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PubMed1993

Presynaptic and postsynaptic competition in models for the development of neuromuscular connections.

In the establishment of connections between nerve and muscle there is an initial stage when each muscle fibre is innervated by several different motor axons. Withdrawal of connections then takes place until each fibre has contact from just a single axon. The evidence suggests that the withdrawal process involves competition between nerve terminals. We examine in formal models several types of competitive mechanism that have been proposed for this phenomenon. We show that a model which combines competition for a presynaptic resource with competition for a postsynaptic resource is superior to others. This model accounts for many anatomical and physiological findings and has a biologically plausible implementation. Intrinsic withdrawal appears to be a side effect of the competitive mechanism rather than a separate non-competitive feature. The model's capabilities are confirmed by theoretical analysis and full scale computer simulations.

Animals↗
PubMed1993

Constants underlying frequency changes in biological rhythmic movements.

When an animal increases or decreases the frequency of its limb motions, how should the transformation in timing be characterized? It has been hypothesized that the transformation is adiabatic, even though the biological conditions are nonconservative and non-rate-limited (Kugler and Turvey 1987). An adiabatic transformation requires that the rhythmic system's action (energy/frequency) and entropy production remain time-invariant throughout the transformation. The non-conservative adiabatic hypothesis was evaluated through an experiment on human rhythmic hand movements. On each trial, a subject began at a prescribed frequency and then, over a 30 s interval, increased (or decreased) the frequency continuously at will. For each subject, on each increasing and decreasing trial, cycle kinetic energy was a linear function of cycle frequency with a negative energy intercept. By the adiabatic hypothesis, the slope of the function defines the constant action and the intercept defines the constant dissipation - changes in cycle frequency incur no changes in energy dissipated per cycle. Slopes and intercepts were correlated suggesting a common basis for the two constants, and the variety of cycle amplitude-cycle duration relations were in agreement with the nonmonotonic, nonlinear space-time function predicted by the hypothesis. The possibilities of addressing aspects of the data through (a) muscle modeled as a continuum of Kelvin bodies with a continuous relaxation spectrum, and (b) various classes of autonomous differential equations, were discussed. Most importantly, the discussion focused on the puzzling independence of energy cost and speed exhibited by locomoting animals differing in morphology, physiology, size, and taxa. It was suggested that the independence may reflect a very general principle - adiabatic transformability of biological movement systems.

Adult↗
PubMed1993

A model of the saccadic sensorimotor system of salamanders.

A model of the saccadic system of salamanders on the basis of electrophysiological and anatomical results is presented. The model includes centers found to be significant for the guidance of saccades in these comparatively simple vertebrates. In particular, these are the optic tectum, the bulbar reticular formation and the motor system. The latter consists of two pairs of neck-muscles, an epaxial and a hypaxial one driven by their respective motoneurons. The model includes a visual, a sensori-motor, and a motor level. At the sensory level, the retinal coordinates are transferred to the optic tectum to establish an orthogonal map of visual angles. A secondary visual map of the ipsilateral eye with a pointsymmetrical organization exists in addition. The premotor system of the tectum was modelled according to an ensemble-coding principle. Thus, local activation of the visual map results in recruitment of an appropriate number of tectal premotor units. Simulation of the model reproduces correct metric properties of salamander saccades under varying stimulus presentations.

Animals↗
PubMed1993

Bistability, switches and working memory in a two-neuron inhibitory-feedback model.

It was reported earlier that an inhibitory-feedback network inspired by neostriatal circuitry may exhibit a bistable character and spontaneous switching phenomenon within the neuronal activity. In the presence of noise and external excitation, a few local neurons switch "on" and generate streams of impulses while other neurons remain quiescent. In time, the existing "on" neurons spontaneously switch "off" and other neurons switch "on". In this paper we examine the nature of the bistability and switching phenomenon using a simple model consisting of two mutually inhibitory neurons. For nonspiking neuron model, described by a system of nonlinear differential equations, we present a simple bifurcation analysis, which follows the birth and annihilation of two stable fixed points when model parameters are varied. We show that both nonspiking and spiking models may have two stable states, but only spiking neurons exhibit switching. The mechanism of switching for model spiking neurons, described by an equivalent RC circuit with a number of currents, is analyzed using computer simulations. It is shown that switching can be described by a two-state Markov chain with one parameter, which depends on the set of model physiological parameters, such as duration of afterhyperpolarization (AHP), maximum and the time duration of inhibitory post-synaptic potentials (IPSP's) and amplitude of the neuron noise input. "On" and "off" states of the model can be rapidly changed by localized excitatory input and the network then sustains the pattern of "on" and "off" states. That is, such a network can be used as a programmable memory device.(ABSTRACT TRUNCATED AT 250 WORDS)

Action Potentials↗
PubMed1993

A diffusion model of a neuron and neural nets.

In the paper a diffusion model of a neuron is treated. A new, less restrictive than usually, condition of applicability of a diffusion model is presented. As a result the point-process-to-point-process model of a neuron is obtained, which produces an output signal of the same kind as the accepted input signals.

Action Potentials↗
PubMed1993

A neural model of the dynamic activation of memory.

We study an Attractor Neural Network that stores natural concepts, organized in semantic classes. The concepts are represented by distributed patterns over a space of attributes, and are related by both semantic and episodic associations. While semantic relations are expressed through an hierarchical coding over the attribute space, episodic links are realized via specific synaptic projections. Due to dynamic thresholds expressing neuronal fatigue, the network's behavior is characterized by convergence toward the concept patterns on a short time scale, and by transitions between the various patterns on a longer time scale. In its baseline, undamaged state, the network manifests semantic, episodic, and random transitions, and demonstrates the phenomenon of priming. Modeling possible pathological changes, we have found that increasing the 'noise' level or the rate of neuronal fatigue decreases the frequency of semantic transitions. When neurons characterized by large synaptic connectivity are deleted, semantic transitions decay before the episodic ones, in accordance with the findings in patients with Alzheimer's disease.

Alzheimer Disease↗
PubMed1993

Emergence of orientation selective simple cells simulated in deterministic and stochastic neural networks.

The processing of visual data in area 17 of the mammalian cortex is mainly performed by cells with receptive fields which are tuned to different orientations of input stimuli. The mechanisms underlying the emergence of receptive field properties of orientation selective cells are not well understood up to now. Recently, some models for the prenatal development of the receptive fields of orientation selective simple cells have been proposed, which emerge in neural networks trained by Hebb type unsupervised learning rules. These models, however, use different network architectures and are restricted to the case of identical input neurons. In this work, a biologically motivated neural network model with a general architecture is presented. It is trained with a Hebb type updating rule and with uncorrelated input. The input neurons are identified with retinal ganglion cells and exhibit mature Mexican hat type receptive fields. If the receptive fields of the input neurons have identical properties (deterministic model), a set of parameter domains is found, which characterize different kinds of receptive field maturation behaviour of the network. Results obtained by other authors with similar models are contained in this description as special cases. In addition, the more general and rarely investigated stochastic model, where random variations of the parameters describing the receptive fields of the input neurons occur, is investigated. A high sensitivity of the network against these random variations is obtained. In case of large variations of receptive field parameters of the ganglion cells, a qualitatively new kind of maturation behaviour appears. A significant part of the synaptic connections from ganglion cells to the cortical cell is removed and small simple cell receptive fields with only few lobes emerge. The stochastic model is found to provide a better description of the size, scatter and structure of receptive fields present in biological systems, than the deterministic model.

Animals↗
PubMed1994

Temporal pattern sensitivity of long-term potentiation in hippocampal CA1 neurons.

High-frequency electrical stimulation in the hippocampus leads to an increase in synaptic efficacy that lasts for many hours. This long-term potentiation (LTP) of synaptic transmission is presumed to play a crucial role in learning and memory in the brain. However, the frequency of stimulation generally used to obtain LTP is beyond the normal physiological range of activity of hippocampal neurons. We found that LTP can be induced by an electrical stimulation whose frequency is comparable to that of the naturally occurring firing activity of hippocampal neurons if the stimulating pulse-interval train has a special time structure. In the present experiment, we compared the magnitude of LTP induced by the four types of stimuli which have the same pulse number and the same mean frequency but different time structure in interstimulus intervals. One type of stimuli has regular intervals, and this served as a control stimulus. In the other three types of stimuli, the adjacent interstimulus interval had the following statistical properties: in type 1, their correlations are positive; in type 2, negative; and in type 3, independent. The magnitude of LTP induced by these four types of stimuli showed clear order relationships: type 3/type 1 >> control > type 2. Detailed analysis of the evoked potential during a period of temporal pattern stimulation revealed that the amplitude of the population spikes of repetitive firing, especially of the second and third population spikes, had the same order relationship as the LTP.(ABSTRACT TRUNCATED AT 250 WORDS)

2-Amino-5-phosphonovalerate↗
PubMed1994

Formation of field discontinuities and islands in visual cortical maps.

The representations of visual hemifields in the extrastriate areas of various species exhibit field discontinuities and islands. We propose that these violations of retinotopy are a developmental consequence of the elongated shape of the respective cortical areas. To substantiate this claim, we investigated a model of activity-driven map formation. In agreement with observations, this model yields maps with field discontinuities if the cortical areas exceed a threshold elongation. Moreover, within the same model island representations in the periphery and the area centralis can also be understood. A multistability of the solutions in the model gives a very simple explanation for the observed interindividual variability of maps in cats. The model leads to a prediction of the radial dependence of the areal magnification factor near field discontinuities, which could be accessible for a high precision mapping experiment.

Animals↗
PubMed1994

Abducens nerve responses of the frog during horizontal linear acceleration: data and model.

Abducens nerve responses of frogs were evoked by sinusoidal oscillations on a horizontal linear sled. The depth of modulation of these responses and their phases depended on the orientation of the head with respect to the direction of linear acceleration. Longitudinal acceleration evoked abducens responses that consisted of two discharge maxima per stimulus cycle. At consecutively more oblique head orientations, one of these two discharge maxima increased and the other decreased. Transverse accelerations evoked abducens responses that consisted of only one discharge maximum per stimulus cycle. Removal of the labyrinthine organs on one side abolished these responses in the contralateral abducens nerve but did not affect the responses in the ipsilateral abducens nerve. The latter result indicates that the responses in each abducens nerve originate from hair cells on the contralateral utricle. The experimentally determined modulation and phase values and their dependence on the orientation angle of the acceleration vector were used to characterize a functional cluster of hair cells located medially with respect to the striola in a fan-like sector on the utricle ('lateral rectus fan'). Parameters of this fan were used to develop a model that satisfactorily simulates the recorded abducens responses. This model predicts a majority of afferents with excitatory and a few afferents with inhibitory contributions to the abducens nerve responses. The phasic response components of about 90% of these afferents are larger than their tonic response components.

Abducens Nerve↗
PubMed1994

Bistability and the dynamics of periodically forced sensory neurons.

Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time distributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on non-homogeneous point processes. Apart from looking at models which form the backbone of excitable models, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information.

Acoustic Stimulation↗
PubMed1994

Synapses on axon collaterals of pyramidal cells are spaced at random intervals: a Golgi study in the mouse cerebral cortex.

In this study we investigated the arrangement of synapses on local axon collaterals of Golgi-stained pyramidal neurons in the mouse cerebral cortex. As synaptic markers we considered axonal swellings visible at high magnification under the light microscope. Such axonal swellings coincide with synaptic boutons, as has been demonstrated in a number of combined light and electron microscopic studies. These studies also indicated that, in most cases, one bouton corresponds precisely to one synapse. Golgi-impregnated axonal trees of 20 neocortical pyramidal neurons were drawn with a camera lucida. Axonal swellings were marked on the drawings. Most swellings were 'en passant'; occasionally, they were situated at the tip of short, spine-like processes. On axon collaterals, the average interval between swellings was 4.5 microns. On the axonal main stem, the swellings were always less densely packed than on the collaterals. Statistical analysis of the spatial distribution of the swellings did not reveal any special patterns. Instead, the arrangement of swellings on individual collaterals follows a Poisson distribution. Moreover, the same holds to a large extent for the entire collection of pyramidal cell collaterals. This suggests that a single Poisson process, characterized by only one rate parameter (number of synapses per unit length), describes most of the spatial distribution of synapses along pyramidal cell collaterals. These findings do not speak in favour of a pronounced target specificity of pyramidal neurons at the synaptic level. Instead, our results support a probabilistic model of cortical connectivity.

Animals↗
PubMed1994

A method for calculating the spectral response of a hair cell to a pure tone.

Using Corey and Hudspeth's hair cell transducer function and that of Assad and Corey as models, the output of the haircell is calculated for an input of a single tone. These results are then compared with experimental data obtained by Hubbard et al. (1979) from guinea pig cochlear. The theoretical and experimental data are found to be similar for low to moderate sound pressure levels.

Acoustic Stimulation↗
PubMed1994

Stereo vision by self-organization.

We propose a new algorithm for stereoscopic depth perception, where the depth map is the momentary state of a dynamic process. To each image point we assign a set of possible disparity values. In a dynamic process with competition and cooperation, the correct disparity value is selected for each image point. Therefore, we solve the correspondence problem by a dynamic, self-organizing process, the structure of which shows analogies to the human visual system. The algorithm can be implemented in a massive parallel manner and yields good results for either artificial or natural images.

Algorithms↗
PubMed1994

A theoretical model of phase transitions in the human brain.

An experiment using a multisensor SQUID (superconducting quantum interference device) array was performed by Kelso and colleagues (1992) which combined information from three different sources: perception, motor response, and brain signals. When an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency in both motor behavior and brain signals. Qualitatively analogous transitions are known for physical and biological systems such as changes in the coordination of human hand movements (Kelso 1981, 1984). In this paper we develop a theoretical model based on methods from the interdisciplinary field of synergetics (Haken 1983, 1987) and nonlinear oscillator theory that reproduces the main experimental features very well and suggests a formulation of a fundamental biophysical coupling.

Acoustic Stimulation↗
PubMed1994

Size constancy, depth constancy and vertical disparities: a further quantitative interpretation.

The size and depth constancies considered here operate only at near distances (< about 2 m) in a static stimulus situation with vergence as the only cue to distance. The innervation of the extraocular muscles, as evidenced by the corollary discharge, provides information about the vergence of the eyes and hence about the egocentric distance both for symmetrical and asymmetrical vergences. Size and depth constancies are regarded as the first and second stages of a linked two-stage process. In the lateral geniculate nuclei compensatory adjustments are separately applied to each retinal image as they are received from the two eyes. The modified ocular images, with their associated vertical and horizontal disparities, now provide synaptic inputs to binocularly activated cells in the visual cortex. Then, by a process akin to the induced effect, cortical cells with geniculate afferents with vertical disparities will have their outputs expressed in terms of horizontal disparities. The horizontal disparity outputs of these cortical cells are then further multiplied by the outputs from cortical cells with geniculate afferents with horizontal disparities. It is this second multiplicative process that brings about the quadratic relationship between horizontal retinal disparity and egocentric distance. The proposed mechanisms involve the known ability of the visual system to detect and respond to vertical as well as horizontal disparities and provide a definite role for the induced effect in the perceptual process. The above neural model is based on fairly simple equations that give a remarkably adequate description of the operation of the two constancies.

Cybernetics↗
PubMed1994

Directional operations in the motor cortex modeled by a neural network of spiking neurons.

A neural network with realistically modeled, spiking neurons is proposed to model ensemble operations of directionally tuned neurons in the motor cortex. The model reproduces well directional operations previously identified experimentally, including the prediction of the direction of an upcoming movement in reaching tasks and the rotation of the neuronal population vector in a directional transformation task.

Action Potentials↗
PubMed1994

Abnormal motor patterns in the framework of the equilibrium-point hypothesis: a cause for dystonic movements?

Until now, the equilibrium-point hypothesis (lambda model) of motor control has assumed nonintersecting force-length characteristics of the tonic stretch reflex for individual muscles. Limited data from animal experiments suggest, however, that such intersections may occur. We have assumed the possibility of intersection of the characteristics of the tonic stretch reflex and performed a computer simulation of movement trajectories and electromyographic patterns. The simulation has demonstrated, in particular, that a transient change in the slope of the characteristic of an agonist muscle may lead to temporary movement reversals, hesitations, oscillations, and multiple electromyographic bursts that are typical of movements of patients with dystonia. The movement patterns of three patients with idiopathic dystonia during attempts at fast single-joint movements (in the elbow, wrist, and ankle) were recorded and compared with the results of the computer simulation. This approach considers that motor disorders in dystonia result from faulty control patterns that may not correlate with any morphological or neurophysiological changes. It provides a basis for the high variability of dystonic movements. The uniqueness of abnormal motor patterns in dystonia, that precludes statistical analysis across patients, may result from subtle differences in the patterns of intersecting characteristics of the tonic stretch reflex. The applicability of our analysis to disordered multijoint movement patterns is discussed.

Adult↗