Donald H. Perkel

Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains.

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected-if dependence is attributed to the trains-the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.

Statistical Signs of Synaptic Interaction in Neurons

The influence of basic open-loop synaptic connections on the firing of simultaneously recorded neurons has been investigated with auto- and cross-correlation histograms, using experimental records and computer simulations. The basic connections examined were direct synaptic excitation, direct synaptic inhibition, and shared synaptic input. Each type of synaptic connection produces certain characteristic features in the cross-correlogram depending on the properties of the synapse and statistical features in the firing pattern of each neuron. Thus, empirically derived cross-correlation measures can be interpreted in terms of the underlying physiological mechanisms. Their potential uses and limitations in the detection and identification of synaptic connections between neurons whose extracellularly recorded spike trains are available are discussed.

Simultaneously Recorded Trains of Action Potentials: Analysis and Functional Interpretation

A new kind of statistical display, the joint peri-stimulus-time scatter diagram, facilitates the analysis and interpretation of two or more simultaneously recorded trains of action potentials. The display is a generalization of the cross correlation and the peri-stimulus-time histogram, and it reflects specific underlying neuronal interactions. The technique yields quantitative measures of interaction in terms of effectiveness of synaptic connections.

Motor Pattern Production in Reciprocally Inhibitory Neurons Exhibiting Postinhibitory Rebound

Pairs of neurons which inhibit each other can produce regular alternating bursts of impulses if they also exhibit postinhibitory rebound (PIR). Computer studies show that stable patterns occur spontaneously in systems of pacemaker neurons with PIR, and can be triggered in systems of nonpacemakers without requiring tonic excitation. The repetition rates of these patterns are determined largely by the PIR parameters. The patterns resist perturbation by phasic synaptic inputs, but can be modulated or turned off by tonic inputs. One pair of PIR neurons can be entrained by another pair with a different repetition rate to produce more complex firing patterns.

Pacemaker Neurons: Effects of Regularly Spaced Synaptic Input

The consequences of inhibitory or excitatory synaptic input between pacemaker neurons were predicted mathematically and through digital-computer simulations, and the predicted behavior was found to occur in abdominal ganglia of Aplysia and in stretch receptors of Procambarus. Discharge patterns under conditions that do not involve interneuronal feedback are characteristic and self-stabilizing. Paradoxically, increased arrival rates of inhibitory input can increase firing rates, and increased excitatory input rates can decrease firing rates.

Mutual Temporal Relationships among Neuronal Spike Trains: Statistical Techniques for Display and Analysis

We describe a statistical technique, the joint peristimulus time (PST) scatter diagram, for the analysis of data from simultaneously recorded neurons subjected to repeated stimulation. Distinguishable features in the scatter diagram are related to effects of the stimulus on the observed neurons and to functional relations among the neurons. Properties of this measure and its variants are described and practical aspects of its application to experimental data are discussed.

Identification of functionally related neural assemblies

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.

Dendritic spines: role of active membrane in modulating synaptic efficacy

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.

Nerve fiber conduction-velocity distributions. I. Estimation based on the single-fiber and compound action potentials

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.

Quantitative methods for predicting neuronal behavior

Abstract The electrical behavior of a nerve cell may be described by a system of ordinary first-order differential equations that approximates the partial differential equation of cable theory. The choice among methods for solving this system depends primarily on the physiological questions that are asked, and secondarily on special properties of the neuron. This paper describes several such methods, some of which are new, that are appropriate for the analysis of different classes of physiological questions. For steady-state current flows, the equations may be treated as linear with constant coefficients, and direct matrix manipulations suffice to predict voltage attenuations and input resistances. A simplifying assumption with respect to synaptic currents furnishes an efficient means for calculating steady-state firing rates in a synaptically coupled neuronal circuit. Voltage transients in such a system can be calculated either through numerical evaluation of the matrix exponential or through a direct eigenfunction expansion. Some ‘active’ or nonlinear properties of the neuron can be included within these formulations. More realistic physiological descriptions of synaptic effects and of time- and voltage-dependent ionic conductances lead to nonlinear equations having time-dependent coefficients. This level of description precludes the use of the more direct solution methods and dictates the use of difference techniques. Adoption of a method such as Runge-Kutta numerical integration in turn allows the incorporation of detailed descriptions of membrane and ionic processes. A discussion is given of the theoretical and practical considerations bearing on the choice of solution method.