An adaptive neural model compatible with plastic changes induced in the human vestibulo-ocular reflex by prolonged optical reversal of vision

Temporal integration and 1/f power scaling in a circuit model of cerebellar interneurons

Inhibitory interneurons interconnected via electrical and chemical (GABA_A receptor) synapses form extensive circuits in several brain regions. They are thought to be involved in timing and synchronization through fast feedforward control of principal neurons. Theoretical studies have shown, however, that whereas self-inhibition does indeed reduce response duration, lateral inhibition, in contrast, may generate slow response components through a process of gradual disinhibition. Here we simulated a circuit of interneurons (stellate and basket cells) of the molecular layer of the cerebellar cortex and observed circuit time constants that could rise, depending on parameter values, to >1 s. The integration time scaled both with the strength of inhibition, vanishing completely when inhibition was blocked, and with the average connection distance, which determined the balance between lateral and self-inhibition. Electrical synapses could further enhance the integration time by limiting heterogeneity among the interneurons and by introducing a slow capacitive current. The model can explain several observations, such as the slow time course of OFF-beam inhibition, the phase lag of interneurons during vestibular rotation, or the phase lead of Purkinje cells. Interestingly, the interneuron spike trains displayed power that scaled approximately as 1/f at low frequencies. In conclusion, stellate and basket cells in cerebellar cortex, and interneuron circuits in general, may not only provide fast inhibition to principal cells but also act as temporal integrators that build a very short-term memory.NEW & NOTEWORTHY The most common function attributed to inhibitory interneurons is feedforward control of principal neurons. In many brain regions, however, the interneurons are densely interconnected via both chemical and electrical synapses but the function of this coupling is largely unknown. Based on large-scale simulations of an interneuron circuit of cerebellar cortex, we propose that this coupling enhances the integration time constant, and hence the memory trace, of the circuit.

Extreme vestibulo-ocular adaptation induced by prolonged optical reversal of vision

1. These experiments investigated plastic changes in the vestibulo-ocular reflex (VOR) of human subjects consequent to long-term optical reversal of vision during free head movement. Horizontal vision-reversal was produced by head-mounted dove prisms. Four normal adults were continuously exposed to these conditions during 2, 6, 7 and 27 days respectively.2. A sinusoidal rotational stimulus, previously shown to be nonhabituating (1/6 Hz; 60 degrees /sec amplitude), was used to test the VOR in the dark at frequent intervals both during the period of vision-reversal and an equal period after return to normal vision. D.c. electro-oculography (EOG) was used to record eye movement, taking care to avoid changes of EOG gain due to light/dark adaptation of the retina.3. All subjects showed substantial reduction of VOR gain (eye velocity/head velocity) during the first 2 days of vision-reversal. The 6-, 7- and 27-day subjects showed further reduction of gain which reached a low plateau at about 25% the normal value by the end of one week. At this time the attenuation of some EOG records was so marked as to defy extraction of a meaningful sinusoidal signal.4. After removal of the prisms VOR gain recovered along a time course which approximated that of the original adaptive attenuation.5. In the 27-day experiment large changes of phase developed in the VOR during the second week of vision-reversal. These changes generally progressed in a lagging sense, to reach 130 degrees phase lag relative to normal by the beginning of the third week. Accompanying this was a considerable restoration of gain from 25 to 50% the normal value. These adapted conditions, which approximate functional reversal of the reflex, were then maintained steady, even overnight, until return to normal vision on the 28th day.6. Thereafter, whereas VOR phase returned to near-normal in 2 hr, restoration of gain occupied a further 2-3 weeks.7. There was a highly systematic relation between instantaneous gain and phase, even during periods of widely fluctuating change associated with transition from one steady state to another. During such transition there was a tendency for directional preponderance to occur in the VOR.8. All the observed changes were highly specific to the plane of vision-reversal, no VOR changes being observed in the sagittal plane.9. VOR changes were adaptive, in the sense that they were always goal-directed towards the requirements of retinal image stabilization during head movement. They were plastic to the extent that there was extensive and retained remodelling of the reflex towards this goal.10. It is inferred that all the observed changes in gain and phase are compatible with a simple neural network employing known vestibulo-ocular projections via brainstem and cerebellar pathways, providing that the reversed visual tracking task can produce plastic modulation of efficacy in the cerebellar pathway and that this pathway exhibits a dynamic characteristic producing moderate phase lead in a sinusoidal signal at 1/6 Hz.

Exploring the fundamental dynamics of error-based motor learning using a stationary predictive-saccade task

The maintenance of movement accuracy uses prior performance errors to correct future motor plans; this motor-learning process ensures that movements remain quick and accurate. The control of predictive saccades, in which anticipatory movements are made to future targets before visual stimulus information becomes available, serves as an ideal paradigm to analyze how the motor system utilizes prior errors to drive movements to a desired goal. Predictive saccades constitute a stationary process (the mean and to a rough approximation the variability of the data do not vary over time, unlike a typical motor adaptation paradigm). This enables us to study inter-trial correlations, both on a trial-by-trial basis and across long blocks of trials. Saccade errors are found to be corrected on a trial-by-trial basis in a direction-specific manner (the next saccade made in the same direction will reflect a correction for errors made on the current saccade). Additionally, there is evidence for a second, modulating process that exhibits long memory. That is, performance information, as measured via inter-trial correlations, is strongly retained across a large number of saccades (about 100 trials). Together, this evidence indicates that the dynamics of motor learning exhibit complexities that must be carefully considered, as they cannot be fully described with current state-space (ARMA) modeling efforts.

What muscle variable(s) does the nervous system control in limb movements?

To control force accurately under a wide range of behavioral conditions, the central nervous system would either require a detailed, continuously updated representation of the state of each muscle (and the load against which each is acting) or else force feedback with sufficient gain to cope with variations in the properties of the muscles and loads. The evidence for force feedback with adequate gain or for an appropriate central representation is not sufficient to conclude that force is the major controlled variable in normal limb movements.

Morton's hypothesis, that length is controlled by a follow-up servo, has a number of difficulties related to the delays, gains, variability, and specificity in feedback pathways comprising potential servo loops. However, experimental evidence is consistent with these pathways providing servo assistance for some movements produced by coactivation of α- and static γ-motoneurons. Dynamic γ-motoneurons may provide an additional input for adaptive control of different types of movements.

The idea that feedback is used to compensate for changes in muscle stiffness has received experimental support under static postural conditions. However, reflexes tend to increase rather than decrease the range of variation in muscle stiffness during some cyclic movements. Theoretical problems associated with the regulation of stiffness are also discussed. The possibilities of separate control systems for velocity or viscosity are considered, but the evidence is either negative or lacking. I conclude that different physical variables can be controlled depending on the type of limb movement required. The concept of stiffness regulation is also useful under some conditions, but should probably be extended to the regulation of the visco-elastic properties (i.e., the mechanical impedance) of a muscle or joint.

A computational study of synaptic mechanisms of partial memory transfer in cerebellar vestibulo-ocular-reflex learning

There is a debate regarding whether motor memory is stored in the cerebellar cortex, or the cerebellar nuclei, or both. Memory may be acquired in the cortex and then be transferred to the cerebellar nuclei. Based on a dynamical system modeling with a minimal set of variables, we theoretically investigated possible mechanisms of memory transfer and consolidation in the context of vestibulo-ocular reflex learning. We tested different plasticity rules for synapses in the cerebellar nuclei and took robustness of behavior against parameter variation as the criterion of plausibility of a model variant. In the most plausible scenarios, mossy-fiber nucleus-neuron synapses or Purkinje-cell nucleus-neuron synapses are plastic on a slow time scale and store permanent memory, whose content is passed from the cerebellar cortex storing transient memory. In these scenarios, synaptic strengths are potentiated when the mossy-fiber afferents to the nuclei are active during a pause in Purkinje-cell activities. Furthermore, assuming that mossy fibers create a limited variety of signals compared to parallel fibers, our model shows partial memory transfer from the cortex to the nuclei.

Normal and adapted visuooculomotor reflexes in goldfish

Under normal physiological conditions, whole field visual motion generally occurs in response to either active or passive self-motion. In the laboratory, selective movement of the visual surround produces an optokinetic response (OKR) that acts primarily to support the vestibuloocular reflex (VOR). During visual world motion, however, the OKR can be viewed as operating independently over frequency and amplitude ranges insufficient for vestibular activation. The goal of the present study was to characterize this isolated behavior of the OKR in goldfish as an essential step for studying central neuronal correlates of visual-vestibular interactions and the mechanisms underlying oculomotor adaptation. After presentation of either binocular sinusoidal or step visual stimuli, conjugate eye movements were elicited with an amplitude and phase profile similar to that of other vertebrates. An early and a delayed component were measured with different dynamics that could be altered independently by visual training. The ensuing visuomotor plasticity was robust and exhibited five major characteristics. First, the gain of both early and delayed components of the OKR increased > 100%. Second, eye velocity decreased 0.5-2.0 s before the change in direction of stimulus velocity. Third, on lengthening the duration of a constant velocity visual stimulus (e.g., from 8 to 16 s), eye velocity decreased toward 0 degrees/s. This behavior was correlated with the direction and period as opposed to the frequency of the visual stimulus ("period tuning"). Fourth, visual stimulus training increased VOR eye velocity with a ratio of 0.6 to 1 to that measured for the OKR. Fifth, the OKR adaptation, eye velocity consistently oscillated in a conjugate, symmetrical fashion at 2.4 Hz in the light, whereas in the dark, a rhythmical low-amplitude eye velocity occurred at the visual training frequency. We conclude that the frequency and amplitude of visual stimuli for eliciting the goldfish OKR are well suited for complementing the VOR. Unlike most mammals, OKR adaptive modifications significantly alter VOR gain, whereas the effects of VOR training are much less on OKR gain. These observations suggest that both distributed circuits and discrete neuronal populations control visuo- and vestibulomotor performance. Finally, the existence of a rhythmic, "period tuned" visuomotor behavior provides a unique opportunity to examine the neuronal mechanisms of adaptive plasticity.

Changes in gain of the vestibulo-ocular reflex induced by combined visual and vestibular stimulation in goldfish

Adaptive changes in the vestibulo-ocular reflex (VOR) of goldfish were produced in a few hours by sinusoidally rotating restrained fish in the horizontal plane inside a vertically striped drum. The drum could also be sinusoidally rotated so that the gain of the VOR (the ratio of eye to head angular velocity) would have to increase to two or decrease to zero in order to maintain a stable retinal image. During 'training' towards two VOR gain measured at the stimulation frequency of 0.125 Hz increased rapidly over 6 h of stimulation to about 1.5 from an initial gain of 0.7. Half of that change occurred in the first 30 min. During training towards zero VOR gain measured at the stimulation frequency decreased to 0.15. About one-third of that change occurred in the first 30 min. Testing at different sinusoidal frequencies after 6 h stimulation showed that increases in VOR gain were generated across a 6-octave range; however, reductions in gain were produced over a narrow frequency range close to the training frequency. Gain reductions occurred more rapidly on a second day of stimulation. In a paradigm simulating reversing prisms, partial reversal of the VOR was observed in some fish. However, these fish also demonstrated spontaneous slow sinusoidal eye movements that may have represented a different means of adjusting eye movements to stabilize the retinal image. Goldfish provide a useful preparation for the study of adaptive gain changes in vertebrate oculomotor systems.

Oculomotor response to rapid head oscillation (0.5-5.0 Hz) after prolonged adaptation to vision-reversal. "Simple" and "complex" effects

This study examined long-term (up to 27 days) effects of maintained vision reversal on (i) smooth visual tracking with head still, (ii) oculomotor response to actively, generated head oscillation and (iii) "spontaneous" saccades. Dove prism goggles produced horizontal, but not vertical (sagittal plane), vision reversal. Eye movements were recorded by EOG; head movements by an electro-magnetic search coil. Both visual tracking and saccade dynamics remained unchanged throughout. In contrast, both the ocular response to active head oscillations (goggles off and subject looking at a stationary target) and associated retinal image blur showed substantial and retained adaptive changes, akin to those previously found in the vestibulo-ocular reflex as tested in darkness at 0.17 Hz. However, several addition unexpected results emerged. First, in the fully adapted state smooth eye movements tended to be of reversed phase in the range 0.5-1.0 Hz (in spite of normal vision during tests), but of normal phase from about 2 Hz and above (in spite of negligible visual tracking in this upper range). Second, after permanent removal of the inverting goggles, this peculiar frequency response of the fully adapted state quickly (36 h) reverted to a dynamically simpler condition manifest as retained (2-3 weeks) attenuation of gain (eye vel./head vel.) which, as in control conditions, was monotonically related to frequency. From these two findings it is inferred that the fully adapted state may have comprised two separate components: (i) A "simple element of monotonic and long-lasting gain attenuation and (ii) a "complex", frequency labile, element which could be quickly rejected. Dynamic characteristics of the putative "complex" element were estimated by vectorial subtraction of the "simple" one from that of the fully adapted condition. The outcome suggests that the inferred "complex" condition might represent a predictive element. Two further findings are reported: (i) Substantially different vectors of the adapted response were obtained with normal and reversed vision at 3.0 Hz head oscillation, indicating a novel visual tracking. (ii) During head oscillation in the vesicle sagittal plane (in which vision was not reversed) there was never any image blur, indicating high geometric specificity in the adaptive process.

Adaptive filter model of the cerebellum

The Marr-Albus model of the cerebellum has been reformulated with linear system analysis. This adaptive linear filter model of the cerebellum performs a filtering action of a phase lead-lag compensator with learning capability, and will give an account for the phenomena which have been termed "cerebellar compensation". It is postulated that a Golgi cell may act as a phase lag element; for example, as a leaky integrator with time constant about several seconds. Under this assumption, a mossy fiber - granule cell - Golgi cell input network functions as a phase lead-lag compensator. Output signals from Golgi-granule cell systems, namely, parallel fiber signals, are gathered together through variable synaptic connections to form a Purkinje cell output. From a general theory of adaptive linear filters, learning principles for these modifiable connections are derived. By these learning principles, a Purkinje cell output converges to the "desired response" to minimize the mean square error of the performance. In a more general sense, a Purkinje cell acquires a filtering function on the basis of multiple pairs of input signals and corresponding desired output signals. The mode of convergence of the output signal is described when the input signal is sinusoidal.

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

An adaptive linear filter model of the cerebellum (Fujita, 1982), which functions as a phase lead or lag compensator with learning capability, is applied to a problem of the cerebellar control of the vestibuloocular reflex (VOR). Under the assumption that the cerebellar flocculus accounts for adaptive modification of dynamic characteristics of the VOR, the cerebellar model was incorporated into a linear control model of the oculomotor system. The results of a simulation study are in good agreement with experimental data on eye movement.

Differential visual adaptation of vertical canal-dependent vestibulo-ocular reflexes

Reversing vision in the horizontal (left-right) plane in humans induces adaptive mechanisms and even reversal of the horizontal vestibulo-ocular reflex (HVOR). The present experiments were aimed at investigating if such adaptive modifications could be observed in the frontal plane by reversal of the torsional visual world movements. Torsional vestibulo-ocular reflex (TVOR) was measured in one subject who wore Dove prisms for 19 days. The gain of TVOR was tested in the dark with the head leaned backward and rotating around an earth vertical axis with sinusoidal rotation (1/6 HZ). The gain decreased from 0.27 to 0.13 at 70 degrees peak-to-peak amplitude, and from 0.3 to 0.11 at 45 degrees peak-to-peak amplitude after 19 days of prism-wearing. Full gain recovery was observed 10 days after prism removal. The results are compared with the observation that in the same situation the vertical VOR (up-down) is not reversed (Dove prisms do not reverse visual images in this plane). As the same four (vertical) canals produce both reflexes, it is suggested that central neuronal mechanisms allow the recognition of the geometrical pattern of visual reversals and selectively adapt the reflex in the relevant planes.

Adaptability of the vestibulo-ocular reflex to vision reversal in strobe reared cats

Optical reversal of vision brings about adaptive changes in the vestibulo-ocular reflex (VOR) tending to reduce retinal image slip during head movement. The present experiments investigated this form of adaptation in cats whose complement of direction sensitive central visual cells had been substantially reduced by rearing in 8 Hz stroboscopic light. Horizontal vision reversal was produced by dove prisms carried in a skull-mounted mask. A scleral eye coil was used to measure horizontal eye movements. VOR gain and phase were measured in the dark during sinusoidal rotation using test stimuli of 1/8 Hz and 5- or 20 degrees/sec velocity amplitude. Initially, strobe reared cats produced virtually normal VOR in the dark, except for slight but significant exaggeration of the normal phase advancement to be expected at 1/8 Hz. Addition of their familiar strobe illumination produced almost perfect oculomotor compensation. Maintained vision reversal in both strobe and normal illumination produced similar patterns of adaptive change in normal and strobe reared subjects, i.e. all animals exhibited an initial fast, and subsequent much slower, stage of gain attenuation, with similar changes in phase. Thus, strobe rearing did not prevent the development of an essentially normal VOR, nor did it interfere significantly with the ability to adapt in response to vision reversal. Since strobe rearing depletes direction selective visual movement detectors in the cortex and superior colliculi, it is inferred that signals responsible for activating the adaptive process are probably carried mainly in the accessory optic, rather than cortical and collicular, visual system.