CAREER: Bridging dynamical and statistical models of neural circuits -- a mechanistic approach to multi-spike synchrony

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Questions of neural synchrony -- correlations in cell-to-cell spiking -- have driven decades of research. However, recent technological and theoretical advances have thrust open two lines of inquiry. The first is understanding the combinatorial scale of the correlations that occur in natural and model neural networks. It is well known that describing neural activity requires pairwise statistical interactions -- but we do not yet understand when network dynamics produce patterns of correlations that extend beyond this pairwise description, when the pairwise descriptions will be complete, and what the overall implications are for neural coding and signal processing. The Principal Investigator will address these questions for a set of "canonical" neural circuits, or motifs, and will build toward networks of gradually increasing complexity in their dynamics and architecture. Further, extending beyond intrinsic network dynamics, he will ask how these basic network properties determine the ways in which patterns of synchrony can be controlled by external stimulation. Answering these complementary questions requires synergies between methods of stochastic processes, dynamical systems, and statistical inference.How do how networked neurons work together to produce the brain's astonishing computational ability? Such coordinated neural dynamics are characterized by synchrony among different neurons. One prospect is that this coordinated activity opens new channels for signal processing: there is a combinatorial explosion in the number of possible multi-neuron patterns that can occur in increasingly large networks. However, we only have the first hints at whether and when these patterns systematically occur in the brain's networks, and what information they might (or might not) carry. Shea-Brown will study the fundamental properties of neural dynamics, connectivity, and noise that determine the level and impact of multi-neuron synchrony in a series of networks of gradually increasing complexity. He will use interdisciplinary tools from both deterministic and statistical branches of applied mathematics to understand how levels of synchrony are created, destroyed, and manipulated by external stimulation. These findings will contribute to experimental and clinical neuroscience: working in collaboration with experimentalists, the investigator will make predictions for light stimuli that evoke higher-order correlations in the retina, and for electrical stimuli that suppress pathological synchrony in neurodegenerative disease. These questions, as part of theoretical neuroscience -- an emerging field that is rich in open questions and highly varied interdisciplinary techniques -- present a strong opportunity for recruiting, engaging, and training undergraduates in the mathematical sciences. Shea-Brown will direct this opportunity toward the underrepresented groups from which new scholars are most urgently needed, through an integrated four-year research pathway for undergraduates. This will be developed together with newly designed units in the computational science and mathematical biology courses taught by the investigator.