Theta oscillations at different stimulus sizes: example

(A) Top: Schematic of the stimulus, a black disk, presented at three different sizes, with diameter in visual degrees, while the animal (monkey AL) fixated at the white fixation spot. Sizes are not drawn to scale. Middle and bottom: Raster plots and peri stimulus time histogram (PSTH) of an example single unit activity aligned to stimulus onset for 0.3° (left), 1° (middle), and 4° (right). Note the rhythmic activity elicited explicitly by the 1° stimulus. (B) Top: Mean power spectra of multi-unit activity (MUA) for each stimulus size. The MUA was obtained from the same electrode from which the single unit activity in A was isolated. Bottom: Mean power spectra for LFP. Dashed lines delineate theta frequency range. Error bars are ± 1 standard error of the mean (SEM).

Theta oscillations at different stimulus sizes: population results

(A) Normalised population power spectra of MUA for each size averaged across channels for monkey AL (n = 248 channels). Dashed lines delineate theta frequency range. Error bars are ± 1 standard error of the mean (SEM). (B) Normalised mean MUA (blue), MUA theta power (red continuous line), and LFP theta power (red dashed line) across different sizes averaged across all channels for monkey AL. Error bars are ± 1 SEM. (C) Same as A, but for monkey DP (n = 390 channels). (D) Same as B, but for monkey DP.

Theta oscillations at different stimulus sizes: population results

(A) Behavioural task. The monkeys had to detect a small luminance change (grey dot), in the centre of a stimulus (black disk) and make a saccade toward the stimulus. The interval between stimulus and luminance change, stimulus onset asynchrony (SOA), was varied densely between 500 to 1500 ms. (B) Reaction times (RT) as a function of SOA from one session. (C) Power spectrum of the time course of the RT in B (blue), superimposed with the average neural power spectra recorded during the task (orange). Black dashed line is the threshold of statistical significance for the RT power spectrum after correction for multiple comparisons (α = 0.05 / 15 frequencies = 0.0033). (D) Scatter plot showing the relationship between peak frequency of MUA power spectra and peak frequency of RT power spectra (n = 14 sessions). Sessions are combined for both monkeys. We introduced a small jittering to the data points in the scatter plot for illustration purposes only to improve visibility because of the overlaps of some data points. The correlation coefficient and regression line were calculated from the non-jittered data. There was a significant positive relationship between MUA peak frequency and RT peak frequency. Marginal histograms showed the concentration of peak frequency of both MUA (top histogram) and RT (bottom histogram) in the theta range.

The phase of theta oscillations is correlated with reaction times

(A) An illustration of Phase Opposition Sum (POS) calculation from an example channel at one time point. We calculated Intertrial Phase Coherence (ITPC) for fast, slow, and fast + slow trials. The top row shows the phase distribution across trials, while the bottom row shows the ITPC (red lines). The line direction shows the mean phase angle, while the length shows how tightly the phase distribution clusters. POS was calculated according to the equation at the bottom. A larger value means a larger ITPC difference between fast and slow trials, implying a stronger correlation between theta phase and RT. (B) Population POS across channels (top) and p-value (bottom). We calculated POS for every channel and every time point around the target presentation (t = 0s, vertical line). Blue lines are the POS of individual channels, and the black line is the mean POS across channels. P-value was calculated for every channel and combined (bottom row). Note that we plotted the p-value as 1 - p-value. The red dashed line is the significance threshold (p = 0.05, corrected for false discovery rate (FDR).

Example single trial time course and power spectra

(A) Five example trials of MUA (purple, left y-axis) and LFP (green, right y-axis) response to three different stimulus sizes on each row. The signals were obtained from the same channel in Figure 1. Each column corresponds to one trial. Oscillatory activity is clearly seen for 1° stimulus size for both MUA and LFP. (B) Single-trial power spectra (grey) of post-stimulus MUA (top) and LFP (bottom). Dashed lines delineate the theta frequency band. The red dots are peak frequencies for every trial.

Method to calculate theta power

To calculate theta power, we first limited the power spectra in the 1 - 15 Hz range (step 1). Next, we log-transformed both the x (frequency) and y-axis (power) and fit a robust regression model (step 2). Last, we removed the linear trend and obtained the residual power (step 3). Theta power was the largest peak in the residual spectra.

(A) Normalised population LFP power spectra for each size averaged across channels for monkey AL (n = 248 channels) and DP (n = 390 channels). Dashed lines delineate theta frequency range. Error bars are ± 1 standard error of the mean (SEM). (B) Peak frequency distribution across channels at different stimulus sizes for each monkey, for MUA (top) and LFP (bottom) separately. We calculated the mean power spectra across trials for every channel and identified the peak with the strongest power. Theta frequency band is delineated by horizontal dashed lines.

Microsaccades main sequence showing the positive relationship between amplitude and peak velocity.

Mean percentage of trials with microsaccades across stimulus sizes.

Each dot represents a single session. Microsaccades were rare events. Microsaccades occurred on ∼ 10 - 15 % of trials across sizes. This microsaccades occurrence pattern differed substantially from our observations that post-stimulus neural theta oscillations are consistently present across trials (Supplementary Figure 1 as an example).

Number of microsaccades in the post-stimulus period in trials where microsaccades occurred after stimulus onset.

Each dot represents a single session. On average, microsaccades occurred once during the whole post-stimulus period. The number of microsaccades during the post-stimulus period was not different across stimulus sizes (p > 0.05, Friedman test). These findings are inconsistent with rhythmic saccades inducing theta rhythmic neural activity.

Microsaccade raster plot for size 0.75° combined across sessions.

Each dot shows the onset time of microsaccades during a particular trial. The vertical line shows the stimulus onset. There is no apparent rhythmicity in the microsaccades timing across trials.

(A) An example trial without (left) and with (right) microsaccade. The top panels show the horizontal (blue) and vertical (red) eye traces. Black lines show a detected microsaccade. The bottom panel shows MUA from the same trials. Notice that on the left panels, theta oscillations are apparent even without a microsaccade. On the right panels, there are no obvious theta oscillations following a microsaccade. (B) Power spectra of stimulus size 0.75° before (solid line) and after (dashed line) removing trials with microsaccades in the post-stimulus period, separately for each monkey. If microsaccades are the generator of neural theta oscillations, we expect their disappearance after the removal of microsaccades. We found that theta oscillations were still present after removing trials with microsaccades.

(A) Five example trials of MUA (purple, left y-axis) and LFP (green, right y-axis) response to three different stimulus contrasts on each row Each column corresponds to one trial. Oscillatory activity is clearly seen for 100° stimulus contrast. (B) Mean power spectra of post-stimulus MUA (left) and LFP (right) from the example channel in (A). Dashed lines delineate the theta frequency band.

(A) Normalised population MUA (top) and LFP (bottom) power spectra for each contrast, averaged across channels for monkey AL (n = 104 channels). Dashed lines delineate theta frequency range. Error bars are ± 1 standard error of the mean (SEM). (B) Normalised mean MUA (top, blue), MUA theta power (top, red), and LFP theta power (bottom, red) across different contrasts averaged across all channels for monkey AL. Error bars are ± 1 SEM. (C) Peak frequency distribution across channels at different stimulus contrast for monkey AL, for MUA (top) and LFP (bottom) separately. We calculated the mean power spectra across trials for every channel and identified the peak with the strongest power. Theta frequency band is delineated by horizontal dashed lines. (D-F) Same plots but for the monkey DP (n = 126 channels).