Gomi, Hiroaki, Munetaka Shidara, Aya Takemura, Yuka Inoue, Kenji Kawano, and Mitsuo Kawato. Temporal firing patterns of Purkinje cells in the cerebellar ventral paraflocculus during ocular following responses in monkeys. I. Simple spikes. J. Neurophysiol. 80: 818–831, 1998. The simple-spike firing frequency of 30 Purkinje cells (P cells) in the ventral paraflocculus (VPFL) of alert monkeys was studied in relation to vertical slow eye movements, termed ocular following response (OFR), induced by large-field visual motions of different velocities and durations. To quantitatively analyze the relationship between eye movement and firing frequency, an inverse dynamics representation of the eye movement was used for reconstructing the temporal waveform of firing. Coefficients of eye-acceleration, velocity, and position, bias, and time lag between firing and eye movement were estimated by least-square error method. In the regression analyses for each stimulus condition, 86% (146/170) of the well-modulated temporal firing patterns taken from those 30 P cells were reconstructed successfully from eye movement. The model with acceleration, velocity, and position terms, which we used, was shown as the best among several potential models by Cp statistics, consistent with t-test of significance of each term. Reliable coefficients were obtained from 75% (109/146) of the well-reconstructed firing patterns of 28 cells among 30. The estimated coefficients were larger (statistically significant) for slow stimuli than for fast stimuli, suggesting changes in sensitivities under different conditions. However, firing patterns of each cell under several different conditions were frequently well reconstructed by an inverse dynamics representation with a single set of coefficients (13 cells among 21). This indicates that the relationships between P cell firing and OFR are roughly linear in those stimulus ranges. The estimated coefficients for acceleration and velocity suggested that the VPFL P cells properly encode the dynamic components of the motor command during vertical OFR. As for the positional component, however, these P cells are correlated with eye movement in the opposite direction. In the regression analysis without positional component, remarkable differences between observed and reconstructed firing patterns were noted especially in the initial phase of the movements, indicating that the negative positional component was not negligible during OFR. Thus we conclude that, during OFR, the VPFL P cells cannot provide the necessary final motor command, and other brain regions, downstream neural structures, or other types of P cells must provide lacking position-dependent motor commands. This finding about the negative correlation with the position is in the opposite sign with previous studies obtained from the fixation and the smooth pursuit movement. From these comparisons, how the VPFL contributes to a part of the final motor command or how other brain regions complement the VPFL is suggested to be different for early and late phases of the movements.