Locking of correlated neural activity to ongoing oscillations

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks. Two distinct mechanisms cause time-dependent covariances: the modulation of the susceptibility of single neurons (via the external input and network feedback) and the time-varying variances of single unit activities. For some parameters, the effectively inhibitory recurrent feedback leads to resonant covariances even if mean activities show non-resonant behavior. Our analytical results open the question of time-modulated synchronous activity to a quantitative analysis.Author summary: In network theory, statistics are often considered to be stationary. While this assumption can be justified by experimental insights to some extent, it is often also made for reasons of simplicity. However, the time-dependence of statistical measures do matter in many cases. For example, time-dependent processes are examined for gene regulatory networks or networks of traders at stock markets. Periodically changing activity of remote brain areas is visible in the local field potential (LFP) and its influence on the spiking activity is currently debated in neuroscience. In experimental studies, however, it is often difficult to determine time-dependent statistics due to a lack of sufficient data representing the system at a certain time point. Theoretical studies, in contrast, allow the assessment of the time dependent statistics with arbitrary precision. We here extend the analysis of the correlation structure of a homogeneously connected EI-network consisting of binary model neurons to the case including a global sinusoidal input to the network. We show that the time-dependence of the covariances—to first order—can be explained analytically. We expose the mechanisms that modulate covariances in time and show how they are shaped by inhibitory recurrent network feedback and the low-pass characteristics of neurons. These generic properties carry over to more realistic neuron models.