A proposed neural network for the integrator of the oculomotor system

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

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

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

A neural network model of the vestibulo-ocular reflex using a local synaptic learning rule.

Vertebrates use the vestibulo-ocular reflex to maintain clear vision during head movements. This reflex requires eye-velocity commands from the semicircular canals to be integrated (mathematically) to produce eye-position commands for the extraocular muscles. This is accomplished by a neural network in the caudal pons. A model of this network is proposed using positive feedback via lateral inhibition. The model has been adapted to a learning network. We have developed a synaptic learning rule using only local information to make the model more physiological.     

Neural network models of velocity storage in the horizontal vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR) produces compensatory eye movements by utilizing head rotational velocity signals from the semicircular canals to control contractions of the extraocular muscles. In mammals, the time course of horizontal VOR is longer than that of the canal signals driving it, revealing the presence of a central integrator known as velocity storage. Although the neurons mediating VOR have been described neurophysiologically, their properties, and the mechanism of velocity storage itself, remain unexplained. Recent models of integration in VOR are based on systems of linear elements, interconnected in arbitrary ways. The present study extends this work by modeling horizontal VOR as a learning network composed of nonlinear model neurons. Network architectures are based on the VOR arc (canal afferents, vestibular nucleus (VN) neurons and extraocular motoneurons) and have both forward and lateral connections. The networks learn to produce velocity storage integration by forming lateral (commissural) inhibitory feedback loops between VN neurons. These loops overlap and interact in a complex way, forming both fast and slow VN pathways. The networks exhibit some of the nonlinear properties of the actual VOR, such as dependency of decay rate and phase lag upon input magnitude, and skewing of the response to higher magnitude sinusoidal inputs. Model VN neurons resemble their real counterparts. Both have increased time constant and gain, and decreased spontaneous rate as compared to canal afferents. Also, both model and real VN neurons exhibit rectification and skew. The results suggest that lateral inhibitory interactions produce velocity storage and also determine the properties of neurons mediating VOR. The neural network models demonstrate how commissural inhibition may be organized along the VOR pathway.     

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

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

Neural simulations of adaptive reafference suppression in the elasmobranch electrosensory system

The electrosensory system of elasmobranchs is extremely sensitive to weak electric fields, with behavioral thresholds having been reported at voltage gradients as low as 5 nV/cm. To achieve this amazing sensitivity, the electrosensory system must extract weak extrinsic signals from a relatively large reafferent background signal associated with the animal's own movements. Ventilatory movements, in particular, strongly modulate the firing rates of primary electrosensory afferent nerve fibers, but this modulation is greatly suppressed in the medullary electrosensory processing nucleus, the dorsal octavolateral nucleus. Experimental evidence suggests that the neural basis of reafference suppression involves a common-mode rejection mechanism supplemented by an adaptive filter that fine tunes the cancellation. We present a neural model and computer simulation results that support the hypothesis that the adaptive component may involve an anti-Hebbian form of synaptic plasticity at molecular layer synapses onto ascending efferent neurons, the principal output neurons of the nucleus. Parallel fibers in the molecular layer carry a wealth of proprioceptive, efference copy, and sensory signals related to the animal's own movements. The proposed adaptive mechanism acts by canceling out components of the electrosensory input signal that are consistently correlated with these internal reference signals.Abbreviations AEN ascending efferent neuron - AFF primary afferent nerve fiber - DGR dorsal granular ridge - DON dorsal octavolateral nucleus - ELL electrosensory lateral line lobe - GABA -aminobutyric acid - IN inhibitory interneuron - ISI interspike interval - ST stellate cell     

Synchronized firing in the retina

Synchronized firing in neural populations has been proposed to constitute an elementary aspect of the neural code, but a complete understanding of its origins and significance has been elusive. Synchronized firing has been extensively documented in retinal ganglion cells, the output neurons of the retina. However, differences in synchronized firing across species and cell types have led to varied conclusions about its mechanisms and role in visual signaling. Recent work on two identified cell populations in the primate retina, the ON-parasol and OFF-parasol cells, permits a more unified understanding. Intracellular recordings reveal that synchronized firing in these cell types arises primarily from common synaptic input to adjacent pairs of cells. Statistical analysis indicates that local pairwise interactions can explain the pattern of synchronized firing in the entire parasol cell population. Computational analysis reveals that the aggregate impact of synchronized firing on the visual signal is substantial. Thus, in the parasol cells, the origin and impact of synchronized firing on the neural code may be understood as locally shared input which influences the visual signals transmitted from eye to brain.     

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

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

The role of the medial preoptic area in the organization of paradoxical sleep

Influence of electrical stimulation of the medial preoptic area of cats on characteristics of paradoxical sleep and activity of medial preoptic neurons were studied in the course of sleep-waking cycle. Low-frequency stimulation of this structure in the state of slow-wave sleep evoked short-latency electrocortical desynchronization and induced transition to paradoxical sleep or paradocical sleep-like state. The same stimulation during the whole period of paradoxical sleep results in a reduction of its duration, practically complete disappearance of tonic stage, and increase in the density of rapid eye movements in phasic stage. The vast majority of meurons in the medial preoptic area decreased their firing rates during quiet waking and slow-wave sleep and dramatically increased their activity during paradoxical sleep. More than 50% of such neurons displayed activation 20-70 s prior to the appearance of electrocorticographic correlates of paradoxical sleep. Some neurons were selectively active during paradoxical sleep. Approximately 50% of cells increased their firing rates a few seconds prior to and/or during series of rapid eye movements. The results suggest that the medial preoptic area contains the units of the executive system (network) of paradoxical sleep and are involved in the mechanisms of neocortical desynchronization.     

Sensory convergence solves a motion ambiguity problem

Our inner ear is equipped with a set of linear accelerometers, the otolith organs, that sense the inertial accelerations experienced during self-motion. However, as Einstein pointed out nearly a century ago, this signal would by itself be insufficient to detect our real movement, because gravity, another form of linear acceleration, and self-motion are sensed identically by otolith afferents. To deal with this ambiguity, it was proposed that neural populations in the pons and midline cerebellum compute an independent, internal estimate of gravity using signals arising from the vestibular rotation sensors, the semicircular canals. This hypothesis, regarding a causal relationship between firing rates and postulated sensory contributions to inertial motion estimation, has been directly tested here by recording neural activities before and after inactivation of the semicircular canals. We show that, unlike cells in normal animals, the gravity component of neural responses was nearly absent in canal-inactivated animals. We conclude that, through integration of temporally matched, multimodal information, neurons derive the mathematical signals predicted by the equations describing the physics of the outside world.     

Three-dimensional head angular velocity detection from otolith afferent signals

Afferent signals from the otolith organs can produce compensatory eye position and velocity signals which has been described as linear vestibulo-ocular reflex (LVOR). The afferent otolith signals carry information about head orientation and changes of head orientation relative to gravity. A head orientation (tilt) related position signal can be obtained from population vector coding of tonic otolith afferent signals during static or dynamic head tilts, which in turn could produce compensatory eye position signals in the LVOR. On the other hand, eye angular velocity signals may be extracted, as proposed in this study, from the population response of tilt-velocity sensitive otolith afferents. Such afferents are shown to encode instantaneous head orientation relative to gravity at onset of a head movement and, as the movement continues, the projection of head angular velocity onto the earth-horizontal plane, indicating the instantaneous direction of movement relative to gravity. Angular velocity components along the earth-vertical direction which are not directly encoded by otolith afferents can be detected by central signal processing. Central reconstruction of 3D head angular velocity allows to obtain information about absolute head orientation in space even in the absence of semicircular canal related information. Such information is important for generating compensatory eye movements as well as for dynamic control of posture.     

Acetylcholine-gated current translates wake neuronal firing rate information into a spike timing-based code in Non-REM sleep,stabilizing neural network dynamics during memory consolidation

Sleep is critical for memory consolidation, although the exact mechanisms mediating this process are unknown. Combining reduced network models and analysis of in vivo recordings, we tested the hypothesis that neuromodulatory changes in acetylcholine (ACh) levels during non-rapid eye movement (NREM) sleep mediate stabilization of network-wide firing patterns, with temporal order of neurons’ firing dependent on their mean firing rate during wake. In both reduced models and in vivo recordings from mouse hippocampus, we find that the relative order of firing among neurons during NREM sleep reflects their relative firing rates during prior wake. Our modeling results show that this remapping of wake-associated, firing frequency-based representations is based on NREM-associated changes in neuronal excitability mediated by ACh-gated potassium current. We also show that learning-dependent reordering of sequential firing during NREM sleep, together with spike timing-dependent plasticity (STDP), reconfigures neuronal firing rates across the network. This rescaling of firing rates has been reported in multiple brain circuits across periods of sleep. Our model and experimental data both suggest that this effect is amplified in neural circuits following learning. Together our data suggest that sleep may bias neural networks from firing rate-based towards phase-based information encoding to consolidate memories.     

Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning

 Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals. Received: 28 January 2000 / Accepted in revised form: 2 August 2000     

The Y cell visual pathway implements a demodulating nonlinearity

Neural encoding of sensory signals involves both linear and nonlinear processes. Determining which nonlinear operations are implemented by neural systems is crucial to understanding sensory processing. Here, we ask if demodulation, the process used to decode AM radio signals, describes how Y cells in the cat LGN nonlinearly encode the visual scene. In response to visual AM signals across?a wide range of carrier frequencies, Y cells were found to transmit a demodulated signal, with the firing rate of single-units fluctuating at the envelope frequency but not the carrier frequency. A comparison of temporal frequency tuning properties between LGN Y cells and neurons in two primary cortical areas suggests that Y cells initiate a distinct pathway that carries a demodulated representation of the visual scene to cortex. The nonlinear signal processing carried out by the Y cell pathway simplifies the neural representation of complex visual features and allows high spatiotemporal frequencies to drive cortical responses.     

The role of intrinsic neuronal properties in the encoding of auditory information in the cochlear nuclei.

It is now possible to relate the intrinsic electrical properties of particular cells in the cochlear nuclei of mammals with their biological function. In the layered dorsal cochlear nucleus, information concerning the location of a sound source seems to be contained in the spatial pattern of activation of a population of neurons. In the unlayered, ventral cochlear nucleus, however, neurons carry information in their temporal firing patterns. The voltage-sensitive conductances that make responses to synaptic current brief enable bushy cells to convey signals from the auditory nerve to the superior olivary complex with a temporal precision of at least 120 microseconds.     

A role for the cerebellum in the control of limb movement velocity

Accepting, rejecting or modifying the many different theories of the cerebellum's role in the control of movement requires an understanding of the signals encoded in the discharge of cerebellar neurons and how those signals are transformed by the cerebellar circuitry. Particularly challenging is understanding the sensory and motor signals carried by the two types of action potentials generated by cerebellar Purkinje cells, the simple spikes and complex spikes. Advances have been made in understanding this signal processing in the context of voluntary arm movements. Recent evidence suggests that mossy fiber afferents to the cerebellar cortex are a source of kinematic signals, providing information about movement direction and speed. In turn, the simple spike discharge of Purkinje cells integrates this mossy fiber information to generate a movement velocity signal. Complex spikes may signal errors in movement velocity. It is proposed that the cerebellum uses the signals carried by the simple and complex spike discharges to control movement velocity for both step and tracking arm movements.     

Monitoring and control of action by the frontal lobes

Success requires deciding among alternatives, controlling the initiation of movements, and judging the consequences of actions. When alternatives are difficult to distinguish, habitual responses must be overcome, or consequences are uncertain, deliberation is necessary and a supervisory system exerts control over the processes that produce sensory-guided movements. We have investigated these processes by recording neural activity in the frontal lobe of macaque monkeys performing a countermanding task. Distinct neurons in the frontal eye field respond to visual stimuli or control the production of the movements. In the supplementary eye field and anterior cingulate cortex, neurons appear not to control directly movement initiation but instead signal the production of errors, the anticipation and delivery of reinforcement, and the presence of processing conflict. These signals form the core of current models of supervisory control of sensorimotor processes.     

Population Coding of Forelimb Joint Kinematics by Peripheral Afferents in Monkeys

Various peripheral receptors provide information concerning position and movement to the central nervous system to achieve complex and dexterous movements of forelimbs in primates. The response properties of single afferent receptors to movements at a single joint have been examined in detail, but the population coding of peripheral afferents remains poorly defined. In this study, we obtained multichannel recordings from dorsal root ganglion (DRG) neurons in cervical segments of monkeys. We applied the sparse linear regression (SLiR) algorithm to the recordings, which selects useful input signals to reconstruct movement kinematics. Multichannel recordings of peripheral afferents were performed by inserting multi-electrode arrays into the DRGs of lower cervical segments in two anesthetized monkeys. A total of 112 and 92 units were responsive to the passive joint movements or the skin stimulation with a painting brush in Monkey 1 and Monkey 2, respectively. Using the SLiR algorithm, we reconstructed the temporal changes of joint angle, angular velocity, and acceleration at the elbow, wrist, and finger joints from temporal firing patterns of the DRG neurons. By automatically selecting a subset of recorded units, the SLiR achieved superior generalization performance compared with a regularized linear regression algorithm. The SLiR selected not only putative muscle units that were responsive to only the passive movements, but also a number of putative cutaneous units responsive to the skin stimulation. These results suggested that an ensemble of peripheral primary afferents that contains both putative muscle and cutaneous units encode forelimb joint kinematics of non-human primates.     

Optimal control of saccades by spatial-temporal activity patterns in the monkey superior colliculus

A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades.     

Interactions of glutamate and dopamine in a computational model of the striatum

A network model of simplified striatal principal neurons with mutual inhibition was used to investigate possible interactions between cortical glutamatergic and nigral dopaminergic afferents in the neostriatum. Glutamatergic and dopaminergic inputs were represented by an excitatory synaptic conductance and a slow membrane potassium conductance, respectively. Neuronal activity in the model was characterized by episodes of increased action potential firing rates of variable duration and frequency. Autocorrelation histograms constructed from the action potential activity of striatal model neurons showed that reducing peak excitatory conductance had the effect of increasing interspike intervals. On the other hand, the maximum value of the dopamine-sensitive potassium conductance was inversely related to the duration of firing episodes and the maximal firing rates. A smaller potassium conductance restored normal firing rates in the most active neurons at the expense of a larger proportion of neurons showing reduced activity. Thus, a homogeneous network with mutual inhibition can produce equally complex dynamics as have been proposed to occur in a striatal network with two neuron populations that are oppositely regulated by dopamine. Even without mutual inhibition it appears that increased dopamine concentrations could partially compensate for the effects of reduced glutamatergic input in individual neurons.