Correlograms & ISI#

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import pynapple as nap
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
custom_params = {"axes.spines.right": False, "axes.spines.top": False}
sns.set_theme(style="ticks", palette="colorblind", font_scale=1.5, rc=custom_params)

Let’s generate some data. Here we have two neurons recorded together. We can group them in a TsGroup.

ts1 = nap.Ts(t=np.sort(np.random.uniform(0, 1000, 2000)), time_units="s")
ts2 = nap.Ts(t=np.sort(np.random.uniform(0, 1000, 1000)), time_units="s")
epoch = nap.IntervalSet(start=0, end=1000, time_units="s")
ts_group = nap.TsGroup({0: ts1, 1: ts2}, time_support=epoch)
print(ts_group)

  Index    rate
-------  ------
      0       2
      1       1

Autocorrelograms#

We can compute their autocorrelograms meaning the number of spikes of a neuron observed in a time windows centered around its own spikes. For this we can use the function compute_autocorrelogram. We need to specifiy the binsize and windowsize to bin the spike train.

autocorrs = nap.compute_autocorrelogram(
    group=ts_group, binsize=100, windowsize=1000, time_units="ms", ep=epoch  # ms
)
print(autocorrs)

           0     1
-0.9  0.9875  1.14
-0.8  0.9750  1.10
-0.7  1.0525  0.97
-0.6  1.1150  0.98
-0.5  0.9575  1.05
-0.4  1.0150  1.10
-0.3  0.9850  0.95
-0.2  1.0500  0.84
-0.1  1.0350  1.07
 0.0  0.0000  0.00
 0.1  1.0350  1.07
 0.2  1.0500  0.84
 0.3  0.9850  0.95
 0.4  1.0150  1.10
 0.5  0.9575  1.05
 0.6  1.1150  0.98
 0.7  1.0525  0.97
 0.8  0.9750  1.10
 0.9  0.9875  1.14

The variable autocorrs is a pandas DataFrame with the center of the bins for the index and each column is an autocorrelogram of one unit in the TsGroup.

Cross-correlograms#

Cross-correlograms are computed between pairs of neurons.

crosscorrs = nap.compute_crosscorrelogram(
    group=ts_group, binsize=100, windowsize=1000, time_units="ms"  # ms
)
print(crosscorrs)

          0
          1
-0.9  0.885
-0.8  0.930
-0.7  1.045
-0.6  0.895
-0.5  1.020
-0.4  1.045
-0.3  1.020
-0.2  0.970
-0.1  0.995
 0.0  0.950
 0.1  0.990
 0.2  0.885
 0.3  1.030
 0.4  0.920
 0.5  1.060
 0.6  0.925
 0.7  1.110
 0.8  1.040
 0.9  0.865

Column name (0, 1) is read as cross-correlogram of neuron 0 and 1 with neuron 0 being the reference time.

Event-correlograms#

Event-correlograms count the number of event in the TsGroup based on an event timestamps object.

eventcorrs = nap.compute_eventcorrelogram(
    group=ts_group, event = nap.Ts(t=[0, 10, 20]), binsize=0.1, windowsize=1
    )
print(eventcorrs)

             0         1
-0.9  0.000000  0.000000
-0.8  0.000000  0.000000
-0.7  0.000000  2.777778
-0.6  0.000000  0.000000
-0.5  0.000000  2.777778
-0.4  0.000000  0.000000
-0.3  0.000000  2.777778
-0.2  0.000000  0.000000
-0.1  0.000000  0.000000
 0.0  1.282051  0.000000
 0.1  0.000000  2.777778
 0.2  2.564103  0.000000
 0.3  0.000000  2.777778
 0.4  2.564103  2.777778
 0.5  1.282051  0.000000
 0.6  2.564103  2.777778
 0.7  0.000000  0.000000
 0.8  0.000000  0.000000
 0.9  0.000000  0.000000

Interspike interval (ISI) distribution#

The interspike interval distribution shows how the time differences between subsequent spikes (events) are distributed. The input can be any object with timestamps. Passing epochs restricts the computation to the given epochs. The output will be a dataframe with the bin centres as index and containing the corresponding ISI counts per unit.

isi_distribution = nap.compute_isi_distribution(
    data=ts_group, bins=10, epochs=epoch
    )
print(isi_distribution)

             0    1
0.361842  1536  511
1.085429   349  266
1.809016    86  107
2.532603    23   56
3.256189     2   28
3.979776     3   17
4.703363     0    5
5.426950     0    4
6.150537     0    4
6.874123     0    1

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for col in isi_distribution.columns:
    plt.bar(
        isi_distribution.index,
        isi_distribution[col].values,
        width=np.diff(isi_distribution.index).mean(),
        alpha=0.5,
        label=col,
        align='center',
        edgecolor='none'
    )
plt.xlabel("ISI (s)")
plt.ylabel("Count")
plt.legend(title="Unit")
plt.show()
../_images/6513334bf7c8d15d5fc65eb21fffaf1b66425320712ed7347bfae4c56832cc27.png

The bins argument allows for choosing either the number of bins as an integer or the bin edges as an array directly:

isi_distribution = nap.compute_isi_distribution(
    data=ts_group, bins=np.linspace(0, 3, 10), epochs=epoch
    )
print(isi_distribution)

            0    1
0.166667  990  274
0.500000  497  213
0.833333  239  149
1.166667  123  114
1.500000   77   73
1.833333   31   46
2.166667   22   32
2.500000    5   29
2.833333   10   15

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for col in isi_distribution.columns:
    plt.bar(
        isi_distribution.index,
        isi_distribution[col].values,
        width=np.diff(isi_distribution.index).mean(),
        alpha=0.5,
        label=col,
        align='center',
        edgecolor='none'
    )
plt.xlabel("log ISI (s)")
plt.ylabel("Count")
plt.legend(title="Unit")
plt.show()
../_images/ab578f42eed5ab9abbea80d7da4c5ccf0f561d8f93d15d96903d19009b17c1f2.png

The log_scale argument allows for applying the log-transform to the ISIs:

isi_distribution = nap.compute_isi_distribution(
    data=ts_group, bins=10, log_scale=True, epochs=epoch
    )
print(isi_distribution)

             0    1
-9.334036    1    1
-8.143184    0    1
-6.952332    7    2
-5.761480   22    5
-4.570628   51    9
-3.379777  164   41
-2.188925  454  124
-0.998073  789  308
 0.192779  485  394
 1.383631   26  114

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for col in isi_distribution.columns:
    plt.bar(
        isi_distribution.index,
        isi_distribution[col].values,
        width=np.diff(isi_distribution.index).mean(),
        alpha=0.5,
        label=col,
        align='center',
        edgecolor='none'
    )
plt.xlabel("log ISI (s)")
plt.ylabel("Count")
plt.legend(title="Unit")
plt.show()
../_images/133c65fb5af483a7da2e39fe16442282e26032524a31b1645d35e061bec1ddf3.png