Zeiser Stefan, Liebscher H Volkmar, Tiedemann Hendrik, Rubio-Aliaga Isabel, Przemeck Gerhard K H, de Angelis Martin Hrabé, Winkler Gerhard
Institute of Biomathematics and Biometry, GSF-National Research Centre for Environment and Health, Ingolstädter Landstrasse 1, D-85764 Neuherberg, Germany.
Theor Biol Med Model. 2006 Feb 23;3:11. doi: 10.1186/1742-4682-3-11.
It is commonly accepted that embryonic segmentation of vertebrates is regulated by a segmentation clock, which is induced by the cycling genes Hes1 and Hes7. Their products form dimers that bind to the regulatory regions and thereby repress the transcription of their own encoding genes. An increase of the half-life of Hes7 protein causes irregular somite formation. This was shown in recent experiments by Hirata et al. In the same work, numerical simulations from a delay differential equations model, originally invented by Lewis, gave additional support. For a longer half-life of the Hes7 protein, these simulations exhibited strongly damped oscillations with, after few periods, severely attenuated the amplitudes. In these simulations, the Hill coefficient, a crucial model parameter, was set to 2 indicating that Hes7 has only one binding site in its promoter. On the other hand, Bessho et al. established three regulatory elements in the promoter region.
We show that--with the same half life--the delay system is highly sensitive to changes in the Hill coefficient. A small increase changes the qualitative behaviour of the solutions drastically. There is sustained oscillation and hence the model can no longer explain the disruption of the segmentation clock. On the other hand, the Hill coefficient is correlated with the number of active binding sites, and with the way in which dimers bind to them. In this paper, we adopt response functions in order to estimate Hill coefficients for a variable number of active binding sites. It turns out that three active transcription factor binding sites increase the Hill coefficient by at least 20% as compared to one single active site.
Our findings lead to the following crucial dichotomy: either Hirata's model is correct for the Hes7 oscillator, in which case at most two binding sites are active in its promoter region; or at least three binding sites are active, in which case Hirata's delay system does not explain the experimental results. Recent experiments by Chen et al. seem to support the former hypothesis, but the discussion is still open.
脊椎动物胚胎的体节分割通常被认为受分割时钟调控,该时钟由循环基因Hes1和Hes7诱导产生。它们的产物形成二聚体,与调控区域结合,从而抑制自身编码基因的转录。Hes7蛋白半衰期的增加会导致体节形成不规则。这在平田等人最近的实验中得到了证实。在同一研究中,最初由刘易斯提出的延迟微分方程模型的数值模拟提供了额外支持。对于Hes7蛋白更长的半衰期,这些模拟显示出强烈衰减的振荡,经过几个周期后,振幅严重衰减。在这些模拟中,关键模型参数希尔系数被设定为2,这表明Hes7在其启动子中只有一个结合位点。另一方面, Bessho等人在启动子区域确定了三个调控元件。
我们表明,在半衰期相同的情况下,延迟系统对希尔系数的变化高度敏感。小幅增加会极大地改变解的定性行为。会出现持续振荡,因此该模型无法再解释分割时钟的中断。另一方面,希尔系数与活性结合位点的数量以及二聚体与它们的结合方式相关。在本文中,我们采用响应函数来估计不同数量活性结合位点的希尔系数。结果表明,与单个活性位点相比,三个活性转录因子结合位点可使希尔系数至少增加20%。
我们的研究结果导致了以下关键的二分法:要么平田的模型适用于Hes7振荡器,在这种情况下,其启动子区域中最多有两个结合位点是活跃的;要么至少有三个结合位点是活跃的,在这种情况下,平田的延迟系统无法解释实验结果。陈等人最近的实验似乎支持前一种假设,但讨论仍在进行中。