Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics. Received: 8 August 1997 / Accepted in revised form: 18 June 1998     

A matrix analysis for a conjugate vestibulo-ocular reflex

The technique of matrix analysis is used to compare the connectivity between vestibular neurons and oculomotor neurons of the two eyes that would generate a conjugate vestibulo-ocular reflex (VOR). The technique shows that the connectivity is normally anatomically symmetric. The technique is also used to determine the types and loci of adaptation within the VOR that will maintain conjugacy. Adaptation is divided into1) that evoked by changes in visual feedback, which requires VOR or system-specific changes and2) that produced by changes in the canals or muscles, which requires deficit-specific adaptation. In the former case, the adaptation could best be achieved by an additive alteration of the vestibularmotoneuron projections. In the latter case, the appropriate adaptations would be serial, multiplicative changes, applied at the level of the vestibular neurons when the canals are at fault or at the level of the motoneurons of the eye whose muscles are impaired. The analysis thus suggests multiple loci of plasticity within the VOR, specialized for adapting to different deficits.     

Video-oculography in Mice

Eye movements are very important in order to track an object or to stabilize an image on the retina during movement. Animals without a fovea, such as the mouse, have a limited capacity to lock their eyes onto a target. In contrast to these target directed eye movements, compensatory ocular eye movements are easily elicited in afoveate animals^1,2,3,4. Compensatory ocular movements are generated by processing vestibular and optokinetic information into a command signal that will drive the eye muscles. The processing of the vestibular and optokinetic information can be investigated separately and together, allowing the specification of a deficit in the oculomotor system. The oculomotor system can be tested by evoking an optokinetic reflex (OKR), vestibulo-ocular reflex (VOR) or a visually-enhanced vestibulo-ocular reflex (VVOR). The OKR is a reflex movement that compensates for "full-field" image movements on the retina, whereas the VOR is a reflex eye movement that compensates head movements. The VVOR is a reflex eye movement that uses both vestibular as well as optokinetic information to make the appropriate compensation. The cerebellum monitors and is able to adjust these compensatory eye movements. Therefore, oculography is a very powerful tool to investigate brain-behavior relationship under normal as well as under pathological conditions (f.e. of vestibular, ocular and/or cerebellar origin).Testing the oculomotor system, as a behavioral paradigm, is interesting for several reasons. First, the oculomotor system is a well understood neural system⁵. Second, the oculomotor system is relative simple⁶; the amount of possible eye movement is limited by its ball-in-socket architecture ("single joint") and the three pairs of extra-ocular muscles⁷. Third, the behavioral output and sensory input can easily be measured, which makes this a highly accessible system for quantitative analysis⁸. Many behavioral tests lack this high level of quantitative power. And finally, both performance as well as plasticity of the oculomotor system can be tested, allowing research on learning and memory processes⁹.Genetically modified mice are nowadays widely available and they form an important source for the exploration of brain functions at various levels¹⁰. In addition, they can be used as models to mimic human diseases. Applying oculography on normal, pharmacologically-treated or genetically modified mice is a powerful research tool to explore the underlying physiology of motor behaviors under normal and pathological conditions. Here, we describe how to measure video-oculography in mice⁸.     

A learning network model of the neural integrator of the oculomotor system

Certain premotor neurons of the oculomotor system fire at a rate proportional to desired eye velocity. Their output is integrated by a network of neurons to supply an eye positon command to the motoneurons of the extraocular muscles. This network, known as the neural integrator, is calibrated during infancy and then maintained through development and trauma with remarkable precision. We have modeled this system with a self-organizing neural network that learns to integrate vestibular velocity commands to generate appropriate eye movements. It learns by using current eye movement on any given trial to calculate the amount of retinal image slip and this is used as the error signal. The synaptic weights are then changed using a straightforward algorithm that is independent of the network configuration and does not necessitate backwards propagation of information. Minimization of the error in this fashion causes the network to develop multiple positive feedback loops that enable it to integrate a push-pull signal without integrating the background rate on which it rides. The network is also capable of recovering from various lesions and of generating more complicated signals to simulate induced postsaccadic drift and compensation for eye muscle mechanics.     

Distributed parallel processing in the vertical vestibulo-ocular reflex: Learning networks compared to tensor theory

The vestibulo-ocular reflex (VOR) is capable of producing compensatory eye movements in three dimensions. It utilizes the head rotational velocity signals from the semicircular canals to control the contractions of the extraocular muscles. Since canal and muscle coordinate frames are not orthogonal and differ from one another, a sensorimotor transformation must be produced by the VOR neural network. Tensor theory has been used to construct a linear transformation that can model the three-dimensional behavior of the VOR. But tensor theory does not take the distributed, redundant nature of the VOR neural network into account. It suggests that the neurons subserving the VOR, such as vestibular nucleus neurons, should have specific sensitivity-vectors. Actual data, however, are not in accord. Data from the cat show that the sensitivity-vectors of vestibular nucleus neurons, rather than aligning with any specific vectors, are dispersed widely. As an alternative to tensor theory, we modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm. Units in mature networks had divergent sensitivity-vectors which resembled those of actual vestibular nucleus neurons in the cat. This similarity suggests that the VOR sensorimotor transformation may be represented redundantly rather than uniquely. The results demonstrate how vestibular nucleus neurons can encode the VOR sensorimotor transformation in a distributed manner.     

Afferent signals from the extraocular muscles of the pigeon modify the electromyogram of these muscles during the vestibulo-ocular reflex.

There is no general agreement on whether afferent signals from the extraocular muscles play any part in oculomotor control. However, we have previously shown that they modify the responses of cells in the oculomotor control system during the vestibulo-ocular reflex (VOR). If, as we suspect, these signals have an important role in the control of the VOR from moment-to-moment, we should be able to demonstrate similar, functionally significant, modifications at the output of the reflex. We have recorded the electromyographic activity of several extraocular muscles of the right eye during the VOR and while imposing movements on the left eye. We describe how the activity of the muscles, reflected in the electromyogram, is modified in specific ways depending on the parameters of the imposed eye movements. The effects of the extraocular afferent signals on the eye-muscle responses to vestibular drive during the slow phase of the VOR appear to be corrective. Thus the present results provide strong evidence that afferent signals from the extraocular muscles are concerned in the control of the reflex from moment-to-moment, and suggest that the wider question of their role in oculomotor control merits further consideration.     

Synaptic Plasticity in Medial Vestibular Nucleus Neurons: Comparison with Computational Requirements of VOR Adaptation

Background

Vestibulo-ocular reflex (VOR) gain adaptation, a longstanding experimental model of cerebellar learning, utilizes sites of plasticity in both cerebellar cortex and brainstem. However, the mechanisms by which the activity of cortical Purkinje cells may guide synaptic plasticity in brainstem vestibular neurons are unclear. Theoretical analyses indicate that vestibular plasticity should depend upon the correlation between Purkinje cell and vestibular afferent inputs, so that, in gain-down learning for example, increased cortical activity should induce long-term depression (LTD) at vestibular synapses.

Methodology/Principal Findings

Here we expressed this correlational learning rule in its simplest form, as an anti-Hebbian, heterosynaptic spike-timing dependent plasticity interaction between excitatory (vestibular) and inhibitory (floccular) inputs converging on medial vestibular nucleus (MVN) neurons (input-spike-timing dependent plasticity, iSTDP). To test this rule, we stimulated vestibular afferents to evoke EPSCs in rat MVN neurons in vitro. Control EPSC recordings were followed by an induction protocol where membrane hyperpolarizing pulses, mimicking IPSPs evoked by flocculus inputs, were paired with single vestibular nerve stimuli. A robust LTD developed at vestibular synapses when the afferent EPSPs coincided with membrane hyperpolarisation, while EPSPs occurring before or after the simulated IPSPs induced no lasting change. Furthermore, the iSTDP rule also successfully predicted the effects of a complex protocol using EPSP trains designed to mimic classical conditioning.

Conclusions

These results, in strong support of theoretical predictions, suggest that the cerebellum alters the strength of vestibular synapses on MVN neurons through hetero-synaptic, anti-Hebbian iSTDP. Since the iSTDP rule does not depend on post-synaptic firing, it suggests a possible mechanism for VOR adaptation without compromising gaze-holding and VOR performance in vivo.     

Vestibular mechanisms involved in idiopathic scoliosis

Patients affected by idiopathic scoliosis (IS) show not only a spinal deformity, but also postural and oculomotor deficits suggesting that such syndrome can be related to a vestibular disfunction. It appears, however, that, in children, a slight unbalance in the activity of vestibular complex of both sides escapes the neuronal mechanisms responsible for vestibular compensation and leads to the spinal curvature which characterises IS. Such process could be reinforced by a disrupted integration of vestibular and visual signals at cortical level, leading to an altered perception of the vertical and to abnormal motor commands. In addition to the classical ascending and descending pathways arising from the vestibular nuclei, which utilize glutamate or GABA as neurotransmitters, labyrinthine afferents may also affect spinal, cerebellar and cerebrocortical structures, through the noradrenergic and serotoninergic systems, which originate from the locus coeruleus and the raphe nuclei, respectively. Due to the role of these neuromodulators in brain plasticity, a disruption in the activity of monoaminergic neurons could favour the development of postural and oculomotor deficits. An impaired release of monoamine at cerebrocortical level could also explain the cognitive deficits which may occur in IS patients.     

The vestibulo-ocular reflex and velocity storage in spinocerebellar ataxia 8

The autosomal dominant spinocerebellar ataxias (SCAs) are a group of neurodegenerative diseases characterized by progressive instability of posture and gait, incoordination, ocular motor dysfunction, and dysarthria due to degeneration of cerebellar and brainstem neurons. Among the more than 20 genetically distinct subtypes, SCA8 is one of several wherein clinical observations indicate that cerebellar dysfunction is primary, and there is little evidence for other CNS involvement. The aim of the present work was to study the decay of the horizontal vestibulo-ocular reflex (VOR) after a short period of constant acceleration to understand the pathophysiology of the VOR due to cerebellar Purkinje cell degeneration in SCA8. The VOR was recorded in patients with genetically defined SCA8 during rotation in the dark. Moderate to severely affected patients had a qualitatively intact VOR, but there were quantitative differences in the gain and dynamics compared to normal controls. During angular velocity ramp rotations, there was a reversal in the direction of the VOR that was more pronounced in SCA8 compared to controls. Modeling studies indicate that there are significant changes in the velocity storage network, including abnormal feedback of an eye position signal into the network that contributes to this reversal. These and other results will help to identify features that are diagnostic for SCA subtypes and provide new information about selective vulnerability of neurons controlling vestibular reflexes.     

A mathematical model for the mechanism of rapid eye movements induced by an anticholinesterase in the decerebrate cat.

The oculomotor pattern which appears in intact preparations during desynchronized sleep is characterized by the irregular occurrence of isolated ocular movements and bursts of rapid eye movements (REM). This complex oculomotor pattern results from the activity of two premotor structures which influence the extraocular motoneurons during this phase of sleep: one is located in the pontine reticular formation, the other in the vestibular nuclei. In the decerebrate preparation the intravenous injection of an anticholinesterase leads to the appearance of a typical pattern of oculomotor activity, which differs from that occurring during physiological sleep in so far as it consists quite exclusively of bursts of REM which appear at very regular intervals. Lesion experiments as well as unit recordings have shown that these bursts of REM depend in particular upon rhythmic discharges of the vestibular nuclear neurons. The underlying anatomical structures responsible for these bursts of REM are therefore the vestibular nuclei, the oculomotor nuclei and the oculo-orbital system. This mechanism is under the influence of cholinergic reticular neurons which generate the oculomotor rhythm. We have postulated the existence of a self-excitatory cholinergic system, located in the pontine reticular formation, whose steady discharge impinges upon an oscillatory neuronal system located in the dorso-lateral pontine tegmentum, which transforms the tonic input into a sinusoidal final output. We have assumed also that the periodic increases in the discharge frequency of this oscillatory system trigger a fast phase generator acting on the different components of the REM system, and that the behavior of each component follows a first-order differential equation. The state of excitation of the components of the system is defined as proportional to frequency of nerve impulses. Assuming ipsilateral and crossed connections, a pattern of oculomotor activity is obtained that simulates the experimental oculomotor output fairly well. The repetition of the eye jerks is described by a Fourier series. The model proposed in this paper may be taken as a first approach in describing the generation mechanism of REM, and as a theoretical guide to new experimental researches and the development of other more realistic models.     

Transplantation of Xenopus laevis Tissues to Determine the Ability of Motor Neurons to Acquire a Novel Target

The evolutionary origin of novelties is a central problem in biology. At a cellular level this requires, for example, molecularly resolving how brainstem motor neurons change their innervation target from muscle fibers (branchial motor neurons) to neural crest-derived ganglia (visceral motor neurons) or ear-derived hair cells (inner ear and lateral line efferent neurons). Transplantation of various tissues into the path of motor neuron axons could determine the ability of any motor neuron to innervate a novel target. Several tissues that receive direct, indirect, or no motor innervation were transplanted into the path of different motor neuron populations in Xenopus laevis embryos. Ears, somites, hearts, and lungs were transplanted to the orbit, replacing the eye. Jaw and eye muscle were transplanted to the trunk, replacing a somite. Applications of lipophilic dyes and immunohistochemistry to reveal motor neuron axon terminals were used. The ear, but not somite-derived muscle, heart, or liver, received motor neuron axons via the oculomotor or trochlear nerves. Somite-derived muscle tissue was innervated, likely by the hypoglossal nerve, when replacing the ear. In contrast to our previous report on ear innervation by spinal motor neurons, none of the tissues (eye or jaw muscle) was innervated when transplanted to the trunk. Taken together, these results suggest that there is some plasticity inherent to motor innervation, but not every motor neuron can become an efferent to any target that normally receives motor input. The only tissue among our samples that can be innervated by all motor neurons tested is the ear. We suggest some possible, testable molecular suggestions for this apparent uniqueness.     

Activity of premotor vestibular neurons in the alert cat

The activity of medial vestibular nucleus neurons projecting to the contralateral abducens nucleus (premotor vestibular neurons) has been recorded during spontaneous and vestibular induced eye movements in the alert cat. Recorded neurons were identified by their antidromic activation from the abducens nucleus and by the post-synaptic field potential induced in this nucleus. The activity of identified medial vestibular neurons increased significantly with horizontal eye position and velocity toward the contralateral side, and decreased abruptly during ipsilateral saccades. The activity of these neurons was also related to head velocity toward the ipsilateral side. The functional role and origin of eye position and velocity signals present in these vestibular neurons are discussed.     

The control of gaze (3). Neurological defects

Eye movements serve vision, which has two different aims: changing images using saccades, i.e. rapid eye movements, and stabilizing new images on the retina using slow eye movements. Eye movements are performed by ocular motor nuclei in the brainstem, on which supranuclear pathways--originating in the cerebral cortex, cerebellum and vestibular structures--converge. It is useful for the neurologist to know the clinical abnormalities of eye movements visible at the bedside since such signs are helpful for localization. Eye movement paralysis may be nuclear or infranuclear (nerves), involving all types of eye movements, i.e. saccades as well as the vestibulo-ocular reflex (VOR), or supranuclear, in which case the VOR is usually preserved. Lateral eye movements are organized in the pons, with paralysis of adduction (and preservation of convergence) when the lesion affects the medial longitudinal fasciculus (internuclear ophthalmoplegia), paralysis of conjugate lateral eye movements when the lesion affects the abducens nucleus (VI) and the "one-and-a-half" syndrome when both these structures are involved. Vertical eye movements are organized in the midbrain, with ipsilateral oculomotor (III) paralysis and contralateral paralysis of the superior rectus muscle when the third nerve nucleus is unilaterally damaged, supranuclear upward gaze paralysis when the posterior commissure is unilaterally damaged and supranuclear downward gaze paralysis (often coupled with upward gaze paralysis) when the mesencephalic reticular formations are bilaterally damaged. Numerous types of abnormal eye movements exist, of which nystagmus is the most frequent and usually due to damage to peripheral or central vestibular pathways. Cerebral hemispheric or cerebellar damage results in subtle eye movement abnormalities at the bedside, in general only detected using eye movement recordings, because of the multiplicity of eye movement pathways at these levels and their reciprocal compensation in the case of a lesion. Lastly, eye movements can also help the neuroscientist to understand the organization of the brain. They are a good model of motricity allowing us, using eye movement recordings, to study the afferent pathways of the cortical areas that trigger them, and thus to analyze relatively complex neuropsychological processes such as visuo-spatial integration, spatial memory, motivation and the preparation of motor programs.     

Sparse cerebellar innervation can morph the dynamics of a model oculomotor neural integrator

The oculomotor integrator is a brainstem neural network that converts velocity signals into the position commands necessary for eye-movement control. The cerebellum can independently adjust the amplitude of eye-movement commands and the temporal characteristics of neural integration, but the percentage of integrator neurons that receive cerebellar input is very small. Adaptive dynamic systems models, configured using the genetic algorithm, show how sparse cerebellar inputs could morph the dynamics of the oculomotor integrator and independently adjust its overall response amplitude and time course. Dynamic morphing involves an interplay of opposites, in which some model Purkinje cells exert positive feedback on the network, while others exert negative feedback. Positive feedback can be increased to prolong the integrator time course at virtually any level of negative feedback. The more these two influences oppose each other, the larger become the response amplitudes of the individual units and of the overall integrator network. Action Editor: Jonathan D. Victor     

Cerebellar Motor Learning: When Is Cortical Plasticity Not Enough?

Classical Marr-Albus theories of cerebellar learning employ only cortical sites of plasticity. However, tests of these theories using adaptive calibration of the vestibulo–ocular reflex (VOR) have indicated plasticity in both cerebellar cortex and the brainstem. To resolve this long-standing conflict, we attempted to identify the computational role of the brainstem site, by using an adaptive filter version of the cerebellar microcircuit to model VOR calibration for changes in the oculomotor plant. With only cortical plasticity, introducing a realistic delay in the retinal-slip error signal of 100 ms prevented learning at frequencies higher than 2.5 Hz, although the VOR itself is accurate up to at least 25 Hz. However, the introduction of an additional brainstem site of plasticity, driven by the correlation between cerebellar and vestibular inputs, overcame the 2.5 Hz limitation and allowed learning of accurate high-frequency gains. This “cortex-first” learning mechanism is consistent with a wide variety of evidence concerning the role of the flocculus in VOR calibration, and complements rather than replaces the previously proposed “brainstem-first” mechanism that operates when ocular tracking mechanisms are effective. These results (i) describe a process whereby information originally learnt in one area of the brain (cerebellar cortex) can be transferred and expressed in another (brainstem), and (ii) indicate for the first time why a brainstem site of plasticity is actually required by Marr-Albus type models when high-frequency gains must be learned in the presence of error delay.     

A proposed neural network for the integrator of the oculomotor system

Single-unit recordings, stimulation studies, and eye movement measurements all indicate that the firing patterns of many oculomotor neurons in the brain stem encode eye-velocity commands in premotor circuits while the firing patterns of extraocular motoneurons contain both eye-velocity and eye-position components. It is necessary to propose that the eye-position component is generated from the eye-velocity signal by a leaky hold element or temporal integrator. Prior models of this integrator suffer from two important problems. Since cells appear to have a steady, background signal when eye position and velocity are zero, how does the integrator avoid integrating this background rate? Most models employ some form of lumped, oositive feedback the gain of which must be kept within totally unreasonable limits for proper operation. We propose a lateral inhibitory network of homogeneous neurons as a model for the neural integrator that solves both problems. Parameter sensitivity studies and lesion simulations are presented to demonstrate robustness of the model with respect to both the choice of parameter values and the consequences of pathological changes in a portion of the neural integrator pool.     

Simulating vestibular compensation using recurrent back-propagation

Vestibular compensation is simulated as learning in a dynamic neural network model of the horizontal vestibulo-ocular reflex (VOR). The bilateral, three-layered VOR model consists of nonlinear units representing horizontal canal afferents, vestibular nuclei (VN) neurons and eye muscle motoneurons. Dynamic processing takes place via commissural connections that link the VN bilaterally. The intact network is trained, using recurrent back-propagation, to produce the VOR with velocity storage integration. Compensation is simulated by removing vestibular afferent input from one side and retraining the network. The time course of simulated compensation matches that observed experimentally. The behavior of model VN neurons in the compensated network also matches real data, but only if connections at the motoneurons, as well as at the VN, are allowed to be plastic. The dynamic properties of real VN neurons in compensated and normal animals are found to differ when tested with sinusoidal but not with step stimuli. The model reproduces these conflicting data, and suggests that the disagreement may be due to VN neuron nonlinearity.     

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.     

Neuronal correlates of a perceptual decision in ventral premotor cortex

The ventral premotor cortex (VPC) is involved in the transformation of sensory information into action, although the exact neuronal operation is not known. We addressed this problem by recording from single neurons in VPC while trained monkeys report a decision based on the comparison of two mechanical vibrations applied sequentially to the fingertips. Here we report that the activity of VPC neurons reflects current and remembered sensory inputs, their comparison, and motor commands expressing the result; that is, the entire processing cascade linking the evaluation of sensory stimuli with a motor report. These findings provide a fairly complete panorama of the neural dynamics that underlies the transformation of sensory information into an action and emphasize the role of VPC in perceptual decisions.