Experimental methods. (A) Memory-guided saccade task. After an initial fixation period, a target stimulus was presented at one of eight peripheral locations. This was followed by a delay period, the duration of which was chosen at random from a uniform distribution spanning 600-1100ms. The subjects’ task was to remember the location of the target stimulus and make a saccade to it when the fixation point was extinguished. (B) Neurophysiological recordings. The spiking responses of neuronal populations in the SC were recorded using a 16-channel linear microelectrode array that was lowered into the brain through a recording chamber. The mean waveform for each channel during a single recording session is shown alongside a schematic of the linear array for one session. PSTHs aligned to target onset (left) and saccade onset (right) were computed to determine the response properties of individual SC neurons. Firing rates were computed in 1ms bins, averaged across trials, and smoothed using a Gaussian function for visualization purposes only (σ = 5ms).

(A) Histogram showing the distribution of motor index values computed across sessions for all recorded SC neurons. The mean value across sessions is denoted by the dashed line. (B) Scatter plot showing the relationship between motor index and squared component loadings for the SC slow drift axis. The line of best fit was computed using multiple regression. Motor index was entered as a continuous predictor variable along with subject name to control for differences between subjects. As described in the Results section, the model explained a significant amount of the variance in the data. A negative correlation was also found between motor index and squared loadings. (C) Scatter plot showing the relationship between motor index and the strength of the relationship between single SC neurons responses and projections onto the PFC slow drift axis, as measured by computing r2. As in (B), the line of best fit was computed using multiple regression. Results showed that the model explained a significant amount of the variance in the data. Furthermore, a negative correlation was found between motor index and the r2 between single neuron SC responses and projections onto the PFC slow drift axis.

Arousal-related fluctuations are present in the SC and correlated with pupil size and fluctuations in PFC activity. (A) Computing the slow drift axis. Three example SC neurons from the same recording session (left). Each point represents the mean residual firing rate during the delay period. When PCA was applied to binned spike counts (solid line overlaid on each neuron’s spike count residuals) it yielded a vector of loadings for the first principal component, which we will term the “slow drift axis” (middle). trial-to-trial residual SC responses during the delay period were then projected onto this vector (bottom right). The histogram in the top right shows the proportion of variance explained by the slow drift axis across sessions. The median value is indicated by the verical dashed line overlaid on the histogram. A p-value was computed by comparing the actual distribution of values to a shuffled distribution (see Methods). (B) Histogram showing the proportion of variance explained between projections onto the SC slow drift axis and projections onto the PFC slow drift axis. Note that in this analysis, the slow drift axis was computed separately for each region using the method shown in (A). Trial-to-trial residual SC responses during the delay period and trial-to-trial residual PFC responses were then projected onto the SC slow drift axis and the PFC slow drift axis, respectively. The median value across sessions is denoted by the vertical dashed line overlaid on the histogram. A p-value was computed by comparing the actual distribution of values to a shuffled distribution (see Methods). (C) Same as (B) but in this case the histogram shows the proportion of variance explained between projections onto the slow drift axis and pupil size. p < 0.05*, p < 0.01**, p < 0.001***.

(A) Horizontal and vertical eye position on a single trial during the MGS task. Microsaccades were detected using the delay period using a velocity-base algorithm (Engbert and Kliegl, 2003) and are indicated by black crosses. (B) PSTHs aligned to microsaccade onset. Firing rates were computed in 1ms bins, averaged across trials and smoothed using a Gaussian function (σ = 5ms). (C) Scatter plot showing the relationship between normalized mean firing rate in and around the time of a microsaccade and motor index for each recorded SC neuron. For each neuron, mean firing rates were computed in the period spanning 25ms before and 25m after a detected microsaccade, and were normalized by subtracting the mean activity across all trials during the same time period. This was done to control for the fact that some SC neurons (e.g. buildup neurons) have been found to increase their activity during the delay period on MGS tasks (Munoz and Wurtz, 1995). A multiple regression analysis was then performed to determine if normalized mean firing rate was associated with motor index. Results showed that the proportion of variance explained by the model, after controlling for possible intersubject differences, was 0.0791 (F(2, 368) = 15.8089; p < 0.001). Normalized mean firing rate was significantly associated with motor index such that it was higher for neurons that reside closer to the motor output (t = 5.3747; p < 0.001). (D) Histogram showing the proportion of variance explained between projections onto the SC slow drift axis and microsaccade rate. The median value across sessions is denoted by the dashed line. A p-value was computed by comparing the actual distribution of values to a null distribution (see Methods). p < 0.05*, p < 0.01**, p < 0.001***.

Arousal-related fluctuations are isolated from SC neurons closer to the motor output. (A) Loadings for the slow drift axis for an example session. Motor index is represented by the colorbar. Note that loadings were weaker for neurons recorded from channels at the bottom of the probe, which targeted neurons in the deep layers of the SC. These neurons also had higher motor indices, consistent with their role in eye movement generation. (B) Scatter plot for the across session analysis showing squared loadings for the slow drift axis pooled across all recorded SC neurons. The neurons were discretized into four equally spaced bins based on motor index, and permutation tests performed to investigate if neurons with a high motor index explained less variance in the slow drift axis. The resultant p-values were then corrected for multiple comparisons using Bonferroni adjustment. p < 0.05*, p < 0.01**, p < 0.001***.

SC neurons closer to the motor output are less correlated with the PFC slow drift axis. (A) Example SC neuron with a relatively low motor index that exhibited a significant correlation between its residual spiking response and projections onto the PFC slow drift axis (r2 = 0.5346, p < 0.001). (B) Example SC neuron with a relatively high motor index that did not exhibit a correlation between its residual spiking response and projections onto the PFC slow drift axis (r2 = 0.001, p = 0.2650). (C) Scatter plot for the across session analysis showing the mean variance explained between residual spiking responses and projections onto the PFC slow drift axis for all recorded SC neurons. The neurons were discretized into four equally spaced bins based on motor index, and permutation tests performed to investigate if the variance explained between residual SC spiking responses and projections onto the PFC slow drift was lower for neurons with a higher motor index. The resultant p-values were then corrected for multiple comparisons using Bonferroni adjustment. p < 0.05*, p < 0.01**, p < 0.001***.

The relationship between SC neuron responses and pupil size is modulated by motor index. (A) Example SC neuron with a relatively low motor index that exhibited a significant correlation between its spiking response and pupil size. (B) Example SC neuron with a relatively high motor index that did not exhibit a correlation between its spiking response and pupil size (r2 = 0.1601, p < 0.001). (C) Scatter plot showing that the strength of the relationship between individual SC neuron responses and pupil size is inversely related to motor index (r2 = 0.0263, p = 0.0074). p < 0.05*, p < 0.01**, p < 0.001***.

Arousal-related signals in the SC reside in an orthogonal subspace to saccade-related signals. (A) Computing the pupil size axis for an example session. Three example SC neurons from the same recording session (left). Each data point represents the mean spiking response after trial-to-trial pupil size had been discretized into eight equally spaced bins. Note that pupil size increases with bin number such that bin 1 contains trials in which the pupil was most constricted, whereas bin 8 contains trials in which the pupil was most dilated When PCA was applied to the data it yielded a vector of loadings for the first principal component (right). (B) Computing the saccade tuning axis for the same session shown in (A). Three example SC neurons (right). Each point represents the mean spiking response during the saccade epoch (25ms before to 25ms after the onset of the saccade) for each target angle. When PCA was applied to the data it yielded a vector of loadings for the first principal component (left). (C) A scatter plot showing the relationship between projections onto the pupil size axis and the saccade tuning axis for the same example session shown in (A) and (B). The color scale represents projections onto the slow drift axis. Note that the same data (i.e. residual SC responses during the delay period) were projected onto the three axes. (D) Histogram showing the proportion of variance explained between projections onto the pupil size axis and projections onto the saccade tuning axis. A p-value was computed by comparing the actual distribution of values to a null distribution (see Methods). (E) Scatter plot comparing the variance explained between projections onto the pupil size axis and the slow drift axis, and projections onto the saccade tuning axis and the slow drift axis. A p-value was computed using a paired-sample t-test. p < 0.05*, p < 0.01**, p < 0.001***.