Spatial Bistability Generates <em>hunchback</em> Expression Sharpness in the <em>Drosophila</em> Embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information.在胚胎发育过程中，母源因子（maternal factors）浓度梯度所提供的位置信息，通过为基因表达提供空间依赖性的调控信号，指导胚胎的模式形成（pattern formation）。在黑腹果蝇（Drosophila melanogaster）中，该调控过程的经典范例为：胚胎中部的驼背基因（hunchback, hb）可响应平滑的前后轴Bicoid蛋白（Bcd）浓度梯度的局部浓度，呈现出鲜明的“开-关”式激活。hb基因的调控区域既包含多个Bcd蛋白结合位点，也包含多个Hb蛋白结合位点。既往多项研究曾提出，仅Bcd即可实现hb基因表达的精准锐化，但另有实验证据表明，其表达调控还需额外的调控机制参与。本研究通过实验量化了四类果蝇的hb基因表达动态：分别为野生型（wild-type）果蝇、携带hb自我调控突变或Bcd结合位点突变的果蝇，以及搭载由6个Bcd结合位点与2个Hb结合位点组成的人工启动子构建体（artificial promoter construct）的果蝇。除上述实验外，本研究还构建了包含Bcd协同结合（cooperative binding）与hb自我调控的hb基因转录反应-扩散模型（reaction-diffusion model），并通过零本征值分析（Zero Eigenvalue Analysis）探究了该反应网络中的多重平稳态（stationary state）。该模型能够复现hb基因的发育动态，并准确预测各类突变体的表达模式。模型分析结果表明，hb表达的锐化效应可通过空间双稳态（spatial bistability）实现：其中hb的自我调控会产生两种稳定的表达水平。当缺乏自我调控时，双稳态现象会消失，hb表达的锐化效应也会被破坏。Bcd的协同结合仅会影响双稳态发生的位置，但其本身并不足以形成锐化的hb表达模式。本研究结果显示，hb表达的锐化与位置定位分别由hb自我调控与Bcd协同结合介导，二者为可独立调控的独立过程。本模型与不同实验中观测到的hb表达位置与锐化程度的变化均相符，为理解相关实验数据提供了理论框架，尤其表明空间双稳态在位置信息的阈值依赖型读取机制中发挥核心作用。