Population dynamics and entrainment of basal ganglia pacemakers are shaped by their dendritic arbors

The theory of phase oscillators is an essential tool for understanding population dynamics of pacemaking neurons. GABAergic pacemakers in the substantia nigra pars reticulata (SNr), a main basal ganglia (BG) output nucleus, receive inputs from the direct and indirect pathways at distal and proximal regions of their dendritic arbors, respectively. We combine theory, optogenetic stimulation and electrophysiological experiments in acute brain slices to ask how dendritic properties impact the propensity of the various inputs, arriving at different locations along the dendrite, to recruit or entrain SNr pacemakers. By combining cable theory with sinusoidally-modulated optogenetic activation of either proximal somatodendritic regions or the entire somatodendritic arbor of SNr neurons, we construct an analytical model that accurately fits the empirically measured somatic current response to inputs arising from illuminating the soma and various portions of the dendritic field. We show that the extent of the dendritic tree that is illuminated generates measurable and systematic differences in the pacemaker's phase response curve (PRC), causing a shift in its peak. Finally, we show that the divergent PRCs correctly predict differences in two major features of the collective dynamics of SNr neurons: the fidelity of population responses to sudden step-like changes in inputs; and the phase latency at which SNr neurons are entrained by rhythmic stimulation, which can occur in the BG under both physiological and pathophysiological conditions. Our novel method generates measurable and physiologically meaningful spatial effects, and provides the first empirical demonstration of how the collective responses of SNr pacemakers are determined by the transmission properties of their dendrites. SNr dendrites may serve to delay distal striatal inputs so that they impinge on the spike initiation zone simultaneously with pallidal and subthalamic inputs in order to guarantee a fair competition between the influence of the monosynaptic direct- and polysynaptic indirect pathways.