Burst Firing Synchronizes Prefrontal and Anterior Cingulate Cortex

Current Biology, Volume 24
Supplemental Information
Burst Firing Synchronizes Prefrontal
and Anterior Cingulate Cortex
during Attentional Control
Thilo Womelsdorf, Salva Ardid, Stefan Everling, and Taufik A. Valiante
Proportion of
Burst Events
(ISI!s ”5ms)
Supplemental Figures
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Proportion of bursts for a pure Poisson
process (without refractory period)
0.5 7 13 19
30
45
60
75
90
100
Average firing rate (Spk / sec.)
Figure S1. Proportion of bursts under a Poisson point process
The figure shows the proportion of burst spikes (≥2 spikes within 5ms) relative to all spikes of a
spiketrain simulated under the assumption of a pure Poisson point process (having no
refractoriness). The simulation was run for different average firing rates (x-axis). Errorbars are
standard deviations across n=10000 simulations. Figure S1 is related to Figure 1.
Figure S2. Example cells showing significant burst-LFP synchronization at low beta and at
gamma band frequencies
(A, B) For each example, the left panel shows the LFP phase consistency of burst (red) and nonburst (grey) spikes. Phase consistency is measured as PPC (see Supplemental Experimental
Procedures). Horizontal red/grey bars denote frequency range with Rayleigh significant (p ≤
0.05) phase consistency. The middle panel shows the amplitude normalized action potential
waveform of the example cell in black, against a semitransparent background of all narrow (red)
and broad (blue) spiking neurons. The right panel shows the normalized return maps of the
interspike interval (ISI) distribution of the cells firing, plotting the pre-ISI’s (x-axis) against the
post-ISI’s (y-axis). The return maps were smoothed with a 5ms Gaussian window. ‘LV’ provides
the information of the ‘Local Variability’ statistics of the spiketrains of the cell across trials
(Error is SE). The Local Variability [S1] indexes whether the firing of a cell is more ‘regular’
than a Poisson process (LV<1), ‘Poisson’ (LV~1), or more irregular and bursty (LV>1) than
expected for a Poisson process (see Supplemental Experimental Procedures). Figure S2 is related
to Figure 2.
0
ï
40 60 80 100 +#0C"0-<1*DEFG
!
+,#,-.*/0-$,%1
2'#*3,22)*$4,50*$"6$0%
1
7 !"
>? *(; #$%
?*- %<
'- =0
0@ 3
6"
#$
%
?'B
:4,50
/0-$,%1
=,.=
?'B
A",-%,?0*$4?,%*'2
-'-@6"#$%*:4,50$
9:
=,.=
78
!"#$%*IIJ*K$)
8;%09$4,50-"(
(;%<=03*$4,50$
ï
x 10
4
&'#()*+,#,-.
/0-$,%1
/,220#0-<0H*!"#$%@IIJ
%'*-'-@6"#$%*IIJ
"
Figure S3. Enhanced burst synchronization relative to non-burst spike events at different
firing rate regimes.
(A) Average phase locking difference of burst spikes relative to non-burst spikes of increasing
local firing rate density (increasing green saturation of the lines). For comparison, the red line
shows the difference in synchronization of burst firing after the local firing rate and spike
numbers were matched to the non-burst single spiking (same red line as in Fig. 1D).
(B) Average normalized firing density for the different sets of spikes across all cells with >1%
burst events. The red dot indicates the local firing density of a set of non-burst spikes that were
matched in spike number and in the local firing rate to the set of burst spikes (black dot). The
green to gray dots show the average firing rates relative to the burst spike in the five percentiles.
Note that spikes in the top percentile bin showed an average larger firing rate than was evident
for firing bursts. Figure S3 is related to Figure 3.
Figure S4. Illustration of the reconstruction of recording sites
(A, B) Reconstruction of a medial PFC (area 32, A), and a lateral PFC (area 46, B) recording site
started from the 7T anatomical MR, which was obtained with (iodine based) visualization of
electrode trajectories within the electrode grid placed inside the recording chamber. The outline
of the cortical folding was sketched on the coronal MR slice to ease identification of areas and
landmarks according to standard brain atlases, and to place the depth of the electrode tip (red dot
in A and yellow dot in B) with custom MATLAB code. The electrode position was then placed
into a standardized macaque brain available in the MR Caret software package. Caret allowed
rendering the MR slice into a 3D volume and to inflate the volume before it the spherically
inflated brain was cut (indicated as yellow line) to represent it as 2D flat map. White lines on the
flat map demarcate the principal sulcus (PS), the arcuate sulcus (ARC), and the cingulate sulcus
(CS). The location of the FEF (frontal eye field) within the ARC is indicated by a green patch.
(C) As a last step, the anatomical subdivision of areas in the prefrontal-cingulate cortex were
visualized following the nomenclature from Barbas and Zikopoulus, 2007[S2]. The area 32 and
area 46 recording sites are visualized throughout the panels by a red and a yellow dot,
respectively. Adapted from[S3]. Figure S4 is related to Figure 4.
!"#$%#&'()*+,20 40 60 80 100 120
."/01)/2
3/4&5)6%"75
8/'94&:
20
60
0.2
0.1
0
beta-gamma
burst locking
r = 0.037 (n.s)
80
100
!"#$%#&'()*+,-
40
120
Figure S5. Independence of burst specific phase locking at beta and gamma frequency
bands
The adjacency matrix shows the proportion of cells with significant phase locking at
combinations of two frequencies. The black rectangle highlights the low beta to gamma band
frequency combination, which contained the cells with burst-LFP synchronization. There was no
joint probability of sign. locking, and neither was there any correlation of locking strength at beta
and gamma bands (r = 0.037, non sign.). Figure S5 is related to Figure 7.
=M1"$,1&.D$31&#N&-O"35
2#0*)+,&3()*1&P)+&"$%)$+3Q&
!
!"#$%&'()*)+,&-../
012234&!15$&2#0*)+,
6$""#7&'()*)+,&-../
012234&!15$&2#0*)+,
!15$
R:G>G<&STU
-9.43
"
!"#$%&'()*)+,&-../
012234&8$99$&2#0*)+,
6$""#7&'()*)+,&-../
012234&8$99$&2#0*)+,
-9.43
6.28
6.28
3.14
3.14
0
0
-3.14
-3.14
-6.28
-6.28
-9.43
-9.43
2.2
6.1
1.7 4.2
17.2
.1"01+5)21&%)35$+01&#N&01223
5#&?@.&12105"#%1&P)+&99Q
#
8$99$
R;<>L;&STU
$
=+$5#9)0$2&0122>5#>?@.
A)35$+01&)+&99B
: ; :<
15.7
.1"01+5)21&%)35$+01&#N&01223
5#&?@.&12105"#%1&P)+&99Q
=+$5#9)0$2&0122>5#>?@.
A)35$+01&)+&99B
:
G<
; :<
G<
<C:L&"$%C&(D$31
0D$+,1&(1"&99
%)35$+01
<C::&"$%C&(D$31
0D$+,1&(1"&99
%)35$+01
E!15$&F&>GCH<&I&J&K&<C::
E8$99$&F&><CGL&I&J&K&<C:L
Figure S6. LFP phase of burst firing changes with anatomical separation from LFP site
(A) The average beta (12-20 Hz) phase of bursts to the LFP (y-axis) with increasing anatomical
distance to the LFP (x-axis). The blue data shows the phases of BS cells binned into three
percentile distances (to ensure n≥6 cells per distance bin before computing the mean phase per
bin). The blue line shows the best fitting regression with a slope of 0.11 radians per mm distance.
The red data-points show the mean phase across the narrow spiking (NS) neurons at their
average anatomical distance. The error bars are angular STD. Please note that the data from a
single oscillation cycle were reproduced for neighboring cycles for illustration purposes.
(B) Same format as in (A) but for cells with significant gamma band bPPC. The regression slope
indicates a phase change of 0.17 radians per mm anatomical distance. Gamma locking cells were
percentile split into three distance percentile bins independently from the beta cells to have the
same number of cells per bin and a similar distance range than the beta locking cells.
(C, D) Illustration of the distance dependent change in burst phases to the LFP assuming a linear
relationship of distance and burst phase (regression lines in A,B). The blue (green) spikes on top
of the cosine illustrate the beta (gamma) phase at 1, 5, 10 and 20 mm distance between burst
firing cells and LFP site. This analysis shows that burst-to-LFP phases increase with anatomical
distance of cell and LFP recording site (which precluded simple pooling of the absolute burst
phases for other analysis). The regression analysis estimates that phases changed on average 0.11
(0.17) radians per mm cortical distance for beta (gamma) synchronizing burst spikes. Figure S6
is related to Figure 5.
K$G)&*"L%*M%#IN(%OPQ%;HI-$
/*H$&$G/$%I&*,GL%)"#$%*M%+,&-)
"
12%/$''-3
45#-%.670
2
;<=(>9
1
0
-100 -50
0
50
100
!"#$%&$'(%)*%+,&-)%.#-$/0
DEF(%G*&#(%+,&-)
;HI-$%'*/J"GF
DEF(%G*&#(%+,&-)
;HI-$%'*/J"GF
!
?@=4:@%ABC
82%/$''-3
9#-%.6:0
1.5
;<=(:@
0
-100 -50
0
50
100
!"#$%&$'(%)*%+,&-)%.#-$/0
Figure S7. Temporal relation of burst firing and phase locking to distant LFP at the gamma
frequency band.
(A) Same format as Figure 6B,C in the main text. Average normalized burst locked LFP
coherence for bursts of NS cell’s at 50-75 Hz (y-axis) at different times (x-axis) relative to the
first spike of the burst. The arrowhead demarcates the time lag centroid of the curve. The red
shading denotes the STD of the centroid computation obtained through a randomization
procedure.
(B) Same format as (A) but for BS cells. The blue shading denotes STD as in (A). Figure S7 is
related to Figure 6.
Supplemental Experimental Procedures:
Electrophysiological Recording and Data Acquisition. We recorded spiking activity and the
local field potential (LFP) in two awake and behaving macaque monkeys as outlined in detail in
Kaping et al. (2011) [S3] and following guidelines of the Canadian Council of Animal Care
policy on the use of laboratory animals and of the University of Western Ontario Council on
Animal Care. Extra-cellular recordings commenced with 1-6 tungsten electrodes (impedance
1.2-2.2 MΩ, FHC, Bowdoinham, ME) through standard recording chambers (19mm inner
diameter) implanted over the left hemisphere in both monkeys. Electrodes were lowered through
guide tubes with software controlled precision microdrives (NAN Instruments Ltd., Israel) on a
daily basis, through a recording grid with 1 mm inter-hole spacing. Before recordings began,
anatomical 7T MRIs were obtained from both monkeys, visualizing possible electrode
trajectories through a recording grid within the chamber using iodine.
Data amplification, filtering, and acquisition were done with a multi-channel processor
(Map System, Plexon, Inc.), using headstages with unit gain. Spiking activity was obtained
following a 100-8000 Hz passband filter and further amplification and digitization at 40kHz
sampling rate. During recording, the spike threshold was always adjusted such that there was a
low proportion of multiunit activity visible against which we could separate single neuron action
potentials in a 0.85 to 1.1 ms time window. Sorting and isolation of single unit activity was
performed offline with Plexon Offline Sorter (Plexon Inc., Dallas, TX), based on principal
component analysis of the spike waveforms, and strictly limiting unit isolation to periods with
temporal stability. We limited all analysis to the subset of maximally isolated single units whose
waveform 2D principle components were clearly separated, and whose density profile was
separated from influences from other simultaneously recorded waveforms and from multiunit
activities.
The recording experiments were performed in a sound attenuating isolation chamber
(Crist Instrument Co., Inc.) with monkeys sitting in a custom made primate chair viewing visual
stimuli on a computer monitor (85 Hz refresh rate, distance of 58 cm). The monitor covered 36º
x 27º of visual angle at a resolution of 28.5 pixel/deg. Eye positions were monitored using a
video-based eye-tracking system (ISCAN, Woburn, US, sampling rate: 120 Hz) calibrated prior
to each experiment to a 5 point fixation pattern (one central fixation point and the remaining four
points offset by vertical 8.8º and horizontal 6º toward the 4 corners of the monitor). Eye fixation
was controlled within a 1.4-2.0 degree radius window. During the experiments, stimulus
presentation, monitored eye positions and reward delivery were controlled via the software
MonkeyLogic (open-source software http://www.monkeylogic.net) running on a Pentium III PC
[S4, S5]. Liquid reward was delivered by a custom made, air-compression controlled,
mechanical valve system with a noise level during valve openings of 17 dB within the isolation
chamber.
Behavioral Task. Single cell local field potentials (LFP's) were recorded while the monkeys
were performing a selective attention, 2-forced choice discrimination task (see [S3]). The task
involved 2 s intertrial intervals with a blank dark screen, before a small gray fixation point was
presented centrally on the monitor. Monkeys had to direct their gaze and keep fixation onto that
fixation point until the end of the trial. After 300 ms fixation, two black/white grating stimuli
were presented to the left and right of the center and contained oblique movements of the grating
within their circular aperture. After 0.4 s each stimuli changed color to either black/red or black/
green. The colors were associated with differential fluid reward if acted upon at a later stage
during the trial (when the monkeys knew which color had to be attended). After a variable time
(0.05 to 0.75 s) the color of the central fixation point changed to either red or green, which cued
the monkeys to covertly shift attention towards the location where the color of the grating
matched the color of the fixation point. Monkeys maintained central fixation and sustained
covert peripheral attention on the cued stimulus until it underwent a transient clockwise or
counterclockwise rotation, ignoring possible rotations of the non-attended (uncued) stimulus,
which occurred in 50% of the trials. In order to obtain a liquid reward, the monkeys had to
discriminate the rotation by making up- or downward saccades for clockwise /counterclockwise
rotations (the mapping was reversed between monkeys). Following this choice and a 0.4 s
waiting period the animals received fluid reward. The magnitude of the fluid reward varied as a
function of the color of the attended stimulus that the monkeys acted upon. High/low rewards
were linked to the red/green color of the attended stimuli (with the color – reward mapping
changing in blocks of 30 correctly performed trials). A key component of the task is that the
location of covert spatial attention on one of the two colored stimuli (left or right periphery) is
distinct from the possible locations to which the animal made a saccade (up- and downwards) to
indicate the transient rotation of the attended stimulus.
Anatomical Reconstruction. The anatomical site of each recorded cell was reconstructed for
each monkey and projected onto the 2D flat map representation of a standardized macaque brain
(‘F99’) available within the MR software Caret [S6]. Figure S4 survey’s the main procedure for
two example reconstructions. Reconstruction began by projecting each electrodes trajectory onto
the two dimensional brain slices obtained from 7T anatomical MRI images, using the opensource OsiriX Imaging software [S7] and custom-written MATLAB programs (The Mathworks
Inc.), utilizing the iodine visualized electrode trajectory within the electrode grid placed within
the recording chamber during MR scanning. We drew the coronal outline of the cortical folding
of the MR gray scale image to ease the comparison of the individuals monkey brain slices to
standard anatomical atlases, before projecting the electrode tip position into the standardized
macaque brain (F99) available in Caret. Note that we initially reproduced the individual monkey
brains within the Caret software to validate similarity and derive the scaling factors to match the
lower resolution monkey MRs to the higher resolution standard F99 brain. We then manually
projected, under visual guidance, the electrode position to the matched location in the standard
brain in Caret [S8].
After identifying all recording sites within the standard brain, we used the Caret software
to render the sliced brain into a 3-dimensional volume, spherically inflated and cut it to unfold
the brain into 2-dimensional space (see Figure S4). In an independent procedure we visualized
major anatomical subdivision schemes of the fronto-cingulate cortex, using the scheme from
Barbas and Zikopoulos [S2] as reference.
Spike waveform analysis to distinguish putative interneurons and pyramidal cell types.
Previous studies have shown that the action potential waveform of a cell is a good indicator of
whether the cell belongs most likely to an inhibitory interneuron class (basket cells, Martinotti
cells, etc.), or to a pyramidal cell type [S9, S10]. To test for putative cell type specificity of bursttriggered synchronization we classified cells into putative interneurons (‘narrow spiking neurons)
and putative pyramidal cells (‘broad spiking neurons’) with an improved classification method as
we have outlined before in [S11] and briefly summarize. First, we extracted the average action
potential waveform (AP) of each cell and increased the waveforms temporal resolution from 25
µs per sample (sampling frequency 40kHz) to 2.5 µs precision using cubic interpolation. On the
resultant waveform, we analyzed two measures (Figure 5A): the peak-to-trough duration and the
time for repolarization. The time for repolarization was defined as the time at which the
waveform amplitude decayed 25% from its peak value. These two measures were highly, albeit
not perfectly, correlated (r = 0.68, p < 0.001, Pearson correlation). We computed the Principal
Component Analysis and used the first component (84.5 % of the total variance), as it allowed
for better discrimination between narrow and broad spiking neurons, compared to any of the two
measures alone. We used the calibrated version of the Hartigan Dip Test [S12] that increases the
sensitivity of the test for unimodality [S13, S14]. Results from the calibrated Dip Test discarded
unimodality for the first PCA component (p < 0.01) and for the peak to trough duration (p <
0.05) but not for the duration of 25% repolarization (p > 0.05). In addition, we applied Akaike's
and Bayesian information criteria for the two- vs one- Gaussian model to determine whether
using extra parameters in the two-Gaussian model is justified (Figure 5A). In both cases, the
information criteria decreased (from -669.6 to -808.9 and from -661.7 to -788.9, respectively),
confirming that the two-Gaussian model is better. We then used the two-Gaussian model and
defined two cutoffs that divided neurons into three groups (Figure 5A). The first cutoff was
defined as the point at which the likelihood to be a narrow spiking cell was 10 times larger than a
broad spiking cell. Similarly, the second cutoff was defined as the point at which the likelihood
to be a broad spiking cell was 10 times larger than a narrow spiking cell. Thus, 95% of neurons
(n = 384) were reliably classified: neurons at the left side of the first cutoff were reliably
classified as narrow spiking neurons (20%, n = 79), neurons at the right side of the second cutoff
were reliably classified as broad spiking neurons (75%, n = 305). The remaining neurons were
labeled as ‘fuzzy’ neurons as they fell in between the two cutoffs and were not reliably classified
(5%, n = 20).
Definition of burst events. We defined bursts in four different ways and studied their probability
of occurrence across task epochs (Figure 1A-C). Bursts were defined a rapid succession of ≥2
spikes within defined intervals of either 5ms, or 20ms. Two spikes within 5ms interspikeintervals (ISIs) signify a 200Hz firing event and characterizes bursts as used previously in the
monkey field [S15]. A definition of burst firing with longer, 20ms ISIs is used in studies of
anaesthetized animals and in in-vitro recordings, where bursts are identified as the occurrence of
≥2 spikes within a 20 msec or a 30 msec interspike interval [S16, S17]. In addition, researchers
have distinguished bursts that follow pre-burst silent periods from burst events that occur without
a prolonged quite period [S18, S19]. We thus tested the 5ms and 20ms ISI burst definitions
described above with and without enforced pre-burst quiet period (Figure 1B). We did not
identify a difference in our recordings between bursts with and without a silent period before the
spike. Figure 1B illustrates for 5ms and 20ms ISI defined bursts that the average proportion of
bursts and how they distribute across non-attention and attention states were not different for
bursts defined with versus without pre-burst silent period.
We also report for the cell examples the ‘Local Variability’ [S1], which is a second order
spiketrain statistics that describes how variable the interspike intervals of a cell are distributed
(Figure S2). The values of Local Variability indexes whether a cells’ firing is ‘regular’ (LV<1),
‘Poisson’ (LV~1), or irregular and bursty (LV>1).
Analysis of spike- and burst-triggered phase locking using the pairwise phase consistency.
We analyzed burst-triggered phase locking to the LFP by first cutting LFP segments around the
first spike of a burst, Hanning tapering the burst-triggered LFP and decomposing it using the Fast
Fourier Transform. Identical Fourier transforms were done for non-burst spikes. Burst-triggered
and spike-triggered Fourier transforms were obtained for frequencies ranging from 3-120 Hz.
The time windows for calculating the Fourier transforms were adaptive to contain 5 complete
cycles at each frequency. For frequencies ≤30 Hz we calculated spike LFP coupling every 1.5 Hz
and for higher frequencies we used a frequency increment of 4 Hz. For all analysis we
exclusively used the LFP recorded from different electrodes than the electrode that recorded the
bursting and spiking activity (see below ‘distance dependence of burst-triggered phase locking’).
Burst-triggered phase locking was then calculated as pairwise phase consistency (PPC),
which is an unbiased estimator of the squared spike-LFP phase locking value, described in detail
in [S20, S21]. In brevity, for the j−th spike in the m-th trial we denote the average spike-LFP
phase as θm,j , where dependence on frequency is omitted in what follows. The PPC is then
defined as
(equation 1),
The PPC quantifies the average similarity (i.e., in- phaseness) of any pair of two spikes
from the same cell in the LFP phase domain [S20]. While the PPC solves the problem of samplesize bias, PPC estimates are highly variable for units with a low number of spikes [S21]. To
address this problem, we only considered PPC values if they were based on a sample of more
than 30 spikes, which reduces the variance of the group average [S21].
Values of the PPC close to 0.01 correspond approximately to a phase locking value of
0.1. Values of the PPC can be directly translated in the modulation depth of phase modulated
firing, i.e. the proportion of spikes falling at peak vs. trough of the oscillation cycle, which can
be estimated by:
(equation 2),
This equation provides the effect size of phase locking for burst- and non-burst spikes.
For example, a PPC value of 0.01 corresponds to observing 1.5 times more spikes at the cells’
preferred oscillation phase compared to the spikes at the non-preferred oscillation phase.
Comparison of burst-triggered and spike-triggered phase locking. We compared bursttriggered phase locking to (i) the phase locking of all non-burst spikes, (ii) the phase locking of
non-burst spikes that were matched in spike number and local firing density to burst spikes, and
(iii) to the phase locking of non-burst spikes resampled to have varying local firing density (see
Figure S3B). For all comparisons, we only considered cells with at least one percent of burst
firing events in their total distribution of spike events.
We compared burst-triggered phase locking to phase locking of all single spikes of cells
by calculating for each cell the difference in PPC. The distribution of PPC differences across all
cells was then tested against the null hypothesis of no difference using the non-parametric
Wilcoxon signed rank test. To compare burst-triggered phase locking to the phase-locking of
non-burst spikes that were matched in number and local firing density for each cell, we used a
resampling permutation approach (similar to [S22]). For each of n=1000 random non-burst spike
selections we rank-ordered the local firing density of non-burst spikes (computed with a 50msec
SD Gaussian spike density kernel) and drew a random subset of spikes that exceeded the median
firing density of the burst-spikes (likewise calculated with a 50msec spike density kernel), and
we drew a random subset of spikes with a local firing density lower then the burst-spike. This
provided an equal number of non-burst spikes with higher and lower local firing density.
Combining these subsets of non-burst spikes equates the number of burst events. Importantly,
this procedure ensured that the median firing density of the total of randomly drawn single spikes
was equated to the firing density of the burst spikes (see the two leftmost data points in Figure
S3B). For each random draw we then calculated the non-burst spike phase locking using the
pairwise phase consistency (PPC, see above) and obtained in this way the spikenumber-matched
and rate-matched PPC across the all PPC’s of n=1000 permutations of each cell. Across all cells,
we calculated the difference of burst-triggered PPC and spikenumber and rate-matched PPC
using the non-parametric Wilcoxon rank sum test.
For a third comparison of burst-triggered PPC with non-burst PPC, we quantile split the
distribution of non-burst spikes of each cell according to the local firing density (calculated with
a 50msec kernel, see above). For each of the five sets of spikes (with equal number but
increasing local firing density), we calculated the spike-LFP PPC as described above and
computed the difference of the quantile based rate-specific PPCs with the burst-triggered PPC
for each cell (Figure 2A,B). We tested for a pairwise median difference of rate-specific versus
burst-triggered PPCs across cells using the non-parametric Wilcoxon rank-sum test.
Testing for distance dependence of burst-triggered phase locking. In order to test whether
burst-triggered phase locking can be observed between cells and LFPs independent of their
actual anatomical distance, we used a randomization procedure. We tested the null hypothesis
that the anatomical (3D) distance of the spiking cell to the LFP recording site does not influence
whether a burst firing cell shows significant burst-triggered PPC or not. To this end we first
obtained for all cells with at least 1% burst firing events (see above) their 3D distances to the
recorded LFPs. We then percentile-split the distance distributions into four ‘distance bins’ to
ensure equal number of cells at each distance level. We then used the distance bins of this
histogram (that considered all burst cells) to bin the distances of those cell-LFP pairs that showed
significant burst-triggered PPC for beta (12-20 Hz) and gamma (55-75 Hz) frequencies. They
reveal the likelihood to see a bursting cell to significantly phase lock given the number of
bursting cell that were recoded in the respective distance bin. These distance-dependence curves
are shown in Figure S6. We then obtained n=1000 distance-dependence curves for random
subsets of cell-LFP distances by randomly drawing from the overall population of burst firing
cells as many pairs as there were cell-LFP pairs that showed beta band burst-triggered phase
locking. We then identified the 97.5% largest and the 2.5% smallest distance value in each of the
distance bins of the random distribution and compared it to the truly observed distance of the
subset of spike-LFP pairs that showed significant burst-triggered PPC. When the truly observed
distance value exceeded the 97.5% value of the random distribution, or fell below the 2.5%
distance value of the random distribution this corresponds to a refutation of the null hypothesis
with a two - tailed significance value of p≤0.05. We performed the same procedure for the
number of cell-LFP pairs that showed significant burst-triggered PPC in the gamma frequency
range (55-70 Hz), as well as for those with significant burst-triggered PPC in the 12-20 Hz beta
frequency range.
We also tested whether the strength of phase locking of burst events changed with the
distance between the recorded cell and the LFP electrode (Figure 3). We used the same binning
procedure of the distances as described above, i.e. four percentile bins based on the distances
observed across all recorded cells that showed burst firing events. We then obtained for each
distance bin the maximum burst-triggered PPC within the beta (12-20 Hz) and gamma (50-75
Hz) band for those cells that showed significant burst-triggered PPC at the respective
frequencies. We then transformed the burst-triggered PPC values into the effect size measure that
directly reveals the peak-to-trough modulation depth of burst spiking by the LFP phase (see
above, [S21]). The burst-triggered PPC effect size values across bins were then tested for a
distance dependent difference using the non-parametric Kruskal Wallis Test (i.e. with ‘Distance
Bins’ as group variable).
Testing for Inter-area specificity of burst-triggered phase locking at beta and gamma
frequency bands. To identify whether the anatomical location of the cell and/or of the local field
potential determined whether there was significant burst-triggered phase locking at beta and/or
gamma band frequencies, we first reconstructed their recording location within prefrontal cortex
(see Figure S5). We then assigned each recording site to an anatomical brain area, i.e. a ‘cortical
field’, in prefrontal cortex following the nomenclature of Barbas and Zikopoulos[S2] (For a
comparison to other prominent prefrontal subdivision schemata, see Figure S4 in [S11]). We then
counted the number of cell - LFP pairs separately for each combination of brain areas. Fig. 4B in
the main text shows the absolute number of cell-LFP pairs recorded within each area and
between areas.
Next, we calculated for each area combination the proportion of cell-LFP pairs that
showed significant burst-triggered PPC (at 12-20 Hz beta or 55-70 Hz gamma frequencies)
relative to all pairs recorded for that area combination. We show the proportion of significant
burst-triggered PPC independently for the beta frequency band (Fig. 4D) and the gamma
frequency band (Fig. 4E), and likewise perform all following statistical tests separately for each
frequency band.
We then tested the null hypothesis that the observed proportion of cell-LFP pairs with
significant burst-triggered PPC was homogeneously distributed across all possible area
combinations using a permutation test that controlled for the uneven sampling of recorded cells
and LFP channels across brain areas. For this test we calculated the proportion of significant
burst-triggered PPC per area combinations after randomly shuffling the area label of the LFP
recording without changing the number pairs drawn for each combinations. We repeated this
procedure n=1000 times to obtain a distribution of the proportions of significant pairs per area
combination that would be expected by chance. We inferred statistical significance at an alpha
value of p < 0.05 when the truly observed proportion of burst-triggered PPC pairs for an area
combination exceeded the 95th percentile of the randomization distribution. Area combinations
with a significantly larger likelihood to show significant burst synchronizations are marked with
a white star inside the adjacency matrices in Fig. 4D and Fig. 4E.
Phase difference of burst specific phase locking versus non-burst phase locking. To test
whether bursts phase lock at different phases of an oscillation cycles compared to single spike
events of the same cell, we calculated for each cell the difference of the average burst-LFP phase
and the single spike-LFP at the beta (12-20Hz) and gamma (55-70 Hz) frequency band (see
Figure 5D,E). We then tested whether the median phase difference across cells was statistically
different from an expected median phase difference of zero using a binomial test applied to
circular data as described in [S23]. The test was applied to the distribution of phase differences
of all those cells with burst firing (of 1%, see above) and significant burst-triggered phase
locking in the respective frequency band. See also the matlab implementation circ_med in the
Circular Statistics Toolbox for Matlab [S23].
Temporal relation of burst specific phase locking and LFP power. To study the phase
consistency and power modulation of LFP’s around the time of burst firing with fine, millisecond
temporal resolution we decomposed the LFP into phase and power using the Hilbert transform
(see also [S24]). The Hilbert transform provides a spectral decomposition of the data that is
equivalent to the Hanning-window tapered fast Fourier transform and is computationally
efficient (see [S25]). First, we bandpass filtered (using the Buttwerworth filter) the LFP segments
around each burst of a cell, providing burst triggered LFP segments for each burst event.
Filtering was applied to partly overlapping frequency ranges spanning 1 to 150 Hz, in steps of 2
Hz for lower frequencies (1 - 40 Hz), and in steps of 4 Hz for higher frequency ranges (44 - 150
Hz). The bandpass filtered, burst triggered LFP was then Hilbert transformed providing phase
and power estimates every 5 milliseconds around the time of a burst. For each time step and
frequency, we calculated the phase consistency across all burst events of a cell using the
Rayleigh Z score.
To test for a possible time lag of maximal synchronization of burst events with the LFP,
we calculated for each cell the average (median) phase consistency (indexed as Rayleigh’s Z) at
each frequency band every 5 msec from ± 0.1 sec. around the time of the first spike of the burst
event. We then averaged (using medians) the time-resolved phase consistency across all cells that
showed at least one percent burst events in their spiketrains and that showed reliable burst
triggered PPC in the previous analysis. We then calculated the center of mass of the phase
consistency within ± 0.1 sec. around the burst event. To test whether the centroid was preceding
or following the burst event, we applied a permutation test testing the null hypothesis that the
sign of the time axis of individual cells’ burst triggered phase estimate does not influence the
center of mass of the population average across cells. This null hypothesis is true when the
average center of mass of the modulation has no bias to be left (preceding) or right (following)
relative to the zero time point, which is the time of the burst firing. To test the null hypothesis we
calculated a random distribution of 1000 centroids, each obtained after randomly flipping the
time axis of half of the cells before calculating the average centroid. We then determined the 2.5
% and the 97.5 % values of the random distribution. The truly observed centroid was then
considered significant when it fell below the 2.5% value or above the 97.5 value of the shuffle
distribution. This procedure corresponds to a two-sided test with a cut off p-value of p≤0.05,
signifying that the observed centroid is consistently earlier (below 2.5%) or later (above 97.5%)
than expected by chance.
The described test showed only statistical trends and no significant difference from zero
for the groups of NS or BS cells at gamma and beta frequencies. To provide an independent
validation of this result for selected cases (see main text) we compared the results of the
permutation centroid statistics to a statistics that compared the overall area under the modulation
curves before and after the burst event. We then computed the difference of the areas before
versus after the burst event as an index [ (beforeBurst - afterBurst) ./ (beforeBurst + afterBurst) ]
and applied a sign test that tested the null hypothesis that the number of cells with a larger
modulation area before the burst event is the same as the number of cells with a larger
modulation area after the burst event. Signtest and permutation statistics agreed perfectly despite
their different test statistics (relative time of the center of mass versus area differences). We thus
concluded that across NS cells and across BS cells, there is statistically no homogeneous overall
temporal effect, i.e. on average, the burst triggered phase locking is maximal at the time of the
burst.
We next tested whether the population of NS cells and the population of BS cells differed
when compared directly against each other. We used t-tests to directly compare whether the LFP
phase consistency of burst events emerged at the same time for burst firing NS cells and BS
cells. The t-test (main test: Figure 6E) quantifies whether the center of mass of the phase
modulation in NS and BS cells was at significantly different time points relative to the time of
the burst event.
Supplemental Discussion:
Our main results showed that burst firing of different subpopulations of cells synchronizes at
beta frequencies and at gamma frequencies (Figure 4, 5, S5). Moreover, the timing of burst
firing to LFP phase coherence at remote channel locations differed between putative interneurons
and putative pyramidal cells (Figure 6). These results suggest that burst synchronization is
realized by different circuit mechanisms, or motifs. In the following we discuss and speculate
about possible motifs for beta band and gamma band synchronization and how interneurons and
pyramidal cell subclasses have been implicated to subserve burst firing in cortical circuits from
in-vitro and from theoretical perspectives and how these insights might relate to the attentional
burst synchronize we observe in macaque prefrontal cortex.
Possible burst motifs underlying beta synchronization
At the cellular level our results suggest that burst firing mechanisms are a possible source for
generating attentional gating signals in the ACC/PFC [S26, S27]. Burst firing not only indexed
that cells in the ACC/PFC engaged in selective attentional processing but they were coordinated
with network activity (indexed as LFP) across those brain areas that are supposed to
communicate control and performance monitoring of information during goal-directed behavior
[S3, S28-30]. Importantly, this long distance coordination was based on bursts from largely
independent cell groups showing bursts synchronizing at low beta, or at gamma band frequencies
and that the timing of bursts to remote LFPs differed for beta synchronizing narrow spiking cells
(putative interneurons) and broad spiking (putative pyramidal) cells, but not for gamma band
burst synchrony. We can thus speculate that possibly four distinct underlying burst firing
mechanisms are needed to account for these findings (see Figure 7).
One of the best documented mechanism of 200 Hz fast burst firing events has been
reported in whole cell, in-vitro-recordings and is based on activating calcium spikes by distal
dendritic depolarization of infragranular layer pyramidal cells [S27]. We believe that calciumspike dependent bursting could underlie in particular the burst firing of putative pyramidal cells
synchronizing to beta band oscillations for three reasons. First, Ca2+ mediated bursting is a
ubiquitous property across all regular spiking L5 pyramidal cells and is not restricted to so called
‘intrinsic bursting’ cells [S31]. This characteristic is consistent with our finding that burst
synchronization is not restricted to cells with a particularly high incidence of burst spikes, and is
evident across putative pyramidal cells classified according to their broader spike waveforms.
Secondly, calcium dependent bursting most likely follows in time a period of joint activation of
(possibly rhythmic) subthreshold activation at distal dendrites and at the soma [S27, S32]. This
joint activation is reminiscent of an association mechanism that activates with burst firing
whenever there is joint distal and proximal input to a cell [S27], or alternatively when dendritic
(GABAergic) inhibition is removed [S26, S31]. Importantly, recent biophysical modeling
identified that burst firing is facilitated by proximal rhythmic inhibition during intermediate
levels of dendritic depolarization [S32]. These findings suggest that beta LFP coherent
subthreshold fluctuations at dendrites precede the emergence of burst firing, which is consistent
with what we found for the group of putative pyramidal cells synchronizing at beta frequencies
(see Figure 7A).
Thirdly, the calcium mediated bursts are evident in those cortical pyramidal cells that are
at the same time major recipients of feedback type inputs (through L1 tufts) and major projection
cells whose output affect distant target areas [S16]. This property makes these cells ideally suited
to propagate activity through bursts across those distant brain areas that are activated through
feedforward and feedback type of inputs. Indeed, this propensity of long dendritic trees to
integrate ‘top-down’ information before combining it with local, peri-somatically arriving
information has been proposed as one key mechanism to gate attention information in a detailed
and biophysically realistic spiking model of attentional routing [S33]. Our results support these
recent data proposing that burst firing of a subset of pyramidal cells indicate the integration and
gating of goal-relevant information. We critically extend this set of literature by suggesting that
burst firing coordinates brain areas at a characteristic narrow-band 12-20 Hz beta frequency.
Long distance connections at this low beta frequency has very recently been documented to
index large scale interactions of lateral prefrontal cortex and intra-parietal cortex during
attention, working memory, and decision making tasks [S34-37] (for related 12-20 Hz beta
network dynamics see: [S38-42]). Our results thus suggest that burst firing is a key mechanism
underlying this long-range coordination of top-down information.
Putative interneurons and burst motifs underlying beta synchronization
Beta band burst synchronization was likewise evident in putative interneurons identified by their
narrow spike width. It has long been known from slice work that the major classes of inhibitory
neurons include subclasses showing fast burst firing [43-45]. Our result of narrow spiking
neurons with a limited number of burst events that synchronize long-range to the LFP during the
awake attentive state at beta frequencies has to our knowledge no precedent in the literature. We
can infer, however, from patch clamp studies that our results are consistent with a feedforward
inhibition (FFI) motif whereby slow-acting interneurons impose a widespread phase reset on
subnetworks of pyramidal cells [S46, S47]. Such FFI mediated control of spike timing can serve
as a robust mechanism for input selection [S48], suggesting that network selection may rely on
burst firing impulses mediated by beta frequency resonant interneurons [S49, S50]. Figure 7B
illustrates how somatostatin expressing (SOM+) Martinotti type interneurons in deep cortical
layers were found to impose synchronized inhibition onto multiple connected pyramidal cells
when stimulated with a 20 Hz rhythmic current train [S49]. This finding from rodent frontal
cortex slices provides a proof of principle that activation of interneurons at 20 Hz can powerfully
reset activity across a large subnetworks of connected pyramidal cells. Consistent with this
scenario, we observed that LFP activity in remote brain areas was maximally beta-coherent after
the burst event of the interneurons, suggesting that synchronized rebound of activation
synchronized the remote LFPs. Whether such a temporal precedence of putative burst inhibition
translates into a causal effect will be an important experimental question for future studies.
Gamma band synchronization and burst firing in a recurrent motif
Beyond the beta band, a large set of putative pyramidal cells and interneurons synchronized in
the gamma frequency band. A possible tentative circuit motif supporting gamma bursting
acknowledges that fast spiking interneurons have the propensity to fire fast ~200 Hz events
during high levels of depolarization [S44, S51] and that subsets of pyramidal cells engage in
persistent-sodium-channel dependent, fast gamma-rhythmic bursting [S52-54]. We speculate
(Figure 7C) that gamma burst synchrony is thus maintained by a recurrent feedback inhibition
motif [S47, S55] whereby occasional burst spikes of pyramidal cells phase couple to the distant
gamma band rhythm to synchronize local recurrent processes and thereby maintaining selective
neuronal communication among nodes processing relevant information [S9, S22, S56-58].
Consistent with this functional interpretation burst synchrony at gamma frequencies was
less likely sustained across long distances than at shorter distances, but it remained evident
between those specific cortical subfields in ACC (area 24) and lateral PFC (area 46) that are the
two interacting key nodes controlling and biasing attention during goal-directed behavior [S3,
S28-30]. Gamma burst synchronization had two particular, distinguishing characteristics. Firstly,
for gamma synchronizing neurons the burst spikes preceded non-burst spikes in the gamma
cycle. This earlier firing suggests that burst spikes emerged in the circuit from a larger and or
faster local excitation, allowing the burst spike to affect postsynaptic targets earlier than nonburst spikes happening later in the cycle [S59-62]. Secondly, the gamma burst events of putative
interneurons and putative pyramidal cells on average coincided in time with the period of
maximal LFP gamma coherence at the remotely recorded location. Although this finding does
not rule out causal relationships, it suggests that gamma bursts are more akin to transient
impulses with an equal timing across distant nodes. Such equal timing of spiking and LFP
events (akin to zero-time lag synchrony) between distant brain circuits with non-zero conduction
delays can be realized in brain circuits in the presence of reciprocal connections that establish socalled resonant pairs [S63]. Alternatively, similar timing of burst-LFP synchronization may
indicate a synchronizing pulse from a common third source (see Discussion in the main text).
Possible external sources common to ACC and PFC are cholinergic inputs from the basal
forebrain that have previously been shown to depolarize cells and induce gamma bursts in rodent
frontal cortex [S64-66], or common norepinephrine projections from the locus coeruleus
implicated to phase align (or: reset) activity across multi-node networks [S67].
In summary, the particular characteristics of gamma burst synchronization suggest a burst
motif (Figure 7C) different to the beta burst motifs (Figure 7A,B). We believe that the gamma
bursts are suggestive of local computations within the cortical columns that phase synchronizes
across long distance when local computational operations are part of larger common processes
such as the maintenance of goal information. As such, gamma burst synchrony may reflect the
maintenance of common communication, while beta burst synchrony is hypothesized to
instantiate and implement the selective routing between distant network nodes during goal
directed behaviors.
Supplemental References
S1.
S2.
S3.
S4.
S5.
S6.
S7.
S8.
S9.
S10.
S11.
S12.
S13.
S14.
S15.
Shinomoto, S., Kim, H., Shimokawa, T., Matsuno, N., Funahashi, S., Shima, K., Fujita,
I., Tamura, H., Doi, T., Kawano, K., et al. (2009). Relating neuronal firing patterns to
functional differentiation of cerebral cortex. PLoS Computational Biology 5, e1000433.
Barbas, H., and Zikopoulos, B. (2007). The prefrontal cortex and flexible behavior.
Neuroscientist 13, 532-545.
Kaping, D., Vinck, M., Hutchison, R.M., Everling, S., and Womelsdorf, T. (2011).
Specific contributions of ventromedial, anterior cingulate, and lateral prefrontal cortex for
attentional selection and stimulus valuation. PLoS Biology 9, e1001224.
Asaad, W.F., and Eskandar, E.N. (2008). Achieving behavioral control with millisecond
resolution in a high-level programming environment. Journal of Neuroscience Methods
173, 235-240.
Asaad, W.F., and Eskandar, E.N. (2008). A flexible software tool for temporally-precise
behavioral control in Matlab. Journal of Neuroscience Methods 174, 245-258.
Van Essen, D.C., Drury, H.A., Dickson, J., Harwell, J., Hanlon, D., and Anderson, C.H.
(2001). An integrated software suite for surface-based analyses of cerebral cortex. J Am
Med Inform Assoc 8, 443-459.
Rosset, A., Spadola, L., and Ratib, O. (2004). OsiriX: an open-source software for
navigating in multidimensional DICOM images. J Digit Imaging 17, 205-216.
Van Essen, D.C. (2002). Windows on the brain: the emerging role of atlases and
databases in neuroscience. Curr Opin Neurobiol 12, 574-579.
Vinck, M., Womelsdorf, T., Buffalo, E.A., Desimone, R., and Fries, P. (2013). Attentional
modulation of cell-class-specific gamma-band synchronization in awake monkey area v4.
Neuron 80, 1077-1089.
McCormick, D.A., Connors, B.W., Lighthall, J.W., and Prince, D.A. (1985). Comparative
electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex.
Journal of Neurophysiology 54, 782-806.
Shen, C., Ardid, S., Kaping, D., Westendorff, S., Everling, S., and Womelsdorf, T. (2014).
Anterior Cingulate Cortex Cells Identify Process-Specific Errors of Attentional Control
Prior to Transient Prefrontal-Cingulate Inhibition. Cerebral Cortex. doi:10.1093/cercor/
bhu028.
Hartigan, J.A., and Hartigan, P.M. (1985). The dip test of unimodality. Annals of
Statistics 13, 70-84.
Cheng, M.-Y., and Hall, P. (1998). Calibrating the excess mass and dip tests of modality.
Journal of the Royal Statistical Society. Series B, Statistical Methodology 60, 579–589.
Henderson, D.J., Parmeter, C.F., and Russell, R.R. (2008). Modes, weighted modes, and
calibrated modes: evidence of clustering using modality tests. Journal of Applied
Economics 23, 607–638.
Anderson, E.B., Mitchell, J.F., and Reynolds, J.H. (2013). Attention-dependent reductions
in burstiness and action-potential height in macaque area V4. Nature Neuroscience 16,
1125-1131.
S16.
S17.
S18.
S19.
S20.
S21.
S22.
S23.
S24.
S25.
S26.
S27.
S28.
S29.
S30.
S31.
Larkum, M.E., Senn, W., and Luscher, H.R. (2004). Top-down dendritic input increases
the gain of layer 5 pyramidal neurons. Cerebral Cortex 14, 1059-1070.
Chen, D., and Fetz, E.E. (2005). Characteristic membrane potential trajectories in primate
sensorimotor cortex neurons recorded in vivo. Journal of Neurophysiology 94,
2713-2725.
Harris, K.D., Hirase, H., Leinekugel, X., Henze, D.A., and Buzsaki, G. (2001). Temporal
interaction between single spikes and complex spike bursts in hippocampal pyramidal
cells. Neuron 32, 141-149.
Swadlow, H.A., and Gusev, A.G. (2001). The impact of 'bursting' thalamic impulses at a
neocortical synapse. Nature Neuroscience 4, 402-408.
Vinck, M., Battaglia, F.P., Womelsdorf, T., and Pennartz, C. (2012). Improved measures
of phase-coupling between spikes and the Local Field Potential. Journal of
Computational Neuroscience 33, 53-75.
Vinck, M., van Wingerden, M., Womelsdorf, T., Fries, P., and Pennartz, C.M. (2010). The
pairwise phase consistency: A bias-free measure of rhythmic neuronal synchronization.
Neuroimage 51, 112-122.
Womelsdorf, T., Schoffelen, J.M., Oostenveld, R., Singer, W., Desimone, R., Engel, A.K.,
and Fries, P. (2007). Modulation of neuronal interactions through neuronal
synchronization. Science 316, 1609-1612.
Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular Statistics. J Stat Softw 31,
1-21.
Womelsdorf, T., Johnston, K., Vinck, M., and Everling, S. (2010). Theta-activity in
anterior cingulate cortex predicts task rules and their adjustments following errors. Proc
Natl Acad Sci U S A 107, 5248-5253.
Bruns, A. (2004). Fourier-, Hilbert- and wavelet-based signal analysis: are they really
different approaches? Journal of Neuroscience Methods 137, 321-332.
Lovett-Barron, M., Turi, G.F., Kaifosh, P., Lee, P.H., Bolze, F., Sun, X.H., Nicoud, J.F.,
Zemelman, B.V., Sternson, S.M., and Losonczy, A. (2012). Regulation of neuronal input
transformations by tunable dendritic inhibition. Nature Neuroscience 15, 423-430,
S421-423.
Larkum, M. (2013). A cellular mechanism for cortical associations: an organizing
principle for the cerebral cortex. Trends in Neurosciences 36, 141-151.
Shenhav, A., Botvinick, M.M., and Cohen, J.D. (2013). The expected value of control: an
integrative theory of anterior cingulate cortex function. Neuron 79, 217-240.
Miller, E.K., and Buschman, T.J. (2013). Cortical circuits for the control of attention.
Current Opinion in Neurobiology 23, 216-222.
Rushworth, M.F., Kolling, N., Sallet, J., and Mars, R.B. (2012). Valuation and decisionmaking in frontal cortex: one or many serial or parallel systems? Current Opinion in
Neurobiology.
Larkum, M.E., Zhu, J.J., and Sakmann, B. (1999). A new cellular mechanism for
coupling inputs arriving at different cortical layers. Nature 398, 338-341.
S32.
S33.
S34.
S35.
S36.
S37.
S38.
S39.
S40.
S41.
S42.
S43.
S44.
S45.
S46.
S47.
Li, X., Morita, K., Robinson, H.P., and Small, M. (2013). Control of layer 5 pyramidal
cell spiking by oscillatory inhibition in the distal apical dendrites: a computational
modeling study. Journal of Neurophysiology 109, 2739-2756.
Bobier, B., Stewart, T.C., and Eliasmith, C. (2014). A unifying mechanistic model of
selective attention in spiking neurons. PLoS Computational Biology 10, e1003577.
Salazar, R.F., Dotson, N.M., Bressler, S.L., and Gray, C.M. (2012). Content-specific
fronto-parietal synchronization during visual working memory. Science 338, 1097-1100.
Pesaran, B., Nelson, M.J., and Andersen, R.A. (2008). Free choice activates a decision
circuit between frontal and parietal cortex. Nature 453, 406-409.
Bastos, A.M., Vezoli, J., Bosman, C.A., Schoffelen, J.M., Oostenveld, R., Dowdall, J.R.,
De Weerd, P., Kennedy, H., and Fries, P. (2014). Visual areas exert feedforward and
feedback influences through distinct frequency channels. bioRxiv, 1-11.
Siegel, M., Donner, T.H., and Engel, A.K. (2012). Spectral fingerprints of large-scale
neuronal interactions. Nature Reviews Neuroscience 13, 121-134.
Lipsman, N., Kaping, D., Westendorff, S., Sankar, T., Lozano, A.M., and Womelsdorf, T.
(2014). Beta coherence within human ventromedial prefrontal cortex precedes affective
value choices. Neuroimage 85 Pt 2, 769-778.
Gross, J., Schmitz, F., Schnitzler, I., Kessler, K., Shapiro, K., Hommel, B., and Schnitzler,
A. (2004). Modulation of long-range neural synchrony reflects temporal limitations of
visual attention in humans. Proc Natl Acad Sci U S A 101, 13050-13055.
Siegel, M., Donner, T.H., Oostenveld, R., Fries, P., and Engel, A.K. (2008). Neuronal
synchronization along the dorsal visual pathway reflects the focus of spatial attention.
Neuron 60, 709-719.
Roopun, A.K., Kramer, M.A., Carracedo, L.M., Kaiser, M., Davies, C.H., Traub, R.D.,
Kopell, N.J., and Whittington, M.A. (2008). Temporal Interactions between Cortical
Rhythms. Frontiers Neuroscience 2, 145-154.
Kopell, N., Whittington, M.A., and Kramer, M.A. (2011). Neuronal assembly dynamics
in the beta1 frequency range permits short-term memory. Proc Natl Acad Sci U S A 108,
3779-3784.
Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., and Wu, C.
(2004). Interneurons of the neocortical inhibitory system. Nature Reviews Neuroscience
5, 793-807.
Kawaguchi, Y. (2001). Distinct firing patterns of neuronal subtypes in cortical
synchronized activities. Journal of Neuroscience 21, 7261-7272.
Kawaguchi, Y. (1997). Selective cholinergic modulation of cortical GABAergic cell
subtypes. Journal of Neurophysiology 78, 1743-1747.
Pouille, F., Marin-Burgin, A., Adesnik, H., Atallah, B.V., and Scanziani, M. (2009). Input
normalization by global feedforward inhibition expands cortical dynamic range. Nature
Neuroscience 12, 1577-1585.
Womelsdorf, T., Valiante, T.A., Sahin, N.T., Miller, K.J., and Tiesinga, P. (2014).
Dynamic circuit motifs underlying rhythmic gain control, gating and integration. Nature
Neuroscience 17, 1031-1039.
S48.
S49.
S50.
S51.
S52.
S53.
S54.
S55.
S56.
S57.
S58.
S59.
S60.
S61.
S62.
S63.
Akam, T., and Kullmann, D.M. (2010). Oscillations and filtering networks support
flexible routing of information. Neuron 67, 308-320.
Berger, T.K., Silberberg, G., Perin, R., and Markram, H. (2010). Brief bursts self-inhibit
and correlate the pyramidal network. PLoS Biology 8.
Mancilla, J.G., Lewis, T.J., Pinto, D.J., Rinzel, J., and Connors, B.W. (2007).
Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex.
Journal of Neuroscience 27, 2058-2073.
Kawaguchi, Y., and Kubota, Y. (1997). GABAergic cell subtypes and their synaptic
connections in rat frontal cortex. Cerebral Cortex 7, 476-486.
Wang, X.J. (1999). Fast burst firing and short-term synaptic plasticity: a model of
neocortical chattering neurons. Neuroscience 89, 347-362.
Brumberg, J.C., Nowak, L.G., and McCormick, D.A. (2000). Ionic mechanisms
underlying repetitive high-frequency burst firing in supragranular cortical neurons.
Journal of Neuroscience 20, 4829-4843.
Cunningham, M.O., Whittington, M.A., Bibbig, A., Roopun, A., LeBeau, F.E., Vogt, A.,
Monyer, H., Buhl, E.H., and Traub, R.D. (2004). A role for fast rhythmic bursting
neurons in cortical gamma oscillations in vitro. Proc Natl Acad Sci U S A 101,
7152-7157.
Borgers, C., Epstein, S., and Kopell, N.J. (2005). Background gamma rhythmicity and
attention in cortical local circuits: a computational study. Proc Natl Acad Sci U S A 102,
7002-7007.
Bosman, C.A., Schoffelen, J.M., Brunet, N., Oostenveld, R., Bastos, A.M., Womelsdorf,
T., Rubehn, B., Stieglitz, T., De Weerd, P., and Fries, P. (2012). Attentional Stimulus
Selection through Selective Synchronization between Monkey Visual Areas. Neuron 75,
875-888.
Gregoriou, G.G., Gotts, S.J., Zhou, H., and Desimone, R. (2009). High-frequency, longrange coupling between prefrontal and visual cortex during attention. Science 324,
1207-1210.
Buschman, T.J., and Miller, E.K. (2007). Top-down versus bottom-up control of attention
in the prefrontal and posterior parietal cortices. Science 315, 1860-1862.
Fries, P., Nikolic, D., and Singer, W. (2007). The gamma cycle. Trends Neurosci 30,
309-316.
Vinck, M., Lima, B., Womelsdorf, T., Oostenveld, R., Singer, W., Neuenschwander, S.,
and Fries, P. (2010). Gamma-phase shifting in awake monkey visual cortex. J Neurosci
30, 1250-1257.
de Almeida, L., Idiart, M., and Lisman, J.E. (2009). The input-output transformation of
the hippocampal granule cells: from grid cells to place fields. J Neurosci 29, 7504-7512.
Womelsdorf, T., Lima, B., Vinck, M., Oostenveld, R., Singer, W., Neuenschwander, S.,
and Fries, P. (2012). Orientation selectivity and noise correlation in awake monkey area
V1 are modulated by the gamma cycle. P Natl Acad Sci USA 109, 4302-4307.
Gollo, L.L., Mirasso, C., Sporns, O., and Breakspear, M. (2014). Mechanisms of zero-lag
synchronization in cortical motifs. PLoS computational biology 10, e1003548.
S64.
S65.
S66.
S67.
Lin, S.C., Gervasoni, D., and Nicolelis, M.A. (2006). Fast modulation of prefrontal
cortex activity by basal forebrain noncholinergic neuronal ensembles. J Neurophysiol 96,
3209-3219.
Hasselmo, M.E., and Sarter, M. (2011). Modes and models of forebrain cholinergic
neuromodulation of cognition. Neuropsychopharmacology : official publication of the
American College of Neuropsychopharmacology 36, 52-73.
Sarter, M., Hasselmo, M.E., Bruno, J.P., and Givens, B. (2005). Unraveling the
attentional functions of cortical cholinergic inputs: interactions between signal-driven and
cognitive modulation of signal detection. Brain research. Brain research reviews 48,
98-111.
Sara, S.J., and Bouret, S. (2012). Orienting and reorienting: the locus coeruleus mediates
cognition through arousal. Neuron 76, 130-141.