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Inverse and forward dynamic models have been conceptually important in computational motor control. In particular, inverse models are thought to convert desired action into appropriate motor commands. In parallel, forward models predict the consequences of the motor command on behavior by constructing an efference copy of the actual movement. Despite theoretical appeal, their neural representation has remained elusive. Here, we provide evidence supporting the notion that a group of premotor neurons called burst-tonic (BT) cells represent the output of the inverse model for eye movements. We show that BT neurons, like extraocular motoneurons but different from the evoked eye movement, do not carry signals appropriate for the half-angle rule of ocular kinematics during smooth-pursuit eye movements from eccentric positions. Along with findings of identical response dynamics as motoneurons, these results strongly suggest that BT cells carry a replica of the motor command. In contrast, eye-head (EH) neurons, a premotor cell type that is the target of Purkinje cell inhibition from the cerebellar flocculus/ventral paraflocculus, exhibit properties that could be consistent with the half-angle rule. Therefore, EH cells may be functionally related to the output of a forward internal model thought to construct an efference copy of the actual eye movement.

Neural Correlates of Forward and Inverse Models for Eye Movements: Evidence from Three-Dimensional Kinematics