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RESEARCH ARTICLE
Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves
Ahmet Ay, Jack Holland, Adriana Sperlea, Gnanapackiam Sheela Devakanmalai, Stephan Knierer, Sebastian Sangervasi, Angel Stevenson, Ertuğrul M. Özbudak
Development 2014 141: 4158-4167; doi: 10.1242/dev.111930
Ahmet Ay
1Department of Mathematics, Colgate University, Hamilton, NY 13346, USA
2Department of Biology, Colgate University, Hamilton, NY 13346, USA
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  • For correspondence: aay@colgate.edu ertugrul.ozbudak@einstein.yu.edu
Jack Holland
3Department of Computer Science, Colgate University, Hamilton, NY 13346, USA
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Adriana Sperlea
3Department of Computer Science, Colgate University, Hamilton, NY 13346, USA
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Gnanapackiam Sheela Devakanmalai
4Department of Genetics, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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Stephan Knierer
4Department of Genetics, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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Sebastian Sangervasi
1Department of Mathematics, Colgate University, Hamilton, NY 13346, USA
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Angel Stevenson
4Department of Genetics, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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Ertuğrul M. Özbudak
4Department of Genetics, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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  • For correspondence: aay@colgate.edu ertugrul.ozbudak@einstein.yu.edu
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    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.

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    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.

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    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.

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    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.

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    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).

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    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).

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Keywords

  • Segmentation clock
  • Oscillation
  • Traveling wave
  • Systems biology
  • Computational modeling
  • Gene expression

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RESEARCH ARTICLE
Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves
Ahmet Ay, Jack Holland, Adriana Sperlea, Gnanapackiam Sheela Devakanmalai, Stephan Knierer, Sebastian Sangervasi, Angel Stevenson, Ertuğrul M. Özbudak
Development 2014 141: 4158-4167; doi: 10.1242/dev.111930
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RESEARCH ARTICLE
Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves
Ahmet Ay, Jack Holland, Adriana Sperlea, Gnanapackiam Sheela Devakanmalai, Stephan Knierer, Sebastian Sangervasi, Angel Stevenson, Ertuğrul M. Özbudak
Development 2014 141: 4158-4167; doi: 10.1242/dev.111930

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