Biomedical Engineering Reference
In-Depth Information
4. To establish significance, peaks obtained in the cross-
correlation of interest should be compared with peaks derived
from time-shuffled data.
Cross-correlation measures the distance in time between the
spikes of one neuron and the spikes of another neuron. If the
spikes of one neuron tend to occur at a fixed time relative to
the spikes of another neuron, a peak in the cross-correlogram
should occur. Though the algorithm is simple, it is computation-
ally intensive, and in MATLAB, relies on the compiled function
xcorr:
t1 = sort(rand(1, 100)
*
10); % random timestamps,10s @ 10 Hz
t2 = sort(rand(1, 100)
*
10); % random timestamps,10s @
10 Hz
edges = 0:0.001:10; % 1 ms bins
t1_binned = histc(t1, edges); % timestamps to binned
t2_binned = histc(t2, edges); % timestamps to binned
xc = xcorr(t1\_binned, t2_binned); % actual cross-
correlation
xc = xc(round(length(xc)/2)-200:round(length(xc)/2)+200);
In the above sample code, two random spike trains are gen-
erated lasting 10 s long, firing at approximately 10 Hz. In order
for the cross-correlation to be performed, the spike trains must be
binned; 1 ms bins is standard for visualizing short-latency synaptic
interactions. In MATLAB, histc is a compiled routine that rapidly
bins data. The xcorr command computes the cross-correlation.
As we are interested only in short latency interactions, the cross-
correlation is only kept at latencies
200 ms.
For sessions from behaving animals (tens of minutes to
hours), it is preferable to select epochs of interest on the order of
tens of seconds for cross-correlation analysis. This selection helps
in both computing the random cross-correlation, and in deter-
mining confidence intervals via time shuffling.
We performed cross-correlation analysis on neural data
from prefrontal and motor cortices during delayed-response
performance. In our example data set of 21 neurons, we find
rare evidence for synaptic interactions in rodent frontal cortex.
One pair of dmPFC neurons (4B and C) had a peak and a
trough at 2-4 ms (
Fig. 7.4D
), hinting that this pair of neurons
are monosynaptically connected or driven by common input. An
examination of their response properties reveals that both cells
become inhibited as animals initiate lever presses, and stay inhib-
ited until after responses are complete and reward acquisition
begins. These interactions provide a glimpse of how information
might flow through the rodent dmPFC.
To determine which neurons had significant cross-correlation
peaks, we calculated cross-correlation functions from time-
shuffled data and compared the ratios of peak sizes for the
±
