Optimal control of saccades by spatial-temporal activity patterns in the monkey superior colliculus.

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.

Linear visuomotor transformations in midbrain superior colliculus control saccadic eye-movements.

It is well established that a localized population of neurons in the motor map of the midbrain superior colliculus (SC) drives a saccadic eye-head gaze shift. However, there is controversy as to how the brainstem saccade burst generators decode the SC activity. We focus on eye-movement generation by comparing two competing schemes from the recent literature that are both supported by neurophysiological evidence: the vector-averaging scheme versus the vector summation model. Whereas the former contains at least four nonlinearities to explain visuomotor planning and saccade execution, the latter relies predominantly on linear operations. We have demonstrated that the summation model accounts for the nonlinear main sequence of saccade kinematics, and predicted that this results from a spatial gradient in temporal burst profiles of SC cells: rostral cells have higher peak-firing rates and shorter burst durations than caudal cells. Yet, the number of spikes in their saccade-related bursts is identical. In contrast, the averaging model does not predict such activity profiles. We now also show that by incorporating the concept of predictive remapping in the spatial updating of saccade sequences, the phenomenon of target averaging in double-stimulation experiments, and the occurrence of goal-directed, but highly curved saccades in the double-step paradigm, can all be explained by the same linear summation mechanism. We argue that the linear model is more in line with neurophysiological data, while relying on fewer ad-hoc assumptions than the nonlinear vector-averaging scheme.

Differential effects of reflex blinks on saccade perturbations in humans.

Studies in both humans and monkeys have indicated that blinks affect the central programming of saccades. In this study, we compared the influence of two types of reflex blinks on the trajectories and kinematics of memory-guided saccades in human subjects. We found that electrical stimulation of the supraorbital nerve shortly before or during a saccade briefly halts or decelerates the eye in midflight. After this short interruption, the eye always resumed its course and reached the target location in the absence of visual feedback. Air puff stimuli produced significant decreases in mean eye velocity too, but in addition to these changes in saccade kinematics, they produced much larger and more variable perturbations of the two-dimensional saccade trajectories. Even so, the endpoints of blink-perturbed saccades obtained under both test conditions remained as accurate and as precise as those observed in the control condition. We hypothesize that the reduction in mean eye velocity is not caused by a trigeminal reactivation of brain stem omnipause neurons but could instead arise from a trigeminal transient inhibition of saccade-related activity in the midbrain superior colliculus (SC). These findings support the theory that blink-perturbed saccades are programmed as slow, but straight, saccades onto which blink-related eye movements are superimposed. This linear superposition occurs downstream from the SC.

Increased noise level of purkinje cell activities minimizes impact of their modulation during sensorimotor control.

While firing rate is well established as a relevant parameter for encoding information exchanged between neurons, the significance of other parameters is more conjectural. Here, we show that regularity of neuronal spike activities affects sensorimotor processing in tottering mutants, which suffer from a mutation in P/Q-type voltage-gated calcium channels. While the modulation amplitude of the simple spike firing rate of their floccular Purkinje cells during optokinetic stimulation is indistinguishable from that of wild-types, the regularity of their firing is markedly disrupted. The gain and phase values of tottering's compensatory eye movements are indistinguishable from those of flocculectomized wild-types or from totterings with the flocculus treated with P/Q-type calcium channel blockers. Moreover, normal eye movements can be evoked in tottering when the flocculus is electrically stimulated with regular spike trains mimicking the firing pattern of normal simple spikes. This study demonstrates the importance of regularity of firing in Purkinje cells for neuronal information processing.

Optics of the human cornea influence the accuracy of stereo eye-tracking methods: a simulation study.

Current stereo eye-tracking methods model the cornea as a sphere with one refractive surface. However, the human cornea is slightly aspheric and has two refractive surfaces. Here we used ray-tracing and the Navarro eye-model to study how these optical properties affect the accuracy of different stereo eye-tracking methods. We found that pupil size, gaze direction and head position all influence the reconstruction of gaze. Resulting errors range between ± 1.0 degrees at best. This shows that stereo eye-tracking may be an option if reliable calibration is not possible, but the applied eye-model should account for the actual optics of the cornea.

Linear ensemble-coding in midbrain superior colliculus specifies the saccade kinematics.

Recently, we proposed an ensemble-coding scheme of the midbrain superior colliculus (SC) in which, during a saccade, each spike emitted by each recruited SC neuron contributes a fixed minivector to the gaze-control motor output. The size and direction of this 'spike vector' depend exclusively on a cell's location within the SC motor map (Goossens and Van Opstal, in J Neurophysiol 95: 2326-2341, 2006). According to this simple scheme, the planned saccade trajectory results from instantaneous linear summation of all spike vectors across the motor map. In our simulations with this model, the brainstem saccade generator was simplified by a linear feedback system, rendering the total model (which has only three free parameters) essentially linear. Interestingly, when this scheme was applied to actually recorded spike trains from 139 saccade-related SC neurons, measured during thousands of eye movements to single visual targets, straight saccades resulted with the correct velocity profiles and nonlinear kinematic relations ('main sequence properties' and 'component stretching'). Hence, we concluded that the kinematic nonlinearity of saccades resides in the spatial-temporal distribution of SC activity, rather than in the brainstem burst generator. The latter is generally assumed in models of the saccadic system. Here we analyze how this behaviour might emerge from this simple scheme. In addition, we will show new experimental evidence in support of the proposed mechanism.

Dynamic ensemble coding of saccades in the monkey superior colliculus.

The deeper layers of the midbrain superior colliculus (SC) contain a topographic motor map in which a localized population of cells is recruited for each saccade, but how the brain stem decodes the dynamic SC output is unclear. Here we analyze saccade-related responses in the monkey SC to test a new dynamic ensemble-coding model, which proposes that each spike from each saccade-related SC neuron adds a fixed, site-specific contribution to the intended eye movement command. As predicted by this simple theory, we found that the cumulative number of spikes in the cell bursts is tightly related to the displacement of the eye along the ideal straight trajectory, both for normal saccades and for strongly curved, blink-perturbed saccades toward a single visual target. This dynamic relation depends systematically on the metrics of the saccade displacement vector, and can be fully predicted from a quantitative description of the cell's classical movement field. Furthermore, we show that a linear feedback model of the brain stem, which is driven by dynamic linear vector summation of measured SC firing patterns, produces realistic two-dimensional (2D) saccade trajectories and kinematics. We conclude that the SC may act as a nonlinear, vectorial saccade generator that programs an optimal straight eye-movement trajectory.

Simple spike and complex spike activity of floccular Purkinje cells during the optokinetic reflex in mice lacking cerebellar long-term depression.

Cerebellar long-term depression (LTD) at parallel fibre-Purkinje cell (P-cell) synapses is thought to embody neuronal information storage for motor learning. Transgenic L7-protein kinase C inhibitor (PKCI) mice in which cerebellar LTD is selectively blocked do indeed exhibit impaired adaptation in the vestibulo-ocular reflex (VOR) while their default oculomotor performance is unaffected. Although supportive, these data do not definitively establish a causal link between memory storage required for motor learning and cerebellar LTD. As the L7-PKCI transgene is probably activated from the early stages of P-cell development, an alternative could be that P-cells develop abnormal signals in L7-PKCI mutants, disturbing mechanisms of motor learning that rely on proper P-cell outputs. To test this alternative hypothesis, we studied simple spike (SS) and complex spike (CS) activity of vertical axis P-cells in the flocculus of L7-PKCI mice and their wild-type littermates during sinusoidal optokinetic stimulation. Both SS and CS discharge dynamics appeared to be very similar in wild-type and transgenic P-cells at all stimulus frequencies (0.05-0.8 Hz). The CS activity of all vertical axis cells increased with contralateral stimulus rotation and lagged ipsiversive eye velocity by 165-180 degrees. The SS modulation was roughly reciprocal to the CS modulation and lagged ipsiversive eye velocity by approximately 15 degrees. The baseline SS and CS discharge characteristics were indistinguishable between the two genotypes. We conclude that the impaired VOR learning in L7-PKCI mutants does not reflect fundamental aberrations of the cerebellar circuitry. The data thus strengthen the evidence that cerebellar LTD is implicated in rapid VOR learning but not in the development of normal default response patterns.