M-type channels selectively control bursting in rat dopaminergic neurons

Midbrain dopaminergic neurons in the substantia nigra, pars compacta and ventral tegmental area are critically important in many physiological functions. These neurons exhibit firing patterns that include tonic slow pacemaking, irregular firing and bursting, and the amount of dopamine that is present in the synaptic cleft is much increased during bursting. The mechanisms responsible for the switch between these spiking patterns remain unclear. Using both in-vivo recordings combined with microiontophoretic or intraperitoneal drug applications and in-vitro experiments, we have found that M-type channels, which are present in midbrain dopaminergic cells, modulate the firing during bursting without affecting the background low-frequency pacemaker firing. Thus, a selective blocker of these channels, 10,10-bis(4-pyridinylmethyl)-9(10H)- anthracenone dihydrochloride, specifically potentiated burst firing. Computer modeling of the dopamine neuron confirmed the possibility of a differential influence of M-type channels on excitability during various firing patterns. Therefore, these channels may provide a novel target for the treatment of dopamine-related diseases, including Parkinson's disease and drug addiction. Moreover, our results demonstrate that the influence of M-type channels on the excitability of these slow pacemaker neurons is conditional upon their firing pattern. © 2010 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

A perturbation approach to the stabilization of nonlinear cascade systems with time-delay

The effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.

A duality principle for homogeneous vectorfields with applications

A duality transformation principle was proposed for converting a positive order homogeneous vectorfield into a negative order homogeneous vectorfield. The principle also converted a uniformly locally asymptotically stable differential equation into a uniformly bounded differential equation. The duality transformations included the geometric framework for homogeneity and the removal of origin from the state space.