Simulation of adaptive modification of the vestibulo-ocular reflex with an adaptive filter model of the cerebellum

Distributed sensory coding by cerebellar complex spikes in units of cortical segments

Sensory processing is essential for motor control. Climbing fibers from the inferior olive transmit sensory signals to Purkinje cells, but how the signals are represented in the cerebellar cortex remains elusive. To examine the olivocerebellar organization of the mouse brain, we perform quantitative Ca²⁺ imaging to measure complex spikes (CSs) evoked by climbing fiber inputs over the entire dorsal surface of the cerebellum simultaneously. The surface is divided into approximately 200 segments, each composed of ∼100 Purkinje cells that fire CSs synchronously. Our in vivo imaging reveals that, although stimulation of four limb muscles individually elicits similar global CS responses across nearly all segments, the timing and location of a stimulus are derived by Bayesian inference from coordinated activation and inactivation of multiple segments on a single trial basis. We propose that the cerebellum performs segment-based, distributed-population coding that represents the conditional probability of sensory events.

A Biomimetic Control Method Increases the Adaptability of a Humanoid Robot Acting in a Dynamic Environment

One of the big challenges in robotics is to endow agents with autonomous and adaptive capabilities. With this purpose, we embedded a cerebellum-based control system into a humanoid robot that becomes capable of handling dynamical external and internal complexity. The cerebellum is the area of the brain that coordinates and predicts the body movements throughout the body-environment interactions. Different biologically plausible cerebellar models are available in literature and have been employed for motor learning and control of simplified objects. We built the canonical cerebellar microcircuit by combining machine learning and computational neuroscience techniques. The control system is composed of the adaptive cerebellar module and a classic control method; their combination allows a fast adaptive learning and robust control of the robotic movements when external disturbances appear. The control structure is built offline, but the dynamic parameters are learned during an online-phase training. The aforementioned adaptive control system has been tested in the Neuro-robotics Platform with the virtual humanoid robot iCub. In the experiment, the robot iCub has to balance with the hand a table with a ball running on it. In contrast with previous attempts of solving this task, the proposed neural controller resulted able to quickly adapt when the internal and external conditions change. Our bio-inspired and flexible control architecture can be applied to different robotic configurations without an excessive tuning of the parameters or customization. The cerebellum-based control system is indeed able to deal with changing dynamics and interactions with the environment. Important insights regarding the relationship between the bio-inspired control system functioning and the complexity of the task to be performed are obtained.

Computational Theory Underlying Acute Vestibulo-ocular Reflex Motor Learning with Cerebellar Long-Term Depression and Long-Term Potentiation

The vestibulo-ocular reflex (VOR) can be viewed as an adaptive control system that maintains compensatory eye movements during head motion. As the cerebellar flocculus is intimately involved in this adaptive motor control of the VOR, the VOR has been a popular model system for investigating cerebellar motor learning. Long-term depression (LTD) and long-term potentiation (LTP) at the parallel fiber-Purkinje cell synapses are considered to play major roles in cerebellar motor learning. A recent study using mutant mice demonstrated cerebellar motor learning with hampered LTD; the study concluded that the parallel fiber-Purkinje cell LTD is not essential. More recently, multiple forms of plasticity have been found in the cerebellum, and they are believed to contribute to cerebellar motor learning. However, it is still unclear how synaptic plasticity modifies the signal processing that underlies motor learning in the flocculus. A computational simulation suggested that the plasticity present in mossy fiber-granule cell synapses improves VOR-related sensory-motor information transferred into granule cells, whereas the plasticity in the molecular layer stores this information as a memory under guidance from climbing fiber teaching signals. Thus, motor learning and memory are thought to be induced mainly by LTD and LTP at parallel fiber-Purkinje cell synapses and by rebound potentiation at molecular interneuron-Purkinje cell synapses among the multiple forms of plasticity in the cerebellum. In this study, we focused on the LTD and LTP at parallel fiber-Purkinje cell synapses. Based on our simulation, we propose that acute VOR motor learning accomplishes by simultaneous enhancement of eye movement signals via LTP and suppression of vestibular signals via LTD to increase VOR gain (gain-up learning). To decrease VOR gain (gain-down learning), these two signals are modified in the opposite directions; namely, LTD suppresses eye movement signals, whereas LTP enhances vestibular signals.

The Roles of the Olivocerebellar Pathway in Motor Learning and Motor Control. A Consensus Paper

For many decades, the predominant view in the cerebellar field has been that the olivocerebellar system's primary function is to induce plasticity in the cerebellar cortex, specifically, at the parallel fiber-Purkinje cell synapse. However, it has also long been proposed that the olivocerebellar system participates directly in motor control by helping to shape ongoing motor commands being issued by the cerebellum. Evidence consistent with both hypotheses exists; however, they are often investigated as mutually exclusive alternatives. In contrast, here, we take the perspective that the olivocerebellar system can contribute to both the motor learning and motor control functions of the cerebellum and might also play a role in development. We then consider the potential problems and benefits of it having multiple functions. Moreover, we discuss how its distinctive characteristics (e.g., low firing rates, synchronization, and variable complex spike waveforms) make it more or less suitable for one or the other of these functions, and why having multiple functions makes sense from an evolutionary perspective. We did not attempt to reach a consensus on the specific role(s) the olivocerebellar system plays in different types of movements, as that will ultimately be determined experimentally; however, collectively, the various contributions highlight the flexibility of the olivocerebellar system, and thereby suggest that it has the potential to act in both the motor learning and motor control functions of the cerebellum.

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

Synaptic Plasticity in the Cerebellar Cortex and its Role in Motor Learning

Synaptic plasticity plays a role in the learning capability of brain tissues. Long-term depression (LTD) of parallel fiber synapses in cerebellar Purkinje cells occurs when these synapses are activated in conjunction with climbing fiber synapses. Signal transduction mechanisms underlying LTD have recently been investigated extensively. It has also become apparent that climbing fiber signals encode errors in the motor performance of an animal. It is therefore hypothesized that learning proceeds in cerebellar tissues in such a way that error signals of climbing fibers act to depress by LTD those parallel fiber synapses responsible for the errors. The cerebellum contains a large number of corticonuclear microcomplexes. Each microcomplex is connected to an extracerebellar system and is presumed to endow the system with learning capability. The hypothesis accounts for the adaptation of the vestibuloocular reflex and probably also for other forms of motor and cognitive learning.

Velocity-selective adaptation of the horizontal and cross-axis vestibulo-ocular reflex in the mouse

One commonly observed phenomenon of vestibulo-ocular reflex (VOR) adaptation is a frequency-selective change in gain (eye velocity/head velocity) and phase (relative timing between the vestibular stimulus and response) based on the frequency content of the adaptation training stimulus. The neural mechanism behind this type of adaptation is not clear. Our aim was to determine whether there were other parameter-selective effects on VOR adaptation, specifically velocity-selective and acceleration-selective changes in the horizontal VOR gain and phase. We also wanted to determine whether parameter selectivity was also in place for cross-axis adaptation training (a visual-vestibular training stimulus that elicits a vestibular-evoked torsional eye movement during horizontal head rotations). We measured VOR gain and phase in 17 C57BL/6 mice during baseline (no adaptation training) and after gain-increase, gain-decrease and cross-axis adaptation training using a sinusoidal visual-vestibular (mismatch) stimulus with whole-body rotations (vestibular stimulus) with peak velocity 20 and 50°/s both with a fixed frequency of 0.5 Hz. Our results show pronounced velocity selectivity of VOR adaptation. The difference in horizontal VOR gain after gain-increase versus gain-decrease adaptation was maximal when the sinusoidal testing stimulus matched the adaptation training stimulus peak velocity. We also observed similar velocity selectivity after cross-axis adaptation training. Our data suggest that frequency selectivity could be a manifestation of both velocity and acceleration selectivity because when one of these is absent, e.g. acceleration selectivity in the mouse, frequency selectivity is also reduced.

A cerebellar learning model of vestibulo-ocular reflex adaptation in wild-type and mutant mice

Mechanisms of cerebellar motor learning are still poorly understood. The standard Marr-Albus-Ito theory posits that learning involves plasticity at the parallel fiber to Purkinje cell synapses under control of the climbing fiber input, which provides an error signal as in classical supervised learning paradigms. However, a growing body of evidence challenges this theory, in that additional sites of plasticity appear to contribute to motor adaptation. Here, we consider phase-reversal training of the vestibulo-ocular reflex (VOR), a simple form of motor learning for which a large body of experimental data is available in wild-type and mutant mice, in which the excitability of granule cells or inhibition of Purkinje cells was affected in a cell-specific fashion. We present novel electrophysiological recordings of Purkinje cell activity measured in naive wild-type mice subjected to this VOR adaptation task. We then introduce a minimal model that consists of learning at the parallel fibers to Purkinje cells with the help of the climbing fibers. Although the minimal model reproduces the behavior of the wild-type animals and is analytically tractable, it fails at reproducing the behavior of mutant mice and the electrophysiology data. Therefore, we build a detailed model involving plasticity at the parallel fibers to Purkinje cells' synapse guided by climbing fibers, feedforward inhibition of Purkinje cells, and plasticity at the mossy fiber to vestibular nuclei neuron synapse. The detailed model reproduces both the behavioral and electrophysiological data of both the wild-type and mutant mice and allows for experimentally testable predictions.

Nonvisual complex spike signals in the rabbit cerebellar flocculus

In addition to the well-known signals of retinal image slip, floccular complex spikes (CSs) also convey nonvisual signals. We recorded eye movement and CS activity from Purkinje cells in awake rabbits sinusoidally oscillated in the dark on a vestibular turntable. The stimulus frequency ranged from 0.2 to 1.2 Hz, and the velocity amplitude ranged from 6.3 to 50°/s. The average CS modulation was evaluated at each combination of stimulus frequency and amplitude. More than 75% of the Purkinje cells carried nonvisual CS signals. The amplitude of this modulation remained relatively constant over the entire stimulus range. The phase response of the CS modulation in the dark was opposite to that during the vestibulo-ocular reflex (VOR) in the light. With increased frequency, the phase response systematically shifted from being aligned with contraversive head velocity toward peak contralateral head position. At fixed frequency, the phase response was dependent on peak head velocity, indicating a system nonlinearity. The nonvisual CS modulation apparently reflects a competition between eye movement and vestibular signals, resulting in an eye movement error signal inferred from nonvisual sources. The combination of this error signal with the retinal slip signal in the inferior olive results in a net error signal reporting the discrepancy between the actual visually measured eye movement error and the inferred eye movement error derived from measures of the internal state. The presence of two error signals requires that the role of CSs in models of the floccular control of VOR adaption be expanded beyond retinal slip.

Optimal properties of analog perceptrons with excitatory weights

The cerebellum is a brain structure which has been traditionally devoted to supervised learning. According to this theory, plasticity at the Parallel Fiber (PF) to Purkinje Cell (PC) synapses is guided by the Climbing fibers (CF), which encode an 'error signal'. Purkinje cells have thus been modeled as perceptrons, learning input/output binary associations. At maximal capacity, a perceptron with excitatory weights expresses a large fraction of zero-weight synapses, in agreement with experimental findings. However, numerous experiments indicate that the firing rate of Purkinje cells varies in an analog, not binary, manner. In this paper, we study the perceptron with analog inputs and outputs. We show that the optimal input has a sparse binary distribution, in good agreement with the burst firing of the Granule cells. In addition, we show that the weight distribution consists of a large fraction of silent synapses, as in previously studied binary perceptron models, and as seen experimentally.

A computational mechanism for unified gain and timing control in the cerebellum

Precise gain and timing control is the goal of cerebellar motor learning. Because the basic neural circuitry of the cerebellum is homogeneous throughout the cerebellar cortex, a single computational mechanism may be used for simultaneous gain and timing control. Although many computational models of the cerebellum have been proposed for either gain or timing control, few models have aimed to unify them. In this paper, we hypothesize that gain and timing control can be unified by learning of the complete waveform of the desired movement profile instructed by climbing fiber signals. To justify our hypothesis, we adopted a large-scale spiking network model of the cerebellum, which was originally developed for cerebellar timing mechanisms to explain the experimental data of Pavlovian delay eyeblink conditioning, to the gain adaptation of optokinetic response (OKR) eye movements. By conducting large-scale computer simulations, we could reproduce some features of OKR adaptation, such as the learning-related change of simple spike firing of model Purkinje cells and vestibular nuclear neurons, simulated gain increase, and frequency-dependent gain increase. These results suggest that the cerebellum may use a single computational mechanism to control gain and timing simultaneously.

Physiology of clinical dysfunction of the cerebellum

Experimental and theoretical research into cerebellar function has begun to converge toward understanding the cerebellum as a "controller" in the engineering sense. The purpose of a controller is to convert high-level intent commands and information describing the current state of a system into low-level control signals suitable for maintaining or changing system behavior. The cerebellar subsystem appears to play this role for parts of the body and other parts of the brain. As with engineering controllers, fundamental functions include stabilization at a fixed posture or state, adjustment of movement or transition amplitude, facilitation of movement/transition speed and crispness of launch and braking, improvement of resistance to disturbances, coordination of control across multiple degrees of freedom, and assistance with estimation and/or prediction of current and future system states. As with adaptive engineering controllers, the cerebellar subsystem also readily tunes itself over time. At a more detailed level, many of the specific actions of cerebellar circuits can be understood in terms of proportional (P), integrator-like (I), and differentiator-like (D) signal processing which are fundamental components of many engineering control systems. This chapter presents an integrated, mechanistic view of ataxia, tremor, and several cerebellar oculomotor signs in terms of PID control and the neural centers that appear to subserve these functions. It also suggests the manner in which impairments in motor learning, perception, and cognition that are associated with cerebellar dysfunction may be viewed from a similar perspective.

Are mushroom bodies cerebellum-like structures?

The mushroom bodies are distinctive neuropils in the protocerebral brain segments of many protostomes. A defining feature of mushroom bodies is their intrinsic neurons, masses of cytoplasm-poor globuli cells that form a system of lobes with their densely-packed, parallel-projecting axon-like processes. In insects, the role of the mushroom bodies in olfactory processing and associative learning and memory has been studied in depth, but several lines of evidence suggest that the function of these higher brain centers cannot be restricted to these roles. The present account considers whether insight into an underlying function of mushroom bodies may be provided by cerebellum-like structures in vertebrates, which are similarly defined by the presence of masses of tiny granule cells that emit thin parallel fibers forming a dense molecular layer. In vertebrates, the shared neuroarchitecture of cerebellum-like structures has been suggested to underlie a common functional role as adaptive filters for the removal of predictable sensory elements, such as those arising from reafference, from the total sensory input. Cerebellum-like structures include the vertebrate cerebellum, the electrosensory lateral line lobe, dorsal and medial octavolateral nuclei of fish, and the dorsal cochlear nucleus of mammals. The many architectural and physiological features that the insect mushroom bodies share with cerebellum-like structures suggest that it might be fruitful to consider mushroom body function in light of a possible role as adaptive sensory filters. The present account thus presents a detailed comparison of the insect mushroom bodies with vertebrate cerebellum-like structures.

Spatiotemporal firing patterns in the cerebellum

Neurons are generally considered to communicate information by increasing or decreasing their firing rate. However, in principle, they could in addition convey messages by using specific spatiotemporal patterns of spiking activities and silent intervals. Here, we review expanding lines of evidence that such spatiotemporal coding occurs in the cerebellum, and that the olivocerebellar system is optimally designed to generate and employ precise patterns of complex spikes and simple spikes during the acquisition and consolidation of motor skills. These spatiotemporal patterns may complement rate coding, thus enabling precise control of motor and cognitive processing at a high spatiotemporal resolution by fine-tuning sensorimotor integration and coordination.

Neural dynamics of autistic behaviors: cognitive, emotional, and timing substrates

What brain mechanisms underlie autism, and how do they give rise to autistic behavioral symptoms? This article describes a neural model, called the Imbalanced Spectrally Timed Adaptive Resonance Theory (iSTART) model, that proposes how cognitive, emotional, timing, and motor processes that involve brain regions such as the prefrontal and temporal cortex, amygdala, hippocampus, and cerebellum may interact to create and perpetuate autistic symptoms. These model processes were originally developed to explain data concerning how the brain controls normal behaviors. The iSTART model shows how autistic behavioral symptoms may arise from prescribed breakdowns in these brain processes, notably a combination of underaroused emotional depression in the amygdala and related affective brain regions, learning of hyperspecific recognition categories in the temporal and prefrontal cortices, and breakdowns of adaptively timed attentional and motor circuits in the hippocampal system and cerebellum. The model clarifies how malfunctions in a subset of these mechanisms can, through a systemwide vicious circle of environmentally mediated feedback, cause and maintain problems with them all.

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 study on monkey VOR adaptation and smooth pursuit based on the parallel control-pathway theory

Much controversy remains about the site of learning and memory for vestibuloocular reflex (VOR) adaptation in spite of numerous previous studies. One possible explanation for VOR adaptation is the flocculus hypothesis, which assumes that this adaptation is caused by synaptic plasticity in the cerebellar cortex. Another hypothesis is the model proposed by Lisberger that assumes that the learning that occurs in both the cerebellar cortex and the vestibular nucleus is necessary for VOR adaptation. Lisberger's model is characterized by a strong positive feedback loop carrying eye velocity information from the vestibular nucleus to the cerebellar cortex. This structure contributes to the maintenance of a smooth pursuit driving command with zero retinal slip during the steady-state phase of smooth pursuit with gain 1 or during the target blink condition. Here, we propose an alternative hypothesis that suggests that the pursuit driving command is maintained in the medial superior temporal (MST) area based on MST firing data during target blink and during ocular following blank, and as a consequence, we assume a much smaller gain for the positive feedback from the vestibular nucleus to the cerebellar cortex. This hypothesis is equivalent to assuming that there are two parallel neural pathways for controlling VOR and smooth pursuit: a main pathway of the semicircular canals to the vestibular nucleus for VOR, and a main pathway of the MST-dorsolateral pontine nuclei (DLPN)-flocculus/ventral paraflocculus to the vestibular nucleus for smooth pursuit. First, we theoretically demonstrate that this parallel control-pathway theory can reproduce the various firing patterns of horizontal gaze velocity Purkinje cells in the flocculus/ventral paraflocculus dependent on VOR in the dark, smooth pursuit, and VOR cancellation as reported in Miles et al. at least equally as well as the gaze velocity theory, which is the basic framework of Lisberger's model. Second, computer simulations based on our hypothesis can stably reproduce neural firing data as well as behavioral data obtained in smooth pursuit, VOR cancellation, and VOR adaptation, even if only plasticity in the cerebellar cortex is assumed. Furthermore, our computer simulation model can reproduce VOR adaptation automatically based on a heterosynaptic interaction model between parallel fiber inputs and climbing fiber inputs. Our results indicate that different assumptions about the site of pursuit driving command maintenance computationally lead to different conclusions about where the learning for VOR adaptation occurs. Finally, we propose behavioral and physiological experiments capable of discriminating between these two possibilities for the site of pursuit driving command maintenance and hence for the sites of learning and memory for VOR adaptation.

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.

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

A neural network model based on the anatomy and physiology of the cerebellum is presented that can generate both simple and complex predictive pursuit, while also responding in a feedback mode to visual perturbations from an ongoing trajectory. The model allows the prediction of complex movements by adding two features that are not present in other pursuit models: an array of inputs distributed over a range of physiologically justified delays, and a novel, biologically plausible learning rule that generated changes in synaptic strengths in response to retinal slip errors that arrive after long delays. To directly test the model, its output was compared with the behavior of monkeys tracking the same trajectories. There was a close correspondence between model and monkey performance. Complex target trajectories were created by summing two or three sinusoidal components of different frequencies along horizontal and/or vertical axes. Both the model and the monkeys were able to track these complex sum-of-sines trajectories with small phase delays that averaged 8 and 20 ms in magnitude, respectively. Both the model and the monkeys showed a consistent relationship between the high- and low-frequency components of pursuit: high-frequency components were tracked with small phase lags, whereas low-frequency components were tracked with phase leads. The model was also trained to track targets moving along a circular trajectory with infrequent right-angle perturbations that moved the target along a circle meridian. Before the perturbation, the model tracked the target with very small phase differences that averaged 5 ms. After the perturbation, the model overshot the target while continuing along the expected nonperturbed circular trajectory for 80 ms, before it moved toward the new perturbed trajectory. Monkeys showed similar behaviors with an average phase difference of 3 ms during circular pursuit, followed by a perturbation response after 90 ms. In both cases, the delays required to process visual information were much longer than delays associated with nonperturbed circular and sum-of-sines pursuit. This suggests that both the model and the eye make short-term predictions about future events to compensate for visual feedback delays in receiving information about the direction of a target moving along a changing trajectory. In addition, both the eye and the model can adjust to abrupt changes in target direction on the basis of visual feedback, but do so after significant processing delays.

The Hippocampus and Cerebellum in Adaptively Timed Learning, Recognition, and Movement

The concepts of declarative memory and procedural memory have been used to distinguish two basic types of learning. A neural network model suggests how such memory processes work together as recognition learning, reinforcement learning, and sensorimotor learning take place during adaptive behaviors. To coordinate these processes, the hippocampal formation and cerebellum each contains circuits that learn to adaptively time their outputs. Within the model, hippocampal timing helps to maintain attention on motivationally salient goal objects during variable task-related delays, and cerebellar timing controls the release of conditioned responses. This property is part of the model's description of how cognitive-emotional interactions focus attention on motivationally valued cues, and how this process breaks down due to hippocampal ablation. The model suggests that the hippocampal mechanisms that help to rapidly draw attention to salient cues could prematurely release motor commands were not the release of these commands adaptively timed by the cerebellum. The model hippocampal system modulates cortical recognition learning without actually encoding the representational information that the cortex encodes. These properties avoid the difficulties faced by several models that propose a direct hippocampal role in recognition learning. Learning within the model hippocampal system controls adaptive timing and spatial orientation. Model properties hereby clarify how hippocampal ablations cause amnesic symptoms and difficulties with tasks which combine task delays, novelty detection, and attention toward goal objects amid distractions. When these model recognition, reinforcement, sensorimotor, and timing processes work together, they suggest how the brain can accomplish conditioning of multiple sensory events to delayed rewards, as during serial compound conditioning.

Role of visuo-vestibular interaction in pathological ocular oscillation: new model and control system analysis

Control system engineering is a relatively newer field of engineering which is directly applicable to performance analysis of neuronal networks. Visuo-vestibular interaction (VVI) represents a neuronal control system which has most benefited from such analysis. In this paper, we present a new model of VVI derived from our previously reported model by adding cortical pursuit feedback. Mathematical analysis of abnormal eye oscillations and stability analysis of the VVI system provided us with a plausible hypothesis that the pathological ocular oscillations seen in oculopalatal myoclonus and see-saw nystagmus are indeed due to an unstable VVI control system. The former is due to degeneration of the inferior olivary nucleus resulting in loss of cerebellar learning effects, while the latter is due to disruption of the pathway conveying retinal error signals.

A neural network model of adaptively timed reinforcement learning and hippocampal dynamics

A neural model is described of how adaptively timed reinforcement learning occurs. The adaptive timing circuit is suggested to exist in the hippocampus, and to involve convergence of dentate granule cells on CA3 pyramidal cells, and N-methyl-D-aspartate (NMDA) receptors. This circuit forms part of a model neural system for the coordinated control of recognition learning, reinforcement learning, and motor learning, whose properties clarify how an animal can learn to acquire a delayed reward. Behavioral and neural data are summarized in support of each processing stage of the system. The relevant anatomical sites are in thalamus, neocortex, hippocampus, hypothalamus, amygdala and cerebellum. Cerebellar influences on motor learning are distinguished from hippocampal influences on adaptive timing of reinforcement learning. The model simulates how damage to the hippocampal formation disrupts adaptive timing, eliminates attentional blocking and causes symptoms of medial temporal amnesia. Properties of learned expectations, attentional focussing, memory search and orienting reactions to novel events are used to analyze the blocking and amnesia data. The model also suggests how normal acquisition of subcortical emotional conditioning can occur after cortical ablation, even though extinction of emotional conditioning is retarded by cortical ablation. The model simulates how increasing the duration of an unconditioned stimulus increases the amplitude of emotional conditioning, but does not change adaptive timing; and how an increase in the intensity of a conditioned stimulus 'speeds up the clock', but an increase in the intensity of an unconditioned stimulus does not. Computer simulations of the model fit parametric conditioning data, including a Weber law property and an inverted U property. Both primary and secondary adaptively timed conditionings are simulated, as are data concerning conditioning using multiple interstimulus intervals (ISIs), gradually or abruptly changing ISIs, partial reinforcement and multiple stimuli that lead to time-averaging of responses. Neurobiologically testable predictions are made to facilitate further tests of the model.

Predicting the Future: Advantages of Semilocal Units

In investigating gaussian radial basis function (RBF) networks for their ability to model nonlinear time series, we have found that while RBF networks are much faster than standard sigmoid unit backpropagation for low-dimensional problems, their advantages diminish in high-dimensional input spaces. This is particularly troublesome if the input space contains irrelevant variables. We suggest that this limitation is due to the localized nature of RBFs. To gain the advantages of the highly nonlocal sigmoids and the speed advantages of RBFs, we propose a particular class of semilocal activation functions that is a natural interpolation between these two families. We present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks, and, very importantly, are more accurate than RBF networks in the presence of irrelevant inputs. On the Mackey-Glass and Coupled Lattice Map problems, the speedup over sigmoid networks is so dramatic that the difference in training time between RBF and gaussian bar networks is minor. Gaussian bar architectures that superpose composed gaussians (gaussians-of-gaussians) to approximate the unknown function have the best performance. We postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics, which we call automatic connection pruning, is an important factor in the success of this representation.

Learning causes synaptogenesis, whereas motor activity causes angiogenesis, in cerebellar cortex of adult rats

The role of the cerebellar cortex in motor learning was investigated by comparing the paramedian lobule of adult rats given difficult acrobatic training to that of rats that had been given extensive physical exercise or had been inactive. The paramedian lobule is activated during limb movements used in both acrobatic training and physical exercise. Acrobatic animals had greater numbers of synapses per Purkinje cell than animals from the exercise or inactive groups. No significant difference in synapse number or size between the exercised and inactive groups was found. This indicates that motor learning required of the acrobatic animals, and not repetitive use of synapses during physical exercise, generates new synapses in cerebellar cortex. In contrast, exercise animals had a greater density of blood vessels in the molecular layer than did either the acrobatic or inactive animals, suggesting that increased synaptic activity elicited compensatory angiogenesis.

A new theory of cerebellar function: movement control through phase-independent recognition of identities between time-based neural informational symbols

A new theory designed to explain the functions of the cerebellum in the control of movement and the unique anatomy of that structure is presented. The heart of this proposed explanation is that the cerebellum generates increased numbers of outputs from particular Purkinje cells whenever the same pattern of pulses in time is presented both to its mossy fiber and its climbing fiber input systems. The postulated function of the unusual anatomy of the cerebellum is to permit it instantly to recognize and respond to identical patterns presented through these two channels regardless of the phase differences between these two signal sources, where phase differences are defined as differences in times of arrival of patterns of inputs from these two sources. The first means putatively used involves the summation of pulses comprising a given pattern of inputs simultaneously at many different Purkinje cells by virtue of the different speeds of conduction of the parallel fiber axons of granule cells. The second means is the addition of an input from the climbing fiber system that, together with the simultaneous parallel fiber inputs, leads to a discharge of particular Purkinje cells, which discharge temporarily increases the size of EPSP's generated by the parallel fiber synapses involved in the cell's discharge. This specific synaptic potentiation, in turn, makes it possible for the cell to respond by generating closely consecutive additional discharges provided that the same patterns of discharge are presented both to the climbing fiber system and the mossy fiber system. This happens because later pulses in identical patterns will arrive simultaneously at previously facilitated synapses via parallel fibers and at synapses of the climbing fibers, thereby causing additional spatial summations and discharges to occur. According to this explanation the patterns that are compared in the above manner are symbols (patterns of pulses) produced by sensors of current positions and symbols derived from memory and also representing these same positions. When patterns from these two sources are identical, the multiple outputs of specific Purkinje cells inhibit an automatic feedback loop and thereby indirectly cause the attenuation and arrest of movement. The evolution of these concepts resulted in very specific "predictions" of particular connections involving the olive, pons, red nucleus, dentate, thalamus, and sensory-motor cortex. All of these predictions were found to be consistent with evidence in the literature. Points of difference between this theory and all prior ones are discussed as are several critical tests of its validity, and the putative evolution of cerebellar structure and function.(ABSTRACT TRUNCATED AT 400 WORDS)

Phase conjugation model for information transfer in the nervous system

In the nervous system, dispersion in propagation time sometimes brings delay distortion or phase distortion on the information transmission. Also in the memory retrieval processes in the brain, some parts of images may be retrieved more slowly than others. For smooth control of fast movements as well as for keeping exact thinking, these distortions have to be taken out. To understand the distortion cancelling mechanism, new neural network models for compensating the phase distortion are proposed. The models stand on the concept of "phase conjugate mirror" which is used in optical image processing. Simulation studies based on the model resulted in successful cancellation of the delay dispersion involved in the information transmission in the nervous system.

Localized metabolic responses to optokinetic stimulation in the brain stem nuclei and the cerebellum investigated with the [14C]2-deoxyglucose method in rats

The localized metabolic effects of monocular optokinetic stimulation to the cerebellar flocculus and brain stem nuclei were measured in pigmented rats. Quantitative [14C]2-deoxyglucose autoradiography was performed on alert rats stimulated with a drum either rotated horizontally in the temporonasal direction (optokinetic group) or kept stationary (control group). The superior colliculus in both groups showed a higher amount of activity on the contralateral side to the stimulated eye than on the ipsilateral side. The dorsal cap of the inferior olive, the nucleus of the optic tract, and the lateral pontine nucleus showed a higher amount of activity on the contralateral side only in the optokinetic group. The nucleus reticularis tegmenti pontis and the ventromedial aspect of the cerebellar paraflocculus showed no lateralized activity in either group. Local glucose utilization rates of both flocculi were significantly enhanced in the optokinetic group. Only in the optokinetic group did the ipsilateral flocculus show a higher local glucose utilization rate than the contralateral flocculus. The most enhanced activity was localized in the middle aspect of the rostrocaudal extent of the ipsilateral flocculus. The activity was greater in the granular layer than in the molecular layer or in the white matter. The pattern of activation in the granular layer was characterized by a patchy appearance in the frontal sections. Serial reconstruction of these sections showed metabolic blobs appearing with intervals of several hundred micrometers.

A hierarchical neural-network model for control and learning of voluntary movement

In order to control voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: the determination of a desired trajectory in the visual coordinates, the transformation of its coordinates to the body coordinates and the generation of motor command. Based on physiological knowledge and previous models, we propose a hierarchical neural network model which accounts for the generation of motor command. In our model the association cortex provides the motor cortex with the desired trajectory in the body coordinates, where the motor command is then calculated by means of long-loop sensory feedback. Within the spinocerebellum--magnocellular red nucleus system, an internal neural model of the dynamics of the musculoskeletal system is acquired with practice, because of the heterosynaptic plasticity, while monitoring the motor command and the results of movement. Internal feedback control with this dynamical model updates the motor command by predicting a possible error of movement. Within the cerebrocerebellum--parvocellular red nucleus system, an internal neural model of the inverse-dynamics of the musculo-skeletal system is acquired while monitoring the desired trajectory and the motor command. The inverse-dynamics model substitutes for other brain regions in the complex computation of the motor command. The dynamics and the inverse-dynamics models are realized by a parallel distributed neural network, which comprises many sub-systems computing various nonlinear transformations of input signals and a neuron with heterosynaptic plasticity (that is, changes of synaptic weights are assumed proportional to a product of two kinds of synaptic inputs). Control and learning performance of the model was investigated by computer simulation, in which a robotic manipulator was used as a controlled system, with the following results: (1) Both the dynamics and the inverse-dynamics models were acquired during control of movements. (2) As motor learning proceeded, the inverse-dynamics model gradually took the place of external feedback as the main controller. Concomitantly, overall control performance became much better. (3) Once the neural network model learned to control some movement, it could control quite different and faster movements. (4) The neural network model worked well even when only very limited information about the fundamental dynamical structure of the controlled system was available.(ABSTRACT TRUNCATED AT 400 WORDS)

Long-term depression as a memory process in the cerebellum

When details of neuronal network structures of the cerebellum were uncovered in the 1960's, a hope emerged that functions of the cerebellum would eventually be explained in terms of operation of the cerebellar neuronal network. While various network models were proposed, involvement of synaptic plasticity in the cerebellar neuronal network as a memory process became a focus of discussion. The characteristic dual inputs to Purkinje cells, one from parallel fibers (axons of granule cells) and the other from climbing fibers, were suggested to represent such synaptic plasticity, and under this assumption, the cerebellar cortex was envisaged as a learning machine for pattern recognition. Despite these theoretical suggestions, earlier efforts to reveal the postulated synaptic plasticity in the cerebellar cortex were unsuccessful. It had then to wait for a decade before long-term depression (LTD) was finally found as its possible substrate. LTD is a long-lasting depression of parallel fiber-to-Purkinje cell transmission that occurs following conjunctive activation of parallel fibers and a climbing fiber both converging onto one and the same Purkinje cell. LTD has now been established by means of various testing methods, and recent efforts have been directed toward its molecular mechanisms. Efforts have also been devoted to demonstrate roles of LTD in motor learning through studies of adaptation of the vestibulo-ocular reflex, adaptive adjustment of hand movement, and more recently eyelid blink conditioned reflex. This article reviews recent efforts to characterize the LTD as a memory process, presumably the major, in the cerebellum.

Elasmobranch eye motor dynamics characterised using pseudorandom stimulus

A pseudorandom binary sequence electrical pulse rate stimulus was delivered to the abducens nerve of an elasmobranch preparation. Ipsilateral eye movements were recorded using a position-sensitive photodiode to measure the position of a reflective patch attached to the fish's eye. Eye position data was cross-correlated with the stimulus pattern, and exponential decay curves were fitted to the cross-correlograms to estimate the time constant of a linear first order low-pass filter model. The cross-correlograms were transformed into the frequency domain using a Digital Fourier Transform, and Bode plots of eye dynamics were plotted. Eye motor plant dynamics in the elasmobranch Cephaloscyllium isabella can be accurately characterised by a linear first order low-pass filter model with a corner frequency of 0.73 +/- 0.10 Hz. Non-minimum phase lag reaches 90 degrees at about 4 Hz, indicating a time delay of some 50-60 ms. Integration of the canal signal is not required for producing compensatory eye movements above the characteristic frequency of the eye motor plant. However, the canal signal may be integrated to ensure that the vestibulo-ocular reflex is compensatory at lower frequencies. Substantial phase compensation or prediction is required for effective control of the vestibulo-ocular reflex.

Sensori-motor transformations in the brain (with a critique of the tensor theory of cerebellum)

Section 1 lists 12 points which must be addressed by neural models of sensorimotor coordination. Section 2 addresses the problem of extrapolating motor output from noisy data or from sensory input. The Pellionisz-Llinas cerebellar lookahead module addresses this problem for the noise-free case, and we suggest theoretical and experimental tests of the model; we then suggest the investigation of neural analogs of the Kalman-Bucy filter. Section 3 offers a brief exposition of mechanics in a tensor framework to provide the irreducible minimum of mathematical machinery to evaluate the Pellionisz-Llinás tensor theory of brain function and to suggest fruitful new hypotheses. Our critique of this theory in section 4 leads us to conclude that what they offer is based on metaphorical use of terminology from Euclidean tensors, not on rigorous application of the mathematics of tensor analysis. The central claim of their theory--that the input is a covariant intention vector transformed by a metric tensor encoded in the cerebellum to a contravariant execution vector--has not been substantiated and probably cannot be substantiated. However, we do point the way to further use of tensor analysis in the study of neural control of movement. The concluding section then returns to the points raised in section 1 with a highly selective survey of models of cerebellum and tectum.