Architecture for robust spatiotemporal dynamics in neuronal networks

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A major challenge in neuroscience is to understand how the brain reliably completes cognitive tasks, despite a great deal of intrinsic variability. Cognitive tasks often require coordinated spatiotemporal activity, which experimentalists can measure using multiple electrodes, voltage sensitive dye, and optical techniques. The main goal of this research project is to develop mathematical tools to study how spatially structured networks in the brain produce reliable activity in the face of noise. Specifically, we will be interested in how the spatial architecture of synaptic connections interacts with noise on multiple scales to influence network activity. Thus, linking our theory with experimental data will require the development of new techniques in stochastic and nonlinear analysis, multiscale methods, and symmetric bifurcation theory. Neuronal network models that incorporate space often assume synaptic connectivity depends only on the distance between neurons. Such dynamical systems tend to be marginally stable, so solutions diffuse in the presence of noise. More realistic models of neuronal connectivity do not produce such degeneracies. We propose to examine how spatial heterogeneity can improve or limit the robustness of neuronal networks. We will analyze models that encode neural activity linked to working memory, decision making, and place localization. Our work will contribute mathematical methods to other current research areas in math biology concerned with analyzing the effect of noise on spatially extended systems. Everyday, humans make decisions, use memory, and navigate their environment. Spatially structured activity in the brain underlies all these processes. Spatially localized "bumps" of activity are thought to encode short term memories of spatial position. Propagating waves of activity represent visual inputs and the movement of limbs. These activity patterns must be generated in networks of the brain that are fraught with noise. Despite the noisiness of the brain, we execute cognitive tasks faithfully. How does this happen? We will develop mathematical techniques to address this major question. Mainly, we will explore how neuronal networks can be structured to support robust spatiotemporal dynamics. Insight into the robustness of cognitive processes can be used to develop therapeutic solutions for various mental disorders. Alzheimer's, dementia, and Parkinson's present more commonly as human lifespans grow. Treatments are not possible without well-developed theory. Our analysis of spatiotemporal neural coding will also help understanding of how spatial arrays of multielectrodes should best be designed for applications like neural prosthetics.