| Abstract | 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 system and realize synchronization. Under Delta-Notch system, however, a cell with a high expression of the segmentation clock gene tends to suppress the expression in its adjacent cells, which might produce spatial heterogeneity, instead of synchronized oscillation. Here we study the condition for pre-somitic mesoderm cells to show the synchronized oscillation of gene expression mathematically. We adopt a model which considers kinetics of mRNA and proteins of segmentation clock gene and cell-cell interaction by Delta-Notch system explicitly. From statistical study of the model with randomly generated parameters, we conclude that synchronized oscillation tends to be stable when reactions included in the intracellular negative feedback loop of her gene are fast and when reactions included in the intercellular interaction are slow. Further we discuss mechanisms for cells to achieve synchronization in a sufficiently short time. |
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