This project involves computational and mathematical studies to elucidate signal processing performed by the midbrain dopaminergic (DA) neuron. The central dopamine system has implications in many behavioral and cognitive tasks. A high-frequency response of the DA neuron is one of a few cellular events for which a clear physiological meaning has been proposed, and an immediate behavioral implication is the main determinant for great interest in properties of this cell. In a two-compartmental model of the DA cell, the canard and singular perturbation analysis will be applied to the bifurcation transition that corresponds to the onset of high-frequency oscillations. Timescale separations will be introduced to make the analysis possible. Then, the accuracy of proposed asymptotic approximations will be evaluated by comparison with simulations. In a morphological reconstruction, the investigators will reproduce distinctive properties of the spike generation mechanism of DA cells: 1. Its dependence on the subthreshold currents; 2. the contribution of active dendritic properties; 3. axonal initiation and presence of two components of a spike. Modeling will combine data on identified currents. Functional criteria will be applied to validate the model. Using the constructed model, synaptic integration properties of the DA neuron will be identified. Attenuation properties for a single spike and spike trains evoked at different dendritic locations will be measured in simulations. The dendritic tree is expected to be compartmentalized in such a way that synaptic inputs at certain locations elicit only somatic or only axonal spiking due to a significant spatial separation of the axon origin from the soma in DA neurons. Additionally, compartmentalization of the neuron may depend on the stimulation frequency because distal dendrites and the axon have much higher natural frequencies than the soma. Synchronization of spontaneously-evoked dendritic spikes and classical coincidence detection of synaptic inputs will be addressed in the model.

The above research will integrate experimental data on firing patterns and spike initiation of the DA cell to make conclusions about functional properties of the neuron. The project will open new possibilities to move the investigation of various behavioral functions involving the DA cells from the abstract to the biophysical context. It will layout the groundwork for further experiments. In its analytical part, the research will advance dynamical explanations to nontrivial biological phenomena and contribute to the extension of singular perturbation techniques to the vicinity of a bifurcation boundary. In the long perspective, understanding of DA cell functions will advance the development of new therapies to cure numerous disorders in which the central dopamine system is impaired. This interdisciplinary study will promote the usage of mathematical and modeling methods in biosciences. The models will be submitted in a public domain database to be used for educational and scientific purposes. The project will involve graduate students and postdocs, both through mentoring and by seminar activities. The project has a potential for attracting female students and scholars from biology to mathematical sciences, were women are underrepresented.

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