Correlated Neuronal Activity: High- and Low-Level Views - Computational Neuroscience: A Comprehensive Approach - page 346

responses: the spike trains are more irregular; the spikes of a single neuron tend to
appear in clusters. The two timescales show up in the cross-correlogram as a sharp
peak superimposed on a wider one. Figure 12.1c shows what happens when both
synaptic time constants are set to 20 ms. Now the clustering of spikes in individual
spike trains is even more apparent and the cross-correlogram shows a single, wide
peak.
The correlations between conductances parameterize the degree of synchrony a-
mong output responses. When the correlations are 0 the responses are independent
and the cross-correlogram is flat; when the correlations are equal to 1 all neurons
are driven by the exact same signals and thus produce the same spike train — this
is perfect synchrony. Figures 12.1a-12.1c were generated with correlations of 0.2,
whereas Figures 12.1d-12.1f were generated with correlations of 0.5. Notice that
the shapes of the histograms in the top and bottom rows are the same, but the y-
axis scales in the latter are much larger. Larger correlations always produce more
synchrony and larger fluctuations in instantaneous firing rates (continuous traces).
In addition, they may also alter the postsynaptic firing rates, but this effect was in-
tentionally eliminated in Figure 12.1 so that different synchrony patterns could be
compared at approximately equal firing rates.
These examples show that there are at least two important factors determining
the synchronous responses caused by common input: the amount of common input,
which corresponds to the magnitudes of the correlations between conductances, and
the timescales of the input signals, which in this case are determined by synaptic
parameters. Analogously, there are two aspects of the cross-correlation function that
are important, the height of the peak and its width.

12.4 Correlations arising from local network

interactions

Networks of recurrently interconnected neurons may naturally give rise to oscillatory
and synchronous activity at various frequencies; this is a well documented finding
[94-17]. The type of activity generated depends on the network's architecture, on
its inputs, and on single-cell parameters. Here we illustrate this phenomenon with a
highly simplified network with the following properties. (1) Model neurons, excita-
tory and inhibitory, are of the integrate-and-fire type, without any intrinsic oscillatory
mechanisms. (2) Synaptic connections between them are all-to-all and random, with
strengths drawn from a uniform distribution between 0 and a maximum value g max ;
this is both for excitatory and inhibitory contacts. (3) All neurons receive an external
input drive implemented through fluctuating conductances g E ( t ) and g I ( t ) , which are

uncorrelated across neurons.
Figure 12.2 illustrates some of the firing patterns produced by such a network.
For Figure 12.2a the recurrent connections were weak, i.e., g max was small.

The