Direction-Dependent Encoding of Forward and Inverse Models in the Same Purkinje Cells

Saccadic eye movements are too fast to be guided by sensory feedback and therefore depend on precisely calibrated internal models. The cerebellum is widely thought to compute both forward and inverse models, yet how these two computations coexist in the same circuit remains unclear. We hypothesized that the same Purkinje cells (PCs) can serve as a forward model for saccades in one direction and as an inverse model for saccades in the opposite direction, because target neurons on either side of the cerebellar nuclei contribute differently to leftward and rightward saccades. To test this hypothesis, we recorded from PCs in the oculomotor vermis of macaque monkeys during repetitive saccade paradigms that induce adaptation and fatigue. Using the preferred error direction of each PC conveyed by increased complex spike (CS) activity (CS-on direction) as a proxy of the side of the cerebellar nuclei it projects to, we compared population activity for saccades directed against the CS-on direction (CS-on opposed) and along it (CS-on aligned). CS-on opposed saccades, (toward the PC's projection side) were accompanied by a precisely timed, sharp burst of simple spike (SS) activity at saccade onset that scaled with peak velocity, and CS error sensitivity was highest after the saccade. SS activity also changed systematically after adaptation, reflecting the altered kinematics of the adapted saccade. These properties are consistent with a forward model that estimates ongoing movement and updates itself based on post-movement error. In contrast, the CS-on aligned saccades, (away from the PC's projection side) were accompanied by broader SS modulation around saccade offset, and the CS error sensitivity was highest before the saccade. CSs around saccade onset encoded target location and initial eye position, and their occurrence was associated with reduced saccade amplitude. This reduction likely adjusts the motor command to the starting eye position, as expected for an inverse model that pre-programs the motor command before movement begins. Together, these findings provide neural evidence that the same PC population can contribute to both forward and inverse model computations, depending on saccade direction.