Properties of saccades and models of saccade generation.

<p><b>A</b>) Left: main sequence relationship between saccade amplitude, duration and peak velocity. Right: component stretching. Here, an oblique saccade (blue) has very different component amplitudes (top), but horizontal and vertical velocity profiles ( and ) have equal durations and similar shapes (bottom). The horizontal saccade (red) has a much shorter duration and higher velocity than the equally large horizontal component of the oblique saccade. <b>B</b>) Classic one-dimensional model which assumes that the superior colliculus (SC) specifies a desired displacement vector (after <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002508#pcbi.1002508-Jrgens1" target="_blank">[12]</a>). Main sequence properties are attributed to a saturating nonlinearity of the burst generator which is controlled through local feedback. Cross-coupling between horizontal and vertical components (not shown) is needed to produce straight saccades. <b>C</b>) Linear two-dimensional model of the SC – brainstem saccade generator (after <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002508#pcbi.1002508-Goossens1" target="_blank">[33]</a>). In this scheme, spatial-temporal activity patterns in the SC specify an intended movement trajectory, which is decoded downstream by ‘spike-vector’ summation: each spike from each neuron adds a site-specific vectorial contribution to movement command. The actual movement is generated by pulse-step activation of the extra-ocular motor neurons, as in B, but the burst generator, which produces the pulse, is linear. ΔE, desired eye displacement; Δ<i>e</i>(<i>t</i>), current eye displacement; <i>me</i>(<i>t</i>), dynamic motor error; , current eye velocity; <i>w</i>(<i>R</i>), exponential weighting function; <i>∫dt</i> temporal integration; Burst, brainstem burst generator; NI, neural eye position integrator; NDI, resettable neural eye displacement integrator; MN, motor neurons; innerv., eye plant pulse-step innervation signal.