Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement

Cerebellar learning of bio-mechanical functions of extra-ocular muscles: modeling by artificial neural networks

A control circuit is proposed to model the command of saccadic eye movements. Its wiring is deduced from a mathematical constraint, i.e. the necessity, for motor orders processing, to compute an approximate inverse function of the bio-mechanical function of the moving plant, here the bio-mechanics of the eye. This wiring is comparable to the anatomy of the cerebellar pathways. A predicting element, necessary for inversion and thus for movement accuracy, is modeled by an artificial neural network whose structure, deduced from physical constraints expressing the mechanics of the eye, is similar to the cell connectivity of the cerebellar cortex. Its functioning is set by supervised reinforcement learning, according to learning rules aimed at reducing the errors of pointing, and deduced from a differential calculation. After each movement, a teaching signal encoding the pointing error is distributed to various learning sites, as is, in the cerebellum, the signal issued from the inferior olive and conveyed to various cell types by the climbing fibers. Results of simulations lead to predict the existence of a learning site in the glomeruli. After learning, the model is able to accurately simulate saccadic eye movements. It accounts for the function of the cerebellar pathways and for the final integrator of the oculomotor system. The novelty of this model of movement control is that its structure is entirely deduced from mathematical and physical constraints, and is consistent with general anatomy, cell connectivity and functioning of the cerebellar pathways. Even the learning rules can be deduced from calculation, and they reproduce long term depression, the learning process which takes place in the dendritic arborization of the Purkinje cells. This approach, based on the laws of mathematics and physics, appears thus as an efficient way of understanding signal processing in the motor system.

Modeling cerebellar flocculus and paraflocculus involvement in complex predictive smooth eye pursuit in monkeys

The role of flocculus and paraflocculus neurons in the cerebellar control of predictive eye movements was examined using two modeling techniques. The first study characterized the dependence of individual Purkinje-cell firing patterns on oculomotor output, visual input, and response timing using multilinear regression techniques. Interestingly, no dependence on visual input was detected. Purkinje cell firing was explained by sensitivities to eye position and eye velocity alone. However, complex responses occurred when sensitivity vectors pointed in different directions. For example, some neurons showed a preference for circular pursuit in a particular rotation direction. Responses also tended to lead the eye during predictable pursuit and to lag during unpredictable, visually driven pursuit. This suggests that flocculus and paraflocculus neurons played a stronger role during predictive pursuit than visually driven pursuit. A second modeling study demonstrated how the flocculus/paraflocculus system might generate predictive pursuit. A biologically realistic neural network was simulated based on the known anatomy and physiology of this cerebellar system. It included mossy and climbing fibers with realistic responses, Purkinje cells acting on well-characterized brain-stem circuits, and granule, Golgi, basket, and stellate cells with appropriate connections. The network was able to learn new pursuit trajectories based on long-term alterations in synaptic connectivity at parallel-to-Purkinje synapses. Interestingly, this model was able to generate predictive pursuit without visual input based only on eye-motion input. Thus, both models provide complementary evidence for the generation of nonvisual predictive control by flocculus and paraflocculus neurons.

Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo-ocular reflex (VOR). Using an adaptive-filter representation of cerebellar cortex and an anti-Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye-movement command) and a target variable (retinal slip), without requiring a motor-error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus unifies motor and sensory cerebellar functions.

Computational studies on acquisition and adaptation of ocular following responses based on cerebellar synaptic plasticity

To investigate how cerebellar synaptic plasticity guides the acquisition and adaptation of ocular following response (OFR), a large-scale network model was developed. The model includes the cerebral medial superior temporal area (MST), Purkinje cells (P cells) of the ventral paraflocculus, the accessory optic and climbing fiber systems, the brain stem oculomotor network, and the oculomotor plant. The model reconstructed temporal profiles of both firing patterns of MST neurons and P cells and eye movements. Model MST neurons (n = 1,080) were set to be driven by retinal error and exhibited 12 preferred directions, 30 preferred velocities, and 3 firing waveforms. Correspondingly, each model P cell contained 1,080 excitatory synapses from granule cell axons (GCA) and 1,080 inhibitory synapses. P cells (n = 40) were classified into four groups by their laterality (hemisphere) and by preferred directions of their climbing fiber inputs (CF) (contralateral or upward). The brain stem neural circuit and the oculomotor plant were modeled on the work of Yamamoto et al. The initial synaptic weights on the P cells were set randomly. At the beginning, P cell simple spikes were not well modulated by visual motion, and the eye was moved only slightly by the accessory optic system. The synaptic weights were updated according to integral-differential equation models of physiologically demonstrated synaptic plasticity: long-term depression and long-term potentiation for GCA synapses and rebound potentiation for inhibitory synapses. We assumed that maximum plasticity was induced when GCA inputs preceded CF inputs by 200 ms. After more than 10,000 presentations of ramp-step visual motion, the strengths of both the excitatory and inhibitory synapses were modified. Subsequently, the simple spike responses became well developed, and ordinary OFRs were acquired. The preferred directions of simple spikes became the opposite of those of CFs. Although the model MST neurons were set to possess a wide variety of firing characteristics, the model P cells acquired only downward or ipsilateral preferred directions, high preferred velocities and stereotypical firing waveforms. Therefore the drastic transition of the neural representation from the population codes in the MST to the firing-rate codes of simple spikes were learned at the GCA-P cell synapses and inhibitory cells-P cell synapses. Furthermore, the model successfully reproduced the gain- and directional-adaptation of OFR, which was demonstrated by manipulating the velocity and direction of visual motion, respectively. When we assumed that synaptic plasticity could only occur if CF inputs preceded GCA inputs, the ordinary OFR were acquired but neither the gain-adaptation nor the directional adaptation could be reproduced.

Prospective control of manual interceptive actions: comparative simulations of extant and new model constructs

Two prospective controllers of hand movements in catching-both based on required velocity control-were simulated. Under certain conditions, this required velocity control led to overshoots of the future interception point. These overshoots were absent in pertinent experiments. To remedy this shortcoming, the required velocity model was reformulated in terms of a neural network, the Vector Integration To Endpoint model, to create a Required Velocity Integration To Endpoint model. Addition of a parallel relative velocity channel, resulting in the Relative and Required Velocity Integration To Endpoint model, provided a better account for the experimentally observed kinematics than the existing, purely behavioral models. Simulations of reaching to intercept decelerating and accelerating objects in the presence of background motion were performed to make distinct predictions for future experiments.

Horizontal vestibuloocular reflex (VOR) head velocity estimation in Purkinje cell degeneration (pcd/pcd) mutant mice

The horizontal vestibuloocular reflex (VOR) of Purkinje cell degeneration (pcd/pcd) mutant mice, which lack a functional cerebellar cortex, was compared in darkness to that of wild-type animals during constant velocity yaw rotations about an earth-horizontal axis and during sinusoidal yaw rotations about an earth-vertical axis. Both wild-type and pcd/pcd mice showed a compensatory average VOR eye velocity, or bias, during constant velocity horizontal axis rotations, evidence of central neural processing of otolith afferent signals to create a signal proportional to head angular velocity. Eye velocity bias was greater in pcd/pcd mice than in wild-type mice at a low rotational velocity (32 degrees/s), but less at higher velocities (128 and 200 degrees/s). Lesion of the medial nodulus severely attenuated eye velocity bias in two wild-type mice, without attenuating VOR during sinusoidal vertical axis yaw rotations at 0.2 Hz. These results show that while head velocity estimation in mice, as in primates, depends on the cerebellum, pcd/pcd mutant mice develop velocity estimation without a functional cerebellar cortex. We conclude that neural circuits that exclude cerebellar cortex are capable of the signal processing necessary for head angular velocity estimation, but that these circuits are insufficient for normal estimation at high velocities.

Input minimization: a model of cerebellar learning without climbing fiber error signals

The cerebellum is critical for motor learning. Current cerebellar learning models follow the Marr/Albus paradigm, in which climbing fibers provide error signals that shape plastic synapses between parallel fibers and Purkinje cells. However, climbing fibers have slow and largely random discharge, and seem unlikely to provide error signals with resolution sufficient to guide cerebellar learning. Parallel fibers carry error signals and could direct the plasticity of their own synapses, but the error signals are carried along with other signals. This report presents the new input minimization (InMin) model, in which Purkinje cells reduce error by minimizing their overall parallel fiber input. The slowly, randomly firing climbing fiber provides only synchronization pulses. InMin offers an alternative that can unify cerebellar findings.

Unsupervised learning of granule cell sparse codes enhances cerebellar adaptive control

Marr [J. Physiol. (1969) 202, 437-470] and Albus [Math. Biosci. (1971) 10, 25-61] hypothesized that cerebellar learning is facilitated by a granule cell sparse code, i.e. a neural code in which the fraction of active neurons is low at any one time. In this paper, we re-examine this hypothesis in light of recent experimental and theoretical findings. We argue that cerebellar motor learning is enhanced by a sparse code that simultaneously maximizes information transfer between mossy fibers and granule cells, minimizes redundancies between granule cell discharges, and re-codes the mossy fiber inputs with an adaptive resolution such that inputs corresponding to large errors are finely encoded. We then propose that a set of biologically plausible unsupervised learning rules can produce such a code. To maintain a low mean firing rate compatible with a sparse code, an activity-dependent homeostatic mechanism sets the cells' thresholds. Then, to maximize information transfer, the mossy fiber--granule cell synapses are adjusted by a Hebbian rule. Furthermore, to minimize redundancies between granule cell discharges, the inhibitory Golgi cell--granule cell synapses are tuned by an anti-Hebbian rule. Finally, to allow adaptive resolution, a performance-based neuromodulator-like signal gates these three plastic processes. We integrate these gated learning rules into a simplified model of the cerebellum for arm movement control, and show that unsupervised learning of granule cell sparse codes greatly improves cerebellar adaptive motor control in comparison to a "fixed" Marr--Albus-type model. Until recently, activity-dependent cerebellar plasticity was thought to be largely confined to the granule cell--Purkinje cell synapses. This static view of the cerebellum is, however, quickly being replaced by an extremely dynamic view in which plasticity is omnipresent. The present theoretical study shows how several forms of plasticity in the granular layer of the cerebellum can produce fast, accurate and stable cerebellar learning.

Biomimetic gaze stabilization based on feedback-error-learning with nonparametric regression networks

Oculomotor control in a humanoid robot faces similar problems as biological oculomotor systems, i.e. the stabilization of gaze in face of unknown perturbations of the body, selective attention, stereo vision, and dealing with large information processing delays. Given the nonlinearities of the geometry of binocular vision as well as the possible nonlinearities of the oculomotor plant, it is desirable to accomplish accurate control of these behaviors through learning approaches. This paper develops a learning control system for the phylogenetically oldest behaviors of oculomotor control, the stabilization reflexes of gaze. In a step-wise procedure, we demonstrate how control theoretic reasonable choices of control components result in an oculomotor control system that resembles the known functional anatomy of the primate oculomotor system. The core of the learning system is derived from the biologically inspired principle of feedback-error learning combined with a state-of-the-art non-parametric statistical learning network. With this circuitry, we demonstrate that our humanoid robot is able to acquire high performance visual stabilization reflexes after about 40 s of learning despite significant nonlinearities and processing delays in the system.

A pattern correlation model of vestibulo-ocular reflex habituation

Through the process of habituation, the response of the vestibulo-ocular reflex (VOR) is decreased by prolonged, sinusoidal stimulation at lower frequencies (< or =0.1 Hz). Research on goldfish has uncovered frequency-specific and nonlinear behaviors associated with habituation of the goldfish VOR, which include phenomena that cannot be explained using dynamic linear and static nonlinear models. The unexplained phenomena are abrupt decreases at peak response, gain decreases far in excess of linear predictions based on phase, and violation of superposition. Their existence was attributed to a hypothetical switch that closed in the appropriate context. The pattern correlation model provides a new perspective on the process of VOR habituation. Rather than treat the stimulus as a continuous sinusoid, the pattern correlation model breaks it up into a number of discontinuous patterns. The pattern most closely correlated with the current stimulus then decreases the VOR response by the amount of that correlation times a pre-assigned weight. The pattern correlation model explains how the frequency-specific and the nonlinear behaviors may be related, and how the apparent switching phenomena may occur.

The functions of the proprioceptors of the eye muscles

This article sets out to present a fairly comprehensive review of our knowledge about the functions of the receptors that have been found in the extraocular muscles--the six muscles that move each eye of vertebrates in its orbit--of all the animals in which they have been sought, including Man. Since their discovery at the beginning of the 20th century these receptors have, at various times, been credited with important roles in the control of eye movement and the construction of extrapersonal space and have also been denied any function whatsoever. Experiments intended to study the actions of eye muscle receptors and, even more so, opinions (and indeed polemic) derived from these observations have been influenced by the changing fashions and beliefs about the more general question of how limb position and movement is detected by the brain and which signals contribute to those aspects of this that are perceived (kinaesthesis). But the conclusions drawn from studies on the eye have also influenced beliefs about the mechanisms of kinaesthesis and, arguably, this influence has been even larger than that in the converse direction. Experimental evidence accumulated over rather more than a century is set out and discussed. It supports the view that, at the beginning of the 21st century, there are excellent grounds for believing that the receptors in the extraocular muscles are indeed proprioceptors, that is to say that the signals that they send into the brain are used to provide information about the position and movement of the eye in the orbit. It seems that this information is important in the control of eye movements of at least some types, and in the determination by the brain of the direction of gaze and the relationship of the organism to its environment. In addition, signals from these receptors in the eye muscles are seen to be necessary for the development of normal mechanisms of visual analysis in the mammalian visual cortex and for both the development and maintenance of normal visuomotor behaviour. Man is among those vertebrates to whose brains eye muscle proprioceptive signals provide information apparently used in normal sensorimotor functions; these include various aspects of perception, and of the control of eye movement. It is possible that abnormalities of the eye muscle proprioceptors and their signals may play a part in the genesis of some types of human squint (strabismus); conversely studies of patients with squint in the course of their surgical or pharmacological treatment have yielded much interesting evidence about the central actions of the proprioceptive signals from the extraocular muscles. The results of experiments on the eye have played a large part in the historical controversy, now in at least its third century, about the origin of signals that inform the brain about movement of parts of the body. Some of these results, and more of the interpretations of them, now need to be critically re-examined. The re-examination in the light of recent experiments that is presented here does not support many of the conclusions confidently drawn in the past and leads to both new insights and fresh questions about the roles of information from motor signals flowing out of the brain and that from signals from the peripheral receptors flowing into it. There remain many lacunae in our knowledge and filling some of these will, it is contended, be essential to advance our understanding further. It is argued that such understanding of eye muscle proprioception is a necessary part of the understanding of the physiology and pathophysiology of eye movement control and that it is also essential to an account of how organisms, including Man, build and maintain knowledge of their relationship to the external visual world. The eye would seem to provide a uniquely favourable system in which to study the way in which information derived within the brain about motor actions may interact with signals flowing in from peripheral receptors. The review is constructed in relatively independent sections that deal with particular topics. It ends with a fairly brief piece in which the author sets out some personal views about what has been achieved recently and what most immediately needs to be done. It also suggests some lines of study that appear to the author to be important for the future.

Ocular pursuit responses to repeated, single-cycle sinusoids reveal behavior compatible with predictive pursuit

The link between anticipatory smooth eye movements and prediction in sinusoidal pursuit was investigated by presentation of series of identical, single-cycle, sinusoidal target motion stimuli. Stimuli occurred at randomized intervals (1.2-2.8 s) but were preceded by an audio warning cue 480 ms before each presentation. Cycle period (T) varied from 0.64 to 2.56 s and target displacement from 4 to 20 degrees in separate series. For T </= 1.28 s, responses to the first stimulus of each series exhibited a time delay across the whole cycle (mean = 121 ms for T = 0.8 s). But, in the second and subsequent (steady-state) presentations, anticipatory movements, proportional to target velocity, were made and time delay was significantly reduced (mean = 43 ms for T = 0.8 s). Steady-state time delays were comparable to those evoked during continuous sinusoidal pursuit and less than pursuit reaction time. Even when subjects did not follow the target in the first presentation, they responded to the second presentation with reduced time delay. Throughout the experiments, three types of catch trial (A-C) were introduced. In A, the target failed to appear as expected after the warning cue. Anticipatory smooth movements were initiated, reaching a peak velocity proportional to prior target velocity around 200 ms after expected target onset. In B, the target stopped midway through the cycle. Even if the target remained on and was stationary, the eye movement continued to be driven away from the stationary target with a velocity similar to that of prior responses, reaching a peak velocity that was again proportional to expected target velocity after >/=205 ms. In C, the amplitude of the single sinusoid was unexpectedly increased or decreased. When it decreased, eye velocity throughout the first half-cycle of the response was close to that executed in response to prior stimuli of higher velocity and did not return to an appropriate level for 382-549 ms. Conversely, when amplitude increased, eye velocity remained inappropriately low for the first half-cycle. Results of A and C indicate that subjects are able to use velocity information stored from prior presentations to initiate an oculomotor drive that predominates over visual feedback for the first half-cycle. Results of B indicate that the second part of the cycle is also preprogrammed because it continued despite efforts to suppress it by fixation. The results suggest that initial retinal velocity error information can be sampled, stored, and subsequently replayed as a bi-directional anticipatory pattern of movement that reduces temporal delay and could account for predictive control during sinusoidal pursuit.

Cerebellar flocculus and ventral paraflocculus Purkinje cell activity during predictive and visually driven pursuit in monkey

Purkinje cells in the flocculus and ventral paraflocculus were studied in tasks designed to distinguish predictive versus visually guided mechanisms of smooth pursuit. A sum-of-sines task allowed studies of complex predictive pursuit. A perturbation task examined visually driven pursuit during unpredictable right-angle changes in target direction. A gap task examined pursuit that was maintained when the target was turned off. Neural activity patterns were quantified using multi-linear models with sensitivities to the position, velocity, and acceleration of both motor output (eye motion) and visual input (retinal slip). During the sum-of-sines task, neural responses led eye motion by an average of 12 ms, a value larger than the 9-ms transmission delay between flocculus stimulation and eye motion. This suggests that flocculus/paraflocculus neurons drove pursuit along predictable sum-of-sines trajectories. In contrast, neural responses led eye motion by an average of only 2 ms during the perturbation task and by 6 ms during the gap task. These values suggest a follow-up role during tasks more heavily dependent on visual processing. Activity in all three tasks was explained primarily by sensitivities to eye position and velocity. Eye acceleration played a minor role during ongoing pursuit, although its influence on firing rate increased during the high accelerations following unexpected changes in target motion. Retinal slip had a relatively small influence on responses during pursuit. This was particularly true for the sum-of-sines and gap tasks where predictive control eliminated any consistent retinal-slip signals that might have been used to drive the eye. Surprisingly, the influence of retinal slip did not increase appreciably during unpredictable perturbations in target direction that generated large amounts of retinal slip. Thus although visual control signals are needed in varying amounts during the three pursuit tasks, they have been converted to motor control signals by the time they leave the flocculus/paraflocculus system. Individual neurons showed a remarkable constancy in eye-sensitivity direction across tasks that indicated direct links to oculomotor neurons. However, some neurons showed changes in sensitivity magnitude that suggested changes in control strategy for different tasks. Magnitude differences were largest for the perturbation task. We conclude that the flocculus/paraflocculus system plays a major role in driving predictive pursuit. It also processes visually driven control signals that originate in other brain regions after a slight delay.

Neuronal coding of prediction errors

Associative learning enables animals to anticipate the occurrence of important outcomes. Learning occurs when the actual outcome differs from the predicted outcome, resulting in a prediction error. Neurons in several brain structures appear to code prediction errors in relation to rewards, punishments, external stimuli, and behavioral reactions. In one form, dopamine neurons, norepinephrine neurons, and nucleus basalis neurons broadcast prediction errors as global reinforcement or teaching signals to large postsynaptic structures. In other cases, error signals are coded by selected neurons in the cerebellum, superior colliculus, frontal eye fields, parietal cortex, striatum, and visual system, where they influence specific subgroups of neurons. Prediction errors can be used in postsynaptic structures for the immediate selection of behavior or for synaptic changes underlying behavioral learning. The coding of prediction errors may represent a basic mode of brain function that may also contribute to the processing of sensory information and the short-term control of behavior.

Cerebellar function: coordination, learning or timing?

Theories of cerebellar function have largely involved three ideas: movement coordination, motor learning or timing. New evidence indicates these distinctions are not particularly meaningful, as the cerebellum influences movement execution by feedforward use of sensory information via temporally specific learning.

Cerebellar flocculus and paraflocculus Purkinje cell activity during circular pursuit in monkey

Responses from 69 Purkinje cells in the flocculus and paraflocculus of two rhesus monkeys were studied during smooth pursuit of targets moving along circular trajectories and compared with responses during sinusoidal pursuit and fixation. A variety of interesting responses was observed during circular pursuit. Although some neurons fired most strongly in a single preferred direction during clockwise (CW) and counterclockwise (CCW) pursuit, others had directional preferences that changed with rotation direction. Some of these neurons showed similar modulation amplitudes during CW and CCW pursuit, whereas other neurons showed a preference for a particular rotation direction. Response specificity also was observed during sinusoidal pursuit. Some neurons showed responses that were much stronger during centrifugal pursuit, others showed a preference for centripetal pursuit, and still others showed responses during both centripetal and centrifugal motion. Differences in preferred response direction were sometimes observed for centripetal versus centrifugal pursuit. CW/CCW and centrifugal/centripetal preferences were not explained by a breakdown in component additivity. That is, modulations in firing rate during pursuit along a circular trajectory equaled the sum of modulations during horizontal and vertical sinusoidal components as well as for diagonal components. Instead all responses were well fit by a model that expressed the instantaneous firing rate of each neuron as a multilinear function of the two-dimensional position and velocity of the eye. This model generalized well to performance at different sinusoidal frequencies. It did somewhat less well for responses during fixation, suggesting some separation in the neural mechanisms of dynamic and static positioning. The model indicates that position sensitivity accounted for approximately 36% of the modulation during circular pursuit, and velocity sensitivity accounted for approximately 64%. When position and velocity sensitivity vectors were aligned, responses were simpler and modulations were similar during CW versus CCW pursuit. In contrast, when these vectors pointed in different directions, response complexity increased. Nonaligned position and velocity influences tended to reinforce during circular pursuit in one direction and to cancel each other during pursuit in the opposite direction. They also tended to produce response differences during centripetal versus centrifugal sinusoidal pursuit. The distinct roles played by position and velocity in shaping Purkinje cell responses are compatible with the control signals required to generate smooth pursuit along circular and other two-dimensional trajectories.

What are the computations of the cerebellum, the basal ganglia and the cerebral cortex?

The classical notion that the cerebellum and the basal ganglia are dedicated to motor control is under dispute given increasing evidence of their involvement in non-motor functions. Is it then impossible to characterize the functions of the cerebellum, the basal ganglia and the cerebral cortex in a simplistic manner? This paper presents a novel view that their computational roles can be characterized not by asking what are the "goals" of their computation, such as motor or sensory, but by asking what are the "methods" of their computation, specifically, their learning algorithms. There is currently enough anatomical, physiological, and theoretical evidence to support the hypotheses that the cerebellum is a specialized organism for supervised learning, the basal ganglia are for reinforcement learning, and the cerebral cortex is for unsupervised learning.This paper investigates how the learning modules specialized for these three kinds of learning can be assembled into goal-oriented behaving systems. In general, supervised learning modules in the cerebellum can be utilized as "internal models" of the environment. Reinforcement learning modules in the basal ganglia enable action selection by an "evaluation" of environmental states. Unsupervised learning modules in the cerebral cortex can provide statistically efficient representation of the states of the environment and the behaving system. Two basic action selection architectures are shown, namely, reactive action selection and predictive action selection. They can be implemented within the anatomical constraint of the network linking these structures. Furthermore, the use of the cerebellar supervised learning modules for state estimation, behavioral simulation, and encapsulation of learned skill is considered. Finally, the usefulness of such theoretical frameworks in interpreting brain imaging data is demonstrated in the paradigm of procedural learning.

Cerebellar Purkinje cell simple spike discharge encodes movement velocity in primates during visuomotor arm tracking

Pathophysiological, lesion, and electrophysiological studies suggest that the cerebellar cortex is important for controlling the direction and speed of movement. The relationship of cerebellar Purkinje cell discharge to the control of arm movement parameters, however, remains unclear. The goal of this study was to examine how movement direction and speed and their interaction-velocity-modulate Purkinje cell simple spike discharge in an arm movement task in which direction and speed were independently controlled. The simple spike discharge of 154 Purkinje cells was recorded in two monkeys during the performance of two visuomotor tasks that required the animals to track targets that moved in one of eight directions and at one of four speeds. Single-parameter regression analyses revealed that a large proportion of cells had discharge modulation related to movement direction and speed. Most cells with significant directional tuning, however, were modulated at one speed, and most cells with speed-related discharge were modulated along one direction; this suggested that the patterns of simple spike discharge were not adequately described by single-parameter models. Therefore, a regression surface was fitted to the data, which showed that the discharge could be tuned to specific direction-speed combinations (preferred velocities). The overall variability in simple spike discharge was well described by the surface model, and the velocities corresponding to maximal and minimal discharge rates were distributed uniformly throughout the workspace. Simple spike discharge therefore appears to integrate information about both the direction and speed of arm movements, thereby encoding movement velocity.

A cerebellar model of timing and prediction in the control of reaching

A simplified model of the cerebellum was developed to explore its potential for adaptive, predictive control based on delayed feedback information. An abstract representation of a single Purkinje cell with multistable properties was interfaced, using a formalized premotor network, with a simulated single degree-of-freedom limb. The limb actuator was a nonlinear spring-mass system based on the nonlinear velocity dependence of the stretch reflex. By including realistic mossy fiber signals, as well as realistic conduction delays in afferent and efferent pathways, the model allowed the investigation of timing and predictive processes relevant to cerebellar involvement in the control of movement. The model regulates movement by learning to react in an anticipatory fashion to sensory feedback. Learning depends on training information generated from corrective movements and uses a temporally asymmetric form of plasticity for the parallel fiber synapses on Purkinje cells.

On the role of anatomy in learning by the cerebellar cortex

The properties due to the location of neurons, synapses, and possibly even synaptic channels, in neuron networks are still unknown. Our preliminary results suggest that not only the interconnections but also the relative positions of the different elements in the network are of importance in the learning process in the cerebellar cortex. We have used neural field equations to investigate the mechanisms of learning in the hierarchical neural network. The numerical resolution of these equations reveals two important properties: (i) The hierarchical structure of this network has the expected effect on learning because the flow of information at the neuronal level is controlled by the heterosynaptic effect through the synaptic density-connectivity function, i.e. the action potential field variable is controlled by the synaptic efficacy field variable at different points of the neuron. (ii) The geometry of the system involves different velocities of propagation along different fibers, i.e. different delays between cells, and thus has a stabilizing effect on the dynamics, allowing the Purkinje output to reach a given value. The field model proposed should be useful in the study of the spatial properties of hierarchical biological systems.

Learning in the oculomotor system: from molecules to behavior

A combination of system-level and cellular-molecular approaches is moving studies of oculomotor learning rapidly toward the goal of linking synaptic plasticity at specific sites in oculomotor circuits with changes in the signal-processing functions of those circuits, and, ultimately, with changes in eye movement behavior. Recent studies of saccadic adaptation illustrate how careful behavioral analysis can provide constraints on the neural loci of plasticity. Studies of vestibulo-ocular adaptation are beginning to examine the molecular pathways contributing to this form of cerebellum-dependent learning.

A role for the cerebellum in the control of limb movement velocity

Accepting, rejecting or modifying the many different theories of the cerebellum's role in the control of movement requires an understanding of the signals encoded in the discharge of cerebellar neurons and how those signals are transformed by the cerebellar circuitry. Particularly challenging is understanding the sensory and motor signals carried by the two types of action potentials generated by cerebellar Purkinje cells, the simple spikes and complex spikes. Advances have been made in understanding this signal processing in the context of voluntary arm movements. Recent evidence suggests that mossy fiber afferents to the cerebellar cortex are a source of kinematic signals, providing information about movement direction and speed. In turn, the simple spike discharge of Purkinje cells integrates this mossy fiber information to generate a movement velocity signal. Complex spikes may signal errors in movement velocity. It is proposed that the cerebellum uses the signals carried by the simple and complex spike discharges to control movement velocity for both step and tracking arm movements.

Neural learning rules for the vestibulo-ocular reflex

Mechanisms for the induction of motor learning in the vestibulo-ocular reflex (VOR) were evaluated by recording the patterns of neural activity elicited in the cerebellum by a range of stimuli that induce learning. Patterns of climbing-fiber, vestibular, and Purkinje cell simple-spike signals were examined during sinusoidal head movement paired with visual image movement at stimulus frequencies from 0.5 to 10 Hz. A comparison of simple-spike and vestibular signals contained the information required to guide learning only at low stimulus frequencies, and a comparison of climbing-fiber and simple-spike signals contained the information required to guide learning only at high stimulus frequencies. Learning could be guided by comparison of climbing-fiber and vestibular signals at all stimulus frequencies tested, but only if climbing fiber responses were compared with the vestibular signals present 100 msec earlier. Computational analysis demonstrated that this conclusion is valid even if there is a broad range of vestibular signals at the site of plasticity. Simulations also indicated that the comparison of vestibular and climbing-fiber signals across the 100 msec delay must be implemented by a subcellular "eligibility" trace rather than by neural circuits that delay the vestibular inputs to the site of plasticity. The results suggest two alternative accounts of learning in the VOR. Either there are multiple mechanisms of learning that use different combinations of neural signals to drive plasticity, or there is a single mechanism tuned to climbing-fiber activity that follows activity in vestibular pathways by approximately 100 msec.