The asynchronous state in cortical circuits

Abstract

Correlated spiking is often observed in cortical circuits, but its functional role is controversial. It is believed that correlations are a consequence of shared inputs between nearby neurons and could severely constrain information decoding. Here we show theoretically that recurrent neural networks can generate an asynchronous state characterized by arbitrarily low mean spiking correlations despite substantial amounts of shared input. In this state, spontaneous fluctuations in the activity of excitatory and inhibitory populations accurately track each other, generating negative correlations in synaptic currents which cancel the effect of shared input. Near-zero mean correlations were seen experimentally in recordings from rodent neocortex in vivo. Our results suggest a reexamination of the sources underlying observed correlations and their functional consequences for information processing.

Fig. 1. Effect of shared inputs and correlated inputs on output correlation

(A) Shared excitatory (E, green) or inhibitory (I, red) inputs induce positive correlations in the synaptic currents of two cells (c > 0). (B) Correlation coefficient of synaptic currents c (dashed) and output spikes r_out (circles, count window T = 50 ms) of a postsynaptic pair of integrate-and-fire neurons as a function of the shared input fraction p (21). Each post-synaptic cell received N_E = 250 Poisson input spike trains. (C) Input spike raster (top), synaptic currents (middle) and membrane potentials (bottom) of a post-synaptic pair receiving weakly correlated E inputs (black circle in (E), r_in = 0.025). (D) Whereas correlations between E inputs or between I inputs contribute positively to c, correlations between E and I inputs have a decorrelating effect. (E) Correlations c (dashed) and r_out (circles) as a function of the input spike correlation r_in at fixed p = 0.2. E inputs only: each cell receives N_E = 250 correlated Poisson spike trains (21), E and I inputs: N_I = 220 inhibitory input trains were added with identical statistics and correlations. (F) Same as (C) but for the case with E and I inputs (blue circle in (E), r_in = 0.025). E and I currents are shown separately from the total currents (black and gray).

Fig. 2. Asynchronous activity in a binary recurrent network

(A) Schematic of the network architecture. The shared input fraction is p. (B) Strong coupling produces irregular spiking activity due to a dynamic balance between the large excitatory (E and X) and inhibitory (I) currents to each cell (19, 22). Dashed line represents threshold. (C) Population-averaged correlation coefficients of the firing activity (r‾, open squares), total current (c, filled squares) and current components vs. network size N. Dashed lines show $1∕\sqrt{N}$ and 1/N scaling for comparison. (D) Instantaneous population-averaged activities (transformed to z-scores) of the E, I and X neurons, showing that tracking becomes more accurate with increasing N. Insets show instances of the lag between E and I activities (EI-Lag). Color code as in (B). (E) Population-averaged cross-correlograms (CCGs) of the current components (N = 8192). Color code as in (C). Insets: magnification of the peak of the IE and EI CCGs (bottom) shows that the EI-Lag decreases with N, leading to the decrease in the magnitude and width of the total current CCG (top). (F) Description of the asynchronous self-consistent solution (see text). (G) The histogram of correlations in the network (EE pairs; N = 8192) is wide: σ_r ≫ r‾.

Fig. 3. Cancelation of correlations in a recurrent network of spiking neurons

(A) Raster (top) of 500 E (green) and I (red) neurons in a conductance-based integrate-and-fire network receiving shared independent Poisson inputs (p = 0.2). Bottom curves show tracking of instantaneous population-averaged activities (transformed to z-scores, bin size 3 ms). Average firing rate of E and I cells were 1 and 3.6 spike/s, respectively. (B) Histogram of spike count correlations (black; count window 50 ms) and of jittered spike trains (gray, jitter ± 500 ms (21)). (C) Population-averaged CCGs of the membrane potential containing mostly EPSPs (green) or IPSPs (red) in both cells, or EPSPs for one cell and IPSPs for the other (gold). The black curve is from pairs at resting potential. (D) Peak height of the membrane potential CCG as a function of the mean holding potential of both neurons in the pair. Green and red circles correspond the reversal of inhibition and excitation and the black circle corresponds to rest.

Fig. 4. Distribution of correlations in the rat neocortex in vivo

(A) Raster (top) and instantaneous population activity (bottom) for a population of 100 simultaneously recorded neurons (sorted by rate) during a period of cortical activation (ACT). (B) Histogram of spike count correlations of the population in (A) is wide (σ_r ≫ r‾). The white curve is the mean histogram of the jittered spike trains (jitter ± 200 ms, gray shade 95% confidence interval; count window 50 ms (21)). Insets show average raw cross-correlograms of all negatively (left) and positively (right) significantly correlated pairs (p < 0.01). (C-D) Same as (A-B) for the same population of cells during a period of cortical inactivation (InACT). Histogram of correlations during InACT is biased towards positive values (red). Restricting the analysis to Up-state activity by removing Down-state periods (black brackets in (C), (21)) largely eliminates the positive bias (Up-St, orange). (E) Box-whisker plots showing the distribution of mean correlations across experiments for different conditions. Crosses represent outliers. (F) Median fraction of significantly correlated pairs (p < 0.01, empty bars) and of significantly and negatively correlated pairs (solid bars) across experiments. Error bars represent interquartile range.