Spatial symmetries in vestibular projections to the uvula-nodulus

The discharge of secondary vestibular neurons relays the activity of the vestibular endorgans, occasioned by movements in three-dimensional physical space. At a slightly higher level of analysis, the discharge of each secondary vestibular neuron participates in a multifiber projection or pathway from primary afferents via the secondary neurons to another neuronal population. The logical organization of this projection determines whether characteristics of physical space are retained or lost. The logical structure of physical space is standardly expressed in terms of the mathematics of group theory. The logical organization of a projection can be compared to that of physical space by evaluating its symmetry group. The direct projection from the semicircular canal nerves via the vestibular nuclei to neck motor neurons has a full three-dimensional symmetry group, allowing it to maintain a three-dimensional coordinate frame. However, a projection may embed only a subgroup of the symmetry group of physical space, which incompletely mirrors the properties of physical space. The major visual and vestibular projections in the rabbit via the inferior olive to the uvula-nodulus carry three degrees of freedom—rotations about one vertical and two horizontal axes—but do not have full three dimensional symmetry. Instead, the vestibulo-olivo-nodular projection has symmetries corresponding to a product of two-dimensional vestibular and one-dimensional optokinetic spaces. This combination of projection symmetries provides the foundation for distinguishing horizontal from vertical rotations within a three dimensional space. In this study, we evaluate the symmetry group given by the physiological organization of the vestibulo-olivo-nodular projection. Although it acts on the same sets of elements and mirrors the rotations that occur in physical space, the physiological transformation group is distinct from the spatial group. We identify symmetries as products of physiological and spatial transformations. The symmetry group shapes the information the projection conveys to the uvula-nodulus; this shaping may depend on a physiological choice of generators, in the same way that function depends on the physiological choice of coordinates. We discuss the implications of the symmetry group for uvula-nodulus function, evolution, and functions of the vestibular system in general.     

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.     

Multimodal integration for the representation of space in the posterior parietal cortex.

The posterior parietal cortex has long been considered an ''association'' area that combines information from different sensory modalities to form a cognitive representation of space. However, until recently little has been known about the neural mechanisms responsible for this important cognitive process. Recent experiments from the author''s laboratory indicate that visual, somatosensory, auditory and vestibular signals are combined in areas LIP and 7a of the posterior parietal cortex. The integration of these signals can represent the locations of stimuli with respect to the observer and within the environment. Area MSTd combines visual motion signals, similar to those generated during an observer''s movement through the environment, with eye-movement and vestibular signals. This integration appears to play a role in specifying the path on which the observer is moving. All three cortical areas combine different modalities into common spatial frames by using a gain-field mechanism. The spatial representations in areas LIP and 7a appear to be important for specifying the locations of targets for actions such as eye movements or reaching; the spatial representation within area MSTd appears to be important for navigation and the perceptual stability of motion signals.     

Head Movements Evoked in Alert Rhesus Monkey by Vestibular Prosthesis Stimulation: Implications for Postural and Gaze Stabilization

The vestibular system detects motion of the head in space and in turn generates reflexes that are vital for our daily activities. The eye movements produced by the vestibulo-ocular reflex (VOR) play an essential role in stabilizing the visual axis (gaze), while vestibulo-spinal reflexes ensure the maintenance of head and body posture. The neuronal pathways from the vestibular periphery to the cervical spinal cord potentially serve a dual role, since they function to stabilize the head relative to inertial space and could thus contribute to gaze (eye-in-head + head-in-space) and posture stabilization. To date, however, the functional significance of vestibular-neck pathways in alert primates remains a matter of debate. Here we used a vestibular prosthesis to 1) quantify vestibularly-driven head movements in primates, and 2) assess whether these evoked head movements make a significant contribution to gaze as well as postural stabilization. We stimulated electrodes implanted in the horizontal semicircular canal of alert rhesus monkeys, and measured the head and eye movements evoked during a 100ms time period for which the contribution of longer latency voluntary inputs to the neck would be minimal. Our results show that prosthetic stimulation evoked significant head movements with latencies consistent with known vestibulo-spinal pathways. Furthermore, while the evoked head movements were substantially smaller than the coincidently evoked eye movements, they made a significant contribution to gaze stabilization, complementing the VOR to ensure that the appropriate gaze response is achieved. We speculate that analogous compensatory head movements will be evoked when implanted prosthetic devices are transitioned to human patients.     

Afferent signals from pigeon extraocular muscles modify the vestibular responses of units in the abducens nucleus.

Although the extraocular muscles contain stretch receptors it is generally believed that their afferents exert no influence on the control of eye movement. However, we have shown previously that these afferent signals reach various brainstem centres concerned with eye movement, notably the vestibular nuclei, and that the decerebrate pigeon is a favourable preparation in which to study their effects. If the extraocular muscle afferents do influence oculomotor control from moment-to-moment they should exert a demonstrable effect on the oculomotor nuclei. We now present evidence that extraocular muscle afferent signals do, indeed, alter the responses of units in an oculomotor nucleus (the abducens, VI nerve nucleus, which supplies the lateral rectus muscle) to horizontal, vestibular stimulation induced by sinusoidal oscillation of the bird. Such stimuli evoke a vestibulo-ocular reflex in the intact bird. The extraocular stretch receptors were activated by passive eye movement within the pigeon's saccadic range; such movements modified the vestibular responses of all 19 units studied which were all, histologically, in the abducens nucleus. The magnitude of the effects, purely inhibitory in 15 units, depended both on the amplitude and the velocity of the eye movement and most units showed selectivity for particular combinations of plane (e.g. horizontal versus vertical) and direction (e.g. rostral versus caudal) of eye movement. The results show that an afferent signal from the extraocular muscles influences vestibularly driven activity in the abducens nucleus to which it carries information related to amplitude, velocity, plane and direction of eye movement in the saccadic range. They thus strongly support the view that extraocular afferent signals are involved in the control of eye movement.     

Frequency-independent synaptic transmission supports a linear vestibular behavior

The vestibular system is responsible for transforming head motion into precise eye, head, and body movements that rapidly stabilize gaze and posture. How do central excitatory synapses mediate behavioral outputs accurately matched to sensory inputs over a wide dynamic range? Here we demonstrate that vestibular afferent synapses in vitro express frequency-independent transmission that spans their in vivo dynamic range (5-150 spikes/s). As a result, the synaptic charge transfer per unit time is linearly related to vestibular afferent activity in both projection and intrinsic neurons of the vestibular nuclei. Neither postsynaptic glutamate receptor desensitization nor saturation affect the relative amplitude or frequency-independence of steady-state transmission. Finally, we show that vestibular nucleus neurons can transduce synaptic inputs into linear changes in firing rate output without relying on one-to-one calyceal transmission. These data provide a physiological basis for the remarkable linearity of vestibular reflexes.     

The neural encoding of self-motion

As we move through the world, information can be combined from multiple sources in order to allow us to perceive our self-motion. The vestibular system detects and encodes the motion of the head in space. In addition, extra-vestibular cues such as retinal-image motion (optic flow), proprioception, and motor efference signals, provide valuable motion cues. Here I focus on the coding strategies that are used by the brain to create neural representations of self-motion. I review recent studies comparing the thresholds of single versus populations of vestibular afferent and central neurons. I then consider recent advances in understanding the brain's strategy for combining information from the vestibular sensors with extra-vestibular cues to estimate self-motion. These studies emphasize the need to consider not only the rules by which multiple inputs are combined, but also how differences in the behavioral context govern the nature of what defines the optimal computation.     

Vestibular reafference shapes voluntary movement

The vestibular organs in the inner ear are commonly thought of as sensors that serve balance, gaze control, and higher spatial functions such as navigation. Here, we investigate their role in the online control of voluntary movements. The central nervous system uses sensory feedback information during movement to detect and correct errors as they develop. Vestibular organs signal three-dimensional head rotations and translations and so could provide error information for body movements that transport the head in space. To test this, we electrically stimulated human vestibular nerves during a goal-directed voluntary tilt of the trunk. The stimulating current waveform was made identical to the angular velocity profile of the head in the roll plane. With this, we could proportionally increase or decrease the rate of vestibular nerve firing, as if the head were rotating faster or slower than it actually was. In comparison to movements performed without stimulation, subjects tilted their trunk faster and further or slower and less far, depending upon the polarity of the stimulus. The response was negligible when identical stimulus waveforms were replayed to stationary subjects. We conclude that the brain uses vestibular information for online error correction of planned body-movement trajectories.     

The Importance of Postural Cues for Determining Eye Height in Immersive Virtual Reality

In human perception, the ability to determine eye height is essential, because eye height is used to scale heights of objects, velocities, affordances and distances, all of which allow for successful environmental interaction. It is well understood that eye height is fundamental to determine many of these percepts. Yet, how eye height itself is provided is still largely unknown. While the information potentially specifying eye height in the real world is naturally coincident in an environment with a regular ground surface, these sources of information can be easily divergent in similar and common virtual reality scenarios. Thus, we conducted virtual reality experiments where we manipulated the virtual eye height in a distance perception task to investigate how eye height might be determined in such a scenario. We found that humans rely more on their postural cues for determining their eye height if there is a conflict between visual and postural information and little opportunity for perceptual-motor calibration is provided. This is demonstrated by the predictable variations in their distance estimates. Our results suggest that the eye height in such circumstances is informed by postural cues when estimating egocentric distances in virtual reality and consequently, does not depend on an internalized value for eye height.     

Emerging Object Representations in the Visual System Predict Reaction Times for Categorization

Recognizing an object takes just a fraction of a second, less than the blink of an eye. Applying multivariate pattern analysis, or “brain decoding”, methods to magnetoencephalography (MEG) data has allowed researchers to characterize, in high temporal resolution, the emerging representation of object categories that underlie our capacity for rapid recognition. Shortly after stimulus onset, object exemplars cluster by category in a high-dimensional activation space in the brain. In this emerging activation space, the decodability of exemplar category varies over time, reflecting the brain’s transformation of visual inputs into coherent category representations. How do these emerging representations relate to categorization behavior? Recently it has been proposed that the distance of an exemplar representation from a categorical boundary in an activation space is critical for perceptual decision-making, and that reaction times should therefore correlate with distance from the boundary. The predictions of this distance hypothesis have been born out in human inferior temporal cortex (IT), an area of the brain crucial for the representation of object categories. When viewed in the context of a time varying neural signal, the optimal time to “read out” category information is when category representations in the brain are most decodable. Here, we show that the distance from a decision boundary through activation space, as measured using MEG decoding methods, correlates with reaction times for visual categorization during the period of peak decodability. Our results suggest that the brain begins to read out information about exemplar category at the optimal time for use in choice behaviour, and support the hypothesis that the structure of the representation for objects in the visual system is partially constitutive of the decision process in recognition.     

Motion parallax contribution to perception of self-motion and depth

The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system may estimate self-motion and depth from motion parallax, using equations for the visual velocity field generated by translation of the eye through space. Our results focus on information provided by the movement and deformation of three-dimensional objects and on local flow behavior around a fixated point. All of these issues are addressed mathematically in terms of definite equations for the optic flow. This formal characterization of the visual information presented to the observer is then considered in parallel with other sensory cues to self-motion in order to see how these contribute to the effective use of visual motion parallax, and how parallactic flow can, conversely, contribute to the sense of self-motion. This article will focus on a central case, for understanding of motion parallax in spacious real-world environments, of monocular visual cues observable during pure horizontal translation of the eye through a stationary environment. We suggest that the global optokinetic stimulus associated with visual motion parallax must converge in significant fashion with vestibular and proprioceptive pathways that carry signals related to self-motion. Suggestions of experiments to test some of the predictions of this study are made.     

Squirrel monkey--an ideal primate (correction of prmate) model of space physiology]

Investigation of the vestibulo-ocular system of the squirrel monkey was reviewed in consideration of space motion sickness (SMS), or which is recently more often termed as space adaptation syndrome (SAS). Since the first launching of the space satellite, Sputnik [correction of Sputonik] in October 1957, many experiments were carried out in biological and medical fields. A various kind of creatures were used as experimental models from protozoa to human beings. Rats and monkeys are most favorite animals, particularly the non-human primate seems to be the one, because of its phylogenetic relatives akin to the human beings. Chimpanzees, rhesus monkeys, pig tailed-monkeys, red-faced monkeys and squirrel monkeys have been used mostly in American space experiments. Russian used rhesus monkeys. Among these, however, the squirrel monkey has an advantage of the small size of the body, ranging from 600- l000g in adult. This small size as a primate is very advantageous in experiments conducted in a narrow room of the space satellite or shuttle because of its space-saving. The squirrel monkey has another advantage to rear easily as is demonstrated to keep it as a pet. Accordingly, this petit animal provides us a good animal model in biological and medical experiments in space craft. The size of the brain of the squirrel monkey is extraordinary large relative to the body size, which is even superior to that of the human beings. This is partly owed to enlargement of the occipito-temporal cortices, which are forced to well develop for processing a huge amount of audio-visual information indispensable to the arboreal habitant to survive in tropical forest. The vestibular system of the squirrel monkey seems to be the most superior as well, when judged from it relative size of the vestibular nuclear complex. Balancing on swinging twigs or jumping from tree to tree developed the capability of this equilibrium system. Fernandez, Goldberg and his collaborators used the squirrel monkey to elucidate functions of the peripheral vestibular system. A transfer function was proposed to explain the behaviors of regular and irregular unit activity of vestibular nerve fibers. The physiologic characteristics of the second order vestibular neuron was investigated in combination of electrophysiological and micro-morphological way, with using WGA-HRP methods, in relation to somato-motor and eye movements. Interconnections between vestibular neurons and cerebellum, interstitial nucleus of Cajal, oculomotor nuclear complex, superior colliculus and cervical spinal cord were elucidated. In physiological field of the vestibular system, the vestibulo-ocular reflex is well studied and results obtained from the squirrel monkey experiments were reviewed. The squirrel monkey, particularly the Bolivian, is a unique animal in that it is vulnerable to motion sickness induced by visual-motion stimulation with phase mismatch of the two stimuli. Experimental results of labyrinthectomy or bilateral ablation of the maculae staticae led to the conclusion that both semicircular and otolith organs are involved in the genesis of space motion sickness. On the other hand, destruction of the area postrema, acknowledged as the vomiting center to chemical stimulants, produced controversial results. However, it must be pointed out that the a human subject underwent to resection of the area postrema, became insensitive to administration of apomorphine, a well known chemical stimulant of vomiting. Finally the experiments in space revealed the presence of at least two origins of caloric nystagmus, that is, attributable to convection and non-convection current of the endolymphatic fluid.     

Integration of Retinal and Extraretinal Information across Eye Movements

Visual perception is burdened with a highly discontinuous input stream arising from saccadic eye movements. For successful integration into a coherent representation, the visuomotor system needs to deal with these self-induced perceptual changes and distinguish them from external motion. Forward models are one way to solve this problem where the brain uses internal monitoring signals associated with oculomotor commands to predict the visual consequences of corresponding eye movements during active exploration. Visual scenes typically contain a rich structure of spatial relational information, providing additional cues that may help disambiguate self-induced from external changes of perceptual input. We reasoned that a weighted integration of these two inherently noisy sources of information should lead to better perceptual estimates. Volunteer subjects performed a simple perceptual decision on the apparent displacement of a visual target, jumping unpredictably in sync with a saccadic eye movement. In a critical test condition, the target was presented together with a flanker object, where perceptual decisions could take into account the spatial distance between target and flanker object. Here, precision was better compared to control conditions in which target displacements could only be estimated from either extraretinal or visual relational information alone. Our findings suggest that under natural conditions, integration of visual space across eye movements is based upon close to optimal integration of both retinal and extraretinal pieces of information.     

Fix your eyes in the space you could reach: neurons in the macaque medial parietal cortex prefer gaze positions in peripersonal space

Interacting in the peripersonal space requires coordinated arm and eye movements to visual targets in depth. In primates, the medial posterior parietal cortex (PPC) represents a crucial node in the process of visual-to-motor signal transformations. The medial PPC area V6A is a key region engaged in the control of these processes because it jointly processes visual information, eye position and arm movement related signals. However, to date, there is no evidence in the medial PPC of spatial encoding in three dimensions. Here, using single neuron recordings in behaving macaques, we studied the neural signals related to binocular eye position in a task that required the monkeys to perform saccades and fixate targets at different locations in peripersonal and extrapersonal space. A significant proportion of neurons were modulated by both gaze direction and depth, i.e., by the location of the foveated target in 3D space. The population activity of these neurons displayed a strong preference for peripersonal space in a time interval around the saccade that preceded fixation and during fixation as well. This preference for targets within reaching distance during both target capturing and fixation suggests that binocular eye position signals are implemented functionally in V6A to support its role in reaching and grasping.     

Vestibular facilitation of optic flow parsing

Simultaneous object motion and self-motion give rise to complex patterns of retinal image motion. In order to estimate object motion accurately, the brain must parse this complex retinal motion into self-motion and object motion components. Although this computational problem can be solved, in principle, through purely visual mechanisms, extra-retinal information that arises from the vestibular system during self-motion may also play an important role. Here we investigate whether combining vestibular and visual self-motion information improves the precision of object motion estimates. Subjects were asked to discriminate the direction of object motion in the presence of simultaneous self-motion, depicted either by visual cues alone (i.e. optic flow) or by combined visual/vestibular stimuli. We report a small but significant improvement in object motion discrimination thresholds with the addition of vestibular cues. This improvement was greatest for eccentric heading directions and negligible for forward movement, a finding that could reflect increased relative reliability of vestibular versus visual cues for eccentric heading directions. Overall, these results are consistent with the hypothesis that vestibular inputs can help parse retinal image motion into self-motion and object motion components.     

The effect of clinorotation on vestibular compensation in upside-down swimming catfish.

Upside-down swimming catfish Synodontis nigriventris can keep upside-down swimming posture stably under pseudo-microgravity generated by clinostat. When the vestibular organ is unilaterally ablated, the operated S. nigriventris shows disturbed swimming postures under the clinorotation condition. However, about 1 month after the operation, unilateral vestibular organ-ablated S. nigriventris shows stable upside-down swimming posture under the condition (vestibular compensation). In contrast, a closely related upside-up swimming catfish Synodontis multipunctatus belonging to same Synodontis family can not keep stable swimming postures under the clinorotation conditions. In this study, we examined the effect of continuous clinorotation on vestibular compensation in intact and unilateral vestibular organ-ablated Synodontis nigriventris and Synodontis multipunctatus. After the exposure to continuous clinorotation, the postures of the catfish were observed under microgravity provided by parabolic flights of an aircraft. Unilateral vestibular organ-ablated S. nigriventris which had been exposed to continuous clinorotation showed stable swimming postures and did not show dorsal light reaction (DLR) under microgravity. This postural control pattern of the operated catfish was similar to that of intact catfish. Intact and unilateral vestibular organ-ablated S. multipunctatus showed DLR during microgravity. Our results confirmed that S. nigriventris has a novel balance sensation which is not affected by microgravity. DLR seems not to play an important role in postural control. It remains unclear that the continuous clinorotation effects on vestibular compensation because we could not keep used unilateral vestibular organ-ablated fish alive under continuous clinorotation for uninterrupted 25 days. This study suggests that space flight experiments are required to explore whether gravity information is essential for vestibular compensation.     

Rotations in a vertebrate setting: evaluation of the symmetry group of the disynaptic canal-neck projection

Organizational structures intrinsic to nervous systems can be more precisely analyzed and compared with other logical structures once they are expressed in mathematical languages. A standard mathematical language for expressing organizational structure is that of groups. Groups are especially well suited to organizational structures involving multiple symmetries such as spatial structures. The vestibular system is widely believed to mediate many neural functions involving spatial structure. The vestibular nuclei receive direct projections from the vestibular endorgans, the semicircular canals and the otolith organs. The near-orthogonal directions of the semicircular canals are embedded in the bone. However, those canal directions are external to the nervous system. This study addresses the way the three-dimensional space of rotations is also embedded in the group structure of neural connectivity. Although we know a great deal about physical rotation, it is not clear that nervous systems organize rotations in the same way as physicists do. It would make sense for nervous systems to organize rotations in such a way as to provide physiologically relevant information about performing or compensating for rotations. The vestibular nuclei, which might be expected to display an organization that binds rotations into a rotation space, do not give a clear organization. This may be because of the multiplicity of spatial functions performed by the vestibular nuclei; rather than one spatial organization, the vestibular nuclei are likely to accommodate multiple, related spatial organizations. This study evaluates one particular data set from the literature that specifies the organization of the disynaptic canal-neck projection; other projections and neuronal populations may have other intrinsic organizations. The data are evaluated directly for their symmetry group. In the symmetry group, the vertebrate requirement that physiology have a right and left is found to be satisfied in two ways: (i) by a hexagonal symmetry arising from the right-left doubling of front and back, (ii) along with separate organizations on the two sides that may be required to operate independently to some extent. The eight observed muscle innervation patterns from the data are the complete set of possible combinations of inhibitory/excitatory polarities from three canal pairs. These eight innervation patterns are organized as the vertices of a cube. The two types of side muscles provide the vertical direction. As the head rotates in physical space, the cube rotates in sensorimotor space. Like the canal-neck projection, otolith projections and proprioceptive afferents contact both the vestibular nuclei and neck motoneurons. They may have a similar organization, perhaps with extensions of the same pattern. Otherwise, like a checkerboard superimposed over a paisley, they will form an overlapping organization with the disynaptic canal-neck projection. Further research is required to determine whether the sensorimotor spatial structure of the canal-neck projection is widespread in nervous systems or whether there are several complete structures that are fragmented and reintegrated.     

Flight Distance and Eye Size in Birds

Larger eyes capture more information from the environment than small eyes, but also require more brain space for information processing. Therefore, individuals have to optimize the size of their eyes, leading to the prediction that larger eyes should have evolved in species with greater benefits from large eyes, such as species subject to intense predation risk. In a comparative analysis of 97 bird species, we found that species that fled at longer distances from an approaching potential predator indeed had relatively large eyes for their body size. In contrast, there was no indication that large eyes had evolved in species living in secluded habitats, or in species eating mobile prey. These findings are consistent with the assumption that eye size is labile and can evolve in response to changing predator environments. They also suggest that eye size may act as a constraint on optimal anti‐predator behavior, if the predator community changes as a consequence of introductions or invasions.     

Identification of head motions by central vestibular neurons receiving linear and angular input

Most naturally occurring displacements of the head in space, due to either an external perturbation of the body or a self-generated, volitional head movement, apply both linear and angular forces to the head. The vestibular system detects linear and angular accelerations of the head separately, but the succeeding control of gaze and posture often relies upon the combined processing of linear and angular motion information. Thus, the output of a secondary neuron may reflect the linear, the angular, or both components of the head motion. Although the vestibular system is typically studied in terms of separate responses to linear and angular acceleration of the head, many secondary and higher-order neurons in the vestibular system do, in fact, receive information from both sets of motion sensors. The present paper develops methods to analyze responses of neurons that receive both types of information, and focuses on responses to sinusoidal motions composed of a linear and an angular component. We show that each neuron has a preferred motion, but a single neuron cannot code for a single motion. However, a pair of neurons can code for a motion by the relative phases of firing-rate modulation. In this way, information about motion is enhanced by neurons combining information about linear and angular motion. Received: 5 November 1998 / Accepted in revised form: 19 March 1999