Normal eye drift and saccadic drift correction in darkness

A re-examination of the time constant of the oculomotor neural integrator in human

We studied the horizontal oculomotor neural integrator in healthy human subjects during gaze holding in darkness. We found large variability among subjects with respect to the estimated time constants and the integrator's null position. We also found that individual subjects could demonstrate significantly nonlinear drift velocities as a function of eye position. Nevertheless, a consistent trend did not emerge. Consequently, cross subject averaging eliminates idiosyncratic nonlinear patterns and the average can be approximated by a linear function inside the range that was tested.

Fine-tuning and the stability of recurrent neural networks

A central criticism of standard theoretical approaches to constructing stable, recurrent model networks is that the synaptic connection weights need to be finely-tuned. This criticism is severe because proposed rules for learning these weights have been shown to have various limitations to their biological plausibility. Hence it is unlikely that such rules are used to continuously fine-tune the network in vivo. We describe a learning rule that is able to tune synaptic weights in a biologically plausible manner. We demonstrate and test this rule in the context of the oculomotor integrator, showing that only known neural signals are needed to tune the weights. We demonstrate that the rule appropriately accounts for a wide variety of experimental results, and is robust under several kinds of perturbation. Furthermore, we show that the rule is able to achieve stability as good as or better than that provided by the linearly optimal weights often used in recurrent models of the integrator. Finally, we discuss how this rule can be generalized to tune a wide variety of recurrent attractor networks, such as those found in head direction and path integration systems, suggesting that it may be used to tune a wide variety of stable neural systems.

Alexander's law in patients with acute vestibular tone asymmetry--evidence for multiple horizontal neural integrators

Alexander's law (AL) states that the slow-phase velocity of spontaneous nystagmus of peripheral vestibular origin is dependent on horizontal gaze position, with greater velocity when gaze is directed in the fast-phase direction. AL is thought to be a compensatory reaction resulting from adaptive changes in the horizontal ocular motor neural integrator. Until now, only horizontal eye movements have been investigated with respect to AL. Because spontaneous nystagmus usually includes vertical and torsional components, we asked whether horizontal gaze changes would have an effect on the 3D drift of spontaneous nystagmus and, thus, on the vertical/torsional neural integrator. We hypothesized that AL reduces all nystagmus components proportionally. Moreover, we questioned the classical theory of a single bilaterally organized horizontal integrator and searched for nonlinearities of AL implying a network of multiple integrators. Using dual scleral search coils, we measured AL in 17 patients with spontaneous nystagmus. Patients followed a pulsed laser dot at eye level jumping in 5 degrees steps along the horizontal meridian between 25 degrees right and left in otherwise complete darkness. AL was observed in 15 of 17 patients. Whereas individual patients typically showed a change of 3D-drift direction at different horizontal eye positions, the average change in direction was not different from zero. The strength of AL (= rate of change of total velocity with gaze position) correlated with nystagmus slow-phase velocity (Spearman's rho = 0.5; p < 0.05) and, on average, did not change the 3D nystagmus drift direction. In general, eye velocity did not vary linearly with eye position. Rather, there was a stronger dependence of velocity on horizontal position when subjects looked in the slow-phase direction compared to the fast-phase direction. We conclude that the theory of a simple leak of a single horizontal neural integrator is not sufficient to explain all aspects of AL.

Spontaneous eye movements in goldfish: oculomotor integrator performance, plasticity, and dependence on visual feedback

To quantify performance of the goldfish oculomotor neural integrator and determine its dependence on visual feedback, we measured the relationship between eye drift-velocity and position during spontaneous gaze fixations in the light and in the dark. In the light, drift-velocities were typically less than 1 deg/s, similar to those observed in humans. During brief periods in darkness, drift-velocities were only slightly larger, but showed greater variance. One hour in darkness degraded fixation-holding performance. These findings suggest that while visual feedback is not essential for online fixation stability, it may be used to tune the mechanism of persistent neural activity in the oculomotor integrator.

Stability of the memory of eye position in a recurrent network of conductance-based model neurons

Studies of the neural correlates of short-term memory in a wide variety of brain areas have found that transient inputs can cause persistent changes in rates of action potential firing, through a mechanism that remains unknown. In a premotor area that is responsible for holding the eyes still during fixation, persistent neural firing encodes the angular position of the eyes in a characteristic manner: below a threshold position the neuron is silent, and above it the firing rate is linearly related to position. Both the threshold and linear slope vary from neuron to neuron. We have reproduced this behavior in a biophysically plausible network model. Persistence depends on precise tuning of the strength of synaptic feedback, and a relatively long synaptic time constant improves the robustness to mistuning.

Continuous attractors and oculomotor control

A recurrent neural network can possess multiple stable states, a property that many brain theories have implicated in learning and memory. There is good evidence for such multistability in the brainstem neural network that controls eye position. Because the stable states are arranged in a continuous dynamical attractor, the network can store a memory of eye position with analog neural encoding. Continuous attractors in model networks depend on precisely tuned positive feedback, and their robust maintenance requires mechanisms of synaptic plasticity. These ideas may have wider scope than just the oculomotor system. More generally, the internal models postulated by theories of biological motor control may be recurrent networks with continuous attractors.

How the brain keeps the eyes still

The brain can hold the eyes still because it stores a memory of eye position. The brain's memory of horizontal eye position appears to be represented by persistent neural activity in a network known as the neural integrator, which is localized in the brainstem and cerebellum. Existing experimental data are reinterpreted as evidence for an "attractor hypothesis" that the persistent patterns of activity observed in this network form an attractive line of fixed points in its state space. Line attractor dynamics can be produced in linear or nonlinear neural networks by learning mechanisms that precisely tune positive feedback.

Lid-opening apraxia in Wilson's disease

A student was diagnosed as having Wilson's disease only after the severe, intermittent inability to open his eyes led him to seek neurologic evaluation. Although lid-opening apraxia is usually a symptom of diffuse extrapyramidal disease, it has not previously been reported in Wilson's disease.