Correlated Neuronal Activity: High- and Low-Level Views - Computational Neuroscience: A Comprehensive Approach - page 351

synaptic current is depolarizing and the mean steady-state voltage is near or above
threshold. In this case the main driving force is the drift toward steady state, and input
fluctuations have a small effect on the rate of output spikes [67, 33]. On the other
hand, when the neuron is balanced, both excitation and inhibition are strong, the
mean input current is zero or very small, and the mean steady-state voltage remains
below threshold. However, the neuron may still fire because there are large voltage
fluctuations that lead to random threshold crossings. In this mode, any factor that
enhances the fluctuations will produce more intense firing [67, 32].
There is a subtle but important distinction between mechanisms that may alter in-
put fluctuations. Higher rates should be seen in a balanced neuron if fluctuations
increase without affecting the mean synaptic conductances, as when only the corre-
lations change [67]. But if stronger fluctuations are accompanied by increases in
total conductance, as when both excitatory and inhibitory inputs fire more intensely,
the firing rate may actually decrease [32-22]. In a complex network these effects
may be hard to disentangle.
Figure 12.3 compares the responses of balanced (upper traces) and unbalanced
(lower traces) model neurons [67]. These were driven by excitatory and inhibitory
input spike trains similar to those illustrated in Figure 12.1 . For the balanced neuron
both excitatory and inhibitory synaptic conductances were strong, and the combined
current they generated near threshold was zero. In contrast, for the unbalanced unit
both conductances were weak, but their combined current near threshold was ex-
citatory. The four panels correspond to different correlation patterns in the inputs.
In Figure 12.3a all inputs are independent, so all cross-correlograms are flat. The
voltage traces reveal a typical difference between balanced and unbalanced modes:
although the output rate is approximately the same, the subthreshold voltage of the
balanced neuron is noisier and its interspike intervals are more variable [67, 82].
Figure 12.3b shows what happens when the excitatory inputs fire somewhat syn-
chronously due to common input. The firing rate of the balanced neuron always
increases relative to the response to independent inputs, whereas the rate of the un-
balanced neuron may show either a smaller (although still substantial) increase or a
decrease [13, 60]. Another effect of synchrony is to increase the variability of the
output spike trains, both for balanced and unbalanced configurations [67, 69, 78, 80];
this can be seen by comparing Figures 12.3b and 3d with Figure 12.3a. Correlations
between inhibitory inputs can also produce stronger responses. When the inhibitory
drive oscillates sinusoidally, as in Figure 12.3c, the balanced neuron practically dou-
bles its firing rate compared to no oscillations; in contrast, the unbalanced does not
change.
The balance of a neuron is important in determining its sensitivity to correlations,
but there is another key factor [67]. There are three correlation terms: correlations
between pairs of excitatory neurons, between pairs of inhibitory neurons, and be-
tween excitatory-inhibitory pairs. The first two terms increase the voltage fluctua-
tions but the last one acts in the opposite direction, decreasing them. The total effect
on the postsynaptic neuron is a function of the three terms. In Figure 12.3 d, all
inputs to the model neurons are equally correlated, but the balanced model shows
no change in firing rate. Thus, it is possible to have strong correlations between all