The relation between discharge frequency and rotational acceleration was determined for 94 VIIIth nerve vestibular neurons of the barbiturate-anesthetized cat. Response gain and phase of each cell were estimated at seven to nine frequencies between 0.005 and 3.7 Hz. To determine whether dynamic properties were correlated with resulting discharge variability, cells were classified into three groups according to the coefficient of variation (CV) of the resting discharge [low-variability (LV) cells had CVs less than 10%, high-variability (HV) cells had CVs greater than 30%, and IV cells were of intermediate variability]. The response properties of individual cells were described by Bode plots of gain and phase for each cell. The gains and phases were averaged across cells at individual test frequencies to describe the response properties of the entire population of cells, and of the LV, IV, and HV groups. Both the individual and the averaged data were then described mathematically with a transfer-function equation, which reduced to a minimum the squared error of the fitted function to the gain and phase points. Each transfer function had a gain constant and zero-pole terms; from the poles, a dominant time constant (τ) and up to three additional time constants were determined. These parameters were used to summarize the dynamic properties. Gain and phase values at any test frequency varied widely from one cell to another, demonstrating that a rotational stimulus may be encoded differently by each member of this population of afferents. Gain and phase measurements for individual cells were, however, repeatable both from trial to trial and under different stimulus conditions, indicating that the observed between-cell differences were not the result of measurement error. The transfer functions of individual LV, IV, and HV cells differed from one another; those of LV cells typically required a mathematical description with two poles and one zero, while those of IV and HV cells usually needed three poles and two zeros. Qualitatively, there was a tendency for cells with more irregular discharge properties to have less phase lag (re acceleration) than regularly discharging cells at frequencies higher than about 0.25 Hz. The description of dynamic properties of some HV cells was improved by using transfer-function equations with fractional exponents. Values of the gain constant of individual cells ranged from 0.11 to 5.6 spikes x sec-1/deg x sec-2. x Sec-2. The average gain constants of LV, IV, and HV cells did not differ significantly 1.2 to 14 sec. LV and HV neurons' τ's values of 5.9 and 4.2 sec, respectively). When population gains and phases were averaged at each frequency, the gain curves of LV and IV populations were parallel, differing only in the IV neurons had gains about 1.5 times higher. The gain function for HV neurons had a shallower slope. The phase curves of LV and IV neurons were also parallel, with IV neurons having 10-15° less phase lag re acceleration. The HV neurons' phase reached an asymptote of about -60° at frequencies above 0.7 Hz, in contrast to the -90° asymptote of the LV neurons. The transfer-function equations that described the averaged data of the LV, IV, and HV groups were similar to those needed to describe the individual cells of the three groups. The relationship between the gain constant, τ, and the resulting discharge rate was examined for LV, IV, and HV cells. LV cells tended to have low gains, intermediate values of τ, and high resting discharge. HV cells had lower resting discharge rates, in general, a broad range of values of τ and the largest proportions of high gain cells of the entire population. IV cells had intermediate values of τ and a wide range of both resting discharge frequencies and gain constants. These relationships imply that irregularly discharging cells are more likely to be silenced by an inhibitory acceleration than are regularly discharging ones. Our results suggest that each eighth nerve afferent studied may be 'tuned' to respond maximally to certain kinds of head movements. We conclude that the wide variability seen in gain and phase from one cat canal afferent to another suggest that the concept of an 'average transfer function' is an oversimplification, since different cells in the same animal can have different dynamic properties. The quantification of the variety of dynamic response properties among the members of this population enhances our understanding of how between-cell differences might contribute to the encoding of head movements.
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