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.

SUMMARYAND CONCLUSIONS 1. We reexamine the possibilities for analyzing and interpreting the time course of correlation in spike trains simultaneously and separably recorded from two neurons.2. We develop procedures to quantify and properly normalize the classical joint peristimulus time scatter diagram. These allow separation of the "raw" correlation into components caused by direct stimulus modulations of the single-neuron firing rates and those caused by various types of interaction between the two neurons.3. A newly developed significance test ("surprise") is applied to evaluate such inferences.4. Application of the new procedures to simulated spike trains allowed the recovery of the known circuitry. In particular, it proved possible to recover fast stimulus-locked modulations of "effective connectivity," even if they were masked by strong direct stimulus modulations of individual firing rates. These procedures thus present a clearly superior alternative to the commonly used "shift predictor."5. Adopting a model-based approach, we generalize the classical measures for quantifying a direct intemeuronal connection ("efficacy" and "contribution") to include possible stimuluslocked time variations.6. Application of the new procedures to real spike trains from several different preparations showed that fast' stimulus-locked modulations of "effective connectivity" also occur for real neurons.

Quantitative methods for the study of the statistical properties of spontaneously occurring spike trains from single neurons have recently been presented. Such measurements suggest a number of descriptive mathematical models. One of these, based on a random walk towards an absorbing barrier, can describe a wide range of neuronal activity in terms of two parameters. These parameters are readily associated with known physiological mechanisms.

In a growing class of neurophysiological experiments, the train of impulses ("spikes") produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.

The function of the massive feedback projection from visual cortex to its thalamic relay nucleus has so far eluded any clear overview. This feedback exerts a range of effects, including an increase in the inhibition elicited by moving contours, but the functional logic of the direct connections to the thalamic cells that relay the retinal input to the cortex remains largely unknown. In contrast to its thalamic nucleus, the visual cortex is characterized by cells that are strongly sensitive to the orientation of moving contours. Here we report that when driven by moving oriented visual stimuli the cortical feedback induces correlated firing in relay cells. This cortically induced correlation of relay cell activity produces coherent firing in those groups of relay cells with receptive field alignments appropriate to signalling the particular orientation of the moving contour to the cortex. Synchronization of relay cell firing means that they will elicit temporally overlapping excitatory postsynaptic potentials in their cortical target cells, thus increasing the chance that the cortical cells will fire. Effectively this increases the gain of the input for feature-linked events detected by the cortex. We propose that this feedback loop serves to lock or focus the appropriate circuitry onto the stimulus feature.

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.

No abstract

This paper examines the concept of neuronal assembly as it has appeared in selected portions of the literature. The context is experimental access to real neuronal assemblies in working brains, as made possible by recent technological progress. One current measure of assembly organization is based on correlation of firing among neurons; recent observations show that such correlations can vary rapidly. In this paper, we demonstrate that dynamic firing correlation can be caused either by dynamic changes in neuronal connection strengths or, alternatively, by the effects of an unobserved (large) pool of other neurons. The static connectivity within the pool appears to be important in determining these effects.