A nonlinear model for collicular spatial interactions underlying the metrical properties of electrically elicited saccades

An earlier model for the collicular role in the generation of saccades (Van Gisbergen et al. 1987), based on ensemble coding and linear vector addition of movement contributions from independent movement cells, yields normometric saccades in all directions over a considerable range of amplitudes. The model, however, cannot account for two nonlinear phenomena which are known from collicular electrical stimulation experiments: 1) saccade amplitude has a roughly sigmoid dependence upon current strength and 2) two electrical stimuli applied simultaneously at different sites yield a response that resembles a weighted average of the individual responses. In the present paper we propose an intracollicular mechanism which, based on lateral spatial interactions in the deeper layers of the colliculus, results in nearby excitation and remote inhibition when current is applied. Both nonlinear phenomena can thus be explained. The possibility of excitatory and inhibitory collicular interactions is supported by recent evidence in the literature. The nonlinearity in the model, essential to explain the electrical stimulation findings, resides in the input-output characteristic of the deeper layer movement cells. The results, obtained by quantitative simulations with the model, are discussed together with possible alternative explanations.