The superior colliculus and spatiotemporal translation in the saccadic system

Abstract The superior colliculus (SC) plays an important part in generating saccadic eye movements, sending signals coding desired eye rotation to the brainstem. These signals must be translated from the topographic (spatial) representation used in the SC to the firing frequency (temporal) code used downstream. We show that a model of the saccadic system using the quaternion representation of eye rotations yields a spatiotemporal translation with all the experimentally observed properties: activation of a particular site in the SC generates a saccade of a particular amplitude and direction; activation of multiple sites evokes a vector average (weighted by activity levels) of the saccades coded by the individual sites; the intensity and temporal profile of activation determine saccade speed but not metrics. The feature of the model that is essential to these results is a particular sort of redundancy in the quaternion representation, coupled with multiplicative downstream handling of SC outputs.