a spatio-temporal model of notch signalling in the zebrafish segmentation clock conditions for synchronised oscillatory dynamics斑马鱼notch信号的时空模型分割时钟同步振荡动力学条件.pdfVIP

A Spatio-Temporal Model of Notch Signalling in the Zebrafish Segmentation Clock: Conditions for Synchronised Oscillatory Dynamics 1 1 2 2 1 Alan J. Terry *, Marc Sturrock , J. Kim Dale , Miguel Maroto , Mark A. J. Chaplain 1 Division of Mathematics, University of Dundee, Dundee, United Kingdom, 2 Division of Cell and Developmental Biology, University of Dundee, Dundee, United Kingdom Abstract In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explictly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimen