Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves

Abstract

The vertebrate segmentation clock is a gene expression oscillator controlling rhythmic segmentation of the vertebral column during embryonic development. The period of oscillations becomes longer as cells are displaced along the posterior to anterior axis, which results in traveling waves of clock gene expression sweeping in the unsegmented tissue. Although various hypotheses necessitating the inclusion of additional regulatory genes into the core clock network at different spatial locations have been proposed, the mechanism underlying traveling waves has remained elusive. Here, we combined molecular-level computational modeling and quantitative experimentation to solve this puzzle. Our model predicts the existence of an increasing gradient of gene expression time delays along the posterior to anterior direction to recapitulate spatiotemporal profiles of the traveling segmentation clock waves in different genetic backgrounds in zebrafish. We validated this prediction by measuring an increased time delay of oscillatory Her1 protein production along the unsegmented tissue. Our results refuted the need for spatial expansion of the core feedback loop to explain the occurrence of traveling waves. Spatial regulation of gene expression time delays is a novel way of creating dynamic patterns; this is the first report demonstrating such a control mechanism in any tissue and future investigations will explore the presence of analogous examples in other biological systems.

Keywords: Computational modeling; Gene expression; Oscillation; Segmentation clock; Systems biology; Traveling wave.

Fig. 1.

The traveling segmentation clock waves. (A) In one oscillation cycle, the expression profiles (purple corresponds to higher levels of her1 mRNA) return back to the original phase, and one somite segments at the anterior end of the PSM. Oscillations of neighboring cells are locally synchronized by Notch signaling. (B) The regulatory interactions in the zebrafish segmentation clock network. Her1, Her7 and Hes6 proteins can form homo- and heterodimers. However, only the Her1-Her1 homodimer and the Her7-Hes6 heterodimer repress transcription of her1, her7 and deltaC. Notch signaling activates transcription of her1 and her7.

Fig. 2.

Sensitivity analysis. (A) The period of the segmentation clock is sensitive to eight model parameters: transcriptional time delays of deltaC (delaymd), her1 (delaymh₁) and her7 (delaymh₇); translational time delays of DeltaC (delaypd) and Her1 (delayph₁); and degradation rates of her1 (mdh₁), her7 (mdh₇) and Her1-Her1 (ddgh₁h₁). (B) Eight sensitive parameters are used to create ten parameter groups to be varied from posterior to anterior. The gradients of six out of ten parameter groups resulted in similar period behavior to previously measured oscillation period data (Giudicelli et al., 2007). The distributions of successful numbers of parameter sets (out of 165 tested) for varying gradients are shown. Triple transcriptional and translational time delays lead to the highest frequency of parameter sets satisfying the period condition.

Fig. 3.

her1 mRNA levels in the whole PSM in different genetic backgrounds under the influence of a Her1-Her7-DeltaC translational time delay gradient. (A) Snapshots of 6×50 cells located along the PSM in different genetic backgrounds. Images are obtained by setting an increasing gradient to the translational time delay of Her1, Her7 and DeltaC proteins. Traveling waves are readily generated under these conditions. Darker color corresponds to higher levels of her1 mRNA. (B) her1 mRNA levels in six cells for the 300 min have been plotted as they travel from the posterior to anterior PSM in different genetic backgrounds. Period and amplitude increase in all genetic backgrounds. Early arrest of oscillations in the her1^−/− mutant and loss of synchronization in her7^−/− and notch1a^−/− mutants are observed.

Fig. 4.

Spatial profiling of period, amplitude and synchronization scores along the PSM in all genetic backgrounds under the influence of a Her1-Her7-DeltaC translational time delay gradient. (A,B) The period (A) and amplitude (B) of oscillations are increased as cells traverse from the posterior to the anterior PSM in all genetic backgrounds. (C) The oscillations are locally synchronized in wild type, her1^−/−, hes6^−/− and her7^−/−;hes6^−/− mutants. The synchrony is lost in her7^−/− and notch1a^−/− mutants; however, the synchrony in her7^−/− mutants is increased in the anterior PSM. (A-C) x-axis corresponds to spatial location in the PSM; y-axis corresponds to the period, amplitude or synchrony score, which are normalized to corresponding wild-type values in the posterior PSM.

Fig. 5.

Density plots of traveling waves in all genetic backgrounds under the influence of a Her1-Her7-DeltaC translational time delay gradient. (A-F) Traveling waves are observed in wild-type, her1^−/−, hes6^−/− and her7^−/−;hes6^−/− but are blurred in her7^−/− and notch1a^−/− embryos. The oscillations in her1^−/− mutants arrest at more posterior locations. The x-axis reflects time (min) and the y-axis maps spatial locations in the PSM (posterior is top and anterior is bottom).

Fig. 6.

Effective Her1 translational time delay increases in the anterior PSM. (A-C) Fluorescent in situ hybridization of Tg(her1:her1-Venus) transgenic embryos with a Venus antisense probe (A), immunohistochemistry against Venus protein (B) and merge of RNA and protein staining with DAPI counterstaining (blue) (C). (D) Spatial profiles of RNA (green) and protein (red) levels from A-C. Solid lines are smoothed profiles. The short arrow indicates d (spatial interval) and the long arrow indicates S (spatial wavelength). (E) Effective Her1 protein production time delay is plotted along normalized PSM length. The measurements are made from intermediate to anterior PSM. The data are binned at equal spatial distances and the mean (±s.e.m.) is plotted along the axis. (F) The number of parameter sets (out of the 165 robust parameter sets satisfying posterior PSM experimental conditions) that reproduce period elongation in the tissue as the effective protein production time delay for Her proteins increases at different times (DeltaC protein production time delay is set to a 2.5-fold increase along the full PSM).