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  0.9650  0.95
-0.8  1.0775  0.98
-0.7  0.9000  0.94
-0.6  1.0375  0.99
-0.5  0.9675  0.98
-0.4  1.0375  0.95
-0.3  0.9050  0.98
-0.2  1.0175  0.98
-0.1  1.0500  0.99
 0.0  0.0000  0.00
 0.1  1.0500  0.99
 0.2  1.0175  0.98
 0.3  0.9050  0.98
 0.4  1.0375  0.95
 0.5  0.9675  0.98
 0.6  1.0375  0.99
 0.7  0.9000  0.94
 0.8  1.0775  0.98
 0.9  0.9650  0.95

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  1.025
-0.8  1.090
-0.7  1.030
-0.6  0.895
-0.5  1.030
-0.4  1.055
-0.3  1.000
-0.2  1.035
-0.1  1.075
 0.0  0.985
 0.1  0.950
 0.2  1.090
 0.3  1.080
 0.4  0.975
 0.5  0.930
 0.6  1.070
 0.7  0.955
 0.8  0.995
 0.9  1.080

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  1.801802  0.000000
-0.8  0.000000  0.000000
-0.7  5.405405  3.174603
-0.6  0.000000  0.000000
-0.5  3.603604  0.000000
-0.4  0.000000  0.000000
-0.3  1.801802  0.000000
-0.2  1.801802  3.174603
-0.1  0.000000  0.000000
 0.0  0.000000  0.000000
 0.1  1.801802  0.000000
 0.2  0.000000  3.174603
 0.3  0.000000  0.000000
 0.4  1.801802  0.000000
 0.5  1.801802  0.000000
 0.6  0.000000  0.000000
 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
0.292762  1375  436
0.877336   424  248
1.461909   136  143
2.046483    49   76
2.631056    11   41
3.215630     2   25
3.800204     0   14
4.384777     0    8
4.969351     2    7
5.553924     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()

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  970  285
0.500000  498  189
0.833333  248  147
1.166667  139  105
1.500000   74   86
1.833333   31   54
2.166667   24   37
2.500000    8   25
2.833333    4   18

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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()

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
-7.180847    5    2
-6.239096    8    6
-5.297344   21    3
-4.355592   55    8
-3.413840  129   36
-2.472089  281   73
-1.530337  500  165
-0.588585  664  289
 0.353166  318  320
 1.294918   18   97

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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()