The asynchronous state in the cerebral cortex
Center for Molecular and Behavioral Neuroscience, Rutgers University
Cortical circuits can operate in different dynamical regimes. Extra-cellular recordings over the last decade, and recent paired whole-cell recordings in vivo suggest that, under certain conditions, the spike trains of nearby cortical neurons are very weakly correlated. How this type of activity is sustained in the cortex seems mysterious, as both the high connection probability and the large magnitude of the typical mono-synaptic input would seem to lead to the amplification of small synchronous events into globally synchronous network states. We investigated this issue by considering the effect of common input on balanced recurrent neural networks composed of N excitatory and inhibitory binary neurons. Neurons are connected randomly with probability p and receive projections with the same probability from an excitatory external population leading to an average fraction p of shared inputs. Synaptic connections are 'strong', i.e., they scale as ~O(1/sqrt(N)). This has two consequences: a) The excitatory and inhibitory components of the total synaptic input become very large. b) Weak correlations in the activity of the neurons are greatly amplified, leading to strong correlations among these components. Despite of this, we show analytically that, under general conditions, the activity in the network is asynchronous, i.e. the average pair-wise correlation scales as ~O(1/N). This is possible due to a cancellation, not only between the mean excitatory and inhibitory inputs, but also between the large positive terms of the input correlation (arising from common input as well as network amplification of exc-exc and inh-inh correlations) and a large negative term resulting from exc-inh correlations. These exc-inh correlations are the reflection of an internally generated tracking of excitatory activity fluctuations by the inhibitory population. The accuracy and speed of this tracking improves as the network size increases, and it is, in fact, becomes perfect asymptotically. We have tested the predictions of the model at two different levels: (1) Numerical simulations of biophysically plausible cortical circuits confirm that exc-inh tracking underlies weakly synchronized activity in spiking networks. (2) According to the model, both the mean and the variance of the distribution of pair-wise correlations should scale as ~O(1/N). This implies that the distribution of correlations should be 'wide', with approximately equal numbers of positively and negatively correlated pairs. Simultaneous extra-cellular recordings of large populations of cortical neurons in the absence of slow global oscillations (activated state) confirmed this prediction with remarkable accuracy: over many thousands of neuronal pairs, the number of positively and negatively correlated pairs differs by only a few percent, and the standard deviation of the distribution (~0.1) is much larger than the mean (~0.005). Our results characterize theoretically the asynchronous state in strongly-coupled, densely-connected recurrent networks and provide strong experimental evidence that the cortex can operate in a state which is remarkably similar. These results unify a large body of work and provide a foundation for firing rate computation in the cortex.
Last Modified: Nov 28, 2007
Horacio G. Rotstein
h o r a c i o @ n j i t . e d u
Last modified: Thu Jan 29 11:10:02 EST 2009