Hopf bifurcation in the presomitic mesoderm during the mouse segmentation

Abstract

Vertebrae and ribs arise from embryonic tissues called somites. Somites arise sequentially from the unsegmented embryo tail, called presomitic mesoderm (PSM). The pace of somite formation is controlled by gene products such as hairy and enhancer of split 7 (Hes7) whose expression oscillates in the PSM. In addition to the cyclic genes, there is a gradient of fibroblast growth factor 8 (Fgf8) mRNA from posterior to anterior PSM. Recent experiments have shown that in the absence of Fgf signaling, Hes7 oscillations in the anterior and posterior PSM are lost. On the other hand, Notch mutants reduce the amplitude of posterior Hes7 oscillations and abolish anterior Hes7 oscillations. To understand these phenotypes, we delineated and simulated a logical and a delay differential equation (DDE) model with similar network topology in wild-type and mutant situations. Both models reproduced most wild-type and mutant phenotypes suggesting that the chosen topology is robust to explain these phenotypes. Numerical continuation of the model showed that even in the wild-type situation, the system changed from sustained to damped, i.e. a Hopf bifurcation occurred, when the Fgf concentration decreased in the PSM. This numerical continuation analysis further indicated that the most sensitive parameters for the oscillations are the parameters of Hes7 followed by those of Lunatic fringe (Lfng) and Notch1. In the wild-type, the damping of Hes7 oscillations was not so strong so that cells reached the new somites before they lose Hes7 oscillations. By contrast, in the fibroblast growth factor receptor 1 (Fgfr1) conditional knock-out (cKO) mutant simulation, Notch signaling was not able to maintain sustained Hes7 oscillations. Our analysis suggests that Fgf signaling makes cells enter an oscillatory state of Hes7 expression. After moving to the anterior PSM, where Fgf signaling is missing, Notch signaling compensates the damping of Hes7 oscillations in the anterior PSM.