Genetics, Geometry and Evolution

在这个项目中，PI开发了基于模拟和分岔理论（或微分方程的几何理论）的基因网络收敛进化的论据。这需要定义一个网络优化的适应度度量，并显示突变率（未知）不会影响结果。达尔文明白，像眼睛这样的复杂器官可以通过不断的微小变化来进化，如果所有的中间步骤都增加了适应性。同样的问题也会出现在网络上，并通过计算得到答案：通过梯度上升（即爬山）可以学习到什么网络。当进化以爬坡的方式进行时，无论突变率如何，都能找到相同的局部最大值。胚胎模式和信号系统的输入-输出响应的通用适应度测量被认为可能捕获发育网络的门范围特性。在网络产生静态模式的情况下，分岔理论列举了随着参数不断变化而出现的模式类型。在分岔点附近有一些简单的多项式方程，这些方程将许多物理变量分解为几个，从而提供了数学允许的尽可能少的参数对系统的描述。具有不动点、鞍点和源的几何模型可能是定量模拟生物网络，甚至可能是进化本身的有效方法。一个补充的实验项目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它们的输入-输出反应中理解，我们将通过时间和空间依赖刺激和胚胎细胞片的延时成像来探索非洲爪蟾的tgf - β通路。学生和博士后将从事与本提案相关的研究项目。

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.