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The visual system of lower vertebrates has served as an important testing ground for the mechanisms that generate topographic neuronal connections. During both the outgrowth and the regeneration of the optic nerve, a smoothly ordered map of the retina is formed on its major target, the optic tectum (the retinotectal projection). Experiments performed on this projection have offered support for a variety of mechanisms, including the matching of positional cues in the retina and tectum, the guidance of nerve fibers by interactions between fibers, competition for synaptic space, and the refinement of connections based on neuronal activity. Unfortunately, individual experiments that support any one of these mechanisms have been taken at times as evidence against the involvement of any other mechanism; for example, experiments demonstrating the importance of positional cues have been thought mistakenly to indicate that activity-based interactions are unimportant. Computer simulations, in which multiple, somewhat opposed, mechanisms are allowed to operate in concert demonstrate that such a hybrid model is able to generate a full range of experimental results. More importantly, the elimination of any one of the mechanisms renders the model unable to fit entire classes of findings. Thus, the patterning of the retinotectal projection is best viewed as a process in which the optic nerve terminals attempt to satisfy multiple constraints in selecting their target sites.

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The discovery of dendritic spines in the late nineteenth century has prompted nearly 90 years of speculation about their physiological importance. Early observations that bulbous spine heads had very close approximations with the axon terminals of other neurons, confirmed later by ultrastructural study, led to ideas that spines enhance dendritic surface areas for making synaptic contacts. More recent application of cable and core-conductor theory to the anatomical study of spines has raised a number of new ideas about spine function. One important issue was derived from the theoretical treatment of spines as tiny dendrites with much higher input resistances than those of the larger parent dendrites. The high spine-stem resistance results in relative electrical isolation of the spine head; this causes large local depolarizations in the spine head. Several theoretical studies have also shown that if the spine-head input resistances are substantially higher than those of the parent dendrites, spines have the potential for modulating a host of biochemical and biophysical processes that might regulate synaptic efficacy. Empirical studies have documented that spine heads increase rapidly in size after afferent projections have been stimulated electrically and after animals have engaged in a single bout of ecologically important behavioral activity. Such spine head enlargement dilates the portion of the spine stem adjacent to the spine head and this process shortens the spine stem without appreciably altering overall spine length. Theoretical study shows that spine-stem shortening lowers the spine-head input resistance relative to the branch input resistance. This reduction in input resistance can enhance the transfer of electrical charge from the spine head to the parent dendrite, especially when the synaptic conductance is large relative to the spine-head input conductance. Spine-stem shortening also lowers the peak transient membrane potential in the spine head and this factor could delimit Ca2+ influx into the spine head via voltage-dependent Ca2+ channels. The modulation of Ca2+ influx by spine-stem shortening has the potential for regulating Ca2+-sensitive enzymatic activity in the spine head that could affect phosphorylation of cytoskeletal proteins maintaining spine shape and phosphorylation of proteins in the postsynaptic density. Finally, theoretical findings are described that examine the effects of voltage-dependent inward-current channels in the spine head and their ability to amplify the charge transfer due to transmitter-dependent synaptic conductances.

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Recent advances in techniques for chronic recording from multiple extracellular microelectrodes allow simultaneous observation of firings of substantial populations of neurons. We describe a new conceptual representation of cooperative behavior within the observed neuronal population. This representation leads to a new technique for detecting and studying functional neuronal assemblies that are characterized by temporally related firing patterns. The representation may be applied to both dynamic and long-term aspects of cooperativity. The basic idea is to map activity of neurons into motions of particles in a multidimensional Euclidean space. Each neuron is represented by a point particle located in this space. In the simplest version of the mapping, each nerve impulse results in an increment in a "charge" associated with that particle; between firings the charges decay. The force exerted by any such particle on any other is, by analogy with some physical forces, proportional to the product of their charges and may depend on the Euclidean distance separating them. The force on a particle directly affects its velocity rather than its acceleration, as with actual particles in a viscous medium. These forces result in aggregation of those particles that correspond to neurons tending to fire together; separate clusters represent independent cooperative groups. Modification of the charges and forces permits inclusion of inhibitory interactions. Identification, measurement, and display of the resulting clusters can be performed with any of a number of algorithms. We illustrate the application of this approach to populations of computer-simulated neurons having both direct and indirect excitatory coupling.

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Dendritic spines have been increasingly implicated as sites for neuronal plasticity. Earlier-theoretical studies of dendritic-spine function have assumed passive membrane, and have consequently predicted that postsynaptic potentials in the dendrite are attenuated when the synapse is located on the spine head rather than on the dendritic shaft. Our studies show that active membrane in the spine head (e.g. voltage-dependent Na+ or Ca2+ channels) can produce amplification rather than attenuation of the postsynaptic potential. The presence and amount of amplification depend on the density of active channels and on the spine-neck resistance. For a given type of spine head, there is an optimal spine-neck resistance; a given change in neck resistance can therefore either increase or decrease the amplitude of postsynaptic potentials. These results support the idea that spines mediate synaptic plasticity and suggest a variety of modulatory mechanisms.

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A number of speculations have been made on the functional role of dendritic spines. Some emphasize that a spine modulates the effect of a chemical synapse on the spine head. Others propose that spines isolate neighboring synapses from each others' effects. Still others suggest that spines play a role in short- or long-term plasticity, while others deny any functional role for spines at all. This paper brings some quantitative calculations to bear on these questions. In contrast to previous studies of the steady-state voltage attenuation in dendrites having spines, our calculations predict the voltage transient throughout a dendrite due to activation of a chemical synapse on a spine-head, causing a time-dependent postsynaptic conductance change associated with a depolarizing reversal potential. We assume passive membrane in the spine and the dendrite. Computations were performed using a compartmental model of a long dendrite and a single spine, having parameters described by Jack et al. (1975). Voltage-divider approximations to the spine-neck were compared with direct compartmental models and with eigenfunction expansions to check the validity of the numerical integrations. In the spine-head, a pronounced transient depolarization is produced, more than twice that predicted by Jack et al. (1975) for steady-state current injection. The EPSP amplitude at the base of the spine was much smaller, and was slightly reduced by placing the synapse on the head of the spine rather than on the dendritic shaft.(ABSTRACT TRUNCATED AT 250 WORDS)

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A pair of neurons exhibiting postinhibitory rebound, if connected through reciprocally inhibitory chemical synapses, will exhibit a stable pattern of alternating bursts. If two such oscillating pairs, of similar but not identical properties are connected by means of an electrical synapse and an inhibitory chemical synapse between two neurons, one in each pair, the burst patterns may drift, may lock in synchrony, may entrain in antiphase, may entrain at an intermediate phase, or may be suppressed in the inhibited pair. The behavior depends on the strengths of the chemical and electrical coupling as well as on the degree of depression at the chemical synapse. There relationships of the motor patterns are illustrated quantitatively through theoretical calculations.

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A model was presented describing the nerve-bundle CAP in terms of its constituent SFAPs. The model has a general structure capable of accommodating a large variety of specific assumptions regarding the nature of the CAP. Using this model, several techniques were presented for estimating the DCV of a nerve bundle. One method, refered to as the 2CAP method, was presented in detail. This method does not require explicit knowledge of the SFAP waveshapes in order to yield an estimate of the DCV, but does require that the CAP be recorded at two sites along the course of the nerve. In order to evaluate the clinical utility of the 2CAP method of DCV analysis, the following factors were studied: reproducibility, sensitivity to temperature and stimulus intensity, and variation within a normal population. The results indicate that the 2CAP method, when controlled for stimulus intensity and temperature, provides a reproducible measure of nerve function with the capacity to distinguish subtle differences in conduction properties of normal human nerves. Further application of this technique to patients with diabetes mellitus indicates that the DCV can demonstrate subtle electrophysiologic abnormality, even in patients with normal conventional nerve conduction studies. Although DCV analysis cannot accurately characterize all types of nerve abnormalities (such as focal nerve lesions), it will likely become a tool for earlier detection and more accurate diagnosis of many nerve diseases, and provide a key to the better understanding of the dynamics of nerve growth, development, damage, healing, and response to treatment.

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A method is described for estimating the distribution of nerve-fiber conduction velocities in a nerve bundle. This method is based on a detailed general model of the nerve bundle compound action potential, which is characterized as a weighted sum of delayed single-fiber action potentials. The non-iterative estimation method is applied to two examples taken from existing literature, demonstrating the similarity of conduction velocity and fiber diameter distributions, sensitivity of the estimate to variations in important model parameters, and applicability to the differentiation of normal and abnormal nerve function.

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A method is presented for estimating nerve fiber conduction velocity distributions from non-invasive measurements of the compound action potential at two distinct locations separated by a known distance along the nerve bundle. This method is based on a model of the compound action potential as a weighted sum of delayed single-fiber action potentials, but does not require explicit knowledge of the single-fiber action potential wave shapes in order to yield a unique estimate of the conduction velocity distribution. Illustrative examples are presented from normal and diseases nerves. This method appears to have clinical applications in the electrophysiological assessment of peripheral nerve function.

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Evoked release of quanta of neurotransmitter is generally treated as a set of homogeneous, stationary Bernoulli trials, hence governed by the binomial distribution. Relaxing the assumptions of uniformity and stationarity leads to a more realistic physiological model of transmitter release but also introduces systematic biases in the moment estimates of the binomial parameters. We derive probability generating functions for quantal release and expressions for the moment estimates of n and p for a generalized model that incorporates temporal variation and nonuniformity in individual release probabilities and in numbers of release sites.

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Numerical parameters for a compartmental model of a neuron can be chosen to conform both to the neuron's structure and to its measured steady-state electrical properties. A systematic procedure for assigning parameters is described that makes use of the matrix of coefficients of the set of differential equations that embodies the compartmental model. The inverse of this matrix furnishes input resistances and voltage attenuation factors for the model, and an interactive modification of the original matrix and its inverse may be used to fit the model to anatomic and electrical measurements.

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1. If a neuron is represented by a network of resistively coupled isopotential regions, the passive flow of current in its dendritic structure and soma is described by a matrix differential equation. The matrix elements are defined in terms of membrane resistances and capacitances and of coupling resistances between adjoining regions. 2. A uniform cylidrical dendrite can be represented by a chain of identical regions. In this case, a closed-form mathematical expression is derived for the voltage attenuation factor of the dendrite at steady state in terms of the ratio of membrane resistance to coupling resistance. A numerical method is given to determine the coupling resistances, which in turn yield a specified attenuation factor. Related expressions are given for a dendrite coupled to a soma. Formulas are also derived for the input resistance in these configurations. 3. For more complicated neuronal structures, matrix manipulations are described which yield values for input resistances in all regions, attenuation factors between all pairs of regions, and values of applied voltages necessary to attain specified steady-state potentials. 4. Dynamic solutions to the differential equation provide voltage transients (PSPs). Comparison of the shape paramenters of these transients with those of experimental or cable-theoretical PSPs establishes the number of regions necessary to achieve a given degree of approximation to the transients predicted by cable theory.

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Present-day techniques of multiple-electrode together with computer-aided separation of impulses arising from different neurons permit the simultaneous recording of nerve-impulse timings in sets of neurons exceeding 20 in number. This in turn makes it feasible to search for functional groups of neurons, defined as subsets that tend to fire in near simultaneity significantly more often than would independent neurons at corresponding mean rates. A statistical technique is described that permits the detection and identification of such functional groups. The method is accretional, based on identification of associated neurons through interative application of a significance test on multiple coincidences of neuronal firings within an observational window. Examples of the operation of the method and indications as to its sensitivity are furnished through computer simulations of neural networks. The entire algorithm may be used as a screening technique to select smaller groups of neurons for cross-correlational and related finer-grained temporal analyses, or it may be used in its own right to detect and characterize functional groups that are not distinguishable by other statistical procedures.

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Recent studies of the mechanism of quantal neurotransmitter release have assumed that the number of quanta released at each stimulation is binomially distributed and have sought to estimate the binomial parameters n and p. Mathematical analysis and computer simulations show that temporal variation in the number of eligible or filled release sites and either spatial or temporal variation in the probability of release at a site can drastically bias such estimates, while the experimental histograms remain statistically indistinguishable from those predicted by the binomial law. Interpretation of the estimates n and p in terms of ultrastructural or physiological characteristics of the nerve terminal is liable to significant error if departures from the binomial assumptions are not suitably assessed.

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