We have investigated the relationships among the firing frequency B(t) of inhibitory burst neurons (IBNs) and the metrics and dynamics of the eye, head, and gaze (eye + head) movements generated during voluntary combined eye-head gaze shifts in monkey. The same IBNs were characterized during head- fixed saccades in our first of three companion papers. In head-free gaze shifts, the number of spikes (NOS) in a burst was, for 82% of the neurons, better correlated with gaze amplitude than with the amplitude of either the eye or head components of the gaze shift. A multiple regression analysis confirmed that NOS was well correlated to the sum of head and eye amplitudes during head-free gaze shifts. Furthermore, the mean slope of the relationship between NOS and gaze amplitude was significantly less for head-free gaze shifts than for head-fixed saccades. NOS is a global parameter. To refine we used system identification techniques to evaluate a series of dynamic models in which IBN spike trains were related to gaze or eye movements. We found that gaze- and eye-based models predicted the discharges of IBNs equally well. However, the bias values required by gaze-based models were comparable to those required in our head-fixed models whereas those required by eye- based models were significantly larger. The difference in biases between gaze- and eye-based models was very strongly correlated to the mean head velocity (Ḣ) during gaze shifts [R = -0.93 ± 0.15 (SD)]. This result suggested that the increased bias required by the eye-based models reflected an unmodeled Ḣ input onto these cells. To pursue this argument further we investigated a series of dynamic models that included both eye velocity (Ė) and Ḣ terms and this confirmed the importance of these two terms. As in our head-fixed analysis of companion paper I, the most valuable model formulation also included an eye saccade amplitude term (ΔE) and was given by B(t) = r0 + r1ΔE + b:1Ė + g1Ḣ where r0, r1, b1, and g1 are constants. The amplitude of the head velocity coefficient was significantly less than that of the eye velocity coefficient. Furthermore, in our population long-lead IBNs tended to have a smaller head velocity coefficients than short-lead IBNs. We conclude that during head-free gaze shift, the head velocity signal carried to the abducens nucleus by primate excitatory burst neurons (EBNs; if EBNs and IBNs carry similar signals) must be offset by other premotor cells.
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