CRCNS Research Proposal:Topological and Dynamical Structures of Brain Development and Sexual-Dimorphism in C. Elegans

神经系统的发展，特别是神经元的动态发展和连接，以建立大脑结构及其在紧急大脑活动中的建设性作用，构成了生命系统中一个无法解释的中心现象。对发育中的大脑的研究需要对不同年龄的生物体的大脑进行全面和系统的表征，以及一个合适的数学框架，能够捕捉到生长中的神经系统的结构及其中新兴的网络。我们建议通过开发这样一个数学框架来解决这一根本性的挑战，该框架能够描述活体大脑中潜在的网络变化及其对功能性神经活动和由此产生的行为的影响。这个数学框架将被应用于分析完整的神经系统，在单细胞精度，模式生物秀丽隐杆线虫。为了应对这些重要的挑战，我们组建了一个跨学科的团队，他们在拓扑学、计算生物学、统计学、理论物理学、神经科学和模式生物生物学方面具有专业知识。我们的团队将开发新的数学、统计和计算工具来描述发展中的大脑网络的结构。这种分析将揭示神经系统发展和功能的共享组织、涌现原则。基于生物数据作为复杂网络的广泛表示，以及我们将开发的数学、统计和计算方法的普遍性，我们期望在原始系统之外具有广泛的适用性。上述方法将由旨在提供发展中的网络及其对全脑活动的功能后果的多种观点的实验来主导。我们将从两个层面分析大脑：由于广泛的神经添加和连接神经（重新）连接而导致的底层网络的变化。我们将比较两个过渡时期的发育网络：从第一幼虫期到第二幼虫期的早期成熟，以及后来两种不同性别的成熟。在这两个发育阶段，新生的神经元都大大增加了现有大脑网络的大小，大约增加了三分之一。为了描述从这两个不同层（神经网络和大脑活动）收集的数据的全局属性，并研究它们之间的映射，我们将开发基于拓扑数据分析（TDA）和贝叶斯推理技术的工具。TDA提供了派生自代数拓扑的方法，可用于提取大型数据集中的全局特征。作为一个相对较新的领域，有几个主要的障碍阻碍了TDA在生物系统中的广泛应用，包括统计方法的发展、网络（简单复合体）的比较（同态）和时间序列分析。这些工具将被应用于研究描述发育中的大脑网络和其中神经行为活动变化的生物数据集。特别是，我们将在单细胞水平上描述整个大脑的基础网络和那些吸引和厌恶行为的网络，在已知的在输入和输出水平上重构这种行为网络的发育过渡期间。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。

The development of the nervous system, specifically the dynamics of neuronal development and wiring to build brain architecture and their constructive role in emergent brain activity, constitutes a central unexplained phenomenon in living systems. The study of developing brains requires a comprehensive and systematic characterization of the brain of an organism at different ages and a suitable mathematical framework, able to capture the structure of the growing nervous system and the emerging networks therein. We propose to address this fundamental challenge by developing such a mathematical framework capable of characterizing underlying network changes in living brains and their consequences for functional neural activity and resulting behavior. This mathematical framework will be applied to analyze the complete nervous system, at single-cell precision, of the model organism C. elegans. To address these important challenges, we have assembled an interdisciplinary team with expertise in topology, computational biology, statistics, theoretical physics, neuroscience and biology of the model organism. Our group will develop new mathematical, statistical, and computational tools to characterize the structure of developing brain networks. This analysis will reveal shared-organizational, emergent principles of nervous-system development and function. Based on the widespread representation of biological data as complex networks and the universality of the mathematical, statistical, and computational methods we will develop, we expect wide applicability beyond the original system.The aforementioned approach will be led by experiments that aim at providing multiple views of a developing network and their functional consequences to whole-brain activity. We will analyze the brain at two levels: changes to the underlying network as a consequence of extensive neural additions and connective neural (re-)wiring. We will compare the developing network at two transition periods: early maturation from the first to the second larval stage and, later, maturation of the two different sexes. In both of these developmental periods, newborn neurons grow the existing brain network, considerably, by roughly a third in size. In order to characterize the global properties of the data collected from these two different layers (neural network and brain activity) and to study the maps between them, we will develop tools based on topological data analysis (TDA) and Bayesian inference techniques. TDA provides methodology derived from algebraic topology that can be used to extract global features in large datasets. As a relatively new field, there are several major roadblocks that obstruct the wide applicability of TDA to biological systems, including the development of statistical approaches, comparison (homomorphisms) of networks (simplicial complexes), and time-series analysis. These tools will be then applied to study biological datasets that describe the developing brain network and changes to neurobehavioral activity therein. In particular, we will characterize basal networks and those for attractive and aversive behavior, for whole brains at a single-cell level, during developmental transitions that are known to restructure this behavioral network at both the level of input and output.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.