1. Developmental Biology
Download icon

Segmentation of the zebrafish axial skeleton relies on notochord sheath cells and not on the segmentation clock

  1. Laura Lleras Forero
  2. Rachna Narayanan
  3. Leonie FA Huitema
  4. Maaike VanBergen
  5. Alexander Apschner
  6. Josi Peterson-Maduro
  7. Ive Logister
  8. Guillaume Valentin
  9. Luis G Morelli
  10. Andrew C Oates  Is a corresponding author
  11. Stefan Schulte-Merker  Is a corresponding author
  1. WWU Münster, Germany
  2. CiM Cluster of Excellence (EXC-1003-CiM), Germany
  3. Hubrecht Institute-KNAW & UMC Utrecht, Netherlands
  4. The Francis Crick Institute, United Kingdom
  5. Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA), CONICET–Partner Institute of the Max Planck Society, Argentina
  6. FCEyN, UBA, Ciudad Universitaria, Argentina
  7. Max Planck Institute for Molecular Physiology, Germany
  8. University College London, United Kingdom
  9. École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Research Article
  • Cited 7
  • Views 1,950
  • Annotations
Cite this article as: eLife 2018;7:e33843 doi: 10.7554/eLife.33843

Abstract

Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.

https://doi.org/10.7554/eLife.33843.001

Introduction

The segmented vertebral column is the hallmark of vertebrate species. In many vertebrates, each ossified metameric unit starts out as a chordacentrum, a small, mineralized, ring-like structure around the notochord. The chordacentrum is then expanded and later is comprised of a barrel-like centrum (or vertebral body) (Figure 2—figure supplement 1) and protruding neural and hemal arches that enclose and protect the spinal cord throughout the body axis as well as the inner organs. In amniotes, such as mammals and birds, all these elements as well as adjacent muscle and sub-cutis derive from transient embryonic segmented structures termed somites. The sclerotome occupies the bulk of the somite, whereas skin and muscle are derived from the smaller derma-myotome. The cells within the sclerotome responsible for producing and mineralizing the organic aspect of bone (osteoid) are termed osteoblasts. In all vertebrates, somites are formed rhythmically and sequentially along the embryonic axis in a process governed by a multicellular, genetic oscillator termed the segmentation clock. Sequential waves of oscillating gene expression move through the precursor cells of the pre-somitic mesoderm (PSM) from the posterior to the anterior, where their arrest prefigures the timing and location of each newly forming somite boundary (Masamizu et al., 2006; Aulehla et al., 2008; Soroldoni et al., 2014; Shimojo and Kageyama, 2016). The segmentation clock contains a network of oscillating genes that shows differences between species, but members of the Hes/her family of transcriptional repressors appear to form a core negative feedback loop in all species examined (Krol et al., 2011). Mutations that disrupt the mouse clock (e.g. Hes7 [Bessho et al., 2001]) cause defective somitogenesis and corresponding defects to the centra and arches of the spinal column. Similarly, surgical perturbation of somites in chick embryos produce defects in the centra and arches (Stern and Keynes, 1987; Aoyama and Asamoto, 1988). Engineered changes to the mouse clock that shorten the period of oscillations correspondingly produce more vertebral bodies (Harima et al., 2013). Thus, the current model in amniotes proposes that the segmentation clock is the major source of patterning information for the somites, which in turn provides the segmented organization of sclerotomal derivatives that form the individual centra and arches of the spinal column. Remarkably, although somitogenesis is similar in vertebrate classes, whether the cellular lineage(s) and mechanism of segmental patterning of the chordacentra are homologous remains unclear (Fleming et al., 2015).

It has been proposed that in the teleosts zebrafish (Fleming et al., 2004) and salmon (Grotmol et al., 2003; Wang et al., 2013) the notochord and not the sclerotome is the initial source of bone matrix for chordacentra formation, while in other teleost species the classical sclerotome-derived osteoblasts have been suggested as the main drivers of chordacentrum formation (Inohaya et al., 2007; Renn et al., 2013). Chordacentra are first observed as they mineralize as rings around the notochord, forming sequentially along the axis in a process that begins several days after somitogenesis and muscle segmentation is completed and lasts several weeks. This difference in developmental timing between the formation of segmented muscle and segmented skeleton in teleosts raises a registration problem between these mechanical elements, which amniotes do not need to solve. The zebrafish fused somites/tbx6 (fss) mutant, which has unsegmented paraxial mesoderm, has ectopically positioned neural and hemal arches, but was reported to form normal vertebral centra (Fleming et al., 2004; van Eeden et al., 1996). This suggests that a segmented sclerotome is necessary for proper arch development, but not for segmentation of the chordacentra. However, the zebrafish hes6 mutant, which forms somites more slowly than wild type, makes correspondingly fewer centra (Schröter and Oates, 2010), suggesting that the segmentation clock can influence vertebral patterning. Indeed, gene expression studies suggest that the tbx6 mutant retains a dynamic segmentation clock in the posterior of the PSM, but specifically fails to output the clock’s information in the anterior PSM (van Eeden et al., 1998; Holley et al., 2000; Nikaido et al., 2002). The tbx6−/− and hes6−/− phenotypes might be reconciled if, even in the absence of morphological somitogenesis, an active clock in the posterior PSM of the tbx6 mutant is sufficient to correctly pattern the chordacentra. Alternatively, the segmentation clock may not be required for segmental chordacentra formation, but may nevertheless be able to indirectly modulate the pattern.

In this paper, we investigate the developmental origin of segmental patterning of chordacentra in zebrafish, showing that the majority of chordacentra can form normally despite a disrupted segmentation clock. We image the segmentation dynamics of the notochord sheath cell layer directly and document a distinctive set of segmentation errors in mutants. To unify these observations, we describe a model for autonomous segmentation of the notochord and validate this by comparison of simulations to experimental data.

Results

Disruption of the segmentation clock in double and triple mutants

The zebrafish segmentation clock’s core pacemaker circuit consists of her1, her7 and hes6, which display partial and overlapping redundancy (Schröter et al., 2012). The analysis of mutant combinations was previously not possible because her1 and her7 are located ~10 Kb apart on chromosome 5. We generated a her1;her7 double mutant by injecting a TALEN construct directed against her1 in the her7 mutant (Choorapoikayil et al., 2012) and a novel hes6 mutation also using a TALEN approach (Figure 1—figure supplement 1). The her1 TALEN allele has two consecutive premature stop codons (TAA TAA). The predicted Her1 protein from the TALEN-induced mutation lacks the basic DNA-binding domain and the HLH dimerization domain, suggesting that the protein product has no functionality. It has been previously shown that the hu2526 allele is a her7 null mutant resulting from a stop codon in the HLH domain (Schröter et al., 2012). Importantly, the phenotype of her1;her7 double mutants is consistent with the phenotype of her1, her7 double morphants and also of the b567 deletion allele (Henry et al., 2002Oates and Ho, 2002).

To assess patterning in the PSM, we used her7 (Figure 1A–D’), her1 and deltaC expression (Figure 1—figure supplement 2), which show wave-like expression domains, as markers for the oscillation of the clock, and mespb, which shows expression in cells along the anterior border of two newly forming segments, for the clock’s segmental output in the anterior PSM at the 10-somite stage (Figure 1E–H; Figure 1—figure supplement 3A). In tbx6−/−, her7 still oscillated posteriorly (Figure 1B,B´), but mespb was not expressed (Figure 1F), as expected (Oates et al., 2005; Durbin et al., 2000). In her1;her7 double mutants, her7 was expressed throughout the PSM (Figure 1C,C’), but lacked oscillatory waves, and mespb expression in the anterior PSM occurred in a diffuse domain, lacking segmented stripes (Figure 1G; Figure 1—figure supplement 3B), consistent with previous results using anti-sense knock-down reagents (Oates and Ho, 2002). Expression of other markers of segmental patterning in the anterior PSM (papc, ripply1, ripply2) also lacked segmental stripes (Figure 1—figure supplement 3C–H). This reveals that in her1−/−;her7−/−, the segmentation clock is severely disrupted throughout the PSM, and that a correspondingly disordered, non-segmental output is made in the anterior PSM. Triple mutants for her1, her7 and hes6 have the same expression patterns as her1;her7 double mutants for all markers analyzed (Figure 1—figure supplement 2). Hence, and in order to simplify breeding, we focused further analyses on her1−/−;her7−/−. Finally, we examined her1−/−;her7−/−;tbx6−/− and found that her7 expression in the posterior PSM lacked oscillatory waves and neither her7 (Figure 1D,D') nor mespb (Figure 1H) was expressed in the anterior PSM. From these results we conclude that her1−/−;her7−/−;tbx6−/− resembles the simple addition of the tbx6 and her1;her7 double mutant phenotypes; namely a severely disrupted segmentation clock that lacks any output in the anterior. In addition, bright field images at the 18-somite stage (Figure 1I–L’) were taken. Somite boundaries in wild type embryos are periodic and sharp (Figure 1I,I’). Somite boundaries could not be discerned in tbx6 or her1;her7;tbx6 triple mutants (Figure 1J,J’ and L,L’). In her1−/−;her7−/− (Figure 1K,K’), partial boundaries were visible, but were lacking regular shape and periodic arrangement. This indicates that periodic morphology is disrupted in the mutant paraxial mesoderm. We next evaluated the presence of periodic patterns in muscle pioneers by analyzing en2a expression at the 20-somite stage (Figure 1M–P’). The normal periodic pattern is lost in tbx6−/− (Figure 1N,N’), her1−/−;her7−/− (Figure 1O,O’) and her1−/−;her7−/−;tbx6−/− (Figure 1P,P’), indicating that although these cell types are present in these mutants, there is no overt segmental pattern emerging directly from the PSM.

Figure 1 with 3 supplements see all
Disruption of the segmentation clock in tbx6, her1;her7 and her1;her7;tbx6 mutants.

(A–D’) In situ hybridization for segmentation clock marker her7. (B and B') her7 oscillates in the posterior PSM of tbx6−/−, but does not oscillate in her1−/−;her7−/− (C and C´) or her1−/−;her7−/−;tbx6−/− (D and D`). (E–H) In situ hybridization for segmental output marker mespb. mespb is not expressed in tbx6−/− (F) or her1−/−;her7−/−;tbx6−/− (H), but is weakly expressed in her1−/−;her7−/−, albeit not in segmental stripes (G). (I–L’) Somite boundaries in the paraxial mesoderm. In tbx6−/− (J), her1−/−;her7−/− (K) and her1−/−;her7−/−;tbx6−/− (L) mutants, boundaries lose periodic order. (M–P’) Spatial distribution of muscle pioneers marked by in situ hybridization with en2a. In tbx6−/− (N), her1−/−;her7−/− (O) and her1−/−;her7−/−;tbx6−/− (P) muscle pioneers lose segmental pattern. A-H’ are dorsal views of 13.5 hpf (10 somites) embryos, I-P' are lateral views of 18–19.5 hpf (18–20 somites) embryos. a – anterior, p – posterior. Scale bar in A is 100 µm and applies to A-G. Scale bar in I is 150 µm, applies to I-L and in I’ is 100 µm, applies to I’-L’. Scale bars in M and M’ are 150 µm and 100 µm respectively, and apply to M-P and M’-P’ respectively.

https://doi.org/10.7554/eLife.33843.002

The characteristic chevrons of the larval myotome are visible using xirp2a as a boundary marker along the axis at 1.5 days post fertilization (dpf) (Figure 2A,A’). We observed strong disruption of periodic myotome boundaries in all mutants (Figure 2B–D’ and Figure 2—figure supplement 2), with the severity in tbx6−/− and her1−/−;her7−/−;tbx6−/− (Figure 2B,B’ and D,D’) equivalent, and stronger than that found in her1−/−;her7−/− (Figure 2C,C’). The short and scattered boundary fragments visible in her1−/−;her7−/− (Figure 2C’) correlate with earlier expression of mespb and partial somite boundaries in the PSM (Figure 1G, Figure 1K,K’), and may arise from a secondary morphogenetic effect of elongating muscle fibers (van Eeden et al., 1998), some of which are lost in the absence of fss/tbx6 (Windner et al., 2015).

Figure 2 with 4 supplements see all
Myotome boundaries are disrupted in segmentation clock mutants, but chordacentra are still patterned.

(A to D’) In situ hybridization for myotome boundary marker xirp2a. Myotome boundaries are disrupted to differing degrees of severity depending on the genotype. (E–H’) Alizarin Red bone preparations. Centra are well-formed in tbx6−/− (n = 10) (F), while neural and hemal arches are often fused (). Centra are also well-formed in her1−/−;her7−/− (n = 14) (G,G’) and her1−/−;her7−/−;tbx6−/− (n = 15) (H,H’). Occasional defects occur, seen as smaller vertebrae (arrowhead in F’), or as fusions of two vertebrae (arrowheads in G’ and H’). Larvae in A-D are 40 hpf. Adult fish in E-H are between two and six months. All animals in lateral view with anterior to the left. na - neural arch, hr - hemal arch, c - centrum. Scale bars in A and A’ are 150 µm and 100 µm respectively and apply to A-D and A’-D’ respectively. Scale bar in E is 1 mm and applies to E-H, scale bar in E’ is 200 µm and applies to E’-H’. Asterisks highlight fused neural and hemal arches.

https://doi.org/10.7554/eLife.33843.006

Normal centra form in the absence of periodic paraxial patterning

After having established that her1;her7 double mutants, tbx6 single mutants and her1;her7;tbx6 triple mutants display severe disruption of the segmentation clock and its output in the paraxial mesoderm, we examined to what extent these early paraxial defects were reflected in vertebral bodies of the adult. If the previously reported ability of the fss/tbx6 mutant to form normal centra was due to the remaining segmentation clock activity in the posterior PSM, then we expected to see a strong disruption of vertebral bodies in both her1−/−;her7−/− and her1−/−;her7−/−;tbx6−/− adults. Mineralized bone was visualized using Alizarin Red (AR) staining of adult skeletons. We observed duplications, fusions and abnormalities of the neural and hemal arches throughout the axis in every tbx6−/−her1−/−;her7−/− and her1−/−;her7−/−;tbx6−/− adult, consistent with a loss of pattern in the sclerotome. However, the majority of centra in her1−/−;her7−/− and her1−/−;her7−/−;tbx6−/− adults were remarkably well-formed, defined as being cleanly separated from neighboring centra and similar to wildtype in their basic hourglass shape (Figure 2F–H). Furthermore, we confirmed that all centra were well-formed in all her1, her7 and hes6 hetero- and homozygotes (Hanisch et al., 2013), in all heterozygous double and triple crosses, and in hes6;her7 double mutants. In addition, centra were also well-formed in mutants where the segmentation clock’s oscillating cells slowly desynchronize due to a loss in Delta-Notch signaling, such as in beamter/deltaC and after eight/deltaD (Durbin et al., 2000) (Figure 2—figure supplement 3 and Figure 2—figure supplement 4). Thus, the segmentation clock activity remaining in the posterior PSM of tbx6 mutant embryos is not the cause of the well-formed vertebral centra observed in tbx6−/− adults.

However, in some mutant combinations we did observe localized defects, such as a bend in the axis or occasional malformations and fusion of neighboring centra, scattered along every her1;her7 and her1;hes6 double mutant, and her1;her7;hes6 and her1;her7;tbx6 triple mutant skeletons, as well as in 80% of tbx6−/− skeletons (Figure 2F–H and Figure 2—figure supplement 4R,U). This shows that previous reports of normal segmentation of the centra in tbx6−/− were incomplete (Fleming et al., 2004; van Eeden et al., 1996), and indicates that in the absence of periodic order in the early paraxial mesoderm, formation of the centra is error-prone. Given the proximity of the developing chordacentra to the notochord, and the suggestion that the notochord serves as a linear template for the vertebral column (Gray et al., 2014), our findings argue instead that formation of periodic chordacentra may arise from a separate segmentation mechanism intrinsic to the notochord.

Segmental entpd5 expression in notochord sheath cells is the key step for chordacentrum mineralization

Secreted Entpd5 has previously been shown to be required for bone formation in zebrafish, and to be co-expressed with osterix (osx) in craniofacial osteoblasts (Huitema et al., 2012). When examining entpd5 promoter activity outside the craniofacial area, we observed a striking segmented pattern in the sheath cells along the notochord (Figure 3A), well before the onset of chordacentrum mineralization is first observed in the anterior notochord at 6 dpf (Morin-Kensicki et al., 2002). Photoconversion at 3 dpf (Figure 3B) of Kaede expressed from an entpd5:kaede transgene showed that these rings arise from an earlier ubiquitous expression domain by de novo synthesis (Figure 3C), making entpd5 the earliest axial segmented marker known for zebrafish. We found entpd5 to be segmentally expressed first in the dorsal region of the sheath cell layer at the anterior, and new, periodically forming rings of entpd5 expression formed sequentially from anterior to posterior along the axis (Figure 3C and D). entpd5+ sheath cells precisely predicted the position of the mineralized chordacentra and were located centrally to the mineralized matrix as revealed by co-staining with AR (Figure 3E and F). In classical osteoblasts (cells able to produce bone matrix), as are found in the cleithrum or parasphenoid bones of the head, entpd5 is co-expressed with the osteoblast regulator osterix/Sp7 (Figure 3—figure supplement 1A) whereas within the developing vertebral column, osterix expression is first observed after 17 dpf when neural and hemal arches begin to form (Spoorendonk et al., 2008). entpd5 mutants form normally segmented osteoid, but do not mineralize it (Huitema et al., 2012). In contrast, osterix mutants have normal entpd5 expression and ossification in the notochord, but reduced ossification in the head (Figure 3—figure supplement 1B,C).

Figure 3 with 1 supplement see all
Segmental entpd5 expression in notochord sheath cells marks the sites of chordacentrum mineralization.

(A-D) Confocal images of live transgenic entpd5 reporter larvae in lateral view with anterior to left. (A) At 6 dpf, entpd5 is expressed only in notochord sheath cells and not in vacuolated notochord cells, labelled by SAGFF214A;UAS:GFP. (B) At 3 dpf entpd5 is expressed in the whole notochord and does not display a segmented pattern. (C,D) Transgenic entpd5:Kaede embryos were photoconverted at 3 dpf and imaged at 4 dpf (C) and 8 dpf (D), respectively. New axial expression domains (green) are restricted to a segmental pattern within the axis and the cleithrum (cl). (E) Live confocal imaging of entpd5:Kaede expression in larvae also stained with Alizarin Red (AR) in lateral view (left) and sagittal view (SP). entpd5+ expression domains overlap with areas of mineralization (left), and notochord sheath cells (green) localize proximal to the site of mineralization of the future chordacentra. (F) Schematic illustration depicting the innermost vacuolated cells (VC) and the alternating pattern of entpd5+ (red, E) and entpd5- (grey) notochord sheath cells (SC). The sheath cells are surrounded by a fibrous matrix (FM), which in turn becomes mineralized in entpd5+ areas. cl, cleithrum. Scale bar for A and E is 40 µm, scale bar for B and C is 150 µm.

https://doi.org/10.7554/eLife.33843.011

The patterning mechanism in the notochord sheath is influenced, but not determined, by paraxial segmentation

We reasoned that a better understanding of the occasional defects observed in the tbx6−/−,her1−/−;her7−/−, and her1−/−;her7−/−;tbx6−/− chordacentra might provide insight into the mechanism of chordacentra segmentation. To describe the dynamics of these defects we first imaged entpd5 expression in the sheath cells along the axis at intervals of 2 days in each mutant and recorded the distribution in a kymogram (Figure 4A–D). In wildtype larvae (Figure 4A; Figure 4—figure supplement 1), entpd5+ segments are established in an anterior to posterior progression at a rate of ~1.5 per day, with the exception of the first two segments (part of the Weberian apparatus) which appear dorsally at first and are completed 4–6 days later. As each chordacentrum matured, entpd5 expression was down-regulated in the center and was retained at the distal edges of each element, as illustrated in Figure 2—figure supplement 1 and Figure 4—figure supplement 1. This process began around 15 dpf in the anterior chordacentra, and sequentially progressed posterior-wards along the axis.

Figure 4 with 5 supplements see all
Mutants with disturbed segmentation clock form a metameric order of chordacentra with scattered defects.

(A–D) Kymogram representation of virtual time lapse observations of representative entpd5:kaede-expressing larvae of each genotype. (A) In wild type (n = 16), entpd5+ segments are added in an orderly manner from anterior to posterior (black lines). (B) tbx6−/− (n = 4), (C) her1−/−;her7−/− (n = 4), and (D) her1−/−;her7−/−;tbx6−/− mutants (n = 4) also form entpd5+ rings in an anterior to posterior manner, but in an error-prone fashion. Defects such as gaps in the segmental pattern (increased intervertebral spaces), or small vertebrae followed by fusions (black boxes) can be seen scattered along the axis. Red asterisks (*) in her1−/−;her7−/− kymogram (C) represent sites of transient bending of the axis. Blue dots follow the development of the numbered chordacentra over time.

https://doi.org/10.7554/eLife.33843.013

We next examined the dynamics of entpd5 expression rings in different mutant backgrounds. In the case of tbx6 (n = 4), her1;her7 (n = 4), her1;her7;tbx6 (n = 4) and hes6 (n = 6) mutants (Figure 4B–D, Figure 5A and B, Figure 4—figure supplement 2Figure 4—figure supplement 3, Figure 4—figure supplement 4 and Figure 4—figure supplement 5), the chordacentra formed in an anterior to posterior direction as in . However, we observed two types of defects: in the first, a ring was initially not formed, leaving a transient gap (Figure 5A and longer spaces in the kymograms), which was then modified by the subsequent intercalation of a new entpd5 expression ring two or more days later (segment 1’ in Figure 5A, 19 dpf). The intercalated ring was thinner than neighboring elements, likely reflecting an earlier stage in ring development, and remained smaller and distinct from neighboring segments. In the second type of defect, a ring was added (on schedule or out of schedule) in the middle of a normal intervertebral distance, creating a distance shorter than expected between two rings. In this case, the notochord sheath cells of the small segment fused with one or two of its neighboring segments (Figure 5B, black boxes in kymograms). In the cases where two sequential defects are inserted by any of the two processes described above, we observed a transient bending of the axis, which was later modified by fusing segments or leaving two or three contiguous small vertebrae (Figure 4C, her1−/−;her7−/− kymogram and Figure 4—figure supplement 3). The phenotypic defects we see are different to the scoliosis phenotypes reported in mutant leviathan/col8a1a animals with defects in collagen deposition (Gray et al., 2014) or in mutant stocksteif/cyp26b1 animals with increased retinoic acid levels (Spoorendonk et al., 2008). In these cases, the first pattern of mineralization appears correctly segmented, and defects arise because of axial bending of the notochord and bone overgrowth, respectively. In contrast, we have directly observed the initial emergence of defective entpd5+ rings, suggesting that the periodic patterning of the notochord has been affected.

Inaccurate spacing of entpd5+ segments results in erroneous chordacentrum formation.

(A, B) Time series images of entpd5+ segments around the notochord in her1;her7 mutants, in lateral view with anterior to the left. (A) An atypically wide space between entpd5+ segments (arrow) results in the subsequent intercalation of an additional, smaller entpd5+ segment (1´). (B) An additional smaller segment (2') fuses to adjacent vertebra. (C) The length between existing entpd5+ segments was measured in her1;her7 mutants (n = 4) in positions where an entpd5 ring would be intercalated (red dots) and compared to the equivalent axial position in wild type (WT, n = 16) (black crosses). The distance preceding an intercalation in her1;her7 mutants was either similar or larger than wild type. DM, distance measured; E entpd5+ segment. All scale bars are 100 µm.

https://doi.org/10.7554/eLife.33843.019

Segment defects in the paraxial mesoderm occur sequentially along the axis, consistent with a disrupted clock-type mechanism. In contrast, the intercalation defects observed in the mutant axes form out of schedule with the sequence of notochord segmentation. We asked if the intercalation of an entpd5 ring was associated with an error in the initial local spacing of the rings along the notochord. We measured the distance between the entpd5+ rings bordering the location where the intercalated segment was added at the time point immediately before its appearance in her1;her7 mutants (n = 4 animals; 18 intercalations, red squares; Figure 5C) and compared this to equivalent distances in control embryos (n = 16 animals, 288 segments, black crosses). The distance preceding an intercalation was either similar to or larger than expected from the controls, but never smaller (n = 18, 1.4 ± 0.3 fold increase, mean ± SD). Thus, the intercalatory rings formed at a range of distances from their earlier neighbors, suggesting that the defects arise as a response to an error in positioning the earlier rings and are not a simple delay in entpd5 expression. These distinctive intercalations are difficult to reconcile with a clock-type mechanism for segmenting the notochord.

The chordacentra defects described above may reflect some influence of the disrupted paraxial mesoderm pattern on the notochord. Previously, it was shown that hes6 mutants show weak myotome boundary defects in the posterior tail at low penetrance at 1.5 dpf (Schröter and Oates, 2010), and the hes6 mutant generated in this paper also show these defects (9/67 (13.4%)). Nevertheless, the existence and distribution of skeletal defects had not been examined. In hes6−/− skeletons we observed from one to four centra defects, restricted to the caudal vertebrae, in AR stains of adult bone (4/15, 27%) (Figure 6A and B) and in entpd5 expression at 28 dpf (8/41, 20%) (Figure 6C–E). Additional analysis showed that 2/5 (40%) hes6 mutants with a chordacentra defect revealed by entpd5 expression also presented a myotome defect in the same region. The remaining 60% (3/5) had no myotome defect, but still showed a chordacentra defect. This partial overlap of myotome and chordacentra defects in hes6 mutants, as well as the coordinated reduction in total myotome and vertebral number observed previously (Schröter and Oates, 2010) and in our work suggests that the pattern of the paraxial mesoderm can influence the segmentation of the notochord.

hes6 mutant embryos can form defective caudal vertebrae.

(A,B) Alizarin Red bone preparations of wild type and hes6−/− adults. (B) 27% of hes6−/− adult bone stains presented with defects in caudal chordacentra (n=4/15) wildtype. Arrow points at fused hemal arches, arrow head at chordacentra segment defect. (C to E´entpd5:YFP expression in hes6 mutants at 28 dpf . 20% of hes6 mutants have one or more defective small vertebrae (arrows) exclusively in the caudal axis (n=8/41). Scale for A and B is 2.5 mm, C is 300 µm and C´ to E´ is 200 µm.

https://doi.org/10.7554/eLife.33843.020

A reaction-diffusion model of axial patterning in the zebrafish

These findings can be synthesized in a model of axial segmentation in which the notochord possesses an intrinsic segmentation mechanism, likely within the sheath cells, that does not depend on the paraxial segmentation clock to produce periodic entpd5 rings and subsequent mineralization. This mechanism is proposed to act directly upstream of entpd5 expression, but is nevertheless sensitive to information from the paraxial mesoderm, likely from the myotome structure, which can bias the position of a ring to enable coupling of the early-developing myotome with the later-forming skeleton in wildtype.

To assess the plausibility of this hypothesis and to investigate what kind of mechanism has these properties, we developed a theoretical description that formalizes these ideas and incorporates key experimental findings. We describe the intrinsic patterning mechanism operating in the notochord sheath cells as a reaction diffusion system with two components, an activator and an inhibitor (Murray, 1993) (see the Theory section in Materials and methods and Figure 7—figure supplement 1). This theory is capable of producing an autonomous pattern, sequentially adding segments from anterior to posterior (Figure 7A, Figure 7—figure supplement 2 and Video 1). The cues provided by the paraxial mesoderm pattern are introduced as a distribution of sinks for the inhibitor that are of the same order as the mechanism’s intrinsic wavelength (Figure 7). The choice of sinks instead of sources, together with vanishing initial conditions across the notochord except for a perturbation localized at the anterior, are required to preserve the sequential character of notochord segmentation. Although other more complex descriptions that improve robustness to noise are possible (Materials and methods), this simple theory successfully accounts for the sequential formation of regular segments in the presence of sinks as observed in wild type (Figure 7B, Figure 7—figure supplement 3 and Video 2). The intrinsic patterning mechanism allows for a range of pattern wavelengths, providing the plasticity for the sinks to pin segments to specific locations, altering the length of each segment. We conjecture that the mutants do not affect the intrinsic notochord patterning mechanism, but change the features of the sink distribution. The potential of sinks for biasing the pattern can interfere with ring formation, revealing a process that can intercalate a ring into a mispatterned gap in the sequence. Both reducing the sink strength and increasing the noise in the positioning of sinks can induce defects in the intrinsic patterning mechanism (Figure 7—figure supplement 4). Thus, the spatially disordered and variable sized myotomes observed in the mutants (Figure 2A–E) are described in the theory as large fluctuations in the positions and amplitudes of inhibitor sinks (Figure 7C and D). The her1−/−;her7−/− situation is described by strong sinks with large position errors (Figures 2C and 7B, Figure 7—figure supplement 5 and Video 3) while tbx6−/− and her1−/−;her7−/−;tbx6−/− are described by sinks with reduced amplitude and shorter wavelength, accounting for the smaller and scattered myotome fragments (Figures 2B,D and and 7D, Figure 7—figure supplement 6 and Video 4). In the framework of the theory, tbx6−/− and her1−/−;her7−/−;tbx6−/− are described by the same set of parameters. The mechanism has some flexibility and is compatible with a range of wavelengths. For example, the larger myotomes produced by a hes6 mutant provides larger wavelength cues to the notochord resulting in larger and fewer chordacentra (Figure 7E, Figure 7—figure supplement 7 and Video 5).

Video 1
Simulation of the autonomous sinkless condition. 

The absence of sink profile (blue) in the top panel and corresponding activator (green) and inhibitor (red) patterns in the bottom with patterning occurring sequentially from anterior to posterior. Parameters as in Figure 7 of the main text.

https://doi.org/10.7554/eLife.33843.021
Video 2
Simulation of the wild type condition.

The sink profile (blue) for the wild type condition in the top panel and corresponding activator (green) and inhibitor (red) patterns in the bottom. Parameters as in Figure 7 of the main text.

https://doi.org/10.7554/eLife.33843.022
Video 3
Simulation of the her1;her7 mutant condition.

The sink profile (blue) showing the noisy spatial distribution for the her1;her7 mutant condition in the top panel and corresponding activator (green) and inhibitor (red) patterns in the bottom. Parameters as in Figure 7 of the main text.

https://doi.org/10.7554/eLife.33843.023
Video 4
Simulation of the tbx6 mutant condition.

The sink profile (blue) representing the noisy spatial distribution and the reduced amplitude of sinks in the tbx6 mutant in the top panel and corresponding activator (green) and inhibitor (red) patterns in the bottom. This simulation also represents the her1;her7;tbx6 mutant. Parameters as in Figure 7 of the main text.

https://doi.org/10.7554/eLife.33843.024
Video 5
Simulation of the hes6 mutant condition.

The sink profile (blue) representing the longer spatial wavelength of sinks in the hes6 mutant in the top panel and corresponding activator (green) and inhibitor (red) patterns in the bottom. Parameters as in Figure 7 of the main text.

https://doi.org/10.7554/eLife.33843.025
Figure 7 with 9 supplements see all
A reaction diffusion theory accounts for key experimental findings.

A sink profile (blue) describes cues from myotomes that bias the position of segments. The Entpd5 pattern is given by the concentration of an activator (green) that is regulated by an inhibitor (red). (A) The system is capable of autonomous pattern formation in the absence of sinks. (B) Wild type condition is described by regularly placed strong sinks, according to the output of a functioning segmentation clock. (C) In her1−/−;her7−/− strong sinks are misplaced due to a malfunctioning segmentation clock, causing segments to be also misplaced and giving rise to defects. (D) tbx6 and her1;her7;tbx6 mutants are characterized by weaker segmentation clock output and fragmented and scattered myotome boundaries, here described by weaker sinks with a shorter wavelength. (E) The hes6 mutant is here characterized by a sink profile wavelength that is 6% larger than wild type. Parameters: a = 10−3, b = 10−2, τ= 0.1, d = 0.5. Sink profile parameters: (A) S0 = 0, (B) S0 = 8, λ = 0.57, σ = 0.05, (C) S0 = 8, λ = 0.57, σ = 0.18, (D) S0 = 4, λ = 0.30, σ = 0.15, and (E) S0 = 8, λ = 0.60, σ= 0.05. See also Videos 15 and Figure 7—figure supplement 19 for animations and snapshots for all conditions. Source data files for this figure and the supplemental figures have been supplied.

https://doi.org/10.7554/eLife.33843.026

In the simulations of the wild type, there is always a correspondence between the position of the sink and the position of the peak of activator (Figure 7B and E); this situation is also found between the positions of the myotome boundary and the entpd5 expression ring in experimental wild type animals (Figure 7—figure supplement 8A–F). In the simulations of tbx6her1;her7 and her1;her7;tbx6 mutants this strict correspondence between sink and activator is lost (Figure 7C and D); activator peaks occur both together with sinks and in between them. In the case of hes6, the strict correspondence between sink and activator may be lost in the last tail segments. To test this prediction of the model, we examined the distribution of myotome boundaries and entpd5 expression rings in tbx6 and her1;her7 double mutants. We observed that the disorganized myotome boundary fragments in the mutants had lost strict correspondence with the entpd5 rings (Figure 7—figure supplement 8G–R). This lack of spatial correspondence between paraxial structure and axial expression is in agreement with the model, and it supports the hypothesis that the sink is associated with some feature of the myotome boundary.

Lastly, in order to compare the quantitative output of the model against the biological data, we counted the number of vertebral segments as well as the number of segmentation defects (small vertebrae or fusions) in mutant fish using entpd5 expression at 28 dpf, when the vertebral bodies have developed into a mature form (Figure 7—figure supplement 9A,B). All mutants had a greater variability in segment number than wild type (n = 48), where segment number ranged from 29 to 31. In her1−/−;her7−/− (n = 38) the segment number increased up to 37. The increase in her1;her7 was slightly ameliorated by the additional removal of tbx6 in the triple mutants (n = 47). As expected, hes6 mutants (n = 41) had a lower number of segments than the wild type, ranging from 28 to 31 segments. When the same fish were scored for segmentation defects (Figure 7—figure supplement 9B), her1−/−;her7−/− presented a higher frequency and a broader distribution of defects than tbx6 mutants (n = 46). In her1;her7;tbx6 mutants, the number of defects per embryo decreased almost to the distribution seen in tbx6 mutants. The trends in these measurements are captured by the theory, as shown by the number of peaks in the pattern and (Figure 7—figure supplement 9C) the number of defects (Figure 7—figure supplement 9D), defined as segments of lengths outside the wild type segment length range.

Discussion

In order to dissect the interrelationship of paraxial mesoderm segmentation and chordacentrum formation in teleosts, we here use the zebrafish to manipulate the segmentation clock in the paraxial mesoderm, while using a novel marker for axial segmentation to examine chordacentrum and vertebral body patterning at early and late stages.

The zebrafish notochord consists of a core of vacuolated cells responsible for turgor pressure, and an outer, squamous epithelial layer, the sheath cells, that is adjacent to the notochord’s basal lamina or sheath, which provides mechanical stability (Melby et al., 1996; Yamamoto et al., 2010) (Figure 3E). Previously, we described the enzyme ectonucleoside triphosphate/diphosphohydrolase 5 (Entpd5) as essential for ossification in zebrafish (Huitema et al., 2012). Entpd5 mutants fail to mineralize osteoid, leading to a complete absence of bone. entpd5 is co-expressed with osterix in all osteoblasts of the early head skeleton, the cleithrum and the operculum (Huitema et al., 2012), but we here show that entpd5 is also expressed in notochord cells (Figure 3), and that, at 4 dpf, the expression in the axial mesoderm becomes restricted to segmentally organized rings in the notochord sheath cells. osx is not expressed at these early stages in the notochord sheath cells, nor do osx mutant present with an axial mineralization phenotype in zebrafish or Medaka (Figure 3—figure supplement 1Yu et al., 2017). Combined, these results identify the osx-, entpd5+ sheath cells as those osteoblasts responsible for initial chordacentra formation, and indicate that the segmental patterning of the notochord is under way by 4 dpf in these cells. Mechanistically, the segmental expression of Entpd5 in the notochord sheath provides the enzymatic activity to mineralize the fibrous sheath of the notochord. It is possible that the respective contribution of notochord sheath cells in chordacentrum formation versus sclerotome-derived osteoblast function in centrum formation is different in other teleost species (Fleming et al., 2015; Yasutake et al., 2004; Kaneko et al., 2016), and this can be tested by generating entpd5 mutants in some of those species. In zebrafish, our findings settle a long-standing debate on which cells are functionally important for chordacentrum formation.

From an evolutionary perspective, it has been suggested that the chordacentrum is a novelty found only in actinopterygians (Arratia et al., 2001). It seems safe to state that chordacentrum formation is conserved at least among teleosts, while the situation for holosteans (Amia and the gars) is less clear. Whether chondrosteans such as Acipenser, which lack centra but exhibit mineralized neural and hemal arches are different deserves further studies in order to bridge the gap between paleontological, anatomical and molecular studies (Arratia et al., 2001; Laerm, 1976; Laerm, 1979). Recent work has shown that clock-based mechanisms are involved in body segmentation in vertebrates as well as invertebrates (Sarrazin et al., 2012) and there is wide agreement that amniotes segmentally pattern their muscles and axial skeletons at the same time during development using the ‘segmentation clock’. However, from fossil and extant taxa it seems likely that neural and hemal arches are evolutionarily older than vertebral bodies (Cote et al., 2002), and while these structures are homologous across vertebrate classes (Williams, 1959), vertebral bodies are not. The demonstration of periodic entpd5 expression in the notochord sheath cells now provides a tool to study the earliest visible patterning events in the axial skeleton, and also allows an evaluation of the segmentation clock’s input. To perturb the clock, we generated new alleles and new allelic combinations in tbx6 and the central clock genes, her1, hes6, and her7. Analysis using a number of different read-outs demonstrate that the phenotype of her1;her7 double mutants is not exacerbated in the further absence of hes6. Strongest disruption of the clock is seen in the case of her1;her7;tbx6 triple mutants. The mutants we have used to interfere with the segmentation clock and its output leave the PSM without any overt signs of oscillation or segmental pattern. It is of course formally possible that some remaining clock-like activity exists that we cannot detect. However, our argument in this paper does not require that we have removed all segmentation clock activity, but rather that our perturbations of the segmentation clock and its output show highly ordered axial structures despite strong disorder in the early paraxial mesoderm.

An influence of the paraxial mesoderm on axial segmentation may be reflected in the differences between the mutants’ distributions of defects. The strongest axial phenotype is found in her1−/−;her7−/−, which possesses prominent myotome boundary fragments in the paraxial mesoderm, whereas tbx6−/− and her1−/−;her7−/−;tbx6−/− have a slightly weaker axial phenotype, which is preceded by a greater reduction of myotome boundaries. This is consistent with a dominant interfering effect of paraxial structures. The similarities in paraxial and axial phenotypes of tbx6−/− and her1−/−;her7−/−;tbx6−/− is explained by proposing that the effects of a disrupted segmentation clock (that can nevertheless output a disrupted pattern seen in her1−/−;her7−/−) are reduced in her1−/−;her7−/−;tbx6−/− by removing the output function of tbx6 in the anterior PSM.

We have attributed the occasional defects in the mutant centra to the effects of fluctuations in the strength and position of sinks for the inhibitor component of the notochord’s intrinsic segmentation mechanism. In the absence of any sinks, the notochord would in our model segment without any defects with a periodicity determined entirely by the internal dynamics. Thus, the defects can be viewed as a ‘dominant interference’ by the mis-patterned paraxial mesoderm. Unfortunately, due to the random and unpredictable position of the chordacentra defects seen in all mutants analyzed, cell transplantation experiments cannot serve as a suitable experimental strategy to test this. We have also contemplated the possibility that her1, her7 and tbx6 are also expressed in the notochord and may be directly responsible for the centra defects seen in the mutants. However, this appears highly unlikely, because no tbx6 (Wanglar et al., 2014), mespb or her1 expression (In situ hybridization or transgene expression at 5 dpf and 13 dpf, data not shown) has been detected in the notochord at somite stages or during chordacentra formation. A recent report indicates that overexpression of mespbb in the notochord sheath can regulate segment size, possibly via interfering with boundary formation (Wopat et al., 2018).

Another interpretation is possible in which the notochord’s intrinsic mechanism is highly noisy, and the paraxial mesoderm has no influence. While any molecular patterning mechanism would be vulnerable to fluctuations in the embryo, since the notochord’s segments are generated over a long time scale, with a period about 20 times slower than somitogenesis, it seems plausible that the large molecular numbers that could be synthesized in this interval could ensure a low error rate. Furthermore, the transfer of information from a segmentation clock-derived muscle pre-pattern to an autonomous but plastic mechanism in the notochord resolves the apparent discrepancy between tbx6 and hes6 mutant phenotypes, and explains how the animal coordinates segmented muscles and axial skeleton in biomechanical register despite the fact that they develop days to weeks apart in time. Such a coordination mechanism may be a widespread feature of the teleosts and potentially other vertebrates.

In summary, we have proposed a second mechanism for periodic segmentation of the axial skeleton of a vertebrate species, which exists in the sheath cells of the zebrafish notochord. The existence of intercalary defects argues that although there is a sequential generation of periodic entpd5 expression rings, this periodicity does not arise from a clock-type segmentation mechanism as found in the paraxial mesoderm. We have described this dynamic mechanism as a reaction-diffusion process that sweeps down the axis, generating segments autonomously and refining their position using information from the previously segmented myotomes. The genetic basis of the proposed autonomous notochord mechanism and the signal from myotome to notochord are not understood, and our model does not assume any specifics with regard to molecular identities, but it opens the door to the search for these molecules. entpd5 is the earliest known molecular marker for the sites of ossification, with plasticity in the presence of perturbation, suggesting that understanding the control of entpd5 expression may hold the key.

Materials and methods

Key resources table
Reagent type or resourceDesignationSource or referenceIdentifiersAdditional information
Gene (Danio rerio)sagff214NA
Gene (Danio rerio)entpd5NA
Gene (Danio rerio)her1NA
Gene (Danio rerio)her7NA
Gene (Danio rerio)tbx6NA
Gene (Danio rerio)hes6NA
Gene (Danio rerio)deltaDNA
Gene (Danio rerio)deltaCNA
Gene (Danio rerio)osterixNA
Genetic reagent
Genetic reagent (Danio rerio)Tg(entpd5:kaede)Geurtzen et al., 2014
doi: 10.1242/dev.105817
hu6867Same BAC used as
Huitema et al., 2012
with kaede insertion at
first translated ATG
Genetic reagent (Danio rerio)Tg(entpd5:pkred)This paperhu7478Same BAC used as
Huitema et al., 2012
with pkred insertion at
first translated ATG
Genetic reagent (Danio rerio)Tg(SAGFF214:GFP)Yamamoto et al., 2010
DOI: 10.1242/dev.051011
Genetic reagent (Danio rerio)Osterix:mcherrySpoorendonk et al., 2008
DOI: 10.1242/dev.024034
hu4008
Genetic reagent (Danio rerio)her1Schröter et al., 2012
doi: 10.1371/journal.pbio.1001364
hu2124
Genetic reagent (Danio rerio)her7Schröter et al., 2012
doi:10.1371/journal.pbio.1001364
hu2526
Genetic reagent (Danio rerio)tbx6Busch-Nentwich et al., 2013
ZFIN ID: ZDB-PUB-130425–4
sa38869
Genetic reagent (Danio rerio)hes6Schröter and Oates, 2010
doi: 10.1016/j.cub.2010.05.071
zm00012575TgAlso called zf288Tg
Genetic reagent (Danio rerio)deltaDvan Eeden et al., 1996
PMID: 9007237
ar33Also called tr233
Genetic reagent (Danio rerio)deltaCvan Eeden et al., 1996
PMID: 9007237
tm98
Recombinant DNA
reagent (plasmid)
Plasmid (Danio rerio)her7Oates and Ho, 2002
Plasmid (Danio rerio)mespbSawada et al., 2000
Plasmid (Danio rerio)xirp2aDeniziak et al., 2007
Plasmid (Danio rerio)papcYamamoto et al., 1998
Plasmid (Danio rerio)en2aErickson et al., 2007
Plasmid (Danio rerio)ripply1PCR template: Rip1 F
(CGTGGCTTGTGACCAGAAAAG)
Rip1 R T7 325
(TAATACGACTCACTATAGGCT
GTGAAGTGACTGTTGTGT)
Plasmid (Danio rerio)ripply2PCR template: Rip2
F(ACGCGAATCAACCCTGGAGA)
and Rip2 R T7 281
(AATACGACTCACTATAGGGAGA
GAGCTCTTTCTCGTCCTCTTCAT)
Plasmid (Danio rerio)dlcOates and Ho, 2002
Plasmid (Danio rerio)her1Müller et al., 1996
Sequence-based reagent
Talenhes6this paperSee Figure 1,
Figure 1—figure supplement 1
Talenher1this paperSee Figure 1,
Figure 1—figure supplement 1
Commercial assay or kit
Commercial assay or kitRNeasy MinElute
Cleanup Kit
QiagenCat No./ID: 74204
Commercial assay or kitGene jet plasmid
(miniprep kit)
Thermo scientificCat no: K0502
Chemical compound, drug
Chemical compound, drugAlizarin redSigmaCAS Number 130-22-3
Software, algorithm
Software, algorithmLAS XLeica microsystems
Software, algorithmFiji (RRID:SCR_002285)ImageJ 1.51 n
Software, algorithmPython
(RRID:SCR_008394)
Version Python 2.7.14: :
Anaconda custom (64-bit)
Software, algorithmLibraries: numpy
(RRID:SCR_008633),
matplotlib
(RRID:SCR_008624)
Anaconda
distribution
Software, algorithmLleras_fhn_1d_
solve_and_animate_
eLife.py
This paperCustom PDE solver
and animator
Provided as
supplementary data.
Software, algorithmSpyderAnaconda distribution,
Spyder 3.2.6
The Scientific
PYthon
Development
EnviRonment

Animal procedures

All zebrafish strains were maintained at the Hubrecht Institute, the Institute of Cardiovascular Organogenesis and Regeneration, and at University College London. Standard husbandry conditions applied. Animal experiments were approved by the Animal Experimentation Committee (DEC) of the Royal Netherlands Academy of Arts and Sciences and by the UK Home Office under PPL 70/7675. Embryos were kept in E3 embryo medium (5 mM NaCl, 0.17 mM KCl, 0.33 mM CaCl2, 0.33 mM MgSO4) at 28°C. For anesthesia, a 0.2% solution of 3-aminobenzoic acid ethyl ester (Sigma), containing Tris buffer, pH 7, was used.

Zebrafish lines

New transgenic lines (entpd5:pkRED, entpd5:kaede) were generated as described previously (Huitema et al., 2012). Fluorophores were recombined into the ATG site of the entpd5 gene (BAC clone CH211-202H12). fsssa38869, beatm98, aei ar33, her1hu2124 and her7hu2526 mutants were acquired from Prof. Jeroen den Hertog. The Sagff214:galFF line was obtain from K. Kawakami. Double mutants for her1 (in the her7hu2526 background) and mutants for hes6 were generated by TALEN injection (Dahlem et al., 2012) (see Figure 1—figure supplement 1 for details). An Osterix mutant was created by Tilling (Apschner, 2014). The newly generated hes6 mutant allele has one or two somites fewer (15 or 16 somites from anterior to the proctodeum, n = 78) compared to wild types (17 somites n = 15), consistent with the previously reported hes6 mutant (Schröter and Oates, 2010).

Genotyping

DNA was isolated through fin clippings and from embryos. Genotyping was performed as described in Table 1 and Table 2.

Table 1
Genotyping of lines using sequencing or restriction enzyme digestion
https://doi.org/10.7554/eLife.33843.036
Zebrafish lineFWRVRestriction enzymes
her1TCTAGCAAGGACACGCATGAGATGAAGAGGAGTCGGTGGA
her7GATGAAAATCCTGGCACAGACTTCTGAATGCAGCTCTGCTCG
hes6TCACGACGAGGATTATTACGGGGGCGACAACGTAGCGTANHEI
her1−/−;her7−/− and her1−/−;her7−/−;tbx6 −/−ACTCCAAAAATGGCAAGTCGGCCAATTCCAGAATTTCAGCAGEI
aeiAGGGAAGCTACACCTGCTCATTCTCACAGTTGAATCCAGCA
fssGGGTCATTGTTGGGTTGCAATGAACACCGCCCTTCCAAT
Table 2
Genotyping using Kaspar
https://doi.org/10.7554/eLife.33843.037
Zebrafish lineFW XFW YRV
beaGAAGGTGACCAAGTTCATGCTGAAGGTCGGAGTCAACGGATTAGTCCTTGCCTGACAAACCAA

In situ hybridization and alizarin Red bone staining

Riboprobes were generated from either plasmids or PCR templates and in situ hybridisation was performed as previously described (Oates and Ho, 2002). Whole mount stained embryos were documented on an Olympus SZX10 stereoscope with a QImaging Micropublisher camera. Flat-mounted embryos were photographed on an Olympus MVX10 stereoscope with an Olympus DP22 camera. Alizarin Red bone staining was performed as described previously (Spoorendonk et al., 2008) for fish between 8 weeks and one year of age.

Virtual time lapses

Embryos were kept in E3 at 28°C until 7 dpf. At 7 dpf, ten embryos with fully developed swim bladder from mutant (tbx6−/−, her1−/−;her7−/−, her1−/−;her7−/−;tbx6−/−or hes6−/−) or transgenic entpd5: kaede lines were anaesthetized, photographed and then housed individually in the animal facility. Individuals were fed tetrahymena in combination with Gemma 75 for the first two weeks, followed by artemia and Gemma 150 for the following two weeks. Every second day, each individual was, anesthetized (described above) and photographed using a Olympus SXZ16 stereomicroscope (1.5X PlanApo objective) connected to a DFC450C Leica camera. The embryo was placed in a drop of E3 with anesthetic on the lid of a petri dish. Each picture was taken from the cleithrum to the posterior tip of the individual. Immediately afterwards, the embryo was returned to warm E3 without anesthetic. Embryos were returned to their specific tank in the animal facility only when they were completely awake and moving. This procedure was repeated until all entpd5+ segments had developed in the axis. The sedation and photography did not take more than two minutes per embryo, and did not compromise survival.

Imaging

To photograph somite boundaries, 18–19.5 hpf embryos were dechorionated and laterally aligned in conical depressions that fit the yolk, in an agarose pad (Sigma, 2% in E3) cast in a petri dish (Falcon, 50 mm x 9 mm) and topped up with E3. Photomicrographs were taken on an Olympus MVX10 microscope equipped with an Olympus DP22 camera.

For imaging the notochord, embryos were mounted in 0.5% low melting point agarose in a culture dish with a cover slip replacing the bottom. Fluorescent imaging was performed with a Leica SPE 'live' Confocal Microscope, Leica SP8 confocal microscope and a PerkinElmer Ultraview VoX spinning disk microscope using a 10x or 20x objective with digital zoom. Usually, z-stacks with intervals of approximately 2 µm were captured and were then flattened by maximum projection in ImageJ. For photoconversion of whole entpd5:kaede embryos, the green Kaede fluorophore was photoconverted using a Leica fluorescence microscope by 15–30 min exposure through a UV light bandpass filter (360/40 nm, 100 W mercury lamp). For bone stains an Olympus S2 × 16 microscope coupled to a Leica DFC420c camera was used. Photomicrographs were stitched with the pairwise stitching plugin in Fiji (RRID:SCR_002285) (Preibisch et al., 2009).

Theory

The theory describes notochord sheath cells pattern formation in terms of a one dimensional reaction diffusion system with two components, an activator U and an inhibitor V, see Figure 7—figure supplement 1A. The concentration U = [U] of the activator is reflected in Entpd5 concentration. The concentrations of both the activator and inhibitor species U(x,t) and V(x,t) depend on position x and time t. We propose a variant of the FitzHugh-Nagumo (FHN) model (Murray, 1993)

(1) Ut=DU2Ux2+k1Uk3U3k4V+k0
(2) Vt=DV2Vx2+k5Uk6V

where DU and DV are diffusion coefficients for U and V respectively, and ki are rate constants. The choice of the FHN model is based on its simplicity. There are positive linear terms for the activator and negative linear terms for the inhibitor in both Equations (1) and (2), and a single nonlinearity, the cubic term for the activator that limits growth and allows for the stabilization of steady states. The model is meant to represent a plausible mechanism rather than specifying the interactions of particular molecules.

We reduce the number of parameters by transforming this theory to a dimensionless form. We first set the source term k0=0 since as discussed below we need to reproduce a sequential pattern formation. We introduce a lengthscale L that we will take as the system size, and a timescale T and concentration scale U0 to be set below. In terms of these scales we define new variables x, t, u and v such that

(3) x=Lx
(4) t=Tt
(5) U=U0u
(6) V=U0v

and replace in the reaction diffusion equations above dropping the primes for notational convenience

(7) U0Tut=DUU0L22ux2+k1U0uk3U03u3k4U0v
(8) U0Tvt=DVU0L22vx2+k5U0uk6U0v.

We multiply both equations by T/U0 to render them dimensionless

(9) ut=DUTL22ux2+k1Tuk3TU02u3k4Tv
(10) vt=DVTL22vx2+k5Tuk6Tv.

Multiplying the inhibitor equation by k1/k5 and rearranging terms

(11) ut=DUk1L2(k1T)2ux2+(k1T)uk3U02k1(k1T)u3k4k1(k1T)v
(12) k1k5vt=DVk5L2(k1T)2vx2+(k1T)uk6k5(k1T)v

where we have highlighted dimensionless groups in parentheses. We now select a timescale by setting

(13) k1T1

and a concentration scale by setting

(14) k3U02k11

and define dimensionless parameter groups

(15) τk1k5, aDUk1L2, bDVk5L2, κ4k4k1, κ6k6k5.

With these definitions

(16) ut=a2ux2+uu3κ4v
(17) τvt=b2vx2+uκ6v.

We additionally set κ4=1 for simplicity and we call κ6=d

(18) ut=a2ux2+uu3v
(19) τvt=b2vx2+udv.

In the rest of this work we consider this dimensionless form of the theory. Here a and b are dimensionless scaled diffusion coefficients of the activator and inhibitor species respectively, τ is a relative timescale, and d is a dimensionless degradation constant of the inhibitor.

We first consider the homogeneous system xxu=xxv=0. The resulting equations for the local reactions are

(20) u.=uu3v
(21) τv.=udv.

where dots denote time derivatives. Introducing functions

(22) f(u,v)=uu3v
(23) g(u,v)=τ1uτ1dv,

the nullclines of the system, defined by setting f(u,v)=0 and g(u,v)=0, are the curves in the (u,v) plane

(24) v=uu3,
(25) v=d1u.

The first one is an inverted cubic that goes through the origin and the second one is a linear function with slope d1 controlled by the single bifurcation parameter d, see Figure 7—figure supplement 1B. Intersections of these two curves are the solutions to

(26) u(u2+d11)=0

and define the fixed points of the system where u.=v.=0. There is always a solution (u0,v0)=(0,0) and for d>1 there are two additional solutions u± satisfying

(27) u±2=d11.

The linear stability of fixed points is determined by the matrix

(28) A=(fufvgugv)

where

(29) fu=uf(u,v)
(30) fv=vf(u,v)
(31) gu=ug(u,v)
(32) gv=vg(u,v)

and derivatives are evaluated at the fixed point (u,v). The condition for stability is that

(33) detA=fugvfvgu>0

and

(34) trA=fu+gv<0.

For the fixed point (u0,v0)=(0,0) we obtain

(35) A=(11τ1dτ1)

with determinant and trace

(36) detA=(1d)τ1
(37) trA=1dτ1.

Given that τ,d>0 this implies that the origin (0,0) is a stable fixed point if

(38) d < 1 and τ < d.

We consider in the following a situation in which the fixed point (0,0) is stable, setting the dimensionless timescale τ=0.1 and degradation d=0.5. Under appropriate conditions, the dimensionless reaction diffusion theory Equations (18) and (19) can give rise to pattern formation. In particular we require that the activator diffuses slower than the inhibitor, a<b, and here set a=103 and b=102. Because of the signs of the derivatives near the fixed point, the type of pattern predicted is as displayed in Figure 7—figure supplement 1C, where there is coexistence of activator and inhibitor (Murray, 1993).

In the presence of random perturbations distributed along the notochord the homogeneous state loses stability due to differential diffusion. A pattern may form out of this initial random background fluctuation, with segments forming almost simultaneously all along the notochord. Although segment formation is robust in this scenario and can accommodate a broad range of wavelengths, this is at odds with the experimental observation that ENTPD5 segments form sequentially from anterior to posterior.

We conjectured that one way to obtain a sequential segment formation is to start with an initial perturbation localized at the anterior, and vanishing concentrations all across the rest of the notochord. Since the anterior of the vertebrate axis is always more developmentally advanced than the posterior, such an anterior perturbation is a plausible hypothesis. A vanishing concentration along the notochord is important to ensure that patterning is not triggered until the wave of activator and inhibitor arrives at a given point. Therefore, we start simulations with initial conditions that have zero concentration for both u and v across the whole domain x(0,L), except for a small perturbation near the origin x=0. The form of the initial condition is a smooth step

(39) u(x,0)=u02(1tanh(5.0(x0.5)))
(40) v(x,0)=v02(1tanh(5.0(x0.5)))

with a steepness 5.0 and width 0.5. Initial values u0 and v0 are determined randomly from a uniform distribution in the interval (0.1,0.2), see examples in Figure 7—figure supplements 15. Starting from such a small perturbation in the anterior, we observe that the system is able to form a pattern sequentially, from anterior to posterior, see Figure 7A, Figure 7—figure supplement 2 and Video 1. Thus, the theory proposed is capable of autonomous patterning of the notochord in the absence of input from the segmentation clock.

We next introduce the effect of the segmentation clock input into this otherwise autonomous patterning system as a spatial dependent degradation profile of the inhibitor

(41) ut=a2ux2+uu3v
(42) τvt=b2vx2+udvs(x)v.

This sink profile s=s(x) for the inhibitor has peaks at given positions along the x axis, describing the cues that the notochord patterning mechanism receives from myotomes. At positions where s(x) is large, the inhibitor is locally degraded at a larger rate. Note that there is no source term for the activator since we set k0=0 above. This feature together with the choice of sinks instead of sources to describe the segmentation clock cues are motivated from the observation that Entpd5 segments form sequentially. The presence of sources would render pattern formation non sequential.

The sink profile s(x) is characterized by a sink strength S0, a wavelength λ and sink wavelength variability σ. The first sink is positioned at λ/2 and the positions Xi of consecutive sinks are determined by the wavelength λ with an error drawn from a uniform distribution of width σ. The sink profile is built from a combination of tanh(...) functions to produce smooth peaks of steepness α and width δS

(43) s(x)=S02i (tanh(α(Xi+xδS))+tanh(α(Xi+x+δS))).

In this work we fix the values α=100 and δS=0.05. The values of S0, λ and σ are changed to describe the different conditions, see examples in Figure 7 and Figure 7—figure supplement 4.

We consider a system size L that we set to L=17.1 so that the wildtype condition makes 30 segments with the sink profile natural wavelength λ=0.57. We normalize axes length scales to this value in all plots. For simplicity we assume that the activator and inhibitor are restricted to notochord sheath cells and we specify Neumann boundary conditions, that is derivatives at both ends are zero

(44) ux|x=0=vx|x=L=0.

As described above, here we ensure the sequential character of the patterning through an initial perturbation at the anterior and vanishing concentrations across the notochord. One may query the robustness of such scenario, since noise across the notochord hampers sequential patterning. An alternative hypothesis would be to postulate an additional wavefront that propagates through the notochord progressively turning on the reaction diffusion mechanism of Equations (41) and (42) as it goes. To illustrate this we consider an alternative dimensionless form of Equations (1) and (2). Turning back to Equations (9) and (10) we select a timescale and concentration scale setting

(45) DUTL21

and

(46) k3U02k11.

Introducing dimensionless parameter groups

(47) δDVDU, γk1L2DU, κikik1,

and setting for simplicity κ4=κ5=1 and κ6=κ we arrive at the dimensionless form

(48) ut=2ux2+γ(uu3v),
(49) vt=δ2vx2+γ(uκv).

In this alternative dimensionless form it is straightforward to decouple the reactions from diffusion by tuning the value of γ. Thus, we can introduce a wavefront γ(x,t) that moves from anterior to posterior turning on the reactions in its wake. Such a wavefront could have a biological origin in a molecular maturation gradient invading the notochord from the anterior. Due to very slow dynamics before wavefront arrival, this would render the patterning mechanism more robust to noise across the notochord. Yet a different possibility is a scenario of patterning in a growing domain (Crampin et al., 1999), although here the tissue where the pattern forms exists previous to the establishment of the pattern. These alternatives are certainly interesting and the underlying mechanism patterning the notochord will be the subject of future work. However, in the absence of experimental data supporting other hypotheses, here we settle on the perhaps more parsimonious choice of vanishing initial conditions across the notochord.

In this work we solve the partial differential equations described above using a custom python code, see Source code 1. We discretize space with a discretization length Δx=0.01, and time discretization is chosen as Δt=0.9Δx2/2. We integrate the partial differential equations until the pattern reaches a steady state.

References

  1. 1
    Determination of somite cells: independence of cell differentiation and morphogenesis
    1. H Aoyama
    2. K Asamoto
    (1988)
    Development 104:15–28.
  2. 2
    Putting Crystals in Place, the Regulation of Biomineralization in Zebrafish
    1. A Apschner
    (2014)
    Netherlands: Utrecht University.
  3. 3
  4. 4
  5. 5
  6. 6
    Sanger Institute Zebrafish Mutation Project mutant data submission
    1. E Busch-Nentwich
    2. C Dooley
    3. R Kettleborough
    4. DL Stemple
    (authors) (2013)
    The Zebrafish Information Network. ID ZDB-PUB-130425-4.
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
    Anteroposterior patterning is required within segments for somite boundary formation in developing zebrafish
    1. L Durbin
    2. P Sordino
    3. A Barrios
    4. M Gering
    5. C Thisse
    6. B Thisse
    7. C Brennan
    8. A Green
    9. S Wilson
    10. N Holder
    (2000)
    Development 127:1703–1713.
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17
  18. 18
  19. 19
  20. 20
  21. 21
    Two linked hairy/Enhancer of split-related zebrafish genes, her1 and her7, function together to refine alternating somite boundaries
    1. CA Henry
    2. MK Urban
    3. KK Dill
    4. JP Merlie
    5. MF Page
    6. CB Kimmel
    7. SL Amacher
    (2002)
    Development 129:3693–3704.
  22. 22
    Control of her1 expression during zebrafish somitogenesis by a delta-dependent oscillator and an independent wave-front activity
    1. SA Holley
    2. R Geisler
    3. C Nüsslein-Volhard
    (2000)
    Genes & Development 14:1678–1690.
  23. 23
  24. 24
  25. 25
  26. 26
  27. 27
  28. 28
  29. 29
  30. 30
    Specification of cell fates at the dorsal margin of the zebrafish gastrula
    1. AE Melby
    2. RM Warga
    3. CB Kimmel
    (1996)
    Development 122:2225–2237.
  31. 31
    Segmental relationship between somites and vertebral column in zebrafish
    1. EM Morin-Kensicki
    2. E Melancon
    3. JS Eisen
    (2002)
    Development 129:3851–3860.
  32. 32
    Mathematical Biology II: Spatial Models and Biomedical Applications (3rd edn)
    1. JD Murray
    (1993)
    Springer.
  33. 33
    Expression domains of a zebrafish homologue of the Drosophila pair-rule gene hairy correspond to primordia of alternating somites
    1. M Müller
    2. E v Weizsäcker
    3. JA Campos-Ortega
    (1996)
    Development 122:2071–2078.
  34. 34
  35. 35
    Hairy/E(spl)-related (Her) genes are central components of the segmentation oscillator and display redundancy with the Delta/Notch signaling pathway in the formation of anterior segmental boundaries in the zebrafish
    1. AC Oates
    2. RK Ho
    (2002)
    Development 129:2929–2946.
  36. 36
  37. 37
  38. 38
  39. 39
  40. 40
    Zebrafish Mesp family genes, mesp-a and mesp-b are segmentally expressed in the presomitic mesoderm, and Mesp-b confers the anterior identity to the developing somites
    1. A Sawada
    2. A Fritz
    3. YJ Jiang
    4. A Yamamoto
    5. K Yamasu
    6. A Kuroiwa
    7. Y Saga
    8. H Takeda
    (2000)
    Development 127:1691–1702.
  41. 41
  42. 42
  43. 43
  44. 44
  45. 45
  46. 46
    Interactions between somite cells: the formation and maintenance of segment boundaries in the chick embryo
    1. CD Stern
    2. RJ Keynes
    (1987)
    Development 99:261–272.
  47. 47
    Mutations affecting somite formation and patterning in the zebrafish, Danio rerio
    1. FJ van Eeden
    2. M Granato
    3. U Schach
    4. M Brand
    5. M Furutani-Seiki
    6. P Haffter
    7. M Hammerschmidt
    8. CP Heisenberg
    9. YJ Jiang
    10. DA Kane
    11. RN Kelsh
    12. MC Mullins
    13. J Odenthal
    14. RM Warga
    15. ML Allende
    16. ES Weinberg
    17. C Nüsslein-Volhard
    (1996)
    Development 123:153–164.
  48. 48
  49. 49
  50. 50
  51. 51
  52. 52
  53. 53
  54. 54
    Zebrafish paraxial protocadherin is a downstream target of spadetail involved in morphogenesis of gastrula mesoderm.
    1. A Yamamoto
    2. SL Amacher
    3. SH Kim
    4. D Geissert
    5. CB Kimmel
    6. EM De Robertis
    (1998)
    Development 125:3389–3397.
  55. 55
  56. 56
  57. 57

Decision letter

  1. Tanya T. Whitfield
    Reviewing Editor; University of Sheffield, United Kingdom

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article "Segmentation of the zebrafish axial skeleton relies on notochord sheath cells and not on the segmentation clock" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor (Tanya Whitfield) and Didier Stainier as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: Matthew Harris (Reviewer #1).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission

Summary:

Lieras-Forero et al. detail quite novel and important findings on the independent patterning role of the notochord in segmentation of the zebrafish vertebral column in a process that is independent of somite formation. The wavefront model has been accepted as the conserved mechanism by which segmentation in vertebrate organisms occurs. It is/was generally assumed, however, that in fishes the meristic patterning is determined by a wavefront model as shown in beginning mutants in regulators of this patterning mechanism. The authors clearly, and elegantly, demonstrate underlying capacity of the zebrafish notochord to form ordered, meristic array of vertebral bodies even in the case of dysfunctioning segmental patterning in the sclerotome. These data build on classic comparative anatomy and recent genetic data that point to patterning of the chordacentra and the notochord as a key, and ancestral, step to the formation of vertebrae and patterning of the vertebral column. The authors further develop and test a mathematical model that is sufficient to explain the interaction between the dual patterning systems that can explain a number of characteristics seen in the adult phenotypes caused by different mutant combinations.

Essential revisions:

Both reviewers were positive overall, but each had suggestions for improvement. In particular, there are several concerns over the modelling aspect of the paper. Please address the following as essential revisions:

1) Please address all issues raised by both reviewers concerning the mathematical model.

2) Please address the issues concerning the genetic analysis and nomenclature raised by reviewer 1.

3) Please use the Discussion section to set your work in a broader context (see comments and suggestions from reviewer 1).

Reviewer #1:

The findings detailed by this paper are quite interesting and are important for developmental biologists broadly. The paper is very well written, and beyond some small (but essential) comments/critiques that I hope will be taken under consideration to increase the accuracy and impact of the manuscript, I believe it will be a landmark paper.

Genetics:

– Do new alleles generated/described in this manuscript fail to complement the previous described alleles? How do the authors know that these are nulls or severe loss-of-function? The position in of the TALEN alleles would support potential gene fragments to be produced. Similarly, what genetic characterization has been done on the Tilling alleles of her1 and her7 to see if these are true loss-of-function. Some discussion/exploration of characterization of these alleles in the paper would be helpful, however as the phenotype is what is critical in this manuscript, no extensive genetic analysis is necessary to be undertaken to address these questions.

– Giving triple mutants different mutant names is not commonly accepted by the field, nor is it helpful. Gollum, or bachau are not a single locus as the names would suggest. This is quite confusing and severely complicates conceptual understanding of comparisons between the compound mutants. This detracts from an otherwise exceptional and elegantly performed study.

Modeling

– The generation of the reaction diffusion model to integrate the notochordal and somatic patterning events is quite helpful and at least supplemental figure 14 should be in the paper. This is critical.

– The model shows only resting states. Please comment in the text if the model can reproduce the ontological sequence of patterning as shown in this paper (e.g. does it replicate a rostral bias?). Also, does the model cause fill-in responses to perturbations as seen in the mutant phenotypes.

– Subsection “Disruption of the segmentation clock in double and triple mutants” The authors may want to integrate the fact that the reaction diffusion mechanism provides plasticity by the feedback characteristics of the interactions.

Phylogenetic character analysis of notochord induction/association of the chordacentrum.

– At several points the authors detail current thinking of chordacentrum involvement in patterning of the vertebra column and formation of the centra. It would be important, and clarifying, if the authors discuss classical work in basal teleosts such as Amia and Gar suggesting that notochord induction/association of a chordacentrum is ancestral in teleosts (Schultze and Arratia papers in the 1980s) and addressed in Laern, (1976). How much of the discordance between models/species that the authors mention represents different mechanisms or, alternatively, similar mechanisms studied at different levels of analysis?

Reviewer #2:

In this study Forero et al., investigate the role of the segmentation clock in patterning chordacentra in zebrafish. Using a family of segmentation clock mutants, they disrupt segmentation to varying degrees and measure the chordacentra pattering. They propose a model in which the periodic patterning of chordacentra arises from a pattering process that can function independently from the segmentation clock. However, the somite patterns can modify the chordacentra patterning mechanism.

My major issue is that the model ought to generate periodic patterning of chordacentra in the absence of somitogenesis clock input. If the proposed model can do this robustly then some elementary exploration of this case is necessary (i.e. a minimum requirement is to provide enough detail so the results are reproducible and verify that there is a robust patterning mechanism in the case of no sinks). This validation is crucial as later the authors use the model to explain the location of activator peaks relative to sinks.

1) The authors claim that 'in the absence of any sinks, the notochord would in our model segment without any defects with a periodicity determined entirely by the internal dynamics.'

The key figure supporting this statement (Figure 14E) indicates that the mathematical model produces spatially periodic patterns at steady state in the absence of dermatome signal (i.e. s(x)=0 for all x).

It is not adequately explained in the text how the proposed model does this. What is the patterning mechanism?

A standard way to analyse the model is to consider behavior without diffusion. What are the steady states and what is their linear stability?

My analysis suggests that in the absence of diffusion and with s0<1-d (i.e. small influence from the dermatome) there is a unique steady state (0,0) that is stable.

When s0>1-d the origin becomes unstable and there are two non-zero steady states (i.e. presumably the model becomes bistable in this regime).

This analysis is consistent with the authors numerical results; the spatially homogeneous steady state is destabilized in simulations where the sink strength is greater than 0.5. Outside of this region the spatially homogeneous steady state is monostable.

Given the case where s0=0 is stable, the question then is whether the introduction of diffusion could cause an instability (e.g. Turing) and hence periodic patterning. If this is the case the authors should show it. However, even if this were true the wavefront behavior presented by the authors is nontrivial.

I have tried to reproduce Figure 14E with my own code and as many of the details provided but cannot.

2) The PDE model has a parameter that is discontinuous in space. The authors ought to provide details of their discretisation scheme so that the reader can assess how they have dealt with this discontinuity.

I suggest the following improvement: define the sinks independently of the numerical mesh and then approximate the steep switches with a continuous function such as tanh. In this way the sink strength parameter can be guaranteed to be continuous.

3) Stability analysis – is the pattering mechanism robust to small perturbations? It is worrying that the authors initialise on an unstable steady state of the homogeneous problem. Hence an infinitesimally small perturbation from these initial conditions could result in completely different model behaviour.

Could the authors add some small amplitude noise to the initial conditions and present some numerical results. Is the proposed wavefront solution stable?

4) The use of Fitzhugh Nagumo ought to be justified. I am not suggesting that the model needs to be linked to a molecular detail but some insight into the various terms would be helpful. The authors should describe the model assumptions and how they might be relevant to this system.

5) “In the simulations of fss, guu, and fum this strict correspondence between sink and activator is lost (Figure 7B and C); activator peaks occur both together with sinks and in between them.”

Can the authors use the model to provide insight into how this can happen? Is this observation a generic feature of activator-inhibitors models? If it is generic, then showing results from other reaction-diffusion models would help. If it is not generic, then the properties of the proposed model that yield the interesting behaviour ought to be defined and investigated more thoroughly.

6) Given the mathematical model takes up almost two pages of the results then I suggest that a figure exploring the relevant features of the model is appropriate.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Segmentation of the zebrafish axial skeleton relies on notochord sheath cells and not on the segmentation clock" for further consideration at eLife. Your revised article has been evaluated by Didier Stainier (Senior editor), Tanya Whitfield (Reviewing editor), and two reviewers.

The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance. Reviewer 1 only has minor concerns that will be quick to address. Reviewer 2 has some more substantial concerns regarding robustness of the system to small perturbations. The reviewer has given comments together with two video files. Please address the comments from both reviewers.

Reviewer #1:

In the text the authors often list fss, her1;her7, and tbx6;her1;her7 mutant combinations. I assume the fss allele of tbx6 is the one being used (unless another has been generated). If this is the case the text should reflect this as tbx6-/-. her1; her7, tbx6;her1;her7 mutants. The authors have correctly labeled this in the figures, but not the figure legends nor text.

Somewhere in the text the authors should address whether these alleles are thought to be null or strong loss-of-function. Data is not needed, rather citation of previous genetic analysis on available alleles and a statement in the text is just helpful.

Results section “A reaction-diffusion model of axial patterning in the zebrafish”: “intrinsic segmentation mechanism, likely sheath cells" Sheath cells is not a mechanism. Do the authors mean within sheath cells?

Reviewer #2:

1) Whilst the theory section has been improved, now that it is explicit that the authors are proposing the Turing mechanism as the underlying patterning mechanism, can they provide a fuller analysis of the unstable wavenumbers for the parameter values presented in the simulations? It is important to characterize how the unstable wavenumbers (and corresponding wavelengths) relate to the typical inter-sink distance (e.g. presumably the model parameters have been chosen to give a wavenumber that is approximately of the same order as the inter-sink distance).

2) As the authors did not present the results with arbitrarily small noise in the initial data as I requested, I have solved the equations myself.

In Noise.mp4 I solve the model as it is presented in the paper. Note that the key qualitative behaviour is that independent of somite signal, a propagating wavefront leaves a periodic pattern in its wake. This is the behavior observed experimentally that any reasonable model ought to replicate.

In NoNoise.mp4 I have added very low amplitude noise to the initial conditions. Note that the noise destabilises the wavefront solution and the domain patterns simultaneously rather than sequentially.

These numerical results indicate that even the addition of infinitesimally small noise throughout the domain results in the wavefront solution being lost. Given the presence of noise in biological systems, this robustness issue is a fundamental limitation that, by not addressing in the main text of the manuscript, the authors seem to have neglected.

I suggest the following:

i) The authors build a convincing case, with reference to the pattern formation literature, that deals with the robustness issue. i.e. are there other published examples of wavefront propagation mediated spatial patterning with a similar lack or robustness?

or

ii) The authors build on their proposal that robustness could be mediated by a maturation gradient. This could be incorporated into the model by considering a competency domain where the authors solve the reaction diffusion equations on some domain [0, s(t)] where s(t) is a suitably chosen function of time.

Such a model would have a fundamentally different behaviour in that the imposed wavefront would determine the speed of segmentation rather than the Turing instability. Moreover, it would be robust to infinitesimally small noise.

For the suggested approach the authors could see, for example, Madzvamuse et al., 2005 or Crampin et al., 2002.

https://doi.org/10.7554/eLife.33843.042

Author response

Essential revisions:

Both reviewers were positive overall, but each had suggestions for improvement. In particular, there are several concerns over the modelling aspect of the paper. Please address the following as essential revisions:

1) Please address all issues raised by both reviewers concerning the mathematical model.

2) Please address the issues concerning the genetic analysis and nomenclature raised by reviewer 1.

3) Please use the Discussion section to set your work in a broader context (see comments and suggestions from reviewer 1).

Reviewer #1:

The findings detailed by this paper are quite interesting and are important for developmental biologists broadly. The paper is very well written, and beyond some small (but essential) comments/critiques that I hope will be taken under consideration to increase the accuracy and impact of the manuscript, I believe it will be a landmark paper.

We thank the reviewer for the encouraging comments and the suggestions. We have implemented the requested changes and trust that the manuscript has improved.

Genetics:

– Do new alleles generated/described in this manuscript fail to complement the previous described alleles? How do the authors know that these are nulls or severe loss-of-function? The position in of the TALEN alleles would support potential gene fragments to be produced. Similarly, what genetic characterization has been done on the Tilling alleles of her1 and her7 to see if these are true loss-of-function. Some discussion/exploration of characterization of these alleles in the paper would be helpful, however as the phenotype is what is critical in this manuscript, no extensive genetic analysis is necessary to be undertaken to address these questions.

The her1 talen allele has 2 consecutive premature stop codons (TAA TAA) and the her7 (hu2526) also has a premature stop codon (TAA). We cannot determine if her1-/-;her7+/-; tbx6-/- is a null on the protein level, because we don’t have antibodies to detect Her1 and Her7, but protein prediction suggests that the truncated proteins does not have wild type functionality. Her1 and Her7 are members of the bHLH superfamily of transcription factors – they need to dimerise for activity and they do this though the HLH domain and bind DNA with the basic (b) domain. The predicted Her1 protein product from the TALEN induced mutation lacks the basic DNA binding domain and the HLH dimerisation domains, so the prediction suggests that the protein product has no functionality. The predicted Her7 protein product of the hu2526 allele is also truncated because the stop codon is in the HLH domain – hence, this protein product is also predicted to be non-functional as its dimerising ability is lost. Importantly, the phenotype of her1,her7 double mutantsis consistent with the phenotype of her1,her7 double morphants and also of the b567 deletion allele (Henry et. al 2002). We did carry out a cross of her1,her7 to the single her1 mutant, and found that the her1-/-;her7+/- genotype presents a exacerbated phenotype than her1 single mutants.

As describe in the Materials and methods section the Hes6 mutant generated here has the same phenotype as describe in the morpholino injections from Schroter and Oates, 2010.

– Giving triple mutants different mutant names is not commonly accepted by the field, nor is it helpful. Gollum, or bachau are not a single locus as the names would suggest. This is quite confusing and severely complicates conceptual understanding of comparisons between the compound mutants. This detracts from an otherwise exceptional and elegantly performed study.

We thank the reviewers for this comment. Indeed, we had discussed that among ourselves, and had prior to submission asked for input from the ZF nomenclature committee. While we believe the suggested names would have helped readability, we have now removed all names for the triple and double mutants, and now refer to all mutants by the genotype.

Modeling

– The generation of the reaction diffusion model to integrate the notochordal and somatic patterning events is quite helpful and at least supplemental figure 14 should be in the paper. This is critical.

We thank the reviewer for this suggestion. We have moved previous Figure S14 into the main text in the revised manuscript (now Figure 7). Please note that we have also included in this main text figure now a new panel A showing the behavior of the model in the absence of sinks.

– The model shows only resting states. Please comment in the text if the model can reproduce the ontological sequence of patterning as shown in this paper (e.g. does it replicate a rostral bias?). Also, does the model cause fill-in responses to perturbations as seen in the mutant phenotypes.

We provided movies of the numerical simulations of the theory for the different conditions described in main text Figure 7. We also added new figure supplements (Figure 7—figure supplement 1 to Figure 7—figure supplement 5) which show a sequence of snapshots of these movies at several time points.

Both the movies and the snapshots illustrate that the model can reproduce the sequential dynamics of segment formation, from rostral to caudal. We now highlight this aspect of the theory in the main text.

As for fill-in responses observed in experiments, the data we have produced with the model is not conclusive. It may seem from the movies that when a defect is formed in place of a normal segment, the speed at which the activator concentration grows is slower than that of a normal segment. If there is a secondary mechanism reading out this slower and weaker increase, it may be that this could result in a quicker formation of the follow up segment and later formation of the defective one. This could describe the fill-in responses observed in experimental data. However, we have not been able to quantify this.

– Subsection “Disruption of the segmentation clock in double and triple mutants” The authors may want to integrate the fact that the reaction diffusion mechanisms provide plasticity by the feedback characteristics of the interactions.

We thank the reviewer for this suggestion. We now highlight the fact that the reaction diffusion mechanism can support a range of wavelengths and argue how this plasticity may allow the bias introduced by the segmentation clock via the sinks to alter the length of each segment to match with the segmentation clock output. See subsection “A reaction-diffusion model of axial patterning in the zebrafish”.

Phylogenetic character analysis of notochord induction/association of the chordacentrum

– At several points the authors detail current thinking of chordacentrum involvement in patterning of the vertebra column and formation of the centra. It would be important, and clarifying, if the authors discuss classical work in basal teleosts such as Amia and Gar suggesting that notochord induction/association of a chordacentrum is ancestral in teleosts (Schultze and Arratia papers in the 1980s) and addressed in Laern, (1976). How much of the discordance between models/species that the authors mention represents different mechanisms or, alternatively, similar mechanisms studied at different levels of analysis?

This is an extremely interesting point, but we feel that an extensive discussion about this issue goes beyond the scope of this paper, simply because it would take a lot of space to cover this topic. Concerning the relevant remark of this reviewer, we have discussed some aspects of this issue with an expert in the field (PE Witten, Univ Ghent). We have included now a paragraph that cites the Arratia and Laerm papers and makes the statement that in teleosts chordacentrum formation is conserved, and that chordacentrum formation is an evolutionary novelty within Actionpterygians. As the reviewer suggests, many of the possible discrepancies and question marks concerning homology of chordacentrum/centrum formation could well be (and likely are) due to different levels of analysis and use of different methodologies. Only the availability of the entpd5 transgenic line, an entpd5 mutant and histology (AR stain) has allowed us to make strong statements about the situation in zebrafish. We find it difficult to make statements with the same rigor about other species.

Reviewer #2:

In this study Forero et al., investigate the role of the segmentation clock in patterning chordacentra in zebrafish. Using a family of segmentation clock mutants, they disrupt segmentation to varying degrees and measure the chordacentra pattering. They propose a model in which the periodic patterning of chordacentra arises from a pattering process that can function independently from the segmentation clock. However, the somite patterns can modify the chordacentra patterning mechanism.

My major issue is that the model ought to generate periodic patterning of chordacentra in the absence of somitogenesis clock input. If the proposed model can do this robustly then some elementary exploration of this case is necessary (i.e. a minimum requirement is to provide enough detail, so the results are reproducible and verify that there is a robust patterning mechanism in the case of no sinks). This validation is crucial as later the authors use the model to explain the location of activator peaks relative to sinks.

We thank the reviewer for the careful evaluation of our results, comments and suggestions. We completely agree with the reviewer that a key requirement to the theory is that there should be an autonomous patterning mechanism which in the absence of sinks generates a sequential segmented pattern from anterior to posterior. As we argue below this is indeed the case for the theory we propose here. We hope that, with the changes and additions to the manuscript described in detail in our reply, this point is clear and leaves no doubt.

1) The authors claim that 'in the absence of any sinks, the notochord would in our model segment without any defects with a periodicity determined entirely by the internal dynamics.'

The key figure supporting this statement (Figure 14E) indicates that the mathematical model produces spatially periodic patterns at steady state in the absence of dermatome signal (i.e. s(x)=0 for all x).

This is indeed the case. In the absence of sinks, there is an autonomous reaction diffusion system that generates a sequential pattern of segments, starting from a small random perturbation localized at the anterior. The wavelength of the resulting pattern is regular and defined by the autonomous dynamics of the reaction diffusion system. We previously showed this result as Figure 15E. To acknowledge the importance of this aspect of the theory we now reproduce this as panel A of Figure 7, which is part of the main text in the revised manuscript. We also emphasize this aspect in the text before introducing the idea of sinks and the description of the wild type condition.

It is not adequately explained in the text how the proposed model does this. What is the patterning mechanism?

A standard way to analyse the model is to consider behavior without diffusion. What are the steady states and what is their linear stability?

My analysis suggests that in the absence of diffusion and with s0<1-d (i.e. small influence from the dermatome) there is a unique steady state (0,0) that is stable.

When s0>1-d the origin becomes unstable and there are two non-zero steady states (i.e. presumably the model becomes bistable in this regime).

This is correct. The spatially homogeneous theory displays a bifurcation at s0 = 1-d, where a single stable fixed point gives rise to two stable fixed points separated by an unstable fixed point. In the absence of sinks we set s0 = 0 and find that d = 1 marks the onset of bistability. For d < 1 the system has a single stable fixed point. Motivated by the reviewer questions we decided to include this calculation, together with plots of the nullclines, in the Theory section in Materials and methods section. For conditions in which there is a single stable fixed point, like the ones considered in the manuscript, autonomous patterning is caused by diffusion driven destabilization of an otherwise stable homogeneous state.

This analysis is consistent with the authors numerical results; the spatially homogeneous steady state is destabilized in simulations where the sink strength is greater than 0.5. Outside of this region the spatially homogeneous steady state is monostable.

Given the case where s0=0 is stable, the question then is whether the introduction of diffusion could cause an instability (e.g. Turing) and hence periodic patterning. If this is the case the authors should show it. However, even if this were true the wavefront behavior presented by the authors is nontrivial.

Again this is correct: it is differential diffusion that destabilizes the initially homogeneous state and leads to the formation of the periodic pattern in the absence of sinks with s0 = 0. The nullcline plots show that the type of instability that we can expect, as we now explain in more detail in the Theory section. We agree with the reviewer that the wavefront behavior is nontrivial.

I have tried to reproduce Figure 14E with my own code and as many of the details provided but cannot.

We hope that with the more detailed description of the methods and parameters we provide our results are now easier to reproduce.

Furthermore, in the interest of transparency we provide with the revised version of the manuscript the Python code that we use to generate the data, movies and snapshots.

We hope that the comments in the code make it clear. We run it within the Spyder environment, which comes with the Anaconda Python distribution, all free and open.

2) The PDE model has a parameter that is discontinuous in space. The authors ought to provide details of their discretisation scheme so that the reader can assess how they have dealt with this discontinuity.

I suggest the following improvement: define the sinks independently of the numerical mesh and then approximate the steep switches with a continuous function such as tanh. In this way the sink strength parameter can be guaranteed to be continuous.

Concerning the steep sink switches, we had also tried continuous sink profiles like combinations of trigonometric functions and combinations of tanh functions. Since these smooth sink profiles produced qualitatively similar results to the steep sink profiles we settled for the latter in our first submission since they allowed for faster computation when it comes to statistics.

In the revised manuscript, we have chosen to follow the reviewer suggestion and recalculated everything using a smooth sink profile built from a combination of tanh functions, as described in the Theory section. The parameters of single sink shape are its width and steepness. The details of implementation can also be checked in the code provided.

In the numerical results reported in the revised manuscript, we use sinks that are wider that in the original version of the manuscript. We chose wider sinks to allow for smoother changes in the sink profile. For this reason, in the description of the different conditions reported in Figure 7, other parameters like sink strength and wavelength noise also change in the revised manuscript.

We provide full details of the discretization scheme in the Theory section of the Materials and methods section.

3) Stability analysis – is the pattering mechanism robust to small perturbations? It is worrying that the authors initialise on an unstable steady state of the homogeneous problem. Hence an infinitesimally small perturbation from these initial conditions could result in completely different model behaviour.

Could the authors add some small amplitude noise to the initial conditions and present some numerical results. Is the proposed wavefront solution stable?

Concerning initial conditions, we describe in the Theory section how we implement a smooth concentration step localized to the anterior, with a randomly chosen amplitude for both components.

With the parameter choice that we make, the homogeneous system is stable for vanishing concentrations of the activator and the inhibitor. That is, if we start with no activator and no inhibitor, we stay that way in a homogeneous system. How does the pattern begin to form?

One possibility is to start with small random perturbations distributed all along the notochord. In the presence of diffusion, the homogeneous state loses stability and a pattern may form out of this initial random background fluctuation. We have tried this classical scenario, and what happens is that the whole system segments all at once, with all segments forming simultaneously. Segment formation is robust in this scenario and can accommodate a broad range of sink profile wavelengths. However, this is at odds with the experimental observation that ENTPD5 segments form sequentially.

One key feature of the experimental data is that ENTPD5 segments form sequentially, from anterior to posterior. It is interesting that it does this even in the presence of cues by the segmentation clock output: somitogenesis has finished essentially after the first day post fertilization, while notochord ENTPD5 patterning takes about 20 days to complete.

Both the autonomous pattern mechanism, here proposed as a reaction diffusion system, and the cues provided by the segmentation clock have to be consistent with this key observation.

One way to obtain a sequential segment formation is to start with an initial perturbation localized at the anterior and vanishing concentrations all across the rest of the notochord. From a biological perspective, since the anterior of the vertebrate axis is always more developmentally advanced than the posterior, such an anterior perturbation is a plausible hypothesis.

For this to work it is important that the reaction diffusion system does not have any local source terms, since this would trigger patterning all across the notochord at the same time. For this reason, we speculated that the cue from the segmentation clock might come in the form of a sink term, for example as local degradation of one or both the components, instead of a source term. This ensures that patterning is not triggered until the wave of activator and inhibitor arrives at a given point.

We are aware, and we agree with the reviewer that in this scenario, small perturbations might trigger segment formation before the wavefront arrives. Actually, this might be the case of the fill-in responses we observe in the data for some experimental perturbations, although we do not speculate in this respect.

4) The use of Fitzhugh Nagumo ought to be justified. I am not suggesting that the model needs to be linked to a molecular detail but some insight into the various terms would be helpful. The authors should describe the model assumptions and how they might be relevant to this system.

We thank the reviewer for this suggestion. We now describe the different terms in the reaction diffusion system in the Theory section. We argue that this particular model is a good choice for its simplicity and generality, with a single nonlinear term that allows for nontrivial fixed points to be stable. We have chosen to start with a full version of the theory and show how we non-dimensionalize the equations to arrive at the dimensionless form that we use in the manuscript. This gives the reader a good grasp of what parameters are in the different terms and what the assumptions are in this dimensionless theory. We also perform the linear stability analysis of the homogeneous system as described above. We hope that this better justifies the use of this model and highlights its features.

5) “In the simulations of fss, guu, and fum this strict correspondence between sink and activator is lost (Figure 7B and C); activator peaks occur both together with sinks and in between them.”

Can the authors use the model to provide insight into how this can happen? Is this observation a generic feature of activator-inhibitors models? If it is generic, then showing results from other reaction-diffusion models would help. If it is not generic, then the properties of the proposed model that yield the interesting behaviour ought to be defined and investigated more thoroughly.

There is a range of wavelengths that an activator-inhibitor model can support when diffusion drives it out of the homogeneous state. If the sink ahead of the segmentation wave is too close or too far away in a way that compromises the supported wavelengths, then a skipping or intercalation may occur. The existence of a range of wavelengths which are supported is true for all activator-inhibitor models, so we expect sink skipping or segment intercalation to be generic features. The FitzHughNagumo model that we explore is very generic and representative of a large class of systems that can be mapped to this kind of nonlinear dynamics near the bifurcation of a single steady state into two stable states.

6) Given the mathematical model takes up almost two pages of the results then I suggest that a figure exploring the relevant features of the model is appropriate.

We have followed the reviewer suggestion, which is in agreement with reviewer #1. We decided to include Figure 7 in the main text of the revised version of the manuscript. In this figure, we added a top panel showing the behavior of the theory in the absence of sinks, given the key importance of this aspect of the theory as pointed by the reviewer in (1).

We thought that a more thorough exploration of the theory diverts from the main focus of this work, and therefore opted to keep Figure 7—figure supplement 2 showing the behavior of the model as the sink profile is changed in different ways as a supplementary figure. Figure 7—figure supplement 4 compares statistics from experiments and simulations, and new Figure 7—figure supplement 5 illustrates nullclines and stability.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Reviewer #1:

In the text the authors often list fss, her1;her7, and tbx6;her1;her7 mutant combinations. I assume the fss allele of tbx6 is the one being used (unless another has been generated). If this is the case the text should reflect this as tbx6-/-. her1; her7, tbx6;her1;her7 mutants. The authors have correctly labeled this in the figures, but not the figure legends nor text.

Thanks for pointing this out - we have made all these changes.

Somewhere in the text the authors should address whether these alleles are thought to be null or strong loss-of-function. Data is not needed, rather citation of previous genetic analysis on available alleles and a statement in the text is just helpful.

The alleles used in this study are either known to be effectively null or expected to be strong loss-of-function. We have added several sentences to describe what is known about the mutations in the first paragraph of the Results section.

Results section “A reaction-diffusion model of axial patterning in the zebrafish”: “intrinsic segmentation mechanism, likely sheath cells" Sheath cells is not a mechanism. Do the authors mean within sheath cells?

Thank you, we now state “within” the sheath cells.

Reviewer #2:

1) Whilst the theory section has been improved, now that it is explicit that the authors are proposing the Turing mechanism as the underlying patterning mechanism, can they provide a fuller analysis of the unstable wavenumbers for the parameter values presented in the simulations? It is important to characterize how the unstable wavenumbers (and corresponding wavelengths) relate to the typical inter-sink distance (e.g. presumably the model parameters have been chosen to give a wavenumber that is approximately of the same order as the inter-sink distance).

Characterization of the unstable wavenumbers is a good general technical question one could ask about any similar model. The answer to the particular question asked by the reviewer is already there in Figure 7A; in the sink-less simulations, the natural wavelength for the invading wave is smaller than that of the wild type sink wavelengths. Characterizing this relationship more fully, as requested, is technically possible, but we argue that since this would only hold for one particular set of parameters, and not provide a general picture, it is not clear to us that it brings a strong addition. Furthermore, the outcome of this exercise would not affect the conclusions of the paper. We now point out explicitly that the natural wavelength for the invading wave is close to that of the wild type sink wavelength in the text in subsection “A reaction-diffusion model of axial patterning in the zebrafish”.

2) As the authors did not present the results with arbitrarily small noise in the initial data as I requested, I have solved the equations myself and attach the results.

Thank you for the comment – we had also done this previously. However, due to the direction and scope of what we aim to do here, we argue that it is not appropriate for inclusion in this paper.

In Noise.mp4 I solve the model as it is presented in the paper. Note that the key qualitative behaviour is that independent of somite signal, a propagating wavefront leaves a periodic pattern in its wake. This is the behavior observed experimentally that any reasonable model ought to replicate.

We believe that the reviewer means NoNoise.mp4, which is indeed the behaviour that our model replicates as shown in Figure 7 and Figure 7—figure supplement 1 and Figure 7—figure supplement 6A.

In NoNoise.mp4 I have added very low amplitude noise to the initial conditions. Note that the noise destabilises the wavefront solution and the domain patterns simultaneously rather than sequentially.

These numerical results indicate that even the addition of infinitesimally small noise throughout the domain results in the wavefront solution being lost. Given the presence of noise in biological systems, this robustness issue is a fundamental limitation that, by not addressing in the main text of the manuscript, the authors seem to have neglected.

This comment concerns the robustness of the model to a particular kind of noise. The reviewer rightly points out that adding noise to the initial spatial domain breaks the wave-like invasion of the mechanism. We are of course aware of the presence of noise in biological systems, and also the effect of small noise amplitude on the solution. We now include reference to the issue of robustness the Main Text in subsection “A reaction-diffusion model of axial patterning in the zebrafish” and point the reader to the revised Materials and methods section for a fuller discussion.

In this paper, given that we still lack the molecular mechanism or details, our overall goal is to present as simple a picture for the segmental gene expression phenomenon as possible. This necessitates an abstraction of the problem and an idealization of the biological context. There are several ways to extend or adapt the model to make its wavefront solution stable to noise, yet these introduce additional complexity (see below), which we have no biological data support for. Also, we are concerned that making the model more complex may distract from the main conclusions of the paper, while not altering them.

I suggest the following:

i) The authors build a convincing case, with reference to the pattern formation literature, that deals with the robustness issue. i.e. are there other published examples of wavefront propagation mediated spatial patterning with a similar lack or robustness?

We are not aware of any in the literature. Nevertheless, we note that the absence of a previous example in the literature is not a strong test for the validity of a new proposal.

or

ii) The authors build on their proposal that robustness could be mediated by a maturation gradient. This could be incorporated into the model by considering a competency domain where the authors solve the reaction diffusion equations on some domain [0, s(t)] where s(t) is a suitably chosen function of time.

Such a model would have a fundamentally different behaviour in that the imposed wavefront would determine the speed of segmentation rather than the Turing instability. Moreover, it would be robust to infinitesimally small noise.

For the suggested approach the authors could see, for example, Madzvamuse et al., 2005 or Crampin et al., 2002.

This is an interesting suggestion, but the case in the embryo is probably not well-represented by a growing domain, as suggested by the reviewer. This is because the notochord has reached a length of some millimetres by the time the metameric entpd5 expression domains start to be formed in a wave-like manner along the axis. Although the axis does continue to elongate during this interval, the velocity of the entpd5 expression wavefront is many times higher. To first approximation, growth of the domain is almost certainly not driving the patterning. An alternative approach might be to model a maturation gradient using a time-dependent change in the parameters. However, we argue that although this modification would also cause the wavefront to become robust to noise, it would involve a number of choices about the form of the hypothetical wavefront, about which we have no experimental data. In any case, it is important to point out that a no-noise initial condition as we use, or some form of trigger of the wavefront as suggested by the reviewer, can be viewed as alternative effective descriptions that produce sequential pattern formation. Although these are different in terms of the model structure and properties, in the absence of any experimental data, adding in a new structure is not parsimonious. We argue that pursuing this line of investigation is of great interest, particularly when new experimental evidence comes to light about the molecular details but is well beyond the scope of the current manuscript.

We appreciate the constructive criticism of the model, and indeed these comments have addressed potentially misleading ambiguities in our presentation. We have now included a more extensive discussion of initial conditions in the Materials and methods section, and the caveats or limits to the current description as well as potential approaches that could offer a way forward. We also refer to this explicitly in the Main Text in subsection “A reaction-diffusion model of axial patterning in the zebrafish”.

https://doi.org/10.7554/eLife.33843.043

Article and author information

Author details

  1. Laura Lleras Forero

    1. Institute for Cardiovascular Organogenesis and Regeneration, Faculty of Medicine, WWU Münster, Münster, Germany
    2. CiM Cluster of Excellence (EXC-1003-CiM), Münster, Germany
    3. Hubrecht Institute-KNAW & UMC Utrecht, Utrecht, Netherlands
    Contribution
    Conceptualization, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing
    Competing interests
    No competing interests declared
  2. Rachna Narayanan

    The Francis Crick Institute, London, United Kingdom
    Contribution
    Investigation, Writing—original draft, Writing—review and editing
    Competing interests
    No competing interests declared
  3. Leonie FA Huitema

    Hubrecht Institute-KNAW & UMC Utrecht, Utrecht, Netherlands
    Present address
    Sidney Kimmel Medical College at Thomas Jefferson University, Department of Dermatology and Cutaneous Biology, The Joan and Joel Rosenbloom Center for Fibrotic Diseases, Philadelphia, United States
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  4. Maaike VanBergen

    Institute for Cardiovascular Organogenesis and Regeneration, Faculty of Medicine, WWU Münster, Münster, Germany
    Present address
    Department of Laboratory Medicine, Laboratory of Hematology, Radboud University medical center, Nijmegen, Netherlands
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  5. Alexander Apschner

    Hubrecht Institute-KNAW & UMC Utrecht, Utrecht, Netherlands
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  6. Josi Peterson-Maduro

    Hubrecht Institute-KNAW & UMC Utrecht, Utrecht, Netherlands
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  7. Ive Logister

    Hubrecht Institute-KNAW & UMC Utrecht, Utrecht, Netherlands
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  8. Guillaume Valentin

    The Francis Crick Institute, London, United Kingdom
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  9. Luis G Morelli

    1. Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA), CONICET–Partner Institute of the Max Planck Society, Buenos Aires, Argentina
    2. Departamento de Fisica, FCEyN, UBA, Ciudad Universitaria, Buenos Aires, Argentina
    3. Department of Systemic Cell Biology, Max Planck Institute for Molecular Physiology, Dortmund, Germany
    Contribution
    Conceptualization, Data curation, Software, Funding acquisition, Validation, Writing—original draft, Writing—review and editing
    Contributed equally with
    Andrew C Oates and Stefan Schulte-Merker
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5614-073X
  10. Andrew C Oates

    1. The Francis Crick Institute, London, United Kingdom
    2. Department of Cell and Developmental Biology, University College London, London, United Kingdom
    3. Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
    Contribution
    Conceptualization, Software, Formal analysis, Funding acquisition, Methodology, Writing—original draft, Writing—review and editing
    Contributed equally with
    Luis G Morelli and Stefan Schulte-Merker
    For correspondence
    andrew.oates@epfl.ch
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-3015-3978
  11. Stefan Schulte-Merker

    Institute for Cardiovascular Organogenesis and Regeneration, Faculty of Medicine, WWU Münster, Münster, Germany
    Contribution
    Conceptualization, Funding acquisition, Writing—original draft, Project administration, Writing—review and editing
    Contributed equally with
    Luis G Morelli and Andrew C Oates
    For correspondence
    Stefan.Schulte-Merker@ukmuenster.de
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3617-8807

Funding

Deutsche Forschungsgemeinschaft (CIM1003)

  • Laura Lleras Forero
  • Stefan Schulte-Merker

Medical Research Council (MC_UP_1202/3)

  • Rachna Narayanan
  • Andrew C Oates

Francis Crick Institute

  • Rachna Narayanan
  • Andrew C Oates

Wellcome (WT098025MA)

  • Guillaume Valentin
  • Andrew C Oates

Fondo Para la Convergencia Estructural del MERCOSUR (COF 03/11)

  • Luis G Morelli

Agencia Nacional de Promoción Científica y Tecnológica (PICT 2012 1954)

  • Luis G Morelli

Agencia Nacional de Promoción Científica y Tecnológica (PICT 2013 1301)

  • Luis G Morelli

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank the Schulte-Merker and Oates groups for constructive discussions. The Institute of Biostatistics and Clinical Research University of Münster provided helpful insights, the IT-Zentrum Forschung und Lehre (WWU Münster) rendered IT support. Numerous technicians and part time students helped in genotyping and maintaining zebrafish lines. Prof. J den Hertog provided the her1, her7, tbx6, aei and bea mutant lines to SSM, Prof. K Kawakami the Sagff214:galFF strain. This study was also funded by The Francis Crick Institute, receiving its core funding from Cancer Research UK, the Medical Research Council, and Wellcome to RN and ACO. 

Ethics

Animal experimentation: Animal experiments were approved by the Animal Experimentation Committee (DEC) of the Royal Netherlands Academy of Arts and Sciences and by the UK Home Office under PPL 70/7675

Reviewing Editor

  1. Tanya T. Whitfield, University of Sheffield, United Kingdom

Publication history

  1. Received: November 25, 2017
  2. Accepted: April 4, 2018
  3. Accepted Manuscript published: April 6, 2018 (version 1)
  4. Version of Record published: May 21, 2018 (version 2)

Copyright

© 2018, Lleras Forero et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 1,950
    Page views
  • 340
    Downloads
  • 7
    Citations

Article citation count generated by polling the highest count across the following sources: Crossref, Scopus, PubMed Central.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)

  1. Further reading

Further reading

    1. Computational and Systems Biology
    2. Developmental Biology
    Inna Averbukh et al.
    Research Article
    1. Developmental Biology
    2. Physics of Living Systems
    Silas Boye Nissen et al.
    Research Article Updated