A reevaluation of the inverse dynamic model for eye movements

Role of the Cerebellum in the Construction of Functional and Geometrical Spaces

The perceptual and motor systems appear to have a set of movement primitives that exhibit certain geometric and kinematic invariances. Complex patterns and mental representations can be produced by (re)combining some simple motor elements in various ways using basic operations, transformations, and respecting a set of laws referred to as kinematic laws of motion. For example, point-to-point hand movements are characterized by straight hand paths with single-peaked-bell-shaped velocity profiles, whereas hand speed profiles for curved trajectories are often irregular and more variable, with speed valleys and inflections extrema occurring at the peak curvature. Curvature and speed are generically related by the 2/3 power law. Mathematically, such laws can be deduced from a combination of Euclidean, affine, and equi-affine geometries, whose neural correlates have been partially detected in various brain areas including the cerebellum and the basal ganglia. The cerebellum has been found to play an important role in the control of coordination, balance, posture, and timing over the past years. It is also assumed that the cerebellum computes forward internal models in relationship with specific cortical and subcortical brain regions but its motor relationship with the perceptual space is unclear. A renewed interest in the geometrical and spatial role of the cerebellum may enable a better understanding of its specific contribution to the action-perception loop and behavior's adaptation. In this sense, we complete this overview with an innovative theoretical framework that describes a possible implementation and selection by the cerebellum of geometries adhering to different mathematical laws.

Oculomotor plant and neural dynamics suggest gaze control requires integration on distributed timescales

A fundamental principle of biological motor control is that the neural commands driving movement must conform to the response properties of the motor plants they control. In the oculomotor system, characterizations of oculomotor plant dynamics traditionally supported models in which the plant responds to neural drive to extraocular muscles on exclusively short, subsecond timescales. These models predict that the stabilization of gaze during fixations between saccades requires neural drive that approximates eye position on longer timescales and is generated through the temporal integration of brief eye velocity-encoding signals that cause saccades. However, recent measurements of oculomotor plant behaviour have revealed responses on longer timescales. Furthermore, measurements of firing patterns in the oculomotor integrator have revealed a more complex encoding of eye movement dynamics. Yet, the link between these observations has remained unclear. Here we use measurements from the larval zebrafish to link dynamics in the oculomotor plant to dynamics in the neural integrator. The oculomotor plant in both anaesthetized and awake larval zebrafish was characterized by a broad distribution of response timescales, including those much longer than 1 s. Analysis of the firing patterns of oculomotor integrator neurons, which exhibited a broadly distributed range of decay time constants, demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with distributed response timescales. This work suggests that leaky integration on multiple, distributed timescales by the oculomotor integrator reflects an inverse model for generating oculomotor commands, and that multi-timescale dynamics may be a general feature of motor circuitry. KEY POINTS: Recent observations of oculomotor plant response properties and neural activity across the oculomotor system have called into question classical formulations of both the oculomotor plant and the oculomotor integrator. Here we use measurements from new and published experiments in the larval zebrafish together with modelling to reconcile recent oculomotor plant observations with oculomotor integrator function. We developed computational techniques to characterize oculomotor plant responses over several seconds in awake animals, demonstrating that long timescale responses seen in anaesthetized animals extend to the awake state. Analysis of firing patterns of oculomotor integrator neurons demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with multiple, distributed response timescales. Our results support a formulation of gaze stabilization by the oculomotor system in which commands for stabilizing gaze are generated through integration on multiple, distributed timescales.

Spiking model of fixational eye movements and figure-ground segmentation

We present a model connecting eye movements and cortical state. Its structure includes simulated retinal images, motion detection, feature detectors and layers of spiking neurons. The designed scheme shows how the effect of micro-saccadic scale eye movements can lead to successful figure segregation in a figure-ground paradigm, by inducing changes in the neural dynamics through the time evolution of the inhibition range.

Seeing motion of controlled object improves grip timing in adults with autism spectrum condition: evidence for use of inverse dynamics in motor control

Previous studies (Haswell et al. in Nat Neurosci 12:970-972, 2009; Marko et al. in Brain J Neurol 138:784-797, 2015) reported that people with autism rely less on vision for learning to reach in a force field. This suggested a possibility that they have difficulties in extracting force information from visual motion signals, a process called inverse dynamics computation. Our recent study (Takamuku et al. in J Int Soc Autism Res 11:1062-1075, 2018) examined the ability of inverse computation with two perceptual tasks and found similar performances in typical and autistic adults. However, this tested the computation only in the context of sensory perception while it was possible that the suspected disability is specific to the motor domain. Here, in order to address the concern, we tested the use of inverse dynamics computation in the context of motor control by measuring changes in grip timing caused by seeing/not seeing a controlled object. The motion of the object was informative of its inertial force and typical participants improved their grip timing based on the visual feedback. Our interest was on whether the autism participants show the same improvement. While some autism participants showed atypical hand slowing when seeing the controlled object, we found no evidence of abnormalities in the inverse computation in our grip timing task or in a replication of the perceptual task. This suggests that the ability of inverse dynamics computation is preserved not only for sensory perception but also for motor control in adults with autism.

Translation information processing is regulated by protein kinase C-dependent mechanism in Purkinje cells in murine posterior vermis

The cerebellar posterior vermis generates an estimation of our motion (translation) and orientation (tilt) in space using cues originating from semicircular canals and otolith organs. Theoretical work has laid out the basic computations necessary for this signal transformation, but details on the cellular loci and mechanisms responsible are lacking. Using a multicomponent modeling approach, we show that canal and otolith information are spatially and temporally matched in mouse posterior vermis Purkinje cells and that Purkinje cell responses combine translation and tilt information. Purkinje cell-specific inhibition of protein kinase C decreased and phase-shifted the translation component of Purkinje cell responses, but did not affect the tilt component. Our findings suggest that translation and tilt signals reach Purkinje cells via separate information pathways and that protein kinase C-dependent mechanisms regulate translation information processing in cerebellar cortex output neurons.

A Neuroanatomically Grounded Optimal Control Model of the Compensatory Eye Movement System in Mice

We present a working model of the compensatory eye movement system in mice. We challenge the model with a data set of eye movements in mice (n =34) recorded in 4 different sinusoidal stimulus conditions with 36 different combinations of frequency (0.1-3.2 Hz) and amplitude (0.5-8°) in each condition. The conditions included vestibular stimulation in the dark (vestibular-ocular reflex, VOR), optokinetic stimulation (optokinetic reflex, OKR), and two combined visual/vestibular conditions (the visual-vestibular ocular reflex, vVOR, and visual suppression of the VOR, sVOR). The model successfully reproduced the eye movements in all conditions, except for minor failures to predict phase when gain was very low. Most importantly, it could explain the interaction of VOR and OKR when the two reflexes are activated simultaneously during vVOR stimulation. In addition to our own data, we also reproduced the behavior of the compensatory eye movement system found in the existing literature. These include its response to sum-of-sines stimuli, its response after lesions of the nucleus prepositus hypoglossi or the flocculus, characteristics of VOR adaptation, and characteristics of drift in the dark. Our model is based on ideas of state prediction and forward modeling that have been widely used in the study of motor control. However, it represents one of the first quantitative efforts to simulate the full range of behaviors of a specific system. The model has two separate processing loops, one for vestibular stimulation and one for visual stimulation. Importantly, state prediction in the visual processing loop depends on a forward model of residual retinal slip after vestibular processing. In addition, we hypothesize that adaptation in the system is primarily adaptation of this model. In other words, VOR adaptation happens primarily in the OKR loop.

The Macaque Cerebellar Flocculus Outputs a Forward Model of Eye Movement

The central nervous system (CNS) achieves fine motor control by generating predictions of the consequences of the motor command, often called forward models of the movement. These predictions are used centrally to detect not-self generated sensations, to modify ongoing movements, and to induce motor learning. However, finding a neuronal correlate of forward models has proven difficult. In the oculomotor system, we can identify neuronal correlates of forward models vs. neuronal correlates of motor commands by examining neuronal responses during smooth pursuit at eccentric eye positions. During pursuit, torsional eye movement information is not present in the motor command, but it is generated by the mechanic of the orbit. Importantly, the directionality and approximate magnitude of torsional eye movement follow the half angle rule. We use this rule to investigate the role of the cerebellar flocculus complex (FL, flocculus and ventral paraflocculus) in the generation of forward models of the eye. We found that mossy fibers (input elements to the FL) did not change their response to pursuit with eccentricity. Thus, they do not carry torsional eye movement information. However, vertical Purkinje cells (PCs; output elements of the FL) showed a preference for counter-clockwise (CCW) eye velocity [corresponding to extorsion (outward rotation) of the ipsilateral eye]. We hypothesize that FL computes an estimate of torsional eye movement since torsion is present in PCs but not in mossy fibers. Overall, our results add to those of other laboratories in supporting the existence in the CNS of a predictive signal constructed from motor command information.

Role of Rostral Fastigial Neurons in Encoding a Body-Centered Representation of Translation in Three Dimensions

Many daily behaviors rely critically on estimates of our body motion. Such estimates must be computed by combining neck proprioceptive signals with vestibular signals that have been transformed from a head- to a body-centered reference frame. Recent studies showed that deep cerebellar neurons in the rostral fastigial nucleus (rFN) reflect these computations, but whether they explicitly encode estimates of body motion remains unclear. A key limitation in addressing this question is that, to date, cell tuning properties have only been characterized for a restricted set of motions across head-re-body orientations in the horizontal plane. Here we examined, for the first time, how 3D spatiotemporal tuning for translational motion varies with head-re-body orientation in both horizontal and vertical planes in the rFN of male macaques. While vestibular coding was profoundly influenced by head-re-body position in both planes, neurons typically reflected at most a partial transformation. However, their tuning shifts were not random but followed the specific spatial trajectories predicted for a 3D transformation. We show that these properties facilitate the linear decoding of fully body-centered motion representations in 3D with a broad range of temporal characteristics from small groups of 5-7 cells. These results demonstrate that the vestibular reference frame transformation required to compute body motion is indeed encoded by cerebellar neurons. We propose that maintaining partially transformed rFN responses with different spatiotemporal properties facilitates the creation of downstream body motion representations with a range of dynamic characteristics, consistent with the functional requirements for tasks such as postural control and reaching.SIGNIFICANCE STATEMENT Estimates of body motion are essential for many daily activities. Vestibular signals are important contributors to such estimates but must be transformed from a head- to a body-centered reference frame. Here, we provide the first direct demonstration that the cerebellum computes this transformation fully in 3D. We show that the output of these computations is reflected in the tuning properties of deep cerebellar rostral fastigial nucleus neurons in a specific distributed fashion that facilitates the efficient creation of body-centered translation estimates with a broad range of temporal properties (i.e., from acceleration to position). These findings support an important role for the rostral fastigial nucleus as a source of body translation estimates functionally relevant for behaviors ranging from postural control to perception.

The Cerebellum: Adaptive Prediction for Movement and Cognition

Over the past 30 years, cumulative evidence has indicated that cerebellar function extends beyond sensorimotor control. This view has emerged from studies of neuroanatomy, neuroimaging, neuropsychology, and brain stimulation, with the results implicating the cerebellum in domains as diverse as attention, language, executive function, and social cognition. Although the literature provides sophisticated models of how the cerebellum helps refine movements, it remains unclear how the core mechanisms of these models can be applied when considering a broader conceptualization of cerebellar function. In light of recent multidisciplinary findings, we examine how two key concepts that have been suggested as general computational principles of cerebellar function- prediction and error-based learning- might be relevant in the operation of cognitive cerebro-cerebellar loops.

Eye Movements in Darkness Modulate Self-Motion Perception

During self-motion, humans typically move the eyes to maintain fixation on the stationary environment around them. These eye movements could in principle be used to estimate self-motion, but their impact on perception is unknown. We had participants judge self-motion during different eye-movement conditions in the absence of full-field optic flow. In a two-alternative forced choice task, participants indicated whether the second of two successive passive lateral whole-body translations was longer or shorter than the first. This task was used in two experiments. In the first (n = 8), eye movements were constrained differently in the two translation intervals by presenting either a world-fixed or body-fixed fixation point or no fixation point at all (allowing free gaze). Results show that perceived translations were shorter with a body-fixed than a world-fixed fixation point. A linear model indicated that eye-movement signals received a weight of ∼25% for the self-motion percept. This model was independently validated in the trials without a fixation point (free gaze). In the second experiment (n = 10), gaze was free during both translation intervals. Results show that the translation with the larger eye-movement excursion was judged more often to be larger than chance, based on an oculomotor choice probability analysis. We conclude that eye-movement signals influence self-motion perception, even in the absence of visual stimulation.

Mechanisms and functional roles of glutamatergic synapse diversity in a cerebellar circuit

Synaptic currents display a large degree of heterogeneity of their temporal characteristics, but the functional role of such heterogeneities remains unknown. We investigated in rat cerebellar slices synaptic currents in Unipolar Brush Cells (UBCs), which generate intrinsic mossy fibers relaying vestibular inputs to the cerebellar cortex. We show that UBCs respond to sinusoidal modulations of their sensory input with heterogeneous amplitudes and phase shifts. Experiments and modeling indicate that this variability results both from the kinetics of synaptic glutamate transients and from the diversity of postsynaptic receptors. While phase inversion is produced by an mGluR2-activated outward conductance in OFF-UBCs, the phase delay of ON UBCs is caused by a late rebound current resulting from AMPAR recovery from desensitization. Granular layer network modeling indicates that phase dispersion of UBC responses generates diverse phase coding in the granule cell population, allowing climbing-fiber-driven Purkinje cell learning at arbitrary phases of the vestibular input.

DOI:http://dx.doi.org/10.7554/eLife.15872.001

Whether walking, riding a bicycle or simply standing still, we continually adjust our posture in small ways to prevent ourselves from falling. Our sense of balance depends on a set of structures inside the inner ear called the vestibular system. These structures detect movements of the head and relay this information to the brain in the form of electrical signals. A brain area called the vestibulo-cerebellum then combines these signals with sensory input from the eyes and muscles, before sending out further signals to trigger any adjustments necessary for balance.

One of the main cell types within the vestibulo-cerebellum is the unipolar brush cell (or UBC for short). UBCs pass on signals to another type of neuron called Purkinje cells, which support the learning of motor skills such as adjusting posture. Zampini, Liu et al. set out to test the idea that UBCs transform inputs from the vestibular system into a format that makes it easier for cerebellar Purkinje cells to drive this kind of learning.

First, recordings from slices of rodent brain revealed that UBCs respond in highly variable ways to vestibular input, with both the size and timing of responses varying between cells. This is because vestibular signals trigger the release of a chemical messenger called glutamate onto UBCs, but UBCs possess a variety of different types of glutamate receptors. Vestibular input therefore activates distinct signaling cascades from one UBC to the next. According to a computer model, this variability in UBC responses ensures that a subset of UBCs will always be active at any point during vestibular input. This in turn means that Purkinje cells can fire at any stage of a movement, which boosts the learning of motor skills.

The next steps will be to test this hypothesis using mutant mice that lack specific receptor subtypes in UBCs or UBCs completely. A further challenge for the future will be to build a computer model of the vestibulo-cerebellar system that includes all of its component cell types.

DOI:http://dx.doi.org/10.7554/eLife.15872.002

Cerebellar Premotor Output Neurons Collateralize to Innervate the Cerebellar Cortex

Motor commands computed by the cerebellum are hypothesized to use corollary discharge, or copies of outgoing commands, to accelerate motor corrections. Identifying sources of corollary discharge, therefore, is critical for testing this hypothesis. Here we verified that the pathway from the cerebellar nuclei to the cerebellar cortex in mice includes collaterals of cerebellar premotor output neurons, mapped this collateral pathway, and identified its postsynaptic targets. Following bidirectional tracer injections into a distal target of the cerebellar nuclei, the ventrolateral thalamus, we observed retrogradely labeled somata in the cerebellar nuclei and mossy fiber terminals in the cerebellar granule layer, consistent with collateral branching. Corroborating these observations, bidirectional tracer injections into the cerebellar cortex retrogradely labeled somata in the cerebellar nuclei and boutons in the ventrolateral thalamus. To test whether nuclear output neurons projecting to the red nucleus also collateralize to the cerebellar cortex, we used a Cre-dependent viral approach, avoiding potential confounds of direct red nucleus-to-cerebellum projections. Injections of a Cre-dependent GFP-expressing virus into Ntsr1-Cre mice, which express Cre selectively in the cerebellar nuclei, retrogradely labeled somata in the interposed nucleus, and putative collateral branches terminating as mossy fibers in the cerebellar cortex. Postsynaptic targets of all labeled mossy fiber terminals were identified using immunohistochemical Golgi cell markers and electron microscopic profiles of granule cells, indicating that the collaterals of nuclear output neurons contact both Golgi and granule cells. These results clarify the organization of a subset of nucleocortical projections that constitute an experimentally accessible corollary discharge pathway within the cerebellum.

Local population synchrony and the encoding of eye position in the primate neural integrator

Encoding horizontal eye position in the oculomotor system occurs through temporal integration of eye velocity inputs to produce tonic outputs. The nucleus prepositus is commonly believed to be the "neural integrator" that accomplishes this function through the activity of its ensemble of predominantly burst-tonic neurons. Single-unit characterizations and labeling studies of these neurons have suggested that their collective output is achieved through local feedback loops produced by direct connections between them. If this is the case, then the ensemble of burst-tonic neurons should exhibit correlated activity. To obtain electrophysiological evidence of local interactions between neurons, we simultaneously recorded pairs (n = 29) of burst-tonic neurons in the nucleus prepositus of rhesus macaque monkeys using eight-channel linear microelectrode arrays. We computed the magnitude of synchrony between their spike trains as a function of eye position during ocular fixations and as a function of distance between neurons. Importantly, we found that neurons exhibit unexpected levels of positive synchrony, which is maximal during contralateral fixations and weakest when neurons are located far apart from one another (>300 μm). Together, our results support a role for shared inputs to ipsilateral pairs of burst-tonic neurons in the encoding of eye position in the primate nucleus prepositus.

Multiple timescales in the adaptation of the rotational VOR

Goal-directed movements, such as pointing and saccades, have been shown to share similar neural architectures, in spite of the different neuromuscular systems producing them. Such structure involve an inverse model of the actuator being controlled, which produces the commands innervating the muscles, and a forward model of the actuator, which predicts the sensory consequences of such commands and allows online movement corrections. Recent studies have shown that goal-directed movements also share similar motor-learning and motor-memory mechanisms, which are based on multiple timescales. The hypothesis that also the rotational vestibulo-ocular reflex (rVOR) may be based on a similar architecture has been presented recently. We hypothesize that multiple timescales are the brain's solution to the plasticity-stability dilemma, allowing adaptation to temporary and sudden changes while keeping stable motor-control abilities. If that were the case, then we would also expect the adaptation of reflex movements to follow the same principles. Thus we studied rVOR gain adaptation in eight healthy human subjects using a custom paradigm aimed at investigating the existence of spontaneous recovery, which we considered as the hallmark of multiple timescales in motor learning. Our experimental results show that spontaneous recovery occurred in six of eight subjects. Thus we developed a mathematical model of rVOR adaptation based on two hidden-states processes, which adapts the cerebellar-forward model of the ocular motor plant, and show that it accurately simulates our experimental data on rVOR gain adaptation, whereas a single timescale learning process fails to do so.

Neural representation of orientation relative to gravity in the macaque cerebellum

A fundamental challenge for maintaining spatial orientation and interacting with the world is knowledge of our orientation relative to gravity, i.e., head tilt. Sensing gravity is complicated because of Einstein's equivalence principle, in which gravitational and translational accelerations are physically indistinguishable. Theory has proposed that this ambiguity is solved by tracking head tilt through multisensory integration. Here we identify a group of Purkinje cells in the caudal cerebellar vermis with responses that reflect an estimate of head tilt. These tilt-selective cells are complementary to translation-selective Purkinje cells, such that their population activities sum to the net gravitoinertial acceleration encoded by the otolith organs, as predicted by theory. These findings reflect the remarkable ability of the cerebellum for neural computation and provide quantitative evidence for a neural representation of gravity, whose calculation relies on long-postulated theoretical concepts such as internal models and Bayesian priors.

Diversity of vestibular nuclei neurons targeted by cerebellar nodulus inhibition

A functional role of the cerebellar nodulus and ventral uvula (lobules X and IXc,d of the vermis) for vestibular processing has been strongly suggested by direct reciprocal connections with the vestibular nuclei, as well as direct vestibular afferent inputs as mossy fibres. Here we have explored the types of neurons in the macaque vestibular nuclei targeted by nodulus/ventral uvula inhibition using orthodromic identification from the caudal vermis. We found that all nodulus-target neurons are tuned to vestibular stimuli, and most are insensitive to eye movements. Such non-eye-movement neurons are thought to project to vestibulo-spinal and/or thalamo-cortical pathways. Less than 20% of nodulus-target neurons were sensitive to eye movements, suggesting that the caudal vermis can also directly influence vestibulo-ocular pathways. In general, response properties of nodulus-target neurons were diverse, spanning the whole continuum previously described in the vestibular nuclei. Most nodulus-target cells responded to both rotation and translation stimuli and only a few were selectively tuned to translation motion only. Other neurons were sensitive to net linear acceleration, similar to otolith afferents. These results demonstrate that, unlike the flocculus and ventral paraflocculus which target a particular cell group, nodulus/ventral uvula inhibition targets a large diversity of cell types in the vestibular nuclei, consistent with a broad functional significance contributing to vestibulo-ocular, vestibulo-thalamic and vestibulo-spinal pathways.

The nucleus prepositus predominantly outputs eye movement-related information during passive and active self-motion

Maintaining a constant representation of our heading as we move through the world requires the accurate estimate of spatial orientation. As one turns (or is turned) toward a new heading, signals from the semicircular canals are relayed through the vestibular system to higher-order centers that encode head direction. To date, there is no direct electrophysiological evidence confirming the first relay point of head-motion signals from the vestibular nuclei, but previous anatomical and lesion studies have identified the nucleus prepositus as a likely candidate. Whereas burst-tonic neurons encode only eye-movement signals during head-fixed eye motion and passive vestibular stimulation, these neurons have not been studied during self-generated movements. Here, we specifically address whether burst-tonic neurons encode head motion during active behaviors. Single-unit responses were recorded from the nucleus prepositus of rhesus monkeys and compared for head-restrained and active conditions with comparable eye velocities. We found that neurons consistently encoded eye position and velocity across conditions but did not exhibit significant sensitivity to head position or velocity. Additionally, response sensitivities varied as a function of eye velocity, similar to abducens motoneurons and consistent with their role in gaze control and stabilization. Thus our results demonstrate that the primate nucleus prepositus chiefly encodes eye movement even during active head-movement behaviors, a finding inconsistent with the proposal that this nucleus makes a direct contribution to head-direction cell tuning. Given its ascending projections, however, we speculate that this eye-movement information is integrated with other inputs in establishing higher-order spatial representations.

Contributions of ocular vestibular evoked myogenic potentials and the electrooculogram to periocular potentials produced by whole-body vibration

In this paper we report the results of an experiment to investigate the emergence of ocular vestibular evoked myogenic potentials (OVEMPs) during the linear vestibular ocular reflex (LVOR) evoked by whole-body vibration (WBV). OVEMP and electrooculogram (EOG) montages were employed to record periocular potentials (POPs) from six subjects during WBV in the nasooccipital (NO) axis over a range of frequencies from 0.5 to 64 Hz with approximately constant peak head acceleration of 1.0 ms(-2) (i.e., 0.1 g). Measurements were made in two context conditions: a fixation context to examine the effect of gaze eccentricity (0 vs. 20°), and a visual context, where a target was either head-fixed or earth-fixed. The principal results are that from 0.5 to 2 Hz POP magnitude in the earth-fixed condition is related to head displacement, so with constant acceleration at all frequencies it reduces with increasing frequency, but at frequencies greater than 2 Hz both POP magnitude and POP gain, defined as the ratio of POP magnitude at 20 and 0°, increase with increasing frequency. By exhibiting this high-pass characteristic, a property shared with the LVOR, the results are consistent with the hypothesis that the OVEMP, as commonly employed in the clinical setting, is a high-frequency manifestation of the LVOR. However, we also observed low-frequency acceleration following POPs in head-fixed conditions, consistent with a low-frequency OVEMP, and found evidence of a high-frequency visual context effect, which is also consistent with the OVEMP being a manifestation of the LVOR.

Does orbital proprioception contribute to gaze stability during translation?

Translational motion induces retinal image slip which varies with object distance. The brain must know binocular eye position in real time in order to scale eye movements so as to minimize retinal slip. Two potential sources of eye position information are orbital proprioception and an internal representation of eye position derived from central ocular motor signals. To examine the role of orbital proprioceptive information, the position of the left eye was perturbed by microstimulation of the left abducens nerve during translational motion to the right or left along the interaural axis in two rhesus macaques. Microstimulation rotated the eye laterally, activating eye muscle proprioceptors, while keeping central motor commands undisturbed. We found that microstimulation-induced eye position changes did not affect the translational VOR in the abductive (lateral rectus) direction, but it did influence the responses in the adductive (medial rectus) direction. Our findings demonstrate that proprioceptive inputs appear to be involved in the TVOR responses at least during ipsilateral head movements and proprioceptive influences on the TVOR may involve vergence-related signals to the oculomotor nucleus. However, internal representation of eye position, derived from central ocular motor signals, likely plays the dominant role in providing eye position information for scaling eye movements during translational motion, particularly in the abducent direction.

Quick phases control ocular torsion during smooth pursuit

One of the open questions in oculomotor control of visually guided eye movements is whether it is possible to smoothly track a target along a curvilinear path across the visual field without changing the torsional stance of the eye. We show in an experimental study of three-dimensional eye movements in subhuman primates (Macaca mulatta) that although the pursuit system is able to smoothly change the orbital orientation of the eye's rotation axis, the smooth ocular motion was interrupted every few hundred milliseconds by a small quick phase with amplitude <1.5° while the animal tracked a target along a circle or ellipse. Specifically, during circular pursuit of targets moving at different angular eccentricities (5°, 10°, and 15°) relative to straight ahead at spatial frequencies of 0.067 and 0.1 Hz, the torsional amplitude of the intervening quick phases was typically around 1° or smaller and changed direction for clockwise vs. counterclockwise tracking. Reverse computations of the eye rotation based on the recorded angular eye velocity showed that the quick phases facilitate the overall control of ocular orientation in the roll plane, thereby minimizing torsional disturbances of the visual field. On the basis of a detailed kinematic analysis, we suggest that quick phases during curvilinear smooth tracking serve to minimize deviations from Donders' law, which are inevitable due to the spherical configuration space of smooth eye movements.

Golgi cells operate as state-specific temporal filters at the input stage of the cerebellar cortex

Cerebellar processing of incoming information begins at the synapse between mossy fibers and granule cells, a synapse that is strongly controlled through Golgi cell inhibition. Thus, Golgi cells are uniquely positioned to control the flow of information into the cerebellar cortex and understanding their responses during behavior is essential to understanding cerebellar function. Here we show, for the first time, that Golgi cells express a unique oculomotor-related signal that can be used to provide state- and time-specific filtering of granule cell activity. We used newly established criteria to identify the unique electrophysiological signature of Golgi cells and recorded these neurons in the squirrel monkey ventral paraflocculus during oculomotor behaviors. We found that they carry eye movement, but not vestibular or visual, information and that this eye movement information is only expressed within a specific range of eye positions for each neuron. In addition, simultaneous recordings of Golgi cells and nearby mossy fibers revealed that Golgi cells have the opposite directional tuning of the mossy fiber(s) that likely drive their responses, and that these responses are more sluggish than their mossy fiber counterparts. Because the mossy fiber inputs appear to convey the activity of burst-tonic neurons in the brainstem, Golgi cell responses reflect a time-filtered negative image of the motor command sent to the extraocular muscles. We suggest a role for Golgi cells in the construction of forward models of movement, commonly hypothesized as a major function of the cerebellar cortex in motor control.

The cerebellar nodulus/uvula integrates otolith signals for the translational vestibulo-ocular reflex

Background

The otolith-driven translational vestibulo-ocular reflex (tVOR) generates compensatory eye movements to linear head accelerations. Studies in humans indicate that the cerebellum plays a critical role in the neural control of the tVOR, but little is known about mechanisms of this control or the functions of specific cerebellar structures. Here, we chose to investigate the contribution of the nodulus and uvula, which have been shown by prior studies to be involved in the processing of otolith signals in other contexts.

Methodology/Principal Findings

We recorded eye movements in two rhesus monkeys during steps of linear motion along the interaural axis before and after surgical lesions of the cerebellar uvula and nodulus. The lesions strikingly reduced eye velocity during constant-velocity motion but had only a small effect on the response to initial head acceleration. We fit eye velocity to a linear combination of head acceleration and velocity and to a dynamic mathematical model of the tVOR that incorporated a specific integrator of head acceleration. Based on parameter optimization, the lesion decreased the gain of the pathway containing this new integrator by 62%. The component of eye velocity that depended directly on head acceleration changed little (gain decrease of 13%). In a final set of simulations, we compared our data to the predictions of previous models of the tVOR, none of which could account for our experimental findings.

Conclusions/ Significance

Our results provide new and important information regarding the neural control of the tVOR. Specifically, they point to a key role for the cerebellar nodulus and uvula in the mathematical integration of afferent linear head acceleration signals. This function is likely to be critical not only for the tVOR but also for the otolith-mediated reflexes that control posture and balance.

Canal-otolith interactions and detection thresholds of linear and angular components during curved-path self-motion

Gravitational signals arising from the otolith organs and vertical plane rotational signals arising from the semicircular canals interact extensively for accurate estimation of tilt and inertial acceleration. Here we used a classical signal detection paradigm to examine perceptual interactions between otolith and horizontal semicircular canal signals during simultaneous rotation and translation on a curved path. In a rotation detection experiment, blindfolded subjects were asked to detect the presence of angular motion in blocks where half of the trials were pure nasooccipital translation and half were simultaneous translation and yaw rotation (curved-path motion). In separate, translation detection experiments, subjects were also asked to detect either the presence or the absence of nasooccipital linear motion in blocks, in which half of the trials were pure yaw rotation and half were curved path. Rotation thresholds increased slightly, but not significantly, with concurrent linear velocity magnitude. Yaw rotation detection threshold, averaged across all conditions, was 1.45 +/- 0.81 degrees/s (3.49 +/- 1.95 degrees/s(2)). Translation thresholds, on the other hand, increased significantly with increasing magnitude of concurrent angular velocity. Absolute nasooccipital translation detection threshold, averaged across all conditions, was 2.93 +/- 2.10 cm/s (7.07 +/- 5.05 cm/s(2)). These findings suggest that conscious perception might not have independent access to separate estimates of linear and angular movement parameters during curved-path motion. Estimates of linear (and perhaps angular) components might instead rely on integrated information from canals and otoliths. Such interaction may underlie previously reported perceptual errors during curved-path motion and may originate from mechanisms that are specialized for tilt-translation processing during vertical plane rotation.

Internal models and neural computation in the vestibular system

The vestibular system is vital for motor control and spatial self-motion perception. Afferents from the otolith organs and the semicircular canals converge with optokinetic, somatosensory and motor-related signals in the vestibular nuclei, which are reciprocally interconnected with the vestibulocerebellar cortex and deep cerebellar nuclei. Here, we review the properties of the many cell types in the vestibular nuclei, as well as some fundamental computations implemented within this brainstem-cerebellar circuitry. These include the sensorimotor transformations for reflex generation, the neural computations for inertial motion estimation, the distinction between active and passive head movements, as well as the integration of vestibular and proprioceptive information for body motion estimation. A common theme in the solution to such computational problems is the concept of internal models and their neural implementation. Recent studies have shed new insights into important organizational principles that closely resemble those proposed for other sensorimotor systems, where their neural basis has often been more difficult to identify. As such, the vestibular system provides an excellent model to explore common neural processing strategies relevant both for reflexive and for goal-directed, voluntary movement as well as perception.

Forward models and state estimation in compensatory eye movements

The compensatory eye movement (CEM) system maintains a stable retinal image, integrating information from different sensory modalities to compensate for head movements. Inspired by recent models of the physiology of limb movements, we suggest that CEM can be modeled as a control system with three essential building blocks: a forward model that predicts the effects of motor commands; a state estimator that integrates sensory feedback into this prediction; and, a feedback controller that translates a state estimate into motor commands. We propose a specific mapping of nuclei within the CEM system onto these control functions. Specifically, we suggest that the Flocculus is responsible for generating the forward model prediction and that the Vestibular Nuclei integrate sensory feedback to generate an estimate of current state. Finally, the brainstem motor nuclei – in the case of horizontal compensation this means the Abducens Nucleus and the Nucleus Prepositus Hypoglossi – implement a feedback controller, translating state into motor commands. While these efforts to understand the physiological control system as a feedback control system are in their infancy, there is the intriguing possibility that CEM and targeted voluntary movements use the same cerebellar circuitry in fundamentally different ways.

Internal models of eye movement in the floccular complex of the monkey cerebellum

Internal models are a key feature of most modern theories of motor control. Yet, it has been challenging to localize internal models in the brain, or to demonstrate that they are more than a metaphor. In the present review, I consider a large body of data on the cerebellar floccular complex, asking whether floccular output has features that would be expected of the output from internal models. I argue that the simple spike firing rates of a single group of floccular Purkinje cells could reflect the output of three different internal models. (1) An eye velocity positive feedback pathway through the floccular complex provides neural inertia for smooth pursuit eye movements, and appears to operate as a model of the inertia of real-world objects. (2) The floccular complex processes and combines input signals so that the dynamics of its average simple spike output are appropriate for the dynamics of the downstream brainstem circuits and eyeball. If we consider the brainstem circuits and eyeball as a more broadly conceived "oculomotor plant," then the output from the floccular complex could be the manifestation of an inverse model of "plant" dynamics. (3) Floccular output reflects an internal model of the physics of the orbit where head and eye motion sum to produce gaze motion. The effects of learning on floccular output suggest that it is modeling the interaction of the visually-guided and vestibular-driven components of eye and gaze motion. Perhaps the insights from studying oculomotor control provide groundwork to guide the analysis of internal models for a wide variety of cerebellar behaviors.

The first second: models of short-term memory traces in the brain

Many network models in computational neuroscience rise to the challenge of explaining behavioural phenomena ranging from microseconds to tens of seconds using components operating mostly on a time-scale of milliseconds. These models have in common that the underlying system has a memory, which implies that its output depends on its past input history. In this review we compare how such memory traces or delayed responses may be implemented in different brain areas supporting a diversity of functions.

Vestibular signals in macaque extrastriate visual cortex are functionally appropriate for heading perception

Visual and vestibular signals converge onto the dorsal medial superior temporal area (MSTd) of the macaque extrastriate visual cortex, which is thought to be involved in multisensory heading perception for spatial navigation. Peripheral otolith information, however, is ambiguous and cannot distinguish linear accelerations experienced during self-motion from those resulting from changes in spatial orientation relative to gravity. Here we show that, unlike peripheral vestibular sensors but similar to lobules 9 and 10 of the cerebellar vermis (nodulus and uvula), MSTd neurons respond selectively to heading and not to changes in orientation relative to gravity. In support of a role in heading perception, MSTd vestibular responses are also dominated by velocity-like temporal dynamics, which might optimize sensory integration with visual motion information. Unlike the cerebellar vermis, however, MSTd neurons also carry a spatial orientation-independent rotation signal from the semicircular canals, which could be useful in compensating for the effects of head rotation on the processing of optic flow. These findings show that vestibular signals in MSTd are appropriately processed to support a functional role in multisensory heading perception.

An internal model of a moving visual target in the lateral cerebellum

In order to overcome the relatively long delay in processing visual feedback information when pursuing a moving visual target, it is necessary to predict the future trajectory of the target if it is to be tracked with accuracy. Predictive behaviour can be achieved through internal models, and the cerebellum has been implicated as a site for their operation. Purkinje cells in the lateral cerebellum (D zones) respond to visual inputs during visually guided tracking and it has been proposed that their neural activity reflects the operation of an internal model of target motion. Here we provide direct evidence for the existence of such a model in the cerebellum by demonstrating an internal model of a moving external target. Single unit recordings of Purkinje cells in lateral cerebellum (D2 zone) were made in cats trained to perform a predictable visually guided reaching task. For all Purkinje cells that showed tonic simple spike activity during target movement, this tonic activity was maintained during the transient disappearance of the target. Since simple spike activity could not be correlated to eye or limb movements, and the target was familiar and moved in a predictable fashion, we conclude that the Purkinje cell activity reflects the operation of an internal model based on memory of its previous motion. Such a model of the target's motion, reflected in the maintained modulation during the target's absence, could be used in a predictive capacity in the interception of a moving object.

Computational approaches to spatial orientation: from transfer functions to dynamic Bayesian inference

Spatial orientation is the sense of body orientation and self-motion relative to the stationary environment, fundamental to normal waking behavior and control of everyday motor actions including eye movements, postural control, and locomotion. The brain achieves spatial orientation by integrating visual, vestibular, and somatosensory signals. Over the past years, considerable progress has been made toward understanding how these signals are processed by the brain using multiple computational approaches that include frequency domain analysis, the concept of internal models, observer theory, Bayesian theory, and Kalman filtering. Here we put these approaches in context by examining the specific questions that can be addressed by each technique and some of the scientific insights that have resulted. We conclude with a recent application of particle filtering, a probabilistic simulation technique that aims to generate the most likely state estimates by incorporating internal models of sensor dynamics and physical laws and noise associated with sensory processing as well as prior knowledge or experience. In this framework, priors for low angular velocity and linear acceleration can explain the phenomena of velocity storage and frequency segregation, both of which have been modeled previously using arbitrary low-pass filtering. How Kalman and particle filters may be implemented by the brain is an emerging field. Unlike past neurophysiological research that has aimed to characterize mean responses of single neurons, investigations of dynamic Bayesian inference should attempt to characterize population activities that constitute probabilistic representations of sensory and prior information.

Neural correlates of forward and inverse models for eye movements: evidence from three-dimensional kinematics

Inverse and forward dynamic models have been conceptually important in computational motor control. In particular, inverse models are thought to convert desired action into appropriate motor commands. In parallel, forward models predict the consequences of the motor command on behavior by constructing an efference copy of the actual movement. Despite theoretical appeal, their neural representation has remained elusive. Here, we provide evidence supporting the notion that a group of premotor neurons called burst-tonic (BT) cells represent the output of the inverse model for eye movements. We show that BT neurons, like extraocular motoneurons but different from the evoked eye movement, do not carry signals appropriate for the half-angle rule of ocular kinematics during smooth-pursuit eye movements from eccentric positions. Along with findings of identical response dynamics as motoneurons, these results strongly suggest that BT cells carry a replica of the motor command. In contrast, eye-head (EH) neurons, a premotor cell type that is the target of Purkinje cell inhibition from the cerebellar flocculus/ventral paraflocculus, exhibit properties that could be consistent with the half-angle rule. Therefore, EH cells may be functionally related to the output of a forward internal model thought to construct an efference copy of the actual eye movement.

A model-based theory on the origin of downbeat nystagmus

The pathomechanism of downbeat nystagmus (DBN), an ocular motor sign typical for vestibulo-cerebellar lesions, remains unclear. Previous hypotheses conjectured various deficits such as an imbalance of central vertical vestibular or smooth pursuit pathways to be causative for the generation of spontaneous upward drift. However, none of the previous theories explains the full range of ocular motor deficits associated with DBN, i.e., impaired vertical smooth pursuit (SP), gaze evoked nystagmus, and gravity dependence of the upward drift. We propose a new hypothesis, which explains the ocular motor signs of DBN by damage of the inhibitory vertical gaze-velocity sensitive Purkinje cells (PCs) in the cerebellar flocculus (FL). These PCs show spontaneous activity and a physiological asymmetry in that most of them exhibit downward on-directions. Accordingly, a loss of vertical floccular PCs will lead to disinhibition of their brainstem target neurons and, consequently, to spontaneous upward drift, i.e., DBN. Since the FL is involved in generation and control of SP and gaze holding, a single lesion, e.g., damage to vertical floccular PCs, may also explain the associated ocular motor deficits. To test our hypothesis, we developed a computational model of vertical eye movements based on known ocular motor anatomy and physiology, which illustrates how cortical, cerebellar, and brainstem regions interact to generate the range of vertical eye movements seen in healthy subjects. Model simulation of the effect of extensive loss of floccular PCs resulted in ocular motor features typically associated with cerebellar DBN: (1) spontaneous upward drift due to decreased spontaneous PC activity, (2) gaze evoked nystagmus corresponding to failure of the cerebellar loop supporting neural integrator function, (3) asymmetric vertical SP deficit due to low gain and asymmetric attenuation of PC firing, and (4) gravity-dependence of DBN caused by an interaction of otolith-ocular pathways with impaired neural integrator function.