Robust spatiotemporal dynamics in multi-layer neuronal networks

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To navigate in a constantly changing world, humans and other animals continually make decisions and store memories. Since the world is noisy and brain activity is highly variable, it is remarkable that organisms can perform cognitive tasks as accurately as they do. One feature of the human brain that may account for its exceptional computational ability is its modular structure. The entire network of the brain is organized into a collection of densely connected subnetworks, helping to localize certain neural computations. Studying the effects of this underlying structure could ultimately help in the analysis of increasingly large data sets collected by experimental neuroscientists. This project will consider the impact of modular structures in the brain, focusing on networks known to perform specific cognitive tasks like categorization, short-term memory, and spatial navigation. These computations are performed by networks that can represent spatial position, and the associated mathematical models often describe variables that change in space and time. This project will facilitate the development of new methods for studying how noise impacts the dynamics of neuronal networks with multiple temporal and spatial scales, specifically in networks with a multi-layered structure. This project will contribute to the national BRAIN initiative by identifying new computational tools for understanding the role of the brain's network architecture in cognition. Furthermore, trainees supported by this award will learn cutting-edge methods in statistics, nonlinear dynamics, and stochastic processes. These methods are broadly applicable to many fields in science that utilize large-scale data such as genetics, social science, and climatology.This research project addresses the problem of understanding how the multi-layered structure of many areas of the brain shape neural computation. This problem will be addressed in three main ways: (i) building multi-layer network models of observed brain circuits that process spatial information; (ii) developing mathematical tools for studying these equations to extract information about their dynamics; and (iii) corroborating this work with experimental collaborators that record and image propagating activity in brain tissue. The cognitive tasks of spatial navigation, spatial working memory, and visual input categorization will be studied. Spatial navigation requires the integration of both angular and linear self-motion cues, and models developed in the project will explore different ways multi-layered network architecture can dampen variability in position codes. The investigation of how multi-layered architectures with different scales of spatial heterogeneity can robustly represent spatial position will improve our insights into the function of spatial working memory. Experimental recordings from visual brain areas have found that interfaces between network layers modify the propagation of stimulus-related activity. The impact of this phenomenon on stimulus processing will be explored in detail using mathematical models of sensory brain activity. All these projects require the development of new tools for determining how noise influences multi-scale systems, metastability, and spatiotemporal patterns, of broad applicability to other scientific fields including epidemiology, systems biology, and ecology.