Hysteresis and slow drift in abducens unit activity

Oculomotor plant and neural dynamics suggest gaze control requires integration on distributed timescales

A fundamental principle of biological motor control is that the neural commands driving movement must conform to the response properties of the motor plants they control. In the oculomotor system, characterizations of oculomotor plant dynamics traditionally supported models in which the plant responds to neural drive to extraocular muscles on exclusively short, subsecond timescales. These models predict that the stabilization of gaze during fixations between saccades requires neural drive that approximates eye position on longer timescales and is generated through the temporal integration of brief eye velocity-encoding signals that cause saccades. However, recent measurements of oculomotor plant behaviour have revealed responses on longer timescales. Furthermore, measurements of firing patterns in the oculomotor integrator have revealed a more complex encoding of eye movement dynamics. Yet, the link between these observations has remained unclear. Here we use measurements from the larval zebrafish to link dynamics in the oculomotor plant to dynamics in the neural integrator. The oculomotor plant in both anaesthetized and awake larval zebrafish was characterized by a broad distribution of response timescales, including those much longer than 1 s. Analysis of the firing patterns of oculomotor integrator neurons, which exhibited a broadly distributed range of decay time constants, demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with distributed response timescales. This work suggests that leaky integration on multiple, distributed timescales by the oculomotor integrator reflects an inverse model for generating oculomotor commands, and that multi-timescale dynamics may be a general feature of motor circuitry. KEY POINTS: Recent observations of oculomotor plant response properties and neural activity across the oculomotor system have called into question classical formulations of both the oculomotor plant and the oculomotor integrator. Here we use measurements from new and published experiments in the larval zebrafish together with modelling to reconcile recent oculomotor plant observations with oculomotor integrator function. We developed computational techniques to characterize oculomotor plant responses over several seconds in awake animals, demonstrating that long timescale responses seen in anaesthetized animals extend to the awake state. Analysis of firing patterns of oculomotor integrator neurons demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with multiple, distributed response timescales. Our results support a formulation of gaze stabilization by the oculomotor system in which commands for stabilizing gaze are generated through integration on multiple, distributed timescales.

Dynamics of plant mechanics

Muscle and plant dynamics are most important during the high acceleration of saccades. Models have been developed to characterize muscle and plant dynamics. Building these models require an understanding of the length-tension (elastic) and force-velocity (viscous) relationships. Much work has been done to characterize these nonlinear functions, as they are influenced by innervation. However, the active force generator (active-state tension) in the muscle is still poorly understood. Thus, these models serve more to reveal where new studies of muscle behavior are needed than to explain what happens during a saccade.

Extraocular Motoneurons and Neurotrophism

Extraocular motoneurons are located in three brainstem nuclei: the abducens, trochlear and oculomotor. They control all types of eye movements by innervating three pairs of agonistic/antagonistic extraocular muscles. They exhibit a tonic-phasic discharge pattern, demonstrating sensitivity to eye position and sensitivity to eye velocity. According to their innervation pattern, extraocular muscle fibers can be classified as singly innervated muscle fiber (SIF), or the peculiar multiply innervated muscle fiber (MIF). SIF motoneurons show anatomical and physiological differences with MIF motoneurons. The latter are smaller and display lower eye position and velocity sensitivities as compared with SIF motoneurons.

Why do oVEMPs become larger when you look up? Explaining the effect of gaze elevation on the ocular vestibular evoked myogenic potential

OBJECTIVES

The ocular vestibular evoked myogenic potential (oVEMP) is a vestibular reflex recorded from the inferior oblique (IO) muscles, which increases in amplitude during eye elevation. We investigated whether this effect of gaze elevation could be explained by movement of the IO closer to the recording electrode.

METHODS

We compared oVEMPs recorded with different gaze elevations to those recorded with constant gaze position but electrodes placed at increasing distance from the eyes. oVEMPs were recorded in ten healthy subjects using bursts of skull vibration.

RESULTS

oVEMP amplitude decreased more with decreasing gaze elevation (9 μV from 24° up to neutral) than with increasing electrode distance (2.7 μV from baseline to 6.4 mm; P<0.005). The oVEMP recorded with gaze 24° down had delayed latency (by 4.5 ms).

CONCLUSION

The effect of gaze elevation on the oVEMP cannot be explained by changes in position of the muscle alone and is likely mainly due to increased tonic contraction of the IO muscle in up-gaze. The oVEMP recorded in down-gaze (when the IO is inactivated, but the IR activated) likely originates in the adjacent IR muscle.

SIGNIFICANCE

Our results suggest that oVEMP amplitudes in extraocular muscles scale in response to changing tonic muscle activity.

Dynamics of abducens nucleus neurons in the awake mouse

The mechanics of the eyeball and orbital tissues (the "ocular motor plant") are a fundamental determinant of ocular motor signal processing. The mouse is used increasingly in ocular motor physiology, but little is known about its plant mechanics. One way to characterize the mechanics is to determine relationships between extraocular motoneuron firing and eye movement. We recorded abducens nucleus neurons in mice executing compensatory eye movements during 0.1- to 1.6-Hz oscillation in the light. We analyzed firing rates to extract eye position and eye velocity sensitivities, from which we determined time constants of a viscoelastic model of the plant. The majority of abducens neurons were already active with the eye in its central rest position, with only 6% recruited at more abducted positions. Firing rates exhibited largely linear relationships to eye movement, although there was a nonlinearity consisting of increasing modulation in proportion to eye movement as eye amplitudes became small (due to reduced stimulus amplitude or reduced alertness). Eye position and velocity sensitivities changed with stimulus frequency as expected for an ocular motor plant dominated by cascaded viscoelasticities. Transfer function poles lay at approximately 0.1 and 0.9 s. Compared with previously studied animal species, the mouse plant is stiffer than the rabbit but laxer than cat and rhesus. Differences between mouse and rabbit can be explained by scaling for eye size (allometry). Differences between the mouse and cat or rhesus can be explained by differing ocular motor repertoires of animals with and without a fovea or area centralis.

Motor nucleus activity fails to predict extraocular muscle forces in ocular convergence

For a given eye position, firing rates of abducens neurons (ABNs) generally (Mays et al. 1984), and lateral rectus (LR) motoneurons (MNs) in particular (Gamlin et al. 1989a), are higher in converged gaze than when convergence is relaxed, whereas LR and medial rectus (MR) muscle forces are slightly lower (Miller et al. 2002). Here, we confirm this finding for ABNs, report a similarly paradoxical finding for neurons in the MR subdivision of the oculomotor nucleus (MRNs), and, for the first time, simultaneously confirm the opposing sides of these paradoxes by recording physiological LR and MR forces. Four trained rhesus monkeys with binocular eye coils and custom muscle force transducers on the horizontal recti of one eye fixated near and far targets, making conjugate saccades and symmetric and asymmetric vergence movements of 16-27°. Consistent with earlier findings, we found in 44 ABNs that the slope of the rate-position relationship for symmetric vergence (k(V)) was lower than that for conjugate movement (k(C)) at distance, i.e., mean k(V)/k(C) = 0.50, which implies stronger LR innervation in convergence. We also found in 39 MRNs that mean k(V)/k(C) = 1.53, implying stronger MR innervation in convergence as well. Despite there being stronger innervation in convergence at a given eye position, we found both LR and MR muscle forces to be slightly lower in convergence, -0.40 and -0.20 g, respectively. We conclude that the relationship of ensemble MN activity to total oculorotary muscle force is different in converged gaze than when convergence is relaxed. We conjecture that LRMNs with k(V) < k(C) and MRMNs with k(V) > k(C) innervate muscle fibers that are weak, have mechanical coupling that attenuates their effective oculorotary force, or serve some nonoculorotary, regulatory function.

Dual encoding of muscle tension and eye position by abducens motoneurons

Extraocular muscle tension associated with spontaneous eye movements has a pulse-slide-step profile similar to that of motoneuron firing rate. Existing models only relate motoneuron firing to eye position, velocity and acceleration. We measured and quantitatively compared lateral rectus muscle force and eye position with the firing of abducens motoneurons in the cat to determine fundamental encoding correlations. During fixations (step), muscle force increased exponentially with eccentric eye position, consistent with a model of estimate ensemble motor innervation based on neuronal sensitivities and recruitment order. Moreover, firing rate in all motoneurons tested was better related to eye position than to muscle tension during fixations. In contrast, during the postsaccadic slide phase, the time constant of firing rate decay was closely related to that of muscle force decay, suggesting that all motoneurons encode muscle tension as well. Discharge characteristics of abducens motoneurons formed overlapping clusters of phasic and tonic motoneurons, thus, tonic units recruited earlier and had a larger slide signal. We conclude that the slide signal is a discharge characteristic of the motoneuron that controls muscle tension during the postsaccadic phase and that motoneurons are specialized for both tension and position-related properties. The organization of signal content in the pool of abducens motoneurons from the very phasic to the very tonic units is possibly a result of the differential trophic background received from distinct types of muscle fibers.

Primate disconjugate eye movements during the horizontal AVOR in darkness and a plausible mechanism

Disconjugate eye movements during the horizontal angular vestibulo-ocular reflex (AVOR) evoked in response to steps or pulses of head velocity have been previously reported in lateral eyed animals. In this study, we measured binocular responses to sustained sinusoidal and pseudo-random vestibular stimuli in yaw, delivered in darkness, in both human and monkey. The vestibular stimuli used in our experiments had peak velocities in the range of 120-200 degrees /s, frequencies in the range of 0.17-0.5 Hz, and durations between 60 and 75 s. Our results show a large vergence component to the AVOR response that systematically modulated with head velocity. We also examined our results for temporal-nasal preponderance in slow eye velocity. Although each subject showed some degree of directional preference, we did not find a systematically greater eye velocity for temporal-nasal direction across all subjects. Here, we present these findings and discuss that at least two possible sources could result in disconjugate eye movements during the horizontal rotational VOR in darkness: peripheral and central mechanisms.

Spatiotemporal Properties of Eye Position Signals in the Primate Central Thalamus

Although both sensory and motor signals in multiple cortical areas are modulated by eye position, the origin of eye position signals for cortical neurons remains uncertain. One likely source is the central thalamus, which contains neurons sensitive to eye position. Because the central thalamus receives inputs from the brainstem, these neurons may transmit eye position signals arising from the neural integrator or from proprioceptive feedback. However, because the central thalamus also receives inputs from many cortical areas, eye position signals in the central thalamus could come from the cerebral cortex. To clarify these possibilities, spatial and temporal properties of eye position signals in the central thalamus were examined in trained monkeys. Data showed that eye position signals were decomposed into horizontal and vertical components, suggesting that the central thalamus lies within pathways that transmit brainstem eye position signals to the cortex. Further quantitative analyses suggested that 2 distinct groups of thalamic neurons mediate eye position signals from different subcortical origins, and that the signals are modified dynamically through ascending pathways. Eye position signals through the central thalamus may play essential roles in spatial transformation performed by cortical networks.

Long Time-Constant Behavior of the Oculomotor Plant in Barbiturate-Anesthetized Primate

The mechanics of the extraocular muscles and orbital tissue (“oculomotor plant”) can be approximated by a small number of viscoelastic (Voigt) elements in series. Recent analysis of the eye's return from displacement in lightly anesthetized rhesus monkeys has suggested a four-element plant model with time constants (TCs) of ∼0.01, 0.1, 1, and 10 s. To demonstrate directly the presence of long (1,10 s) TC elements and to assess their contribution quantitatively, horizontal eye displacement was induced in Cynomolgus monkeys under deep barbiturate anesthesia that prevented interference from spontaneous eye movements. The displacement was maintained for either a prolonged (30 s) or brief (0.2 s) period before release. Return to resting position took 20–30 s after prolonged displacement but only 1–2 s after brief displacement, consistent with the presence of long TC elements that would only be substantially stretched in the former condition. Quantitative fitting of the release curves after prolonged displacement indicated that the two long TC elements contribute a substantial proportion (∼30%) of the total plant compliance. A model based on the estimated compliance values is shown to account quantitatively both for our release data and for Goldstein and Robinson's data on hysteresis of ocular motoneuron firing rates measured after centripetal saccades following prolonged eccentric fixation. Long time-constant elements in the plant thus make a substantial contribution to some types of eye movement, and their inclusion in plant models can help interpret the firing patterns of single units in the oculomotor system.

Variability of motoneuron activation and the modulation of force production in a postural reflex of the hermit crab abdomen

The tri-phasic reflex in hermit crab (Pagurus pollicarus) abdomen is triggered by local mechanoreceptors and is essential for postural control. The reflex consists of three stereotypical phases: a brief, high-frequency burst, a transient cessation of firing, and a late-discharge that is much lower in frequency than the initial burst. To better understand the reflex generation of force, variability of motoneuron discharge in each of five parameters of reflex activation was assessed. An intracellular current injection routine was used to correlate each of these parameters with force production. Phase 3 motoneuron firing frequency showed the greatest correlation with force production. Phase 3 spike rate increased as a function of phase 2 duration, but the relationship between phase 2 duration and force produced by the reflex was weak. Junction potential amplitude decreased as phase 2 duration increased, and we hypothesize that this trend counteracts the increased phase 3 frequency, explaining the weak relationship of phase 2 duration and force production. Surprisingly, when phase 3 frequency was held constant and phase 2 was increased in duration, the concurrent decrease in junction potential amplitude did not reduce force production.

Evidence for wide range of time scales in oculomotor plant dynamics: implications for models of eye-movement control

Oculomotor-plant dynamics are not well characterised, despite their importance for modelling eye-movement control. We analysed the time course of the globe's return after horizontal displacements in three rhesus monkeys lightly anaesthetised with ketamine. The eye-position traces were well fitted by a sum of four exponentials (time constants 0.012, 0.099, 0.46, 7.8 s). The two long time-constant terms accounted for 25% of plant compliance, and led to a model that accounted for hitherto unexplained features of ocular motoneuron firing such as (i) hysteresis, and (ii) the inability of a 2 time-constant model to fit data for both fast and slow eye-movements.

Recruitment order of cat abducens motoneurons and internuclear neurons

Abducens neurons undergo a dose-dependent synaptic blockade (either disinhibition or complete blockade) when tetanus neurotoxin (TeNT) is injected into the lateral rectus muscle at either a low (0.5) or a high dose (5 ng/kg). We studied the firing pattern and recruitment order in abducens neurons both in control and after TeNT injection. The eye position threshold for recruitment of control abducens neurons was exponentially related to the eye position and velocity sensitivities. We also found a constancy of recruitment threshold for different eye movement modalities (spontaneous, optokinetic, and vestibular). Exponential relationships were found, as well, for eye velocity sensitivity during saccades and for position and velocity sensitivities during the vestibulo-ocular reflex. Likewise, inverse relationships were found between recruitment threshold or position sensitivity with the antidromic latency in control abducens neurons. These relationships, however, did not apply following TeNT treatment. Neuronal firing after TeNT appeared either disinhibited (low dose) or depressed (high dose), but the relationships between neuronal sensitivities and recruitment still applied. However, the pattern of recruitment shifted toward the treated side as more inputs were blocked by the low- and high-dose treatments, respectively. Nonetheless, although the recruitment-to-sensitivity relationships persisted under the TeNT synaptic blockade, we conclude that synaptic inputs are determinant for establishing the recruitment threshold and recruitment spacing of abducens motoneurons and internuclear neurons.

Missing lateral rectus force and absence of medial rectus co-contraction in ocular convergence

For a given position of the eye in the orbit, most abducens motoneurons (LRMNs) fire at higher rates in converged gaze than when convergence is relaxed, implying that lateral rectus (LR) muscle force will be higher for a given eye position in convergence. If medial rectus (MR) muscle force balances LR force, it too would be higher in convergence, that is, LRMN recording studies predict horizontal rectus co-contraction in convergence. Three trained rhesus monkeys with binocular eye coils and custom muscle force transducers (MFTs) on LR and MR of one eye alternately fixated near (approximately 7 cm) and far (200 cm) targets with vergence movements of 20-30 degrees. Tonic muscle forces were also measured during conjugate fixation of far targets over a 30 x 30 degrees field. MFT characteristics and effects on oculomotility were assessed. Contrary to predictions, we found small (<1 g) decreases in both LR and MR forces in convergence, for those gaze positions that were used in the brain stem recording studies. This missing LR force paradox (higher LRMN firing rates in convergence but lower LR forces) suggests that motoneurons or muscle fibers contribute differently to oculorotary forces in converged and unconverged states, violating the final common path hypothesis. The absence of MR co-contraction is consistent with, and supports, the missing LR force finding. Resolution of the missing LR force paradox might involve nonlinear interactions among muscle fibers, mechanical specialization of muscle fibers and other articulations of the peripheral oculomotor apparatus, or extranuclear contributions to muscle innervation.

Neural basis of disjunctive eye movements

New evidence has challenged a widely accepted interpretation of Hering's law of equal innervation, which states that disjunctive saccades are produced by the linear addition of conjugate and vergence innervation commands produced by independent oculomotor subsystems. We hypothesize, instead, that saccades are produced by a monocular premotor control network. A model, based on this hypothesis and consistent with known brain-stem anatomy, simulates realistic disjunctive saccades including initial and late slow vergence movements.

Change in neuronal firing patterns in the process of motor command generation for the ocular following response

To explore the process of motor command generation for the ocular following response, we recorded the activity of single neurons in the medial superior temporal (MST) area of the cortex, the dorsolateral pontine nucleus (DLPN), and the ventral paraflocculus (VPFL) of the cerebellum of alert monkeys during ocular following elicited by sudden movements of a large-field pattern. Using second-order linear-regression models, we analyzed the quantitative relationships between neuronal firing frequency patterns and eye movements or retinal errors specified by three parameters (position, velocity, and acceleration). We first attempted to reconstruct the temporal waveform of each neuronal response to each visual stimulus and computed the coefficients for each parameter using the least-square error method for each stimulus condition. The temporal firing patterns were generally well reconstructed [coefficient of determination index (CD) > 0.7] from either the retinal error or the associated ocular following response. In the MST and DLPN datasets, however, the fit with the retinal error model was generally better than with the eye-movement model, and the estimated coefficients of acceleration and velocity ranged widely, indicating that temporal patterns in these regions showed considerable diversity. The acceleration component is greater in MST and DLPN than in VPFL, suggesting that an integration occurs in this pathway. When we determined how well the temporal patterns of the neuronal responses of a given cell could be reconstructed for all visual stimuli using a single set of coefficients, good fits were found only for Purkinje cells (P- cells) in the VPFL using the eye-movement model. In these cases, the coefficients of acceleration and velocity for each cell were similar, and the mean ratio of the acceleration and velocity coefficients was close to that of motor neurons. These results indicate that individual MST and DLPN neurons are each encoding some selective aspects of the sensory stimulus (visual motion), whereas the P-cells in VPFL are encoding the complete dynamic command signals for the associated motor response (ocular following). We conclude that the sensory-to-motor transformation for the ocular following response occurs at the P-cells in VPFL.

A simple control law generates Listing's positions in a detailed model of the extraocular muscle system

The neural commands for maintaining static Listing's positions were identified using a detailed model of extraocular muscle based on Miller and Shamaeva (Orbit 1.5 gaze mechanics simulation 1995). The commands were approximately separable, suggesting a simple control law whereby independent horizontal and vertical commands are combined to generate tertiary positions. Tests showed that this control law (i) generated Listing' s positions to reasonable accuracy over+/-30 deg, provided pulleys were represented in the model; (ii) if driven by retinal coordinates, produced errors close to the theoretical minimum for a commutative system. The proposed commands appear consistent with electrophysiological evidence.

The characteristics of dynamic overshoots in square-wave jerks, and in congenital and manifest latent nystagmus

Dynamic overshoots are seen after voluntary re-fixation saccades. They are microsaccadic movements which follow primary saccades and have no delay. The purpose of this study was to examine the prevalence and metrics of the dynamic overshoots seen after involuntary saccades. Using infra-red oculography we demonstrate that dynamic overshoots are a common occurrence in physiological square-wave jerks, congenital nystagmus and manifest latent nystagmus and that these overshoots are saccadic in nature and have the same dynamic characteristics as those seen following voluntary saccades. It is therefore likely that they share common neural commands to those dynamic overshoots seen after a volitional saccade. All dynamic overshoots are postulated to be the unwanted consequence of making a saccade and are simulated in a model of fast oculomotor behaviour which is consistent with known experimental results.

Anatomy and discharge properties of pre-motor neurons in the goldfish medulla that have eye-position signals during fixations

Previous work in goldfish has suggested that the oculomotor velocity-to-position neural integrator for horizontal eye movements may be confined bilaterally to a distinct group of medullary neurons that show an eye-position signal. To establish this localization, the anatomy and discharge properties of these position neurons were characterized with single-cell Neurobiotin labeling and extracellular recording in awake goldfish while monitoring eye movements with the scleral search-coil method. All labeled somata (n = 9) were identified within a region of a medially located column of the inferior reticular formation that was approximately 350 microm in length, approximately 250 microm in depth, and approximately 125 microm in width. The dendrites of position neurons arborized over a wide extent of the ventral half of the medulla with especially heavy ramification in the initial 500 microm rostral of cell somata (n = 9). The axons either followed a well-defined ventral pathway toward the ipsilateral abducens (n = 4) or crossed the midline (n = 2) and projected toward the contralateral group of position neurons and the contralateral abducens. A mapping of the somatic region using extracellular single unit recording revealed that position neurons (n > 120) were the dominant eye-movement-related cell type in this area. Position neurons did not discharge below a threshold value of horizontal fixation position of the ipsilateral eye. Above this threshold, firing rates increased linearly with increasing temporal position [mean position sensitivity = 2.8 (spikes/s)/ degrees, n = 44]. For a given fixation position, average rates of firing were higher after a temporal saccade than a nasal one (n = 19/19); the magnitude of this hysteresis increased with increasing position sensitivity. Transitions in firing rate accompanying temporal saccades were overshooting (n = 43/44), beginning, on average, 17.2 ms before saccade onset (n = 17). Peak firing rate change accompanying temporal saccades was correlated with eye velocity (n = 36/41). The anatomical findings demonstrate that goldfish medullary position neurons have somata that are isolated from other parts of the oculomotor system, have dendritic fields overlapping with axonal terminations of neurons with velocity signals, and have axons that are capable of relaying commands to the abducens. The physiological findings demonstrate that the signals carried by position neurons could be used by motoneurons to set the fixation position of the eye. These results are consistent with a role for position neurons as elements of the velocity-to-position neural integrator for horizontal eye movements.

Quantitative analysis of abducens neuron discharge dynamics during saccadic and slow eye movements

The mechanics of the eyeball and its surrounding tissues, which together form the oculomotor plant, have been shown to be the same for smooth pursuit and saccadic eye movements. Hence it was postulated that similar signals would be carried by motoneurons during slow and rapid eye movements. In the present study, we directly addressed this proposal by determining which eye movement-based models best describe the discharge dynamics of primate abducens neurons during a variety of eye movement behaviors. We first characterized abducens neuron spike trains, as has been classically done, during fixation and sinusoidal smooth pursuit. We then systematically analyzed the discharge dynamics of abducens neurons during and following saccades, during step-ramp pursuit and during high velocity slow-phase vestibular nystagmus. We found that the commonly utilized first-order description of abducens neuron firing rates (FR = b + kE + r, where FR is firing rate, E and are eye position and velocity, respectively, and b, k, and r are constants) provided an adequate model of neuronal activity during saccades, smooth pursuit, and slow phase vestibular nystagmus. However, the use of a second-order model, which included an exponentially decaying term or "slide" (FR = b + kE + r + uE - c), notably improved our ability to describe neuronal activity when the eye was moving and also enabled us to model abducens neuron discharges during the postsaccadic interval. We also found that, for a given model, a single set of parameters could not be used to describe neuronal firing rates during both slow and rapid eye movements. Specifically, the eye velocity and position coefficients (r and k in the above models, respectively) consistently decreased as a function of the mean (and peak) eye velocity that was generated. In contrast, the bias (b, firing rate when looking straight ahead) invariably increased with eye velocity. Although these trends are likely to reflect, in part, nonlinearities that are intrinsic to the extraocular muscles, we propose that these results can also be explained by considering the time-varying resistance to movement that is generated by the antagonist muscle. We conclude that to create realistic and meaningful models of the neural control of horizontal eye movements, it is essential to consider the activation of the antagonist, as well as agonist motoneuron pools.

Extraocular motor unit and whole-muscle responses in the lateral rectus muscle of the squirrel monkey

Because primate studies provide data for the current experimental models of the human oculomotor system, we investigated the relationship of lateral rectus muscle motoneuron firing to muscle unit contractile characteristics in the squirrel monkey. Also examined was the correlation of whole-muscle contractile force with the degree of evoked eye displacement. A force transducer was used to record lateral rectus whole-muscle or muscle unit contraction in response to abducens whole-nerve stimulation or stimulation of single abducens motoneurons or axons. Horizontal eye displacement was recorded using a magnetic search coil. (1) Motor units could be categorized based on contraction speed (fusion frequency) and fatigue. (2) The kt value (change in motoneuronal firing necessary to increase motor unit force by 1.0 mg) of the units correlated with maximum tetanic tension. (3) There was some tendency for maximum tetanic tension of this unit population to separate into three groups. (4) At a constant frequency of 100 Hz, 95% of the motor units demonstrated significantly different force levels dependent on immediately previous stimulation history (hysteresis). (5) A mean force change of 0.32 gm/ degrees and a mean frequency change of 4.7 Hz/ degrees of eye displacement were observed in response to whole-nerve stimulation. These quantitative data provide the first contractile measures of primate extraocular motor units. Models of eye movement dynamics may need to consider the nonlinear transformations observed between stimulation rate and muscle tension as well as the probability that as few as two to three motor units can deviate the eye 1 degrees.

Optimality of position commands to horizontal eye muscles: A test of the minimum-norm rule

Six muscles control the position of the eye, which has three degrees of freedom. Daunicht proposed an optimization rule for solving this redundancy problem, whereby small changes in eye position are maintained by the minimum possible change in motor commands to the eye (the minimum-norm rule). The present study sought to test this proposal for the simplified one-dimensional case of small changes in conjugate eye position in the horizontal plane. Assuming such changes involve only the horizontal recti, Daunicht's hypothesis predicts reciprocal innervation with the size of the change in command matched to the strength of the recipient muscle at every starting position of the eye. If the motor command to a muscle is interpreted as the summed firing rate of its oculomotor neuron (OMN) pool, the minimum-norm prediction can be tested by comparing OMN firing rates with forces in the horizontal recti. The comparison showed 1) for the OMN firing rates given by Van Gisbergen and Van Opstal and the muscle forces given by Robinson, there was good agreement between the minimum-norm prediction and experimental observation over about a +/-30 degrees range of eye positions. This fit was robust with respect to variations in muscle stiffness and in methods of calculating muscle innervation. 2) Other data sets gave different estimates for the range of eye-positions within which the minimum-norm prediction held. The main sources of variation appeared to be disagreement about the proportion of OMNs with very low firing-rate thresholds (i.e., less than approximately 35 degrees in the OFF direction) and uncertainty about eye-muscle behavior for extreme (>30 degrees ) positions of the eye. 3) For all data sets, the range of eye positions over which the minimum-norm rule applied was determined by the pattern of motor-unit recruitment inferred for those data. It corresponded to the range of eye positions over which the size principle of recruitment was obeyed by both agonist and antagonist muscles. It is argued that the current best estimate of the oculomotor range over which minimum-norm control could be used for conjugate horizontal eye position is approximately +/-30 degrees. The uncertainty associated with this estimate would be reduced by obtaining unbiased samples of OMN firing rates. Minimum-norm control may result from reduction of the image movement produced by noise in OMN firing rates.

Pseudo-inverse control in biological systems: a learning mechanism for fixation stability

The problem of redundancy in motor control is common to both robotics and biology. Pseudo-inverse control has been proposed as a solution in robotics and appears to be used by the oculomotor system for eye position. Learning mechanisms for implementing pseudo-inverse control using a distributed system of ocular motor units were investigated by modelling integrator calibration for horizontal eye movements. Ocular motoneuron (OMN) input weights were adjusted with a gradient-descent learning rule, using a retinal-slip estimate as an error signal. Firing-rate threshold only became related to motor-unit strength when a noise term was added to OMN firing rates. The learning rule suppressed those units making the largest contribution to the noise-related error, causing the strongest units to have the highest thresholds (size principle). Because the size principle and pseudo-inverse control are related, the trained system approximated pseudo-inverse control over the central +/-35 degrees of the oculomotor range.

Effects of botulinum neurotoxin type A on abducens motoneurons in the cat: alterations of the discharge pattern

The discharge characteristics that abducens motoneurons exhibit after paralysis of the lateral rectus muscle with botulinum neurotoxin type A were studied in the alert cat. Antidromically identified motoneurons were recorded during both spontaneous and vestibularly induced eye movements. A single injection of 0.3 ng/kg produced a complete paralysis of the lateral rectus muscle lasting for about 12-15 days, whereas after 3 ng/kg the paralysis was still complete at the longest time checked, three months. Motoneurons recorded under the effect of the low dose showed differences in their sensitivities to both eye position and velocity according to the direction of the previous and ongoing movements, respectively. These directional differences could be explained by post-saccadic adaptation of the non-injected eye in the appropriate direction for reducing ocular misalignment. Thus, backward and forward post-saccadic drifts accompanied on- and off-directed saccades, respectively. The magnitude of the drift was similar to the magnitude of changes in eye position sensitivity. The discharge of the high-dose-treated motoneurons could be described in a three-stage sequence. During the initial 10-12 days, motoneuronal discharge resembled the effects of axotomy, particularly in the loss of tonic signals and the presence of exponential-like decay of firing after saccades. In this stage, the conduction velocity of abducens motoneurons was reduced by 21.4%. The second stage was characterized by an overall reduction in firing rate towards a tonic firing at 15-70 spikes/s. Motoneurons remained almost unmodulated for all types of eye movement and thus eye position and velocity sensitivities were significantly reduced. Tonic firing ceased only when the animal became drowsy, but was restored by alerting stimuli. In addition, the inhibition of firing for off-directed saccades was more affected than the burst excitation during on-directed saccades, since in many cells pauses were almost negligible. These alterations could not be explained by adaptational changes in the movement of the non-injected eye. Finally, after 60 days the initial stages of recovery were observed. The present results indicate that the high dose of botulinum neurotoxin produces effects on the motoneuron not attributable to the functional disconnection alone, but to a direct effect of the neurotoxin in the motoneuron and/or its synaptic inputs.

Summation of extraocular motor unit tensions in the lateral rectus muscle of the cat

Contractile measures on 67 single muscle units in the cat lateral rectus muscle were made in response to motoneuron stimulation. Simultaneous activation of four to five additional units, using muscle nerve stimulation, allowed an examination of unit force summation. Linear force addition was found in 73% of the units, while 25% added only about half of their twitch force to the twitch force of the nerve-activated units. "Nonadditive" units had significantly weaker twitch tensions than the units which added linearly. Lengthening or shortening the whole muscle, from maximal isometric settings, reduced whole muscle twitch tension as well as muscle unit tension. Injury to the lateral rectus muscle did not significantly alter whole muscle tension. These findings suggest that the known serial and branching arrangement of these muscle fibers, as well as the complex interfiber matrix, may help explain the force reduction in some muscle units and the whole muscle's resistance to insult.

The fractional-order dynamics of brainstem vestibulo-oculomotor neurons

The vestibulo-ocular reflex (VOR) and other oculomotor subsystems such as pursuit and saccades are ultimately mediated in the brainstem by premotor neurons in the vestibular and prepositus nuclei that relay eye movement commands to extraocular motoneurons. The premotor neurons receive vestibular signals from canal afferents. Canal afferent frequency responses have a component that can be characterized as a fractional-order differentiation (dkx/dtk where k is a nonnegative real number). This article extends the use of fractional calculus to describe the dynamics of motor and premotor neurons. It suggests that the oculomotor integrator, which converts eye velocity into eye position commands, may be of fractional order. This order is less than one, and the velocity commands have order one or greater, so the resulting net output of motor and premotor neurons can be described as fractional differentiation relative to eye position. The fractional derivative dynamics of motor and premotor neurons may serve to compensate fractional integral dynamics of the eye. Fractional differentiation can be used to account for the constant phase shift across frequencies, and the apparent decrease in time constant as VOR and pursuit frequency increases, that are observed for motor and premotor neurons. Fractional integration can reproduce the time course of motor and premotor neuron saccade-related activity, and the complex dynamics of the eye. Insight into the nature of fractional dynamics can be gained through simulations in which fractional-order differentiators and integrators are approximated by sums of integer-order high-pass and low-pass filters, respectively. Fractional dynamics may be applicable not only to the oculomotor system, but to motor control systems in general.

Neural network simulations of the primate oculomotor system. I. The vertical saccadic burst generator

The performance of a neural network that simulates the vertical saccade-generating portion of the primate brain is evaluated. Consistent with presently available anatomical evidence, the model makes use of an eye displacement signal for its feedback. Its major features include a simple mechanism for resetting its integrator at the end of each saccade, the ability to generate staircases of saccades in response to stimulation of the superior colliculus, and the ability to account for the monotonic relation between motor error and the instantaneous discharge of presaccadic neurons of the superior colliculus without placing the latter within the local feedback loop. Several experimentally testable predictions about the effects of stimulation or lesion of saccade-related areas of the primate brain are made on the basis of model output in response to "stimulation" or "lesion" of model elements.

Testing the common neural integrator hypothesis at the level of the individual abducens motoneurones in the alert cat

1. As far as horizontal eye movements are concerned, the well-known hypothesis of a common neural integrator states that the eye-position signal is generated by a common network, regardless of the type of versional movement. The aim of this study was to evaluate the validity of this hypothesis by analysing the behaviour of the abducens motoneurones, the system into which the horizontal neural integrator(s) project(s). If there were a common neural integrator, the different motoneurones would receive the eye position signal through the same pathway and the sensitivity to eye position would be the same regardless of the type of versional movement. If there were multiple integrators, the sensitivity to eye position in one type of versional movement might be different from the sensitivity to eye position in another type of versional movement, at least for occasional motoneurones. 2. The discharge of thirty-one antidromically identified abducens motoneurones was recorded in the alert cat during spontaneous eye movements made in the light and in response to sinusoidal rotations of the head in complete darkness. 3. All of the abducens motoneurones exhibited a burst of action potentials for lateral saccades. During fixation between saccades, they maintained a steady firing rate that increased as the cat fixated increasingly lateral eye positions. 4. For each abducens motoneurone, the sensitivity to eye position (Kf) was determined from measurements carried out during intersaccadic fixations. Kf was calculated from the slope of the firing rate-eye position linear regression line. 5. The discharge rate of the identified motoneurones was observed during four sinusoidal vestibular stimulations (+/- 10 deg, 0.10 Hz; +/- 20 deg, 0.10 Hz; +/- 30 deg, 0.10 Hz; +/- 40 deg, 0.10 Hz). The motoneurones exhibited a burst of activity during fast phases in the lateral direction and paused during fast phases in the opposite direction. During slow phases, motoneurones modulated their activity as a function of the vestibularly induced eye movements except for slow phases that occurred in position ranges below their recruitment threshold. In these cases their activity was cut off. 6. A new method was developed to measure the sensitivity to eye position of neurones during vestibular slow phases. The difficulty came from the fact that, during slow phases, eye velocity and eye position changed simultaneously and that each of those two variables could influence neuronal activity.(ABSTRACT TRUNCATED AT 400 WORDS)

Extraocular motor units: type classification and motoneuron stimulation frequency-muscle unit force relationships

Extracellular and intracellular techniques were used to study single motor units of the abducens nucleus and lateral rectus muscle in the cat. Using a combination of two motor unit properties, the fusion frequency and an index of fatigability, the population of twitch motor units could be separated into 4 subgroups: fast fatigable (FF), fast fatigue resistant (FR), slow fatigable (SF) and slow fatigue resistant (S). Nontwitch motor units, a fifth subgroup (NT), formed 10% of the total studied population. The twitch tension and the maximum tetanic tension of the FF motor unit type were significantly stronger than all other motor unit types. The use of frequency varying stimulation patterns did not further differentiate the motor unit types. The relation between a series of single motoneuron stimulation frequencies and the resultant single muscle unit forces generated a slope defined as a motor unit's kt value. Motor units with low kt values had higher twitch tensions, higher maximum tetanic tensions, higher fusion frequencies and lower fatigue indices than motor units with high kt values. Motoneuron recruitment was tested by electrical stimulation of the medial rectus subdivision of the contralateral oculomotor nucleus. No correlations were seen between recruitment order and the mechanical parameters of the single abducens motor units.

Extraocular muscle forces in alert monkey

We describe an extraocular muscle (EOM) force transducer that provides low-noise signals from an alert animal for several months, is implanted without disinserting the muscle, and is well-tolerated by the body, and present results obtained with the device. The transducer can be used to study orbital statics and dynamics, and oculomotor control signals undiminished by orbital low-pass filtering and antagonistic pairing of muscles. It may provide an index of effective EOM innervation, useful in studies of orbital tissue healing and plasticity, and oculomotor (OM) signal adaptation. During horizontal saccades transducers implanted in the lateral rectus (LR) and medial rectus (MR) of a monkey trained to fixate revealed an agonist muscle tension waveform corresponding to the "pulse-slide-step" pattern of saccadic innervation, and an antagonist waveform that was similar within a scale factor. We never observed transient increases in antagonist force at the ends of saccades (active braking) or at the beginnings. Onset of saccadic force in LR preceded that in MR by 1.6 msec for abducting saccades, and lagged that in MR by 1.1 msec for adducting saccades. During vertical saccades, transient force changes were found in LR and MR, which were likely due, at least in part, to globe translation. LR and MR forces during fixation tended to be largest with the eye about 10 degrees in elevation, and smallest in depression, indicating that effective total innervation was a function of vertical gaze, or that there was variation in the elastic component of muscle force related to orbital geometry, with LR and MR innervation independent of vertical gaze. An exponential decrease in fixation force, having a time constant of about 10 days, was observed after implantation. This may have reflected adaptive muscle lengthening or post-surgical healing.

Behaviour of Medial Rectus Motoneurons in the Alert Cat

The activity of identified medial rectus motoneurons was recorded in alert cats during spontaneous and vestibular induced eye movements. Medial rectus motoneurons fired a burst of spikes slightly preceding adducting saccades and increased their discharge rate linearly with successive eye positions in the adducting direction. Conduction velocity (21.3 - 98.2 m/s), eye position sensitivity (ks, 7.1 +/- 1.5 spikes/s/deg), and eye velocity sensitivity (rs, 1 +/- 0.2 spikes/s/deg/s) during spontaneous eye movements, and time constants calculated from phase lead analysis (To, 135 +/- 36 ms) showed values similar to those described previously for cat abducens motoneurons. The firing rate during repeated fixation of the same eye position was affected significantly by the direction of the preceding saccade and by the animal's level of alertness. Eye velocity sensitivity was not significantly affected by changes in the animal's level of alertness. A weak negative relationship (coefficient of correlation=-0.56) was observed between eye velocity sensitivity (rv) and sinusoidal rotational frequency, with no change in eye position sensitivity (kv) with stimulus frequency. The subsequent changes in the time constant (Tv) calculated as Tv=rv/kv in relation to stimulus frequency suggests that the oculomotor system deviates from a (linear) first-order model.

Evolutionary adaptation of a reflex system: sensory hysteresis counters muscle 'catch' tension

The metathoracic femoral chordotonal organ is a receptor of the locust, Schistocerca, hindleg that encodes the angle of the femoro-tibial joint. However, the discharge of the organ shows considerable hysteresis, in that there is a substantial decline in the level of afferent firing when the tibia is moved and then returned to its initial position. Similar hysteresis is also seen in some joint receptors and interneurons of other invertebrates and vertebrates. When the chordotonal organ is stimulated in freely moving locusts, mimicking sudden changes in joint angle, reflex discharges can be elicited in the tibial extensor muscle that resist apparent joint movement and also show similar hysteresis. This pattern of motoneuron activity is demonstrated to potentially function to eliminate residual, 'catch' muscle tensions that result from increases in motoneuron firing frequency. This adaptation could also serve to produce accurate load compensation.