Stochastic perturbations

Similar random perturbations were applied during simulations of the Lunatic fringe secretion model, and of the model given by J. Lewis as supplemental data to the article by Palmeirim et al. (1997), which considers cell-autonomous oscillations (see Appendix D for simulation details). Results are shown in Figures 6 to 8 (see Movies 3 and 4 for a complete time-animation). With the Lunatic fringe secretion model, the overall pattern is totally preserved; some variations of expression intensity can be observed in the caudal PSM, but the different phases of oscillation can still be sharply distinguished (Figures 7 and 8). In the case of the cell-autonomous model (Figure 6), stripes of expression corresponding to already-segmented somites are discernable, but levels of Lunatic fringe are extremely heterogeneous in unsegmented PSM.

The model is also robust against parameter variations, as discussed in section B.

**Figure 6:** Simulation of the cell-autonomous model proposed by Palmeirim et al. (1997), with random perturbations in the phase of each cell. A pattern in unsegmented PSM is barely discernable. Abscissae correspond to cell number in the PSM (anterior is to the left, posterior to the right), and ordinates to L-Fringe expression levels (in arbitrary units). The model was originally proposed for c-hairy1 oscillations, but L-Fringe oscillates with the same pattern.
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**Figure 7:** Phase 1 in the Lunatic fringe secretion model, with random perturbations: the pattern is still very similar to that shown in Figure 2. Abscissae correspond to cell number in the PSM (anterior is to the left, posterior to the right), and ordinates to L-fringe expression levels (in arbitrary units).
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**Figure 8:** Phase 2 in the Lunatic fringe secretion model, with random perturbations: the pattern is still very similar to that shown in Figure 3. Abscissae correspond to cell number in the PSM (anterior is to the left, posterior to the right), and ordinates to L-fringe expression levels (in arbitrary units).
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**Movie 3:** Simulation of the cell-autonomous model, with random perturbations. The pattern is disrupted.
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**Movie 4:** Simulation of the L-fng secretion model, with random perturbations. The disruption is minimal.
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