Geometry, Genetics and Development

发育生物学已经非常成功地将受精卵到胎儿和成人的看似神奇的自我组织简化为一系列基因及其在非编码基因组中的调节指令。但是，了解这些部分（基本上是所有基因）与了解它们的自我组织能力是不相称的。因此，我们需要从还原论转向整合，而物理学，特别是凝聚态物理和统计物理学，在现象学上有着悠久而成功的历史，但仍然是对自然的定量描述。干细胞技术允许人们从细胞中构建胚胎，从而测试人们的理解力。新的成像模式和遗传干预提供了重新编程简单模式生物发展的早期步骤和量化结果的手段。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的，关键思想是在20世纪形成的。这项工作的要素为发展提供了一个数学上严谨的景观类比，使非常紧凑的现象学描述能够适合于数据。PI先前的工作已经表明，简单地将干细胞限制在二维空间中是如何激发它们自组织的潜力的，这是令人惊讶的复杂，并使用与胚胎中相同的细胞通信系统。这个项目将使用合成系统的简单性和几何方法来量化哺乳动物自组织的遗传系统。我们需要类似的数学机制来理解最近在秀丽隐杆线虫（C. elegans）中进行的实验，该实验利用RNA干扰对胚胎中的初始细胞进行重新编程，使其获得新的命运。这些新的命运如何适应它们的异位环境，为胚胎如何自我组织和适应现象学治疗提供了强有力的可量化约束。PI将继续研究导致人类亨廷顿病的确切突变，这种疾病在微模式分化的干细胞中具有戏剧性的表型。沃丁顿景观是一个经常被引用的发展比喻，特别是在讨论干细胞时。Smale定理似乎适用于Waddington所设想的基因调控网络，并证明了这种系统可以用黎曼流形上的势流来表示。PI将在几个示例中展示这种表示的效用。这是实现我们的直觉的唯一一般方法，即发展“决定”发生在低维空间中，它提供了一个紧凑的功能形式，用数据挑战直觉，从而减少了基本自由度所在的维度数量，与标准的Michaelis-Menten基因调控网络表示相比，后者通常具有比它们描述的吸引子维度更多的变量。PI在干细胞和秀丽隐杆线虫发展方面的实验合作将提供将这些理论表示应用于数据的手段。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.