Applied Mathematics Department, University of Granada, Granada, Spain.
Excellence Research Unit "Modeling Nature" (MNat), University of Granada, Granada, Spain.
PLoS One. 2019 Jan 7;14(1):e0209349. doi: 10.1371/journal.pone.0209349. eCollection 2019.
This work provides theoretical tools to analyse the transcriptional effects of certain biochemical mechanisms (i.e. affinity and cooperativity) that have been proposed in previous literature to explain the proper spatial expression of Hedgehog target genes involved in Drosophila development. Specifically we have focused on the expression of decapentaplegic, wingless, stripe and patched. The transcription of these genes is believed to be controlled by enhancer modules able to interpret opposing gradients of the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach, which provides expression rates for these genes. These expression rates are controlled by transcription factors which are competing and cooperating for common binding sites. We have made mathematical representations of the different expression rates which depend on multiple factors and variables. The expressions obtained with the model have been refined to produce simpler equivalent formulae which allow for their mathematical analysis. Thanks to this, we can evaluate the correlation between the different interactions involved in transcription and the biological features observed at tissular level. These mathematical models can be applied to other morphogenes to help understand the complex transcriptional logic of opposing activator and repressor gradients.
这项工作提供了理论工具来分析某些生化机制（即亲和力和协同作用）的转录效应，这些机制在前文献中被提出，以解释参与果蝇发育的 Hedgehog 靶基因的适当空间表达。具体来说，我们专注于 decapentaplegic、wingless、stripe 和 patched 的表达。这些基因的转录被认为是由增强子模块控制的，这些模块能够解释转录因子 Cubitus interruptus（Ci）的激活和抑制形式的相反梯度。本研究基于热力学方法，为这些基因提供表达率。这些表达率受竞争和合作的转录因子控制，这些转录因子争夺共同的结合位点。我们对不同的表达率进行了数学表示，这些表达率取决于多个因素和变量。通过模型获得的表达式经过改进，生成更简单的等效公式，以便进行数学分析。有了这些，我们可以评估转录过程中涉及的不同相互作用与组织水平上观察到的生物学特征之间的相关性。这些数学模型可以应用于其他形态发生素来帮助理解对抗激活剂和抑制剂梯度的复杂转录逻辑。
