Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator

Connecting Connectomes to Physiology

With the advent of volumetric EM techniques, large connectomic datasets are being created, providing neuroscience researchers with knowledge about the full connectivity of neural circuits under study. This allows for numerical simulation of detailed, biophysical models of each neuron participating in the circuit. However, these models typically include a large number of parameters, and insight into which of these are essential for circuit function is not readily obtained. Here, we review two mathematical strategies for gaining insight into connectomics data: linear dynamical systems analysis and matrix reordering techniques. Such analytical treatment can allow us to make predictions about time constants of information processing and functional subunits in large networks.SIGNIFICANCE STATEMENT This viewpoint provides a concise overview on how to extract important insights from Connectomics data by mathematical methods. First, it explains how new dynamics and new time constants can evolve, simply through connectivity between neurons. These new time-constants can be far longer than the intrinsic membrane time-constants of the individual neurons. Second, it summarizes how structural motifs in the circuit can be discovered. Specifically, there are tools to decide whether or not a circuit is strictly feed-forward or whether feed-back connections exist. Only by reordering connectivity matrices can such motifs be made visible.

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.

Combined mechanisms of neural firing rate homeostasis

Spikes in the membrane potential of neurons comprise the currency of information processing in the brain. The ability of neurons to convert any information present across their multiple inputs into a significant modification to the pattern of their emitted spikes depends on the rate at which they emit spikes. If the mean rate is near the neuron's maximum, or if the rate is near zero, then changes in the inputs have minimal impact on the neuron's firing rate. Therefore, a neuron needs to control its mean rate. Protocols that either dramatically increase or decrease a neuron's firing rate lead to multiple compensatory changes that return the neuron's mean rate toward its prior value. In this primer, first as a summary of our previous work (Cannon and Miller in J Neurophysiol 116(5):2004-2022, 2016; Cannon and Miller in J Math Neurosci 7(1):1, 2017), we describe the advantages and disadvantages of having more than one such control mechanism responding to the neuron's firing rate. We suggest how problems of two, coexisting, potentially competing mechanisms can be overcome. Key requirements are: (1) the control be of a distribution of values, which the controlled variable achieves over a fast timescale compared to the timescale of the control system; (2) at least one of the control mechanisms be nonlinear; and (3) the two control systems are satisfied by a stable distribution or range of values that can be achieved by the variable. We show examples of functional control systems, including the previously studied integral feedback controller and new simulations of a "bang-bang" controller, that allow for compensation when inputs to the system change. Finally, we present new results describing how the underlying signal processing pathways would produce mechanisms of dual control, as opposed to a single mechanism with two outputs, and compare the responses of these systems to changes of input statistics.

Computational models of motivated frontal function

Computational models of frontal function have made important contributions to understanding how the frontal lobes support a wide range of important functions, in their interactions with other brain areas including, critically, the basal ganglia (BG). We focus here on the specific case of how different frontal areas support goal-directed, motivated decision-making, by representing three essential types of information: possible plans of action (in more dorsal and lateral frontal areas), affectively significant outcomes of those action plans (in ventral, medial frontal areas including the orbital frontal cortex), and the overall utility of a given plan compared to other possible courses of action (in anterior cingulate cortex). Computational models of goal-directed action selection at multiple different levels of analysis provide insight into the nature of learning and processing in these areas and the relative contributions of the frontal cortex versus the BG. The most common neurologic disorders implicate these areas, and understanding their precise function and modes of dysfunction can contribute to the new field of computational psychiatry, within the broader field of computational neuroscience.

Synaptic and intrinsic homeostasis cooperate to optimize single neuron response properties and tune integrator circuits

Homeostatic processes that provide negative feedback to regulate neuronal firing rate are essential for normal brain function, and observations suggest that multiple such processes may operate simultaneously in the same network. We pose two questions: why might a diversity of homeostatic pathways be necessary, and how can they operate in concert without opposing and undermining each other? To address these questions, we perform a computational and analytical study of cell-intrinsic homeostasis and synaptic homeostasis in single-neuron and recurrent circuit models. We demonstrate analytically and in simulation that when two such mechanisms are controlled on a long time scale by firing rate via simple and general feedback rules, they can robustly operate in tandem to tune the mean and variance of single neuron's firing rate to desired goals. This property allows the system to recover desired behavior after chronic changes in input statistics. We illustrate the power of this homeostatic tuning scheme by using it to regain high mutual information between neuronal input and output after major changes in input statistics. We then show that such dual homeostasis can be applied to tune the behavior of a neural integrator, a system that is notoriously sensitive to variation in parameters. These results are robust to variation in goals and model parameters. We argue that a set of homeostatic processes that appear to redundantly regulate mean firing rate may work together to control firing rate mean and variance and thus maintain performance in a parameter-sensitive task such as integration.

Local population synchrony and the encoding of eye position in the primate neural integrator

Encoding horizontal eye position in the oculomotor system occurs through temporal integration of eye velocity inputs to produce tonic outputs. The nucleus prepositus is commonly believed to be the "neural integrator" that accomplishes this function through the activity of its ensemble of predominantly burst-tonic neurons. Single-unit characterizations and labeling studies of these neurons have suggested that their collective output is achieved through local feedback loops produced by direct connections between them. If this is the case, then the ensemble of burst-tonic neurons should exhibit correlated activity. To obtain electrophysiological evidence of local interactions between neurons, we simultaneously recorded pairs (n = 29) of burst-tonic neurons in the nucleus prepositus of rhesus macaque monkeys using eight-channel linear microelectrode arrays. We computed the magnitude of synchrony between their spike trains as a function of eye position during ocular fixations and as a function of distance between neurons. Importantly, we found that neurons exhibit unexpected levels of positive synchrony, which is maximal during contralateral fixations and weakest when neurons are located far apart from one another (>300 μm). Together, our results support a role for shared inputs to ipsilateral pairs of burst-tonic neurons in the encoding of eye position in the primate nucleus prepositus.

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.

Computational approaches to spatial orientation: from transfer functions to dynamic Bayesian inference

Spatial orientation is the sense of body orientation and self-motion relative to the stationary environment, fundamental to normal waking behavior and control of everyday motor actions including eye movements, postural control, and locomotion. The brain achieves spatial orientation by integrating visual, vestibular, and somatosensory signals. Over the past years, considerable progress has been made toward understanding how these signals are processed by the brain using multiple computational approaches that include frequency domain analysis, the concept of internal models, observer theory, Bayesian theory, and Kalman filtering. Here we put these approaches in context by examining the specific questions that can be addressed by each technique and some of the scientific insights that have resulted. We conclude with a recent application of particle filtering, a probabilistic simulation technique that aims to generate the most likely state estimates by incorporating internal models of sensor dynamics and physical laws and noise associated with sensory processing as well as prior knowledge or experience. In this framework, priors for low angular velocity and linear acceleration can explain the phenomena of velocity storage and frequency segregation, both of which have been modeled previously using arbitrary low-pass filtering. How Kalman and particle filters may be implemented by the brain is an emerging field. Unlike past neurophysiological research that has aimed to characterize mean responses of single neurons, investigations of dynamic Bayesian inference should attempt to characterize population activities that constitute probabilistic representations of sensory and prior information.

Control of neuronal persistent activity by voltage-dependent dendritic properties

Neural integrators and working memory rely on persistent activity, a widespread neural phenomenon potentially involving persistent sodium conductances. Using a unique combination of voltage-clamp, dynamic-clamp, and frequency-domain techniques, we have investigated the role of voltage-dependent conductances on the dendritic electrotonic structure of neurons of the prepositus hypoglossi nucleus (PHN), which is known to be involved in oculomotor integration. The PHN contains two main neuronal populations: type B neurons with a double afterhyperpolarization and type D neurons, which not only are oscillatory but also have a greater electrotonic length than that of type B neurons. The persistent sodium conductance is present in all PHN neurons, although its effect on the dynamic electrotonic structure is shown to significantly differ in the two major cell types present in the nucleus. The electrotonic differences are such that the persistent sodium conductance can be almost perfectly manipulated in a type B neuron using an on-line dynamic clamp to add or subtract virtual sodium ion channels. The dynamic-clamp results are confirmed by data-fitted models, which suggest that the persistent sodium conductance has two different roles depending on its somatic versus dendritic location: perisomatic conductances could play a major role in maintaining action potential discharge and dendritic conductances would be more involved in other computational properties, such as those involving remote synaptic processing or bistable events.

Dynamics of saccadic oscillations

The brainstem circuitry underlying saccades is symmetrical with respect to the midline. The oculomotor behaviour generated by the circuitry depends on a combination of signals passed along fibre tracts and less easily identifiable connections, such as those across the midline. The midline crossing connections are often affected by developmental disorders which give rise to unstable eye movements (see J. Jen, this volume). The connections at the levels of the colliculus, pause cells, and neural integrator generate different dynamical mechanisms for the development of instabilities, which can be identified in eye movement recordings using phase space analysis techniques.

A reevaluation of the inverse dynamic model for eye movements

To construct an appropriate motor command from signals that provide a representation of desired action, the nervous system must take into account the dynamic characteristics of the motor plant to be controlled. In the oculomotor system, signals specifying desired eye velocity are thought to be transformed into motor commands by an inverse dynamic model of the eye plant that is shared for all types of eye movements and implemented by a weighted combination of eye velocity and position signals. Neurons in the prepositus hypoglossi and adjacent medial vestibular nuclei (PH-BT neurons) were traditionally thought to encode the "eye position" component of this inverse model. However, not only are PH-BT responses inconsistent with this theoretical role, but compensatory eye movement responses to translation do not show evidence for processing by a common inverse dynamic model. Prompted by these discrepancies between theoretical notions and experimental observations, we reevaluated these concepts using multiple-frequency rotational and translational head movements. Compatible with the notion of a common inverse model, we show that PH-BT responses are unique among all premotor cell types in bearing a consistent relationship to the motor output during eye movements driven by different sensory stimuli. However, because their responses are dynamically identical to those of motoneurons, PH-BT neurons do not simply represent an internal component of the inverse model, but rather its output. They encode and distribute an estimate of the motor command, a signal critical for accurate motor execution and learning.

Anatomical and pharmacological relationship between acetylcholine and nitric oxide in the prepositus hypoglossi nucleus of the cat: Functional implications for eye-movement control

The prepositus hypoglossi (PH) nucleus has been proposed as a pivotal structure for horizontal eye-position generation in the oculomotor system. Recent studies have revealed that acetylcholine (ACh) in the PH nucleus could mediate the persistent activity necessary for this process, although the origin of this ACh remains unknown. It is also known that nitric oxide (NO) in the PH nucleus plays an important role in the control of velocity balance, being involved in a negative feedback control of tonic signals arriving at the PH nucleus. As it could be expected that neurons taking part in eye-position generation must control their tonic background inputs, the existence of a relationship between nitrergic and cholinergic neurons is hypothesized. In the present study we analyzed the distribution, size, and morphology of choline acetyltransferase-positive neurons, and their relationship with neuronal nitric oxide synthase in the PH nucleus of the cat. As presumed, some 96% of cholinergic neurons were also nitrergic in the PH nucleus, suggesting that NO is regulating the level of ACh released by cholinergic PH neurons. Furthermore, we studied the alterations induced by muscarinic-receptor agonists and antagonists on spontaneous and vestibularly induced eye movements in the alert cat and compared them with those induced in previous studies by modification of NO levels in the same animal preparation. The results suggest that ACh is necessary for the generation of saccadic and vestibular eye-position signals, whereas the NO is stabilizing the eye-position generator by controlling background activity reaching cholinergic neurons in the PH nucleus.

Tests of models for saccade-vergence interaction using novel stimulus conditions

During natural activities, two types of eye movements - saccades and vergence - are used in concert to point the fovea of each eye at features of interest. Some electrophysiological studies support the concept of independent neurobiological substrates for saccades and vergence, namely saccadic and vergence burst neurons. Discerning the interaction of these two components is complicated by the near-synchronous occurrence of saccadic and vergence components. However, by positioning the far target below the near target, it is possible to induce responses in which the peak velocity of the vertical saccadic component precedes the peak velocity of the horizontal vergence component by approximately 75 ms. When saccade-vergence responses are temporally dissociated in this way, the vergence velocity waveform changes, becoming less skewed. We excluded the possibility that such change in skewing was due to visual feedback by showing that similar behavior occurred in darkness. We then tested a saccade-related vergence burst neuron (SVBN) model proposed by Zee et al. in J Neurophysiol 68:1624-1641 (1992), in which omnipause neurons remove inhibition from both saccadic and vergence burst neurons. The technique of parameter estimation was used to calculate optimal values for responses from human subjects in which saccadic and convergence components of response were either nearly synchronized or temporally dissociated. Although the SVBN model could account for convergence waveforms when saccadic and vergence components were nearly synchronized, it could not when the components were temporally dissociated. We modified the model so that the saccadic pulse changed the parameter values of the convergence burst units if both components were synchronized. The modified model accounted for velocity waveforms of both synchronous and dissociated convergence movements. We conclude that both the saccadic pulse and omnipause neuron inhibition influence the generation of vergence movements when they are made synchronously with saccades.

Oscillatory and Intrinsic Membrane Properties of Guinea Pig Nucleus Prepositus Hypoglossi Neurons In Vitro

Numerous models of the oculomotor neuronal integrator located in the prepositus hypoglossi nucleus (PHN) involve both highly tuned recurrent networks and intrinsic neuronal properties; however, there is little experimental evidence for the relative role of these two mechanisms. The experiments reported here show that all PHN neurons (PHNn) show marked phasic behavior, which is highly oscillatory in ∼25% of the population. The behavior of this subset of PHNn, referred to as type D PHNn, is clearly different from that of the medial vestibular nucleus neurons, which transmit the bulk of head velocity-related sensory vestibular inputs without integrating them. We have investigated the firing and biophysical properties of PHNn and developed data-based realistic neuronal models to quantitatively illustrate that their active conductances can produce the oscillatory behavior. Although some individual type D PHNn are able to show some features of mathematical integration, the lack of robustness of this behavior strongly suggests that additional network interactions, likely involving all types of PHNn, are essential for the neuronal integrator. Furthermore, the relationship between the impulse activity and membrane potential of type D PHNn is highly nonlinear and frequency-dependent, even for relatively small-amplitude responses. These results suggest that some of the synaptic input to type D PHNn is likely to evoke oscillatory responses that will be nonlinearly amplified as the spike discharge rate increases. It would appear that the PHNn have specific intrinsic properties that, in conjunction with network interconnections, enhance the persistent neural activity needed for their function.

Nonlinear time series analysis of jerk congenital nystagmus

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system.This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses.

Saccadic instabilities in albinism without nystagmus

Albinism effects a surprising manipulation of the visual pathway in which some of the normally uncrossed axons of the temporal retina instead cross at the chiasm. An expected consequence of this misrouting is that subjects with albinism will have difficulty in specifying the targets of saccades. Usually albinos have nystagmus so the stability of their saccadic eye movements is not readily accessible, but some albinos do not have nystagmus. In these subjects it was found that they had frequent saccadic intrusions, the sizes of which were correlated with velocities of steady drifts in fixations (r = 0.802, P < 0.05). An explanation for the correlation between the amplitudes of the intrusions and the velocities of the drifts is that it is due to a common failure in the development of a saccadic system which is responsible for converting a given retinal displacement into a matching eye movement, with the extent of the failure reflecting the severity of the misrouting.

Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making

Decision-making often requires the accumulation and maintenance of evidence over time. Although the neural signals underlying sensory processing have been studied extensively, little is known about how the brain accrues and holds these sensory signals to guide later actions. Previous work has suggested that neural activity in the lateral intraparietal area (LIP) of the monkey brain reflects the formation of perceptual decisions in a random dot direction-discrimination task in which monkeys communicate their decisions with eye-movement responses. We tested the hypothesis that decision-related neural activity in LIP represents the time integral of the momentary motion "evidence." By briefly perturbing the strength of the visual motion stimulus during the formation of perceptual decisions, we tested whether this LIP activity reflected a persistent, integrated "memory" of these brief sensory events. We found that the responses of LIP neurons reflected substantial temporal integration. Brief pulses had persistent effects on both the monkeys' choices and the responses of neurons in LIP, lasting up to 800 ms after appearance. These results demonstrate that LIP is involved in neural time integration underlying the accumulation of evidence in this task. Additional analyses suggest that decision-related LIP responses, as well as behavioral choices and reaction times, can be explained by near-perfect time integration that stops when a criterion amount of evidence has been accumulated. Temporal integration may be a fundamental computation underlying higher cognitive functions that are dissociated from immediate sensory inputs or motor outputs.

Intrinsic membrane properties of vertebrate vestibular neurons: function, development and plasticity

Central vestibular neurons play an important role in the processing of body motion-related multisensory signals and their transformation into motor commands for gaze and posture control. Over recent years, medial vestibular nucleus (MVN) neurons and to a lesser extent other vestibular neurons have been extensively studied in vivo and in vitro, in a range of species. These studies have begun to reveal how their intrinsic electrophysiological properties may relate to their response patterns, discharge dynamics and computational capabilities. In vitro studies indicate that MVN neurons are of two major subtypes (A and B), which differ in their spike shape and after-hyperpolarizations. This reflects differences in particular K(+) conductances present in the two subtypes, which also affect their response dynamics with type A cells having relatively low-frequency dynamics (resembling "tonic" MVN cells in vivo) and type B cells having relatively high-frequency dynamics (resembling "kinetic" cells in vivo). The presence of more than one functional subtype of vestibular neuron seems to be a ubiquitous feature since vestibular neurons in the chick and frog also subdivide into populations with different, analogous electrophysiological properties. The ratio of type A to type B neurons appears to be plastic, and may be determined by the signal processing requirements of the vestibular system, which are species-variant. The membrane properties and discharge pattern of type A and type B MVN neurons develop largely post-natally, through the expression of the underlying ion channel conductances. The membrane properties of MVN neurons show rapid and long-lasting plastic changes after deafferentation (unilateral labyrinthectomy), which may serve to maintain their level of activity and excitability after the loss of afferent inputs.

Integrator function in the oculomotor system is dependent on sensory context

The oculomotor integrator is usually defined by the characteristics of decay in gaze after saccades to flashed targets or after spontaneous gaze shifts in the dark. This property is then presumed fixed and accessed by other ocular reflexes, such as the vestibuloocular reflex (VOR) or pursuit, to shape motoneural signals. An alternate view of this integrator proposes that it relies on a distributed network, which should change its properties with sensory-motor context. Here we demonstrate in 10 normal subjects that the function of integration can vary in an individual with the imposed test. The value of the time constant for the decay of gaze holding in the dark can be significantly different from the effective integration time constant estimated from VOR responses. Hence analytical tools for the study of dynamics in ocular reflexes must allow for nonideal and labile integrator function. The mechanisms underlying such labile integration remain to be explored and may be different in various ocular reflexes (e.g., visual versus vestibular).

Directional asymmetry during combined saccade-vergence movements

We investigated relationships between saccadic and vergence components of gaze shifts as 10 human subjects switched visual fixation between targets aligned in the midsagittal plane that lay in different vertical directions and at different distances. When fixation was shifted between a higher distant target and a lower near target, peak convergence velocity followed peak vertical saccadic velocity by a median interval of 12 ms. However, when fixation was shifted between a lower distant target and a higher near target, peak convergence velocity followed peak vertical saccadic velocity by a median interval of 76 ms. For the 2 stimulus arrangements, the median intervals by which peak divergence velocity followed the peak vertical saccadic velocity were 4 and 20 ms, respectively. The dissociation interval between the peak velocities of convergence and upward saccades increased with vertical saccade size, required convergence angle, and elevation of the endpoint of the movement. Velocity waveforms of vergence responses were more skewed when peak velocity was closely associated with saccadic peak velocity than when the vergence responses were delayed. Convergence peak velocities did not vary in any consistent pattern, but divergence peak velocities were generally smaller with responses that were delayed. Vergence movements were accompanied by small, high-frequency conjugate oscillations, suggesting that omnipause neurons were inhibited for both types of responses. In conclusion, the present findings indicate that the dynamic properties of horizontal vergence movements depend on the direction and timing of vertical saccades; these findings suggest experimental tests for current models of saccade-vergence interaction.

Plasticity and tuning of the time course of analog persistent firing in a neural integrator

In a companion paper, we reported that the goldfish oculomotor neural integrator could be trained to instability or leak by rotating the visual surround with a velocity proportional to +/- horizontal eye position, respectively. Here we analyze changes in the firing rate behavior of neurons in area I in the caudal brainstem, a central component of the oculomotor neural integrator. Persistent firing could be detuned to instability and leak, respectively, along with fixation behavior. Prolonged training could reduce the time constant of persistent firing of some cells by more than an order of magnitude, to <1 s. Normal visual feedback gradually retuned persistent firing of integrator neurons toward stability, along with fixation behavior. In animals with unstable fixations, approximately half of the eye position-related cells had upward or unstable firing rate drift. In animals with leaky fixations, two-thirds of the eye position-related cells showed leaky firing drift. The remaining eye position-related cells, generally those with lower eye position thresholds, showed a more complex pattern of history-dependent/predictive firing rate drift in relation to eye drift. These complex drift cells often showed a drop in maximum persistent firing rate after training to leak. Despite this diversity, firing drift and the degree of instability or leak in firing rates were broadly correlated with fixation performance. The presence, strength, and reversibility of this plasticity demonstrate that, in this system, visual feedback plays a vital role in gradually tuning the time course of persistent neural firing.

Plasticity and tuning by visual feedback of the stability of a neural integrator

Persistent neural firing is of fundamental importance to working memory and other brain functions because it allows information to be held "online" following an input and to be integrated over time. Many models of persistent activity rely on some kind of positive feedback internal to the neural circuit concerned; however, too much feedback causes runaway firing (instability), and too little results in loss of persistence (leak). This parameter sensitivity leads to the hypothesis that the brain uses an error signal (external feedback) to tune the stability of persistent firing by adjusting the amount of internal feedback. We test this hypothesis by manipulating external visual feedback, a putative sensory error signal, in a model system for persistent firing, the goldfish oculomotor neural integrator. Over tens of minutes to hours, electronically controlled visual feedback consistent with a leaky or unstable integrator can drive the integrator progressively more unstable or leaky, respectively. Eye fixation time constants can be reduced >100-fold to <1 s. Normal visual feedback gradually retunes the integrator back to stability. Changes in the phase of the sinusoidal vestibulo-ocular response are consistent with integrator detuning, as are changes in ocular drift following eye position shifts compensating for brief passive head movements during fixations. Corresponding changes in persistent firing of integrator neurons are presented in the accompanying article. The presence, strength, and reversibility of the plasticity demonstrate that, in this system, external visual feedback plays a vital role in gradually tuning the stability of the neural integrator.

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.

Correlated discharge among cell pairs within the oculomotor horizontal velocity-to-position integrator

In the oculomotor system, temporal integration of velocity commands into position signals may depend on synaptic feedback among neurons of a bilateral brainstem cell assembly known as the "neural integrator." Both ipsilateral excitatory and contralateral inhibitory projections between eye position-related integrator cells are hypothesized as a substrate for positive feedback supporting integration. Presence of feedback interactions should be evident in cross-correlation functions of neuron pairs. Here, unilateral and bilateral paired recordings were obtained during fixation behavior from neurons in goldfish brainstem area I, a key element of the integrator. During fixations, discharge of most unilateral pairs, composed of cells with eye position sensitivities of the same sign, was positively correlated with lag of 0-10 msec (n = 11 of 14 significant). Typically, a very narrow peak (mean half-width <4 msec) near zero lag was observed. Discharge of bilateral pairs, composed of cells with position sensitivities of the opposite sign, was either negatively correlated with lag of 0-10 msec (n = 5 of 13 significant) or not correlated. Troughs in negative correlations always had minima between 3 and 5 msec lag. These results are consistent with the feedback hypothesis of temporal integration, highlighting excitation unilaterally and inhibition bilaterally. Absence of visual input did not weaken correlations, but other sources of correlated input extrinsic to area I were not ruled out. Triplet recordings revealed that unilateral pairwise correlations were primarily independent. Correlation between unilateral pairs systematically decreased with increasing eye position, demonstrating that synchrony is not necessary for persistent activity at high firing rates.

A Role for Neural Integrators in Perceptual Decision Making

Decisions based on uncertain information may benefit from an accumulation of information over time. We asked whether such an accumulation process may underlie decisions about the direction of motion in a random dot kinetogram. To address this question we developed a computational model of the decision process using ensembles of neurons whose spiking activity mimics neurons recorded in the extrastriate visual cortex (area MT or V5) and a sensorimotor association area of the parietal lobe (area LIP). The model instantiates the hypothesis that neurons in sensorimotor association areas compute the time integral of sensory signals from the visual cortex, construed as evidence for or against a proposition, and that the decision is made when the integrated evidence reaches a threshold. The model explains a variety of behavioral and physiological measurements obtained from monkeys.