Kinematic model relating complex 2D smooth pursuit eye movements and Purkinje cell firing rate in cerebellar flocculus and paraflocculus of the rhesus monkey

Single-neuron responses from the flocculus and paraflocculus of the cerebellum were recorded from rhesus monkeys while they tracked targets moving along complex and simple 2D trajectories. Each neuron was analyzed using a multi-linear regression model that expressed the instantaneous firing rate of the neuron as a function of the instantaneous 2D position, velocity, and acceleration of the eye. In all cases, the model provided a good description of the data. In addition, the model explains why some neurons show relatively complex responses including a systematic preference for clockwise (CW) versus counterclockwise (CCW) circular target motions, while others show simpler responses. Most neurons had position and velocity preferred directions that were in alignment. These neurons had relatively simple response profiles with similar response amplitudes during CW versus CCW circular pursuit. Other neurons had position and velocity preferred directions that were not aligned and that differed by as much as 90°. These neurons had more complex response properties including a preference for either CW or CCW circular pursuit. This suggests that neurons with simple responses receive inputs with similar spatial tuning properties, while complex responses result from inputs with different spatial tuning properties.