Tissue-wide, synchronous Erk oscillations time the segmentation of the zebrafish notochord

Abstract

The generation of a periodic body plan is a fundamental property of vertebrates. While biological oscillators provide a mechanism for timing the formation of repeated structures, few examples of signaling oscillators have been identified in development. Here, we show that the addition of repeating mineralizing segments in the zebrafish notochord is timed by tissue-wide, synchronous oscillations of Erk activity. The oscillations are mediated by delayed negative feedback from spry and dusp and expression of the Egf ligand. The uniform increase in egf expression controls the emergence of the oscillations, revealing the mechanism controlling the onset of notochord segmentation. Together, our work reveals an instance of synchronous clocks timing a patterning process and controlling the development of the vertebral column from the notochord.

Introduction:

The generation of periodic structures is a hallmark of embryogenesis; it allows duplication of tissues into units and is a crucial mechanism for segmenting the anterior-posterior axis in vertebrates. Somitogenesis is the first patterning process that sets the periodic blueprint of the vertebrate body (1–2). However, the formation and positioning of vertebrae is controlled many days later by morphogenetic processes that remain poorly understood. Work in zebrafish has shown that vertebrae assemble using a blueprint generated by the segmentation of the sheath cells surrounding the notochord (3–6). This process begins around 5 days post fertilization (dpf) and continues for 2 weeks. It results in the sequential segmentation of the tissue into mineralizing and inter-segment domains while the fish elongates between 4–5 mm. The sequentiality of the process and the repeated addition of new segments requires accurate spatiotemporal control of biochemical activities across multiple tissue scales. While boundaries established by somitogenesis at 2 dpf and propagation of BMP signaling may explain aspects of segment positioning (7–9), it remains unclear what sets up the tempo of notochord segmentation allowing it to slowly build this template. Here, we provide evidence that the underlying time-keeping mechanism is driven by intrinsic oscillations of Erk activity within the notochord sheath itself.

Segmentation of the notochord occurs periodically

To quantitatively capture the dynamic features of notochord segmentation, we performed live imaging in larvae beginning at 7–8 dpf (larvae length: 4–4.25 mm). The analysis occurred over a period of around 30 hours, covering around 1mm of the notochord and with images acquired roughly every 4 hours. In the notochord, the expression of the mineralization marker entpd5a coincides with activation of Notch signaling (4). We used a transgenic reporter (entpd5a:pkRed) to monitor segment progression (schematic in Fig. 1A, fig. S1A). To this end, we computationally extracted entpd5a+ cells (Fig. 1A) and tracked fluorescence levels across individual segments over time. We found segments mature by the combined differentiation of sheath cells into entpd5a+ cells and an increase in fluorescence of previously differentiated cells in segments. Moreover, anterior segments grow more than posterior segments during the period, pointing to the sequential nature of the segmentation pattern (Fig. 1A-C). This also indicates that development of segmented domains occurs gradually along the anterior posterior axis. Given that segmenting regions continue to mature over time, we investigated entpd5a dynamics by quantifying the total fluorescence of all detected cells across the notochord (Fig. 1D). Monitoring differences in total fluorescence levels between subsequent time points (Fig. 1E, additional segment data in fig. S1B) suggested that increases in entpd5a expression appear in periodic bursts, occurring on average every 10–12 hours under our imaging conditions.

Fig. 1. Oscillations of Erk Activity in the zebrafish notochord.

(A) Top, Schematic of a zebrafish larva (4–4.25mm). Bottom, images showing the initial and final image from a time course over 30 hours with segmented entpd5a:pKRed cells, color coded by their mean fluorescence levels. (B) Total fluorescence of entpd5a:pKRed in segments as a function of time. Different lines indicate different regions along the AP axis, as shown by the color bar. (C) Fluorescence gain per segment as a function of segment number ordered from Anterior to Posterior, calculated across multiple fishes (N=4). (D) Total fluorescence levels in the notochord, normalized by mean expression over time per larva show discrete jumps in expression (N=3). (E) Timepoint-by-timepoint difference in total fluorescence levels shows bursts in time, indicating periodic activation (N=3). (F) Top, Cartoons showing how phosphorylation affect the localization of the sensor along with images and quantification of two individual cells at low and high activity (see colorbar). Bottom, Heat maps displaying Erk activity, reported by cmn-hsp70I:erk-ktr-gfp, quantified in individual cells. These maps show oscillatory behaviors in the notochord. (G) Average Erk activity as a function of time in 2 larvae confirms the oscillatory behavior in the notochord. (H) Erk activity as a function of time, separated in segmented and unsegmented regions, demonstrates that these regions have similar behaviors.

Erk activity oscillates synchronously across the entire notochord

To identify the molecular mechanism controlling the periodic nature of segmentation, we postulated that segmentation is controlled by a clock driving intracellular oscillations, similarly to what is observed in other systems undergoing periodic patterning (10–16). We suspected that the MAPK/Erk pathway might contribute to the timing of segmentation, as this pathway can generate oscillations in certain developmental and regenerative contexts (17–20).

To visualize and quantify the activity of the MAPK/Erk pathway in the zebrafish notochord, we generated new transgenic lines driving the expression of an Erk sensor (20–21) from the calymmin locus or from a collagen 9a2 regulatory sequence, which are specifically expressed in the notochord sheath (22–23). The Erk sensor is a translocation reporter, in which phosphorylation favors cytoplasmic localization of the reporter. Thus, Erk activity can be estimated by the ratio of cytoplasmic and nuclear fluorescence (schematic in Fig. 1F). These transgenic tools allowed us to visualize and quantify the dynamics of Erk activity in the notochord sheath with cellular resolution. Computational segmentation of individual cells over time (fig. S2) revealed that Erk activity is highly dynamic (Fig. 1F, Movie. S1, fig. S1C, Movie. S2) with levels in the notochord periodically transitioning between low and high activity. This suggested evidence of intracellular oscillations in the zebrafish notochord (Fig. 1G). We used two metrics to quantify the oscillations – average Erk activity across all the cells (Fig. 1G) and percentage of cells that have high Erk activity at a given time (ratio of cytoplasmic to nuclear fluorescence > 1) (fig. S1D). Both these metrics revealed clear oscillations and allowed us to estimate a mean time-period for the oscillations of 10 ± 3 hours (N=7) (fig. S1E). Oscillations are seen in unsegmented and segmenting regions with similar behavior (Fig. 1H, fig. S1F). Consistently, we estimated the ratios of time periods in individual segments compared to the rest of the tissue to be 1 (N=2, fig. S1G).

Visual inspection of heat maps of activity suggests that Erk oscillations extend across the entire notochord sheath without notable spatiotemporal patterns or localization. Specifically, we could identify images in which the fraction of cells with high activity, in 45 μm bins along a 1 mm region of the AP axis, ranged from 0.8–1.0 (Fig. 2A, colors indicate different fishes). By quantifying the oscillations in individual bins as a function of time, we found that that the behavior across the entire region was similar. This confirmed that there were no large-scale tissue differences in the oscillator phase at these sampled times (Fig. 2B, individual lines indicate activity averages in a particular bin). To describe the observed synchrony of Erk oscillations, we used the Hilbert transform (24) to infer the phases of the oscillations in the different spatial regions. We then used these inferred phases to calculate the Kuramoto parameter, a standard mathematical tool to describe the synchronicity of oscillators (25). For systems oscillating out of synchrony, the Kuramoto order parameter r (Eq 1, Materials and Methods) is close to zero, while for synchronous oscillators, the order parameter has a value close to 1. Graphically, this can be visualized by plotting the phases of each binned region on the unit circle and seeing if the phases are clustered (synchronous oscillators) or dispersed across the circle (non-synchronous oscillators). Our data showed strong clustering and allowed us estimate that the Kuramoto order parameter is typically above 0.9, indicating a high degree of synchrony in the entire notochord (Fig. 2C, 2D quantified over two fishes).

Fig. 2. Erk Oscillations are synchronous across the entire notochord and are born via a SNIC-bifurcation.

(A) Fraction of cells with high activity quantified in 45 μm bins along the AP axis over a 1 mm region of the notochord. This analysis identifies time-points in which a large fraction of cells is active throughout the tissue. (B) Erk activity as a function time in the different bins. The activity in individual bins shows similar behavior across time. (C) Estimated phases from each binned regions plotted on the unit circle. Different colors indicate different timepoints in the oscillations (see colorbar). The Kuramoto order parameter (r) for each time point is shown as a square of the appropriate color. The amplitude of the Kuramoto parameter is given by the distance to the origin, and its phase by the angle along the circle. (D) The amplitude of the Kuramoto parameter across time quantified over 2 fishes (different colors) shows synchronous behavior. (E) Heat map of Erk activity at three different time points between 3–5 dpf. Scale bar 100 μm. Transition to high Erk activity seen around 5 dpf (see colorbar). (F) Erk activity (measured in a larva expressing the col9a2:erk-ktr-cer reporter) as a function time in individual cells (N=50). Analysis shows the emergence of high Erk activity in the notochord around 5 dpf. (G) Expected dynamic behaviors for different types of bifurcation leading to an oscillatory system. (H) Fraction of cells with high Erk activity as a function of time. This analysis shows a bifurcation into oscillatory state, reported by cmn-hsp70I:erk-ktr-gfp and col9a2:erk-ktr-cer. (I) Oscillation time period as function of developmental time. Data were pooled from fish imaged beginning at different stages of development and show the presence of a longer oscillation cycle early on at 5 dpf. (J) Amplitude of the oscillation as a function of developmental time for the same larvae shown in (I). Note that the amplitude is in large part similar across all stages, with few outliers showing reduced amplitude, likely due to poor sampling near the oscillation peak given our time resolution.

Tissue-wide emergence of Erk oscillations

We asked how synchronization emerges in the tissue by investigating regulation of the Erk oscillations and by imaging the notochord earlier than 7dpf, when 8–9 segments have already formed. By imaging larvae every few hours for 2–3 days beginning at 3 dpf, we found that Erk activity is initially low prior to 5 dpf, but transitions to high activity (Fig. 2E-F, Movie. S3), in a synchronous manner across individual cells, indicating that the system has undergone a bifurcation. Furthermore, analysis of individual trajectories by monitoring cells crossing a threshold of Erk activity, suggested that Erk dynamics is excitable prior to the bifurcation, as cells getting past the threshold undergo significant excursions before returning to low Erk activity (fig. S3A). To investigate the properties of this transition, we considered two main types of bifurcations typically observed in systems undergoing a transition from a non-oscillatory to an oscillatory pattern (26–30) – namely, the super-critical Hopf bifurcation and the Saddle Node on an Invariant Cycle (SNIC) bifurcation. These two bifurcation types are distinguished by how the amplitude and frequency behaves as the system transitions from one state to the other. The Hopf bifurcation is characterized by increasing amplitude and fixed frequency, while the SNIC bifurcation is characterized by fixed amplitude and increasing frequency (Fig. 2G). Distinguishing between these two bifurcations provides insight on the properties of the system near transition, specifically on whether the build-up to rhythmicity is gradual, frequency tunable and the range of response fixed or variable. Our analysis argues that the notochord sheath undergoes a SNIC bifurcation, as the first Erk oscillation is significantly longer (~24 hours) than subsequent ones (~10–12 hours) (Fig. 2H-I, fig. S1E), while the amplitude is similar to the one observed for later oscillations (few larvae display lower amplitude likely due to limited sampling) (Fig. 2J). Collectively, these observations indicate that the zebrafish notochord displays a rare example of synchronous, tissue-wide signaling oscillations spanning millimeters and that the oscillations are born via a SNIC bifurcation.

Erk oscillations are controlled by negative feedback and uniform expression of an activator

To gain insight on the potential mechanisms controlling the Erk oscillations and the observed bifurcation, we built a mathematical model that can generate oscillations through a SNIC bifurcation (Fig. 3A). This model assumes uniform increase over time in the expression of an Erk activator and the presence of delayed negative feedback, generated by Erk activation of its own inhibitors. Analysis of time-courses with faster sampling near the oscillation peaks suggested rapid spikes in Erk activity (fig. S3B). Thus, similar to other models (20), we included a positive feedback loop to facilitate sustained oscillations and model an oscillatory cycle with multiple time scales as can be seen in systems containing positive and negative feedback loops (31–33) (fig. S3C-D).

Fig. 3. Identification of players involved in the MAPK/Erk Pathway Oscillator.

(A) Left, cartoon representing the molecular interactions described by our mathematical model. Right, dependency of the time period and amplitude of oscillations on the bifurcation parameter. This analysis confirms that our model is consistent with a SNIC bifurcation. (B) Image showing a 6 dpf TgKI(spry2-hsp70I:venus-Pest) larva and the subsequent computational extraction of the notochord region, followed by extraction of spry2+ individual cells color coded by their mean fluorescence levels. (C) spry2:venus-Pest fluorescence as a function of time for single cell tracks from a 8 dpf larva. This analysis demonstrates oscillations. (D) Average spry2:venus-Pest fluorescence as a function of time from two larvae stage matched by entpd5a expression. (E) Detrended spry2:venus-Pest expression levels along with timepoint-by-timepoint difference in entpd5a fluorescence as a function of time. This analysis shows concurrent oscillations between spry2 expression and entpd5a bursts. (F) Time averaged spry2:venus-Pest expression as a function of position along the AP axis quantified in entpd5a+ (blue dots) and entpd5a- (purple dots) populations. (G) Detrended single cell tracks of dusp6-hsp70I:venus-Pest fluorescence (n=16) as function of time in an individual 7 dpf larva. Data are compatible with an oscillatory behavior. (H) Averaged egf-hsp70I:venus-Pest and entpd5a:pKRed fluorescence levels as a function of time. This analysis indicates an increase in egf expression around 5 dpf, similar to when the first bursts of entpd5a expression can be detected. (I) Segmented cells detected by venus-Pest fluorescence in the notochord, color coded by mean fluorescence levels per cell. (J) Erk levels in individual cells as function of position along the AP axis following an EGFR inhibition by treating 3 dpf larvae for 50 hours with Afatinib at 50 μM (N=3 per condition).

Our model and the observed oscillation period of several hours suggest that the inhibitors in this system are controlled by Erk via transcriptional regulation, and that delays in protein production result in delayed oscillation cycles of the inhibitors relative to Erk (Fig. 3A, fig. S3D). To identify candidate genes, we reanalyzed a transcriptomic dataset from 13 dpf larvae in which notochord sheath cells were FACS-sorted into three separate populations: unsegmented, transitional or segmented domains (4). We found evidence for the expression of several sprouty (spry) and dual-specificity phosphatases (dusp) genes, known Erk transcriptional targets and negative regulators of the MAPK pathway (34–36). To test the hypothesis that these genes are expressed in an oscillatory manner, we first focused on spry2 whose expression is enriched in the unsegmented region (fig. S4A). To test whether spry2 expression oscillates, we generated a destabilized transcriptional reporter (TgKI(spry2-hsp70I:venus-Pest)) that allowed us to visualize endogenous expression in zebrafish larvae (fig. S4B). We found that spry2 is expressed in multiple cell types in larvae (Fig. 3B). Thus, we developed a computational pipeline for the identification of the notochord sheath and for the extraction of any spry2+ cells in the notochord (Fig. 3B, Materials and Methods). Using this pipeline, we were able to quantify single cell traces and show that spry2 expression oscillates in the notochord sheath (Fig. 3C, Fig. 3D showing two larvae which were staged by aligning the entpd5a levels displayed in fig. S4C). The spry2 oscillations have similar period to the Erk oscillations and are concurrent with bursts in entpd5a expression (Fig. 3E, fig. S4D). Similar analysis revealed that Erk activity precedes entpd5a expression by few hours confirming the prediction that spry2 expression is delayed relative to Erk activity (fig. S6C; the maturation time and lifetime of Venus likely contribute to part of the estimated delay). Consistent with the transcriptomic results, the expression of the spry2 reporter is not uniform across the notochord but enriched in the unsegmented regions (fig. S4E-F). Extracting the average expression levels in segmenting and non-segmenting cells (Fig. 3F) shows this difference. Since Erk oscillations are present across the entire notochord sheath, we reasoned that other factors must be complementarily enriched in the transitional and entpd5a+ zones to drive Erk oscillations. To test this idea, we focused on dusp6 as its expression is enriched in the transitional population in the transcriptomic data (fig. S4H). We generated a similar transcriptional reporter (TgKI(dusp6-hsp70I:venus-Pest)) to analyze dusp6 expression (fig. S4G). Analysis of the spatial expression pattern confirmed that dusp6 is enriched in the entpd5a+ cells (fig. S4I-J). Moreover, dusp6 expression is also oscillatory in the notochord sheath (Fig. 3G, fig. S4K-L).

Next, we tested the model prediction that the synchronous Erk oscillations and SNIC bifurcation require the increasing, uniform expression of an Erk activator across the notochord. Analysis of the transcriptomics data revealed the possible involvement of the Epidermal Growth Factor (EGF) pathway (fig. S5A). Thus, we generated a transcriptional reporter to study the expression of egf (TgKI(egf-hsp70I:venus-Pest), fig. S5B). Remarkably, we found egf expression increasing in the notochord prior to the SNIC bifurcation at 5 dpf, around the time when the first jumps in entpd5a:pkRed expression occur, marking the beginning of segmentation. (Fig. 3H, fig. S5C). Increased egf expression was independently confirmed by Hybridization Chain Reaction (HCR) in-situ (fig. S5E). While there is some variability in the cell-to-cell level of expression, egf expressing cells are observed uniformly across the entire tissue, as confirmed by both binning fluorescence expression for the egf reporter in 15 μm bins (fig. S5C) and roughly segmenting cells marked by the reporter (Fig. 3I). Notably, pharmacological inhibition of EGF receptors (EGFR) between 3–5 dpf resulted in a significant decrease of Erk activity uniformly across the notochord, at a time when we would have expected Erk activity to be high post bifurcation (N=3 per condition, Fig. 3J, fig. S5D). These observations support our model for Erk oscillations: negative feedback, mediated by expression of spry and dusp genes, together with uniform and increasing expression of Egf ligand can drive a bifurcation in Erk dynamics and later ensure synchronous oscillations in the entire tissue.

Erk oscillations time notochord segmentation

Having characterized the properties of the Erk oscillator, we set out to test its functional significance. The period of the Erk oscillations was very similar to the duration between increases in entpd5a expression, suggesting a direct link between Erk oscillations and the development of mineralizing domains in the notochord. Analysis of entpd5a expression and Erk activity in the same larvae indicated that the bursts of entpd5a expression closely follow Erk activity peaks (Fig. 4A, fig. S6A-B). Within the limits of our sampling window, we estimate a delay of a few hours between Erk activation and the next burst of entpd5a expression (fig. S6C; the maturation time of the reporter likely contribute to the estimated delay). These observations strongly implicate Erk activity in controlling the timing of segment specification. As such, blocking Erk activity with a pharmacological inhibitor should interfere with segmentation. To test this prediction, we used the Mek inhibitor PD0325901, which can reduce Erk activity within 2 hours (fig. S6D-F). Starting at both 5 and 7 dpf, larvae were exposed over 50 hours to 2 μM of PD0325901 (Fig. 4B). We found that the number of entpd5a+ cells added in forming segments was significantly reduced (Fig. 4C, N=26 over 4 replicate trials, p=0.0028). We also observed a significant reduction in the gain of overall entpd5a+ fluorescence, suggesting that in addition to the specification of new entpd5a+ cells, Erk activity also promotes the continued expression of entpd5a in already differentiated cells (Fig. 4D, p=0.0001). Similar results were obtained by blocking EGF receptor signaling at 7dpf pharmacologically (fig. S6G-H). Taken together, these observations support the view that Erk activity is required for segmentation.

Fig. 4. Erk Oscillations Control the Pace of Segmentation.

(A) Fraction of cells with high Erk activity and timepoint-by-timepoint difference in entpd5a:pKRed fluorescence as a function of time. entpd5a:pKRed fluorescence bursts are delayed with respect to the oscillation cycle. (B) Heat maps of entpd5a expression quantified in single cells in larvae treated with DMSO or 2 μM Mek inhibitor for 50 hours. (C) Number of newly added cells in control larvae and larvae in which Mek was inhibited pharmacologically. (D) Relative change in segment fluorescence in cells already differentiated in control larvae and larvae in which Mek was inhibited pharmacologically. Data indicate that Mek inhibition results in fewer newly added cells and less maturation of existing segments.

To test whether Erk activation indeed affects differentiation timing, we designed an experiment to block Erk activity transiently and determine whether that induces a predicted delay in the segmentation process. To this end, we selected larvae that on average had high Erk activity and treated them with the Mek inhibitor for about two hours, after which the drug was washed out (Fig. 5A). In the control larvae, we were able to identify an Erk peak within the next 10 hours (Movie. S4); in contrast, Erk activity in treated larvae showed a delay, peaking at around 14 hours (Movie. S5, Fig. 5B). Remarkably, a similar delay was also reflected in the overall entpd5a:pKRed fluorescence levels, which peaked later than in the control. The delay relative to the Erk peak was similar to control and wild type larvae, arguing that Erk oscillations indeed time the bursts of entpd5a expression (Fig. 5C). Finally, we tested whether the onset of Erk oscillations coincides with the onset of sheath segmentation. To this end, we combined both Erk and entpd5a dynamics between 3–6 dpf. We observed a rapid increase in the rate of entpd5a addition that coincided with the onset of Erk oscillations (Fig. 5D-E, Fig. 2H). Collectively, these experiments validate a role for Erk oscillations in controlling the timing of segmentation of the notochord sheath.

Fig. 5. Altering Erk dynamics changes the dynamics of segmentation.

(A) Top, Experimental design to alter segmentation dynamics. Starting with similar high Erk activity, 8 dpf larvae were exposed to DMSO (control) or Mek inhibitor for about 2 hours and monitored for an additional oscillation period. Bottom panels, heat maps of Erk activity in DMSO (left) or Mek inhibited (right) at different times following post treatment. Scale bar 100 μm. (B) Erk activity as function of time, dotted lines indicate treatment window. Treated larvae reach a new peak Erk activity with a delay relative to control larvae. (C) Timepoint-by-timepoint difference in entpd5a:pKRed fluorescence levels as a function of time shows a similar delay in the progression of mineralization. (D) Heatmap quantification of entpd5a:pKRed around 5 dpf shows the first forming segments. (E) Fraction of cells with high Erk activity and timepoint-by-timepoint difference in entpd5a:pKRed fluorescence levels as a function of developmental time. This analysis shows how the first oscillation cycle correlates with the first burst in entpd5a expression (onset of mineralization).

Discussion

In this study we have identified oscillations of Erk activity in the zebrafish notochord sheath. The oscillations time the segmentation of the notochord, controlling the tempo at which mineralizing segments are established to build the vertebral column. We have dissected the properties of the oscillator and shown that the onset of oscillations occurs through a SNIC bifurcation, implying that the build-up to rhythmicity is gradual, frequency tunable and the amplitude of response fixed. Following the onset, oscillations are synchronous across the entire tissue. Through a combination of mathematical modeling and experimental analysis, we argue that the onset of the oscillations and their synchrony are controlled by uniform and increasing expression of the Egf ligand and delayed negative feedback mediated by spry and dusp. We suggest that the features observed here, of bifurcation and synchronization, allow the tissue to control biological function, namely the initiation and maintenance of segments. Synchronization is a general feature of natural phenomena observed across physical, chemical and biological systems (24). Yet, despite the ubiquity of synchronization phenomena, there are very few cases where synchronization of signaling dynamics has been described in animal development. We propose that the use of biosensors and quantitative methods, similar to the ones we have developed here, will yield more examples of signaling oscillations and synchrony controlling developmental processes.

The formation of vertebrae in zebrafish occurs at the larval stage. This could explain why the temporal regulation of this process occurs independently of somitogenesis, which sets up a periodic blueprint of the vertebrate body much earlier in the embryo (1–2). However, the positions of the vertebrae are dependent on the somite boundaries (5,7), as well as the activity of other signaling pathways (8), which essentially regulate the number of vertebrae that will form to build the spine. Together, this framework suggests how the integration of spatial and temporal signaling processes can drive robust patterning and segmentation of biological tubes. We speculate that similar insights will emerge in the study of other biological tubes which show segmented gene expression patterns (37–38).

Materials and Methods

Zebrafish husbandry

Zebrafish of Ekkwill and AB strains were housed and bred under standard conditions (39). No statistical methods were used to pre-determine sample size for experiments. Larvae were picked randomly from a clutch at different age stages and assessed for Standard Length (40), measured in a straight line between the snout to the tip of the notochord. Any larvae with measurements that deviated from the rest of the experimental group were not followed for imaging or subsequent computational analysis. Where possible, additional stage matching was done with the presence of genetic markers that indicated the number of segments. Replicates were performed with independent clutches. Where applicable, equivalent number of larvae were used per replicate, per treatment condition. Researchers were not blinded during data visualization or analysis. All fish experiments were approved by the Institutional Animal Care and Use Committee at Duke University and followed all the relevant guidelines and regulations. Transgenic lines used in the study are listed in Table 1.

Generation of transgenic Lines

Our strategy for generating endogenous reporters was adapted from previous studies (8, 42). A donor sequence containing the heat shock promoter (hsp70l) and a destabilized form of Venus (venus-Pest) was generated in a puc19 plasmid. Additionally, donor sequence containing the heat shock promoter (hsp70l) and erk-ktr-gfp was generated in a puc19 plasmid using In-Fusion cloning (Takara).

Then PCR donor were amplified from the plasmids using the following primers: puc19_F: 5′ gcgattaagttgggtaacgc 3’; puc19_R: 5′ tccggctcgtatgttgtgtg 3’.

The following gRNA target sites were used to generate the endogenous reporters: spry2 (GGAAGGCTGGTCATCAATGGGG), dusp6 (GCGATCGTCGCCTGGAAACGGGG), egf (AGCCTCAAAGTCCTACACCAGGG), cmn (TGACACATGCTGTTCCTTATTGG).

A stock injection solution containing the following was injected at the single cell stage: PCR donor (10 ng/μL), Cas9 protein (500ng/μL), target site gRNA (50 ng/μL), phenol red.

The erk-ktr-cerulean cassette was subcloned from pSKS-I:osx-erk-ktr-cerulean (20) using the following primers:

F- 5’ GGGGACAAGTTTGTACAAAAAAGCAGGCTCcATGAAGGGCCGAAAGCCTCG 3’

R- 5’ GGGGACCACTTTGTACAAGAAAGCTGGGTcGATCTAGAGGATCATAATCA 3’

A BP clonase reaction generated a pME-erk-ktr-mcerulean plasmid. A subsequent Gateway LR reaction produced the final pTol2CG2:col9a2-erk-ktr-mcerulean plasmid.

One-cell stage embryos were co-injected with the Tol2 construct and transposase cRNA.

Microscopy

All microscopy was performed on a Leica SP8 inverted confocal scope equipped with Leica Application Suite. Larvae were anesthetized with 0.04% Tricaine (VWR:MSPP-MS222) and mounted on glass bottom dishes using 0.9% low melt agarose in egg water. Imaging parameters were kept constant across each experiment. Time courses with GFP, Venus or PKRed fluorescent proteins were performed using a Fluortar VISIR 25x/0.95 water based objective. Experiments with mCerulean were performed with a HC PL APO CS2 40x/1.25 Glycerol objective or HC PL APO CS2 20x/0.75 Immersion Oil based objective. Whole fish images were taken on a HC PL APO CS2 10x/0.40 dry objective. The fluorescent proteins were excited with the following lasers: 405 nm for mCerulean, 488 nm for GFP/Venus, 552 nm for PKRed. The notochord was divided into individual tiled regions and the region that could be covered, optimized by imaging duration was dependent on the fluorophore. Typical regions of the notochord with transgenic lines containing GFP, Venus, PKRed fluophores were 1000 μm, while experiments with mCerulean covered around 500 μm. This region was divided into individual tiled regions, (e.g a tile using a 25x objective at 3x optical zoom covered 155 μm) and then stitched using Leica software unless specified otherwise. Larvae were revived in between time points.

Data Analysis

entpd5a fluorescence extraction

Image segmentation was performed on 2D max projections spanning the Anterior-Posterior (X) axis and the Dorsal Ventral (Y) axis (fig. S2A). The surface of the notochord maps out a cylindrical tube with entpd5a+ cells arranged around in a ring. To avoid overlapping signal in the max projections, the notochord was cut in half along the medial-lateral (Z) axis. This was possible in larvae combined with the transgenic line TgKI(cmn-hsp70I:erk-ktr-gfp), as the specificity of the fluorescence expression pattern enabled computational extraction of the notochord region. First, for each X position on the AP axis, the fluorescent GFP signal in the Y-Z plane was thresholded. Next, a binary mask was generated by removing any pixels beyond the center of the thresholded signal along the Z axis. After multiplying the modified mask with the original fluorescence reported in the Y-Z plane (either for PKRed or GFP) (fig. S2B), the slices were combined to reconstruct the notochord along the AP axis and finally max projected along the Z axis (fig. S2C). Cells were segmented using Cellpose (43). Total fluorescence from individual cells was used to map expression over time. Special attention was paid at each time while adding new cells to the detected count, especially at the periphery of the DV axis, as remounting the larvae during subsequent time-points might have shifted the orientation of the notochord. Fluorescence intensities were rescaled by the time average for better comparison between fish samples.

Total intensities per segment were calculated by automatically assigning cells to different segment clusters. All individual cell positions along the Anterior Posterior axis were first sorted. Differences in positions with any large breaks helped separate the cells into the clusters. Individual intensities were summed up for the whole segment and the averaged centroid position of the cells was taken to be the segment location. Segments were then tracked by finding the nearest cluster match between time points. Any segment clusters which couldn’t be assigned to a nearest position in the previous image was assigned as a new segment formed.

Extraction of Erk activity

Individual GFP-expressing cells were segmented using Cellpose using models trained on notochord specific datasets in combination with pre-trained models from the Cellpose repository. After manual curation of any incorrect masks, another model was trained to detect nuclei within each cell corresponding to regions of low intensity pixels or high intensity. The efficiency of the model was also tested on a dataset generated manually by calculating intersection over union of the masks (fig. S2D).

The cytoplasmic intensity from the Erk sensor was estimated in a ring, 3 pixels out from the detected nucleus (fig. S2E). This was done to best avoid any overlapping cytoplasmic signal that could arise from neighboring cells after the max projection. Sensor activity was calculated as a ratio of the intensity in the cytoplasm compared to the nuclear intensity.

Erk activity was then averaged across all detected cells over time. We also calculated the fraction of cells whose cytoplasmic levels were greater compared to intensity in the nucleus, indicating a cell with high activity. Time period of oscillations was calculated by measuring trough-trough distances from the time series. Fig. 1H was generated by identifying larvae which were sampled close to an oscillation peak. For detected PKRed+ cells, Euclidean distances were then calculated to find the closest GFP+ cell and calculate the corresponding Erk activity. Cells were then assigned into segments and the average Erk activity calculated for the entire segment (Materials and Methods: entpd5a fluorescence extraction). For Fig. 2I, data from fig. S1E was separated by developmental time and combined with data from Fig. 2H.

For larvae expressing mCerulean as a fluorophore, microscopy parameters were optimized to maximize the signal-to-noise ratio over imaging durations that did not impact fish health. Different methods were used to extract cells and nuclei. Cells were extracted either by training a separate Cellpose model or manually. Nuclei were then estimated by training either a separate model or eroding cells by 10 pixels, to approximate the nuclear region. The same analysis was used across a time-course or control vs treated conditions. The data in Fig. 2F was collected with larvae crossed to ubi:h2a-mcherry. This allowed easier estimation of the nuclear region, but we were limited by the number of nuclei that could be separated out from the surrounding tissues, given the ubiquitous expression of ubi:h2a-mcherry.

Kuramoto Parameter

Individual images over a time series were first cropped using ImageJ/Fiji to cover the same region. Erk activity was then binned in 45 μm bins along the AP axis (containing on an average of 18 cells). After identifying an oscillation cycle using the average activity for the whole notochord, a Hilbert transform was applied to each binned trace $(j)$ to extract a phase ${\theta }_j$. The phases were combined over $N$ bins using the equation:

$$r{e}^{i\varphi }=\frac{1}{N}{\sum }_{\text{j}=1}^{\text{j}=\text{N}}{\text{e}}^{i{\theta }_j}$$ (1)

Finally, the average phase $(\varphi )$ and amplitude (r) were plotted on the unit circle along with the phase distributions at each time point.

Mathematical Modeling

Our model is composed of ODEs representing activator-inhibitor interactions. We model a negative feedback loop with inhibitor suppressing activator production and a positive feedback loop for the activator, modeling a term where the activator enhances its own production. Combination of positive and negative feedback loops have been used to study other oscillatory systems (20,44) and methods for modeling oscillators have been reviewed in (45).

Our equations have the following form and are assumed to be similar in each cell-

$$\begin{gathered} \frac{dE}{dt}={\alpha }_1-E\ast \left({\beta }_1\ast S+{\beta }_2\right)+{\gamma }_1\ast (1-E)\ast \left(\frac{E^{n1}}{E^{n1}+K_1^{n1}}\right) \\ \frac{dS}{dt}={\alpha }_2\left(\frac{E^{n2}}{E^{n2}+K_2^{n2}}\right)-{\beta }_3\ast S \end{gathered}$$

Here, $E$ and $S$ represent the activator and inhibitor respectively. Here, ${\beta }_1$ is the inhibitor-controlled inactivation rate and ${\beta }_2$ is the autonomous inactivation rate. ${\gamma }_1$ controls the non-linear positive feedback for the activator which is represented as a Hill function. For the inhibitor equation, ${\alpha }_2$ is the activator dependent production rate and ${\beta }_3$ is the inhibitor autonomous inactivation rate. We have assumed that the activator influences inhibitor production in a Hill function like manner as well.

We assume ${\alpha }_1$, the activator production rate, increases linearly in this system and solve the system of equations using ODE23s in MATLAB. The behavior of the nullclines as a function of ${\alpha }_1$ is plotted in fig. S3C with corresponding trajectories in fig. S3D. The other parameters are set at ${\alpha }_2=0.4$, ${\beta }_1=3$, $n_1=8$, $n_2=8$, $K_1=0.42$, $K_2=0.47$, ${\gamma }_1=2.5$, ${\beta }_2=1.0$, ${\beta }_3=0.3$. In this model, with increase in ${\alpha }_1$, a stable node and saddle collide and then disappear generating oscillations. Subsequent increases in ${\alpha }_1$ is accompanied by a decrease in the time period.

Extraction of spry2 expression

Max projections from the transgenic line TgKI(spry2-hsp70I:venus-Pest) were difficult to analyze for notochord cells because of signal from the surrounding tissues (Fig. 3B). To extract out the notochord, best match using cross-correlation were made between sections along the Y-Z axis and generated circles with varying radii and centers. The process was applied every 25 slices and the extracted parameters of the circle were separately fit to the X axis using least-squares. This then allowed the extraction of the extent of the notochord tube for each position on the X axis, any other signal beyond the fitted circles were removed, along with cutting the circle in half to remove part of the medial-lateral signal. Individual tiles were evaluated separately, then stitched together using cross-correlation over overlapping regions. Detected cells were then segmented with Cellpose.

In Situ Hybridization Chain Reaction (HCR)

Protocol for performing HCR was adopted from other published methods (46). HCR Probes were obtained from IDT (Oligo Pools, oPools). Larvae at 3 and 5 dpf were anesthetized in 10X tricaine for 30 mins, then fixed in 4% PFA at 1X PBS for 2 hours at room temperature. Following two 1X PBS washes, the samples were then added to acetone for 20 mins and stored at −20 °C. After performing 3 PBS washes, the samples were pre-hybridized in probe hybridization buffer for 30 mins and then incubated in solution containing 0.5 pmol of each probe in 125μL at 37 °C for 40 hours. Following hybridization, larvae were washed in a probe wash buffer followed by two 5X SSCT washes for 10 minutes. The next step was addition to the amplification buffer, first only the samples were incubated for 30 mins. Then 7.5 pmol of hairpin 1 and 2 were separately snap cooled (heated to 95 °C for 90 seconds and cooled to room temperature) and added to 125μL of amplification buffer. Samples were then left overnight in a dark compartment. Hairpin solution was washed out the next day with 5X SSCT and mounted for confocal microscopy.

Drug Treatments

Frequency Change

8 dpf larvae containing cmn-hsp70I:erk-ktr-gfp;entpd5a:pKRed were pre-imaged. Larvae displaying high Erk activity were subsequently followed. They were immersed in 2 μM PD0325901(Selleck Chem:S1036) or equivalent amount of DMSO (Sigma-Aldrich: D8418) in fish system water for about 2 hours. This was then washed out, by rinsing the larvae 3 times in system water. Following a post-treatment image, larvae were imaged every 4 hours while monitoring signs of high ERK activity, indicating the next occurrence of an oscillation cycle. If any high activity was detected, another image was taken within the next 30 mins to capture the peak of the oscillation cycle.

Continuous Treatment

3 dpf transgenic larvae containing col9:erk-ktr-cer were immersed in 50 μM Afatinib/ BIBW2992 (Selleck Chem: S1011) or an equivalent amount of DMSO in fish egg water for about 50 hours. Post treatment images were taken to assess Erk activity.

Larvae at 7 dpf expressing entpd5a:pKRed were immersed in 2 μM PD0325901/ Mirdametinib (Fig. 4C-D) or 20 μM Afatinib/BIBW2992 (fig. S6G-H) for about 50 hours. An equivalent amount of DMSO in fish system was used for each control group. Larvae were kept off the system and fed once per day. Drug solutions were replaced about every 24 hours. To assess changes in individual segment fluorescence, different segment regions were tracked between the pre and post images (see section entpd5a+ fluorescence extraction). Any cell clusters in the post-treated image which couldn’t be assigned to a previous position in the pre-treated image were marked as new cells added to segments. To account for differences in imaging time within an experiment, the number of cells added or changes in fluorescence per segment, were rescaled by the exact time differences for each larva between pre and post treated images. Statistical differences were evaluated using the two sample Kolmogorov-Smirnov Test.

Supplementary Material

Supplement 1. Movie. S1 Heat Maps of ERK Activity Show Oscillation Cycles.

Oscillations in an 8 dpf larvae plotted as a heat map over 30 hours. Related to Fig. 1F (see associated colorbar). Scale bar 100 μm.

Supplement 2. Movie. S2 Raw data representing Erk Sensor Activity.

Corresponding raw data of Erk sensor activity for Fig. 1F, Movie. S1, following an 8 dpf larvae over 30 hours. Related to fig. S1C. Scale bar 100 μm.

Supplement 3. Movie. S3 Heat Maps Showing Increase in Erk Activity around 5 dpf.

Heat maps of Erk activity between 3–5 dpf. Related to Fig. 2E (see colorbar). Scale bar 100 μm.

Supplement 4. Movie. S4 Heat Maps of Erk Activity in a Control Larvae Following a Washout Experiment.

Images of Erk activity following an 8 dpf larvae post DMSO treatment. Related to Fig. 5A (see associated colorbar). Scale bar 100 μm.

Supplement 5. Movie. S5 Heat Maps of Erk Activity in a Mek Inhibited Larvae Following a Washout Experiment.

Images of Erk activity following an 8 dpf larvae post Mek inhibition. Related to Fig. 5A (see associated colorbar). Scale bar 100 μm.