Balanced Synaptic Input Shapes the Correlation between Neural Spike Trains
Figure 3
Pairwise cell statistics in low and high rate synaptic input regimes.
(A) Schematic of low (left) and high (center) states with sample membrane traces. The marginal statistics of both cells are as reported in Figure 2, with a fixed overlap of excitatory and inhibitory pre-synaptic inputs for the cell pair. The input correlation is for membrane traces and
otherwise, in both low and high states. Right: Spike train cross-correlation functions for the firing of the two neurons when receiving correlated input, showing state dependent shaping. (B) Relationship between spike count correlation
for windows of length
and input correlation
, showing linearity for small
and a dependence on
. (C) Output correlation as a function of window size in the high and low states. Asterisks mark the values of
that correspond to the plots in Figure 3B. (D) Ratio of correlations as a function of window size in the high and low states, showing favoring of short timescale synchrony in the high state. For comparison, the lack of correlation shaping for a purely linear neural transfer is indicated. (E) RMS coherence (
) between spike trains showing a decrease in low-frequency coherence and increase in high frequency coherence in the high state. The theoretical results (solid lines) shown in in panels (B) through (E) were derived from a linear response calculation valid in the small
limit (see Methods). Bars denote standard error in (B) through (D). In (B), standard error is smaller than the width of the dots.