Beta oscillations define discrete perceptual cycles in the somatosensory domain
Thomas J. Baumgarten, Alfons Schnitzler, and Joachim Lange
PNAS September 29, 2015 112 (39) 12187-12192; first published August 31, 2015; https://doi.org/10.1073/pnas.1501438112
Thomas J. Baumgarten
Institute of Clinical Neuroscience and Medical Psychology, Medical Faculty, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
For correspondence: thomas.baumgarten@med.uni-duesseldorf.de
Alfons Schnitzler
Joachim Lange
Edited by Ranulfo Romo, Universidad Nacional Autonóma de México, Mexico City, D.F., Mexico, and approved July 31, 2015 (received for review January 22, 2015)
Our sensory system constantly receives multiple inputs, which are usually perceived as a seamless stream. Thus, perception is commonly regarded as a continuous process. Alternatively, a few phenomena and recent studies suggest that perception might work in a discrete and periodic sampling mode. In a human magnetoencephalography study, we challenged the common view of continuous perception. We demonstrate that neuronal oscillations in the alpha band and low beta band determine discrete perceptual sampling windows in primary somatosensory cortex. The current results elucidate how ongoing neuronal oscillations shape discrete perceptual cycles, which constitute the basis for a discontinuous and periodic nature of somatosensory perception.
Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8–20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain.
somatosensory perception
beta oscillations
oscillatory phase
The sensory system continuously receives and processes numerous stimuli. Subjective experience implies that conscious perception, and thus cortical processing, of this stimulation is also continuous. This view of continuous cortical processing, however, has been challenged by several studies proposing that the brain operates discontinuously within a framework of discretely sampled "perceptual cycles" (1⇓⇓–4). This process of perceptual cycles is thought to create a temporally defined window, with discrete stimuli falling inside this window being consciously perceived as a single event (4). Discrete sampling of sensory information allows for the possibility of transforming perceptual input into temporal code (5, 6), metabolic efficiency (7), and the efficient organization of information, thereby preventing information overload (6). Over the past decades, however, there has been an ongoing discussion about the nature of perception. Several studies have argued against the theory of discontinuous perceptual cycles (8, 9). In recent years, the hypothesis of a discontinuous cyclic perception received new support by electroencephalography (EEG) and magnetoencephalography (MEG) studies investigating neuronal oscillations. This novel support is attributable to the theory that serial perceptual sampling is thought to depend on the temporal relationship between external stimuli and some ongoing internal neurophysiological process (4) providing a temporal reference frame (5), with neuronal oscillations representing a probable candidate measure for this underlying process.
There is growing evidence that oscillatory power and phase influence cortical processing (10, 11) and perception (3, 12⇓–14). Most of these studies investigated perception of single near-threshold stimuli. Although these studies demonstrate that neuronal oscillations play a critical role in defining neuronal states, which, in turn, influence perception and neuronal processing (5, 15, 16), these studies do not provide direct evidence for or against the theory of perceptual cycles. Recent studies, however, argued that parietooccipital alpha oscillations (∼8–12 Hz) might define cycles of perception (6, 15, 17⇓–19). However, they only provide evidence for discrete perceptual sampling in the visual domain. To claim that discrete perception is not domain-specific, it is critical to demonstrate discrete and cyclic perception also for other sensory modalities and whether different modalities work via the same mechanism (e.g., whether alpha cycles generally define critical perceptual cycles for all modalities). Because sensory modalities work on different time scales, there is some indication that the mechanisms might differ.
We investigated whether discrete perceptual cycles exist in the somatosensory domain. Contrary to most studies in the visual domain, we used discrete rather than continuous stimuli, which differed only in perceptual impact, yet not in physical stimulation parameters. By this method, we could study whether two successively presented stimuli are perceived as either one single or two separate sensory events, depending on their temporal relationship to discrete perceptual cycles defined by the ongoing neuronal oscillatory phase. This setup allowed us to test the theory of discrete perceptual sampling critically in the somatosensory domain, and thus whether cycles of perception represent a mechanism of conscious perception that exists beyond the visual domain.
Behavioral Results.
Subjects received one or two electrical pulses separated by a specific stimulus onset asynchrony (SOA; nomenclature is provided in Materials and Methods) and had to perform a forced-choice temporal perceptual discrimination task (Fig. 1), wherein they had to report whether they perceived one or two stimuli. Subjects made negligible errors for the conditions 0 ms and 100 ms [SOA 0 ms: 97.7 ± 0.4% (mean ± SEM) reports of correctly perceiving one stimulus, SOA 100 ms: 94.6 ± 2.3% reports of correctly perceiving two stimuli]. Individually determined, intermediate SOAs yielded correct perception of two stimuli in ∼50% of the trials (58.0 ± 3.1% reports). For the condition intermediate − 10 ms, subjects perceived two stimuli in 25.6 ± 4.7% reports, and for intermediate + 10 ms, subjects perceived two stimuli in 79.1 ± 4.7% reports. A one-way repeated measures ANOVA comparing average hit rates between conditions demonstrated a highly significant difference [F(4,60) = 141.25, P < 0.001]. Post hoc t tests revealed significant differences between the condition 0 ms vs. intermediate − 10 ms [t(15) = 5.14, P < 0.01], 0 ms vs. intermediate [t(15) = 18.34, P < 0.001], 0 ms vs. intermediate + 10 ms [t(15) = 15.79, P < 0.001], 0 ms vs. 100 ms [t(15) = −37.15, P < 0.001], intermediate − 10 ms vs. intermediate [t(15) = 7.36, P < 0.001], intermediate − 10 ms vs. intermediate + 10 ms [t(15) = −7.15, P < 0.001], intermediate − 10 ms vs. 100 ms [t(15) = −13.1, P < 0.001], intermediate vs. intermediate + 10 ms [t(15) = −5.35, P < 0.001], intermediate vs. 100 ms [t(15) = −12.54, P < 0.001], and intermediate + 10 ms vs. 100 ms [t(15) = −3.79, P < 0.01].
Experimental paradigm. The sequence of events begins with presentation of a central fixation dot (500 ms). Luminance decrease signals start at the prestimulus epoch (900–1,100 ms), after which tactile stimulation is applied to the left index finger with varying SOAs (0 ms, intermediate − 10 ms, intermediate, intermediate + 10 ms, 100 ms). Stimulation is followed by a jittered poststimulus period (500–1,200 ms), after which written instructions signal subjects to report their respective perception of the stimulation by pressing a button.
Phase Angle Contrast.
To study the influence of oscillatory phase angles on perception, we sorted trials with intermediate SOA according to perceptual response (perceived one or two stimuli), resulting in two perceptual conditions (intermediate1 vs. intermediate2). We computed phase angles for each condition in source space by means of a virtual channel in the primary somatosensory cortex (S1) (Fig. 2A) and contrasted the phases of intermediate2 with intermediate1 (Fig. S1). The analysis revealed a significant positive cluster (P < 0.05; Fig. 2B) in the prestimulus epoch (−0.53 to −0.09 s) for frequencies in the alpha band and lower beta band (8–20 Hz). Notably, the effect was more prominent and temporally extended in the beta band (14–20 Hz, −0.53 to −0.09 s) compared with the alpha band (8–12 Hz, −0.39 to −0.24 s). That is, the phase difference between perceptual conditions differed significantly more in this time-frequency range compared with randomly distributed phases. For frequencies in the lower beta band, phase difference fluctuated around maximum (i.e., π) in the prestimulus period (Fig. 2C). To exclude any bias due to power differences, we analyzed power differences between perceptual conditions for those time-frequency elements exhibiting significant phase differences (analysis parameters are provided in ref. 14). The results did not reveal any significant power differences (P > 0.05, uncorrected). Regarding phase angle differences, we found an additional significant negative cluster (P < 0.05; Fig. 2B) between 2 and 28 Hz and between −0.1 and 0.24 s. Here, phase differences were significantly smaller compared with randomly distributed phases. This effect presumably resembles the phase resetting after stimulus presentation (18, 20).
Virtual sensor location and phase angle differences. (A) Virtual sensor location based on the voxel of maximum activity of the contrast M50 vs. prestimulus baseline. The voxel is highlighted on a slice plot of the Montreal Neurological Institute (MNI) template brain (MNI coordinates: 50 −10 50). (B) Time-frequency plot showing the results of the statistical analysis of phase angle differences between intermediate2 vs. intermediate1. Significant clusters (P < 0.05, corrected) are highlighted. Red colors indicate higher phase differences compared with randomly distributed phases. t = 0 indicates onset of the first stimulus. (C) Phase angle difference (black solid line) between intermediate2 (Intermed2) and intermediate1 (Intermed1) for an exemplary 14-Hz band. The upper dashed line indicates the maximum phase angle difference (π). (Insets) Phase angles for intermediate2 (blue lines) and intermediate1 (red lines) for exemplary time points (Left, t = −420 ms; Right, t = −50 ms) (D) Relationship between the momentary phase (Materials and Methods) and the normalized perceptual response rate. The probability of perceiving two stimuli significantly depends on the phase angle and differs maximally between opposite phase angles (ANOVA, P < 0.001).
Time-frequency plot showing the phase angle differences between intermediate2 vs. intermediate1. Red colors indicate a higher angular difference. Black outlines represent the extent of the significant group-level phase angle difference effect. t = 0 indicates the onset of the first stimulus.
Phase Angles and Perception.
To analyze the extent by which perception was influenced by phase, we computed for each subject the momentary phase for each single trial for both perceptual conditions at the time point showing the largest statistical phase difference effect (Materials and Methods). Trials were placed in one of six different phase bins and aligned for each subject so that the highest probability for perceiving two stimuli corresponded to a zero phase angle. For each subject, we calculated the normalized perceptual response rate per bin, and we then averaged normalized response rates across subjects (Fig. 2D). Although this analysis resembles a post hoc test (because it is based on the time-frequency points of maximal phase difference determined in the previous analysis), it quantifies the magnitude by which phase influences perception, as well as the grade by which performance varies over different phase bins. A one-way repeated measures ANOVA comparing normalized perceptual response rates between bins demonstrated a highly significant difference [F(4,60) = 6.53, P < 0.001]. Post hoc t tests revealed significant differences between bin 1 vs. bin 3 [t(5) = −4.17, P < 0.01], bin 1 vs. bin 5 [t(5) = −4.21, P < 0.01], bin 1 vs. bin 6 [t(5) = −4.13, P < 0.01], bin 2 vs. bin 3 [t(5) = −2.77, P < 0.05], and bin 2 vs. bin 5 [t(5) = −3.16, P < 0.01]. The results indicate a monotonic decrease of mean response rate from zero phase angle to π, with the response rates differing by 13% points between the lowest (−π, 38%) and highest (1/3 π, 51%) phase bins (with exclusion of the zero phase bin).
Beta-Band Cycles Determine Perceptual Cycles.
Fig. 3 illustrates a model derived from the analysis of phase angle contrasts and the theory of temporal framing (3, 19, 21). The model proposes that the temporal resolution of perception is defined by one cycle of a specific frequency. If presented within one cycle, the two stimuli are merged into one perceptual event and perceived as one single stimulus (Fig. 3A, white rectangles). If presented within two separate cycles, they will be perceived as two temporally separate perceptual events (Fig. 3A, black rectangles). Although the neural representation of the first stimulus can arrive at any point in the oscillatory cycle (21) for ongoing oscillations, the arrival of the second stimulus is determined by the SOA. For a cycle length twice as long as the respective SOA, a stimulus arriving in the first half of the cycle determines the arrival of the second stimulus in the same cycle (one perceived stimulus). Vice versa, a stimulus arriving in the second half of the cycle determines the arrival of the second stimulus in a subsequent cycle (two perceived stimuli). From the results of the phase angle contrast analysis, we derive that this critical frequency band lies in the alpha band and, particularly, the lower beta band between 8 and 20 Hz (Fig. 2B). Given these model preconditions, we can make two predictions. First, if the SOA between two stimuli equals half the length of the cycle of the critical frequency (e.g., 25 ms for a 20-Hz oscillation), mean phases for the perception of one stimulus (range: 0 to π for the example in Fig. 3A) and two stimuli (range: π to 2π) should differ maximally (∼π). More precisely, perception rates should critically depend on the phase at which the first stimulus arrives (Fig. 3 B–D). That is, if the stimulus arrives at a given phase φ, perception rates should differ significantly from φ + π. Second, if the critical frequency is known, we can predict behavioral response rates for different SOAs. The first prediction is confirmed by the analysis of phase angle contrast (Fig. 2 B and C). Based on these results, the post hoc phase binning analysis shows a monotonic decrease in perception over bins, and, thus, the dependence of perception rates on phase (Fig. 2D). The second prediction will be tested and presented below.
Model for perceptual cycles. (A) Red and blue lines illustrate two perceptual cycles. Two stimuli can occur within one (white rectangles, one stimulus perceived) or two (black rectangles, two separate stimuli perceived) perceptual cycles. (B) Same as in A, but for stimulus pairs with a longer SOA. The blue background illustrates the time frame in which the occurrence of the first stimulus results in one perceived stimulus (○), and the gray background illustrates the time frame in which the occurrence of the first stimulus results in two perceived stimuli (●). (C) Same as in B, but for stimuli with a shorter SOA. Note different lengths of blue and gray time frames. (D) Same as in B, but for examples of three different SOAs. Intermediate SOAs (rectangles) result in time frames for one (blue arrows) or two (gray arrows) perceived stimuli of approximately equal length. For longer SOAs (●), the time frame for two perceived stimuli (gray arrows) is bigger than for one perceived stimulus (blue arrows). For shorter SOAs (♦), the time frame for two perceived stimuli (gray arrows) is smaller than for one perceived stimulus (blue arrows).
Prediction of Perception.
Based on the model (Fig. 3), we predicted response rates for the different SOAs and computed linear regressions between predicted and behaviorally measured response rates. We computed predictions based on (i) group-level effect frequencies determined from MEG experimental data (8–20 Hz; Fig. 2B), (ii) based on single subject-level individual frequencies determined from MEG experimental data (Fig. S2 and Table S1), and (iii) based on frequencies determined from behavioral experimental data (i.e., the intermediate SOAs):
i) Based on group-level effect frequencies (8–20 Hz; Fig. 2B), the linear regression analysis for behavioral response rates and predicted response rates (Fig. 4) resulted in a highly significant correlation coefficient (r = 0.93, P < 0.01). The resulting slope estimate (0.83 ± 0.1) did not differ significantly from 1 [t(4) = −1.8, P > 0.05].
ii) Linear regression analysis of the individual behavioral and predicted individual response rates resulted in a significant correlation coefficient in all 16 subjects (r ranging from 0.69 to 0.96, P < 0.05). For 12 of 16 subjects, the resulting slope estimate did not differ significantly from 1 [t(4) ranging from −2.6 to 2.4, P > 0.05; Fig. S2 and Table S1]. We additionally predicted group-level response rates by averaging the individual response rates over subjects. The resulting predictions were virtually similar to the predictions based on the averaging over group-level effect frequencies (i) (Fig. 4). The resulting slope estimate (0.78 ± 0.1) did not differ significantly from 1 [t(4) = −2.23, P > 0.05].
iii) Predictions based on frequencies determined from behavioral experimental data yielded results highly similar to those results determined from MEG experimental data (details are provided in SI Results).
Model prediction of response rates. Proportion of "perceived two stimuli" reports for conditions with different SOAs for model predictions based on averaged individual response rates (gray bars), significant group-level frequencies (8–20 Hz, white bars), and behavioral data (black bars). Predicted responses based on frequencies were calculated per frequency bin and then averaged over all respective frequencies. Hit rates are presented as mean ± SEM.
Single-subject predicted and behavioral response rates. Proportions of perceived two stimuli reports for conditions with different SOAs for model predictions based on the individual critical frequency determined from MEG experimental data (white bars) and for individual behavioral data (black bars). Hit rates are presented as means. Individual critical frequencies are determined from MEG experimental data, the slopes specify for which the best fit between predicted and behavioral response rates can be achieved, and P values specify if the respective slope differs significantly from 1.
Predicted individual response rates based on individual frequencies determined from MEG experimental data and individual behavioral response rates
SI Results
To compare the predictions of perception based on MEG experimental data (Results and Fig. 4) with a model based on the behavioral experimental data, we computed the critical frequency determined by the average intermediate SOA of 25.9 ms (22.4 Hz) and predicted response rates for this frequency. The linear regression analysis between predicted and behavioral response rates resulted in a highly significant correlation coefficient (r = 0.99, P < 0.01). The resulting slope (1.05 ± 0.04) did not differ significantly from 1 [t(4) = 1.29, P > 0.05]. Finally, we computed critical frequencies determined from behavioral experimental data on the single-subject level (i.e., based on individual intermediate SOAs and behavioral response rates) and averaged the resulting critical frequencies over subjects (23.9 ± 2.0 Hz). Linear regression analysis resulted in a highly significant correlation coefficient (r = 0.99, P < 0.01). The resulting slope estimate (1.08 ± 0.04) did not differ significantly from 1 [t(4) = 2.12, P > 0.05]. Thus, theoretically and experimentally determined frequencies yielded highly similar results: Both reveal significant correlation values and slopes not significantly different from 1.
We investigated the neuronal mechanisms of varying conscious perception in the somatosensory domain. The results argue against a continuous perceptual mechanism and provide evidence that somatosensory perception operates in a discrete mode, with sensory input being sampled by discrete perceptual cycles in the alpha band and, in particular, the lower beta band (8–20 Hz).
Beta-Band Cycles Determine Discrete Perceptual Sampling.
We found that phase angles in S1 in the alpha band and lower beta band (8–20 Hz) before stimulus onset predicted whether subjects perceived two constant electrical stimuli with an SOA of ∼25 ms as one or two stimuli (Fig. 2B). Notably, this effect was most prominent in the lower beta band (14–18 Hz). We put forward a model proposing that somatosensory stimulation is discretely sampled and that the underlying perceptual cycles are determined by ongoing oscillatory alpha and beta cycles (Fig. 3). If multiple discrete stimuli fall within one perceptual cycle, the temporally fine-grained information is lost and the distinct stimuli are fused to a single percept, a phenomenon that has been labeled perceptual or temporal framing in the visual domain (3, 19, 21). The model was confirmed by two theoretical predictions. First, beta oscillations were found to be antiphasic (phase difference of π) for perception of one vs. two stimuli for intermediate SOAs (∼25 ms; Fig. 2 B–D). Based on these results, response rates were shown to depend on the specific phase at which the first stimulus arrives (Fig. 2D). Second, the model predicts behavioral performance on group (Fig. 4) and single-subject (Fig. S2) levels.
Based on behavioral response rates, the model predicted a theoretical critical sampling frequency of ∼23 Hz. The experimentally observed frequency range based on statistical analysis of phase angles revealed a significant effect between 8 and 20 Hz. Whereas the upper end of the experimental frequency range is close to the theoretically assumed frequency, the experimental frequency band also includes lower frequencies. A potential reason for this underestimation of the critical sampling frequency might be a decreased signal-to-noise ratio for higher frequencies. Noninvasive measurement (e.g., via EEG/MEG) of phase has been assumed to be especially susceptible to various interferences (e.g., delays in synaptic transmission) at higher frequencies (5). Likewise, phase differences in lower frequency bands could also resemble processes different than perceptual sampling (e.g., attentional processes) (22). This idea is in line with the different temporal distributions of phase angle differences for alpha- and beta-band frequencies. Finally, the presented model does not claim to cover all portions of the decision process determining the final response but, instead, focuses on early perceptual components. For example, the present data are derived from S1, thus not taking into account other cortical areas involved in the decisional process.
Discrete Perceptual Sampling Is Not a Domain-Specific Mechanism.
The theory of discrete perceptual cycles was introduced decades ago (1, 2). However, it has been controversially discussed (8, 9). Recently, the discussion on discrete perceptual cycles has gained new momentum by studies using EEG, which allows one to study potential neuronal mechanisms of discrete perceptual cycles noninvasively (5, 17, 22). Nonetheless, empirical evidence to support the theory of discrete perceptual cycles remains scarce and focuses mainly on the visual domain (3, 17), whereas evidence for discrete cycles in other domains is largely missing (19). The present study is thus, to our knowledge, the first to demonstrate the existence of perceptual cycles in the somatosensory domain, indicating that the cyclic characteristic of perception is not a domain-specific visual mechanism (19).
Modality-Specific Differences.
For the visual domain, EEG studies propose discrete cycles in perception and attentional updating defined by the alpha cycle (3, 17, 22). Our model agrees with these studies, albeit we propose perceptual cycles to be defined by alpha-band and, decisively, beta-band frequencies in the somatosensory domain. Although the significant group-level phase angle differences cover a rather broad band between 8 and 20 Hz, the major effect can be found in a narrower band between 14 and 18 Hz (Fig. 2B). Because subjects exhibit different individual intermediate SOAs, different individual frequencies for the discrete perceptual cycles are also to be expected (thereby blurring the group-level effect). In fact, the analyses based on individually determined frequencies confirmed that the individual narrow-band frequencies represent an appropriate predictor for individual response rates (Fig. S2). These domain-specific differences agree with a more prominent role of alpha oscillations in the visual domain for perception and neuronal processing (23, 24), whereas there is experimental evidence for a specific role of beta oscillations in the somatosensory domain (10, 13, 25⇓–27). The present findings are in line with studies investigating steady-state somatosensory evoked potentials (SSSEPs). These studies found that the largest SSSEP amplitudes can be achieved by a stimulation frequency of ∼18–26 Hz (i.e., in the beta band) (27⇓–29). Stimulation at this frequency would place every stimulus in a separate beta cycle, therefore enhancing SSSEPs and, consequently, facilitating perceptual detection (26). Finally, the proportion perceiving two stimuli differed by 13% between the lowest (−π) and the highest (1/3 π) phase bins (with exclusion of the zero phase bin). This difference agrees with ranges reported for visual stimuli (5, 15). Thus, both visual and somatosensory perception seems to be influenced by phase with a comparable magnitude.
What About Absolute Phase Angles?
Varela et al. (3) reported that the phase of occipital alpha oscillations determines whether subjects perceive two sequential visual stimuli as one or two stimuli. The respective phase for perceiving one vs. two stimuli was anticyclic (i.e., the phase difference was π). Although later studies failed to replicate this result (19, 30), our results support the finding by Varela et al. (3), because we find a phase difference of π between phases for perceiving one vs. two tactile stimuli. In contrast to Varela et al. (3), however, we do not claim that the specific phase (the peak or trough) is important for perception but, rather, whether two stimuli fall within a single cycle or separate cycles. The majority of studies investigating the influence of oscillatory phase on perception analyzed absolute phase angles within an oscillatory cycle at a specific moment, which are either favorable or unfavorable for subsequent perception (5, 11, 12, 15, 31). Thus, a potential concern might be that our results could be explained by favorable or unfavorable phases within one cycle. In such a framework, one stimulus might be presented at a favorable phase and the other stimulus might be presented at an unfavorable phase, thus leading to the erroneous perception of only one stimulus. The above-mentioned studies, however, used near-threshold stimuli. We presented stimuli with clearly suprathreshold intensities that are presumably perceived independent of the specific phase. Although a hypothesis proposing an influence of (un)favorable phases would predict that ∼50% of the stimuli with SOA 0 ms would be missed, subjects correctly perceived almost all stimuli. Similarly, such a framework would predict a higher percentage of trials with SOA 100 ms to be perceived as one stimulus than found in our behavioral data. Therefore, the present results cannot be explained by favorable or unfavorable phases within one oscillatory cycle.
Differentiating Effects of Phase and Power.
Recent studies demonstrated an influence of oscillatory power for perception of single (near-threshold) tactile stimuli, as well as for the temporal discrimination of two tactile stimuli (10, 25). The majority of these studies [including a previous study by our group on the dataset presented in this study (14)] found prestimulus power differences in the alpha band (8–12 Hz), whereas the present phase angles differed mostly in the lower beta band (14–18 Hz). Further, we found no significant power differences in those time-frequency elements showing significant phase angle differences between perceptual conditions. It is thus unlikely that the presented phase effect was biased by power differences. Indeed, there is experimental evidence for an influence of both oscillatory power (10) and phase (12, 31) for neuronal processing and perception, and recent studies could demonstrate that these measures act largely independently (5, 22). This differentiation is further supported by results showing that phase is able to transport more units of information per time than power changes (32) or spike counts (33), and represents a suitable candidate measure to encode fast-changing stimulus features (21).
Contradicting Subjective Experience.
There is accumulating evidence that our brain processes incoming stimulus information in a phasic mode (3, 17). However, personal experience does not intuitively match with a discrete sequencing approach but, rather, resembles a seamlessly updated percept. This divergence might explain why relatively few studies address this topic, although the concept of discrete perceptual sampling has been put forward at least since the middle of the 20th century (1, 2). It remains an open question how the brain transforms discretely sampled sensory information into a subjectively seamless impression. Although the mechanisms for such perceptual "smoothing" are unknown, there are, at least for the visual domain, several reports where the mechanisms fail to work (34). For example, in akinetopsia, subjects report perceiving a sequence of snapshots rather than a continuous motion (35, 36). Similarly, the ingestion of lysergic acid diethylamide often results in a perceptual disturbance wherein visual motion is perceived as a sequence of discrete stationary images (37, 38).
The present study demonstrates an influence of oscillatory phase on the temporal perception of two stimuli. We propose the existence of discrete perceptual cycles for the conscious perception of subsequently presented tactile stimuli. The perceptual cycles are determined particularly by frequencies in the beta band acting as the specific physiological correlate for perceptual cycles for the somatosensory modality. In combination with previous studies investigating similar paradigms in the visual domain (3, 30), the present results support the theory of temporal framing (1⇓–3, 19, 21) and indicate that perceptual cycles are no domain-specific visual phenomenon, albeit modality-specific frequencies that define perceptual cycles seem to be present.
Subjects.
The subjects, stimuli, paradigm, and MEG recording of the present study were previously reported in detail (14). Here, we present a comprehensive overview. Sixteen right-handed volunteers [seven males, age: 26.1 ± 4.7 y (mean ± SD)] participated in the study. Subjects provided written informed consent before the experiment in accordance with the Declaration of Helsinki and approved by the Ethical Committee of the Medical Faculty, Heinrich-Heine-University Düsseldorf.
Experimental Paradigm.
Details on the paradigm can be found in the study by Baumgarten et al. (14). A comprehensive overview is provided in Fig. 1 and SI Materials and Methods.
MEG Data Recording and Preprocessing.
Electromagnetic brain activity was continuously recorded using a 306-channel, whole-head MEG system (Neuromag Elekta Oy). Analysis was restricted to the gradiometers. Individual structural MRI scans were acquired using a 3-T MRI scanner (Siemens). Offline analysis of the data was carried out using custom-made MATLAB (MathWorks) scripts and the MATLAB-based open-source toolboxes FieldTrip (fieldtriptoolbox.org) (39), CircStat (40), and SPM8 (41). Continuously recorded data were segmented into trials. All trials were semiautomatically and visually inspected for artifacts, whereas artifacts caused by muscle activity, eye movements, or technical artifacts were removed semiautomatically using a z-score–based algorithm implemented in FieldTrip.
Virtual Channel Construction.
To focus on S1, we analyzed oscillatory activity in a predefined region of interest in source space ("virtual sensor"). Details regarding the construction of the virtual sensor are provided in SI Materials and Methods.
Oscillatory phase was calculated for the virtual sensor. We sorted trials with respect to the SOA for each subject separately, resulting in five different conditions defined by the length of the SOA (0 ms, intermediate − 10 ms, intermediate, intermediate + 10 ms, and 100 ms). Subsequently, we separated intermediate trials by perceptual response (perceived one vs. two stimuli, subsequently labeled intermediate1 vs. intermediate2). Because trial numbers are known to influence phase measures crucially (42), trial numbers were equated across conditions in each analysis by determining the condition with the lowest number of trials per subject and randomly selecting the same number of trials from the remaining conditions. To exclude potential effects due to a specific trial selection, we performed trial selection by means of random subsampling 100 times, and subsequently computed the median of the resulting phase parameters over these 100 repetitions (because F values were not normally distributed). The time point t = 0 was defined as the onset of the first stimulus. The oscillatory phase was calculated for each time-frequency element (−650 to 240 ms, 2–40 Hz) of each single trial by applying a discrete Fourier transform (DFT) on fixed sliding time windows with a length of 500 ms, moved in steps of 10 ms. Data segments were tapered with a single Hanning taper, resulting in a spectral smoothing of 2 Hz. For each subject s, trial r, frequency f, and time point t, we normalized the complex outcome Fs,r,f,t of the DFT by dividing it by its absolute (abs) value, thus normalizing the signal by its amplitude:Fs,r,f,tnorm=Fs,r,f,tabs(Fs,r,f,t)[1]
From these normalized values, we computed for each subject s, trial r, frequency f, and time point t, the normalized phase:Φs,r,f,tnorm=atan(Im(Fs,r,f,tnorm)Re(Fs,r,f,tnorm))[2]
where Im and Re are the imaginary part and real part, respectively, of the DFT.
To analyze statistically whether phase angles differed between perceptual conditions, we compared phase angles between the intermediate1 and intermediate2 conditions for each time-frequency element at the within-subject level by means of the Watson–Williams multisample test for equal means [CircStat toolbox (40)]. This test for circular data is equivalent to a two-sample t test for equal angular means. For each randomized trial selection, we compared phase angles for each subject independently for each time-frequency element, resulting in 100 F values for each time-frequency element. We took for each time-frequency element the median of all 100 F values, resulting in a time-channel map of F values for each subject, which constitutes the test distribution. To assess the consistency of phase angle differences over subjects, we performed a nonparametric randomization test identifying clusters in time-frequency space demonstrating a similarly directed phase angle difference relative to a null distribution (43). We computed this null distribution under the null hypothesis that phases are randomly and uniformly distributed, showing no difference between conditions. That is, for each subject, we assigned to each condition random phases (equaling the number of trials for each subject) and then repeated the above-mentioned statistical analysis. We compared (random) phase angles between both conditions for each time-frequency element at the within-subject level by applying the Watson–Williams test. This procedure was repeated 100 times (each time with new, randomly chosen phases), resulting in 100 F values for each time-frequency element. Subsequently, we took the median of all 100 F values for each time-frequency element, resulting in a time-channel map of F values for each subject, which constitutes the null distribution. We then statistically compared the F values of the test distribution with the F values of the null distribution for each time-frequency element by means of a dependent-samples t test, resulting in a time-frequency map of t values. Positive t values for a specific time-frequency element demonstrate a larger phase angle difference compared with randomly distributed phase angles, and vice versa for negative t values (44). To investigate whether the phase angle differences between perceptual conditions were significantly different from randomly distributed phases, we applied a cluster-based randomization approach (14). This statistical approach effectively controls for the type I error rate due to multiple comparisons across time points and channels (43).
To ensure that phase angle differences are not biased by power, we analyzed power differences between perceptual conditions for those time-frequency elements exhibiting significant phase differences. The respective analysis parameters are discussed in ref. 14. To visualize phase angle differences on the group level, we computed phase angle differences for each time-frequency element. We computed the circular distance between the over-trial averages of the intermediate2 and intermediate1 conditions for each subsampling run, and subsequently averaged circular distances over all subsampling runs on the single-subject level and over subjects (Fig. 2C).
To determine to what extent perception of one or two stimuli is associated with different phase angles, we selected for each subject the time-frequency point showing the largest statistical phase angle effect (maximum Watson–Williams test F value) within the time-frequency range of the aforementioned phase contrast effect (8–20 Hz, −0.53 to −0.09 s; Fig. 2B). This analysis resembles a post hoc test based on previous results. For each subject, the momentary phase for the respective time-frequency point was computed for each single trial for both perceptual conditions. Subsequently, the trial was placed in one of six different, equally spaced phase bins (bin width = 1/3 π), ranging from −π to +π. For each subject, we calculated the normalized perceptual response rate per bin. We adjusted phase distributions for each subject so that the bin showing maximum perception of two distinct stimuli was aligned to a phase angle of zero (a similar procedure is described in refs. 5 and 11). This process was repeated for each of the 100 specific randomized trial selections. Subsequently, we computed the median of the normalized perceptual response rates for each bin across the 100 repetitions for random trial selection and averaged response rates over subjects (Fig. 2D). To assess an effect of phase angle on perceptual response rates, a one-way repeated measures ANOVA and post hoc paired sample t tests were conducted. Due to the realignment, we excluded the bin centered on zero from the statistical analyses.
Based on the model (Fig. 3), we predicted response rates for the different SOAs and computed linear regressions between predicted and behaviorally measured response rates. We used different approaches to predict response rates, with each approach based on a slightly different method to determine the critical frequency: (i) based on group-level effect frequencies determined from MEG experimental data (Fig. 2B), (ii) based on single-subject individual frequencies determined from MEG experimental data (Fig. S2 and Table S1), and (iii) based on frequencies determined from behavioral experimental data (i.e., the intermediate SOAs). The approaches are described in detail in SI Materials and Methods.
SI Materials and Methods
Each trial began with a precue period (500 ms; Fig. 1). After 900–1,100 ms, either one or two electrical pulses (0.3 ms) were applied to the subject's left index finger, with the pulse amplitude determined individually to a level above the subjective perception threshold [4.1 ± 1.2 mA (mean ± SD)]. SOAs between the electrical pulses varied from short (0 ms) to long (100 ms), and comprised an individually determined SOA for which subjects reported the perception of one electrical pulse in ∼50% of the trials, whereas two pulses were perceived [SOA: 25.9 ± 1.9 ms (mean ± SEM)] in the other ∼50% of the trials, subsequently labeled intermediate SOA. Two additional SOAs encompassed the intermediate SOA ± 10 ms (subsequently labeled intermediate + 10 ms and intermediate − 10 ms, respectively). After a jittered poststimulus period (500–1,200 ms), a response window indicated that subjects should report their perception (one or two stimuli) by pressing a button with the right hand. No feedback was given.
To focus the analysis on S1, we analyzed oscillatory brain activity in a predefined region of interest in source space. This "virtual channel" was determined by localizing the individual sources of the evoked responses (M50 component) to left index finger stimulation, because this component is known to originate from S1 (45, 46). To determine the virtual channel, all trials on the sensor level were filtered between 2 and 40 Hz and the mean of every epoch was removed from each trial. We then pooled all trials (irrespective of SOA) for each subject and computed the individual event-related fields. Next, we identified the individual M50 component by focusing on the time window of 20–70 ms after stimulation onset. Source localization was performed by means of a linearly constrained minimum variance beam former (47) on 3D grids with a resolution of 1 cm. Individual subject grids were computed by linearly warping the structural MRI of each subject onto the Montreal Neurological Institute (MNI) template brain and applying the inverse of the warp to the regular MNI template grid. For one subject, the MNI template brain was used instead of the individual structural MRI, because no individual MRI was available. A lead-field matrix was computed for each grid point using a realistically shaped single-shell volume conduction model (48). Covariance matrices across all MEG sensors were calculated based on the average across all trials to determine the source of evoked responses. Using the covariance matrices and lead field matrices, separate individual spatial filters of both prestimulus and poststimulus activity were constructed for each grid point. We calculated for each subject the ratio of M50 activity (20–70 ms) relative to baseline activity (−400 to −350 ms) for each grid point. Next, we averaged the source activity for each grid point over subjects and determined the grid point with maximum M50 activity. This grid point was selected as the location of the virtual sensor (Fig. 2A). The corresponding label was identified with the help of the Analysis of Functional NeuroImages atlas (afni.nimh.nih.gov/afni).
Single-trial time courses for this virtual channel were computed from MEG sensor data. We computed covariance matrices across all MEG sensors, based on averaged nonoverlapping trials, from −900 to 500 ms after trials were filtered between 2 and 40 Hz, and the mean of every epoch was removed from each trial. Covariance matrices were used to construct a spatial filter for the selected grid point of maximum M50 activity. The largest of the three dipole directions per spatial filter was used for further analysis (49). We applied this spatial filter on the MEG sensor data to reconstruct the single-trial time series in the virtual channel:sourceTSs,r=sfs∗sensorTSs,r,c,[S1]with sensorTSs,r,c defining the time series data on the sensor level for each subject s, trial r, and channels c projected through the spatial filter sfs to obtain the time series data on source level (sourceTSs,r) for each subject s and trial r. MEG sensor data were first segmented to trials with a length of 1,400 ms (−900 to 500 ms) and then detrended, demeaned, and filtered (2–250 Hz). The resulting source-based time signal was then used as input for the oscillatory phase estimation.
Predictions of response rates and linear regressions between predicted and behaviorally measured response rates were based on three different approaches: (i) group-level effect frequencies determined from MEG experimental data (8–20 Hz; Fig. 2B), (ii) single subject-level individual frequencies determined from MEG experimental data (Fig. S2 and Table S1), and (iii) frequencies determined from behavioral experimental data (i.e., the intermediate SOAs). These approaches are in detail:
i) As the critical frequency of the model, we chose the frequencies showing a significant group-level phase angle difference between the conditions intermediate2 and intermediate1 (8–20 Hz; Fig. 2B). We calculated the cycle length for each frequency and then divided the length of the respective SOA by the cycle length, thus calculating for each cycle the ratio of time points for which the two stimuli would fall into one cycle (one perceived stimulus) or into two cycles (two perceived stimuli) (Fig. 3). Thereby, we calculated the predicted response rate per frequency bin, and subsequently averaged predicted response rates over all frequencies showing a significant group-level phase angle difference between perceptual conditions (8–20 Hz). Finally, we computed the mean response rate and SEM across all frequencies. We statistically compared these predicted response rates with the group-level average of the measured behavioral response rates (Fig. 4) by first computing the correlation coefficients of the linear regression for the predicted and behavioral response rates under the premise of a y-axis intercept at (0,0). The correlation coefficient assesses the goodness of correlation between the predicted response rates and the behavioral response rates. Next, we compared the resulting slope estimate with the slope resulting from an ideal fit (i.e., 1) by means of a one-sample, two-tailed t test. By this approach, we were able to test if the predicted response rate linearly agrees with the behavioral response rate over the different SOAs or if a systematic over- or underestimation is present (which would lead to a significant difference between slope estimate and ideal slope).
ii) Additionally, we predicted response rates on a single-subject level. According to our model, subjects with different intermediate SOAs should exhibit different critical frequencies, which, in turn, determine their respective perceptual cycles and predict individual response rates. To determine individual critical frequencies, individual F values resulting from the Watson–Williams test were summed up over all time points of the significant group-level effect (−0.53 to −0.09 s) separately for each frequency of the significant group-level effect (8–20 Hz). For each subject, the frequency showing the maximum F values was selected as the individual critical frequency, for which we calculated predicted individual response rates according to the analysis on the group level (discussed above). Similarly, we computed and compared the slopes of the linear regressions for the individual predicted and individual behavioral response rates. To compare the individual response rate predictions with the group-level predictions based on the frequencies showing significant group-level phase angle differences (discussed above in i), we averaged predicted individual response rates over subjects and compared the slope of the linear regression for the predicted and behavioral response rates according to the aforementioned analysis.
iii) To compare the predictions based on the critical frequencies determined from MEG experimental data with a model based on the behavioral experimental data, we calculated the critical frequency based on the average intermediate SOA length and group-level behavioral response rates (Fcrit = ratio of perceived two stimuli reports/mean length intermediate SOA ∗ 1,000). We then predicted response rates and computed the resulting slope (discussed above). Likewise, we computed individual critical frequencies determined from behavioral experimental data (based on individual intermediate SOAs and individual response rates). We averaged the resulting individual critical frequencies over subjects, and likewise predicted response rates and computed the resulting slope.
We thank Erika Rädisch for help with the MRI recordings. J.L. was supported by the German Research Foundation (Grant LA 2400/4-1). T.J.B. was supported by the German Research Foundation (SFB 974, B07).
↵1To whom correspondence should be addressed. Email: thomas.baumgarten{at}med.uni-duesseldorf.de.
Author contributions: J.L. designed research; T.J.B. performed research; T.J.B. and J.L. analyzed data; and T.J.B., A.S., and J.L. wrote the paper.
Quastler H
Stroud JM
(1956) in Information Theory in Psychology, ed Quastler H (Free Press, Chicago), pp 174–205
Harter MR
(1967) Excitability cycles and cortical scanning: A review of two hypotheses of central intermittency in perception. Psychol Bull 68(1):47–58
Varela FJ,
Toro A,
John ER,
Schwartz EL
(1981) Perceptual framing and cortical alpha rhythm. Neuropsychologia 19(5):675–686
VanRullen R,
Koch C
(2003) Is perception discrete or continuous? Trends Cogn Sci 7(5):207–213
Busch NA,
Dubois J,
VanRullen R
(2009) The phase of ongoing EEG oscillations predicts visual perception. J Neurosci 29(24):7869–7876
Jensen O,
Gips B,
Bergmann TO,
Bonnefond M
(2014) Temporal coding organized by coupled alpha and gamma oscillations prioritize visual processing. Trends Neurosci 37(7):357–369
Schroeder CE,
Lakatos P
(2009) Low-frequency neuronal oscillations as instruments of sensory selection. Trends Neurosci 32(1):9–18
Allport DA
(1968) Phenomenal simutaneity and the perceptual moment hypothesis. Br J Psychol 59(4):395–406
Kline KA,
Eagleman DM
(2008) Evidence against the temporal subsampling account of illusory motion reversal. J Vis 8(4):1–5
Lange J,
Halacz J,
van Dijk H,
Kahlbrock N,
Schnitzler A
(2012) Fluctuations of prestimulus oscillatory power predict subjective perception of tactile simultaneity. Cereb Cortex 22(11):2564–2574
Ng BS,
Schroeder T,
Kayser C
(2012) A precluding but not ensuring role of entrained low-frequency oscillations for auditory perception. J Neurosci 32(35):12268–12276
Mathewson KE,
Gratton G,
Fabiani M,
Beck DM,
Ro T
(2009) To see or not to see: Prestimulus alpha phase predicts visual awareness. J Neurosci 29(9):2725–2732
Jones SR, et al.
(2010) Cued spatial attention drives functionally relevant modulation of the mu rhythm in primary somatosensory cortex. J Neurosci 30(41):13760–13765
Baumgarten TJ,
Schnitzler A,
Lange J
(2014) Prestimulus alpha power influences tactile temporal perceptual discrimination and confidence in decisions. Cereb Cortex doi:10.1093/cercor/bhu247
Dugué L,
Marque P,
(2011) The phase of ongoing oscillations mediates the causal relation between brain excitation and visual perception. J Neurosci 31(33):11889–11893
Keil J,
Weisz N
(2014) The role of alpha oscillations for illusory perception. Behav Brain Res 271:294–301
Chakravarthi R,
(2012) Conscious updating is a rhythmic process. Proc Natl Acad Sci USA 109(26):10599–10604
Romei V,
Gross J,
Thut G
(2012) Sounds reset rhythms of visual cortex and corresponding human visual perception. Curr Biol 22(9):807–813
Zoefel B,
Ilhan B
(2014) On the cyclic nature of perception in vision versus audition. Philos Trans R Soc Lond B Biol Sci 369(1641):20130214
Lakatos P,
Chen CM,
O'Connell MN,
Mills A,
Schroeder CE
(2007) Neuronal oscillations and multisensory interaction in primary auditory cortex. Neuron 53(2):279–292
Drewes J,
Dubois J
(2011) Ongoing EEG phase as a trial-by-trial predictor of perceptual and attentional variability. Front Psychol 2:60
(2010) Spontaneous EEG oscillations reveal periodic sampling of visual attention. Proc Natl Acad Sci USA 107(37):16048–16053
Romei V, et al.
(2008) Spontaneous fluctuations in posterior α-band EEG activity reflect variability in excitability of human visual areas. Cereb Cortex 18(9):2010–2018
Wyart V,
Tallon-Baudry C
(2009) How ongoing fluctuations in human visual cortex predict perceptual awareness: Baseline shift versus decision bias. J Neurosci 29(27):8715–8725
Linkenkaer-Hansen K,
Nikulin VV,
Palva S,
Ilmoniemi RJ,
Palva JM
(2004) Prestimulus oscillations enhance psychophysical performance in humans. J Neurosci 24(45):10186–10190
Jones SR,
Pritchett DL,
Stufflebeam SM,
Hämäläinen M,
Moore CI
(2007) Neural correlates of tactile detection: A combined magnetoencephalography and biophysically based computational modeling study. J Neurosci 27(40):10751–10764
Haegens S, et al.
(2011) Beta oscillations in the monkey sensorimotor network reflect somatosensory decision making. Proc Natl Acad Sci USA 108(26):10708–10713
Snyder AZ
(1992) Steady-state vibration evoked potentials: Descriptions of technique and characterization of responses. Electroencephalogr Clin Neurophysiol 84(3):257–268
Tobimatsu S,
Zhang YM,
Kato M
(1999) Steady-state vibration somatosensory evoked potentials: Physiological characteristics and tuning function. Clin Neurophysiol 110(11):1953–1958
Gho M,
Varela FJ
(1988-1989) A quantitative assessment of the dependency of the visual temporal frame upon the cortical rhythm. J Physiol (Paris) 83(2):95–101
Neuling T,
Rach S,
Wagner S,
Wolters CH,
Herrmann CS
(2012) Good vibrations: Oscillatory phase shapes perception. Neuroimage 63(2):771–778
Schyns PG,
Thut G,
Gross J
(2011) Cracking the code of oscillatory activity. PLoS Biol 9(5):e1001064
Montemurro MA,
Rasch MJ,
Murayama Y,
Logothetis NK,
Panzeri S
(2008) Phase-of-firing coding of natural visual stimuli in primary visual cortex. Curr Biol 18(5):375–380
(2011) Visual trails: Do the doors of perception open periodically? PLoS Biol 9(5):e1001056
Horton JC,
Trobe JD
(1999) Akinetopsia from nefazodone toxicity. Am J Ophthalmol 128(4):530–531
Tsai PH,
Mendez MF
(2009) Akinetopsia in the posterior cortical variant of Alzheimer disease. Neurology 73(9):731–732
Abraham HD
(1983) Visual phenomenology of the LSD flashback. Arch Gen Psychiatry 40(8):884–889
Kawasaki A,
Purvin V
(1996) Persistent palinopsia following ingestion of lysergic acid diethylamide (LSD). Arch Ophthalmol 114(1):47–50
Oostenveld R,
Fries P,
Maris E,
Schoffelen JM
(2011) FieldTrip: Open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data. Comput Intell Neurosci 2011:156869
Berens P
(2009) CircStat: A MATLAB toolbox for circular statistics. J Stat Softw 31(10):1–21
Litvak V, et al.
(2011) EEG and MEG data analysis in SPM8. Comput Intell Neurosci 2011:852961
Hanslmayr S,
Volberg G,
Wimber M,
Dalal SS,
Greenlee MW
(2013) Prestimulus oscillatory phase at 7 Hz gates cortical information flow and visual perception. Curr Biol 23(22):2273–2278
Oostenveld R
(2007) Nonparametric statistical testing of EEG- and MEG-data. J Neurosci Methods 164(1):177–190
Müller N,
Hartmann T,
(2014) Prestimulus beta power and phase synchrony influence the sound-induced flash illusion. Cereb Cortex 24(5):1278–1288
Suk J,
Ribary U,
Cappell J,
Yamamoto T,
Llinás R
(1991) Anatomical localization revealed by MEG recordings of the human somatosensory system. Electroencephalogr Clin Neurophysiol 78(3):185–196
Iguchi Y,
Hoshi Y,
Tanosaki M,
Taira M,
Hashimoto I
(2005) Attention induces reciprocal activity in the human somatosensory cortex enhancing relevant- and suppressing irrelevant inputs from fingers. Clin Neurophysiol 116(5):1077–1087
Van Veen BD,
van Drongelen W,
Yuchtman M,
Suzuki A
(1997) Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 44(9):867–880
Nolte G
(2003) The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors. Phys Med Biol 48(22):3637–3652
Schoffelen JM,
Poort J,
Fries P
(2011) Selective movement preparation is subserved by selective increases in corticomuscular gamma-band coherence. J Neurosci 31(18):6750–6758
You are going to email the following Beta oscillations define discrete perceptual cycles in the somatosensory domain
β-cycles define somatosensory perception
Thomas J. Baumgarten, Alfons Schnitzler, Joachim Lange
Proceedings of the National Academy of Sciences Sep 2015, 112 (39) 12187-12192; DOI: 10.1073/pnas.1501438112