Analysis of synchrony (correlations) in neural populations by means of unit-to-aggregate coherence computations

This paper presents a general outline of the mathematical basis of an approach for analysis of population synchrony by means of coherence computations, a demonstration of the use of this approach, and a discussion of the potential utility and limitations of the approach. The coherence function for the pair single-unit activity and population-aggregate activity is studied in the light of theoretical considerations on the superposition of partially correlated unitary activities. The theoretical analysis, as well as computer simulations, indicate that when a subset of units in a population are correlated around some frequency, the unit-to-aggregate coherence function for members of this subset shows, in a wide range of conditions, a clear peak around that frequency (and possibly harmonic peaks), being very low at other frequencies where there is no synchrony. Specifically, the value of the peak coherence at the frequency of synchrony reflects the strength of the unitary correlations and their extent within the population, the numerical size of the population, and the degree of phase concentration for the units of the correlated subset. This value remains substantial, or at least significant, for wide ranges of values of these parameters. In contrast, the unit-to-aggregate coherence function for the remaining uncorrelated units has very low values at all frequencies, and tends to zero in the case of a large population. On the basis of these properties, an approach is presented for analysis of synchrony (correlations) in a neural population, which is simple and efficient, particularly when the population is large in numerical size. This approach utilizes unit-to-aggregate coherence computations for a sample of recorded unitary activities as a means for detecting population synchrony and estimating the extent of synchrony. In addition, this analysis can provide useful information on other characteristics of synchrony, such as the strengths of the unitary correlations. The use of the approach is demonstrated with an example from a study of fast rhythms in inspiratory activities, and other applications are also briefly described. The main advantage of unit-to-aggregate coherence analysis is that by using readily recorded activities, it efficiently identifies correlated units in a population and provides information on characteristics of synchrony, at every frequency within the range of interest.