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Janet Best : Parkinsons: two mathematical views of a neurological disease

Parkinson's Disease (PD) is the most common movement disorder in the United States, with symptoms due to progressive loss of neurons within the basal ganglia. In the first part of the talk, we present and analyze a minimal model for the lack of cross-correlations in neuronal activity in the healthy basal ganglia.

The second part of the talk focuses on experimentally-observed changes in neuronal firing patterns that accompany PD and that may result in the motor symptoms. We have constructed a neuronal network model for the increases in correlated activity within the basal ganglia following the onset of PD. We then apply dynamical systems methods to understand transitions between irregular and rhythmic, correlated firing in the model. Geometric singular perturbation theory and one-dimensional maps are used to understand how an excitatory-inhibitory neuronal network with fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. We discuss hypotheses arising from the model as well as ongoing experiments to test these predictions.

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