English: Reconstruction of nine different saccades from measured SC activity patterns using our linear two-dimensional model of the SC – brainstem saccade generator (c.f., Fig. 1C). The video shows the activity patterns in the left, contralateral SC (top left), the two-dimensional eye movement trajectories (bottom left), the horizontal and vertical eye position traces (top and middle right), and the vectorial eye velocity profiles (bottom right). Amplitude and direction of the subsequent movements is indicated by the [R,Φ] coordinates (bottom left). Note that the reconstructions (green) reproduced the straight trajectories, component stretching, and nonlinear kinematics of the measured saccades (blue) quite well, even though none of these properties were built into the model. Details of the reconstruction procedure have been described elsewhere [33]. In short, we first estimated the dynamic SC activity associated with a particular saccade vector from the cells' responses recorded during saccades of that particular amplitude and direction. Towards that end, we mapped each cell's spikes directly onto its location in the SC motor map, and from the measured spike events at each recording site we then calculated spatially smoothed maps of the instantaneous firing rates. The resulting estimates of the SC firing patterns in space and time were subsequently decomposed into dynamic horizontal and vertical movement commands using our spike vector summation model, which assumes that each spike from each SC neuron adds a tiny, site-specific contribution to the horizontal and vertical movement commands. The brainstem circuit for the horizontal and vertical eye-movement components was modeled by two independent linear feedback systems (c.f., Fig. 1C). The three model parameters (a fixed delay between SC and brainstem activation, the feed forward gain of the pulse generators, and a fixed delay in the local feedback loops; fixed for all reconstructions) were determined by fitting the reconstructions to the measured saccades.