Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behaviour. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding implications are still debated. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using 'integrate-and-fire' neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.

Anatomical studies demonstrate that excitatory connections in cortex are not uniformly distributed across a network but instead exhibit clustering into groups of highly connected neurons. The implications of clustering for cortical activity are unclear. We studied the effect of clustered excitatory connections on the dynamics of neuronal networks that exhibited high spike time variability owing to a balance between excitation and inhibition. Even modest clustering substantially changed the behavior of these networks, introducing slow dynamics during which clusters of neurons transiently increased or decreased their firing rate. Consequently, neurons exhibited both fast spiking variability and slow firing rate fluctuations. A simplified model shows how stimuli bias networks toward particular activity states, thereby reducing firing rate variability as observed experimentally in many cortical areas. Our model thus relates cortical architecture to the reported variability in spontaneous and evoked spiking activity.