Understanding Selective Recruitment in Neuronal Networks via Systems Theory

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This project will study the dynamics of systems characterized by a particular interconnection structure, inspired by properties of nerve cells. Nerve cell models typically implement some type of activation function, which determines how the nerve cell responds to input stimuli from other nerve cells. The activation function studied in this project passes an input signal without changes, if the input to the structure is positive. However, if the input to the activation function is negative, then the output is zero. This activation function gives rise to a model of nerve cell dynamics that is capable of accurately representing some behaviors of real neurons. There are powerful mathematical results available for these models. In contrast, nerve cell models with activation functions based on exponentials can be difficult to analyze. This project will create new mathematical tools to study how different subnetworks interact, either to suppress unwanted activity or to synchronize and reinforce their responses. These subnetworks can be built up hierarchically into progressively more complex structures. The project will relate these networks to both normal and abnormal neuronal circuits. The results will be of interest for the insight they provide into the architecture of the human brain, but also for constructing explainable engineered networks that can learn and adapt. This project will advance the national health and welfare by increasing understanding of biological neuronal systems, and by enabling the creation of robotic systems with enhanced resilience and adaptabilty. The project will also impact the training of a new generation of undergraduate and graduate students through undergraduate student involvement in research, graduate supervision and curriculum development, outreach targeted at middle, high school, incoming freshman and transfer students, involvement and retention of minority students, and broad dissemination activities.This project addresses the existing gap between the experimental evidence on selective recruitment in the brain and the theoretical understanding of the mechanisms that explain it. Taking a systems and controls perspective, the research effort aims to develop a mathematical framework to analyze how neuronal networks optimize their computational capabilities and unravel the role that network structure plays in shaping the dynamical behavior of the brain. This research seeks to advance the current knowledge on how the brain selects the relevant subnetworks during each time interval and suppresses the activity of others, and how it efficiently recruits those selected subnetworks and coordinates information transfer to and from them. The research plan is structured along the following interconnected research thrusts: (i) network stability and emergence of oscillations. The project seeks an in-depth characterization of the conditions on network structure that determine its dynamical properties, in particular, existence, uniqueness, and asymptotic stability of equilibrium points and limit cycles; (ii) inhibitory control and dynamic dimensionality. The project aims to characterize the mechanisms by which long-range connections between two networks can be used by one to dynamically inhibit different subset of nodes in the other. An aspect of particular importance is the consideration of physiologically-relevant scenarios involving feedforward and feedback inhibition, and their relation to network size, structure, and robustness; (iii) inter-regional connectivity and information transfer. Building on the lessons learned in the previous two thrusts, the project sets out to characterize the mechanisms of information transfer through coherent oscillations. This involves the study of ways in which neuronal networks can encode and decode information as oscillations and the role that the hierarchical structure and inter-regional connectivity of the brain has on them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.