We investigated the relationship between eye movement and simple-spike (SS) frequency of Purkinje cells in the cerebellar flocculus middle zone during the optokinetic response (OKR) in alert cats. The OKR was elicited by a sequence of a constant-speed visual pattern movement in one direction for 1 s and then in the opposite direction for 1 s. Quick-phase-free trials were selected. Sixty-six cells had direction-selective complex spike (CS) activity that was modulated during horizontal (preferring contraversive) but not vertical stimuli. The SS activity was modulated during horizontal OKR, preferring ipsiversive stimuli. Forty-one cells had well-modulated activity and were suitable for the regression model. In these cells, an inverse dynamics approach was applied, and the time course of the SS rate was reconstructed, with mean coefficient of determination 0.76, by a linear weighted superposition of the eye acceleration (mean coefficient, 0.056 spikes/s per deg/s2), velocity (5.10 spikes/s per deg/s), position (−2.40 spikes/s per deg), and constant (mean 34.3 spikes/s) terms, using a time delay (mean 11 ms) from the unit response to the eye response. The velocity and acceleration terms contributed to the increase in the reconstructed SS rates during ipsilateral movements, whereas the position term contributed during contralateral movements. The standard regression coefficient analyses revealed that the contribution of the velocity term (mean coefficient 0.81) was predominant over the acceleration (0.03) and position (−0.17) terms. Forward selection analysis revealed three cell types: Velocity-Position-Acceleration type ( n = 27): velocity, position, and acceleration terms are significant ( P < 0.05); Velocity-Position type ( n = 12): velocity and position terms are significant; and Velocity-Acceleration type ( n = 2): velocity and acceleration terms are significant. Using the set of coefficients obtained by regression of the response to a 5 deg/s stimulus velocity, the SS rates during higher (10, 20, and 40 deg/s) stimulus velocities were successfully reconstructed, suggesting generality of the model. The eye-position information encoded in the SS firing during the OKR was relative but not absolute in the sense that the magnitude of the position shift from the initial eye position (0 deg/s velocity) contributed to firing rate changes, but the initial eye position did not. It is concluded that 1) the SS firing frequency in the cat middle zone encodes the velocity and acceleration information for counteracting the viscosity and inertia forces respectively, during short-duration horizontal OKR and 2) the apparent position information encoded in the SS firing is not appropriate for counteracting the elastic force during the OKR.
Spatiotemporal Properties of Fast and Slow Neurons in the Pretectal Nucleus Lentiformis Mesencephali in Pigeons
