Neural network simulations of the primate oculomotor system III. An one-dimensional, one-directional model of the superior colliculus

This report evaluates the performance of a biologically motivated neural network model of the primate superior colliculus (SC). Consistent with known anatomy and physiology, its major features include excitatory connections between its output elements, nigral gating mechanisms, and an eye displacement feedback of reticular origin to recalculate the metrics of saccades to memorized targets in retinotopic coordinates. Despite the fact that it makes no use of eye position or eye velocity information, the model can account for the accuracy of saccades in double step stimulation experiments. Further, the model accounts for the effects of focal SC lesions. Finally, it accounts for the properties of saccades evoked in response to the electrical stimulation of the SC. These include the approximate size constancy of evoked saccades despite increases of stimulus intensity, the fact that the size of evoked saccades depends on the time that has elapsed from a previous saccade, the fact that staircases of saccades are evoked in response to prolonged stimuli, and the fact that the size of saccades evoked in response to the simultaneous stimulation of two SC sites is the average of the saccades that are evoked when the two sites are separately stimulated. Received: 3 November 1997 / Accepted in revised form: 30 June 1998     

Neural network simulations of the primate oculomotor system IV. A distributed bilateral stochastic model of the neural integrator of the vertical saccadic system

 The present report examines the performance of a distributed bi-directional neural network that simulates the vertical velocity to position integrator of the primate brain. Consistent with anatomy and physiology, its units receive stochastically weighted input from vertical medium-lead burst neurons. Also consistent with anatomy, units belonging to integrators with opposite on-directions (up or down) are interconnected via the posterior commissure (again in a stochastically weighted manner) and they can be excitatory or inhibitory. To demonstrate that integration can be a one-step process, the output of model units was routed directly to vertical motoneurons. Model units replicate the wide range of saccade-related discharge patterns encountered in the portion of the primate brain that is thought to house the vertical neural integrator (the interstitial nucleus of Cajal) while “lesions” of model units and/or their interconnections replicate the symptoms which follow insults to this brain area. Received: 20 June 2000 / Accepted in revised form: 17 July 2001     

Neural network simulations of the nervous system

Present knowledge of brain mechanisms is mainly based on anatomical and physiological studies. Such studies are however insufficient to understand the information processing of the brain. The present new focus on neural network studies is the most likely candidate to fill this gap. The present paper reviews some of the history and current status of neural network studies. It signals some of the essential problems for which answers have to be found before substantial progress in the field can be made.     

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.     

Neural network model of on-off units in the fly visual system: simulations of dynamic behavior

We analyze the dynamic properties of a neural network model for on-off spiking neurons recorded in the first optic chiasm of the fly visual system. The model consists of two parallel pathways and three sequential processing stages. The first stage models photoreceptors. At the second stage, the signal is segregated into on- and off-pathways. These pathways are proposed to correspond to two populations of amacrine cells. At the third stage, the on- and off-pathways converge to on-off neurons. Furthermore, according to the model, on-off neurons interact via recurrent connections. This stage is proposed to correspond to lamina L4 neurons. In response to luminance increments and decrements, the model exhibits a three-component response and suggests pathways for each of the components. When stimulated by a train of pulses, the model exhibits fast adaptation for frequencies higher than about 5 Hz. Furthermore, adaptation to on- and off-pulses occurs independently. When the frequency of stimulation is reduced, the unit recovers rapidly from its adapted state. The temporal modulation transfer function has its peak around 7 Hz. The phase characteristics show a phase lead for low temporal frequencies changing to a phase lag for high frequencies. These model predictions are compared with data from Jansonius and van Hateren (1991). Received: 26 May 1997 / Accepted in revised form: 19 February 1998     

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.     

Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord

The segmental locomotor network in the lamprey spinal cord was simulated on a computer using a connectionist-type neural network. The cells of the network were identical except for their excitatory levels and their synaptic connections. The synaptic connections used were based on previous experimental work. It was demonstrated that the connectivity of the circuit is capable of generating oscillatory activity with the appropriate phase relations among the cells. Intersegmental coordination was explored by coupling two identical segmental networks using only the cells of the network. Each of the possible couplings of a bilateral pair of cells in one oscillator with a bilateral pair of cells in the other oscillator produced stable phase locking of the two oscillators. The degree of phase difference was dependent upon synaptic weight, and the operating range of synaptic weights varied among the pairs of connections. The coupling was tested using several criteria from experimental work on the lamprey spinal cord. Coupling schemes involving several pairs of connecting cells were found which 1) achieved steadystate phase locking within a single cycle, 2) exhibited constant phase differences over a wide range of cycle periods, and 3) maintained stable phase locking in spite of large differences in the intrinsic frequencies of the two oscillators. It is concluded that the synaptic connectivity plays a large role in producing oscillations in this network and that it is not necessary to postulate a separate set of coordinating neurons between oscillators in order to achieve appropriate phase coupling.     

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     

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus

 Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges. Received: 25 October 1994/Accepted in revised form: 20 June 1995     

Physical model simulations of brain injury in the primate

Diffuse brain injuries resulting from non-impact rotational acceleration are investigated with the aid of physical models of the skull-brain structure. These models provide a unique insight into the relationship between the kinematics of head motion and the associated deformation of the surrogate brain material. Human and baboon skulls filled with optically transparent surrogate brain tissue are subjected to lateral rotations like those shown to produce diffuse injury to the deep white matter in the brain of the baboon. High-speed cinematography captures the deformations of the grids embedded within the surrogate brain tissue during the applied load. The overall deformation pattern is compared to the pathological portrait of diffuse brain injury as determined from animal studies and autopsy reports. Shear strain and pathology spatial distributions mirror each other. Load levels and resulting surrogate brain tissue deformations are related from one species to the other. Increased primate brain mass magnified the strain amplified without significantly altering the spatial distribution. An empirically-derived value for a critical shear strain associated with the onset of severe diffuse axonal injury in primates is determined, assuming constitutive similarity between baboon and human brain tissue. The primate skull physical model data and the critical shear strain associated with the threshold for severe diffuse axonal injury were used to scale data obtained from previous studies to man, and thus derive a diffuse axonal injury tolerance for rotational acceleration for humans.     

Stability of the saccadic oculomotor system

A variety of different types of instability has been found in the saccadic system of humans. Some of the instabilities correspond to clinical conditions, whereas others are inherent in the normal saccadic system. How can these instabilities arise within the mechanism of normal saccadic eye movements? A physiologically-based model of the saccadic system predicts that horizontal saccadic oscillations will occur with excessive mutual inhibition between the left and right burst cells and with underaction of the pause cells. The amplitudes and frequencies of the oscillations had ranges of 0–6° and 6–20 cycles per second, respectively. Application of stability analysis techniques to the model reveals that development of the oscillations can be explained by the Hopf bifurcation mechanism. Future development of this approach will involve classifying pathological instabilities of the saccadic system according to the bifurcation involved in their generation.     

The knowledge base of the oculomotor system.

In everyday life, eye movements enable the eyes to gather the information required for motor actions. They are thus proactive, anticipating actions rather than just responding to stimuli. This means that the oculomotor system needs to know where to look and what to look for. Using examples from table tennis, driving and music reading we show that the information the eye movement system requires is very varied in origin and highly task specific, and it is suggested that the control program or schema for a particular action must include directions for the oculomotor and visual processing systems. In many activities (reading text and music, typing, steering) processed information is held in a memory buffer for a period of about a second. This permits a match between the discontinuous input from the eyes and continuous motor output, and in particular allows the eyes to be involved in more than one task.     

The oculomotor system of Daphnia magna

Summary The highly mobile cyclopic compound eye of Daphnia magna is rotated by six muscles arranged as three bilateral pairs. The three muscles on each side of the head share a common origin on the carapace and insert dorsally, laterally and ventrally on the eye. The dorsal and ventral muscles are each composed of two muscle fibers and the lateral muscle is composed of from two to five fibers, with three the most common number. Individual muscle fibers are spindle-shaped mononucleated cells with organized bundles of myofilaments. Lateral eye-muscle fibers are thinner than those of the other muscles but are otherwise similar in ultrastructure. Two motor neurons innervate each dorsal and each ventral muscle and one motor neuron innervates each lateral muscle. The cell bodies of the motor neurons are situated dorsally in the supraesophageal ganglion (SEG) and are ipsilateral to the muscles they innervate. The dendritic fields of the dorsal-muscle motor neurons are ipsilateral to their cell bodies; those of the ventral-muscle motor neurons are bilateral though predominantly contralateral. The central projections of the lateral-muscle motor neurons are unknown. In the dorsal and ventral muscles one motor axon synapses principally with one muscle fiber; in each lateral muscle the single motor axon branches to, and forms synapses with, all the fibers. The neuromuscular junctions, characterized by pre- and postsynaptic densities and clear vesicles, are similar in all the eye muscles.     

A neurological integrator for the oculomotor control system

This paper describes a mathematical model of a neurological integrator that has been developed to provide the very long leakage time constant required of the intgrator in the oculomotor system. The Gaussian distribution of cell thresholds and the eye-position- related discharge of the individual cells of the integrator model, and the highly specialized short-duration, high-frequency burst required of the input, have been modeled after the single-cell behavior actually observed in the oculomotor control areas of the brain stem of an alert primate.     

A social network analysis of primate groups

Primate social systems are difficult to characterize, and existing classification schemes have been criticized for being overly simplifying, formulated only on a verbal level or partly inconsistent. Social network analysis comprises a collection of analytical tools rooted in the framework of graph theory that were developed to study human social interaction patterns. More recently these techniques have been successfully applied to examine animal societies. Primate social systems differ from those of humans in both size and density, requiring an approach that puts more emphasis on the quality of relationships. Here, we discuss a set of network measures that are useful to describe primate social organization and we present the results of a network analysis of 70 groups from 30 different species. For this purpose we concentrated on structural measures on the group level, describing the distribution of interaction patterns, centrality, and group structuring. We found considerable variability in those measures, reflecting the high degree of diversity of primate social organizations. By characterizing primate groups in terms of their network metrics we can draw a much finer picture of their internal structure that might be useful for species comparisons as well as the interpretation of social behavior.     

Neural model of the genetic network

Many cell control processes consist of networks of interacting elements that affect the state of each other over time. Such an arrangement resembles the principles of artificial neural networks, in which the state of a particular node depends on the combination of the states of other neurons. The lambda bacteriophage lysis/lysogeny decision circuit can be represented by such a network. It is used here as a model for testing the validity of a neural approach to the analysis of genetic networks. The model considers multigenic regulation including positive and negative feedback. It is used to simulate the dynamics of the lambda phage regulatory system; the results are compared with experimental observation. The comparison proves that the neural network model describes behavior of the system in full agreement with experiments; moreover, it predicts its function in experimentally inaccessible situations and explains the experimental observations. The application of the principles of neural networks to the cell control system leads to conclusions about the stability and redundancy of genetic networks and the cell functionality. Reverse engineering of the biochemical pathways from proteomics and DNA micro array data using the suggested neural network model is discussed.     

Parallel network simulations with NEURON

The NEURON simulation environment has been extended to support parallel network simulations. Each processor integrates the equations for its subnet over an interval equal to the minimum (interprocessor) presynaptic spike generation to postsynaptic spike delivery connection delay. The performance of three published network models with very different spike patterns exhibits superlinear speedup on Beowulf clusters and demonstrates that spike communication overhead is often less than the benefit of an increased fraction of the entire problem fitting into high speed cache. On the EPFL IBM Blue Gene, almost linear speedup was obtained up to 100 processors. Increasing one model from 500 to 40,000 realistic cells exhibited almost linear speedup on 2000 processors, with an integration time of 9.8 seconds and communication time of 1.3 seconds. The potential for speed-ups of several orders of magnitude makes practical the running of large network simulations that could otherwise not be explored. Action Editor: Alain Destexhe     

Reflex actions of the functional divisions in the crayfish oculomotor system

Summary The electrical responses of motor neurons in different anatomical subdivisions of the crayfish oculomotor system were examined during various kinds of experimentally manipulated sensory stimulation. Geotactic reflexes are effected by neurons in the anterior motor cluster and the medulla terminalis. Optokinetic and proprioceptive nystagmus are generated by neurons in the lateral motor cluster. This functional diversity in the major subdivisions contrasts with an intradivisional homogeneity of function, in that the different motor neurons of each all contribute to reflexes initiated by different kinds of sensory input.This research was supported by USPHS Research Grant NS 04989.