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.

The Spectro-Temporal Receptive Field (STRF) of an auditory neuron has been introduced experimentally on the base of the average spectro-temporal structure of the acoustic stimuli which precede the occurrence of action potentials (Aertsen et al., 1980, 1981). In the present paper the STRF is considered in the general framework of nonlinear system theory, especially in the form of the Volterra integral representation. The STRF is proposed to be formally identified with a linear functional of the second order Volterra kernel. The experimental determination of the STRF leads to a formulation in terms of the Wiener expansion where the kernels can be identified by evaluation of the system's input-output correlations. For a Gaussian stimulus ensemble and a nonlinear system with no even order contributions of order higher than two, it is shown that the second order cross correlation of stimulus and response, normalized with respect to the spectral contents of the stimulus ensemble, leads to the stimulus-invariant spectro-temporal receptive field. The investigation of stimulus-invariance of the STRF for more general nonlinear systems and for stimulus ensembles which can be generated by nonlinear transformations of Gaussian noise involve the evaluation of higher order stimulus-response correlation functions.

The spectro-temporal sensitivity of auditory neurons has been investigated experimentally by averaging the spectrograms of stimuli preceding the occurrence of action potentials or neural events ( the APES : Aertsen et al., 1980, 1981). The properties of the stimulus ensemble are contained in this measure of neural selectivity. The spectro-temporal receptive field (STRF) has been proposed as a theoretical concept which should give a stimulus-invariant representation of the second order characteristics of the neuron's system function (Aertsen and Johannesma, 1981). The present paper investigates the relation between the experimental and the theoretical description of the neuron's spectro-temporal sensitivity for sound. The aim is to derive a formally based stimulus-normalization procedure for the results of the experimental averaging procedure. Under particular assumptions, regarding both the neuron and the stimulus ensemble, an integral equation connecting the APES and the STRF is derived. This integral expression enables to calculate the APES from the STRF by taking into account the stimulus spectral composition and the characteristics of the spectrogram analysis. The inverse relation, i.e. starting from the experimental results and by application of a formal normalization procedure arriving at the theoretical STRF, is effectively hindered by the nature of the spectrogram analysis. An approximative "normalization" procedure, based on intuitive manipulation of the integral equation, has been applied to a number of single unit recordings from the grassfrog's auditory midbrain area to tonal and natural stimulus ensembles. The results indicate tha spectrogram analysis, while being a useful real-time tool in investigating the spectro-temporal transfer properties of auditory neurons, shows fundamental shortcomings for a theoretical treatment of the questions of interest.

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