Synchronized oscillation of the segmentation clock gene in vertebrate development

In vertebrate somitogenesis, "segmentation clock" genes (her in zebrafish, hes in mouse, and hairy in chick) show oscillation, synchronized over nearby cells through intercellular interaction. In zebrafish, neighboring cells interact by Delta-Notch signaling to realize synchronization. Under Delta-Notch, however, a cell with a high expression of the segmentation clock gene tends to suppress its expression in adjacent cells, which might produce spatial heterogeneity instead of synchronized oscillation. Here we studied the conditions under which pre-somitic mesoderm cells show synchronized oscillation of gene expression mathematically. We adopted a model that explicitly considers the kinetics of the mRNA and proteins of the segmentation clock gene and cell-cell interaction via Delta-Notch signaling. From statistical study of a model with randomly generated parameters, we revealed how the likelihood that the system generates stable synchronized oscillation depends on the rate of each reaction in the gene-protein kinetics.