The primary goal of this project is to provide a new understanding of the neuronal properties that are critical for producing stable slow bursting oscillations and to explore the consequences of their activation when neurons expressing them are embedded in a network. Nonlinear regenerative inward currents are thought to be important in producing slow oscillations and bursting. This project uses a novel approach where the nonlinear inward current is replaced with a linear current of negative conductance. This approach exposes the multiple roles played by regenerative inward currents and simplifies the investigation of the contribution of other ionic currents to oscillatory activity. It also allows for a simpler mathematical analysis of the mechanisms that generate neuronal oscillations. This methodology is used to investigate the role of specific ionic currents in the generation and shaping of oscillations in individual neurons, to examine how synaptic interactions between neurons cooperate or compete with intrinsic properties to produce oscillations in networks of heterogeneous neurons, and to determine if the mechanisms that give rise to oscillations in isolated cells remain unchanged when the neuron is part of a network. These aims are pursued using techniques of dynamical systems and bifurcation theory in reduced mathematical models as well as simulations of detailed biophysical models, and electrophysiological experiments on bursting neurons of the crab pyloric network. These three methods are developed in parallel allowing for continual exchange of findings between the theoretical and experimental approaches.

Numerous behaviors ranging from locomotion to cognitive tasks rely on oscillatory activity generated by networks of neurons in the brain. Despite the predominance and indispensability of brain oscillations, few theoretical tools are available for understanding how such oscillations are generated or controlled. A novel approach is used that combines biological experiments and mathematical analysis to break apart the complex interactions present in network components into simple building blocks. This allows core elements that are important in the generation of oscillations to be extracted and will clarify the role of other existing components in sculpting behavior using mathematical models. The models are tested through experiments that connect real time computer-simulated neurons to small oscillatory networks in the crab central nervous systems. This project provides a framework for developing neural-based control systems with potential applications in robotics and bio-inspired computing.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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Rutgers University
United States
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