Filtered and normalized cross-correlation histogram (FNCCH)

Let us consider a reference neuron x and a target neuron y, and let us suppose that we computed the NCCH between x and y. After the NCCH computation, the maximum value (i.e., the peak) is used as a value reflecting the strength of the estimated functional link. If x and y share an excitatory link, this procedure works well (Fig 6A and 6B). On the other hand, when x inhibits y, the inhibitory trough will be discarded in favor of the NCCH peak (Fig 6C), with a misleading excitatory link detection. The CCH shapes are similar also in the correlograms derived from experimental data, although with an even more jagged behavior. Fig 6F and 6G show two examples of detected putative excitatory and inhibitory connections.

Eq (1) gives the mathematical definition of the FNCCH computation that overcomes this problem. We refer to the filtered peak value as entity of the peak. In this way, it is possible to distinguish between peaks and troughs by taking into account the sign. A positive peak is referred to an excitatory links (Fig 6A and 6B), conversely, a negative peak is referred to an inhibitory link (Fig 6D). We implemented and applied also a post-computation filtering procedure to improve the detectability of inhibitory links on noisy spike trains (cf., Supplementary Information, S1 Fig).

The block diagram and pseudocode depicted in Fig 6E show the sequence of operations executed by the FNCCH. The starting point is the first bin containing a spike in the target train. The binning procedure is directly performed on the time stamps. For each couple of neurons, starting from the first spike of the target train, we slide the time stamps of the reference electrode to find the first spike whose correlation window contains the target spike. Then, we continue to move over the target train to build the entire cross-correlogram (for that reference spike). When the correlation window for the reference spike is completed (i.e., when we have counted the number of spikes for all the bin of the target spike train), we move to the next spike of the reference train, and re-iterate the procedure starting from the first target spike into the correlation window, centered at the current reference spike. Then, we normalize the CC and repeat all the aforementioned operations for the other electrodes. Exploiting the symmetry of the CC function we consider only half of the electrodes for the computation. Moreover, for each pair, we select, as target train, the one with the smallest number of spikes to reduce the number of operations. Once the NCCH is obtained, we apply the filtering operation described by Eq (1) to compute the FNCCH values. Finally, we take the maximum absolute value as estimation of the correlation strength between the two electrodes. If it is negative, the found connection is considered a putative inhibitory link, otherwise is considered an excitatory one.