Genetics, Geometry and Evolution

遗传学、几何学和进化论

• 批准号: 0954398
• 负责人: Eric Siggia
• 金额: $ 72.99万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0954398&HistoricalAwards=false
• 关键词: Genetics; Geometry; Evolution

In this project the PI develops arguments for convergent evolution in gene networks based on simulation and bifurcation theory (or the geometric theory of differential equations). This requires defining a measure of fitness that the network optimizes and showing that mutation rates (which are unknown) to not bias the result. Darwin understood that complex organs such as the eye could evolve by continual small changes if all the intermediate steps increased the fitness. The same question will be posed for networks and answered computationally: what networks can be learned by gradient ascent (ie hill climbing). When evolution proceeds by hill climbing, the same local maxima are found irrespective of mutation rates. Generic fitness measures for embryonic patterning and the input-output response of signaling systems are suggested that may capture the phyla-wide properties of developmental networks. In situations where the network produces a static pattern, bifurcation theory enumerates the types of patterns that occur as parameters change continuously. Near the bifurcation point there are simple polynomial equations that collapse many physical variables into a few, and thus provide a description of the system with as few parameters as mathematics allows. Geometric models with fixed points, saddle points and sources may be an effective way to quantitatively model biological networks, and possibly evolution itself. A complementary experimental program will time cell divisions and other markers during embryonic development in the worm C.elegans to see if their fluctuations conform to geometric models. To see whether the structure of developmental signaling pathways can be understood from their input-output response, TGF-beta pathway in Xenopus will be probed with time and space dependent stimuli and time-lapsed imaged in sheets of embryonic cells. Students and postdocs will be engaged in research projects related to this proposal.

在这个项目中，PI 基于模拟和分岔理论（或微分方程的几何理论），提出了基因网络收敛进化的论据。这需要定义网络优化的适应度度量，并显示突变率（未知）不会使结果产生偏差。达尔文明白，如果所有中间步骤都增加了适应性，那么像眼睛这样的复杂器官就可以通过持续的微小变化而进化。同样的问题将针对网络提出并通过计算来回答：什么网络可以通过梯度上升（即爬山）来学习。当进化通过爬山进行时，无论突变率如何，都会发现相同的局部最大值。建议对胚胎模式和信号系统的输入输出响应进行通用适应性测量，以捕获发育网络的全门特性。在网络产生静态模式的情况下，分叉理论列举了参数连续变化时出现的模式类型。在分叉点附近有一些简单的多项式方程，可以将许多物理变量分解为几个，从而用数学允许的尽可能少的参数来描述系统。具有固定点、鞍点和源的几何模型可能是定量模拟生物网络甚至进化本身的有效方法。一项补充实验计划将对线虫胚胎发育过程中的细胞分裂和其他标记进行计时，以观察它们的波动是否符合几何模型。为了了解发育信号通路的结构是否可以从其输入输出响应中理解，我们将利用时间和空间依赖性刺激以及胚胎细胞片中的延时成像来探测非洲爪蟾的 TGF-β 通路。学生和博士后将从事与该提案相关的研究项目。