The broad, long-term objective of this grant is to advance a new theoretical approach to identify synchronized building blocks of neural circuits based on group theory and its application to understand the permutation symmetries of these circuits. Based on the developed theoretical framework we will validate our theory by probing brain dynamics at single-cell resolution and in real-time, i.e. sub-second scale, in C. elegans, which is a system with a fully mapped synapse-resolution connectome. We will produce a software tool that will allow end-users from the broad neuroscience community to identify and analyze the building blocks of neural circuits and explore their relation with function. Speci?c Aims are: Speci?c Aim 1. Develop a generalized theoretical framework of symmetry groups and their unique decomposition into normal subgroups to identify building blocks made of synchronized neural pop- ulations in brain networks. Based on our preliminary work in locomotion in C. elegans, we will evaluate the application of symmetry groups to more complex functions and more complex neural systems of other species to investigate the relation between symmetries of the connectome and neural synchronization. Speci?c Aim 2. Verify experimentally the predicted building blocks in C. elegans nervous system with system-wide Ca2+-imaging experiments. We will develop an experimental program to test the predictions of the theory on the synchronization of neural populations identi?ed by symmetry groups, and the subsequent breaking of symmetry and asynchrony tested by single-cell laser ablation. Speci?c Aim 3. Resource sharing plan and software development: Develop software and tools based on the algorithms developed in Aim 1 and evaluated in Aim 2 to identify the building blocks of neural circuits to study their synchronization and function. Optimize the usability of the software by experimentalists (end-user PD Manuel Zimmer) and other researchers for use in the larger scienti?c community. Long term goals: The results of the present study should lead to improve our understanding of the designing principles of neural circuits and how this structure in?uences function. Once completed, we trust that the tools developed by this project will be able to be used by the larger neuroscience community to study the building blocks of all connectomes. The development of theories of the organization of the connectome should lead to the inference of general principles regarding network organization applicable to areas outside neuroscience that include information processing complex systems in general.
We will develop a software tool that will allow end-users from the neuroscience community to identify and analyze the most important building blocks made of synchronized circuits of the brain across neural connectomes using theoretical network concepts based on the permutation symmetry groups of the underlying network. Our main goal is to develop our theory alongside ?rst step experimental validations. The tools developed by this project will aid in the understanding on how the structure of the connectome determines the synchronization of neuronal populations that leads to their functional interactions.
