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

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.