A spiking neural network model of the midbrain superior colliculus that generates saccadic motor commands

Single-unit recordings suggest that the midbrain superior colliculus (SC) acts as an optimal controller for saccadic gaze shifts. The SC is proposed to be the site within the visuomotor system where the nonlinear spatial-to-temporal transformation is carried out: the population encodes the intended saccade vector by its location in the motor map (spatial), and its trajectory and velocity by the distribution of firing rates (temporal). The neurons’ burst profiles vary systematically with their anatomical positions and intended saccade vectors, to account for the nonlinear main-sequence kinematics of saccades. Yet, the underlying collicular mechanisms that could result in these firing patterns are inaccessible to current neurobiological techniques. Here, we propose a simple spiking neural network model that reproduces the spike trains of saccade-related cells in the intermediate and deep SC layers during saccades. The model assumes that SC neurons have distinct biophysical properties for spike generation that depend on their anatomical position in combination with a center–surround lateral connectivity. Both factors are needed to account for the observed firing patterns. Our model offers a basis for neuronal algorithms for spatiotemporal transformations and bio-inspired optimal controllers.     

A model of the saccade-generating system that accounts for trajectory variations produced by competing visual stimuli

Variable saccade trajectories are produced in visual search paradigms in which multiple potential target stimuli are present. These variable trajectories provide a rich source of information that may lead to a deeper understanding of the basic control mechanisms of the saccadic system. We have used published behavioral observations and neural recordings in the superior colliculus (SC), gathered in monkeys performing visual search paradigms, to guide the construction of a new distributed model of the saccadic system. The new model can account for many of the variations in saccade trajectory produced by the appearance of multiple visual stimuli in a search paradigm. The model uses distributed feedback about current eye motion from the brainstem to the SC to reduce activity there at physiologically realistic rates during saccades. The long-range lateral inhibitory connections between SC cells used in previous models have been eliminated to match recent physiological evidence. The model features interactions between visually activated multiple populations of cells in the SC and distributed and topologically organized inhibitory input to the SC from the SNr to produce some of the types of variable saccadic trajectories, including slightly curved and averaging saccades, observed in visual search tasks. The distributed perisaccadic disinhibition of SC from the substantia nigra (SNr) is assumed to have broad spatial tuning. In order to produce the strongly curved saccades occasionally recorded in visual search, the existence of a parallel input to the saccadic burst generators in addition to that provided by the distributed input from the SC is required. The spatiotemporal form of this additional parallel input is computed based on the assumption that the input from the model SC is realistic. In accordance with other recent models, it is assumed that the parallel input comes from the cerebellum, but our model predicts that the parallel input is delayed during highly curved saccadic trajectories.     

Distinct cortical and collicular mechanisms of inhibition of return revealed with S cone stimuli

Visual orienting of attention and gaze are widely considered to be mediated by shared neural pathways, with automatic phenomena such as inhibition of return (IOR)--the bias against returning to recently visited locations--being generated via the direct pathway from retina to superior colliculus (SC). Here, we show that IOR occurs without direct access to the SC, by using a technique that employs stimuli visible only to short-wave-sensitive (S) cones. We found that these stimuli, to which the SC is blind , were quite capable of eliciting IOR, measured by traditional manual responses. Critically, however, we found that S cone stimuli did not cause IOR when saccadic eye movement responses were required. This demonstrates that saccadic IOR is not the same as traditional IOR, providing support for two separate cortical and collicular mechanisms of IOR. These findings represent a clear dissociation between visual orienting of attention and gaze.     

The Mechanism of Saccade Motor Pattern Generation Investigated by a Large-Scale Spiking Neuron Model of the Superior Colliculus

The subcortical saccade-generating system consists of the retina, superior colliculus, cerebellum and brainstem motoneuron areas. The superior colliculus is the site of sensory-motor convergence within this basic visuomotor loop preserved throughout the vertebrates. While the system has been extensively studied, there are still several outstanding questions regarding how and where the saccade eye movement profile is generated and the contribution of respective parts within this system. Here we construct a spiking neuron model of the whole intermediate layer of the superior colliculus based on the latest anatomy and physiology data. The model consists of conductance-based spiking neurons with quasi-visual, burst, buildup, local inhibitory, and deep layer inhibitory neurons. The visual input is given from the superficial superior colliculus and the burst neurons send the output to the brainstem oculomotor nuclei. Gating input from the basal ganglia and an integral feedback from the reticular formation are also included.We implement the model in the NEST simulator and show that the activity profile of bursting neurons can be reproduced by a combination of NMDA-type and cholinergic excitatory synaptic inputs and integrative inhibitory feedback. The model shows that the spreading neural activity observed in vivo can keep track of the collicular output over time and reset the system at the end of a saccade through activation of deep layer inhibitory neurons. We identify the model parameters according to neural recording data and show that the resulting model recreates the saccade size-velocity curves known as the saccadic main sequence in behavioral studies. The present model is consistent with theories that the superior colliculus takes a principal role in generating the temporal profiles of saccadic eye movements, rather than just specifying the end points of eye movements.     

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus

 Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges. Received: 25 October 1994/Accepted in revised form: 20 June 1995     

A novel interpretation for the collicular role in saccade generation

Recently, we found evidence that the activity of neurons in the deep layers of the monkey superior colliculus (SC) is modulated by initial eye position (gain fields). In this paper, we propose a quantitative model of the motor SC which incorporates these new findings. Inputs to the motor map represent the desired eye displacement vector (motor error), as well as initial eye position. A unit's activity in the motor map is described by multiplying a weak linear eye position sensitivity with a gaussian tuning to motor error. The motor map projects to several sets of output neurons, representing the coordinates of the desired eye displacement vector, the desired eye position in the head, and the three-dimensional ocular rotation axis for saccades in Listing's plane, respectively. All these signals have been hypothesized in the literature to drive the saccade burst generator. We show that these signals can be extracted from the motor map by a linear weighting of the population activity. The saccadic system may employ all coding strategies in parallel to ensure high spatial accuracy in many complex sensorimotor tasks, such as orienting to multimodal stimuli.     

Signals invisible to the collicular and magnocellular pathways can capture visual attention

The retinal projection to the superior colliculus is thought to be important both for stimulus-driven eye movements and for the involuntary capture of attention. It has further been argued that eye-movement planning and attentional orienting share common neural mechanisms. Electrophysiological studies have shown that the superior colliculus receives no direct projections from short-wave-sensitive cones (S cones), and, consistent with this, we found that irrelevant peripheral stimuli visible only to S cones did not produce the saccadic distractor effect produced by luminance stimuli. However, when involuntary orienting was tested in a Posner cueing task, the same S-cone stimuli had normal attentional effects, in that they accelerated or delayed responses to subsequent targets. We conclude that involuntary attentional shifts do not require signals in the direct collicular pathway, or indeed the magnocellular pathway, as our S-cone stimuli were invisible to this channel also.     

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.     

Accuracy in estimating motor commands using neuronal population coding

We consider the problem of estimating motor commands from an ensemble of neuronal activities. The population vector algorithm proposed by Georgopoulos provides largely biased estimations when preferred directions of neurons are non-uniformly distributed. To improve this, various decoding methods have been proposed. However, dependence of decoding accuracy on the motor command and other features of neural activities, such as baseline firing rates or amplitudes of tuning curves, have not been quantitatively discussed. In this study, we propose a new method to estimate the motor command in the maximum likelihood estimation framework, which is analytically tractable. We find that the estimation accuracy is independent of the motor command. Using our estimation method, we can estimate the motor command with equal accuracy in all directions.     

Blink Perturbation Effects on Saccades Evoked by Microstimulation of the Superior Colliculus

Current knowledge of saccade-blink interactions suggests that blinks have paradoxical effects on saccade generation. Blinks suppress saccade generation by attenuating the oculomotor drive command in structures like the superior colliculus (SC), but they also disinhibit the saccadic system by removing the potent inhibition of pontine omnipause neurons (OPNs). To better characterize these effects, we evoked the trigeminal blink reflex by delivering an air puff to one eye as saccades were evoked by sub-optimal stimulation of the SC. For every stimulation site, the peak and average velocities of stimulation with blink movements (SwBMs) were lower than stimulation-only saccades (SoMs), supporting the notion that the oculomotor drive is weakened in the presence of a blink. In contrast, the duration of the SwBMs was longer, consistent with the hypothesis that the blink-induced inhibition of the OPNs could prolong the window of time available for oculomotor commands to drive an eye movement. The amplitude of the SwBM could also be larger than the SoM amplitude obtained from the same site, particularly for cases in which blink-associated eye movements exhibited the slowest kinematics. The results are interpreted in terms of neural signatures of saccade-blink interactions.     

Estimation of Spatiotemporal Neural Activity Using Radial Basis Function Networks

We report a method using radial basis function (RBF) networks to estimate the time evolution of population activity in topologically organized neural structures from single-neuron recordings. This is an important problem in neuroscience research, as such estimates may provide insights into systems-level function of these structures. Since single-unit neural data tends to be unevenly sampled and highly variable under similar behavioral conditions, obtaining such estimates is a difficult task. In particular, a class of cells in the superior colliculus called buildup neurons can have very narrow regions of saccade vectors for which they discharge at high rates but very large surround regions over which they discharge at low, but not zero, levels. Estimating the dynamic movement fields for these cells for two spatial dimensions at closely spaced timed intervals is a difficult problem, and no general method has been described that can be applied to all buildup cells. Estimation of individual collicular cells' spatiotemporal movement fields is a prerequisite for obtaining reliable two-dimensional estimates of the population activity on the collicular motor map during saccades. Therefore, we have developed several computational-geometry-based algorithms that regularize the data before computing a surface estimation using RBF networks. The method is then expanded to the problem of estimating simultaneous spatiotemporal activity occurring across the superior colliculus during a single movement (the inverse problem). In principle, this methodology could be applied to any neural structure with a regular, two-dimensional organization, provided a sufficient spatial distribution of sampled neurons is available.     

Modeling activity and target-dependent developmental cell death of mouse retinal ganglion cells ex vivo

Programmed cell death is widespread during the development of the central nervous system and serves multiple purposes including the establishment of neural connections. In the mouse retina a substantial reduction of retinal ganglion cells (RGCs) occurs during the first postnatal week, coinciding with the formation of retinotopic maps in the superior colliculus (SC). We previously established a retino-collicular culture preparation which recapitulates the progressive topographic ordering of RGC projections during early post-natal life. Here, we questioned whether this model could also be suitable to examine the mechanisms underlying developmental cell death of RGCs. Brn3a was used as a marker of the RGCs. A developmental decline in the number of Brn3a-immunolabelled neurons was found in the retinal explant with a timing that paralleled that observed in vivo. In contrast, the density of photoreceptors or of starburst amacrine cells increased, mimicking the evolution of these cell populations in vivo. Blockade of neural activity with tetrodotoxin increased the number of surviving Brn3a-labelled neurons in the retinal explant, as did the increase in target availability when one retinal explant was confronted with 2 or 4 collicular slices. Thus, this ex vivo model reproduces the developmental reduction of RGCs and recapitulates its regulation by neural activity and target availability. It therefore offers a simple way to analyze developmental cell death in this classic system. Using this model, we show that ephrin-A signaling does not participate to the regulation of the Brn3a population size in the retina, indicating that eprhin-A-mediated elimination of exuberant projections does not involve developmental cell death.     

The distributed representation of vestibulo-oculomotor signals by brain-stem neurons

The vestibuloocular reflex and other oculomotor functions are subserved by populations of neurons operating in parallel. This distributed aspect of the system's organization has been largely ignored in previous block diagram models. Neurons that transmit oculomotor signals, such as those in the vestibular nucleus (VN), actually combine the different types of signals in a diverse, seemingly random way that could not be predicted from a block diagram. We used the backpropagation learning algorithm to program distributed neural-network models of the vestibulo-oculomotor system. Networks were trained to combine vestibular, pursuit and saccadic eye velocity command signals. The model neurons in these neural networks have diverse combinations of vestibulo-oculomotor signals that are qualitatively similar to those reported for actual VN neurons in the monkey. This similarity implicates a learning mechanism as an organizing influence on the vestibulo-oculomotor system and demonstrates how VN neurons can encode vestibulo-oculomotor signals in a diverse, distributed manner.     

Postnatal development of the occipito-tectal pathway in the rat

The postnatal development of the occipito-tectal pathway was studied by making single injections of 3H-leucine into the striate cortex of rats ranging in age from newborn to postnatal day 50 (P50). After these injections, the earliest age at which autoradiographic labeling was found in the ipsilateral superior colliculus (SC) was P4. Two main stages were recognized in the development of the occipito-tectal pathway. In the first stage, from P4 to P9, the silver grain pattern over the SC was suggestive of axonal labeling. The label was tangentially and radially exuberant involving the prospective stratum opticum, the adjacent part of the stratum griseum superficiale and also the strata intermediale. A rough topographic order in the projection existed at least from P6. The second stage, from P9 to P17, was characterized by the ingrowth of axonal arbors into the collicular strata superficiale and by the disappearance of the tangentially exuberant projections. Quantitative estimations of the degree of tangential exuberancy of the projection showed that it underwent a reduction of almost 50% from P7 to P17. By P17, the radial and tangential patterns of termination of the occipito-tectal pathway appeared virtually mature. No projections to the contralateral SC were observed at any age. The results of the present study indicate that the mature topographic pattern of the occipito-tectal projection is attained through two separate steps which may involve a number of different mechanisms. In the first step, occipital axons grow orderly -although in an exuberant manner- towards their roughly appropriate tectal locations, remaining to a large extent confined to the collicular white matter. In the second step, further refinement of the topographic map is achieved both by selective growing of terminal arbors into tangentially restricted regions of the tectal surface, and, by retraction of tangentially exuberant projections.     

Dissociable spatial and temporal effects of inhibition of return

Inhibition of return (IOR) refers to the relative suppression of processing at locations that have recently been attended. It is frequently explored using a spatial cueing paradigm and is characterized by slower responses to cued than to uncued locations. The current study investigates the impact of IOR on overt visual orienting involving saccadic eye movements. Using a spatial cueing paradigm, our experiments have demonstrated that at a cue-target onset asynchrony (CTOA) of 400 ms saccades to the vicinity of cued locations are not only delayed (temporal cost) but also biased away (spatial effect). Both of these effects are basically no longer present at a CTOA of 1200 ms. At a shorter 200 ms CTOA, the spatial effect becomes stronger while the temporal cost is replaced by a temporal benefit. These findings suggest that IOR has a spatial effect that is dissociable from its temporal effect. Simulations using a neural field model of the superior colliculus (SC) revealed that a theory relying on short-term depression (STD) of the input pathway can explain most, but not all, temporal and spatial effects of IOR.     

Time course of a repetition effect on saccadic reaction time in non-human primates

Repeated training in a stimulus response task can lead to adaptive changes in the resulting behavior. Using a simple saccade task, we investigated the effect that the location of the target in the preceding trial had on the saccadic reaction time (SRT) of the current trial. To determine the time course of this effect, we varied the intertrial interval (ITI). Finally, we examined the pretarget discharge of single neurons in the intermediate layers of the superior colliculus (SC) during the task. Our data reveal that monkeys have a robust repetition effect in which there was an overall decrease in SRT and increase in SC pretarget activity when the target of the previous saccade was in the same location as that of the current trial. Additionally, we have shown a robust time course of this repetition effect, revealing that it exists for only a limited amount of time.     

Geometry of the superior colliculus mapping and efficient oculomotor computation

Numerous brain regions encode variables using spatial distribution of activity in neuronal maps. Their specific geometry is usually explained by sensory considerations only. We provide here, for the first time, a theory involving the motor function of the superior colliculus to explain the geometry of its maps. We use six hypotheses in accordance with neurobiology to show that linear and logarithmic mappings are the only ones compatible with the generation of saccadic motor command. This mathematical proof gives a global coherence to the neurobiological studies on which it is based. Moreover, a new solution to the problem of saccades involving both colliculi is proposed. Comparative simulations show that it is more precise than the classical one.