Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention Pascal Fries, John H. Reynolds, Alan E. Rorie, and Robert Desimone

Supplementary Material

1.) The multi-unit signal:
During recording sessions, we stored all putative spike waveforms (Web fig. 1 for a representative example recording session). Offline, we rejected waveforms corresponding to late parts of multi-phasic spikes and, in a few cases, electrical or movements artifacts due to licking etc.. We used principal component analysis to sort waveforms from different single cells (Web fig. 1A). Clusters that clearly separated from the origin of the PCA plot and from other clusters were considered single units. There was usually one cluster close to the origin with low-amplitude waveforms that could not be clearly differentiated into separate single units. The multi-unit signal used in all of our analyses was pooled from the isolated single units and the non-differentiated cluster of units. This multi-unit signal showed the most reliable oscillatory synchronization. We also analyzed the single units separately and found that whereas some of them showed very strong oscillatory synchronization, many showed little or no synchronization. Whenever there was clear oscillatory synchronization, attention diminished low frequency and enhanced gamma frequency synchronization, irrespective of whether the spikes were from the pooled multi-unit signal or were from an isolated neuron.

Supplemental Figure 1. (A) Each dot in this scatter plot corresponds to the waveform of one spike from one recording site, giving the coefficient of the first principal component on the X-Axis and the coefficient of the second principal component on the Y-Axis (scale not shown). Dots colored in blue had been identified as late parts of a multi-phasic spike and were eliminated. The remaining dots, shown in yellow, form three distinct clusters. Fifty example waveforms from each cluster are shown in (B). We classified the waveforms shown in red and blue as single units and the ones shown in gray as non-differentiated units.

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2.) High sensitivity of the STA in detecting local neuronal synchronization:
In order to measure local neuronal synchronization, we used the spike-triggered average of the LFP (STA). If spike times have a reliable temporal relation to the local neuronal activity as measured by the LFP, then LFP fluctuations add up during the spike triggered averaging process. On the other hand, if spike times have no temporal relation to the activity of surrounding neurons, fluctuations in the LFP average out during STA compilation, resulting in a flat STA. The STA is very sensitive in detecting synchronization because the LFP averages over many neurons. However, the STA possesses all the selectivity that is typical for spike responses, because without spikes or with spikes that have no temporal relation to the LFP fluctuations, the STA is flat.

We also calculated cross-correlation histograms (CCHs) for all pairs of spike recordings. In contrast to STAs, CCHs rarely exhibited modulations, and, if present, they were of small amplitude. The discrepancy between the STA and the CCH is due at least in part to the fact that the STA uses the LFP, which is a reliable measure of the population activity with millisecond resolution. For example, we found that two spike trains can show strong locking to one LFP, but at the same time only weak synchronization with respect to each other. An example of this is given in Web figure 2. Finally, it is clear that only a subpopulation of individual neurons participates in synchronization.

Supplemental Figure 2. (A) A 400 ms segment of LFP from one recording site (Elec 1) and two simultaneously recorded spike trains from two different recording sites (Elec 2 and Elec 3). The LFP shows clear gamma-frequency fluctuations and some spikes seem to be locked to the LFP negativities. (B) STA calculated with the spikes from Elec 2 and the LFP from Elec 1. The graph shows the STA as black line and the STA±2SEM as gray shaded band. (C) shows the same analysis as (B) but with spikes from Elec 3. Both STAs show clear spike-field synchronization with a high signal to noise ratio as can be judged from the width of the gray shaded band. (D) shows the cross-correlation histogram of spikes recorded from Elec 2, normalized for the number of trigger spikes from Elec 3. Note that the y-axis is truncated to allow comparison with the STAs. The CCH shows less modulation and a much lower signal to noise ratio than the STAs. For this example, we picked one of the most strongly modulated CCHs from our sample of CCHs, while the STAs are fairly representative for the whole sample of STAs. Many CCHs do not show any sign of oscillatory synchronization, while almost all STAs do.

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3.) Calculation and interpretation of the spike-field coherence:
The spike-field coherence (SFC) measures phase synchronization between the local field potential (LFP) and spike times as a function of frequency. For the calculation of the SFC, we first obtain for each spike the LFP segment for a short time window around that spike (typically ±100 ms or ±150 ms). Averaging these LFP segments gives the spike-triggered average (STA). Any components of the LFP that are not consistently phase locked to the spikes are averaged out and are not visible in the STA. As the STA is calculated by summing all LFP segments and then dividing by the number of spikes, the STA is normalized for spike number. In order to quantify the STA, we calculate its (absolute) power spectrum. The power spectrum gives the magnitude of all frequency components of the STA as a function of frequency. The power spectrum of the STA is still dependent on the power spectrum of the LFP itself. Multiplying the LFP by a factor F would magnify the STA by that factor and would therefore magnify its power by 0.5*F2, despite the absence of any change in the phase synchronization between spikes and LFP. In order to quantify the phase synchronization between spikes and the LFP, it is therefore necessary to normalize the power spectrum of the STA. We normalize the power spectrum of the STA by the average of all power spectra of all LFP segments that were averaged to obtain the STA. This normalization gives the SFC, which is independent of the firing rate of the spikes and of the power spectrum of the LFP. If the SFC for any given frequency is 1, then this means that all spikes appear at exactly the same phase relation relative to this frequency component. If the SFC for any given frequency is 0, then this means that the spikes do not have any systematic phase relation to the LFP component at this frequency. We illustrate the calculation and interpretation of the SFC in Web figs. 3 and 4.

Supplemental Figure 3. The spike field coherence. In this figure, we use artificially constructed data to demonstrate how the spike field coherence is calculated and to indicate how it should be interpreted. (A) and (B) show two components which constitute a signal (C) that we use here as a hypothetical LFP. The high amplitude component shown in (A) has a frequency of 10 Hz, while the low amplitude signal in (B) has a frequency of 50 Hz. Note that for the purposes of this figure, we have chosen a signal that contains power in only two frequency bins. In a real LFP, the spectral power is typically concentrated in frequency bands, not in single frequency bins of the spectrum. The vertical lines in panels (A) through (C) mark hypothetical spike times, which are the same for all three panels. The spikes are exactly locked to the negativities of the 50 Hz component and occur in a random subset of the 50 Hz periods. The spikes have no phase relation to the 10 Hz component. (D) and (E) show two examples of segments of the artificial LFP from the period around (±100 ms) two spike occurrences. The power spectra of these LFP pieces are shown in (F) and (G), respectively. The 10 Hz component with the amplitude of 1 mV has a power of 0.5*(1 mV)2 = 0.5 mV2 and the 50 Hz component with the amplitude of 0.2 mV has a power of 0.02 mV2, respectively. Note that the two spikes occur at different times during the phase of the 10 Hz oscillation, but this phase information is not represented in the power spectrum. (H) shows the average of the LFP segments around (±100 ms) all 15 spikes. This average is called the spike-triggered average or STA. As the spikes are perfectly phase locked to the 50 Hz component, this component has the same amplitude in the STA as it had in the original signal, namely 0.2 mV. However, the spikes have no phase relation to the 10 Hz component and therefore, the amplitude of this component is strongly reduced in the STA as compared to its amplitude in the original artificial LFP signal. This is true even for the small number of 15 spikes used in this exmple. With increasing numbers of spikes, the 10 Hz component of the STA would quickly disappear completely. This differential reduction in power can be seen in the power spectrum of the STA, that is shown in (I). The power at 50 Hz is 0.02 mV2 just as it was in the original signal, but the power at 10 Hz is only 0.008 mV2, which is only 1.6% of the original 0.5 mV2. (J) shows the average of all power spectra of all the 15 LFP pieces (surrounding the 15 spikes) that were averaged to give the STA. This average power spectrum looks exactly like the power spectra (F) and (G) for the two examples of LFP segments in (D) and (E). Thus, it contains much more power at 10 Hz than at 50 Hz. Dividing (I) by (J) gives the spike-field coherence or SFC, which is shown in (K). Note, that the SFC is not a power measure, but a unitless measure that assumes the value one for perfect phase synchronization and the value zero for no phase synchronization. The SFC for these artificial data shows that the spikes are perfectly locked to the 50 Hz component. At 10 Hz, the SFC also shows some phase synchronization, which is due to the low number of spikes, resulting in insufficient averaging. With increasing numbers of spikes, the SFC at 10 Hz would quickly approximate zero. [Note: A correction has been made to this figure. See below.]

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Note that the 10 and the 50 Hz component of the LFP have a fixed phase relation. But the spikes are only phase locked to the 50 Hz component. The SFC shows this selective synchronization of the spikes to the 50 Hz component. In addition, the SFC ignores the higher amplitude of the 10 Hz component in the LFP, because it is normalized by the average of all power spectra (J).

Supplemental Figure 4. In this figure, we repeat the analysis from Web fig. 3, however, this time only half of the spikes are phase locked to the 50 Hz LFP oscillation, while the other half of the spikes occur at random times. Note that the SFC shown in (K) is now 0.5 for the 50 Hz bin. This reflects the fact that only 50 percent of the spikes are locked to the 50 Hz oscillation. The 10 Hz SFC is further reduced as compared to Web fig. 3, because the 10 Hz oscillation is averaged out more completely, by the larger number of spikes. [Note: A correction has been made to this figure. See below.]

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Correction to supplemental figures 3 and 4 (2 May 2003): Owing to a production error, supplemental figures 3 and 4 were swapped for one another in the original version of this supporting online material. The figures are correct in the current version. Science regrets the error.