Mechanisms Of Frequency Preference In Neurons And Networks: Biophysics And Dynamics

Rhythmic oscillations at characteristic frequency bands are ubiquitous in the nervous systems. They emerge from the cooperative activity of the participating neurons and network synaptic connectivity. Understanding how the intrinsic biophysical properties of neurons interact with oscillatory input currents and synaptic conductances is essential to understand the mechanisms by which preferred frequencies are selected in oscillatory neuronal networks. Resonance refers to the ability of a neuron to exhibit a preferred frequency response to oscillatory inputs. Existing mathematical studies on resonance have focused primarily on linear models or linearized conductance-based models. Nonlinear effects have been examined using numerical simulations. A general theory of resonance in neuronal models is lacking, as are appropriate mathematical tools to answer key biophysical and dynamic questions. The aim of this project is to develop general theoretical principles for the generation of preferred frequency responses in neuronal systems that incorporate the effects of nonlinearities and the diversity of time scales, and to expand existing dynamical systems tools in ways that allow for the investigation of the underlying mechanisms. This project has three specific aims: (i) to identify the neuronal subthreshold mechanisms of generation of preferred frequency responses in both amplitude and phase to oscillatory inputs, (ii) to identify the mechanisms by which subthreshold resonances are communicated from the subthreshold to the spiking regimes, and (iii) to evaluate how resonance and synaptic currents interact to generate preferred frequency responses to oscillatory inputs in networks of neurons. The models in this project have two levels of description. Biophysical models are used to understand the effect of the participating currents on the network dynamics and to make experimentally verifiable predictions. Minimal models are used for mathematical analysis using dynamical systems tools. The mathematical tools to be developed will provide a theoretical framework for the investigation of preferred frequency responses in models with higher levels of descriptions.

Rhythmic oscillations at characteristic frequency bands have been observed in various areas of the brain and have been implicated in cognition and motor behavior in both health and disease. Network oscillations result from the cooperative activity of the participating neurons, but how these neurons interact to produce coherent activity in the brain is only beginning to be understood. This project deals with the responses of neurons to oscillatory inputs, and how these responses can be used to understand the dynamics of neuronal networks. As test cases, we focus primarily on neurons of the hippocampus and the entorhinal cortex. Rhythmic oscillations in these areas of the brain have been implicated in various cognitive processes including learning, memory and navigation. Neuronal networks in these areas are also the focus of diseases of the nervous systems such as epilepsy and Alzheimer''s disease. The purpose of this project is to understand the biophysical and dynamic mechanisms that underlie the generation of preferred frequency responses to oscillatory inputs in neurons and neuronal networks, and to develop the appropriate mathematical tools to answer key mechanistic questions. This work will be carried out in the context of ongoing collaborations with experimental neuroscientists, and is designed to achieve a close integration between our modeling and theoretical efforts and the experimental efforts of various collaborators so that findings from one side will inform the other. Students participating in this project will be trained at the interface between Mathematics and Neuroscience in the well-established interdisciplinary environment at the NJIT/Rutgers campus, and will be prEnvironmental Protection Agencyred to join the scientific task force in the mathematical and biomedical sciences.