A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.
A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.
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DOI：
10.1371/journal.pone.0016980
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发表时间：
2011-02-28
期刊：
影响因子：
3.7
通讯作者：
Chaplain MA
中科院分区：
文献类型：
--
作者：
Terry AJ;Sturrock M;Dale JK;Maroto M;Chaplain MA
在脊椎动物的胚胎中，被称为体节的组织块以头到尾的顺序排列，这一过程被称为体节发生。对体节发生的研究既有实验性的，也有数学性的。对于斑马鱼，有实验证据表明，振荡基因表达的细胞中的preomitic中胚层（PSM），以及证据表明，Notch信号同步的振荡在相邻的PSM细胞。以前有人提出了一种生物学机制来解释这些现象。在这里，我们已经转换成一个数学模型的偏微分方程中的蛋白质和mRNA分子的细胞核和细胞质的扩散被明确认为是这种机制。通过进行模拟，我们发现了模型参数（如扩散和降解速率）的值范围，这些参数在PSM细胞内产生振荡动力学，并使Notch信号能够同步两个接触细胞中的振荡。我们的模型包含希尔系数，该系数测量两种蛋白质（Her1，Her7）和它们抑制的三种基因（her1，her7，deltaC）之间的协同性。这个系数似乎是有界的个别细胞中的振荡的要求和同步的要求以上。与实验数据和以前的空间非明确的数学模型相一致，我们已经发现，信号可以增加Her1蛋白的平均水平。生物模式的形成将是不可能的，如果没有一定的鲁棒性变化的细胞形状和大小;我们的结果具有这样的鲁棒性。我们的空间明确的建模方法，加上新的成像技术，可以测量细胞内蛋白质扩散速率，可能会产生显着的新见解体节发生和其他生物过程。
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 experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.
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