Examining the paradoxical relation between number of spikes and gaze amplitude in abducens neurons

During head-unrestrained gaze shifts, the number of spikes in the burst of abducens neurons increases with gaze amplitude, even when corrected for the component of the discharge related to the change in eye position. We examine this paradoxical dissociation between the number of spikes and eye amplitude, which occurs because eye amplitude in the head saturates for larger gaze shifts. First, we show that the extra spikes are unlikely to be due to antagonist muscle loading because the abducens neurons are completely silent during large gaze shifts when the muscle acts as an antagonist. Next, we divide the firing rate profile of abducens neurons into terms that represent signals related to eye position, velocity, and acceleration; a d.c. offset term specifying the firing associated with straight-ahead gaze; and a slide term, which compensates for the zero of the oculomotor plant. Then we examine the contribution of each term to the number of spikes recorded. A comparison of the number of spikes with the integral of the fitted function, combining all of the terms, for the duration of the burst reveals that the simulation captures much of the actual data. However, even a model with a slide term cannot reproduce the nonlinear relationship of the number of spikes with amplitude that characterizes large gaze shifts.