Diversity, heterogeneity and orientation-dependent variation of spike count correlation in the cat visual cortex
Article first published online: 23 SEP 2013
© 2013 Federation of European Neuroscience Societies and John Wiley & Sons Ltd
European Journal of Neuroscience
Volume 38, Issue 11, pages 3611–3627, December 2013
How to Cite
Maruyama, Y. and Ito, H. (2013), Diversity, heterogeneity and orientation-dependent variation of spike count correlation in the cat visual cortex. European Journal of Neuroscience, 38: 3611–3627. doi: 10.1111/ejn.12363
- Issue published online: 1 DEC 2013
- Article first published online: 23 SEP 2013
- Manuscript Accepted: 25 AUG 2013
- Manuscript Revised: 9 AUG 2013
- Manuscript Received: 17 OCT 2012
- Ministry of Education, Culture, Sports, Science and Technology of Japan. Grant Numbers: 21500226, 24500286
- Kyoto Sangyo University Research Grants
Fig. S1. For all stimuli of all units (N = 310), the relationship between the mean firing rate (M) and the standard deviation (SD) over trials is plotted. Both the abscissa and the ordinate are on a logarithmic scale and in units of spikes per second. Their relationship was well fitted by a power function (regression line, r2 = 0.89) SD = 2.53M0.63 over three orders of magnitude.
Fig. S2. Dependence of the spike count correlation on the physical distance between the unit pairs. For all unit pairs (N = 1090), correlation coefficients were averaged over the 16 stimulus orientations and plotted as a function of physical distance between the electrodes recording the corresponding units. For units isolated from the same electrode (either the tetrode or the single microelectrode), we assigned a zero distance. Distances of the pairs recorded by the tetrodes (represented by ×) were either 0, 500 or 710 μm and those recorded by the microelectrodes (+) were either 0, 310, 430, 610, 680 or 860 μm. At each distance, the mean and the standard deviation of the distribution are indicated (tetrode array: 0 μm: 0.06 ± 0.16, 206 samples; 500 μm: 0.05 ± 0.15, 418 samples; 710 μm: 0.04 ± 0.13, 233 samples, single electrode array: 0 μm: 0.15 ± 0.09, 16 samples; 310 μm: 0.08 ± 0.14, 66 samples; 430 μm: 0.12 ± 0.16, 25 samples; 610 μm: 0.07 ± 0.12, 44 samples; 680 μm: 0.05 ± 0.13, 64 samples; 860 μm: 0.04 ± 0.10, 18 samples). A dashed line represents zero spike count correlation. Because the sample sizes were different over different distances, we performed a χ2 fit of the data to a straight line. Uncertainty of the mean value at each distance was estimated by the standard deviation over the samples divided by the square root of the sample size. For the unit pairs recorded by the tetrode array, the model of linear relationship between the correlation coefficient and the distance was rejected (χ2 = 5.26 for 1 degree of freedom, P < 0.02). Also, the analysis of variance suggested a non-significant difference among the mean values at different distances (P > 0.16, Kruskal–Wallis test). By contrast, for the unit pairs recorded by the single microelectrode array, the model of a linear relationship was not rejected (χ2 = 4.39 for 4 degrees of freedom, P > 0.36). The linear decay had an intercept of 0.138 ± 0.018 and a slope of 0.119 ± 0.031/mm. We found that units isolated from the same microelectrode (zero distance) had a significantly larger correlation than the unit pairs of other distances (P < 0.013, Kruskal–Wallis test). When the data of zero distance were excluded, the data were slightly more consistent with the linear relationship (χ2 = 3.01 for 3 degrees of freedom, P > 0.39) with a more gradual slope of 0.078 ± 0.047/mm and an intercept of 0.112 ± 0.028, and the difference among the mean correlation values of different distances became non-significant (P > 0.17, Kruskal–Wallis test).
Fig. S3. The correlation between the spike count correlation and the similarity in stimulus tuning characteristics. For all unit pairs (N = 1090), the correlation coefficients were averaged over the 16 stimulus orientations and plotted as a function of the similarity between the stimulus tuning curves of the two units (signal correlation, SCm). Two variables show a significant but very weak positive linear correlation (regression by least squares fitting, slope 0.04, P < 0.001, r2 = 0.01). The unit pairs isolated from the same microelectrode (N = 16, indicated by filled squares) tend to have a larger signal correlation and a larger spike count correlation.
Fig. S4. The relationship between spike count correlation and geometric mean of the firing rates of the two units. We first drew a scatter plot between the spike count correlation and the geometric mean over all stimuli for all unit pairs (N = 17 440), and then the data were averaged within bins 5 spikes/s in size. The plot shows the mean and standard deviation of each bin (0–5 spikes/s: 0.052 ± 0.198, 12 612 samples; 5–10: 0.051 ± 0.249, 3574 samples; 10–15: 0.086 ± 0.307, 914 samples; 15–20: 0.168 ± 0.252, 232 samples; 20–25: 0.145 ± 0.267, 60 samples; 25–30: 0.134 ± 0.250, 39 samples). A dashed line represents a zero spike count correlation. We have excluded nine samples corresponding to larger geometric mean rates due to a sample size that was too small (30–35 spikes/s: seven samples; 35–40 spikes/s: two samples). We performed a χ2 fit of the data to a straight line. The uncertainty of the mean value at each bin was estimated by the standard deviation over the samples divided by the square root of the sample size. Although an increase in the correlation can be observed, the model of the linear relationship between the two variables was rejected (χ2 = 33.5 for 4 degrees of freedom, P < 0.001).
Fig. S5. The degree of orientation-dependent variation in the spike count correlation was quantified by the P-value of the Kruskal–Wallis test. The histogram of −log10P over all the samples (N = 575) shown in Fig. 6 was split into three groups: Group A, significant cases consist of only positive correlations (N = 349, 60.7%); Group B, significant cases consist of only negative correlations (N = 118, 20.5%); and Group C, significant cases consist of both positive correlations and negative correlations (N = 108, 18.8%). The variation is judged to be significant when −log10P > 1.3 (P < 0.05, dashed lines). The distributions are significantly different among the three groups (P < 0.0001, Kruskal–Wallis test). Group C (median of −log10P 0.89) has a significantly larger degree of variation than Group A (median 0.45) and B (median 0.53).
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