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Spontaneous travelling cortical waves gate perception in behaving primates


Perceptual sensitivity varies from moment to moment. One potential source of this variability is spontaneous fluctuations in cortical activity that can travel as waves1. Spontaneous travelling waves have been reported during anaesthesia2,3,4,5,6,7, but it is not known whether they have a role during waking perception. Here, using newly developed analytic techniques to characterize the moment-to-moment dynamics of noisy multielectrode data, we identify spontaneous waves of activity in the extrastriate visual cortex of awake, behaving marmosets (Callithrix jacchus). In monkeys trained to detect faint visual targets, the timing and position of spontaneous travelling waves before target onset predicted the magnitude of target-evoked activity and the likelihood of target detection. By contrast, spatially disorganized fluctuations of neural activity were much less predictive. These results reveal an important role for spontaneous travelling waves in sensory processing through the modulation of neural and perceptual sensitivity.

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Fig. 1: Spontaneous LFP fluctuations often travel as waves across the cortex.
Fig. 2: Spontaneous travelling waves modulate ongoing spiking probability.
Fig. 3: Waves facilitate detection when aligned with the retinotopic location of visual targets.
Fig. 4: Wave state predicts target-evoked response magnitude and perceptual sensitivity.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

An open-source code repository for all methods is available on GitHub:


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We thank M. Avery, K. Williams, S. Adams and M. LeBlanc for their contributions to this project and T. Movshon for his feedback in the early stages of this project. This work received funding from The Dan and Martina Lewis Biophotonics Fellowship, Gatsby Charitable Foundation, the Fiona and Sanjay Jha Chair in Neuroscience, the Canadian Institute for Health Research, the Swartz Foundation, BrainsCAN at Western University through the Canada First Research Excellence Fund (CFREF), the Office of Naval Research N00014-16-1-2829, and NIH grants R01-EY028723, U01-NS108683, P30-EY0190005, T32 EY020503-06 and T32 MH020002-16A.

Author information

Authors and Affiliations



Conceptualization: Z.W.D., L.M., J.H.R.; data curation: Z.W.D., L.M.; formal analysis: Z.W.D., L.M.; funding acquisition: Z.W.D., L.M., T.S., J.H.R.; investigation: Z.W.D., L.M.; methodology: Z.W.D., L.M., T.S., J.M.-T., J.H.R.; supervision: T.S., J.M.-T., J.H.R.; visualization: Z.W.D., L.M.; writing original draft: Z.W.D., L.M., J.H.R.; and writing, review and editing: Z.W.D., L.M., T.S., J.M.-T. and J.H.R.

Corresponding authors

Correspondence to Zachary W. Davis or John H. Reynolds.

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Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Retinotopic mapping and motion direction tuning is consistent with the anatomical organization and tuning preferences of marmoset MT.

a, Receptive fields for recorded units were measured by reverse correlation. Monkeys held fixation on a marmoset face while visual probes (drifting Gabor) appeared at random locations in the visual hemifield contralateral to the recording array. Each probe would appear, drift for 200 ms, and disappear after which a new probe would appear in a new random location and the process would repeat until the monkey broke fixation. b, The estimated position and orientation of Utah arrays in area MT based on retinotopy and histological examination for monkey W (blue) and monkey T (red). c, Example receptive fields and their preference for motion direction were consistent with previous reports of marmoset MT58.

Extended Data Fig. 2 Detection of spontaneous travelling waves.

a, The method for detecting spontaneous waves from the Generalized Phase. First, the detection algorithm found the most likely starting point for a putative wave as the point that maximizes the divergence of the phase gradient (step 1). b, With this source point found, the algorithm then quantified the spatiotemporal organization about this point from the circular-linear correlation of phase with distance across the whole array (step 2). With this approach, the algorithm can robustly detect arbitrarily shaped wavefronts in the array data. c, The average power spectrum for waves (N = 215) had significantly less power in low frequencies (<12 Hz) as compared to non-wave fluctuations (N = 524). Dotted bounds represent s.e.m. Asterisk: P < 1 × 10−5, two-tailed Wilcoxon rank-sum test. d, Detected waves in both monkeys predominantly travelled at speeds consistent with the conduction velocity of unmyelinated horizontal axons (0.1–0.6 m/s, red dashed lines; monkey W, 5571 waves, blue line; monkey T, 9285 waves, red line). e, There was no difference in the amplitude of fluctuations that were detected as waves (blue line; N = 696 waves) or rejected (non-wave, grey line; N = 565 non-wave fluctuations; example monkey T session).

Extended Data Fig. 3 Wideband GP is better coupled to spike timing than narrowband alpha or theta filters.

a, The phase and amplitude of the raw (5–100 Hz) LFP was poorly captured by narrow-band theta (4–8 Hz, blue dotted line) or alpha (8–13 Hz, red dotted line) filters. b, Scatter plot showing spontaneous spike-phase coupling was greater for GP (5–40 Hz) than alpha or theta narrowband filtered phases. Coupling averaged across electrodes for individual recording sessions is plotted as black dots and each red dot represents the average value across sessions. c, Spontaneous spike-phase coupling remained stronger for GP than the narrow frequency bands even when the spontaneous LFP epochs were restricted to periods where there is large alpha (12.06% of recorded time) or theta (7.24%) LFP power during fixation (5 dB SNR, narrow- to broad-band power ratio). Results are presented from monkey W.

Extended Data Fig. 4 Spike coupling to GP is spatially dependent.

a, Scatter plot showing the average spike–GP coupling across the distances of the array. Each point was averaged across a given spike-phase distance for a single recording session in monkey W (N = 22 sessions). The red dashed line shows the average null distribution for shuffled phases ± 2 s.d. (shaded region). b, Same as a, but for monkey T (N = 18 sessions). c, Scatter plot showing the cross-channel GP correlation for 200 ms of LFP during fixation across the electrode distances of the recording array. Each dot is the average circular correlation within an individual recording session across that channel distance. Shaded region represents the mean (±2 s.d.) correlation after shuffling the spatial position of the electrodes. d, Same as c, but for monkey T.

Extended Data Fig. 5 Spontaneous travelling waves are present during normal viewing of naturalistic visual scenes.

Marmosets freely viewed static natural images for 10 s while head-fixed. a, An example high-contrast image with the gaze of the marmoset over the 10 s viewing interval shown in red. b, An example of a spontaneous travelling wave detected during a period of fixation while monkey T was freely viewing a high-contrast image. c, Across 86 trials, 593 spontaneous travelling waves were detected during spontaneous fixations while the monkey freely viewed the images (−50 to +100 ms perisaccadic activity excluded). d, The density of observed wave speeds was consistent with the conduction velocity of unmyelinated axons (0.1–0.6 m s−1).

Extended Data Fig. 6 False alarms are not predicted by the phase of travelling waves.

To test whether the alignment of waves with the target location produces a bias towards saccading to that location, we examined the spontaneous activity before false alarms, time locked to the eye movement. This is distinct from our analysis of hits, which was time locked to the onset of the target, and is a limitation in our design for comparing hits to false alarms. However, we did find a significant modulation of spontaneous spiking activity that was possibly the sensory signal generating the false alarm, giving us a window to explore their potential relationship with waves62. If waves increase the likelihood of false alarms, they should show some phase-dependent relationship similar to what we observe in hits, but time-locked to the spiking activity predictive of a false alarm. a, Multi-unit spiking activity (normalized to the baseline, shaded regions ± s.e.m.) for monkey W (blue) and monkey T (red) was significantly increased in the interval before a false alarm (grey shaded box, −120 ms to −60 ms, P < 0.001, two-sided Wilcoxon rank-sum test). b, Scatter plot showing the average firing rate before the false alarm (y axis, shaded interval in a) was significantly greater than the spontaneous background firing rate (x axis, −400 ms to −200 ms) for monkey W (blue dots; N = 62 multi-units, P < 0.0001, Wilcoxon signed rank test) and monkey T (red dots; N = 70 multi-units). c, Cross-trial phase alignments for waves aligned to the location of false alarm for the interval preceding the occurrence of a false alarm. There was no strong phase alignment during the period of significant spiking activity (shaded region) for either monkey W (blue line) or monkey T (red line) that would show a wave state is predictive of a false alarm. However, there was a strong phase alignment just before (monkey T −40 ms) and during the eye movement (monkey W, 0 ms). Given their close proximity to the onset of the eye movement we suspect the observed alignment may reflect an efference signal related to the pending saccade63. d, The distribution of observed wave phases was uniform during the period of significantly increased spiking activity (−90 ms before false alarm), indicating there was no relationship between the phase of spontaneous waves and the spontaneous spiking fluctuation associated with false alarms. Data collapsed across both monkeys as there was no difference in their distributions.

Extended Data Fig. 7 Target-evoked response magnitude is correlated with detection performance.

a, Detection performance of different target contrasts for monkey W (blue) and monkey T (red) across training days where those contrasts were presented. Both monkeys had similar psychophysical thresholds, defined as the contrast where the monkey detected the target 50 percent of the time on average (c50) as estimated from a sigmoid fit (grey dashed line). b, c, Distributions of reaction times for monkey W (b) and monkey T (c) during the detection task at their c50 value. The median reaction time for each monkey is shown by a red line. d, Spike rasters for an example neuron with trials sorted into hits (bottom rasters) and misses (top rasters). e, Scatter plot showing the distribution of mean hit (x axis) and miss (y axis) evoked responses (80–200 ms) for all single- (x) and multi-units (dot) recorded across all sessions for monkey W (blue) and monkey T (red). The circled x is the example neuron from d. Target-evoked responses were significantly stronger for detected targets in both monkeys. (monkey W, N = 25 single- and 83 multi-units, P < 0.01; monkey T, N = 27 single and 110 multi-units, P < 1 × 10−5; two-sided Wilcoxon signed-rank test).

Extended Data Fig. 8 Narrowband filters fail to detect any significant wave phase alignment before target onset.

a, The cross-trial phase alignment computed as in Fig. 3, but using a narrowband alpha (8–13 Hz) filter, did not show any significant alignment (grey dashed line) for hits (blue) or misses (grey) before target onset (grey region) for either monkey T (top) or monkey W (bottom). b, The same as in a, but for a beta (15–30 Hz) narrowband filter.

Extended Data Fig. 9 Instantaneous voltage is less predictive of spike timing and perception than GP.

a, Scatter plot showing the relationship between instantaneous LFP amplitude in voltage, and GP. The same voltage value occurred across a broad range of phases. b, While we found wave phase to be predictive of detection, the average LFP voltage was not different preceding a hit (blue) or a miss (red). Shaded area indicates s.e.m. across 18 sessions in monkey T. c, Scatter plot showing the coupling of spike probability to GP. Each point is the probability of a spike occurring in that phase bin within a recording session (N = 18). There was a strong circular-linear correlation of GP with spike probability (r = 0.87). d, Scatter plot showing weaker spike-amplitude coupling. Each point is the relative probability of a spike occurring in each voltage bin, normalized by the amount of time that instantaneous voltage occurs. Spike probability was less correlated with LFP amplitude (Spearman’s rank correlation, r = −0.48).

Supplementary information

Supplementary Information

Table S1. GLM analysis for predictors of network state.

Reporting Summary

Video 1

Example of multiple detected traveling waves. Video with 205 ms of spontaneous LFP data while monkey T is fixating a white dot on a gray screen. The wave examples in Figure 1b begin at 24 ms and 168 ms in this video. Color axis scales from 80 µV (blue) to -80 µV (red).

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Davis, Z.W., Muller, L., Martinez-Trujillo, J. et al. Spontaneous travelling cortical waves gate perception in behaving primates. Nature 587, 432–436 (2020).

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