[POS] Developmental Biology

[POS-09] Mathematical Analysis of Somite Size Scaling

*Yuki Tezuka¹, Koichiro Uriu¹ (1. Institute of Science Tokyo (Japan))

Keywords:

clock and wavefront,segmentation clock,pattern formation

The segmented body plan of vertebrate originates from somites that are formed during embryonic development. Somites bud off from the anterior part of the presomitic mesoderm (PSM) rhythmically. The period of somite formation is determined by the oscillatory gene expression in PSM cells, known as the segmentation clock. In zebrafish, the ERK activity forms an anterior-posterior gradient where its activity is higher in the posterior PSM. The distance that this ERK gradient shifts posteriorly within one cycle of the segmentation clock corresponds to somite size. Importantly, somite size is positively correlated with embryo size—a phenomenon referred to as scaling, thereby, a larger embryo forms larger somites, preserving body proportions. Although it has been proposed that somite size scaling arises from the scaling of the ERK gradient with respect to the PSM length, the underlying mechanism remains unclear. Here we investigate the mechanism of somite size scaling by using a mathematical model based on reaction-diffusion equations. ERK is activated by fibroblast growth factor (FGF) signaling which is higher in the posterior PSM and decreases toward anterior. Our model includes ERK autophosphorylation and its dephosphorylation through the action of the segmentation clock. Furthermore, based on a previous experimental result, we assume an ERK inhibitor that is secreted from formed somites. We show that ERK autophosphorylation causes bistability where high and low ERK activity states coexist stably. The ERK activity gradient undergoes stepwise posterior shifts when the segmentation clock activity increases, as observed in zebrafish embryos. In this model, we find a positive linear correlation between somite size and PSM length in numerical simulations. Then, we obtain the linear relationship analytically and reveal that the slope is determined by the ratio of the decay lengths of the FGF and ERK inhibitor gradients. In contrast, if ERK phosphorylation is not regulated by the inhibitor secreted from formed somites, somite size is not scaled to the PSM length. Our results suggest that the secretion of an ERK inhibitor from somites plays an important role in somite size scaling.