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Areas V1 and V2 show microsaccade-related 3-4 Hz
covariation in gamma power and frequency
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E. LOWET(1,2), M.J. ROBERTS(1,2), C.A.BOSMAN (2,4) , P. FRIES(2,3), P. DE WEERD(1,2)
(1) Fac. Psychol. & Neurosci, Maastricht Univ., NLs;
(2) Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, NLs;
(3) Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, DE.
(4) Center for Neuroscience, Swammerdam Institute for Life Sciences, Faculty of Science, University
of Amsterdam, NLs
Running title: Theta rhythmic variation in V1/V2 gamma-band
To whom correspondence may be addressed: Eric Lowet ([email protected])
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ABSTRACT
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Neuronal gamma-band synchronization (25-90 Hz) in visual cortex appears sustained and stable during
prolonged visual stimulation when investigated with conventional averages across trials. Yet, recent
studies in macaque visual cortex have used single-trial analyses to show that both power and frequency
of gamma oscillations exhibit substantial moment-by-moment variation. This has raised the question
whether these apparently random variations might limit the functional role of gamma-band
synchronization for neural processing. Here, we studied the moment-by-moment variation of gamma
oscillation power and frequency, as well as inter-areal gamma synchronization by simultaneously
recording local field potentials in V1 and V2 of two macaque monkeys. We additionally analyzed
electrocorticographic (ECoG) V1 data from a third monkey. Our analyses confirm that gamma-band
synchronization is not stationary and sustained but undergoes moment-by-moment variations in power
and frequency. However, those variations are neither random and nor a possible obstacle to neural
communication. Instead, the gamma power and frequency variations are highly structured, shared
between areas, and shaped by a microsaccade-related 3-4 Hz theta rhythm. Our findings provide
experimental support for the suggestion that cross-frequency coupling might structure and facilitate the
information flow between brain regions.
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INTRODUCTION
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Visually induced neuronal responses are commonly assessed by averaging trials aligned to the onset of
the visual stimulus (stimulus-triggered averaging). Likewise, stimulus-triggered averaging is a standard
approach to study gamma-band oscillations (25-80 Hz). Stimulus-triggered time-frequency
representations (TFRs) typically show strong, ‘transient’ modulation of gamma, which is described as
‘stimulus-evoked’. This is followed by ‘sustained’ gamma (Hoogenboom et al., 2006; Swettenham et al.,
2009), which is often the target of experimental manipulations and analysis. However, recent V1
recordings indicate that single-trial gamma oscillations in the so-called ‘sustained’ period preserve neither
frequency nor amplitude over time, but seem to have random, ‘burst’-like characteristics (Burns et al.,
2010, 2011; Ray & Maunsell, 2010; Roberts et al., 2013). These findings refute the view of a stationary
oscillation as could be suggested by trial-averaged data. Moreover, the apparent randomness of gamma
may impede its contribution to neural computation (Burns et al., 2011). Gamma randomness may also
impede neural communication (Ray and Maunsell, 2010), possibly in part by preventing the frequency
matching among neural populations necessary for communication (Roberts et al., 2013). However, it is
challenging to distinguish randomness from complexity in experimental data. Hence, it is crucial to
investigate whether fluctuations of gamma frequency and power are structured, regulated and exploited
by other brain processes.
In a number of brain areas, it has been shown that gamma variation depends on slower rhythmic
fluctuations that include delta, theta and alpha/beta frequencies (Lakatos et al., 2005; Jensen & Colgin,
2007; Osipova et al., 2008; Schroeder & Lakatos, 2009; Canolty & Knight, 2010; Jutras et al., 2013) and
that these slower rhythms can affect gamma synchronization among brain areas (Colgin et al., 2009;
Bosman et al., 2012; Schomburg et al., 2014). The dependence of a fast rhythm on a slower rhythm is
often referred to as cross-frequency coupling (CFC). A particular type of CFC represents the linkage
between gamma oscillations and (often rhythmic) movements of sensory organs. For example, in the
visual system, gamma modulations have been linked to saccadic eye movements (Rajkai et al., 2008;
Bosman et al., 2009; Ito et al., 2011; Brunet et al., 2013). CFC has been studied mainly in terms of phaseto-power interactions. However, phase-to-frequency interactions, where the precise frequency of gamma
depends on a slower oscillation phase have been rarely discussed despite the fact that frequency is a
critical factor for enabling synchronization (Pikovsky et al., 2002).
We therefore studied in more detail whether moment-by-moment variation in gamma frequency is
temporally structured by slower rhythms in macaque V1 and V2, and whether it affects gamma
synchronization between these cortical areas. To this aim, we analyzed simultaneous microelectrode
recordings of local field potentials (LFPs) from V1 and V2 sites with (near-) overlapping receptive fields
(RFs) from two macaque monkeys and from an additional monkey with an ECoG grid covering V1.
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MATERIAL AND METHODS
Surgical procedures and electrophysiological methods for monkeys S and K have been described in detail
in Roberts et al. (2013), and for monkey A in (Bosman et al., 2012; Brunet et al., 2013). All three monkeys
were adult, male Maccaca Mulatta (7-10kg). In monkeys S and K, recordings were done with laminar depth
probes in V1 and V2, separated by a distance of 4-6mm. Recording sites were assigned to V1 or V2 using
conventional retinotopic mapping relative to the vertical meridian representation (Gattass et al., 1981);
for details see Suppl.Mat. of Roberts et al. (2013). Based on this mapping procedure, we also chose the
probe positions such that RFs in V1 and V2 were overlapping or near-overlapping (Roberts et al., 2013),
as retinotopic projections between V1 and V2 (Lund, 2003) predict that this enhances the possibility of
finding V1-V2 gamma-range phase locking (Nowak et al., 1999; Bosman et al., 2012; Zandvakili & Kohn,
2015). Note that we did not greatly vary the distance between probes (RFs) and therefore in our own data
did not confirm the decrease in coherence for increasing probe distances (Suppl.Mat. in Roberts et al.,
2013). Note furthermore that for the purposes of the present analysis, we averaged across all cortical
layers.
In monkey A, recordings were obtained by means of an ECoG grid (Rubehn et al., 2009) covering large
parts of the right hemisphere (Bosman et al., 2012; Brunet et al., 2013). V1 recordings were analyzed from
the bipolar electrode pair that yielded the strongest gamma oscillatory response compared to baseline to
allow for robust frequency and power estimations. In this monkey, we could not find electrodes with
strong gamma signal that could be assigned to V2 with sufficient confidence, which may be due to the
limited exposure of V2 at the surface just posterior from the lunate sulcus (Gattass et al., 1981) in this
monkey.
The depth probe V1/V2 data for the theta-triggered gamma oscillation were acquired from recording
chambers implanted above the left hemisphere in monkeys S and K. Depth probe data for microsaccadetriggered analysis in monkey S were acquired from a V1/V2 chamber above the right hemisphere after
removal of the previous chambers. We used ‘U-probes’ (Plexon Inc.), having 8 contacts (200µm intercontact spacing) or 16 contacts (150µm inter-contact spacing). LFPs were filtered (0.7–300 Hz) and
recorded at 1 kHz (Plexon MAP system).
In monkey A, ECoG signals were amplified by a factor 20 using eight Plexon headstage amplifiers (Plexon,
USA). The signals were then low-pass filtered at 8 kHz, followed by digitization at 32 kHz by a Neuralynx
Digital Lynx system (Neuralynx, USA). LFP signals were lowpass filtered at 200 Hz (in the forward direction,
i.e. causally) and downsampled to 1 kHz (Bosman et al., 2012). We used two eye tracking systems in our
experiments. In all three monkeys and in all recording sessions, fixation behavior was monitored using a
low-resolution eye tracker directed at one eye (Arrington, 60 Hz). In addition, in a subset of sessions, we
additionally used a higher resolution eye tracking system (Thomas Recording, 240 Hz) to measure
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microsaccades in one eye (optimized for microsaccade detection in terms of temporal and spatial
resolution). This equipment was acquired after recording in monkey K had stopped, therefore higherresolution eye tracking was done only in monkeys S and A.
In all three monkeys, recordings were done while gratings were presented and while the monkeys directed
their gaze to a fixation point. Trials were aborted after fixation errors. The data for monkeys S (left
hemisphere) and K used for theta-triggered analysis of gamma oscillations were obtained with stationary
square wave gratings (2cpd, 3-5°diameter), shown on an isoluminant gray background. Stimuli were
presented at 8 different luminance contrasts (2%, 3.5%, 6%, 9.7%, 16.3%, 35.9%, 50.3%, 72%). We present
the analysis for a middle contrast (35.9%) that gave strong gamma responses in both monkeys. We
obtained comparable results at other contrasts. The behavioral task was to hold fixation on a fixation spot
in the middle of the computer screen during stimulus presentation (1.500-4.500ms; only trials with
>1800ms were included). The data were acquired as baseline data for an ongoing perceptual learning
project.
The data for the microsaccade-triggered analysis from Monkey S (right hemisphere) was acquired during
a different phase of the perceptual learning experiment. Here, the monkey had to report a color change
at fixation with an upward eye movement to a target. Stimulus gratings of different contrasts (4.9%, 6.1%,
7.3%, 8.5%, 12.7%, 18.7%, 26.7%, 37.4%,54.5%, 73.6%,) were shown (with >1.5s duration). For the present
study, we chose the data from the 37.4% contrast grating because it induced the strongest gamma
response, thus facilitating an investigation of its relation with slower rhythms and microsaccades.
For monkey A, LFP data were acquired in which the monkey had to fixate while a whole-field square-wave
grating (63% contrast) was shown (1sec fixation and 2 sec fixation with stimulus). The present study in
monkey A was conducted after the study reported in (Brunet et al., 2013), and hence stimuli and task used
in the present study differ from those in Brunet et al., (2013).
For the theta-triggered analysis, we filtered the LFP signal (two-pass Butterworth filter) around the theta
peak frequency (±0.5 Hz) observed in the power spectra. For each probe, we used the contact with the
strongest theta power peak as the theta reference for all other contacts. The filtered signal was Hilbert
transformed and the moment-by-moment phase derived. Around zero-phase, we detected the maximum
amplitude peak of the theta wave around which we triggered time-windows [±0.25s]. Only data above
the lower 25th percentile of the theta amplitude distribution were included in further analysis as phase
estimates for data with low amplitude were unreliable.
For the microsaccade (MS)-triggered analysis in monkeys S and A, we smoothed horizontal and vertical
eye signals (rectangular window of ±5ms) and differentiated the signals over time points separated by
10ms to obtain robust eye speed signals. We then used the MS-detection algorithm devised by (Engbert
& Kliegl, 2003). Time windows were aligned to the microsaccade onset [-0.1 to 0.4s].
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For spectral analysis, we used the FieldTrip MATLAB toolbox (Oostenveld et al., 2011). The spectral power
and phase-locking analysis was applied to the current-source density (CSD) of the LFP signals. To obtain
the CSD, we applied a second spatial derivative (Vaknin et al., 1988) along the laminar depth probe. The
CSD was used here mainly to reduce the volume conduction effects potentially affecting gamma-band
phase-locking estimation. Spectral analysis on LFPs gave very similar results (same modulation shapes,
but because of volume conduction inflated PLV values). For theta-triggered and MS-triggered data, we
used wavelets (complex Morlet) to compute time-frequency representations (TFR). We first computed
the single trial wavelet TFR over the whole trial period and then separated into baseline period [-1 to 0sec
from stimulus onset] and stimulation period [0.2 to 2sec after stimulus onset]. For the stimulation periods,
theta- or MS-triggered windowing was then applied. We computed the relative power ratio (stim
power/baseline power) between theta- or MS-triggered stimulus TFR and baseline power spectrum. To
calculate the moment-to-moment (often referred to as “instantaneous”) variation in gamma frequency
and power, we estimated the frequency and power, for a given time point, within the gamma frequency
range [25-60 Hz] of the wavelet TFRs. We obtained similar results by using filtering and application of the
Hilbert transform (Le Van Quyen et al., 2001), although this approach was not as robust against noise.
The phase-locking between V1 and V2 gamma oscillations was estimated as the phase-locking value PLV
(Lachaux et al., 1999) derived from the angles of (single-trial) wavelet transform complex coefficients
(Lachaux et al., 2002). It has been shown that (moment-to-moment) phase estimation using wavelet
transform can give good approximations (Le Van Quyen et al., 2001). For the TFR PLV we computed the
PLV for all time-frequency bins. For the gamma PLV strength estimation, the phase was selected for a
given time-bin from the frequency bin of strongest gamma power (within 25-60 Hz) for each given trial
and contact. This approach is robust against oscillation frequency variations and therefore does not
assume stationarity of the gamma signals (Lachaux et al., 1999).
The PLV estimation is in principle independent from oscillation amplitude. However, if measurement noise
is present, variation of amplitude (or power) is linked to variation of the signal-to-noise ratio (SNR). Hence,
the PLV estimation can be highly sensitive to SNR. As we show below, gamma power is modulated over a
theta-cycle or within a microsaccade interval. Therefore, observed modulations of PLV values could be
due to mere changes of the SNR and might not be biologically relevant. We therefore devised an SNRcorrected PLV estimation approach (Suppl. Text. 1 and Suppl. Fig.1). First, we approximated the SNR by
the relative gamma power ratio between stimulation period and baseline period. The approach assumes
that SNR estimates are proportional to the true SNR values, but not necessarily exactly matching. We then
added different levels of noise to the theta- or MS-triggered signals to manipulate the SNR. For each level
of noise, we recomputed the PLV strength estimates. We then computed a matrix where the PLV value
was a function of time and SNR (relative Power ratio). From the matrix we derived a cross-section in which
each time-bin had equal SNR values. From the equal SNR cross-section we derived the PLV values giving
then SNR-corrected PLV values. We tested this approach on simulation data generated by two mutually
interacting noisy limit-cycle oscillators, described in detail in the Suppl. Text 1. The simulations confirmed
that the approach was robust against SNR fluctuations (Suppl.Fig.1).
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Microsaccade-field coherence is a measure of locking between microsaccades and the local field potential
in the frequency domain. It was calculated by averaging the Fourier‐transformed LFP segments aligned to
microsaccades and normalizing by the average power in those LFP segments (Oostenveld et al., 2011).
With this measure we aimed to quantify the relationship between MS occurrence and LFP rhythmic
fluctuations, particularly the theta rhythm.
We assessed the statistical significance and effect sizes of theta- or microsaccade-triggered modulations
by linear-circular correlation (Berens, 2009) for frequency and power variation on a single-trial level and
for PLV strength and frequency variation on a session-level only (termed here as session level). Single-trial
level analysis is expected to give much lower effect sizes than session-level analysis due to averaging out
of biological as well as measurement-error related variability. For MS-triggered windows, we defined the
time span between the triggered MS onset and the next MS probability peak as a theta cycle. The amount
of data included in the analyses is documented in Table S1.
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3-4 Hz theta-modulation of gamma oscillation frequency and power in V1 and V2
First, we computed the standard trial-averaged stimulus-onset triggered TFR. Fig.1A shows a trialaveraged stimulus-onset triggered TFR for an example session from monkey S in V1. Shortly after stimulus
onset, the gamma band ‘settled’ around a dominant frequency for the remaining part of the trial. This
trial-averaged gamma-band behavior appeared to suggest that gamma oscillations are stationary and
sustained shortly after the stimulus-onset related transient. However, in the LFP of single-trial TFRs
(Fig.1B), we observed ‘bursts’ of gamma oscillations (Burns et al., 2011) with rapidly changing frequencies
that occurred roughly at a low theta frequency (3-4 Hz) and in parallel in both V1 and V2. The relationship
between V1/V2 gamma bursts and the 3-4 Hz theta rhythm was evident from the alignment of gamma
bursts visible in the raw LFP to theta peaks that emerged after filtering the LFP in a 3-4 Hz band (Fig.1B).
To gain further insight into theta-related gamma modulations, we computed theta-triggered wavelet
TFRs. To this end, we selected the peak of each theta cycle as a trigger around which to center timewindows (±0.25sec) for averaging the TFRs (Fig.1C). Fig.1D-E shows the population-averaged thetatriggered (baseline-corrected) TFRs from V1 and V2 of monkeys S and K (both left hemisphere). From the
TFRs the theta-phase dependent modulations in frequency and power of the gamma-band can be clearly
observed in both areas V1 and V2.
Below each TFR in Fig.1D-E, the corresponding time courses of the averaged raw LFP (referred to as
Visually Evoked Potential, VEP), the gamma frequency and the gamma-band relative power are shown.
The theta phase modulated gamma oscillation properties: the oscillation frequency reached its peak
shortly after the trough of the theta cycle, and then decayed slowly. The asymmetry in the frequency
modulation was observable in both monkeys and areas. The median gamma frequency modulation in V1
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was 6.2 Hz in Monkey S (𝑟̅ =0.12, 𝑝̅ =0.006, session level: 𝑟=0.23, 𝑝<10^-5) and 5.1 Hz in Monkey K (𝑟̅ =0.08,
𝑝̅ =0.011, session level: 𝑟=0.04, 𝑝<10^-5). In V2, the modulation was 4.7 Hz in monkey S (𝑟̅ =0.1, 𝑝̅ =0.006,
session level: 𝑟=0.25, 𝑝<10^-5) and 4.9 Hz in monkey K (𝑟̅ =0.06, 𝑝̅ =0.017, session level: 𝑟=0.12, 𝑝<10^-5).
The theta rhythm also modulated gamma band power (Lakatos et al., 2005) in V1 (𝑟̅ =0.07, 𝑝̅ =0.02, session
level: 𝑟=0.44, 𝑝<10^-5) and V2 (𝑟̅ =0.09, 𝑝̅ =0.009, session level: 𝑟=0.6, 𝑝<10^-5) of Monkey S and V1
(𝑟̅ =0.09, 𝑝̅ <10^-4, session level: 𝑟=0.36, 𝑝<10^-5) and V2 (𝑟̅ =0.07, 𝑝̅ =0.001, session level: 𝑟=0.38, 𝑝<10^5) of Monkey K. The gamma power peaked around theta cycle peak (phase 0) in Monkey S and at the
ascending flank of the theta cycle in Monkey K.
3-4 Hz theta-modulation of gamma synchronization between V1 and V2
To assess the theta-triggered gamma synchronization between cortical areas V1 and V2, we computed
the wavelet-based phase-locking value (PLV) using small time windows for both monkeys, taking the peak
of the V1 theta as an alignment trigger. Fig. 1F-G show population average PLV TFRs and below them the
PLV peak frequency and the gamma-band PLV strength. Theta phase significantly modulated the peak
frequency of gamma PLV in monkeys S (modulation of 4.9 Hz, session level: 𝑟=0.09 𝑝<10^-5) and monkey K
(modulation of 4.8 Hz, session level: 𝑟=0.1, 𝑝<10^-5) and the gamma PLV strength in Monkey S (session
level: 𝑟=0.24, 𝑝<10^-5) and monkey K (session level: 𝑟=0.23, 𝑝<10^-5). The PLV strength was corrected
for SNR changes over the theta cycle (see Methods and Supporting Information). The modulation of
gamma PLV strength between V1 and V2 was not consistent in their preferred phase between monkeys S
and K, with the PLV peak occurring earlier in the theta cycle in Monkey K. Possible reasons for the
differences between Monkey S and K in terms of preferred theta phase modulation of gamma power,
frequency and PLV are examined in the Discussion.
The results so far indicate that gamma-band activity during the so-called sustained period occurred in
theta-rhythmic periods within which V1/V2 gamma frequency and power as well as V1/V2 gamma phaselocking strength were systematically modulated.
Although not clearly visible in figure 1 given truncation of TFRs at 20Hz, we also found that theta triggering
also revealed structure in the oscillatory power and phase locking in the lower alpha-beta range, in
addition to that described in the gamma range. Qualitative observations suggest that relative to the theta
trigger, moments of highest power in gamma and in alpha-beta occurred at different phases, perhaps in
line with the idea of a role of alpha in gating neural processing (Jensen & Mazaheri, 2010) or related to
the differential roles of gamma and alpha-beta in feedforward and feedback signaling (van Kerkoerle et
al., 2014; Bastos et al., 2015).
Relation between microsaccades and the 3-4 Hz theta rhythmic modulation of V1/V2 gamma
oscillations
Previous studies have indicated that the 3-4 Hz theta rhythm is linked to (micro)saccades (Bosman et al.,
2009; Ito et al., 2011; Brunet et al., 2013). Microsaccades are small, involuntary eye movements that occur
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during fixation. Although they are transient and typically smaller than 1 degree of visual angle (Fig.2A),
they induce strong modulations of neural activity (Leopold & Logothetis, 1998; Martinez-Conde et al.,
2000, 2009; Bosman et al., 2009; Rolfs, 2009). We tested the relationship between the theta phase
modulation of gamma and microsaccades in the right hemisphere of monkey S (Figure 2), and in an
additional monkey A with an ECoG grid covering the left hemisphere of V1, where we had high-resolution
eye data available (Figure 3).
Before presenting a detailed analysis of the data in the two monkeys, we want to point out the similar
statistics in the two monkeys. We found that the inter-microsaccade interval histogram peaked at around
270 ms in the two monkeys (Fig.2B, Fig.3B), corresponding to a 3-4 Hz theta frequency (see Fig.1B). In
addition, microsaccade probability was linked to the LFP theta phase. This was revealed by an analysis of
MS-field coherence in monkey S (Fig.2C) and A. (Fig.3C). There was a clear peak in the 3-4 Hz theta
frequency range of the MS-field coherence spectrum. In monkey S the MS-field coherence peak was a bit
broader and skewed to the right including also higher theta and alpha frequency. In Monkey A., the MSfield coherence peak in the theta range was narrower, but there was a second peak in the alpha frequency
range. This indicated that there was also a locking between MS and alpha frequencies, which would be
consistent with observed modulation of theta-triggered TFR in the alpha-beta band above (Fig.1). As we
will discuss below, this also suggests that the underlying modulation function related to MS is a complex
shape composite of several relevant frequencies. But the fundamental frequency, related to the MSinterval distribution, is the 3-4 Hz theta rhythm.
In the following section, we will first elaborate on the results of Monkey S (Figure 2). For a better
illustration of the relationship between theta-modulations of the gamma-band and microsaccades, we
first computed the theta-triggered TFRs and the frequency and power quantifications as in Fig.1 for the
datasets including high-resolution eye signals in Monkey S (neurophysiological data from right
hemisphere). Fig.2D shows theta-triggered TFRs for V1 and V2 in monkey S, with bottom panels showing
the corresponding visually evoked potential (EP) and MS-onset probability (red line), gamma frequency
modulation, and relative power modulation. We observed significant theta-modulations of gamma
frequency in V1 (𝑟̅ =0.1, 𝑝̅ =0.002, session level: 𝑟=0.23, 𝑝<10^-5) and V2 (𝑟̅ =0.07, 𝑝̅ =0.02, session level:
𝑟=0.08, 𝑝<10^-5) as well as in relative power in V1 (𝑟̅ =0.082, 𝑝̅ =0.015, session level: 𝑟=0.47, 𝑝<10^-5) and
V2 (𝑟̅ =0.07, 𝑝̅ <10^-4, session level: 𝑟=0.28, 𝑝<10^-5). The theta modulations in gamma frequency and
power in right hemisphere V1 and V2 were similar to the left hemisphere V1/V2 data described in Fig.1.
We then computed the MS-onset probability as a function of the theta cycle (red line in Fig.2D). The MS
probability was significantly modulated by the theta cycle (𝑟̅ =0.1, 𝑝̅ <10^-5) in agreement with the MSfield coherence analysis. This confirms a close link between MS occurrence and LFP theta fluctuations.
The MS probability peaked around the trough of the theta cycle. In Fig.2E we show the theta-triggered
V1-V2 gamma PLV analysis. As in Fig.1, the V1-V2 PLV TFR exhibited similar modulations in the Power TFR
of V1 and V2 respectively. The PLV frequency (session level: 𝑟=0.06, 𝑝<10^-5) as well as PLV strength
(session level: 𝑟=0.07, 𝑝<10^-5) was modulated significantly, albeit weakly, as a function of the theta
cycle.
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We then tested the link between microsaccades and gamma oscillations by computing microsaccadetriggered TFRs. Fig.2F shows MS-triggered TFRs for V1 and V2 in monkey S, with the three panels below
showing the corresponding LFP evoked potentials (EP, back line) shown together with MS probability (red
line) and 3-4 Hz filtered EP (dashed line); and furthermore the gamma frequency modulation, and the
relative power modulation. In the panel below the TFR, the EP showed marked modulations shortly after
MS-onset with a negative peak around ~70ms after onset followed by a positive wave peaking around
~180ms after onset. There was also a weak initial positive peak around ~30ms after onset. The MStriggered EP was clearly not a simple theta wave, but included faster alpha-beta component as well. There
were likely also sharper transients with power distributed widely over the frequency spectrum including
the gamma-frequency range. Despite the likely contribution of evoked transients to gamma power shortly
after MS-onset (Rajkai et al., 2008; Bosman et al., 2009; Ito et al., 2011), we suggest that transients were
not a main contributor for the observed gamma dynamics. This is based on the following arguments: (1)
the gamma band was relatively narrow and modulations occurred over the whole MS-or theta window of
several 100ms; (2) clear gamma cycles and frequency/power modulations could be observed at the single
trial level (see Fig.1B); (3) frequency and power modulations were present also with Hilbert Transform,
which has high temporal resolution. However, future research is needed to clarify better the contributions
of evoked transient gamma to gamma-band dynamics and whether transient and sustained gamma
oscillations share the same neural circuitry. We also suggest that MS-related motor activity (YuvalGreenberg et al., 2008) is unlikely to contribute to the gamma-band as observed in our data in the light of
our use of local LFP/CSD measurements as well as the application of bipolar LFP derivation for the ECoG
data.
We further highlight the link between MS evoked potentials and the theta cycle as obtained by filtering
the MS-triggered EP in the 3-4 Hz range (dashed line). The MS onset occurred close to the trough on the
descending flank of the theta cycle, which was very similar to the relation between MS probability and
theta phase shown in Fig.2D (second row from top). In MS-triggered TFRs, we found a systematic
relationship between gamma periods and microsaccades and a strong resemblance between
microsaccade-triggered TFRs (Fig.2F) and theta-triggered TFRs (Fig.2D). The frequency of gamma was
modulated by (median) 5.2 Hz in V1 (𝑟̅ =0.12, 𝑝̅ <10^-5, session level: 𝑟=0.35, 𝑝<10^-5) and 4.6 Hz in V2
(𝑟̅ =0.09, 𝑝̅ =0.001, session level: 𝑟=0.18, 𝑝<10^-5). Shortly after the MS-onset (~50ms) the gamma
frequency increased sharply followed by a slower decay in agreement with the asymmetric frequency
modulation observed in the theta-triggered analysis. The relative gamma power was also significantly
modulated in V1 (𝑟̅ =0.09, 𝑝̅ =0.004, session level: 𝑟=0.46, 𝑝<10^-5) and V2 (𝑟̅ =0.1, 𝑝̅ =0.02 session level:
𝑟=0.3, 𝑝<10^-5) and peaked later than the gamma frequency similar to Fig.2D. Further, in monkey S
microsaccade-triggered PLV analysis (Fig.2G) confirmed a MS-dependent modulation of V1-V2 gamma PLV
in frequency (session level: 𝑟=0.1, 𝑝<10^-5) and strength (session level: 𝑟=0.33, 𝑝<10^-5) similar to thetatriggered PLV analysis in monkeys S. Generally, the MS-triggered modulations were stronger (in effect size
and significance) compared to theta-triggered modulations, particularly for frequency and PLV
modulations.
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In Fig.3 we present the same analysis as in Fig.2 for monkey A. Monkey A was implanted with an ECoG
grid (Fig.3A) covering a large part of the left hemisphere (Brunet et al., 2013). We restricted the analysis
here to ECoG contacts covering V1 locations with the strongest stimulus induced gamma power. Thanks
to the stability of the ECoG recordings, grid data from different sessions could be concatenated. For the
theta-triggering and the evoked potentials, we used monopolar LFP (to avoid flipping of polarity) and for
spectral analysis we used bipolar LFP to reduce the effect of volume conduction, which in previous analysis
of Monkey S and K was achieved by using CSD.
Fig.3D shows theta-triggered TFRs for V1 in monkey A, with bottom panels showing the corresponding
evoked response (EP) and MS-onset probability (red line), gamma frequency modulation, and relative
power modulation. A striking difference with Monkey S (Fig.2D) was the relationship between theta-cycle
and MS onset probability as well as with gamma frequency/power modulations. We observed that the
MS probability peaked (𝑟=0.17, 𝑝<10^-5) around the theta cycle peak (in contrast to peaking around the
trough in Monkey S). We observed significant modulations in gamma frequency (𝑟=0.12, 𝑝<10^-5) and
relative power (𝑟=0.12, 𝑝<10^-5) as a function of theta phase. Again, the modulation of gamma frequency
by theta phase in monkey A was shifted compared to Monkey S, in a similar manner in which the theta–
MS relation was shifted between the two monkeys. What was consistent however between Monkey S and
A was the relationship between MS onset and the gamma power and frequency modulation.
Fig.3E shows the microsaccade-triggered TFRs for monkey A V1 with bottom panels showing the
corresponding LFP evoked potentials response (EP) with MS probability and 3-4 Hz filtered VEP, gamma
frequency modulation, and relative power modulation. Similar to Monkey S, the MS-triggered EP showed
clear modulations with a positive peak around ~30ms after MS-onset, followed by a negative peak around
~100ms and a positive broader weaker peak around ~200-250ms. A clear difference to the EP of Monkey
S was the more dominant initial positive peak around ~30ms in Monkey A, which in this monkey was
stronger than the later positive peak. The dashed line in Fig3.E represents the filtered EP in the 3-4 Hz
range. Compared to Monkey S (Fig.2F), the filtered theta EP was shifted such that theta cycle peak
occurred around the MS onset confirming the theta-MS relation in Fig.3D. The combination of the more
prominent initial positive peak and the weaker and later second positive peak led to a different
correspondence between MS-triggered EP and the theta-cycle obtained after filtering. The sensitivity to
the shape of the complex (multi-frequency) MS-triggered EP wave indicates an important shortcoming of
theta-triggering that will be elaborated in the discussion. The MS-triggered spectral analysis revealed
modulations in the frequency (median=3.2 Hz, 𝑟=0.09, 𝑝<10^-5) and relative power of the V1 gammaband (𝑟=0.08, 𝑝<10^-5) that were similar to modulations observed in Monkey S (Fig.2E).
Overall, these results from Monkey S and A support the view that microsaccades play a critical role in
theta-rhythmic gamma dynamics in the visual cortex (Bosman et al., 2009; Ito et al., 2011).
Comparison of stimulus-onset trial averaging to microsaccade-triggered trial averaging
The microsaccade-triggered analysis revealed an intricate structure in oscillatory activity that was hidden
in commonly-used stimulus-onset triggered analysis (Fig.1A). We highlight this by directly comparing
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stimulus-onset triggered trial averaging with microsaccade-triggered trial averaging (Fig.4), using a single
session from Monkey S with 667 trials (at a single contrast). From those trials, we selected trials that
contained their second microsaccade within the period of 400-500ms after stimulus-onset (leaving 105
trials) and then realigned those trials to the second MS of the trial. This procedure permitted the
observation of gamma modulations over a 1s time period (Fig.4, right), which were absent after
conventional triggering by stimulus onset (Fig.4, left). Figure 4 illustrates the profound differences in the
effects of stimulus-onset versus microsaccade-triggered averaging (see Fig.4A/B) on TFR (Fig.4C), spike
probability (Fig.4D), LFP evoked potentials (Fig.4E), gamma relative power (Fig.4F), and gamma frequency
(Fig.4G).
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3-4 Hz microsaccade-theta rhythm temporally shapes dynamics of V1/V2 gamma oscillations
Recent studies (Burns et al., 2010, 2011) have shown that gamma oscillations are not stationary (‘clocklike’). In these studies, V1 gamma dynamics were fitted much better by a (stochastic) model of ‘filtered
noise’ than by a fixed-frequency (stationary) model. However, as indicated by (Burns et al., 2010, 2011),
their analysis could not distinguish a stochastic process from a deterministic, yet more complex, process.
Hence, while potentially problematic for neural communication, Burns’ (2010) findings do not per
definition exclude a role of gamma in communication (Fries, 2009b, 2015). Our awake macaque V1 and
V2 data confirm that gamma oscillations occur in ‘bursts’ with rapidly changing frequencies. However we
found that a substantial part of the gamma fluctuations in frequency and power reflect complexity, rather
than randomness, as those fluctuations were structured over time and systematically related to a
microsaccade-related 3-4 Hz theta rhythm. Thus, the modulation of gamma power and frequency with
MSs and theta phase can be seen as a form of cross-frequency coupling, short CFC (Lakatos et al., 2005;
Canolty et al., 2006; Jensen & Colgin, 2007; Schroeder & Lakatos, 2009a; Canolty & Knight, 2010). This is
in line with gamma oscillation dynamics described in other brain structures like olfactory cortex (Kepecs
et al., 2006; Manabe & Mori, 2013), somatosensory cortex (Ito et al., 2014) or the hippocampus (Belluscio
et al., 2012; Lisman & Jensen, 2013; Schomburg et al., 2014), where CFC between delta/theta phase and
gamma power has been studied.
Importantly, we show that not only gamma power variations (Bosman et al., 2009, 2012) but also
frequency variations are linked to a 3-4 Hz MS-related theta rhythm, thus supporting what was reported
as a tentative observation in Bosman et al. (2009). The strength of modulation by the 3-4 Hz theta phase
in V1 and V2 was of similar magnitudes for CFC phase-frequency compared to the more commonly
estimated CFC phase-power. We therefore argue that from an experimental as well as from a theoretical
viewpoint (Pikovsky et al., 2002; Battaglia et al., 2012; Barardi et al., 2014; Cohen, 2014), there is no
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reason to favor reporting one type of CFC over the other. In fact, oscillation frequency, defining the
window length of spiking probability (Fries, 2009a), is a critical factor for enabling synchronization
between interacting oscillations (Pikovsky et al., 2002; Roberts et al., 2013; Barardi et al., 2014; Lowet et
al., 2015). It has been shown in theoretical and experimental work that the frequency of gamma
oscillations adapts as a function of network activity (Tiesinga & Sejnowski, 2009; Ray & Maunsell, 2010b;
Jia et al., 2013; Roberts et al., 2013; Hadjipapas et al., 2015; Lowet et al., 2015). Because both the 3-4 Hz
theta rhythm (Lakatos et al., 2005) and (micro)saccades (Martinez-Conde et al., 2000; Rajkai et al., 2008;
Martinez-Conde, 2013) have been associated with modulations in network activation and excitability,
concurrent variation in gamma oscillation frequency is in line with theoretical predictions from neural
network models (Traub et al., 1996; Tiesinga & Sejnowski, 2009; Jia et al., 2013; Roberts et al., 2013; Lowet
et al., 2015).
Furthermore, we found that V1-V2 gamma PLV strength was modulated by a 3-4 Hz MS-theta rhythm,
suggesting the relevance of CFC in framing communication between cortical areas. Our findings are in line
with previous studies (Colgin et al., 2009; Bosman et al., 2012), which indicate that gamma-mediated
inter-areal communication (Fries, 2009a, 2015) is neither continuous nor sustained during stimulus
processing, but instead occurs in ‘bursts’ that are structured by the theta rhythm. As these slower rhythms
are shared among V1 and V2, they may help in establishing co-occurrence and alignment of phase and
frequency of gamma in the two areas. Inter-areal gamma-band synchronization is related to the
communication of behaviorally relevant and therefore attended stimulus information (Bosman et al.,
2012; Grothe et al., 2012). The theta-rhythmic modulation of gamma-band synchronization therefore
suggests that attention might be structured at a theta rhythm. Recent studies have lend direct support to
this: Two studies used a reset of attention to one of two visual stimuli to demonstrate that subsequently,
attention sampled the two stimuli alternately at a ~4 Hz theta rhythm (Landau & Fries, 2012; Fiebelkorn
et al., 2013). A subsequent study subtracted the gamma-band activities induced by two visual stimuli to
isolate moment-by-moment attentional biases. This revealed that the phase of the ~4 Hz component of
this gamma-difference predicted the behavioral accuracy in detecting stimulus changes (Landau et al.,
2015).
The observed systematic variation of single-trial wavelet TFR shows that V1 and V2 signals are nonstationary (Hammond & White, 1996; Lachaux et al., 1999). As illustrated in Figure 4, the non-stationary
nature is easily hidden in stimulus-onset trial-averaged TFR, where variation in frequency and power could
only be observed shortly after stimulus onset. This has led to the common practice to exclude the transient
changes after stimulus onset and to apply methods assuming stationarity in the later ‘sustained part’. Our
results support the view that the neural dynamics in V1 and V2 are constantly non-stationary.
Linkage between 3-4 Hz theta-rhythm and microsaccades
Microsaccades, small eye movements during fixation (Rolfs, 2009), have long been ignored in visual
neuroscience studies despite their significant impact on spiking activity in the retino-geniculate pathway
(Reppas et al., 2002; Martinez-Conde et al., 2013) and in cortical visual areas (Leopold & Logothetis, 1998;
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Bosman et al., 2009; Martinez-Conde et al., 2013). Previous studies have shown that they relate (similar
to macrosaccades) to slower frequency rhythms including delta/theta (Bosman et al., 2009; Ito et al.,
2011), alpha/beta (Gaarder et al., 1966; Dimigen et al., 2009) as well as higher frequency gamma
oscillations (Bosman et al., 2009; Brunet et al., 2013).
The neural mechanism of the microsaccade rhythmic generation is still not completely understood,
although important advances have been achieved (Otero-Millan et al., 2008; Melloni et al., 2009;
Martinez-Conde, 2013). In this study we confirmed that microsaccades were linked to a 3-4 Hz theta
rhythm in V1 and V2. It is possible that the V1/V2 theta rhythm is a consequence of microsaccades, or in
principle independent but phase-locked to microsaccades. In addition, it is possible that both the theta
rhythm as observed in V1 and V2 and microsaccades originate from a common theta pacemaker. The
present study cannot distinguish among these possibilities.
With regard to the first possibility, the theta rhythm could be related to MS due to retinal image shifts.
However, a top-down modulation (‘corollary discharge’) by higher-order oculomotor regions may also
yield a theta rhythm in V1/V2. A ‘corollary discharge’ is a top-down prediction of upcoming sensory input
induced by self-initiated movements. In this study we cannot determine to what extent the retinal-shift
bottom–up response and top-down corollary discharge contributed to the theta-gamma dynamics.
The comparison of the phase-relation between the theta cycle and the microsaccade probability was not
consistent between monkey S and A, which may be related to the different recording techniques used
(microelectrodes vs. ECoG). Similarly, the theta-gamma relation was not consistent between monkeys. In
contrast, the MS-gamma relation was consistent across theta- or MS triggering and between monkeys.
We observed that the MS-triggered evoked potentials exhibited dissimilarities between monkeys in the
modulation shape. These dissimilarities led to relatively large phase shifts in the corresponding filtered
theta cycle. This indicates that theta-filtering, which assumes relatively symmetric narrow-band theta
fluctuations, might not yield an optimal representation of the MS- related complex rhythmic modulations.
Methods that can capture characteristic yet asymmetric complex patterns in the LFP are advisable for
future studies. Nevertheless, our study emphasize, in line with previous studies (Bosman et al., 2009; Ito
et al., 2011; Martinez-Conde, 2013), that microsaccades are critical for the understanding of neural
dynamics in visual cortex and therefore advisable to include for future studies investigating visual
processes.
Recent studies have shown that performance of subjects in perceptual tasks exhibit 3-4 Hz rhythmic
fluctuations (Bosman et al., 2009; Schroeder & Lakatos, 2009b; Landau & Fries, 2012; Fiebelkorn et al.,
2013; Hafed, 2013; VanRullen, 2013; Morrone et al., 2014; Song et al., 2014; Landau et al., 2015) indicating
that the theta rhythm has consequences for how a subject perceives, attends and responds to the external
world. These results are in line with the broader framework of active sensing (Kleinfeld et al., 2006;
Collewijn & Kowler, 2008; Bosman et al., 2009; Schroeder & Lakatos, 2009b; Schroeder et al., 2010;
Wachowiak, 2011; Kagan & Hafed, 2013; Martinez-Conde, 2013) where the external world is sampled
actively through rhythmic sensory organ movements, which has important implications for the temporal
dynamics of sensory neural processes.
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Figure legends
Fig.1 Stimulus and theta triggered analysis of visual gamma oscillatory responses. (A) Standard stimulus-onset triggered
averaged time-frequency-representation (TFR) (single session, one contact). (B) Single-trial example. Raw LFP with LFP filtered in
the theta range (3-4 Hz) at the top. Below, TFR of a V1 and V2 contact. The green dashed lines represent the peak of the theta
signal. Notice that the gamma bursts in V1 and V2 show locking with respect to the theta peaks. (C) Peaks of LFP theta rhythm
were used as triggers to align the center of 500 ms data snippets (theta-triggered trials). (D&E) Theta-triggered TFRs are shown
for V1 and V2 of both monkeys. Below each TFR, the averaged LFP response (demeaned) and modulations in frequency as well
as relative power of gamma oscillations are shown. Gray bands represent standard error (F&G) Theta-triggered PLV TFR between
V1 and V2 sites. Below, quantifications of the modulation in frequency and strength of gamma PLV (SNR-corrected) are shown.
Gray bands represent standard errors across recording sites (population data).
Fig.2 Theta and microsaccade-triggered analysis in Monkey S (right hemisphere). (A) Example trial showing the X and Y eye
position clearly showing small saccadic deflections. (B) Histogram of microsaccade intervals (C) The MS-LFP-coherence. Similar to
spike-LFP coherence but with MS onsets instead of spikes. A peak in the lower frequency range can be observed with a maximum
in the 3-5 Hz range. (D) Theta-triggered analysis of the V1 and V2 contacts. Top to bottom: Power TFRs, evoked potential (EP) and
MS-onset probability (red line), estimated frequency of gamma and the power. (E) Theta-triggered time-resolved V1/V2 PLV
spectrum, with below gamma PLV frequency and total gamma PLV strength SNR -corrected. (F) Microsaccade-triggered analysis
of the V1 and V2 contacts. Top to bottom: Power TFRs, evoked potential (EP), 3-4 Hz filtered EP (dashed line) and MS-onset
probability (red line), estimated frequency of gamma and the power. (G) Microsaccade-triggered time-resolved V1/V2 PLV
spectrum, with below gamma frequency showing peak PLV, and total gamma PLV strength SNR -corrected.
Fig.3 Microsaccade-triggered analysis in Monkey A (population data). (A) The 256-channel ECoG grid is depicted where each
dot represents the position of a bipolar differentiation between two sensors. The color of the dot represent the relative induced
gamma power by the stimulus compared to baseline. The stimulus induced strong gamma power in sensors covering V1 (posterior
to the lunate sulcus, LS). For the microsaccade-triggered TFR we used the bipolar LFP from the sensors with the higher relative
gamma power. (B) Histogram of microsaccade intervals (C) The MS-LFP-coherence (D) Theta-triggered analysis of the bipolar
LFP from V1.Top to bottom: TFR, evoke potential (EP, black line) and MS-onset probability (red line), estimated frequency of
gamma and the power (E) Microsaccade-triggered analysis .Top to bottom: TFR, evoke potential (EP), 3-4 Hz filtered EP (dashed
line) and MS-onset probability (red line), estimated frequency of gamma and the power. Line width shows standard error.
19
DOI: 10.1111/ejn.13126
Accepted manuscript online: 7 NOV 2015
European Journal of Neuroscience
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Fig.4 Comparison of stimulus-onset triggered and microsaccade-triggered trial averaging (monkey S, single session, N trials=
105). (A) Raster plots of microsaccades (black dots) and stimulus onsets (yellow dots). The left column represents trials defined
in relation to stimulus onset, whereas the right column represents trials defined in relation to the occurrence of the second
microsaccade after stimulus onset. In each panel, the stimulus-onset triggered average (left) and microsaccade triggered average
(right) are shown as a function of time for (B) monocular eye speed (C) time-frequency representation of LFP power, (C) spike
density, (D) the LFP evoked potential (EP) (E) averaged local field potential (LFP), (F) gamma power, and (G) gamma frequency. In
B, D-G line thickness represents standard error.
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γ Rel. Pow
change
LFP
V2
Theta
(V1)
E
4.6
40
20
0
Rel.Pow
0.5
1
1.5
2
Time (s)
7
Hz
Hz
0.7
0.7
0
0
-0.7
-0.2
0
0.2
-0.7
Time from
theta peak (s)
1.7
VEP
µV
C
Theta triggered trials
0
0
average
0
0
γ Rel. Pow
change
γ Freq.
Hz
Theta rhythm
Hz
Freq. (Hz)
35
0.25
0.2
-0.2
0
0.2
Time from
theta peak (s)
-0.2
0
Time from
theta peak (s)
0.2
G
V1 Power TFR
60
1
35
Monkey K LH
Rel.Pow
Hz
40
20
V2
40
2
60
V1
40
34
V2 Power TFR
60
60
40
40
20
20
20
20
0
0
-20
-20
46
46
42
42
0.5
0.5
0
0
-0.5
-0.5
-0.2
0
0.2
Time from
theta peak (s)
V1-V2 PLV TFR
60
3
1.7
-0.2
0
Time from
theta peak (s)
0.2
0.28
PLV
LFP
V1
20
0
-20
38
Hz
γ Freq.
Hz
single trial
20
0
-20
(SNR-corr.)
20
2
0.1
20
γ PLV
Time (s)
1.5
1.4
20
0.35
40
γ PLV strength
5
Rel.Pow
1
µV
B
0.5
VEP
1
0
1.3
40
40
60
4.7
40
0.12
20
γ PLV
Freq. (Hz)
40
60
60
Hz
Rel.Pow
Hz
60
V1-V2 PLV TFR
Rel.Pow
3.5
V2 Power TFR
PLV
V1 Power TFR
trial averaged TFR V1
20
F
Monkey S LH
γ PLV strength
(SNR-corr.)
D
Rel.Pow
A
45
40
0.2
0.15
Time from
theta peak (s)
A
B
C
MS probability
00
11
Time (s)
1.5
1.5
20
0
0.1
20
0
-20
0
35
35
30
30
0.5
0.5
0
0
-0.5
-0.5
0.2
-0.2
Time from
theta peak (s)
0
0.15
20
36
0.1
32
0
0.25
0.2
-0.2
0
0.2
Time from
theta peak (s)
0.2
20
2.2
20
0
-20
0
1
20
0
-20
0
30
30
0.5
0.5
-0.5
0.2
0.4
Time from MS onset (s)
0.1
20
36
1
32
0
0.25
0.2
0
0.2
0.4
Time from MS onset (s)
0
0
40
1.1
35
35
0.35
PLV
20
V1-V2 PLV TFR
0
0.2
0.4
Time from MS onset (s)
MS prob.
V2
Hz
EP
µV
γ Freq.
Hz
40
Hz
V1
40
0
0.3
G
40
-0.5
Hz
Time from
theta peak (s)
1
γ Rel. Pow
change
1.2
40 50 60
V1-V2 PLV TFR
1.1
Rel.Pow
γ Freq.
Hz
γ Rel. Pow
change
0.1
20
0
-20
3.2
30
PLV
20
MS-triggered analysis
(Monkey S RH )
10 20
Hz
40
0
0.2
2.1
Rel.Pow
40
-0.2
0.6
0.4
MS prob.
V2
Hz
1.2
EP
µV
Rel.Pow
0.4
0.6
E
Theta triggered analysis
(Monkey S RH )
V1
Rel.Pow
0.2
MS Interval (s)
3.2
F
0
γ PLV strength γ PLV
(SNR-corr.) Freq. (Hz)
0.5
0.5
γ PLV strength γ PLV
(SNR-corr.) Freq. (Hz)
D
00
0.5
MS prob.
-0.4
−1
1
MS prob.
visual degrees
1
0.4
MS-LFP Coherence
x10-2
D
Data from EcoG Monkey A
E
Theta triggered analysis
(Monkey A LH )
MS triggered analysis
(Monkey A LH )
V1
V1
6
0.5
0.25
0.4
MS interval (s)
0.6
MS-LFP coherence
MS probability
0.75
50
γ Freq.
Hz
C
EP
µV
EP
µV
0
-2
0.2
20
0
-20
1
1
0
0.2
45
Rel.Pow
1.9
1
20
0
-20
0
50
45
0.5
0.4
0.3
0.2
0.1
0
1
γ Rel. Pow
change
x10
4
γ Freq.
Hz
B
6
40
1.9
V1
γ Rel. Pow
change
Rel. Gamma
Power
40
MS prob.
LS
60
Hz
Hz
Rel.Pow
60
6.5
0
-1
-0.2
0
10
20
30
40
50
Frequency (Hz)
60
0
Time from
theta peak (s)
0.2
1
0
-1
0
0.2
0.4
Time from MS onset (s)
MS prob.
A
A
N trials
aligned
Hz
C
MS spped
Deg/ms
B
Spikes/s
D
γ Freq.
Hz
G
γ Rel.
Pow
EP
µV
E
F
stimulus onset
microsaccade
aligned
100
100
50
50
0
0
-2
-2
x10
4.2
2.1
x10
4.2
2.1
60
60
40
40
20
20
100
50
100
50
10
-150
10
-150
25
25
1
1
50
40
30
50
40
30
0
0.5
Time from stimulus onset(s)
1
1
-0.5
20
Relative power
0
Time from second MS(s)
0.5
1
Supplementary Information
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Method Text S1
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SNR-corrected PLV
The phase-locking value (PLV) represents the mean resultant vector length of a phasedifference variable θ (Lachaux et al., 1999) between two signals. PLV can be defined as:
1
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PLV(t) 
1 N iθt ,n 
e
N n1
where N represents the trial number and t a time variable. In this study, N represents
the number of theta- or ms –triggered windows and t is time from the triggering event.
The phase variable θ needs to be estimated in real experimental data either using
Hilbert transform or a time-frequency technique, e.g. using wavelets (Le Van Quyen et
al., 2001).
Because only the phase of an oscillatory signal is considered, the oscillation amplitude
does not affect the PLV. However, if extrinsic (measurement) noise (Ne) is present in the
signal, then the oscillation amplitude defines in relation to the noise amplitude the
signal-to-noise ratio (SNR). The SNR determines the accuracy with which the phase
variable θ can be accurately estimated in real data and thus it affects the PLV estimate.
Hence, fluctuations in oscillation amplitude do affect PLV values due to associated
changes in SNR.
In this study, we observed significant modulations of V1/V2 gamma oscillation
amplitude (power) in respect to the theta cycle or microsaccade onset. At the same time,
we observed concurrent changes in V1-V2 gamma PLV values. With standard PLV, it is
not clear whether the PLV changes are due to modulation in SNR or genuine biological
changes.
We therefore devised a SNR-correction approach for PLV values. The approach is based
on the simple idea to equalize SNR differences by systematically adding noise to the
signals.
We tested the approach using simulation data. For generating simulation data with
plausible synchronization properties and different SNR, we used the phase-oscillator
model as the underlying generative model. The model is very similar to the well-known
Kuramoto model (Hoppensteadt & Izhikevich, 1998; Ermentrout & Kleinfeld, 2001;
Breakspear et al., 2010; Lowet et al., 2015). The advantage of the phase-oscillator model
here is that we can manipulate oscillation amplitude independently of phase-locking
strength.
Here, we simulated two zero-mean gamma oscillatory signals X(t) and Y(t) where the
phase variables φx and φY were governed by two coupled phase-oscillator equations:
d X  t 
 2 dt
  X  t    X (t)sin(  y  t  –  x  t )  Ni X (t )
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dY  t 
 3 dt
 Y  t    y (t)sin(  X  t  – Y  t )  NiY (t )
The differential equations were solved using Euler method with a time step of 1ms.
The variables ωx(t) and ωy(t) represent the intrinsic or natural frequency of the
oscillators, here chosen to be default 40Hz and 41.5Hz respectively. κ x(t) and κ Y(t)
represent the coupling values between the oscillators. They were both defined y default
1. The interaction term sin(…) determines how a given oscillator is affected in its phase
dynamics by another oscillator as a function of their phase-difference. The interaction
term is also known as the phase response curve PRC (Schwemmer & Lewis, 2012). Ni
x(t) and Ni Y(t) are intrinsic phase noise terms defined as a pink noise process
(SD=±0.0115 rad/ms which corresponds to ±1.83Hz). The intrinsic noise was
uncorrelated between oscillators. The oscillators are therefore noisy limit-cycle
oscillators. The PLV of the true phase-difference variable θ(t)= φx(t)- φY(t) defined the
true PLV.
The signals X(t) and Y(t) were then defined as:
X  t   AX  t  cos x  t    NeX t 
59
 4
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5 Y t   AY t  cos Y t   NeY t 
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where A x(t) and A Y(t) are the oscillation amplitudes (default=1). The cos(..) function
converts the phase variables into real-valued signals. Ne x(t) and Ne Y(t) are the extrinsic
(measurement) noise terms added to the signals of interest. The ratio between A(t) and
Ne(t) defined the SNR.
In Fig.S1 we show the behavior of the standard PLV and SNR-corrected PLV using
generated simulation data with the model as defined above. For each simulation dataset,
we created N=500 simulation runs with characteristic theta-modulation (3.3Hz) of
either SNR (relative power) or the true PLV between oscillators.
In Fig.S1A-B we created simulation data with the property of having no modulation of
true PLV over time (κ x(t) and κ Y(t) had constant default values), but 3.3Hz theta
modulation of relative power and frequency. In Fig.S1A the TFR is shown for oscillator
X. Strong modulation in relative power as well as in the frequency can be observed
which are similar to the experimental V1/V2 gamma data in respect to the time scale.
Below the TFR changes relative power, true PLV, the (standard) PLV estimation and the
SNR-corrected PLV estimation are shown. The relative power exhibited 3.3Hz
modulation, whereas the true PLV was basically constant (small fluctuations are due to
the intrinsic noise term Ni). The standard PLV estimation revealed 3.3Hz modulation,
which were completely driven by the relative power modulations. In contrast, the SNRcorrected PLV showed no theta modulation in the estimation and thus it was robust
against relative power (SNR) changes. Notice that the SNR-corrected PLV
underestimated the true PLV even further than the standard PLV. To derive the SNR
corrected PLV values, we added measurement noise of different levels and recomputed
the PLV. In Fig.S1B PLV values are shown as a function of relative power (SNR) and time.
2
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The black line represents the standard PLV. By adding additional noise we could
compute all the PLV values below the black line. The dashed line represents the SNRcorrected PLV estimates. It represents a cross-section over time for a fixed SNR. The
cross section was chosen to be first SNR bin in which 95% of all time points had a PLV
estimate.
In Fig.S1C-D we created simulation data with the property of having 3.3Hz theta
modulation of true PLV over time, but no modulation of relative power and frequency.
Hence, the SNR did not change over time. Fig.S1C shows the respective TFR, relative
power, true PLV, standard PLV and SNR-corrected PLV. Here, in this case, both standard
PLV and SNR-corrected PLV reflected the true PLV changes. In Fig.S1D the
corresponding PLV matrix as function of relative power and time is shown. It can be
seen that true PLV changes are reflected in PLV modulations over the whole ranges of
SNR bins.
The application on well-defined simulation data showed that the SNR-correction
approach can robustly differentiate changes in estimated PLV due to true changes in the
underlying PLV or due to changes in the SNR.
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Schwemmer, M.A. & Lewis, T.J. (2012) Phase Response Curves in Neuroscience. In Phase
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Fig.S1. Simulation test data for SNR-corrected PLV. A-B) 3.3Hz theta modulation of frequency and relative
power (SNR) without any change in true PLV. A) From top to bottom: Power TFR of oscillator X, relative
gamma power of oscillator X, the true PLV between oscillator X and Y, the standard PLV estimates and the
SNR-corrected PLV estimates. B) PLV as a function of time and relative power. This matrix was used to
determine the SNR-corrected PLV. C-D) 3.3Hz theta modulation of true PLV without any change of
frequency and relative power. C-D are structured as A-B.
4
Theta-triggered analysis
Figure 1
MS/Theta-triggered analysis
Figure 2,3 and 4
Monkey S
(V1/V2)
10 sessions X 2 areas X 8 contacts
X 53trials (mean) X 1.8 seconds
Left hemisphere
12 sessions X 2 areas X 16 contacts X 42
trials (mean) X 1.5 seconds
Right hemisphere
Monkey K
(V1/V2)
11 session X 2 area X 8 contacts X
43trials (mean) X 1.8 seconds
Left hemisphere
Not recorded because monkey no longer
available
Monkey A
(V1)
153
154
155
156
3 sessions x 1 bipolar contact (highest
induced gamma power) x (34.5trials
(mean) x 1.8sec
Left hemisphere
Table.S1 Observations comprised in population data listed per monkey/area (rows) and per type of
analysis (columns).
157
5
A
C
TFR oscillator X
TFR oscillator X
4.5
Rel.Pow
0.8
0.6
0.4
0.2
stanard PLV
4
0.8
0.6
0.4
0.2
estim. PLV
SNR corrected
PLV
SNR corrected
0.8
0.6
0.4
0.2
1.5
2
2.5
Rel.Pow
20
0.5
2
40
true PLV
Rel.Pow
0.8
0.6
0.4
0.2
standard PLV
true PLV
20
Hz
40
4
60
Rel.Pow
Hz
60
3.5
0.5
2
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
1.5
Time (s)
2
2.5
Time (s)
D
B
standard PLV
2
0
1.5
Time (s)
2
2
0.5
4
3
2
1
PLV
SNR corrected
standard PLV
PLV
3
Rel.Pow
4
1
5
0.6
PLV
Rel.Pow
5
0
1.5
2
Time (s)
2.5
PLV
SNR corrected