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.
Single-unit recordings in head-restrained monkeys indicated that the population of saccade-related cells in the midbrain Superior Colliculus (SC) encodes the kinematics of desired straight saccade trajectories by the cumulative number of spikes. In addition, the nonlinear main sequence of saccades (their amplitude–peak velocity saturation) emerges from a spatial gradient of peak-firing rates of collicular neurons, rather than from neural saturation at brain-stem burst generators. We here extend this idea to eye-head gaze shifts and illustrate how the cumulative spike-count in head-unrestrained monkeys relates to the desired gaze trajectory and its kinematics. We argue that the output of the motor SC is an abstract desired gaze-motor signal, which drives in a feedforward way the instantaneous kinematics of ongoing gaze shifts, including the strong influence of initial eye position on gaze kinematics. We propose that the neural population acts as a vectorial gaze pulse-generator for eye-head saccades, which is sub-sequently decomposed into signals that drive both motor systems in appropriate craniocentric reference frames within a dynamic gaze-velocity feedback loop.
Graphical processing units (GPUs) can significantly accelerate spiking neural network (SNN) simulations by exploiting parallelism for independent computations. Both the changes in membrane potential at each time-step, and checking for spiking threshold crossings for each neuron, can be calculated independently. However, because synaptic transmission requires communication between many different neurons, efficient parallel processing may be hindered, either by data transfers between GPU and CPU at each time-step or, alternatively, by running many parallel computations for neurons that do not elicit any spikes. This, in turn, would lower the effective throughput of the simulations. Traditionally, a central processing unit (CPU, host) administers the execution of parallel processes on the GPU (device), such as memory initialization on the device, data transfer between host and device, and starting and synchronizing parallel processes. The parallel computing platform CUDA 5.0 introduced dynamic parallelism, which allows the initiation of new parallel applications within an ongoing parallel kernel. Here, we apply dynamic parallelism for synaptic updating in SNN simulations on a GPU. Our algorithm eliminates the need to start many parallel applications at each time-step, and the associated lags of data transfer between CPU and GPU memories. We report a significant speed-up of SNN simulations, when compared to former accelerated parallelization strategies for SNNs on a GPU.
13The midbrain superior colliculus (SC) generates a rapid saccadic eye movement to a sensory stimulus 14 by recruiting a population of cells in its topographically organized motor map. Supra-threshold 15 electrical microstimulation in the SC reveals that the site of stimulation produces a normometric 16 saccade vector with little effect of the stimulation parameters. Moreover, electrically evoked saccades 17 (E-saccades) have kinematic properties that strongly resemble natural, visual-evoked saccades (V-18 saccades). These findings support models in which the saccade vector is determined by a center-of-19 gravity computation of activated neurons, while its trajectory and kinematics arise from downstream 20 feedback circuits in the brainstem. Recent single-unit recordings, however, have indicated that the SC 21 population also specifies instantaneous kinematics. These results support an alternative model, in 22 which the desired saccade trajectory, including its kinematics, follows from instantaneous summation 23 Kasap and Van Opstal: Microstimulation in a spiking neural network model 2 of movement effects of all SC spike trains. But how to reconcile this model with microstimulation 24 results? Although it is thought that microstimulation activates a large population of SC neurons, the 25 mechanism through which it arises is unknown. We developed a spiking neural network model of the 26 SC, in which microstimulation directly activates a relatively small set of neurons around the electrode 27 tip, which subsequently sets up a large population response through lateral synaptic interactions. We 28 show that through this mechanism the population drives an E-saccade with near-normal kinematics 29 that are largely independent of the stimulation parameters. Only at very low stimulus intensities the 30 network recruits a population with low firing rates, resulting in abnormally slow saccades. 31 32 33 34 35 36 37 Author Summary 38 39 The midbrain Superior Colliculus (SC) contains a topographically organized map for rapid goal-40 directed gaze shifts, in which the location of the active population determines size and direction of the 41 eye-movement vector, and the neural firing rates specify the eye-movement kinematics. Electrical 42 microstimulation in this map produces eye movements that correspond to the site of stimulation with 43 normal kinematics. We here explain how intrinsic lateral interactions within the SC network of spiking 44 neurons sets up the population activity profile in response to local microstimulation to explain these 45 results. 46 47 48
In dynamic visual or auditory gaze double-steps, a brief target flash or sound burst is presented in midflight of an ongoing eye-head gaze shift. Behavioral experiments in humans and monkeys have indicated that the subsequent eye and head movements to the target are goal-directed, regardless of stimulus timing, first gaze shift characteristics, and initial conditions. This remarkable behavior requires that the gaze-control system 1) has continuous access to accurate signals about eye-in-head position and ongoing eye-head movements, 2) that it accounts for different internal signal delays, and 3) that it is able to update the retinal ( T) and head-centric ( T) target coordinates into appropriate eye-centered and head-centered motor commands on millisecond time scales. As predictive, feedforward remapping of targets cannot account for this behavior, we propose that targets are transformed and stored into a stable reference frame as soon as their sensory information becomes available. We present a computational model, in which recruited cells in the midbrain superior colliculus drive eyes and head to the stored target location through a common dynamic oculocentric gaze-velocity command, which is continuously updated from the stable goal and transformed into appropriate oculocentric and craniocentric motor commands. We describe two equivalent, yet conceptually different, implementations that both account for the complex, but accurate, kinematic behaviors and trajectories of eye-head gaze shifts under a variety of challenging multisensory conditions, such as in dynamic visual-auditory multisteps.
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