Active dissociation of intracortical spiking and high gamma activity

Lei, Tianhao; Scheid, Michael R.; Flint, Robert D.; Glaser, Joshua I.; Slutzky, Marc W.

doi:10.1038/s41586-026-10331-y

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Published: 01 April 2026

Active dissociation of intracortical spiking and high gamma activity

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Abstract

Cortical high gamma-band activity (HGA) is used in many scientific investigations^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}, yet its biophysical source is a matter of debate. Two leading hypotheses are that HGA predominantly represents summed postsynaptic potentials or—more commonly—that it predominantly represents summed local spikes. If the latter were true, the nearest neurons to an electrode should contribute most to HGA recorded on that electrode. To test these hypotheses, here we trained monkeys (Macaca mulatta) to decouple local spiking from HGA on a single electrode using a brain–machine interface. Their ability to decouple them suggested that HGA is probably not generated simply by summed local spiking. Instead, HGA correlated with co-firing of neuronal populations that were widely distributed across millimetres of cortex. The neuronal spikes that contributed more to this co-firing also contributed more to, and preceded, spike-triggered HGA. These results suggest that HGA arises mainly from summed postsynaptic potentials triggered by the synchronous co-firing of widely distributed neurons.

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Main

High gamma-band activity (HGA; power in the 70–300-Hz band of the local field potential (LFP), sometimes called broadband activity^1,2) is a robust, highly informative mesoscale cortical signal with high spatio-temporal resolution. It has been used to investigate many topics, such as sensory processing³, motor control^4,5,6,7,8, brain–machine interfaces (BMIs)^9,10,11 and cognitive neuroscience, including attention, memory, language and mood^{12,13,14,15,16,17,18}. Despite this broad usage, the origin of HGA remains rather controversial. Many studies have suggested that HGA is an ‘index’ of local neuronal action potentials (spikes), capturing either the total firing rate^{1,2,19,20,21,22} or the synchronous firing of neurons in local populations^{15,23,24,25,26}. Two seminal studies found a modest correlation between HGA and local spiking activity near the recording electrode^23,25. Others suggested that this correlation was due to spectral power from spikes ‘leaking’ into the high-gamma band range^{27,28,29,30,31}. Many subsequent studies cited these findings when equating HGA with summed local-population spiking activity, despite the low correlations with individual neurons.

However, other results suggest that HGA is not simply an index of local spiking activity, finding low correlation between spikes and HGA recorded from the same electrode^14,32. Rather, HGA correlated highly with low-dimensional neuronal population spike rates from a distributed cortical area³² (16 mm²). The mechanism of this higher correlation with population spiking activity is unknown; volume conduction is not the explanation at such a long range. Evidence that HGA is generated mostly by postsynaptic potentials (PSPs)²⁷ might indirectly support this finding. For example, HGA in layer 5 of the visual cortex correlated with spiking, whereas HGA in layers 2–3 did not³³. Furthermore, blocking N-methyl-d-aspartate (NMDA) activity silenced HGA but not local spiking, consistent with HGA being generated by PSPs.

Thus, the biophysical origin of HGA and its relationship with spiking remains controversial. The two main proposed hypotheses are (1) that HGA originates predominantly from summed waveforms of nearby action potentials by volume conduction (‘leakage’), or (2) that it originates mainly from summed postsynaptic activity (Fig. 1). The second hypothesis implies that HGA will be highest when inputs to the local neuronal population fire synchronously. These two hypotheses are not exclusive of each other, and both sources could contribute to HGA; however, the broader literature tends to attribute the biophysical source to one or the other. Further, most previous evidence about HGA’s origins has been based on correlations or modelling.

**Fig. 1: Illustration of potential sources of HGA generation and task schematic.**

Here, we developed a BMI paradigm to causally test these hypotheses. This test required monkeys to modulate HGA independently from spike rate on a single electrode (Fig. 2). We found that monkeys could indeed decouple spiking from HGA on the same electrode in the primary motor cortex (M1) within a few sessions. We also investigated how HGA relates to neural population activity. HGA on the control electrode (CE) did not exclusively correlate with action potentials from nearby neurons. Instead, HGA was correlated with low-dimensional, synchronous neuronal population firing (‘co-firing’)³⁴ patterns spread across the array. Spike-triggered averaging of HGA showed that spikes throughout the network preceded local HGA by a similar lag to that between presynaptic spikes and PSPs. Finally, we investigated how the neuronal population activity could explain the independent modulation of HGA and spike rate. Together, these results provide evidence consistent with the predominant source of HGA being summed nearby postsynaptic activity that is triggered by synchronous firing activity throughout the wider neuronal ensemble. These findings help reconcile previous results showing a high correlation between averaged HGA and spiking across the array with those supporting the hypothesis that PSPs are the main source of HGA.

New BMI enhances the dissociation of spikes from HGA

We designed an orthogonal neurofeedback (ONF) BMI to test whether monkeys could dissociate spiking rates from HGA recorded on the same electrode. Three monkeys first performed a two-dimensional (2D) centre–out cursor control task using a manipulandum (‘hand control’). They then performed the ONF task, which mapped unsorted spikes and HGA from an individual CE to orthogonal components of cursor velocity (Fig. 1c,d). This paradigm, which we have used with myoelectric control in humans^{35,36,37,38,39}, required the monkeys to dissociate HGA from nearby spikes to reach targets on the cardinal axes. For each monkey, we selected three electrodes with relatively high spike–HGA correlation as CEs for the task (Methods). Monkeys performed at least one 10-min file of hand control at the beginning and end of each session (day). Numbers of recording sessions for each monkey–CE combination are summarized in Extended Data Table 1.

Monkeys performed the task proficiently, often within the first session (Fig. 2). Very early in ONF training, there were numerous failed trials and trajectories were longer; these quickly decreased in number and length, respectively, and trajectories straightened (Fig. 2a and Extended Data Fig. 1a). Across CEs and sessions, performance started high and improved slightly, as measured by success rate, time to target and path length (Fig. 2b–d). Take-off and entry angles did not change significantly (Fig. 2e,f). After removing the first session, success rate and time to target did not improve significantly (two-sided t-test, P = 0.87 and 0.17, respectively). Performance improvement occurred mainly within the first 50 trials, then plateaued (Extended Data Fig. 1b). These results suggested that monkeys can innately modulate the two signals independently.

We next examined the independence of spiking and HGA. During hand control (Fig. 3a), trial-averaged HGA and spike rate sometimes modulated together, but often did not. During ONF control (Fig. 3b), they were starkly dissociated. Specifically, during trials to the spike target, spike rate increased whereas HGA did not; during trials to the high gamma (HG) target, the opposite occurred. We compared the correlation coefficient between single-trial spike rate and HGA from the last second of each ONF trial with that during hand-control trials (Fig. 3c). Note that HGA and spike rate were moderately, not highly, correlated even during hand control, either on the CE (0.36 ± 0.34, mean ± s.d.), or on other electrodes (Extended Data Fig. 2a). Correlations decreased significantly during ONF control in all CEs to near 0 (−0.037 ± 0.39). This held true even in the electrodes with the highest hand-control correlation, as well as during the first 1 s of trials (Extended Data Fig. 2b), and from the start of the first session in most cases (Extended Data Fig. 1c). Thus, the monkeys independently modulated spikes and HGA on the same electrode at a single-trial level. As an additional control for the possibility that monkeys were just separating the closest one or two neurons from HGA on the CE, we lowered the spike threshold to 3 s.d. (in the ‘hash’, or multiunit spikes) for two CEs. Although the single unit on the CE in this case was stable over sessions, the unsorted waveforms varied quite widely, implying that they represented the spiking of many local neurons (Extended Data Fig. 3a–d). Even in this case, the monkey could still independently modulate the two control signals (Extended Data Fig. 3e).

**Fig. 3: Independent modulation of spikes and HGA.**

Next, we examined this independent modulation in individual time bins. In the second before reward, we defined the spike–HG angle for each 50-ms bin as the angle of the vector sum of the mean HGA and spike rate on the CE for that bin (Fig. 3d and Extended Data Fig. 4). We defined the SP+ state as times with increased spike rate and a baseline level of HGA (spike–HG angle of 0° ± 15°) and the HG+ state as times with increased HGA and a baseline spike rate (spike–HG angle of 90° ± 15°). During ONF control across all monkey–CE combinations, more bins were in the SP+ states (9.3%) and HG+ states (18.5%) than they were during hand control (SP+ states: 7.2%; HG+ states: 7.4%); that is, there was more independent modulation during ONF control. Moreover, there were fewer bins with spike–HG angles indicating simultaneous increases in HGA and spike rate (45° ± 15°) during ONF control (3.6%) than during hand control (16.1%), showing decorrelation on short timescales. Together, these results consistently showed that HGA and spiking on the same electrode were separable.

Distributed spikes do not leak into HGA

To further investigate the possibility that HGA is generated by spike leakage through volume conduction, we examined the relationship between HGA on the CE and spikes on all electrodes. First, we qualitatively examined the trial-averaged spike rate and HGA on each electrode prior to reward for each trial type (Fig. 4a–d, monkey C, CE 63). During spike target trials, spike rate increased most on the CE, with minimal changes in the spiking on most other electrodes (Fig. 4a) and without changes in HGA on any electrodes (Fig. 4b). During HG target trials, spike rate decreased on the CE and increased on many other electrodes (Fig. 4c), whereas HGA increased strongly on the CE and weakly on other electrodes (Fig. 4d). We then examined the spatial relationship across the array between mean spike rate and HGA over the last second of each trial (Fig. 4e,f and Extended Data Fig. 5). If CE HGA were generated mainly by spike leakage, we would expect higher spike rates on the electrodes surrounding the CE on HG target trials, because spiking on these electrodes would contribute most to the increase of CE HGA when the CE spiking rate did not modulate. Instead, in HG target trials, we observed a widely distributed increase in spike rates across the array, with no bias towards electrodes neighbouring the CE. To quantify this observation, we tested whether CE HGA correlated significantly more with weighted summed spiking activity near the CE than with summed spiking near randomly selected electrodes. We modelled the contribution of nearby spiking activity to HGA on the CE by volume conduction. That is, we computed a sum over electrodes of trial-concatenated spike rates weighted by the inverse of the squared distance from the CE (Methods). In this scenario, the greatest contributor to HGA is spiking activity recorded on the CE itself. We found that this distance-weighted sum of spikes (DWSS) correlated minimally with trial-concatenated HGA on the CE (R = 0.10 ± 0.12, mean ± s.d., n = 9 monkey–CE combinations; Fig. 4g and Extended Data Fig. 6). This was not significantly larger than either (1) the correlation of CE HGA with the DWSS calculated using random electrodes, excluding the CE (one-sided quantile test, P = 0.99), or (2) the correlation between HGA and the DWSS on the same random electrodes (one-sided quantile test, P = 0.92; Fig. 4g and Extended Data Fig. 6). Thus, nearby electrodes were not particularly predictive of the CE HGA.

**Fig. 4: CE HGA correlates closely with population co-firing.**

HGA correlates with distributed neuronal co-firing

To explore the relationship between mesoscale population-level spiking and CE HGA further, we applied factor analysis to extract the common factor that best explained population spiking activity over days. This ‘co-firing pattern’³⁴ is a low-resolution measure of synchrony. In randomly selected single trials, the co-firing pattern was highly correlated with CE HGA but uncorrelated with CE spiking (Fig. 4h). Across monkey–electrode combinations and sessions, regression models fit co-firing better to HGA (R = 0.6 ± 0.13, mean ± s.d.; Fig. 4i) than to spike rate (R = 0.3 ± 0.11), including for greater numbers of factors (Fig. 4j). The correlation between co-firing and HGA held in individual sessions (Extended Data Fig. 7a).

The electrodes with high co-firing pattern weights were spread broadly across the array (Fig. 4k). This was true in all three monkeys, with variable numbers of highly weighted electrodes across monkeys (Extended Data Fig. 7b). Notably, high weights were not concentrated near the CE (Fig. 4k,l and Extended Data Fig. 7c), consistent with the DWSS results.

To more precisely investigate population spiking activity patterns that uniquely relate to the modulation of CE spiking or HGA, we used contrastive principal component analysis (cPCA). We fitted two cPCA models to identify an HG+ subspace (which maximized variance in HG+ time bins and minimized variance in SP+ time bins) and an SP+ subspace (vice-versa). As expected, across all monkey–CE combinations, HG+ subspace activity correlated with CE HGA, whereas SP+ subspace activity correlated with CE spike rate (Extended Data Fig. 8a), including in individual sessions (Extended Data Fig. 8b). High weights for the first HG+ cPCs were distributed across the array (Extended Data Fig. 8c,d). Because the spiking of HG+ states correlated with CE HGA, we would also expect synchronous (co-firing) activity occupying the HG+ neural subspace; that is, lower HG+ subspace dimensionality. In line with this, we found that the HG+ subspace was significantly lower dimensional than was the SP+ subspace (P = 0.02, quantile test on mean difference curve; Extended Data Fig. 8e and Methods). These results corroborate the previous findings with factor analysis.

CE HGA peaks just after co-firing spikes

How does synchronous population firing (co-firing) generate CE HGA? One possibility is the second hypothesis in Fig. 1b: synchronous spikes from broadly distributed neurons arrive at dendrites and/or somas near the CE and elicit PSPs that summate. This would predict an increase in CE HGA following spikes recorded on other electrodes. Furthermore, spikes on the electrodes that contributed more to the co-firing pattern (which correlated with HGA) should contribute more to the increase of CE HGA. To investigate these relationships, we computed the mean CE HGA triggered by the spikes on each electrode during ONF control, or spike-triggered average HGA (Fig. 5a and Methods). An increase in the CE HGA was triggered by spikes on most other electrodes (Fig. 5b and Extended Data Fig. 9). The CE HGA peaked at mean lags of 10.2 ms (95% confidence interval (CI): 5.9–14.5), 10.9 ms (95% CI: 6.0–15.8) and 16.5 ms (95% CI: 13.5–19.5) after the spike time for monkeys C, J and M, respectively (Fig. 5b and Extended Data Fig. 9). This range of delays agrees with the estimated timing of the peak of PSPs relative to presynaptic spike times.

**Fig. 5: Spikes that contribute most to co-firing contribute most to HGA.**

Moreover, spikes on electrodes with higher co-firing weights (Fig. 4k) produced a larger peak in the spike-triggered HGA average (Fig. 5c). To characterize this observation, we used k-means clustering to separate the normalized spike-triggered HGA traces into two clusters on the basis of their shape. This produced two groups of average spike-triggered HGA traces (Fig. 5d). One cluster (‘with response’) clearly increased in HGA after the spikes, whereas the other did not (‘no response’). The co-firing weights of the corresponding electrodes in the with-response cluster were significantly higher than were the weights in the no-response cluster (two-sided Wilcoxon rank-sum test; monkey C, CE 63, P = 0.003; monkey J, CE 52, P = 0.001; Fig. 5e). These effects were observed in all monkeys (Fig. 5d,e and Extended Data Fig. 9). Thus, the neurons that contributed most to the network co-firing pattern also contributed most to the spike-triggered HGA average. Combined with the high correlation of the co-firing pattern and HGA, these results support the hypothesis that synchronized firing activity from the neuronal population arrived at, and elicited synchronized PSPs from, dendrites and somas close to the CE.

HG+ and SP+ subspaces are intrinsically independent

The unique subspaces we identified for CE spike rate and HGA enabled us to further investigate how these signals were dissociated in ONF. Independent control of the two signals was reflected in the close-to-orthogonal relationship between the leading subspace principal angles of SP+ cPCs and HG+ cPCs (Extended Data Fig. 10a). We questioned whether the monkeys had to learn completely new ensemble firing patterns to modulate CE HGA or spike rates in isolation. If this were true, the SP+ and/or HG+ cPCs would explain very little variance of the hand-control data that span the ‘intrinsic manifold’⁴⁰. To test this, we projected the population spiking activity during hand control into the HG+ and SP+ cPC subspaces and computed the variance accounted for in the original hand-control data by these two unique subspaces (Extended Data Fig. 10b,c and Methods). Over all nine CEs, the top ten HG+ cPCs and SP+ cPCs explained 16.7 ± 2.7% and 9.7 ± 1.3%, respectively, of the variance in hand-control data. In comparison, the top ten HG+ cPCs and SP+ cPCs computed from hand-control data explained 26.3 ± 7.0% and 15.9 ± 4.3% of the variance in hand-control data. Thus, the cPCs used for ONF control accounted for more than half of the hand-control-only cPCs comparison. (For reference, the top ten PCs of hand-control data explained 60.9 ± 4.0% of its own variance). These results suggest that the ability to independently modulate HGA and spiking lies partially within the intrinsic neural manifold, which fits with the monkeys’ rapid proficiency in ONF and implies that our findings about the source of HGA are not unique to ONF.

Discussion

High gamma activity is often characterized as a proxy for spiking near the recording electrode^{1,2,19,21,22,41,42,43,44,45}. Here, we provide causal evidence that monkeys can use a novel BMI to decouple spiking and HGA quickly and consistently, even with a very low spike threshold. Furthermore, HGA was correlated with synchronized population spiking activity (co-firing) that was distributed widely across the array, rather than a distance-weighted sum of spikes. Spike-triggered CE HGA peaked about 12.5 ms after spikes occurred on other electrodes and was highest for spikes from electrodes that contributed most to the co-firing pattern. Finally, we identified two orthogonal neuronal subspaces that were associated uniquely with HGA modulation and spiking modulation on the CE. These subspaces overlapped with the neuronal manifold that was active during arm movement. Together with the rapid ability to decouple spiking from HGA, this suggests that this decoupling was intrinsic.

Multiple studies have contributed to the prevalent view of HGA as an index of summed local spiking. Our results in fact mostly agree with their underlying findings. First, the finding that co-firing of distributed neurons correlates highly with HGA agrees with previous findings that HGA was highly correlated with spiking averaged over broadly spaced electrodes. By contrast, those seminal studies showed, as we (Extended Data Fig. 2a) and others^14,32 also found, only modest correlations between HGA and spikes on individual electrodes. Although experimental^25,29 and computational²⁰ modelling studies showed that spike leakage can contribute to HG band power, the proportion contributed was modest³¹.

Our results also concur with computational models^2,46,47 and experimental findings^{18,48,49,50,51} suggesting that HGA is generated by summed PSPs^20,52 and possibly dendritic calcium spikes²⁷. HGA can increase regardless of changes in local spiking⁵³, and retains decodable information even without nearby recorded spiking activity⁵⁴. Most convincingly, blocking NMDA-mediated postsynaptic activity reduced HGA, but not spiking activity³³. Here, we saw that CE spiking, which should contribute the most to leakage, could be voluntarily decoupled from HGA—even from the highest spectral portion of HGA (200–300 Hz). Moreover, monkeys decoupled spikes from HGA even with a spike detection threshold in the hash, resulting in many nearby neurons contributing to the spiking signal (Extended Data Fig. 3). HGA strongly correlated with broad network co-firing, but this was not due to leakage (Fig. 4g). The timing of the spike-triggered CE HGA peak agrees with presynaptic spike to PSP timing⁵⁵. Our findings thus agree with and extend this previous evidence.

Experimental and modelling results suggested that synchronous inputs greatly increase the amplitude of intracortical LFPs⁵² and HGA in electrocorticography⁵⁶. Notably, the latent dynamics of the broader neuronal population during reaching correlated with HGA on individual electrodes after subspace alignment³². Here, both single-factor co-firing and the cPCs for HG+ states correlated highly with HGA without requiring subspace alignment. Furthermore, the co-firing pattern involved neurons distributed over millimetres, not concentrated around the CE. Our results thus corroborate and extend these studies, showing that mesoscale synchrony might be important in generating local HGA.

Our findings help to reconcile previous evidence of the importance of PSPs, synchronous inputs and spike leakage to HGA. The hypothesis that synchronous PSPs are the predominant source of HGA harmonizes our findings most parsimoniously with previous observations. In this hypothesis, high correlations of spatially averaged spikes with HGA are due to both signals being driven by the same underlying synaptic events: PSPs generate HGA and increase the probability of generating nearby spikes. The spectral leakage hypothesis cannot easily explain the active, rapid dissociation of HGA and spikes we observed (even with a low spike threshold), the typically low correlations of HGA and local spikes even during hand control or the strong relationship between HGA and spikes recorded millimetres away. PSPs summate to higher levels when the inputs generating them are more highly synchronized. Their much longer duration than spikes also facilitates summation, compared to spikes. Thus, a PSP source of HGA would predict synchronous firing, but not spatial concentration, of input neurons, consistent with our results. Therefore, our observations are best explained by the predominant source of HGA being summed PSPs in somas and/or dendrites near the recording electrode generated by synchronous spiking of mesoscale-distributed presynaptic neurons.

This study has some limitations. Although the data in Extended Data Fig. 3 suggest that our spike control signal represents many neurons, we cannot precisely quantify that number. The Utah array has limited spatial resolution. Thus, we cannot completely rule out the possibility that a considerable source of HGA is unobserved neurons. Still, for this to happen, those neurons would need to be near enough to leak into the CE HGA band, but not close enough for their spikes to be detected (that is, more than 140–200 μm away^57,58). Higher-density electrodes and broader coverage could help to investigate this possibility of leakage further and determine whether neurons further away than 4 mm contribute to local HGA.

The PSP hypothesis would also explain why HGA has greater longevity than spike recordings with current electrode technologies. In addition, the contribution of distributed neurons to HGA reduces sensitivity to variability in neuronal firing patterns, which makes HGA more stable than spikes^8,9 without requiring subspace alignment³². These factors are attractive for BMI applications. In addition, the contribution of synchronous, widely distributed inputs to HGA could be useful in studies of sensory integration, attention, language and decision-making^{3,12,13,14,59} involving integration of activity from several brain areas. Conversely, this fact might limit conclusions that can be made using HGA about activity in individual neurons in the neighbourhood. HGA can provide a parsimonious marker for mesoscale synchronous firing, which might be involved in many brain functions, including attention and binding⁶⁰. Although we only examined M1, it seems plausible that these findings would apply to many other neocortical areas that have similar cytoarchitectures. Thus, these findings have ramifications for a wide range of neuroscience and neuroprosthetic investigations.

Methods

Experimental procedures and approval

All procedures were performed under protocols approved by the Northwestern University Institutional Animal Care and Use Committee. Three adult rhesus macaque monkeys were trained in the experimental procedures described below.

Surgery

In each monkey, we surgically implanted a 96-electrode silicon electrode array (Blackrock Microsystems) into M1 contralateral to the arm used to control the cursor. During surgery, monkeys were anaesthetized with isoflurane (2–3%). Anaesthetic depth was assessed at all times by monitoring jaw muscle tone and vital signs. A craniotomy was performed above M1, and the dura was incised and reflected. Electrode arrays were implanted in the proximal arm area, as determined by referencing cortical landmarks and by intraoperative electrical stimulation with a silver ball electrode (2–5 mA, 200-μs pulses at 60 Hz). During stimulation, a reduced level of isoflurane (minimum alveolar concentration lower than 0.5) was supplemented with intravenous remifentanil (0.15–0.30 μg per kg per min) to reduce suppression of cortical excitability. The electrode array was positioned on the crown of the right precentral gyrus, approximately in line with the superior ramus (medial edge) of the arcuate sulcus. The electrode shank length was 1.5 mm. The preamplifier was grounded to the CerePort pedestal and referenced to two platinum wires with 3-mm exposed wire length placed under the dura. A piece of artificial pericardium (Preclude, Gore Medical) was applied above the array, and the dura was closed using 4.0 sutures (Nurolon, Ethicon). Another piece of pericardium was applied over the dura, and the craniotomy partially filled with two-part silicone (Kwik-Cast, World Precision Instruments). The craniotomy was then closed, and the skin was closed. All monkeys were given postoperative analgesics buprenorphine and meloxicam for two and four days, respectively.

Neural signal recording

All neural and behavioural data were recorded using a 96-channel Multichannel Acquisition Processor (Plexon). LFP signals were sampled at 1 kHz and band-pass-filtered from 200 Hz to 300 Hz. We deliberately chose this band to be as conservative as possible, because previous studies suggested that components of LFPs above 150 Hz were most contaminated by spike leakage^25,28,29. We computed the spectral power of each electrode from the band-passed LFP by applying a 256-point Hanning window (overlapped by 206 points) and calculating the squared amplitude (power) of the windowed signal’s discrete Fourier transform, yielding 50-ms-binned HGA. Multiunit spikes (threshold crossings) were high-pass-filtered at 300 Hz and sampled at 40 kHz. The signals were further downsampled to 1 kHz. The threshold on each electrode was set at 4.5 s.d. from the root-mean-square baseline activity on the electrode. Note that we also ran a subset of experiments using a lower threshold of 3 s.d. (in the ‘hash’, to reduce the possibility that we were missing some smaller-amplitude spikes near the electrode) and obtained similar results—monkeys could still decorrelate the signals. We defined spikes as unsorted threshold crossings on each electrode. To identify shunted electrodes, we calculated the pairwise R of the spike rates, binned at 1 ms, between all electrode pairs, and removed any electrode that had a pairwise R higher than 0.3 with any other electrodes. For all the analyses except the spike-triggered HGA analysis, we used 50-ms bins for both HGA and spike rates. The above procedures were performed for each file separately. In each file, we also removed electrodes on which the spike rates averaged less than five spikes per second. The available electrodes were used for further analysis after these shunted and low-spike-rate electrodes were removed.

Hand-control task

Three adult rhesus macaques, two male and one female (monkeys C, J and M), used a two-link manipulandum to move a cursor (1-cm-diameter circle) within a rectangular planar workspace (20 cm × 20 cm). The task was a four-target centre–out task, with 2-cm² outer targets spaced at 90° intervals around a circle of radius 10 cm. Each trial began with a target at the centre of the circle. After a random hold time of 0.5–0.6 s within the centre target, a randomly selected outer target was illuminated and the centre target disappeared, signalling the monkey to start a reach. The monkey needed to reach the outer target within 1.5 s and hold for a random amount of time between 0.2 s and 0.4 s to obtain a liquid reward. The task was performed in 10-min files.

ONF task

To maximize monkeys’ ability to control the cursor, we first selected electrodes on which spiking correlated highly with movement during the reach task. First, we computed the absolute value of the Spearman correlation coefficient (|R|) between binned spikes and HGA on each electrode and the velocity in the X and Y directions, respectively, for a total of four correlations (spikes–X, spikes–Y, high gamma–X and high gamma–Y) over a 10-min period. Next, we added the |R| corresponding to X and Y directions for each signal (that is, spikes–X + high gamma–Y; spikes–Y + high gamma–X), giving us two |R| values corresponding to the two possible arrangements of the signals for control. We then selected the electrodes with highest cumulative |R| as inputs (CEs) to use for the ONF task. Later, after monkeys learned to perform ONF control, we selected electrodes that had higher spike–HGA correlations (see below) during hand control.

ONF control was implemented by mapping linear filter outputs of the spike rate and high gamma signals to the X and Y components of cursor velocity, respectively. For either type of signal, we used a linear filter with a set of positive, identical weights set manually on the prior five time bins (50 ms each) of binned spike rates. A bias term was added to the filter output to allow the monkey to reach all parts of the workspace. A dynamic moving mean (averaged over the last 1 min of values) was subtracted from both HGA and spikes before applying filter weights to centre the signals to avoid drift and allow for negative cursor velocity when necessary. Velocity was then integrated to obtain the updated cursor position. Thus, the cursor would have zero velocity when both signals were at their mean activity levels. Both velocity and cursor position signals were computed at 20-Hz resolution.

Initial training involved performing a one-dimensional (1D) BMI task in each of the spike and HG directions. In this case, one 4-cm² target was placed along either the X or the Y axis only, respectively, and the cursor moved directly towards or away from the target. The trials were the same structure as for hand control, except that the hold time was 0.1 s in both centre and outer targets, with a maximum trial time of 15 s for a reward. Trials in which the cursor never reached the target within 15 s or failed to stay in the target for less than 0.1 s were considered failed trials. A typical session (day) lasted approximately 60–90 min (six to nine files), with 10 min (one file) performing hand control and 50–80 min (five to eight files) on BMI control.

Once the number of successes within a file exceeded 40 (typically after 3–7 days), the monkeys were switched to ONF (2D BMI) control. In this case, both filters were applied to their respective signals, and the outputs were mapped to X and Y velocity simultaneously—that is, the cursor moved as a vector sum of filtered spikes and HGA. Targets in this task were the same as in the 1D BMI task, except that they were randomly placed on the X or Y axis in each trial. The rest of the task parameters (hold time, max trial time) were the same as in the 1D task. Because the cursor moved as a vector sum, ONF required the monkeys to increase either spike rate or HGA, while maintaining the other constant, to successfully reach the targets. Target sizes were gradually reduced to operantly condition the monkeys to learn to modulate spike rate and HGA independently. We performed ONF on ten CEs across three monkeys; one was excluded because of noise affecting the spike recordings.

Computing the correlation between spike rate and HGA

To compare the correlation between spike and HGA for each control type (ONF control and hand control), we calculated the Pearson correlation coefficient between single-trial spike rate and HGA of the last second (twenty 50-ms time bins) preceding reward during either ONF control or hand control for every monkey–CE combination. We did this for all trials after the monkeys had become proficient in the ONF task (defined as acquiring at least 40 successes per file). We summarized the distribution of R values for hand control (Fig. 3c, blue) and ONF control (Fig. 3c, red) for every monkey–CE combination.

ONF performance metrics

We measured performance in the ONF task using success rate, time to target, path length, take-off angle and entry angle. We defined success rate as the number of successful trials divided by the total number of trials in each session. We defined time to target as the mean time from the outer target appearance to reward over all trials in each session. We defined path length as the mean cursor path of all the trials in each session. We defined take-off angle as the mode of the distribution of angles formed by the vector of the change in cursor position from 0 to 500 ms after the go cue for all trials in each session. Similarly, we defined entry angle as the mode of the distribution of angles formed by the vector of the change in cursor position in the last 500 ms of the trial for all trials in each session. Take-off and entry angles were further grouped by the target type (spike target versus HG target). To examine whether there were significant changes over sessions and monkey–CE combinations in success rate, path length or time to target, we computed the slopes of the linear fits of the curves of these metrics of every CE across sessions and tested whether the slopes differed from 0 using one-sample t-tests. Similarly, to examine whether the take-off and entry angles converged to 0° (for spike target trials) or to 90° (for HG target trials) over sessions across all monkey–CE combinations, we used one-sample t-tests to test whether the absolute values of the slopes of the fits to these curves were smaller than 0.

DWSS

To examine whether spike leakage from nearby electrodes could explain the HGA during ONF, we computed the DWSS. This assumed that the contribution of spike-related activity to HGA on the CE was inversely proportional to the square of the Euclidean distance between the neuron spiking and the CE⁶¹, and assumed an isotropic medium, which is reasonable within a single cortical layer, which is the case for a Utah array. We calculated the distance-weighted sum of these spike rates (DWSS) from all available electrodes. We considered this sum as a reasonable approximation of the contribution of nearby spike leakage, even with the somewhat sparse sampling of a Utah array, because the listening radius for spikes on an electrode has been estimated^57,58 at 140–200 μm, so most neurons within the plane of the array should be recorded by electrodes spaced apart by 400 μm. This DWSS of CE c was defined as

$${\rm{D}}{\rm{W}}{\rm{S}}{\rm{S}}(c)=\mathop{\sum }\limits_{n}^{N}\frac{{fr}_{n}}{{d}_{n}^{2}};({\rm{D}}{\rm{W}}{\rm{S}}{\rm{S}}(c)\in {{\mathbb{R}}}^{1\times T}),$$

where fr_n ∈ ${\mathbb{R}}$^1 × T is the concatenated spike rate of the last 2 s (40 bins) of all successful ONF-control trials recorded on electrode n; T is the number of successful trials $\times $ 40 bins; d_n is the Euclidean distance between the electrode n and CE; and N is the number of all available electrodes. When n = c, we assumed that the spikes recorded on the CE were from neurons towards the outer part of the listening sphere (d_c = 140 μm, conservative measure⁵⁸) from the recording site, minimizing the impact of the CE spiking on the DWSS.

We then calculated the Pearson’s correlation coefficient between DWSS and HGA of the last 2 s (40 bins) of all concatenated trials on CEs. For CE c, we denote this as: R(DWSS(c),HGA(c)).

To understand the significance of this R value, we compared it to two controls. First, we computed the DWSS for randomly chosen electrodes—each denoted c_random—and calculated its correlation with the HGA of CE c: R(DWSS(c_random),HGA(c)). Second, we calculated the correlation coefficient between DWSS and HGA on that same c_random: R(DWSS(c_random),HGA(c_random)). We performed these calculations for 20 randomly chosen electrodes.

If the value of R(DWSS(c),HGA(c)) were significantly larger than the distribution of R(DWSS(c_random),HGA(c)) across random electrodes, or if it were significantly larger than the distribution of R(DWSS(c_random),HGA(c_random)), it would indicate that the spiking activity on the electrodes near to the CE contributed significantly more to the HGA recorded on the CE than did the spiking activity surrounding a random electrode (Fig. 4g). That is, it would suggest that spike leakage was a significant contributor to HGA.

Factor analysis

To extract the co-firing patterns for every monkey–CE combination, we built a factor analysis model from the z-scored concatenated spike population activity (X ∈ ${\mathbb{R}}$^N × T) recorded on all available electrodes of all successful ONF–control trials (after ONF proficiency was achieved), where N is the number of electrodes and T is the number of time bins of all concatenated trials. The factor analysis model aimed to explain the correlations of spiking activities among electrodes by assuming they were influenced by common underlying factors (co-firing). Given the number of factors k, X was modelled as X = L × F + R, where L ∈ ${\mathbb{R}}$^N × k is the co-firing weight, F ∈ ${\mathbb{R}}$^k × T is the co-firing component and R ∈ ${\mathbb{R}}$^N × T represents the noise independent to each neuron. The goal was to estimate F and L such that the variance–covariance structure of X was well explained by the common factors, thereby reducing the dimensionality of X while preserving its essential patterns. In Figs. 4h–j and 5, we set k = 1 to extract the most common co-firing component and its corresponding weights. In Fig. 4j, we set k = 1–10 to investigate how the number of factors affected the correlation between the co-firing components and CE spiking or CE HGA. We fitted a linear regression (k = 1) or a multiple linear regression model (k = 2–10) for each k between the trial-concatenated factors and trial-concatenated CE HGA or CE spike rates. We plotted the absolute correlation |R| of these regressions for every monkey–CE combination.

To determine whether the absolute first factor weights |l| ∈ ${\mathbb{R}}$^N × 1 were significantly higher around the CE than they were around other electrodes, we calculated the distance-weighted mean (DWM) of the absolute factor weights for the CE and for randomly selected electrodes. For electrode e, this is defined as:

$${\rm{D}}{\rm{W}}{\rm{M}}{(}{e}{)}{=}\mathop{\sum }\limits_{{n}}^{{N}}\frac{{|}{{l}}_{{n}}{|}}{{{d}}_{{n}}^{2}},\,{n}\ne {e},$$

where d_n is the Euclidean distance between electrodes n and e. We compared these DWMs (CE versus random) using a one-sided quantile test.

cPCA

We used cPCA to find subspaces in which the monkeys were modulating only HGA or only spikes independently. cPCA found a subspace that maximized variance in the HG+ data (foreground data) and simultaneously minimized variance in the SP+ data (background data)⁶². The same process was used to find SP+-unique components (SP+ cPCs) but using SP+ data as foreground data and HG+ data as background data. cPCs were the eigenvectors of eigenvalue decomposition result on the matrix (C_foreground − αC_background) ∈ ${\mathbb{R}}$^N × N, where C_foreground ∈ ${\mathbb{R}}$^N × N and C_background ∈ ${\mathbb{R}}$^N × N were the covariance matrices of the foreground data and background data, respectively. cPCA has one hyperparameter α, which balances the importance of maximizing variance in the foreground data versus minimizing variance in the background data. An α value of 10 was found to be sufficient to separate SP+ and HG+ data. We chose the top ten cPCs ranked by their row variances for all analyses.

Subspace angle analysis

The principal angles between two subspaces provided a measure of the alignment of those subspaces in a high-dimensional space. These angles were defined recursively, capturing the smallest angles between vectors in the two subspaces. To compute the angles between two m-dimensional subspaces A and B embedded in a high-dimensional neural space spanned by neurons recorded on N electrodes (m < N), we used the method described by Björck and Golub⁶³. We performed singular value decomposition on the inner product of bases W_A ∈ ${\mathbb{R}}$^N × m and W_B ∈ ${\mathbb{R}}$^N × m from the m leading PCs (or cPCs) of conditions A and B, respectively:

$${{\bf{W}}}_{A}^{{\rm{T}}}{{\bf{W}}}_{B}={{\bf{P}}}_{A}{\bf{C}}{{\bf{P}}}_{B}^{{\rm{T}}}.$$

The principal angles θ_i, i = 1, ... , m were the ranked arccosines of the diagonal elements of C.

To assess whether the subspace angles between pairs of subspaces were significantly small, we compared them to the subspace angles between column-shuffled W_A and W_B, which preserved the key statistics of the individual subspace⁶⁴. We used the 0.1th percentile of the distributions of shuffled subspace angles to define a threshold below which angles can be considered significantly small (with a probability P < 0.001).

Spike-triggered average analysis of CE HGA

To determine the relationship between spikes on all available electrodes and CE HGA with high temporal resolution, we used the spike times of all successful trials sampled at 1 kHz to perform spike-triggered average analysis. To compute instantaneous HGA, we used a fourth-order Butterworth band-pass filter at 200–300 Hz bidirectionally on the raw LFP signals sampled at 1 kHz to remove any absolute time delay. Then we applied the Hilbert transform on the filtered signals and squared the amplitude to compute the instantaneous HGA. This method enabled 1-ms resolution in the spike-triggered signal. For any electrode n and its spike event i_n, we first segmented CE HGA from −50 ms to +70 ms relative to the spike time of i_n as HGA(i_n) and averaged these CE HGA segments:

$${\rm{avgHGA}}(n)=\mathop{\sum }\limits_{i}^{I}{{\rm{HGA}}(i}_{n})/I,$$

where I is the total number of spikes in the concatenated spiking activity recorded on the electrode n. These spike-triggered average segments were further standardized by their population mean and s.d. We found the argmax of the avgHGA(n) to be the peak time p for any given electrode. Finally, we reported the confidence interval from the distribution of p across all electrodes to be the range of peak time of CE HGA triggered by the electrode.

cPC projection of ONF and hand-control data

To investigate how much the cPCs occupied the spaces spanned by hand-control and ONF-control data, we projected the hand-control data and ONF data onto different cPCs. First, we concatenated the trials of population spiking activity during hand control and ONF control ${{\bf{X}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}\in {{\mathbb{R}}}^{N\times {j}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}}$ separately, where ‘ctrl’ is either hand-control or ONF-control type and j_ctrl represents the length of concatenated trials of that control type, respectively. Then, we projected the z-scored X_ctrl into the cPC space to obtain the m-dimensional latent ${{\bf{Z}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}}\in {{\mathbb{R}}}^{{j}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}\times m}$: ${{\bf{Z}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}}={{\bf{X}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{T}{{\bf{W}}}_{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}},$ where ‘cond’ represents the spike–HG angle of either HG+ or SP+, and ${{\bf{W}}}_{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}}\in {{\mathbb{R}}}^{N\times m}$ represents the m-dimensional space provided by the m leading cPCs. Finally, we calculated the variance accounted for (VAF) for each cPC dimension ${{\bf{Z}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}}$: ${\rm{V}}{\rm{A}}{\rm{F}}({{\bf{Z}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}})=\frac{{\rm{c}}{\rm{o}}{\rm{l}}{\rm{v}}{\rm{a}}{\rm{r}}\left({{\bf{Z}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}}^{{\rm{c}}{\rm{o}}{\rm{n}}{\rm{d}}}\right)}{{\rm{v}}{\rm{a}}{\rm{r}}({{\bf{X}}}_{{\rm{c}}{\rm{t}}{\rm{r}}{\rm{l}}})},$ where colvar(*) represents the variance calculation along the matrix column (cPC dimension) and var(*) represents the total variance calculated on the flattened matrix (the asterisk (*) represents any possible value of the variable). We calculated the VAF for every ctrl–cond combination. For example, when ctrl was ONF control and cond was SP+, VAF was calculated on the trial-concatenated ONF-control data projected into SP+ cPC space.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Data used for analysis to support the study results are publicly available via Figshare (ref. ⁶⁵): https://doi.org/10.6084/m9.figshare.31288654.

Code availability

Code related to cPCA can be found at https://github.com/abidlabs/contrastive. Code used for analysis: https://github.com/caraido/spike-highgamma.

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Acknowledgements

We thank Z. Wright for assistance with running experiments and technical support for the study, and L. Miller for the use of laboratory facilities and advice on the manuscript. This study was supported in part by K08NS060223, R01NS094748, R01NS112942, R01NS099210, RF1NS125026 (M.W.S.), T32EB009406 (M.R.S.), R00NS119787(J.I.G.) and T32NS047987 (T.L.). J.I.G. also acknowledges support from the National Institute for Theory and Mathematics in Biology through the National Science Foundation (DMS-2235451) and the Simons Foundation (MPTMPS-545 00005320).

Author information

These authors contributed equally: Tianhao Lei, Michael R. Scheid
These authors jointly supervised this work: Joshua I. Glaser, Marc W. Slutzky

Authors and Affiliations

Department of Neurology, Northwestern University Feinberg School of Medicine, Chicago, IL, USA
Tianhao Lei (雷天浩), Michael R. Scheid, Robert D. Flint, Joshua I. Glaser & Marc W. Slutzky
Department of Computer Science, Northwestern University, Evanston, IL, USA
Joshua I. Glaser
National Institute for Theory and Mathematics in Biology, Chicago, IL, USA
Joshua I. Glaser
Department of Neuroscience, Northwestern University Feinberg School of Medicine, Chicago, IL, USA
Marc W. Slutzky
Department of Physical Medicine and Rehabilitation, Northwestern University Feinberg School of Medicine, Chicago, IL, USA
Marc W. Slutzky
Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA
Marc W. Slutzky

Authors

Tianhao Lei (雷天浩)
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Michael R. Scheid
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Robert D. Flint
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Joshua I. Glaser
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Marc W. Slutzky
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Contributions

M.R.S. and M.W.S. conceived the study. M.R.S. and R.D.F. collected the data. T.L., M.R.S., R.D.F., J.I.G. and M.W.S analysed the data. T.L. prepared the manuscript. T.L., M.W.S., R.D.F., M.R.S. and J.I.G. edited the manuscript. J.I.G. and M.W.S. supervised the project.

Corresponding authors

Correspondence to Michael R. Scheid or Marc W. Slutzky.

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Competing interests

M.W.S. is on the Scientific Advisory Board of Synchron and consults for Vonova and Iota Biosciences. The remaining authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Monkeys quickly became proficient at the ONF task.

a, Example cursor traces of the last 2 s of all trials in 4 sessions for three example monkey–CE combinations. Row: each monkey–CE combination. Column: sessions. b, Path length of the first 50 trials (the minimum number of trials across the monkey–CE combinations within the first two sessions) for each monkey–CE combination showed significant decrease. (p = 0.04, one-sided one-sample t-test) c, R between spike rate and HGA of the first 50 trials for each monkey–CE combination. Six out of 9 CEs had R of 0 or less from the beginning of the first two sessions, and 8 of 9 had R less than 0.25 to start with. Data in b,c were smoothed by a Gaussian kernel with σ = 5.

Extended Data Fig. 2 The correlation between HGA and spike rate is modest across electrodes and does not change across sessions on the CE.

a, Mean correlation (R) between single-trial spike rate and HGA recorded on the same electrodes of the last second preceding reward during hand control for each monkey (monkey C: 32 sessions, monkey J: 6 sessions, monkey M: 6 sessions). b, Correlation coefficient between CE spike rate and CE HGA in the first (red) 1 s of all trials, including failed trials, over sessions. Box plots show the median (centre line) and interquartile range (box; 25th–75th percentiles). Each dot represents one trial. From first to last session, C10: n = 35, 200, 109, 136, 229, 161, 241, 174, 160, 202, 204, 193, 134, 39, 128; J52: n = 286, 292, 286, 276, 226; J31: n = 32, 39, 154, 59; M73: n = 9, 71, 115, 109, 142, 134, 82, 33, 21, 67; M92: n = 22, 52, 90, 145, 208; C63: n = 163, 182, 342, 163, 123; M66: n = 55, 99, 135, 68, 79, 159, 121; J29: n = 83, 76, 60, 120, 131, 53, 88; C81: n = 112, 293, 103, 221, 212, 43.

Extended Data Fig. 3 Examples of inter-spike intervals, waveforms and their clusters, as well as correlation between CE HGA and sorted spikes when using a threshold of three standard deviations.

a,b, Inter-spike intervals (ISIs) from sorted (a; blue) and unsorted (b; grey) spike waveforms in J CE 52 (8 files over 4 sessions). The unsorted waveforms have a relatively high percentage of very short ISIs, indicating multiple (likely many) units. c, Principal component projections (PC1 and PC2) of sorted (blue) and unsorted (grey) spikes on the J CE 52. Axes are in units of s.d. of each PC. The vertical axis indicated the session-file indices. The first and last files (F) of each session (S) are shown. For visualization, the vertical values of the points were randomly jittered in each cloud, which would otherwise occupy a 2D region for each file. Translucent cylinder represents 2 s.d. in each direction of the sorted spikes in session 1, file 1 (S1 F1). d, Twelve examples of waveforms sampled from the PC space in one file. e, Correlation (R) between CE HGA and sorted spikes (blue) or unsorted spikes (grey) over 4 files in 2 sessions in J CE 29 (left; n = 334 trials for sorted, n = 359 for unsorted) and 8 files in 4 sessions in J CE 52 (right; n = 281 for sorted, n = 279 for unsorted). Each dot represents an R value of the last 1 s of a trial. Both sorted and unsorted spikes were uncorrelated with CE HGA. Box plots show the median (centre line), interquartile range (box; 25th–75th percentiles), and whiskers extending to 1.5× the interquartile range. Each dot represents a trial.

Extended Data Fig. 4 Single-bin spike–HG angles indicate dissociation of the two signals.

Polar plot of the 2D distribution of mean spike–HG angles of each 50-ms bin in the 1 s preceding the reward time of ONF files (red) and hand-control files (dark blue) from the learned sessions of all monkey–CE combinations. Orange sector: HG+ state; blue sector: SP+ state. Grey sector: state at which both signals had high modulation. Note that states in the 135° and 315° directions also corresponded to independent modulation of HGA and spiking. States near 225° corresponded to times at which there was minimal spiking and minimal HGA, probably times when the monkey was not actively engaged in the task.

Extended Data Fig. 5 Final-second spike rates across the array.

Trial-averaged, z-scored spike rates across the array over the last second of spike target trials (left plots) and HG target trials (right plots) during ONF control in all monkey–CE combinations besides those shown in Fig. 4e,f. White squares denote shunted electrodes. CEs are outlined in green.

Extended Data Fig. 6 CE HGA is no more correlated with nearby spiking than it is with more distant spiking.

Correlation coefficient (R) between CE HGA and the control-electrode distance-weighted sum of spikes (CE DWSS, red bar), the mean (error bar: ±s.d.) R between CE HGA and DWSS of 20 randomly selected electrodes (random, grey bar, each dot is one R with one electrode; see Methods), and the mean (±s.d.) R between HGA and DWSS pairs from 20 randomly selected electrodes excluding the CE (non-CE, light blue bar, each dot is one R between each pair). The R values between CE HGA and CE DWSS were not significantly larger than those between CE HGA and random DWSS, or than those between the non-CE HGA and DWSS (C10: p(random) = 1.0, p(non-CE) = 0.8; C81: p(random) = 1.0, p(non-CE) = 1.0; J29: p(random) = 1.0, p(non-CE) = 1.0; J31: p(random) = 0.2, p(non-CE) = 0.4; M66: p(random) = 1.0, p(non-CE) = 1.0; M73: p(random) = 1.0, p(non-CE) = 1.0; M92: p(random) = 1.0, p(non-CE) = 1.0; one-sided quantile test). Insets show the weights used to compute the CE DWSS. Plots include all monkey–CE combinations except those in Fig. 4g.

Extended Data Fig. 7 Co-firing pattern is stable across sessions and contributing neurons are distributed across the grid.

a, Correlation (R) of MLR fit from the co-firing pattern to spike rate (magenta) or to the HGA (turquoise). The factor weights were calculated using all the sessions combined and then were used to project in each session separately to generate the co-firing (first factor). We did not observe any increase or decrease in the correlation across sessions (p = 0.15, one-sample two-sided t-test). b, Absolute values of the co-firing weights of all monkey–CE combinations except the two examples shown in Fig. 4k. CEs are outlined in red. White electrodes represent those that either were shunted or did not exceed the minimum firing rate (see Methods). c, The DWM relative to the CE of absolute co-firing weights on the electrodes (red), as well as the mean (error bars: ±s.d.) of the DWMs of absolute co-firing weights on the electrodes relative to 20 randomly selected electrodes (grey) of all monkey–CE combinations besides the two in Fig. 4l. Each dot represents the DWM relative to a randomly selected electrode. These R values were not significantly different for any CE (n = 20, from left to right: p = 0.93, 1.00, 0.19, 0.56, 0.08, 0.05, 0.99, one-sided quantile test).

Extended Data Fig. 8 Spike rate and HGA modulation on the CE involve activity in different subspaces of the neuronal ensemble.

a, Top, correlation of the linear fit of ensemble SP+ cPC projections to CE spike rate (magenta) and CE HGA (grey) separately, with increasing numbers of cPCs. Bottom, fit of ensemble HG+ cPC projections to CE spike rate (grey) and CE HGA (turquoise) separately. Lines and shaded areas: mean ± s.d. Each dot represents one of the 9 monkey–CE combination for each number of cPCs. b, Top: correlation of MLR fit of top 10 SP+ cPC projections to CE spike rate (magenta) and CE HGA (turquoise) over sessions and all 9 CEs (lines). Bottom: same as top but for HG+ cPC projections. The cPC weights were calculated using all the sessions combined and then were projected to each session separately to generate the cPC projections. We did not observe any increase or decrease of R across sessions; n = 9; p(SP+ cPC fitted to spike rate)=0.93, p(SP+ cPC fitted to HGA) = 0.90, p(HG+ cPC fitted to spike rate) = 0.58, p(HG+ cPC fitted to HGA) = 0.96; one-sample two-sided t-test of the slopes. c, Weights of the first HG+ cPC across the array for one CE (red outline) in monkeys C (top) and J (bottom). d, The CE distance-weighted mean (DWM) of the absolute first HG+ cPC weights (red) and the mean (error bars: ±s.d.) of the DWMs on the electrodes relative to 20 randomly selected electrodes (grey) of all monkey–CE combinations. Each dot represents the DWM relative to a randomly selected electrode. The CE DWM was not significantly larger than the DWM relative to the randomly selected electrodes for any CE (n = 20; from left to right: p = 0.99, 0.99, 0.99, 0.07, 0.62, 0.96, 0.99, 0.12, 0.56, one-sided quantile test). e, Cumulative variance accounted for (VAF) by the PCs of SP+ data (magenta) and HG+ data (blue). Lines and shaded areas: mean ± s.d. Each dot represents the value for a monkey–CE combination for the given number of components.

Extended Data Fig. 9 Spikes contributing most to co-firing also contribute most to HGA.

Same as Fig. 5b,d,e for the remainder of the monkey–CE combinations. First and fourth column, spike-triggered averaged HGA of the CE showed a consistent activity pattern when aligned to the spike times from other electrodes. Second and fifth column, K-means clustering results using 2 clusters on the STA HGA traces, colour-coded by the absolute co-firing weights. These clusters correspond generally to the no-response and with-response clusters in Fig. 5d. Third and sixth column, a comparison of the absolute co-firing weights of the two clusters (n.s.: p ≥ 0.05: *: p < 0.05; ***p < 0.005; two-sided Wilcoxon signed-rank test). Third column from top to bottom: p = 3.0 × 10⁻⁴, 0.15, 6.0 × 10⁻⁷, 0.03, n as shown in the plots, representing the number of electrodes. Sixth column from top to bottom: p = 2.3 × 10⁻⁵, 6.3 × 10⁻⁶, 0.67, n as in the plots. Box plots show the median (centre line), interquartile range (box; 25th–75th percentiles), and whiskers extending to 1.5 times the interquartile range. Each dot represents one electrode.

Extended Data Fig. 10 Subspace analysis of cPCs and relationship with hand-control manifold.

a, Subspace angles between the top ten cPCs (sorted by variance accounted for) of SP+ data and HG+ data. Leading subspace angles were significantly different from chance (p = 3.2 × 10⁻⁵; one-sided quantile test on mean difference curve, Methods). Grey lines and shaded areas indicate subspace angles calculated using shuffled subspaces. Solid line: mean; Shaded area: s.d. Each of the 9 dots represents a monkey–CE combination. b,c, Mean ± s.d. VAF when hand-control data were projected into the subspaces defined by the top ten b, HG+ cPCs computed with ONF data (grey, n = 9 monkey–CE combinations) or hand-control data (brown, n = 9 monkey–CE combinations), and c, SP+ cPCs computed with ONF data (grey, n = 9) or hand-control data (brown, n = 9). Each dot represents one monkey–CE combination.

Extended Data Table 1 Number of recording sessions for each control electrode (CE)

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Lei, T., Scheid, M.R., Flint, R.D. et al. Active dissociation of intracortical spiking and high gamma activity. Nature (2026). https://doi.org/10.1038/s41586-026-10331-y

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Received: 06 September 2024
Accepted: 26 February 2026
Published: 01 April 2026
Version of record: 01 April 2026
DOI: https://doi.org/10.1038/s41586-026-10331-y