Pre-saccadic Neural Enhancements in Marmoset Area MT

Subjects and surgery

All experimental protocols were approved by the University of Rochester Institutional Animal Care and Use Committee and were conducted in compliance with the National Institutes of Health guidelines for animal research. Two adult common marmosets (Callithrix jacchus), Marmoset E (female) and Marmoset M (male), were used for neurophysiology recording experiments to measure changes in neuronal tuning during pre-saccadic attention. Subjects were single housed at the University of Rochester with a circadian cycle of 12 h light/dark. Subject M was briefly food scheduled with full access to water during early training but had no restrictions by the time neurophysiological data were collected. Subject E was never food scheduled and always had full access to food and water.

Both subjects were surgically implanted with head caps to stabilize them for head-fixed eye tracking and neural recordings. Two months prior to surgery, subjects were trained to sit in a small primate chair following methods previously described (Lu et al., 2001; Remington et al., 2012; Osmanski et al., 2013; Nummela et al., 2017). Then subjects underwent surgery under sterile conditions to implant an acrylic head cap with titanium posts to stabilize the head using methods described in detail previously (Nummela et al., 2017). During the implant surgery, recording chambers were placed over visual areas MT and V1 based on stereotaxic coordinates (Paxinos et al., 2012). Recording chambers consisted of custom 3D prints (Protolabs) and adhered to the skull using C&B Metabond (Parkell). The skull inside the recording chambers was also covered by a thin layer of C&B Metabond. After initial head implant and chamber placement, marmosets were trained to acclimate to head restraint while sitting comfortably in a custom-designed primate chair. Over several months, they were trained to perform several basic tasks including central fixation (Mitchell et al., 2014) and a saccade task toward a peripherally detected Gabor grating, which we used to measure their visual acuity (Nummela et al., 2017).

After preliminary training, a second surgery was performed to create a craniotomy (2–3 mm in diameter) in the recording chamber over area MT. Craniotomies were sealed with a thick layer of silastic gel (Kwik-Sil; World Precision Instruments) to protect the brain from infection and reduce granulation growth (Spitler and Gothard, 2008). If any bleeding occurred or the Silastic seal leaked clear fluids in the days following surgery, then the chamber was cleaned with sterile saline, and a new Silastic layer was applied. Typically, the chamber stabilized and remained dry with a tight seal after a few days to a week. At that time, we performed a dural scrape to remove any excess tissue over the dura and applied a thin layer (<1 mm) of Silastic, which was thin enough to enable passage of electrodes for recordings. The silastic remained in place for the duration of the study. When applied correctly, the silastic has been observed to limit the growth of granulation tissue on the dura and prevent infection (Spitler and Gothard, 2008) and can also be recorded through tungsten electrodes (Miller et al., 2015, MacDougall et al., 2016). Additionally, it was possible to record through Silastic using linear array silicon probes (NeuroNexus) when the dura was thin.

Electrophysiology

Over the duration of the study, our recordings improved from using single-channel tungsten electrodes to using multichannel linear silicon arrays. The first monkey was recorded entirely with tungsten single electrodes (47 sessions), with fewer tungsten electrode recordings in the second monkey (31 sessions). The bulk of data from the second monkey originated from linear arrays that provide much higher cell counts per session (21 sessions). Due to animal health issues, we were unable to employ linear arrays in the first monkey, which passed away during the pandemic. The current findings focus on behavior and the single-unit neural effects on tuning curves during pre-saccadic attention, which can be addressed well with either of the recording methods used and can include both animals.

In single tungsten electrode recordings, we sampled across recording sites in a 1 mm spaced grid with electrodes advanced through metal guide tubes placed in the grid. We inserted tungsten 2.5–5 MΩ electrodes (1–3 FHC) that were mounted onto a lightweight screw micro-drive (Crist Instrument, 3-NRMD drive) positioned over the spacing grid. Electrodes were passed through a metal guide tube that touched but did not penetrate the Silastic layer covering the brain. Tungsten electrodes reliably penetrated the thin silastic layer and intact dura to enter the brain. A stainless-steel reference wire was implanted under the skull in a 1 mm craniotomy.

Later recording sessions using multichannel linear silicon arrays (NeuroNexus) used a custom-built X–Y stage for submillimeter targeting of recording sites. The X–Y stage was mounted onto the recording chamber and carried a lightweight screw micro-drive (Crist Instrument, 3-NRMD) that could deliver linear arrays mounted to a steel tube (28 gauge) into the brain. Designs for the 3D printed parts used in the X–Y stage and recording chamber are online (https://marmolab.bcs.rochester.edu/resources.html).

All neurophysiology data were amplified and digitized at 30 kHz with Intan headstages (Intan) using the Open Ephys GUI (https://github.com/open-ephs/plugin-GUI). The wideband signal was highpass filtered by the headstage at 0.1 Hz. We corrected for the phase shifts from this filtering (Jun et al., 2017). For linear arrays, the resulting traces were also preprocessed by common-average referencing.

Tungsten spike sorting and cluster isolation

Single-unit and multiunit clusters from tungsten electrodes were identified using custom MATLAB software. First, the raw signal was bandpass filtered from 800 Hz to 6,000 Hz with a sixth-order Butterworth filter. To reduce movement artifacts in recordings (i.e., licking or other movements), we chose a narrower filter for initial spike detection to threshold spike events (1,500 Hz to 4,500 Hz) and then used the wider band pass (800–6,000 Hz) to classify single units based on clustering of their threshold triggered spike waveforms in a principal components analysis (PCA) space that included the first two principal components and time as variables. Clusters identified in PCA space were compared to a noise floor, based on random sampling of threshold events, and clusters that could not be fully separated from other clusters or the noise floor, or that exhibited more than 1% of inter-spike interval violations under 1 ms, were counted as multiunit activity.

Laminar electrophysiology and spike sorting

In later recordings, we were able to use multisite silicon electrode arrays that provided much higher cell counts. These arrays included 1–2 shanks, and each shank consisted of 32 channels with 35 microns spacing between contacts. All arrays were 50 microns thick and had sharpened tips. Arrays that included two shanks spaced 200 μm apart were from NeuroNexus (http://www.neuronexus.com). Although the arrays could penetrate the dura when it was thinned, we found that dimpling of the tissue could still suppress neural activity during insertion and that the best recording quality was achieved by applying a small 1–2 mm horizontal slit in the dura during a dural scape and sealing it under Silastic to prevent infection. For the best recording quality, it was further useful to electrode-plate the silicon electrode arrays with PEDOT, a method that has been shown to increase signal/noise ratios (Ludwig et al., 2006, 2011). Last, the yield of neurons recorded was generally improved by inserting the array electrodes into the cortex slowly. We first lowered the silicon shank quickly until we observed units at the array tip, and then retracted one turn of the micro-drive (250 μm) slowly. Then we lowered the arrays advancing approximately 4–6 turns (1–1.5 mm) over a 20–30 min duration until neurons were evenly distributed across the length of the shank. We aimed to span the entire depth of the cortex (∼1.5 mm) to obtain a more uniform sampling of units across layers. We then slowly retracted the array 1–2 turns (0.25–0.5 mm) to reduce pressure on the tissue during recordings. During this final retraction, neurons did not typically shift vertical locations on the array, suggesting that it primarily acted to reduce pressure on the tissue and that otherwise the arrays would have continued advancing slowly during the recording as the tissue relaxed. After retracting, we waited 20 min before starting the main behavioral task and recordings.

We spike sorted array data after initial filtering from the Intan system (as described earlier) using Kilosort2. Outputs from the spike sorting algorithms were manually labeled using the “phy” GUI (https://github/kwikteam/phy). Units with tiny or physiologically implausible waveforms were classified as noise and excluded. Kilosort can identify multiunit clusters that are not physiologically possible, spanning any channels with unrealistic waveforms. Therefore, to be conservative, we only included units from Kilosort that had clear clusters in PCA space, less than 1% inter-spike interval violations, and biphasic spike waveforms localized to adjacent channels on the linear array.

Stimulus presentation and timing

Stimuli were generated using the Psychophysics toolbox (Brainard, 1997; Pelli, 1997; Kleiner et al., 2007) in MATLAB 2015b (MathWorks) on a PC (Intel i7 CPU, Windows 7, 8 GB RAM, GeForce Ti graphics card). They were presented on a gamma-corrected display (BenQ X2411z LED monitor; resolution, 1920 × 1080 p; refresh rate, 100 Hz; gamma correction, 2.2) that had a dynamic luminance range from 0.5 to 230 cd/m² at a distance of 57 cm in a dark room and viewed under head restraint in custom-designed primate chair as described previously (Nummela et al., 2017). Brightness on the display was set to 100 and contrast to 50, and additional visual features of the monitor, such as blur reduction and low blue light, were turned off. Gamma corrections were verified with measurement by a photometer. Task events and neural responses are recorded using a DATAPixx I/O box (VPixx Technologies) for temporal registration. The MATLAB code is available online (https://github.com/jcbyts/MarmoV5).

Random dot motion fields were used as targets for saccade foraging and also provided a stimulus to validate the motion selective responses on individual neurons as an inclusion criterion. Each aperture contained a field of black dots (each dot 0.15 dva diameter with a density of 2.54 dots per visual degree squared), which moved at 15°/s in one direction (100% coherent). Dot speed was fixed at 15°/s to roughly match the preferred median speed previously reported for neurons in marmoset MT (Lui et al., 2007; Solomon et al., 2011). The dots had limited lifetimes of 50 ms with asynchronous updating to new locations. The radius of the dot field was equal to half the eccentricity of where it was located from the center of the screen and appeared over a gray background (115 cd/m²). The contrast of dots was decreased from black at the center of field (0.5 cd/m²) to zero on the aperture edges according to a Gaussian envelope with a sigma equal to a one-sixth of the aperture's diameter.

Eye tracking

Eye position was acquired at 220 Hz using an Arrington Eye Tracker and ViewPoint software (Arrington Research) or at 1,000 Hz using an EyeLink 1000 Plus eye tracker (SR research). Eye position was collected from infrared light reflected off of a dichroic mirror (part #64-472, Edmund Optics). Each subject's vision was corrected using spherical concave lenses (Optimark Perimeter Lens Set) that were centered 4–5 mm in front of the face as described previously (Nummela et al., 2017). The lens of −2.5 diopters was used for Marmoset M and of −2.0 diopters for Marmoset E. Eye position was calibrated at the start of each behavioral session using a Gabor windowed face detection task described previously (Mitchell et al., 2014, Nummela et al., 2017).

Eye position data were collected during the entire recording session. Raw horizontal and vertical eye position signals were smoothed offline with a median filter (five samples, 5 ms) and convolved with a Gaussian kernel (5 ms half width, out to 3 SD, −15 to 15 ms) to minimize high-frequency noise. For offline detection of saccadic eye movements, we used an automatic procedure that detected deviations in 2D eye velocity space (Engbert and Mergenthaler, 2006; Kwon et al., 2019). We computed horizontal and vertical eye velocity by taking the difference of the smooth eye position and then marked saccades by where the 2D velocity exceeded the median velocity by 10 SD for at least 15 ms (Engbert and Mergenthaler, 2006; Kwon et al., 2019) and merged any two saccadic events into a single saccade if they were separated by less than 5 ms. Saccade onset and offset were determined by the first and last time the 2D velocity crossed the median velocity threshold. Epochs with eye blinks (based on pupil size) are removed from analysis.

RF mapping of MT/MTC during free viewing task

Spatial receptive fields were estimated from the responses to a wide field stimulus consisting of large moving white dots (Fig. 2A). In brief, marmosets freely viewed a full-field display that consisted of white dots (230 cd/m², 1 dva diameter) that appeared against a gray background (115 cd/m²) spanning ±20 dva on the horizontal and 15 ±dva on the vertical of the display. Each dot moved at 15° per second for 50 ms before being replotted to a new location in the full-field display. Dot motion was selected at random from 1 of 16 motion directions sampled around the circle. In each task trial, the screen would contain a fixed number of dots (sampled from 4, 8, 16, or 32) that would be viewed for 10 s. To encourage foraging near the center of the screen, a Gabor target (20% Michelson contrast, 1 dva diameter, one cycle/degree, with random orientation) appeared within 5° of the center superimposed with the dots flashing dots. If the marmoset's eye position acquired the Gabor target within a 2° diameter, a juice reward was delivered, and the Gabor target was replotted to a new location.

Off-line we corrected for eye position to represent the flashed stimuli in a grid of retinal coordinate locations and correlated the stimulus history with spike counts to estimate the RF (Fig. 2B). The full methods for estimating receptive fields have been described previously (Yates et al., 2023) and analysis code is available online (https://github.com/VisNeuroLab/yates-beyond-fixation). In brief, firing rate was computed as a function of the x–y retinal-based grid location (2 × 2° bins) where each bin contained a flashed dot or did not. To reduce correlation in the stimulus history of the moving dots, we only represented dots on the first video frame from their 50 ms lifetime, and the spatial position was registered by their location at the middle of the lifetime. The firing rate was computed for the onset of dots across the grid at different lag times in 10 ms spike counting bins (Fig. 2B, left). Those locations exhibiting firing responses significantly above the pre-stimulus baseline firing (from −100 to 0 ms lag, p < 0.001) were labeled as significant to mark the RF. A smoothed 2D contour was computed to circumscribe the peak of the RF at its half-maximum height relative to the baseline for the peak temporal lag (Fig. 2B, top right). Then the direction selective evoked responses were computed from the flash events inside the defined RF contour as a function of their motion direction, with error bars indicating two standard errors of the mean at each direction (Fig. 2B, bottom).

The tuning for motion in full-field mapping and also later for dot field stimuli in foraging were fit using a modified von Mises function. The tuning curve for firing rate $$mathtex$$R$$mathtex$$ was defined as a piecewise continuous function based on a bandwidth parameter, $$mathtex$$K$$mathtex$$, as:$$mathtex$$R = b + A\;{\rm exp}\lpar {K\lpar \cos \lpar {\theta -\hat{\!\theta }} \rpar -1} \rpar \rpar$$mathtex$$when $$mathtex$$K \gt 0$$mathtex$$ and otherwise as:$$mathtex$$R = b + A\;\lpar {1-{\rm exp}\lpar {-K\lpar \cos \lpar {\theta -\;\hat{\!\theta }-180} \rpar -1} \rpar } \rpar \rpar$$mathtex$$where $$mathtex$$b$$mathtex$$ is the baseline firing rate, $$mathtex$$A$$mathtex$$ is the amplitude, $$mathtex$$K$$mathtex$$ is the bandwidth, and $$mathtex$$\hat{\!\theta }$$mathtex$$ is the preferred direction. Von Mises functions have been used previously to describe motion tuning in area V1 (Patterson et al., 2013). We adapted that function to allow for curves with wider-than-cosine tuning. Cosine tuning in the function occurs as $$mathtex$$K$$mathtex$$ approaches 0. We allowed the curve to continue to be defined for negative values of $$mathtex$$K$$mathtex$$ adopting an inverted von Mises with the opposite direction preference (180° opposite) such that the peak location remained at the same preference but was wider-than-cosine tuning. The modified curve was fit by maximizing the likelihood of the spike counts observed for each motion direction bin assuming Poisson firing statistics (Truccolo et al., 2005). The error bars were generated by a 10-fold Jackknife procedure, and tuning width was estimated from the half width of the curve in degrees.

Neural inclusion criteria

Areas MT and adjacent MTC were identified in targeted recordings based on their direction selective responses and retinotopy (Rosa and Elston, 1998). While we targeted neurons in area MT, a small number of motion selective neurons from adjacent MTC (also called V4t in lower hemifield and MST lateral in upper hemifield for the macaque) may have been included that lay near the vertical meridian. MTC has been reported to contain neurons with similar sized RFs and a significant portion of those cells also have motion selective responses (Rosa and Elston, 1998). We used the response to random dot motion patches placed inside the RF during the foraging task (irrespective of saccade condition) to evaluate if neurons had significant visual and motion selective responses. We only included neurons if they had a significant visual response defined by an increase in spike counts from 50 to 100 ms following the onset of a dot motion stimulus (averaged across sampled directions) as compared to a baseline from −100 to 0 ms before onset (Signrank test, p < 0.05). We also required that neurons had a significant direction selective index (DSI) indicative of motion tuning. The DSI was computed from spike counts from 50 to 150 ms after the stimulus onset as$$mathtex$${\rm DSI} = \displaystyle{{\left\vert {\mathop \sum \nolimits_{{\rm n} = 1}^{16} R_ne^{i\theta_n}} \right\vert } \over {\mathop \sum \nolimits_{{\rm n} = 1}^{16} R_n}}$$mathtex$$where R_n represents the mean spike count in response to a motion direction. To compute confidence intervals on the DSI, we used a 10-fold Jackknife procedure and units were included if the lower bound on the 95% confidence interval was above a DSI of 0.05. Additionally, we required that a minimum of 48 trials with straight single-step saccades be completed for the RF location and at least 48 trials combined for the other two foraging locations.

Saccade foraging task

To study pre-saccadic attentional modulations, we designed a saccade foraging task performed by marmoset monkeys in which a saccade was performed to one of three equally eccentric peripheral motion apertures (Fig. 1A). In each session, one of the apertures was positioned to fall near the center of the RF of a neuron or the set of neurons under study, while the other two were placed 120° apart from it at the same eccentricity. The task trial began with the fixation of a small spot (0.3° radius, 0.5 cd/m² center, 230 cd/m² surround) within a 1.5° radius window for a delay uniformly distributed between 0.1 and 0.3 s, presented on a gray background (115 cd/m²). After the fixation period, the fixation point was offset and three dot motion apertures (as described earlier) appeared in the periphery. The monkey was given up to 1.5 s to make a saccade out of the fixation window to one of the apertures with the final eye position remaining within the target window for 0.25 s to confirm the saccade endpoint. We rewarded saccades to any location as long as they differed from the previous trial to encourage foraging. A correct choice was rewarded with 10–20 μl of liquid reward and the appearance of a marmoset face at the aperture location for 1 s, providing positive feedback. The juice reward consisted of marshmallows blended with water that were prepared fresh for each daily session. An incorrect choice back to a location sampled in the previous trial resulted in a black Gaussian spot filling the chosen aperture, as feedback for choosing the wrong location. The next trial proceeded at an interval of 1–2 s depending on juice rewards.

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Figure 1.

A saccade foraging task to test if pre-saccadic attention involves feature gain. A, The saccade foraging task encouraged sampling between three peripheral apertures, one at the RF location. Subjects fixated centrally for 100–300 ms after which dot motion apertures appeared, and reward was given for making a saccade to an aperture that differed from the previous trial. Apertures contained 100% coherent moving dots, and across apertures, the motion direction was sampled independently. B, Neural recordings were made from areas MT/MTC to measure neural tuning curves for motion direction. C, Example tuning curves demonstrate changes predicted for a spatial gain model (blue) and the feature similarity gain model (dashed line, green), compared against the neutral tuning curve (black). D, The proportional gain as a function of direction would be predicted to be uniform for the spatial gain model (blue). For feature gain, it should have a peak at the preferred direction relative to the flanks (green).

Trial inclusion criteria

We limited analyses to trials in which saccades to foraging targets were executed in a single step without preceding movements and after a minimum latency from stimulus onset. First, we detected any micro-saccades of amplitude greater than 0.5 visual degrees that occurred during the fixation period and excluded those trials. To ensure that the animal had time to see the stimulus before initiating their saccade, we excluded trials where the reaction time (saccade onset from stimulus onset) was smaller than 0.12 s. We also excluded trials where the animal made two smaller saccades that stepped to the aperture and trials in which the saccade end point fell short of the aperture center (>50% of the target eccentricity). Last, we require that saccades fall within a window that has a radius of 50% of the eccentricity of the center of the aperture in order to be counted within that aperture. When all criteria were applied, this resulted in excluding 21.4% and 13.1% of trials across sessions for Marmoset E and Marmoset M, respectively. We included a small percentage (10%) of catch trials that required the monkey to maintain central fixation. In these trials, the fixation period was extended to 0.5 s without any target apertures ever appearing. For holding fixation, the monkey was rewarded with both juice reward and a marmoset face that appeared at fixation.

Temporal separation of the stimulus and saccade onset epochs

We examined the neural firing response time-locked relative to the moment of stimulus and saccade onset. Because there is no extended delay period between stimulus and saccade onset under natural foraging tasks, as in a delayed saccade task, these two intervals will be partly overlapping depending on the saccadic reaction time, and it is important to choose analysis intervals that minimize their overlap. To examine the temporal response of neurons, we smoothed the peri-stimulus time histograms (PSTHs) for the “toward” and “away” conditions using a Gaussian temporal kernel (σ = 5 ms). The stimulus locked onset response revealed a visual latency of approximately 40 ms with a transient peak that rose and fell by 70–80 ms into a sustained response (Fig. 4A,B, left). We defined a stimulus–response epoch to be between 40 and 90 ms after stimulus onset to capture the early peak. The response when instead time-locked to saccade onset reveals a rise in firing rate continuing up to 20 ms after the saccade followed by suppression (Fig. 4A,B, right). We defined the pre-saccadic window to be between −30 and +30 ms from saccade onset. While previous studies using delayed saccade paradigms have used windows that begin from −100 ms, in our paradigm that interval would include trials with shorter saccadic latencies that include the stimulus evoked peak response. It might be difficult to identify the stimulus evoked response, as it would be convolved with the variability in reaction times, but it would still influence the firing rate in those epochs preceding saccade onset. We thus restricted analyses to reaction times later than 120 ms and set our pre-saccadic window to be no earlier than −30 ms from saccade onset such that no part of the stimulus evoked transient, which resolved to a sustained level by 90 ms, would be mixed with the saccade onset response. For the end of the saccade onset epoch, we chose +30 ms because the visual latency of neurons was no earlier than 40 ms, and thus responses out to that period would yet reflect visual motion induced by the saccade itself.

While selection of the stimulus and saccade onset epochs as described above reduces their temporal overlap, it also restricts the extent to which we can time-lock responses after stimulus onset or before the saccade. To address this limitation and extend those intervals, we performed a second analysis on firing responses that preferentially sampled longer reaction time trials at extended latencies. Specifically, at each stimulus locked latency, only trials that were not within 30 ms of saccade onset were included in computing the trial averaged firing rate. Likewise, at each saccade locked latency, only trials that were not within 120 ms of stimulus onset were included. This approach was applied to extend stimulus locked analyses for 65–115 ms and 90–140 ms epochs and also when using 50 ms sliding windows to compute the number of units significantly modulated by attention condition across time (Fig. 5A–C).

Although temporal intervals were selected to minimize overlap between stimulus and saccade epochs, we must also control for any differences in saccade reaction times between “toward” and “away” conditions when comparing modulation in their firing rates or tuning curves. For example, shorter reaction times in one condition could lead to differences in the adaptation state of the neuron, which if not corrected for, could produce differences in firing at the time of saccade onset. To control for those differences, we created resampled trial distributions for the “toward” and “away” conditions that matched the saccadic reaction times between conditions. For each session, the distribution of reaction times was computed in 10 ms bins, and stepping through each bin, we randomly sampled an equal number of trials from the condition with more trials in order to match the number to the condition with fewer trials. There are no clear signs of the stimulus evoked response contaminating the saccade onset epoch, nor of differences in adaptation between conditions. All comparisons between “toward” and “away” conditions applied this correction to be conservative, although all effects reported remained consistent without it throughout the results.

Firing rate and variability analyses

The mean and variability of the firing rate were assessed in the stimulus and saccade onset intervals. The mean firing rate was computed from all trials for either the “toward” and “away” conditions, and thus each of those conditions was sampled randomly over the 16 motion directions used in the task. To measure variability, we computed the Fano factor (FF), which provides a measure of variance in spike counts across trials that is normalized by rate. For a Poisson process, the spike count variability scales in proportion to the mean count, giving unity FF. However, nonlinearities such as the spike refractory period, burst firing, or super-Poisson fluctuations in rate produce dependencies on how the FF scales with a rate that deviates from linearity. Thus, it is necessary to match firing rates between the “toward” and “away” conditions before comparing them in order to disassociate changes in FF from changes in mean rate (Mitchell et al., 2007; Churchland et al., 2010). To match firing rates, we first computed the mean spike counts for each of the 16 motion directions in each of the two saccade conditions (16 points of mean vs variance for each condition). We performed a search in random order for each of the 16 points in the “toward” condition to find the point with the mean rate in the “away” condition most closely matching its mean rate, without reference to whether motion direction matched, and accepted those as a pair if the two rates matched within 5%. Repeating this procedure without replacement across all points identified the region of overlap between the two distributions that were constrained to have nearly matching rates (<5%). The FF was then computed by dividing the spike count variance by the rate at each point and then averaging those ratios for each saccade condition. In one monkey where we performed recordings using linear arrays, it was also possible to isolate many simultaneously recorded pairs of neurons in order to estimate the noise correlations. Spike counts were computed during the pre-saccadic epoch from −30 to 30 ms at saccade onset, and correlations were computed within trial sets where the same motion direction was in the RF and then pooled across motion directions.

Noise correlations

In one marmoset where array recordings were made, it was further possible to analyze noise correlations between pairs of simultaneously recorded neurons. Spike counts for noise correlations were computed during the pre-saccadic epoch from −30 to 30 ms at saccade onset. For each neuron, the mean response to each of the 16 motion directions per attention condition (toward and away) was first subtracted from those pre-saccadic counts to eliminate any stimulus-driven response. Then the correlation coefficient between the residual counts of the pair was computed to give the noise correlation. To measure the signal correlation between pairs, we first averaged the 16 points of the tuning curve for the motion direction of each neuron across both attentional conditions during the stimulus onset period (40–90 ms from stimulus onset). The signal correlation was computed as the correlation coefficient between the 16 points on the tuning curve for each pair of neurons considered. Signal correlation defines how much overlap there is in the motion tuning between neural pairs. Across the population of pairs, the noise correlations were binned and plotted for different signal correlations from −1 to 1 with bins ±0.1 wide and stepping in bin size with increments of 0.05.

Mutual information analysis

In the saccade onset interval, we examined if there was an increase in neural sensitivity for motion direction. We measured sensitivity from the distributions of firing rates across the 16 motion directions by computing the mutual information (MI). The MI quantifies how much information one variable (such as firing rate) provides about another variable (such as motion direction) measured in bits. For our purposes, it provides an estimate of sensitivity, much as classic measures like the AUC in ROC do for the case of discriminating two sensory conditions, but it is readily generalized to more than two stimulus conditions and thus is highly suitable for use with tuning curves (Hatsopoulos et al., 1998). We calculated a MI for both the “toward” and “away” conditions using the equation:$$mathtex$$I\lpar {x\semicolon \;y} \rpar = \sum\nolimits_{x}\sum\nolimits_{y} p\lpar {x \;y} \rpar {\rm log}\lpar {p\lpar {x \;y} \rpar {\rm \sol }p\lpar x \rpar p\lpar y \rpar } \rpar {\rm \;\;\;}$$mathtex$$where x is the motion direction stimulus shown and y is the measured firing rate. Computing the MI requires that we estimate the probability distributions (p(x), p(y), and p(y|x), using histograms and binning of firing rate data per stimulus direction. For the stimulus variable x, we binned based on the motion direction, where we had sampled from 16 possible directions. However, to further enforce a smoothing constraint on our data and represent that adjacent motion directions are related, we further pooled the firing rate data from the two adjacent motion direction bins arranged on the circle, thus giving on average three times as much firing rate data per motion direction bin and forcing a smoothing constraint on the data. The binning of the firing rate, y, was determined based on a “goodbins” function described in Scott (1979), applied to the total firing rate distribution across all motion directions to estimate the marginal distribution p(y). Then the histogram of firing rates conditioned on each stimulus direction, p(y|x), was computed using those bins that were established to describe p(y).

Comparing motion tuning between toward and away conditions

To examine neural tuning changes across the “toward” and “away” conditions, we fit the motion direction tuning of individual MT units with a modified von Mises function as described earlier in methods. The von Mises curves provide parameters for amplitude, baseline, and width for each tuning curve in the two conditions. We constrained fits to share the same preferred direction between saccade conditions. Only units where the net quality of the curve fits for the two conditions (pooled over both curves) exceeding an R-squared of 0.5 were included. This significantly reduced our neural population included for von Mises-based analyses (Marmoset E had 33 units, and Marmoset M had 287 units).

To quantify the modulation of parameters between the “toward” and “away” conditions, we calculated an attention index (AI) for each of the parameters considered as:$$mathtex$${\rm AI} = \lpar {{\rm Towards}-{\rm Away}} \rpar {\rm \sol}\lpar {\rm Towards} + {\rm Away\rpar }$$mathtex$$where AI ranges from −1 to 1, with zero indicating no change. The AI metric is useful for emphasizing percentage changes in a variable. All statistical tests on AI indices were nonparametric (signed-rank or rank-sum tests, p < 0.05).

Linear prediction model

To evaluate which modulations in tuning curves contributed to increases in neural sensitivity, we fit a linear model. The input parameters to the linear regression included the AI for the von Mises fit parameters of baseline, gain, and curve half width, as well as the AI for the rate-matched FF. We also include a constant term, giving five input parameters. The output aimed to predict the AI for MI of each unit. Linear fit coefficients (and error bars) were fit using the “regress” function in MATLAB (version 2018). Only units that had reliable von Mises fits for both the “toward” and “away” conditions (R² = 0.5) were included.

Nonparametric fit of tuning curves

Von Mises fits are biased to fit better for neurons with high firing rates and high motion selectivity. Therefore, we sought an alternative metric to quantify changes in baseline, amplitude, and tuning width in the total population. We smoothed the mean responses per motion direction (raw tuning curve) by pooling across the two adjacent motion directions for each point in the tuning curve. Then we computed the preferred motion direction by computing the resultant vector (circular statistic) on the mean smoothed tuning curve averaged over the “toward” and “away” conditions. Then smoothed responses in each attention condition were rank ordered by their angular distance from that preferred direction, with the least preferred direction being defined as 180° opposite of preferred. Baseline was computed from the rate at the least preferred index while amplitude was the difference between the rate at the most and the least preferred. Tuning width was computed by subtracting the baseline (zeroing any resulting negative values) and computing the width from the preferred direction at which half the area under the baseline subtracted curve was contained.