Figure 1.
Model of the Interactions between Her Proteins in the Zebrafish Network Driving Somitogenesis Oscillations
Her1, Her7, and Her13.2 (abbreviated to Her13) can form heterodimers, and Her1 and Her7 can also form homodimers. Each dimer species competes to set the level of repression of her1, her7, and deltaC to a specific level. (This is inspired by the experimental result that a combination of Her1 and Her13.2 leads to more potent repression than Her1 alone.) Intercellular communication occurs through DeltaC-Notch signaling, which enhances her1, her7, and deltaC transcription. her13.2 mRNA is expressed in a posterior–anterior gradient in the PSM.
Table 1.
Ranges from Which Parameters Were Selected at Random for Numerical Simulations
Figure 2.
Numerical Simulations of the Model Sketched in Figure 1, without DeltaC (See Table 1 for Values of Parameters)
Overlay of deterministic and stochastic simulation results (A) and deterministic simulation results with various simulated knockdowns (B).
Figure 3.
Deterministic Simulations of a Chain of Oscillators Corresponding to the Model Sketched in Figure 1 (See Table 1 for Values of Parameters)
Waves of expression spread from posterior to anterior PSM (A–C), as observed experimentally. To test the effect of oscillator-coupling through DeltaC-Notch signaling, a perturbation was induced by delaying a number of oscillators in the chain by 5 min (D). After 1.3 h, the resulting perturbations in the spatial pattern were reduced (E); note that cells corresponding to indexes smaller than 13 on the x-axis should show no perturbation, because they were added to the chain after the initial perturbation.
Figure 4.
Stochastic Simulations of a Chain of Oscillators Corresponding to the Model Sketched in Figure 1, with Normal Coupling through Delta-Notch Signaling (A–C) and with Disrupted Coupling (D–F)
When coupling was absent, some cells were noticeably out of synchrony with their neighbors (arrowheads), and local synchrony was not as strong. The transcription rate of her1 and her7 was increased in (D–F) to make up for the loss of Notch signaling.
Figure 5.
Simulated Translation Knockdown of her1 (A), her7 (B), and Combined her1 and her7 (C)
For single knockdowns, residual oscillations of diminished relative amplitude were observed, and stripe formation in anterior PSM was disrupted. For the combined knockdown, her1 and her7 were upregulated and did not oscillate in posterior PSM, but did oscillate in a salt-and-pepper pattern in anterior PSM.
Figure 6.
Simulated Grafting of an FGF-8 Coated Bead (Star)
her13.2 mRNA was assumed to be ectopically expressed, at the same level as in posterior PSM, in an area centered around the bead and marked by arrows.