The spatial structure of correlated neuronal variability
Shared neural variability is ubiquitous in cortical populations. While this variability is presumed to arise from overlapping synaptic input, its precise relationship to local circuit architecture remains unclear. We combine computational models and in vivo recordings to study the relationship between the spatial structure of connectivity and correlated variability in neural circuits. Extending the theory of networks with balanced excitation and inhibition we find that spatially localized
... l projections promote weakly correlated spiking, but broader lateral projections produce a distinctive spatial correlation structure: Nearby neuron pairs are positively correlated, pairs at intermediate distances are negatively correlated and distant pairs are weakly correlated. This nonmonotonic dependence of correlation on distance is revealed in a new analysis of recordings from superficial layers of macaque primary visual cortex. Our findings show that incorporating distance-dependent connectivity improves the extent to which balanced network theory can explain correlated neural variability. Early theoretical studies deduced that variable spiking activity could arise through a balancing of strong, yet opposing, excitatory and inhibitory synaptic inputs 5,6 . Expanding on this conjecture, van Vreeswijk and Sompolinsky 7 showed that networks of recurrently coupled model neurons robustly create a state where strong excitation is approximately balanced by inhibition, creating a push-pull dynamic that generates irregular spiking activity. More recently, balanced networks have been implicated in theories of optimal coding 8 , working memory 9 , and stimulus tuning 10 . Numerous experimental studies have established that excitation is often approximately balanced by inhibition in cortical circuits 11, 12, 13, 14, 15, 16, 17 . In sum, balanced networks provide a parsimonious model of the irregular spiking activity observed in cortical circuits. Early balanced network models produced asynchronous activity through sparse connectivity 7,18 . However, several experimental studies reveal that local cortical networks are densely connected, with connection probabilities between nearby neurons sometimes exceeding 40 percent 19, 20, 21, 22 . These data imply substantial overlap between local synaptic inputs, which could, in principle, synchronize cortical networks. However -counter to intuition -balanced networks with dense connectivity show weak spike train correlations 23 . This "asynchronous state" results from the correlated excitatory (e) or inhibitory (i) afferents to neuron pairs being actively cancelled by a strong negative e-i correlation establishing weak correlations even when connectivity is not sparse 23 . Consistent with the predicted asynchronous state, some multi-unit extracellular recordings show noise correlations that are nearly zero on average 24 . However, a majority of population recordings in cortex reveal comparatively large correlations 25, 26 . Several studies suggest that the magnitude of noise correlations is dependent on many factors 27 , including arousal 28 , attention 29 , anesthetic state 23,24,30,31 and cortical layer 32,33 . Finally, while in vivo whole cell recordings reveal strong positive e-e and i-i correlations coexisting with strong e-i correlations 13 , these correlation sources do not always perfectly cancel as predicted by some theoretical models 28 . Taken together, these studies show that cortical circuits can exhibit both weak and moderate noise correlations, at odds with predictions from the current theory of balanced networks 23 . In this study, we generalize the theory of correlations in densely connected balanced networks to include the widely observed dependence of synaptic connection probability on distance 34,21 . We show that spatially broad recurrent projections disrupt the asynchronous state, producing a signature spatial correlation structure: Nearby pairs of neurons are Rosenbaum et al.