, and its magnitude determines the duration of either process. Hence at λ = 0 the collective behavior of these coupled oscillators undergoes a dramatic qualitative change, which marks the critical point at a synchronization phase transition (18, 20, 21), analogous to the freezing point at the water-ice transition (13).

A Hill equation accounts for the inhibitory effect of treatment level, n, with MO and DAPT assumed to act noncooperatively $Math$(5) and where 2δ = [0, 1, 2] is the number of notch1a alleles per embryo, pWT is the WT level of activated protein, and n0 is the treatment level that halves pWT. When applied to WT, n0 would then correspond to the heterozygous condition.

Combining Eqs. 1 to 5 yields an expression that predicts the ALD of the homozygous mutant $Math$(6) $Math$ which is set by the shortest decay time determined by the noise in the system to desynchronize cells in the absence of Notch signaling. More generally, we find the desired expression that predicts the ALD for any reduced Notch coupling strength due to the treatment level, n $Math$(7) Below the critical treatment $Math$(8) in principle infinitely many correct segments could be formed. Here we define $Math$(9) as the robustness (22) of segmentation against changes in Notch signaling, other potential coupling pathways, and noise; a three-way balance that quantifies, for instance, the fold reduction in Notch signaling that is tolerable (13).

Fitting Eq. 7 to the data (Fig. 2, A and B) and with S/ALD and t0 fixed as above, we found the fit parameters for DAPT of R = 8.6 ±2.2 and n0 = 0.66±0.18 μMand for MO, R = 2.1± 0.34 and n0 = 0.021 ± 0.005 pmol; the resulting critical treatment levels, nc,δ, are marked in Fig. 2, A and B. Both values for R are larger than 2, hence consistent with the absence of a segmentation phenotype in the heterozygous mutant. These results provide quantitative evidence for (i) Notch signaling as a coupling mechanism, (ii) desynchronization as the cause of the Delta-Notch mutant phenotype, (iii) the system's robustness of R ∼ 5, and (iv) the existence of a synchronization transition in a population of biological genetic oscillators (18, 20, 21).

More generally, the analysis of other complex developing systems (23) would be amenable to the quantitative strategy used here. In particular, quantitative MO delivery can be interpreted as a tool to speed up mRNA decay with expected in vivo MO-mRNA binding rates of Kb ∼104 M–1 s–1 (13). Consequently, molecular parameters can be estimated, such as the notch1a mRNA decay rate, kd ∼0.1 min–1 (13).

The onset of desynchronization (Fig. 1F) predicts the clock's initiation at or before t0 = 5.8 ± 0.5 hours. Around this developmental time point, the cells of the zebrafish presumptive mesoderm that will later become the somites are found in a marginal ring of the blastoderm; epiboly movements will subsequently draw the blastoderm over the yolk (Fig. 3A). We observed the earliest expression of cyclic genes her1, her7, and dlc at ∼5.25 hours postfertilization (hpf): 10 min elapsed between first detection of scattered her7-positive nuclei and a subsequent ring of expression around the entire margin, which disappeared 30 min later, marking the first cycle of the segmentation clock (Fig. 3B and fig. S1) (13). Hence, the clock's initiation coincides with, or shortly precedes, the inferred onset of desynchronization, and initial synchrony among these genetic oscillators appears to be achieved by simultaneous gene induction.

Three more oscillatory cycles were found confined to the ring of the gastrulating mesoderm with an interval between maximum expression states of around 30 min, corresponding to the period of the segmentation clock (Fig. 3C). During these cycles, dlc expression started at the ventral side of the embryonic margin and moved dorsally, thereby forming a traveling wave (Fig. 3, D and E). Furthermore, period seemed to decrease, whereas cellular expression levels increased, which is characteristic for transients following bifurcation events (18). During the subsequent fifth cycle, a cyclic expression domain separated from the gastrula margin at 8.2 hpf and moved anteriorly. The earliest previously reported wave at 8.7 hpf (15, 24, 25) marked the sixth cycle and prefigured the first segment boundary. These five cycles before somitogenesis in zebra-fish contrast to two observed in chick (26). Thus, throughout development, four related spatiotemporal oscillation patterns of the zebrafish's segmentation clock are now distinguishable (Fig. 3F).

To test the requirement of intercellular Delta-Notch signaling for clock initiation, we subjected WT embryos to DAPT. The oscillating expression patterns of dlc at 65% epibioly were indistinguishable from those of WT (Fig. 3, G and H). In contrast, embryos injected with MOs targeting the h/E(Spl) genes her1 and her7, jointly required for segmentation along the entire axis (15, 27), showed sustained dlc expression (Fig. 3I), indicating loss of cyclic gene oscillations. Thus, the first synchronous oscillations of the segmentation clock require h/E(Spl) transcriptional repressors, but, consistent with the desynchronization hypothesis (5), we found no evidence for a Delta-Notch requirement.

Although the clock attains initial synchrony via simultaneous initiation of its oscillators, according to Eqs. 2 and 3 a coupling-dependent, self-organized synchronization over multiple periods among initially unsynchronized oscillators (18, 20, 21) should also be possible. Embryos subjected to a DAPT pulse from 4 to 15 hpf (Fig. 4A) showed an ALD of SALD = 6.1 ± 1.1 (N = 9) (Fig. 4B) and concomitant, profound loss of synchrony in cells of the tailbud and presomitic mesoderm (PSM) evidenced by a disordered dlc expression pattern (Fig. 4, C to F), equivalent to that in Delta-Notch mutants (5, 15, 28, 29). After DAPT washout, normal segment formation and cyclic gene expression was recovered (Fig. 4, B to G). The position of the last defective segment defines a posterior limit of defects (PLD), which we estimated at SPLD = 23.2±2.1(∼21 hpf), indicating a recovery time of ∼10 oscillation periods. Thus, restoration of Notch coupling is sufficient for self-organized resynchronization (18, 20, 21) of these previously desynchronized genetic oscillators, whereby both decay and recovery processes can be represented as a trajectory in a synchrony-coupling phase diagram (Fig. 4H, top).

We have demonstrated two general mechanisms by which genetic oscillators can attain synchrony: (i) simultaneous induction and (ii) self-organized synchronization, which, in the case of the segmentation clock, were Notch-independent and Notch-dependent, respectively. Delta-Notch mutant zebrafish embryos would allow screening for compounds restoring Delta-Notch coupling (30), with potential therapeutic implications for human genetic mal-segmentation disorders (31). These Delta-Notch mutant phenotypes are now quantitatively understandable from the desynchronization hypothesis (5) in terms of the decay rate λ, that is, the difference in noise, 2σ2, and coupling strength, ϵ (Eq. 3 and Fig. 4H, bottom), which determines the segmentation defect position. From the lowest ALD observed (Eq. 6) and assuming alternative coupling pathways negligible (A = 0), we estimate the clock's noise of 2σ2 ≈ 0.8 hour–1, consistent with our estimates of noise (13) stemming from cell movements (5) and genetic sources. The system's robustness R (Eq. 9) then gives the WT Notch coupling strength of ϵWT = R·2σ2 ≈ 4 hour–1. Thus, by using quantitative techniques for perturbation of gene function in combination with a physical theory of coupled phase oscillators, we were able to determine the essential dynamical properties that quantitatively account for a collective, morphological process in a complex developmental system.

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References

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