Contents

Single Unit Data and Spike Trains

Last updated: 2020-12-22 Tags: #Experitments,#Psychopy See also: Generate and Display Grating Stimuli

Background

Data Source

These data were provided courtesy of Dr. Nathan Crowder, Department of Psychology & Neuroscience, Dalhousie University. Data are from 23 mouse primary visual cortex neurons; for simplicity we are going to work with data firstly from only one neuron, then we’ll load data from 3 neurons to get experience working with a larger data set. Note that these are not data from a multielectrode array. Data were recorded from single electrodes that were embedded directly into single neurons, a technique called patch clamping. We have data from multiple neurons because Dr. Crowder’s team painstakingly recorded from several neurons in each of a few animals.

—–PSYO 3505 Assignment 4 cell1

Experimental Design

The experiment involved presenting drifting (oscillating) sine wave gratings to mice while recording from electrodes in the primary visual cortex. The gratings oscillated (drifted) at a speed of 2 Hz. The contrast of the stimuli were varied systematically over ten levels from 4 (virtually no contrast between the brightest and darkest parts of the sine wave grating, which would appear as uniform grey) to 100% (gratings varying between black and white, as in the example grating in the textbook). Contrast is therefore one of the experimental variables; the levels of contrast used were 4, 8, 12, 16, 24, 32, 48, 64, 84, and 100%.

A second variable is condition:the stimuli were presented under 2 experimental conditions: control (CTRL) and adaptation (ADAPT):

In the CTRL condition, each trial began with a 2000 ms blank grey screen, then the oscillating sine wave grating at the trial’s contrast level (see below) for 1000 ms, then 1000 ms blank grey screen. In the ADAPT condition, each trial started with the adaptation stimulus (a 50% contrast sine wave grating for 2000 ms), then the sine wave grating at the trial’s contrast level (see below), then 1000 ms blank grey screen. A total of 8 trials were presented at each contrast level, in each condition. Each trial was 4000 ms in duration, and data were sampled at 1000 Hz, meaning that we have a data point every 1 ms.

—–PSYO 3505 Assignment 4 cell2

Predictions

  • In the control condition, latency to first spike is expected to decrease with increasing contrast.

  • Some primary visual cortex cells are phase sensitive (so-called simple cells), so in response to a drifting sine wave grating they will oscillate between excitation and inhibition at the same temporal frequency of the stimulus (2 Hz in this case).

—–PSYO 3505 Assignment 4 cell3

Single neuron data

Read file and check it

import pandas as pd
import numpy as np
from matplotlib import pyplot as plt

First of all we need define the experiment parameters

# Conditions
cond_labels = ['CTRL', 'ADAPT'] 

# Labels for the levels of stimulus contrast
contr_labels = [4, 8, 12, 16, 24, 32, 48, 64, 84, 100]

# Labels for repetitions (trials)
rep_labels = list(np.arange(1, 8))
num_reps = len(rep_labels)

# Time point labels - each trial is 4000 ms long
time_labels = list(np.arange(4000))

# Stimulus timing
stim_on_time = 2000
stim_off_time = stim_on_time + 1000

adapt_on_time = 0
adapt_off_time = adapt_on_time + 2000

df = pd.read_csv('crowder_1_neuron.csv')

df.head()
neuron time repetition contrast condition spike
0 m6_11 0 1 4 CTRL 0
1 m6_11 1 1 4 CTRL 0
2 m6_11 2 1 4 CTRL 0
3 m6_11 3 1 4 CTRL 0
4 m6_11 4 1 4 CTRL 0 
df.tail()
neuron time repetition contrast condition spike
639995 m6_11 3995 8 100 ADAPT 0
639996 m6_11 3996 8 100 ADAPT 0
639997 m6_11 3997 8 100 ADAPT 0
639998 m6_11 3998 8 100 ADAPT 0
639999 m6_11 3999 8 100 ADAPT 0

By using .unique() methods We can get idea about number of repertition and contrasts

print(df['repetition'].unique())
print(df['contrast'].unique())

[1 2 3 4 5 6 7 8]
[  4   8  12  16  24  32  48  64  84 100]

We want to know number of spikes in DF

len(df[df['spike'] == 1])

1955

Because the data is stored in the data frames, ‘Advanced indexing’ technique can apply here. like if I want to know the repetion 1 Contrast 100 CTRL and spike data I can write code like this :

df[(df['repetition']==1)&(df['contrast']==100)&(df['condition']=='CTRL')&(df['spike']==1)]
neuron time repetition contrast condition spike
288797 m6_11 797 1 100 CTRL 1
290153 m6_11 2153 1 100 CTRL 1
290362 m6_11 2362 1 100 CTRL 1
290420 m6_11 2420 1 100 CTRL 1
290439 m6_11 2439 1 100 CTRL 1
290473 m6_11 2473 1 100 CTRL 1
290500 m6_11 2500 1 100 CTRL 1
290557 m6_11 2557 1 100 CTRL 1
290633 m6_11 2633 1 100 CTRL 1
290657 m6_11 2657 1 100 CTRL 1
290715 m6_11 2715 1 100 CTRL 1
290759 m6_11 2759 1 100 CTRL 1
290897 m6_11 2897 1 100 CTRL 1
291050 m6_11 3050 1 100 CTRL 1

Visualization

This is a complex experiment so we’ll need lots of subplots to see all trials for all contrast levels, and both conditions. Here we can using Raster plots show the experitement

fig = plt.figure(figsize=[12,18])

subplot_counter = 1 

for contr in contr_labels:
    for cond in cond_labels:

        ax = fig.add_subplot(len(contr_labels), len(cond_labels), subplot_counter)

        # Show adaptation grating at 50% contrast
        if cond == 'ADAPT':
            plt.axvspan(0, stim_on_time-1, alpha=0.5, color='grey')

        # shading indicates stimulus on period
        plt.axvspan(stim_on_time, stim_off_time, alpha=contr/100, color='grey')

        for rep in rep_labels:
            spike_times = df[(df['repetition']==rep)&(df['contrast']==contr)&(df['condition']==cond)&(df['spike']==1)]['time']
            plt.vlines(spike_times, rep-1, rep);

        # Pretty formatting
        plt.xlim([0, max(time_labels)+1])
        plt.ylim([0, len(rep_labels)])
        plt.title(cond + ' ' + str(contr) + '% contrast')
        plt.xlabel('Time (ms)')
        plt.ylabel('Repetition',)
        plt.yticks([x + 0.5 for x in range(num_reps)], [str(x + 1) for x in range(num_reps)], size=8) 
        plt.tight_layout()
        subplot_counter += 1
        
plt.show()
../_images/single_23_0.png

Also, we can draw peri-stimulus time histogram (PTSH) plot rather than rasters. By summing the number of spikes in short time bins, PSTHs allow us to visualize when the neuron is most likely to spike.

hist_bin_width = 50 
time_bins = np.arange(0, max(time_labels), hist_bin_width)

fig = plt.figure(figsize=[12,18])

subplot_counter = 1 

for contr in contr_labels:
    for cond in cond_labels:

        ax = fig.add_subplot(len(contr_labels), len(cond_labels), subplot_counter)

        # Show adaptation grating at 50% contrast
        if cond == 'ADAPT':
            plt.axvspan(0, stim_on_time-1, alpha=0.5, color='grey')
            
        # shading indicates stimulus on period
        plt.axvspan(stim_on_time, stim_off_time, alpha=contr/100, color='grey')
        spike_times = df[(df['contrast']==contr)&(df['condition']==cond)&(df['spike']==1)]['time']
        spike_count, bins = np.histogram(spike_times, bins=time_bins)
        spike_count = spike_count/(num_reps * hist_bin_width)
        plt.bar(bins[:-1], spike_count,width=hist_bin_width)
        
        # Pretty formatting
        plt.xlim([0, max(time_labels)+1])
        plt.ylim([0, 0.05])
        plt.title(cond + ' ' + str(contr) + '% contrast')
        plt.xlabel('Time (ms)')
        plt.ylabel('Spike Probability')
        
        plt.tight_layout()
        subplot_counter += 1
        
plt.show()
../_images/single_25_0.png

Next we try to plot heat map

Like a PSTH, the heat map has time on the x axis, and plots the probability of spikes at each time point. However, the heat maps a more condensed, information-rich, and efficient version of the PSTHs: rather than needing 10 plots to show the histograms for all 10 levels of intensity.

—Neural Data Science Heat Maps, Interpolation, and Colour Map Choice

Using nested list comprehension to create two columns: condition and contrast

condition_labels = pd.DataFrame([[cond, contr] for cond in cond_labels for contr in contr_labels ],columns=['condition', 'contrast'])

condition_labels.head()
condition contrast
0 CTRL 4
1 CTRL 8
2 CTRL 12
3 CTRL 16
4 CTRL 24 
psth_df_list=[]
for cond in cond_labels:
    for contr in contr_labels:
        spike_times = df[(df['contrast']==contr)&(df['condition']==cond)&(df['spike']==1)]['time']
        spike_count, bins = np.histogram(spike_times, bins=time_bins)
        psth_df_list.append(spike_count) 

# Combine labels and data
psth_df = pd.concat([condition_labels, pd.DataFrame(psth_df_list)], axis=1)     

psth_df = psth_df.set_index(['condition','contrast'])

Before the final plot, we need check the dataframe

psth_df.head()
0 1 2 3 4 5 6 7 8 9 ... 69 70 71 72 73 74 75 76 77 78
condition contrast
CTRL 4 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 1 0 1 0 0 0 ... 0 0 0 0 0 0 0 2 0 0
12 0 1 0 2 0 0 0 0 1 0 ... 0 0 0 1 0 0 0 0 0 0
16 0 0 0 1 0 2 0 0 0 0 ... 0 0 0 0 0 1 0 0 0 0
24 0 0 1 0 1 0 0 0 0 0 ... 0 0 0 0 0 1 0 0 0 0

5 rows × 79 columns

fig = plt.figure(figsize=[15,30])
subplot_counter = 1

for cond in cond_labels:
    
    ax = fig.add_subplot(1, 2, subplot_counter)
    plt.imshow(psth_df.loc[cond],origin='lower',cmap='hot',interpolation='bilinear',aspect =5)
    
    plt.title(cond)
    xticks = range(0, len(time_bins), 10)
    plt.xticks(xticks,
               time_bins[xticks])
    plt.xlabel('Time (ms)')
    plt.yticks([x for x,y in enumerate(contr_labels)], 
               [x for x in contr_labels])
    if cond == cond_labels[0]:
        plt.ylabel('Stimulus Contrast')

    subplot_counter += 1
    
plt.show()
../_images/single_36_0.png

Additionally, the colour map parameter can be changed. Consider the colour-blindness and have good perceptually, like ‘viridis’below

fig = plt.figure(figsize=[15,30])
subplot_counter = 1 # used to track subplots

for cond in cond_labels:
    
    ax = fig.add_subplot(1, 2, subplot_counter)
    plt.imshow(psth_df.loc[cond],origin='lower',cmap='viridis',interpolation='bilinear',aspect =5)
    
    plt.title(cond)
    xticks = range(0, len(time_bins), 10)
    plt.xticks(xticks,
               time_bins[xticks])
    plt.xlabel('Time (ms)')
    plt.yticks([x for x,y in enumerate(contr_labels)], 
               [x for x in contr_labels])
    if cond == cond_labels[0]:
        plt.ylabel('Stimulus Contrast')

    subplot_counter += 1
    
plt.show()
../_images/single_38_0.png

Working with multiple neurons

Read file and check it

df3 = pd.read_csv('crowder_3_neurons.csv')

df3.head()
neuron time repetition contrast condition spike
0 m1_6 0 1 4 CTRL 0
1 m1_6 1 1 4 CTRL 0
2 m1_6 2 1 4 CTRL 0
3 m1_6 3 1 4 CTRL 0
4 m1_6 4 1 4 CTRL 0 
df3.tail()
neuron time repetition contrast condition spike
1919995 m6_3a2 3995 8 100 ADAPT 0
1919996 m6_3a2 3996 8 100 ADAPT 0
1919997 m6_3a2 3997 8 100 ADAPT 0
1919998 m6_3a2 3998 8 100 ADAPT 0
1919999 m6_3a2 3999 8 100 ADAPT 0

In this case, we want to know how many neurons in the data

neuron_labels = df3['neuron'].unique()
print(neuron_labels)

['m1_6' 'm3_11' 'm6_3a2']

Visualization

Again, we create labels dataframe first

condition_labels = pd.DataFrame([[neur,cond, contr] for neur in neuron_labels for cond in cond_labels for contr in contr_labels ],columns=['neuron','condition','contrast',])
condition_labels.head(10)
neuron condition contrast
0 m1_6 CTRL 4
1 m1_6 CTRL 8
2 m1_6 CTRL 12
3 m1_6 CTRL 16
4 m1_6 CTRL 24
5 m1_6 CTRL 32
6 m1_6 CTRL 48
7 m1_6 CTRL 64
8 m1_6 CTRL 84
9 m1_6 CTRL 100

Due to we have three neurons and each neruons has two conditions and 10 contrasts, we need douvle check it and make sure no error in here

condition_labels
neuron condition contrast
0 m1_6 CTRL 4
1 m1_6 CTRL 8
2 m1_6 CTRL 12
3 m1_6 CTRL 16
4 m1_6 CTRL 24
5 m1_6 CTRL 32
6 m1_6 CTRL 48
7 m1_6 CTRL 64
8 m1_6 CTRL 84
9 m1_6 CTRL 100
10 m1_6 ADAPT 4
11 m1_6 ADAPT 8
12 m1_6 ADAPT 12
13 m1_6 ADAPT 16
14 m1_6 ADAPT 24
15 m1_6 ADAPT 32
16 m1_6 ADAPT 48
17 m1_6 ADAPT 64
18 m1_6 ADAPT 84
19 m1_6 ADAPT 100
20 m3_11 CTRL 4
21 m3_11 CTRL 8
22 m3_11 CTRL 12
23 m3_11 CTRL 16
24 m3_11 CTRL 24
25 m3_11 CTRL 32
26 m3_11 CTRL 48
27 m3_11 CTRL 64
28 m3_11 CTRL 84
29 m3_11 CTRL 100
30 m3_11 ADAPT 4
31 m3_11 ADAPT 8
32 m3_11 ADAPT 12
33 m3_11 ADAPT 16
34 m3_11 ADAPT 24
35 m3_11 ADAPT 32
36 m3_11 ADAPT 48
37 m3_11 ADAPT 64
38 m3_11 ADAPT 84
39 m3_11 ADAPT 100
40 m6_3a2 CTRL 4
41 m6_3a2 CTRL 8
42 m6_3a2 CTRL 12
43 m6_3a2 CTRL 16
44 m6_3a2 CTRL 24
45 m6_3a2 CTRL 32
46 m6_3a2 CTRL 48
47 m6_3a2 CTRL 64
48 m6_3a2 CTRL 84
49 m6_3a2 CTRL 100
50 m6_3a2 ADAPT 4
51 m6_3a2 ADAPT 8
52 m6_3a2 ADAPT 12
53 m6_3a2 ADAPT 16
54 m6_3a2 ADAPT 24
55 m6_3a2 ADAPT 32
56 m6_3a2 ADAPT 48
57 m6_3a2 ADAPT 64
58 m6_3a2 ADAPT 84
59 m6_3a2 ADAPT 100

This time we no longer plot Raster or PTSH (actually we have 3 neurons * 2 conditions * 10 contrasts need 60 histograms !)instead Heat maps directly

Reformat the data from raw data set

psth_df3_list = []
for neuron in neuron_labels:
     for cond in cond_labels:
        for contr in contr_labels:
            spike_times = df3[(df3['neuron']==neuron)&(df3['contrast']==contr)&(df3['condition']==cond)&(df3['spike']==1)]['time']
            spike_count, bins = np.histogram(spike_times,bins=time_bins)
            psth_df3_list.append(spike_count)

#Combine labels and data together 
psth_df3 = pd.concat([condition_labels,pd.DataFrame(psth_df3_list)],axis =1)
psth_df3 = psth_df3.set_index(['neuron','condition','contrast'])
psth_df3.head(20)
0 1 2 3 4 5 6 7 8 9 ... 69 70 71 72 73 74 75 76 77 78
neuron condition contrast
m1_6 CTRL 4 0 0 3 2 0 1 4 0 1 4 ... 0 2 4 1 1 2 2 4 2 0
8 1 0 0 1 3 5 2 1 5 2 ... 1 3 1 0 1 0 1 1 2 2
12 1 2 2 0 3 2 4 3 5 1 ... 2 4 1 2 3 2 5 0 4 4
16 5 1 4 5 3 1 2 2 2 1 ... 3 3 1 3 2 2 0 5 0 2
24 1 1 2 1 1 4 2 12 5 1 ... 2 0 1 3 1 0 1 0 1 4
32 1 3 3 2 2 1 1 0 1 0 ... 1 3 0 0 0 1 1 1 0 1
48 2 5 5 0 2 1 3 2 1 2 ... 2 1 1 4 0 0 1 0 1 0
64 0 3 4 3 2 1 0 0 4 0 ... 1 2 6 0 3 2 1 0 1 0
84 1 5 1 4 2 2 2 3 3 3 ... 1 0 4 3 1 3 1 3 1 1
100 2 2 2 3 3 2 1 2 0 1 ... 3 0 0 0 0 2 1 0 0 1
ADAPT 4 4 0 13 4 17 10 14 16 10 9 ... 0 4 0 0 3 2 2 0 1 0
8 0 5 16 10 14 8 12 11 9 12 ... 4 4 3 2 3 6 4 4 2 4
12 2 1 9 9 13 5 10 7 8 7 ... 1 1 0 3 0 2 0 0 2 3
16 3 6 14 11 16 11 12 9 10 11 ... 2 1 0 0 0 4 0 4 2 2
24 3 6 13 10 17 12 9 13 10 6 ... 0 2 3 1 1 0 3 1 0 0
32 1 2 12 7 11 11 9 11 8 7 ... 2 1 2 1 0 3 0 1 2 1
48 1 4 12 7 15 14 11 14 11 9 ... 1 2 0 0 2 1 1 2 0 1
64 1 1 14 7 14 13 10 9 8 8 ... 0 3 1 1 0 2 2 3 0 0
84 4 2 18 10 14 8 6 10 11 7 ... 0 0 0 0 0 1 0 0 1 0
100 1 5 11 9 9 8 11 9 11 8 ... 0 0 0 0 1 0 1 3 0 1

20 rows × 79 columns

psth_df3.tail(20)
0 1 2 3 4 5 6 7 8 9 ... 69 70 71 72 73 74 75 76 77 78
neuron condition contrast
m6_3a2 CTRL 4 4 4 0 0 1 3 1 1 3 2 ... 2 1 1 4 2 7 6 3 2 4
8 5 1 2 2 1 5 3 1 2 10 ... 4 7 3 3 0 0 3 4 3 1
12 4 1 3 4 2 2 2 3 1 3 ... 1 3 2 6 5 5 3 2 1 1
16 3 4 1 0 1 1 3 4 8 0 ... 2 1 0 2 2 3 3 3 5 3
24 3 4 0 5 2 3 1 6 3 4 ... 3 0 2 3 9 1 2 3 4 2
32 2 2 1 0 3 0 1 0 4 4 ... 2 3 1 5 5 1 3 3 2 1
48 2 2 4 0 7 3 2 2 2 2 ... 1 3 3 0 6 5 4 6 0 4
64 4 4 6 3 4 0 7 3 2 5 ... 2 3 0 3 2 0 0 0 1 1
84 4 0 2 4 6 4 7 2 0 1 ... 3 4 4 2 0 1 2 0 1 1
100 7 4 0 3 4 2 9 4 2 4 ... 1 0 0 0 0 0 1 2 1 5
ADAPT 4 0 0 11 11 13 15 21 12 12 12 ... 3 0 0 5 3 1 4 0 1 1
8 3 3 18 12 12 14 18 13 7 10 ... 4 1 2 6 9 3 2 3 2 3
12 7 5 16 5 12 21 18 15 12 9 ... 2 2 0 0 0 0 0 0 0 0
16 4 5 17 6 21 14 13 19 10 13 ... 0 0 3 0 4 1 0 1 5 2
24 6 7 13 7 10 21 10 19 9 8 ... 3 3 3 1 5 2 1 0 3 1
32 1 0 10 15 10 13 19 12 12 6 ... 2 0 3 1 3 2 1 2 2 1
48 2 2 18 9 15 12 21 22 12 8 ... 5 2 2 4 3 4 2 2 3 0
64 2 6 8 10 19 16 18 15 9 18 ... 0 2 0 2 6 0 1 2 2 4
84 1 1 11 7 9 16 12 11 12 7 ... 4 4 2 1 0 4 1 0 3 3
100 1 2 10 11 16 20 19 11 15 15 ... 1 0 0 3 2 2 3 3 1 0

20 rows × 79 columns

fig = plt.figure(figsize=[15,15])
subplot_counter = 1 

for neuron in neuron_labels:
      for cond in cond_labels:
        ax = fig.add_subplot(3, 2, subplot_counter)

        data = psth_df3.loc[neuron]
        
        plt.imshow(data.loc[cond],origin='lower',cmap='viridis',interpolation='bilinear',aspect = 5)

        
        # Nice formatting
        plt.title('Neuron ' + neuron + ': ' + cond)

        xticks = range(0, len(time_bins), 10)
        plt.xticks(xticks,time_bins[xticks])
        
        if neuron == neuron_labels[-1]:
            plt.xlabel('Time (ms)')

        plt.yticks([x for x,y in enumerate(contr_labels)], 
                   [x for x in contr_labels])

        if cond == cond_labels[0]:
            plt.ylabel('Stimulus Contrast')
        subplot_counter += 1

plt.show()
../_images/single_56_0.png

Interpretation

According to above heat maps, there are relationship between spike rate (increase) and stimulus onset (regardless of contrast level). Specifically, in m1-6 neuron CTRL condition the ‘hot spot’ is between 2000-2500 (approximately) ms. In m3-11 neuron CTRL condition the ‘hot spot’ is between 2000-2600 (approximately) ms. In m6-3a2 neuron CTRL condition the ‘hot spot is between 2000-3000 (approximately) ms. And this experiment stimulus onset was at 2000ms.

The PTSH graph suggests that 2100 ms at 24% contrast, 2300 at 32%, 2100 at 64%, 2050 at 84%, and 2100 at 100% in the control condition, these number not support the prediction:

  • in the control condition, latency to first spike is expected to decrease with increasing contrast

It is remarkable that In the adaptation condition the neurons do not show a similar or systematic response to the onset of the “main” stimulus (the one that starts at 2000 ms) as in the control condition. The reason is neuronal ‘habituation (or desensitization)’ probably, namely, The neuron will not stimulus again under similar contrasts.

Additionally, With the contrast increase i.e., from 32% to 100%. the spike rate ‘density’ has significant increase. For example, like above heat maps, neuron m3-11 CTRL, from 48% to 100% the ‘hot spot’ area is larger than other stimulus contrast. Same thing we can found in other two neurons.

Neuron m6_3a2 behavior like simple cells, (response to a drifting sine wave grating they will oscillate between excitation and inhibition at the same temporal frequency of the stimulus), We can observe this phenomenon through heatmaps Neuron m6_3a2: ADAPT . About 100ms excitation then inhibition after 500ms, next 800ms excitation 1000ms inhibition, 1300ms excitation 1400 ms inhibition and so on. Therefore these number support the prediction:

  • Some primary visual cortex cells are phase sensitive (so-called simple cells), so in response to a drifting sine wave grating they will oscillate between excitation and inhibition at the same temporal frequency of the stimulus (2 Hz in this case,2 Hz means two peaks per second).

References

[1] NESC 3505 Neural Data Science, at Dalhousie University. Textbook
[2] NESC 3505 Neural Data Science, at Dalhousie University. Assignment 5

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