Project Summary/Abstract: Project 2, Geometry of Neural Representations and Dynamics In this project, we will measure and model the geometry of neural coding and dynamics during an evidence-accumulation decision task. This work will advance the overall goal of this U19 program—elucidating the circuit mechanisms that underlie working memory and decision-making and applying this information to construct a multi-region, mechanistic circuit model. Neural population activity in the dorsal hippocampus of mice is constrained to lie on a low-dimensional manifold during our task. Important behavioral variables like position along the maze, and learned cognitive variables like evidence, are represented as gradients in different directions along this latent space, giving rise to a geometric representation of knowledge. Observed neural activity sequences correspond to trial-specific trajectories along the manifold. The first aim will characterize geometric representations in hippocampus and neocortex, to identify general encoding principles of these representations and provide a richer dataset for comparison with our mechanistic models. We will compare firing fields and manifold structure to predictions from several existing statistical learning models to test the general idea that the manifolds capture task-specific statistical regularities. We will also characterize geometric properties of neural coding and manifold structure across these areas, starting with the prefrontal cortex, using simultaneous Neuropixels recordings from multiple regions. We will identify what attributes, such as intrinsic dimensionality and variable encodings, are preserved in the cortex compared to hippocampal representations. The second aim will evaluate the neural dynamics that govern state space flow along the manifold. So far, we have focused on inferring the geometry of neural representations and have not directly examined dynamics on the manifold. We developed a nonlinear method to simultaneously estimate manifold dimensions and the dynamics on that manifold, based on neural spike data. We will extend this method for use with calcium imaging data and then apply it to spiking and imaging data from other projects to infer manifold state space flow. These data-driven inferences will be compared to the dynamics predicted by existing models. Finally, the third aim will causally probe manifold structure and the mechanisms of sequence generation using optogenetic perturbation. With our new technology for simultaneous optogenetic perturbation and imaging, we will measure changes in neural population activity during multi-neuron perturbations that will be designed using sequence and manifold structure derived from population imaging data. Data, analyses, and modeling from this project will provide key insights into the general properties of neural manifolds in a variety of brain regions, along with the flow-field dynamics along manifolds that define neural trajectories on individual trials. Taken together, these experiments and models will substantially advance three priority areas of the BRAIN Initiative: the brain in action, demonstrating causality, and identifying fundamental principles.