Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning

 Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals. Received: 28 January 2000 / Accepted in revised form: 2 August 2000     

Which retinal and extra-retinal information is crucial for circular vection?

In contradistinction to conventional wisdom, we propose that retinal image slip of a visual scene (optokinetic pattern, OP) does not constitute the only crucial input for visually induced percepts of self-motion (vection). Instead, the hypothesis is investigated that there are three input factors: 1) OP retinal image slip, 2) motion of the ocular orbital shadows across the retinae, and 3) smooth pursuit eye movements (efference copy). To test this hypothesis, we visually induced percepts of sinusoidal rotatory self-motion (circular vection, CV) in the absence of vestibular stimulation. Subjects were presented with three concurrent stimuli: a large visual OP, a fixation point to be pursued with the eyes (both projected in superposition on a semi-circular screen), and a dark window frame placed close to the eyes to create artificial visual field boundaries that simulate ocular orbital rim boundary shadows, but which could be moved across the retinae independent from eye movements. In different combinations these stimuli were independently moved or kept stationary. When moved together (horizontally and sinusoidally around the subject's head), they did so in precise temporal synchrony at 0.05 Hz. The results show that the occurrence of CV requires retinal slip of the OP and/or relative motion between the orbital boundary shadows and the OP. On the other hand, CV does not develop when the two retinal slip signals equal each other (no relative motion) and concur with pursuit eye movements (as it is the case, e.g., when we follow with the eyes the motion of a target on a stationary visual scene). The findings were formalized in terms of a simulation model. In the model two signals coding relative motion between OP and head are fused and fed into the mechanism for CV, a visuo-oculomotor one, derived from OP retinal slip and eye movement efference copy, and a purely visual signal of relative motion between the orbital rims (head) and the OP. The latter signal is also used, together with a version of the oculomotor efference copy, for a mechanism that suppresses CV at a later stage of processing in conditions in which the retinal slip signals are self-generated by smooth pursuit eye movements.     

A ‘tachometer’ feedback model of smooth pursuit eye movements

A new model of smooth pursuit eye movements is presented. We begin by formally analyzing the stability of the proportional-derivative (PD) model of smooth pursuit eye movements using Pontryagin's theory. The PD model is the linearized version of the nonlinear Krauzlis-Lisberger (KL) model. We show that the PD model fails to account for the experimentally observed dependence of the eye velocity damping ratio and the oscillation period on the total delay in the feedback loop. To explain the data, a new `tachometer' feedback model, based on an efference copy signal of eye acceleration, is proposed and analyzed by computer simulation. The model predicts some salient features of monkey pursuit data and suggests a functional role for the extraretinal input to the medial superior temporal area (MST). Received: 9 February 1995 / Accepted in revised form: 13 June 1995     

Cerebellar learning of accurate predictive control for fast-reaching movements

Long conduction delays in the nervous system prevent the accurate control of movements by feedback control alone. We present a new, biologically plausible cerebellar model to study how fast arm movements can be executed in spite of these delays. To provide a realistic test-bed of the cerebellar neural model, we embed the cerebellar network in a simulated biological motor system comprising a spinal cord model and a six-muscle two-dimensional arm model. We argue that if the trajectory errors are detected at the spinal cord level, memory traces in the cerebellum can solve the temporal mismatch problem between efferent motor commands and delayed error signals. Moreover, learning is made stable by the inclusion of the cerebello-nucleo-olivary loop in the model. It is shown that the cerebellar network implements a nonlinear predictive regulator by learning part of the inverse dynamics of the plant and spinal circuit. After learning, fast accurate reaching movements can be generated. Received: 8 February 1999 /Accepted in revised form: 7 August 1999     

The Importance of Lateral Connections in the Parietal Cortex for Generating Motor Plans

Substantial evidence has highlighted the significant role of associative brain areas, such as the posterior parietal cortex (PPC) in transforming multimodal sensory information into motor plans. However, little is known about how different sensory information, which can have different delays or be absent, combines to produce a motor plan, such as executing a reaching movement. To address these issues, we constructed four biologically plausible network architectures to simulate PPC: 1) feedforward from sensory input to the PPC to a motor output area, 2) feedforward with the addition of an efference copy from the motor area, 3) feedforward with the addition of lateral or recurrent connectivity across PPC neurons, and 4) feedforward plus efference copy, and lateral connections. Using an evolutionary strategy, the connectivity of these network architectures was evolved to execute visually guided movements, where the target stimulus provided visual input for the entirety of each trial. The models were then tested on a memory guided motor task, where the visual target disappeared after a short duration. Sensory input to the neural networks had sensory delays consistent with results from monkey studies. We found that lateral connections within the PPC resulted in smoother movements and were necessary for accurate movements in the absence of visual input. The addition of lateral connections resulted in velocity profiles consistent with those observed in human and non-human primate visually guided studies of reaching, and allowed for smooth, rapid, and accurate movements under all conditions. In contrast, Feedforward or Feedback architectures were insufficient to overcome these challenges. Our results suggest that intrinsic lateral connections are critical for executing accurate, smooth motor plans.     

Altered error processing following vascular thalamic damage: evidence from an antisaccade task

Event-related potentials (ERP) research has identified a negative deflection within about 100 to 150 ms after an erroneous response--the error-related negativity (ERN)--as a correlate of awareness-independent error processing. The short latency suggests an internal error monitoring system acting rapidly based on central information such as an efference copy signal. Studies on monkeys and humans have identified the thalamus as an important relay station for efference copy signals of ongoing saccades. The present study investigated error processing on an antisaccade task with ERPs in six patients with focal vascular damage to the thalamus and 28 control subjects. ERN amplitudes were significantly reduced in the patients, with the strongest ERN attenuation being observed in two patients with right mediodorsal and ventrolateral and bilateral ventrolateral damage, respectively. Although the number of errors was significantly higher in the thalamic lesion patients, the degree of ERN attenuation did not correlate with the error rate in the patients. The present data underline the role of the thalamus for the online monitoring of saccadic eye movements, albeit not providing unequivocal evidence in favour of an exclusive role of a particular thalamic site being involved in performance monitoring. By relaying saccade-related efference copy signals, the thalamus appears to enable fast error processing. Furthermore early error processing based on internal information may contribute to error awareness which was reduced in the patients.     

Tuning Properties of MT and MSTd and Divisive Interactions for Eye-Movement Compensation

The primate brain intelligently processes visual information from the world as the eyes move constantly. The brain must take into account visual motion induced by eye movements, so that visual information about the outside world can be recovered. Certain neurons in the dorsal part of monkey medial superior temporal area (MSTd) play an important role in integrating information about eye movements and visual motion. When a monkey tracks a moving target with its eyes, these neurons respond to visual motion as well as to smooth pursuit eye movements. Furthermore, the responses of some MSTd neurons to the motion of objects in the world are very similar during pursuit and during fixation, even though the visual information on the retina is altered by the pursuit eye movement. We call these neurons compensatory pursuit neurons. In this study we develop a computational model of MSTd compensatory pursuit neurons based on physiological data from single unit studies. Our model MSTd neurons can simulate the velocity tuning of monkey MSTd neurons. The model MSTd neurons also show the pursuit compensation property. We find that pursuit compensation can be achieved by divisive interaction between signals coding eye movements and signals coding visual motion. The model generates two implications that can be tested in future experiments: (1) compensatory pursuit neurons in MSTd should have the same direction preference for pursuit and retinal visual motion; (2) there should be non-compensatory pursuit neurons that show opposite preferred directions of pursuit and retinal visual motion.     

A framework for considering the role of afference and efference in the control and perception of ocular position

It has been well established that extra-retinal information is used in the perception of visual direction and distance. Furthermore, a number of studies have established that both efference copy and afferent discharge contribute to the extra-retinal signal. Despite this, no model currently exists to explain how the signals which arise through oculomotor control contribute to perception. This paper attempts to provide such a framework. The first part of the paper outlines the framework [the cyclopean equilibrium point (EP) model] and considers the binoculus or cyclopean eye from the perspective of a current account of motor control (the EP hypothesis). An existing model is used to describe how the nervous system could utilise available efference copy and afferent extra retinal signals when determining the direction and distance of cyclopean fixation. Although the cyclopean EP model is speculative, it allows for a parsimonious framework when considering the oculomotor contribution to perception. The model has the additional advantage of being consistent with current theories regarding the control and perception of limb movement. The second part of the paper shows that the model is biologically plausible, demonstrates the use of the proposed model in describing the central control of eye movements with regard to non-conjugate peripheral adaptation and reconciles seemingly disparate empirical findings.     

A note on the reafference principle

Two alternative circuits to realize the reafference principle are considered and quantitatively analyzed. Both are combinations of a conventional control loop with negative feedback and linear transfer functions, as well as of an efference copy branch. The feedback control loop compensates for passive movements of the body or of its parts, and generates active movements, whenever the set point differs from zero. The efference copy branch should eliminate sensory messages to higher brain centres during active body movements and, thus, mediate perceptual stability. In one of the combinations, discussed also briefly by Mittelstaedt (1971), the efference copy branch interacts with and thus modifies the properties of the feedback loop. The performance of this circuit is very sensitive to variations of the system parameters and, therefore, requires precise adjustment. When the transfer function of the efference copy branch exactly matches that of the feedback loop and its gain amounts to 1, this circuit performs as a control loop with an integrator in the negative feedback branch: there is no steady state control error. However, for certain parameter combination the circuit becomes unstable. In the alternative circuit proposed here, the efference copy branch does not interfere with the feedback loop. It is robust against parameter variations. The transient properties of both circuits are described under simplified assumptions regarding the linear transfer functions in the different branches.     

Saccade control in a simulated robot camera-head system: neural net architectures for efficient learning of inverse kinematics

The high speed of saccades means that they cannot be guided by visual feedback, so that any saccadic control system must know in advance the correct output signals to fixate a particular retinal position. To investigate neural-net architectures for learning this inverse-kinematics problem we simulated a 4 deg-of-freedom robot camera-head system, in which the head could pan and tilt and the cameras pan and verge. The main findings were: (1) Linear nets, multilayer perceptrons (MLPs) trained by backpropagation, and cerebellar model arithmetic computers (CMACs) all learnt rapidly to 5–10% accuracy when given perfect error feedback. (2) For additional accuracy (down to 2%) two-layer nets learnt much faster than a single MLP or CMAC: the best combination tried was to have a CMAC learn the errors of a trained linear net. (3) Imperfect error signals were provided by a crude controller whose output was simply proportional to retinal input in the relevant axis, thereby providing a mechanism for (a) controlling the camera-head system when the feedforward neural net controller was wrong or inoperative, and (b) converting sensory error signals into motor error signals as required in supervised learning. It proved possible to train neural-net controllers using these imperfect error signals over a range of learning rates and crude-controller gains. These results suggest that appropriate neural-net architectures can provide practical, accurate and robust adaptive control for saccadic movements. In addition, the arrangement of a crude controller teaching a sophisticated one may be similar to that used by the primate saccadic system, with brainstem circuitry teaching the cerebellum.     

Linear systems analysis of the relationship between firing of deep cerebellar neurons and the classically conditioned nictitating membrane response in rabbits

The correlation of the activity of neurons in the interposed and dentate nuclei of the cerebellum with conditioned movements of the nictitating membrane was investigated using linear systems analysis. The activity of single deep cerebellar nuclear cells was assumed to be the input to a linear system that produced nictitating membrane movement. Data were initially analyzed with a causal model to assess the degree to which past neural activity predicted the conditioned response. 55 of 165 cells had correlation coefficients of 0.50 or greater between the model's moment-to-moment output and the actual output, with two interpositus cells having correlation coefficients of greater than 0.90. Double-sided impulse responses indicated that afference from the face and efference copy probably affect deep cerebellar neural activity. Nonlinearities were also found in the relationship between neuronal activity and conditioned movement. It was concluded that cerebellar deep nuclear firing is highly correlated with future nictitating membrane movements but that the firing-movement relationship contains noncausal and nonlinear components.     

The neural basis of smooth-pursuit eye movements

Smooth-pursuit eye movements are used to stabilize the image of a moving object of interest on the fovea, thus guaranteeing its high-acuity scrutiny. Such movements are based on a phylogenetically recent cerebro-ponto-cerebellar pathway that has evolved in parallel with foveal vision. Recent work has shown that a network of several cerebrocortical areas directs attention to objects of interest moving in three dimensions and reconstructs the trajectory of the target in extrapersonal space, thereby integrating various sources of multimodal sensory and efference copy information, as well as cognitive influences such as prediction. This cortical network is the starting point of a set of parallel cerebrofugal projections that use different parts of the dorsal pontine nuclei and the neighboring rostral nucleus reticularis tegmenti pontis as intermediate stations to feed two areas of the cerebellum, the flocculus-paraflocculus and the posterior vermis, which make mainly complementary contributions to the control of smooth pursuit.     

Neural simulations of adaptive reafference suppression in the elasmobranch electrosensory system

The electrosensory system of elasmobranchs is extremely sensitive to weak electric fields, with behavioral thresholds having been reported at voltage gradients as low as 5 nV/cm. To achieve this amazing sensitivity, the electrosensory system must extract weak extrinsic signals from a relatively large reafferent background signal associated with the animal's own movements. Ventilatory movements, in particular, strongly modulate the firing rates of primary electrosensory afferent nerve fibers, but this modulation is greatly suppressed in the medullary electrosensory processing nucleus, the dorsal octavolateral nucleus. Experimental evidence suggests that the neural basis of reafference suppression involves a common-mode rejection mechanism supplemented by an adaptive filter that fine tunes the cancellation. We present a neural model and computer simulation results that support the hypothesis that the adaptive component may involve an anti-Hebbian form of synaptic plasticity at molecular layer synapses onto ascending efferent neurons, the principal output neurons of the nucleus. Parallel fibers in the molecular layer carry a wealth of proprioceptive, efference copy, and sensory signals related to the animal's own movements. The proposed adaptive mechanism acts by canceling out components of the electrosensory input signal that are consistently correlated with these internal reference signals.Abbreviations AEN ascending efferent neuron - AFF primary afferent nerve fiber - DGR dorsal granular ridge - DON dorsal octavolateral nucleus - ELL electrosensory lateral line lobe - GABA -aminobutyric acid - IN inhibitory interneuron - ISI interspike interval - ST stellate cell     

Learning to predict the future: the cerebellum adapts feedforward movement control

The role of the cerebellum in motor control and learning has been largely inferred from the effects of cerebellar damage. Recent work shows that cerebellar damage produces greater impairment of movements that require predictive as opposed to reactive control. This dissociation is consistent across many different types of movement. Predictive control is crucial for fast and ballistic movements, but impaired prediction can also affect slow movements, because of increased reliance on time-delayed feedback signals. The new findings are compatible with theories of cerebellar function, but still do not resolve whether the cerebellum operates by predicting the optimal motor commands or future sensory states. Prediction mechanisms must be learned and maintained through comparisons between predicted and observed outcomes. New results show that not all such error information is equivalent in driving cerebellar learning.     

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

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

Saccadic adaptation to moving targets

Saccades are so called ballistic movements which are executed without online visual feedback. After each saccade the saccadic motor plan is modified in response to post-saccadic feedback with the mechanism of saccadic adaptation. The post-saccadic feedback is provided by the retinal position of the target after the saccade. If the target moves after the saccade, gaze may follow the moving target. In that case, the eyes are controlled by the pursuit system, a system that controls smooth eye movements. Although these two systems have in the past been considered as mostly independent, recent lines of research point towards many interactions between them. We were interested in the question if saccade amplitude adaptation is induced when the target moves smoothly after the saccade. Prior studies of saccadic adaptation have considered intra-saccadic target steps as learning signals. In the present study, the intra-saccadic target step of the McLaughlin paradigm of saccadic adaptation was replaced by target movement, and a post-saccadic pursuit of the target. We found that saccadic adaptation occurred in this situation, a further indication of an interaction of the saccadic system and the pursuit system with the aim of optimized eye movements.     

Smooth Pursuit and Visual Occlusion: Active Inference and Oculomotor Control in Schizophrenia

This paper introduces a model of oculomotor control during the smooth pursuit of occluded visual targets. This model is based upon active inference, in which subjects try to minimise their (proprioceptive) prediction error based upon posterior beliefs about the hidden causes of their (exteroceptive) sensory input. Our model appeals to a single principle – the minimisation of variational free energy – to provide Bayes optimal solutions to the smooth pursuit problem. However, it tries to accommodate the cardinal features of smooth pursuit of partially occluded targets that have been observed empirically in normal subjects and schizophrenia. Specifically, we account for the ability of normal subjects to anticipate periodic target trajectories and emit pre-emptive smooth pursuit eye movements – prior to the emergence of a target from behind an occluder. Furthermore, we show that a single deficit in the postsynaptic gain of prediction error units (encoding the precision of posterior beliefs) can account for several features of smooth pursuit in schizophrenia: namely, a reduction in motor gain and anticipatory eye movements during visual occlusion, a paradoxical improvement in tracking unpredicted deviations from target trajectories and a failure to recognise and exploit regularities in the periodic motion of visual targets. This model will form the basis of subsequent (dynamic causal) models of empirical eye tracking measurements, which we hope to validate, using psychopharmacology and studies of schizophrenia.     

Predictability of visual perturbation during locomotion: implications for corrective efference copy signaling

In guiding adaptive behavior, efference copy signals or corollary discharge are traditionally considered to serve as predictors of self-generated sensory inputs and by interfering with their central processing are able to counter unwanted consequences of an animal??s own actions. Here, in a speculative reflection on this issue, we consider a different functional role for such intrinsic predictive signaling, namely in stabilizing gaze during locomotion where resultant changes in head orientation in space require online compensatory eye movements in order to prevent retinal image slip. The direct activation of extraocular motoneurons by locomotor-related efference copies offers a prospective substrate for assisting self-motion derived sensory feedback, rather than being subtracted from the sensory signal to eliminate unwanted reafferent information. However, implementing such a feed-forward mechanism would be critically dependent on an appropriate phase coupling between rhythmic propulsive movement and resultant head/visual image displacement. We used video analyzes of actual locomotor behavior and basic theoretical modeling to evaluate head motion during stable locomotion in animals as diverse as Xenopus laevis tadpoles, teleost fish and horses in order to assess the potential suitability of spinal efference copies to the stabilization of gaze during locomotion. In all three species, and therefore regardless of aquatic or terrestrial environment, the head displacements that accompanied locomotor action displayed a strong correlative spatio-temporal relationship in correspondence with a potential predictive value for compensatory eye adjustments. Although spinal central pattern generator-derived efference copies offer appropriately timed commands for extraocular motor control during self-generated motion, it is likely that precise image stabilization requires the additional contributions of sensory feedback signals. Nonetheless, the predictability of the visual consequences of stereotyped locomotion renders intrinsic efference copy signaling an appealing mechanism for offsetting these disturbances, thus questioning the exclusive role traditionally ascribed to sensory-motor transformations in stabilizing gaze during vertebrate locomotion.     

When Passive Feels Active - Delusion-Proneness Alters Self-Recognition in the Moving Rubber Hand Illusion

Psychotic patients have problems with bodily self-recognition such as the experience of self-produced actions (sense of agency) and the perception of the body as their own (sense of ownership). While it has been shown that such impairments in psychotic patients can be explained by hypersalient processing of external sensory input it has also been suggested that they lack normal efference copy in voluntary action. However, it is not known how problems with motor predictions like efference copy contribute to impaired sense of agency and ownership in psychosis or psychosis-related states. We used a rubber hand illusion based on finger movements and measured sense of agency and ownership to compute a bodily self-recognition score in delusion-proneness (indexed by Peters’ Delusion Inventory - PDI). A group of healthy subjects (n=71) experienced active movements (involving motor predictions) or passive movements (lacking motor predictions). We observed a highly significant correlation between delusion-proneness and self-recognition in the passive conditions, while no such effect was observed in the active conditions. This was seen for both ownership and agency scores. The result suggests that delusion-proneness is associated with hypersalient external input in passive conditions, resulting in an abnormal experience of the illusion. We hypothesize that this effect is not present in the active condition because deficient motor predictions counteract hypersalience in psychosis proneness.     

Conventional synapses for unconventional cells

Powerful synapses between climbing fibers (CF) and Purkinje cells are crucial to cerebellar motor learning. In this issue of Neuron, Lin and colleagues provide compelling evidence for the existence of direct synaptic contacts between CFs and NG2-expressing glia cells, adding to the intrigue of neuro-glial interactions.