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Arvind Kumar (University of Freiburg, Germany)

Title

The critical role of striatal inhibition in shaping the oscillatory activity in the basal ganglia

Abstract

Movement disorders in Parkinson’s disease (PD) are commonly associated with slow oscillations and increased synchrony of neuronal activity in the basal ganglia (subthalamic nucleus - STN, and globus pallidus external- GPe). We investigated the dynamics of the basal ganglia using a reduced mean field model, which resembles the Lotka-Volterra equations used in modeling predator-prey relations in population biology. This model allowed us to isolate several biological plausible mechanism that could induce oscillations. Specifically, I will discuss how both firing rate and correlations among inhibitory inputs from the striatum to the GPe (i.e. increased inhibition of inhibitory network) control the oscillations in the basal ganglia. Consistent with experimental observations, we found that increase in either of these can unleash the oscillations in the basal ganglia, similar to that observed in the PD. This observation allows us to propose a unified explanation for different phenomena: absence of oscillation in the healthy state of the basal ganglia, oscillations in dopamine-depleted state and quenching of oscillations under deep-brain-stimulation (DBS). Finally, studying the model behavior under transient increase of activity of the striatal neurons projecting to the indirect pathway, we are able to account for both motor impairment in PD patients and for reduced response inhibition in DBS implanted patients.

Free Discussion

Uzy Smilansky (Weizmann Institute of Physical Sciences, Israel)

Title

Nonlinear Schroedinger Equation on Networks

Abstract

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. The resonances which dominate linear scattering are shown to be extremely sensitive to the nonlinearity and display multi-stability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks, and for studying universal properties of Bose-Einstein Condensate (BEC) in connected chaotic traps.