Geometry, Genetics and Development

发育生物学取得了巨大的成功，将受精卵对胎儿和成年人看似神奇的自组织减少到了一系列基因及其在非编码基因组中的调节指令。但了解这些部分(基本上是所有基因)与了解它们的自组织能力并不相称。因此，我们需要从简约论走向积分，物理学，特别是凝聚态和统计物理学，在对自然的现象学描述方面有着悠久而成功的历史，但仍然是定量的。干细胞技术使人们能够从细胞中构建胚胎，从而测试自己的理解力。新的成像模式和遗传干预提供了对简单模式生物体的早期发育步骤进行重新编程并量化结果的手段。发育是关于细胞的形态发生和作为时间函数的逐渐特化。动力学的自然数学语言是几何，其核心思想是在20世纪形成的。这项工作的要素为开发提供了数学上严格的景观类比，使得能够进行非常紧凑的现象学描述，可以适合数据。PI之前的工作已经展示了简单地将干细胞限制在二维空间如何引发它们的自组织潜力，这是令人惊讶的复杂的，并使用与胚胎相同的细胞通信系统。这个项目将利用合成系统和几何方法的简单性来量化哺乳动物中负责自组织的遗传系统。理解线虫最近的实验需要类似的数学机制，这些实验使用RNA干扰来重新编程胚胎中的创始细胞以适应新的命运。这些新的命运如何适应他们的异位环境，为胚胎如何自组织和服从现象学治疗提供了一个强大的可量化的约束。PI将继续研究导致人类亨廷顿病的确切突变，这种突变在微模式上分化的干细胞中具有戏剧性的表型。沃丁顿的情况是经常被引用的发展的隐喻，特别是在讨论干细胞时。斯梅尔的一个定理似乎适用于沃丁顿设想的基因调控网络，并证明了这样的系统可以用黎曼流形上的势流来表示。PI将在几个示例中显示此表示的实用性。与基因调控网络的标准Michaelis-Menten表示相比，它提供了一种紧凑的函数形式，可以用数据挑战这种直觉，从而减少了基本自由度所在的维度，而基因调控网络的标准Michaelis-Menten表示通常具有比它们所描述的吸引子的维度多得多的变量。PI在干细胞和线虫开发方面的实验合作将提供将这些理论陈述应用于数据的手段。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Developmental biology has been immensely successful in reducing the seeming miraculous self-organization of a fertilized egg to a fetus and adult to a list of genes and the instructions for their regulation in the noncoding genome. But knowing the parts (essentially all genes) is not commensurate with understanding their capacity to self-organize. Thus, we need to move from reductionism to integration, and physics, particularly condensed matter and statistical physics, has a long and successful history in phenomenological but still quantitative descriptions of Nature. Stem cell technologies allow one to build embryos from cells and thus test one's understanding. New imaging modalities and genetic interventions provide the means to reprogram the earliest steps of development in simple model organisms and quantify the outcomes. Development is about morphogenesis and the progressive specialization of cells as a function of time. The natural mathematical language for dynamics is geometric and the key ideas were formulated in the 20th century. Elements of that work provide a mathematically rigorous landscape analogy to development that enables a very compact phenomenological description that can be fit to data. Prior work by the PI has shown how simply confining stem cells in two dimensions elicits their potential for self-organization, which is surprisingly complex and employs the same cellular communications systems as in the embryo. This project will use the simplicity of synthetic systems and geometrical methods to quantify the genetic systems responsible for self-organization in mammals. Similar mathematical machinery is required to understand recent experiments in the nematode C. elegans that uses RNA interference to reprogram the founder cells in the embryo to new fates. How these new fates accommodate to their ectopic environment provide a strong quantifiable constraint on how the embryo self-organizes and are amenable to phenomenological treatments. The PI will continue to study the exact mutation that leads to Huntington disease in humans, which has a dramatic phenotype in stem cells differentiated on micropatterns.The Waddington landscape is an oft-cited metaphor for development, particularly when discussing stem cells. A theorem of Smale, plausibly applies to the gene regulatory networks as imagined by Waddington and proves that such systems can be represented by potential flow on a Riemannian manifold. The PI will show the utility of this representation in several examples. It is the only general way to implement our intuition that developmental ‘decisions’ take place in a low dimensional space, and it provides a compact functional form with which to challenge that intuition with data, thus reducing the number of dimensions in which the essential degrees of freedom reside, compared to the standard Michaelis-Menten representations of gene regulatory networks, which typically have many more variables than the dimension of the attractor they describe. The PI's experimental collaborations in stem cells and C.elegans development will provide the means to apply these theoretical representations to data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.