Correlated Neuronal Activity: High- and Low-Level Views - Computational Neuroscience: A Comprehensive Approach - page 361

discussion, especially after the work of Softky and Koch [76], who pointed out that
although the CV ISI of typical cortical neurons is close to 1, this number should be
much lower for an integrator that adds up many small contributions in order to fire,
especially at high output rates. However, their arguments applied in the absence of
inhibition, and later work [82, 73] showed that including incoming inhibitory spikes
produces higher CV ISI values even in integrator models without any built-in coinci-
dence detection mechanisms [2-50] or similar nonlinearities [58-64], a result that
is consistent with early stochastic models [41, 84]. So-called 'balanced' models,
in which inhibition is relatively strong, typically bring the CV ISI to the range be-
tween 0.5 and 1 [73, 82], which is still lower than reported from recorded data [25,
75-78]. Other intrinsic factors have also been identified as important in determin-
ing spike train variability; for instance, combining the proper types of conductances
[11], tuning the cellular parameters determining membrane excitability [47, 82], and
bistability [92].
However, several lines of evidence point to correlations in the conductances (or
currents) that drive a neuron as a primary source of variability. First, correlated fir-
ing is ubiquitous. This has been verified through a variety of techniques, including
in vivo experiments in which pairs of neurons are recorded simultaneously. The
widths of the corresponding cross-correlograms may go from a few to several hun-
dred milliseconds [43-77], so they may be much longer than the timescales of com-
mon AMPA and GABA-A synapses [27]. Second, in vitro experiments in which
neurons are driven by injected electrical current suggest that input correlations are
necessary to reproduce the firing statistics observed in vivo [28, 29, 30, 78]. This
is in line with the suggestion that fluctuations in eye position are responsible for a
large fraction of the variability observed in primary visual neurons, because they
provide a common, correlating signal [46]. Third, this also agrees with theoretical
studies [33, 67]; in particular with results for the non-leaky integrate-and fire model
showing that the CV ISI depends strongly on the correlation time of the input [69].
In addition, similar analyses applied to the traditional leaky integrate-and-fire model
reveal the same qualitative dependencies [69]. This, in fact, can be seen in Figure
12.1 , where the model with leak was used: increases in the synaptic time constants
give rise to longer correlation times and to higher CV ISI values (compare Figures
12.1a and 12.1c), an effect that has nothing to do with the synchronization between
output spike trains. Finally, high variability is also observed in simulation studies
in which network interactions produce synchronized recurrent input [85-89], as in
Figure 12.2.

12.8 Conclusion

The activity of a local cortical microcircuit can be analyzed in terms of at least two
dimensions, its intensity, which is typically measured by the mean firing rates of