Abstract
A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades.
Highlights
IntroductionTheir two-dimensional trajectories are virtually straight, there is a near-linear relationship between movement duration and saccade amplitude, and peak eye velocity versus saccade amplitude follows a nonlinear, saturating relationship (Fig. 1A)
Our results reveal a highly systematic organization of burst properties along the rostral-to-caudal extent of the superior colliculus (SC) motor map, which can fully account for the nonlinear kinematics of saccades, their straight trajectories in oblique directions, and the skewed shape of their velocity profiles
If the SC plays a role in optimal control, and if the brainstem acts as a linear system, one would expect that: 1) individual SC neurons exhibit signal-dependent noise, 2) peak firing-rate, burst duration and burst skewness at the center of the recruited population all depend systematically on its rostral-caudal coordinate in the SC motor map, while the number of spikes in the burst remains fixed, 3) the shape of a neuron’s burst depends systematically on the actual movement, and 4) all cells in the recruited population synchronize their burst profiles
Summary
Their two-dimensional trajectories are virtually straight, there is a near-linear relationship between movement duration and saccade amplitude, and peak eye velocity versus saccade amplitude follows a nonlinear, saturating relationship (Fig. 1A). The properties of internal noise within the system (assumed to increase with activity levels), a low spatial resolution in the peripheral retina, and a penalty for overshooting the target (as corrective commands have to cross hemispheres), require a speed-accuracy tradeoff. These studies indicated that the optimal trajectories to satisfy such constraints are met by the main-sequence relationships. The neural mechanisms for implementing the main-sequence relations are unknown
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