Rate-specific synchrony: Using noisy oscillations to
detect equally active neurons
David A. Markowitz*†, Forrest Collman*†, Carlos D. Brody*‡, John J. Hopfield*†§, and David W. Tank*†‡§¶
Departments of *Molecular Biology and¶Physics,†The Lewis Sigler Institute for Integrative Genomics, and‡Princeton Neuroscience Institute, Carl Icahn
Laboratory, Princeton University, Princeton, NJ 08544
Contributed by David W. Tank, April 3, 2008 (sent for review March 18, 2008)
Although gamma frequency oscillations are common in the brain,
their functional contributions to neural computation are not un-
derstood. Here we report in vitro electrophysiological recordings
to evaluate how noisy gamma frequency oscillatory input interacts
with the overall activation level of a neuron to determine the
precise timing of its action potentials. The experiments were
designed to evaluate spike synchrony in a neural circuit architec-
ture in which a population of neurons receives a common noisy
gamma oscillatory synaptic drive while the firing rate of each
individual neuron is determined by a slowly varying independent
input. We demonstrate that similarity of firing rate is a major
determinant of synchrony under common noisy oscillatory input:
Near coincidence of spikes at similar rates gives way to substantial
desynchronization at larger firing rate differences. Analysis of this
rate-specific synchrony phenomenon reveals distinct spike timing
‘‘fingerprints’’ at different firing rates that emerge through a
combination of phase shifting and abrupt changes in spike pat-
robust detection of rate similarity in a population of neurons
ing the biological plausibility of a Many Are Equal computation.
Our results reveal that spatially coherent noisy oscillations, which
are common throughout the brain, can generate previously un-
known relationships among neural rate codes, noisy interspike in-
tervals, and precise spike synchrony codes. All of these can coexist
in a self-consistent manner because of rate-specific synchrony.
gamma oscillations ? neural code ? neural computation
oscillations are typically noisy, exhibiting fluctuations in ampli-
tude and a broad frequency distribution. In vitro experiments
using cortical brain slices (5) have demonstrated that gamma
oscillations can be produced by sustained activation of networks
of inhibitory neurons, which in turn produce highly correlated
rhythmic membrane potential oscillations in the local population
of pyramidal cells (6). This raises the general question of what
role common noisy oscillatory synaptic inputs might play in
producing synchronous action potentials across a population of
neurons with differing mean firing rates. In the presence of
correlated noisy gamma, neurons with the same mean firing rate
would be expected to produce highly correlated spike trains (7).
But what is the level of synchrony that will result when the mean
firing rates are different? These correlations would be function-
ally important because relative spike timing on the millisecond
time scale influences synaptic activation of postsynaptic targets
(8, 9), timing-dependent short-term synaptic plasticity (10, 11),
and pattern recognition (12).
Previous work has shown that weakly correlated noisy input to
a pair of neurons produces an output correlation proportional to
the geometric mean of their firing rates (13). In contrast, we are
interested in the opposite regime of highly correlated common
expected from gamma-producing inhibitory networks; it also is
suggested from in vivo paired intracellular recordings (14).
amma oscillations (30–100 Hz) are observed in field po-
tential recordings from many brain areas (1–4). These
To explore the relationship among common oscillatory drive,
firing rate, and spike synchrony, we developed a network model
(Fig. 1a) in which the average firing rate of each neuron is
independently set by a constant input current, whereas spike
timing is modulated by a common noisy oscillatory current. We
studied this system experimentally by presenting a large se-
quence of stimulus epochs to an individual neuron in a cortical
brain slice. The constant current levels used in the sequence of
epochs were chosen to produce a broad range of mean firing
rates, whereas the amplitude and time course of the noisy
oscillatory current component was unchanged (frozen noise).
We then analyzed spike synchrony for all epoch pairs by numer-
ically simulating synaptic inputs to a postsynaptic coincidence
detector read-out neuron with the timing of the inputs deter-
mined from the spike times from the two recorded spike trains.
In separate analyses, epochs recorded with one neuron also were
compared with those of another neuron recorded in a different
Our analyses reveal that the amount of synchrony between two
neurons is strongly dependent on their relative mean firing rates,
an effect we call rate-specific synchrony. The computational
significance of rate-specific synchrony is that the common noisy
gamma oscillation encrypts the different activation levels of a
population of neurons into a set of distinct neural codes. Each
subgroup of neurons with a similar level of activation has a
and used for pattern recognition or synaptic plasticity.
Whole-cell patch recordings from layer 2/3 pyramidal neurons in
rat somatosensory cortex were stimulated in current clamp for
3-s epochs (Fig. 1). The constant current component was se-
lected from a set of 50 uniformly spaced levels chosen to elicit
action potential rates between 0 and ?30 Hz. The noisy oscil-
lation (Fig. 1c), which was identical for each stimulus epoch and
added to the constant current component, was synthesized in
software to have a Gaussian Fourier spectrum with a charac-
teristic center frequency (Fc) and width (Fw). A run consisted of
150 epochs, with the 50 constant current levels of the stimulus
used in random order and repeated three times. As shown in Fig.
1d, the rate of action potential firing increased with the level of
constant current. Membrane voltage responses to identical
constant current levels demonstrated reproducible spiking be-
havior (Fig. 1d Middle) as reported previously (7). We further
idea of MAE computation with noisy oscillation; D.A.M., F.C., and D.W.T. designed and
performed the electrophysiology experiments; and D.A.M., F.C., C.D.B., J.J.H., and D.W.T.
contributed to analysis methods and wrote the paper.
The authors declare no conflict of interest.
§To whom correspondence may be addressed at: 250 Carl Icahn Laboratory, Princeton
University, Princeton, NJ 08540. E-mail: email@example.com or hopfield@princeton.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2008 by The National Academy of Sciences of the USA
June 17, 2008 ?
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no. 24 www.pnas.org?cgi?doi?10.1073?pnas.0803183105
observed that interspike interval distributions were noisy at each
current level (Fig. 1f i and ii). Spike rasters from the entire run,
ordered from bottom to top by increasing constant current level
used in the stimulus epoch (Fig. 1e), show common firing
patterns within local horizontal strips corresponding to nearby
firing rates. When firing rates differ widely, however, the pat-
terns appear to be qualitatively different, reflecting the com-
bined effects of phase precession and discontinuous changes in
spike timing (see Fig. 1e, shaded vertical box).
The qualitative differences in spike timing observed in raster
plots like those in Fig. 1e suggest that the precise timing of action
potentials might be a ‘‘fingerprint’’ that changes with firing rate.
To quantitatively examine this idea, we evaluated pairwise
synchrony for all possible combinations of rate. Through an
analogy with biological coincidence detectors, the spike re-
sponses from two epochs were treated as distinct inputs to a
simulated postsynaptic coincidence detector neuron. Each input
activated a brief EPSP, and both synaptic inputs were summed
and thresholded (see Methods) (Fig. 2a). The EPSP time con-
stant (2 ms) and spike threshold (1.37) jointly defined a 2-ms
window for synchrony detection; however, the same window
duration was achievable by using longer EPSP time constants
with higher thresholds. For the purposes of analysis, synchrony
was quantified as the number of threshold-crossing events di-
vided by the minimum number of spikes in either epoch. This
measure of synchrony defines the probability of a synchronous
event conditioned on the spikes of the lower firing rate epoch.
In Fig. 2b, synchrony is plotted as a color-coded ‘‘synchrogram’’
for all nonidentical epoch pairs. Epoch number, indexed by
increasing mean firing rate, runs from left to right and bottom
to top along each axis. In general, epochs that are close in
number have higher values of synchrony, producing a blocky
yellow band along the diagonal. To directly examine the depen-
in Fig. 2c. The elevated ridge along the diagonal indicates that
the neuron was synchronously active at identical rates, but
desynchronized when either rate changed (in this example, by
more than ?3 Hz). We also evaluated synchrony restricted to a
shorter time period by producing synchrograms using only the
first 500 ms of spike data from each epoch. This time interval is
consistent with the duration of epochs of elevated gamma power
observed in LFPs in vivo (1, 15, 16). Despite the fact that rates
are not as well sampled within this restricted window, the
resulting synchrogram demonstrates that the ridge develops
shortly after stimulus onset (Fig. 2d).
To evaluate the importance of noisy gamma waveforms for the
generation of rate-specific synchrony, we performed control
experiments using constant current steps without any oscillatory
I S I f o t n
c r e
o i t a l e r r o
modulates spike timing within a population of otherwise independently driven neurons (cells 1 and 2), and synchronous population activity is detected by a
postsynaptic read-out neuron (R). (b and c) To reproduce this model experimentally, whole-cell patch recordings from layer 2/3 pyramidal neurons were
stimulated in current clamp for 3 s with varying levels of constant current (b) combined with a common noisy oscillatory drive (c). The noisy waveform was
levels (Arms? 50%). (d) Four voltage traces from a set of 150 stimulus epochs on a single neuron are shown, including the minimum current (Lower) and the
maximum current (Upper) injected, as well as two examples from an intermediate current. Step amplitudes are 0.12, 0.22, and 0.37 nA. (e) Fifty constant steps
of uniform spacing were presented in random order, with each step repeated three times sequentially for a total of 150 noisy stimulus epochs. Step amplitudes
were chosen to elicit firing between 0 and ?30 Hz. Spike rasters are presented here for all 150 stimulus epochs during the first 500 ms of stimulation. Stimulus
constant current. (f) (i–ii) Interspike interval distributions from a subset of stimulus epochs, pooled into successive 5-Hz ranges. Spike arrival times are irregular.
(iii) Cross-correlograms obtained by comparing spike responses to 0.22-nA epochs only (black line) and all 150 epochs (gray line). Spikes were binned at 2 ms.
Protocol for studying synchrony induced by common noisy oscillations in vitro. (a) In our conceptual network model, a common noisy input (Icommon)
Markowitz et al. PNAS ?
June 17, 2008 ?
vol. 105 ?
no. 24 ?
input, as well as constant steps summed with a pure sinusoid for
the common input. Fig. 2 e and f shows synchrograms from these
control experiments conducted on the same neuron that pro-
duced rate-specific synchrony in response to noisy gamma in Fig.
2c. Rate-specific synchrony does not emerge in response to
constant current steps (Fig. 2e) and only emerges weakly when
a sinusoid is substituted for noisy gamma (Fig. 2f). More
examples are provided in supporting information (SI) Fig. S1 f
To quantify rate-specific synchrony, on-diagonal (ridge) syn-
chrony was defined as the amplitude at zero rate difference,
which is equivalent to calculating the mean of on-diagonal points
in a synchrogram. Off-diagonal (background) synchrony was
defined as the mean across firing rate differences of ?3 Hz,
which corresponds to the area inside the white triangle shown in
Fig. 2c. Strong rate-specific synchrony was consistently observed
(other examples found in Fig. S1a) for our most common
stimulus paradigm of center frequency (Fc? 30 Hz, Fw? 30 Hz,
and Arms? 50%), where Armsrefers to the rms amplitude of the
noisy gamma waveform relative to the range of the constant
current steps. For these synchrograms (n ? 23 runs), mean ridge
amplitude was 0.62 ? 0.16 and mean ridge/background ratio was
3.06 ? 0.41. Similar results were obtained by using stimuli with
other center frequency and bandwidth values (Fig. S1). For
comparison, constant current control experiments (n ? 12) (Fig.
S1f) produced a mean ridge amplitude of 0.06 ? 0.01, and the
mean ridge/background synchrony was 1.02 ? 0.16. For the pure
sinusoid control experiments (n ? 8) (Fig. S1g), the mean ridge
amplitude was 0.33 ? 0.06 and the mean ridge/background
synchrony was 1.52 ? 0.20. These quantifications demonstrate
noisy gamma waveform plays an important role in its generation.
These results suggest that rate-specific synchrony could be
useful as a computational mechanism in a network where each
neuron receives independent time-varying inputs. Specifically, it
might be used to determine whether and when many neurons in
a network share a similar level of activation, thus implementing
a form of pattern recognition known as Many Are Equal (MAE)
(17). To explore this idea, we considered the network architec-
ture shown in Fig. 3a, consisting of 10 neurons that share a
common noisy gamma input, but also have slowly varying
independent inputs (Fig. 3b). To study this experimentally, 10
different input current patterns were sequentially presented to
an individual cortical neuron, and the elicited spike responses
were later used to calculate the response in a postsynaptic
detector cell produced by the summed synaptic responses of the
10 neurons. Each input current pattern started at a different
level, converged to a common sustained level, and then diverged
added to each waveform to produce the 10 stimulus epochs of
10-s duration. Spike rasters obtained from a neuron using this
protocol are shown in Fig. 3c. Elicited firing rates ranged
between 5 and 30 Hz, and the mean firing rate, averaged over all
stimulus epochs, remained relatively constant throughout the
stimulus. Individual spike rasters (Fig. 3d) were used as input to
a synchrony detector (see Methods) (Fig. 3a). When a simple
threshold was applied to this waveform, all threshold-crossing
events occurred during or near the central period when firing
rates were similar (Fig. 3e) despite the fact that mean rate over
all of the inputs was approximately constant across the entire
stimulus epoch (Fig. 3f). Similar results were obtained for a
biologically more realistic stimulus paradigm involving time-
varying independent baseline currents (Fig. S2). This result
directly demonstrates the feasibility of using rate-specific syn-
chrony for MAE computation.
In the preceding analyses, the response of a single neuron was
compared against itself on different epochs to examine whether
synchrony was rate-specific and to demonstrate MAE compu-
tation. These approaches used the repeated stimulation of a
single neuron as a proxy for stimulating a group of neurons of a
similar type. Although this strategy was used for its technical
Gamma (0-3 sec)
Gamma (0-0.5 sec)
DC only (0-3 sec)
30 Hz sine (0-3 sec)
d i R
Gamma (0-3 sec)
Synchronous events between two stimulus epochs (ii) are identified by con-
volving each spike raster with an EPSP synaptic kernel, summing the resulting
waveforms (i) and applying a threshold (indicated by the dotted line). Spike-
conditional synchrony is then quantified by dividing the number of threshold
crossings by the minimum number of spikes in either stimulus epoch. In this
example, taken from the experiment shown in Fig. 1, synchronous spikes are
in red, and threshold crossings in the synaptic trace are marked with an
asterisk. There are 10 synchronous events and 30 reference spikes in stimulus
epoch 51, corresponding to 33% synchrony. An EPSP kernel with a maximum
a synchrony threshold of 1.37. The result is that two spikes must occur within
2 ms to be considered synchronous. (b) A synchrogram is used to visualize
synchrony for all stimulus epoch pairs. The color of each (x,y) location in the
plane corresponds to the degree of synchrony between each epoch pair at x,y
synchrony between all 150 stimulus epochs from Fig. 1. Stimulus epoch num-
to top. In general, stimulus epoch pairs with similar firing rates exhibit higher
synchrony than stimulus epochs with different firing rates, leading to a ridge
of elevated synchrony along the diagonal. Below the x axis of the false color
plot, the inset plots mean firing rate as function of epoch number. Note the
presence of nonlinearities that contribute to the uneven quality of the ridge
in the above plot. (c–f) Rate–rate synchrograms are created by averaging
synchrony values for all epoch pairs that have the same combination of mean
firing rates, rounded to the nearest integer Hz. Synchrograms are plotted as
in b, but with firing rates on the axes. This analysis eliminates the nonlineari-
ties observed in b. (c) Rate–rate synchrogram for all 150 trials evaluated over
a 3-s window. The elevated ridge along the diagonal is characteristic of
rate-specific synchrony, in which spike timing is reliable at similar rates, but
desynchronization occurs at different rates. A quantitative measurement of
rate-specific synchrony is obtained by dividing the mean on-diagonal (ridge)
synchrony by the mean off-diagonal (background) synchrony. Ridge ampli-
tude is calculated by averaging over all identical rate pairs. Background
amplitude is calculated by averaging over all pairs with ?3-Hz rate difference
(area within white triangle). (d) Rate–rate synchrogram for the same data
calculated by using spikes from the first 500 ms of each epoch. (e and f)
Constant current (DC) steps were presented without additive gamma (e) and
with an additive 30-Hz sine wave (f).
www.pnas.org?cgi?doi?10.1073?pnas.0803183105Markowitz et al.
simplicity, it was unable to account for the expected variability
in physiological properties among a population of functionally
similar neurons in an intact circuit. To examine whether rate-
specific synchrony exists in the responses of different neurons,
we compared epochs from all nonidentical neuron pairs that
were stimulated by using our 3-s protocol (Fig. 1). As shown in
Fig. 4a (also see Fig. S1e), rate-specific synchrony was found in
some cross-neuron synchrograms. This result occurred despite
differences in animal age, postdissection incubation time, and
the precise anatomical location of the recorded cell. Some
insight into what conditions might be necessary for rate-specific
synchrony to be produced in vivo were obtained by grouping
neurons based on the evoked rms fluctuations in the recorded
voltage waveforms (Fig. 4b). This analysis reveals that pairs of
neurons that responded with voltage fluctuations of similar
amplitude showed stronger rate-specific synchrony than those
with very different fluctuations. Additionally, neuron pairs with
large absolute voltage fluctuation amplitudes showed strong
rate-specific synchrony. These results suggest that the relative
and absolute stimulus amplitudes are important determinants of
Although our experiments were motivated by evidence for
highly correlated noisy oscillatory input (14), as in the gamma
feedback produced by an activated network of oscillating inhib-
itory interneurons, it is unlikely that the input to any two neurons
in a population will have perfect stimulus correlation. Therefore,
we tested the robustness of pairwise rate-specific synchrony to
reduced correlation of the common noisy gamma input. A
correlation between the common gamma input during different
epochs ranged between 0.8 and 1.0 (see Methods). As with the
original 3-s paradigm, this stimulus ensemble was characterized
by Fc? 30 Hz, Fw? 30 Hz, and Arms? 50%, and data were
analyzed by using a 2-ms synchrony window. To control for
heterogeneity in relative stimulus amplitude and cell properties,
only same-cell comparisons were performed. The results (Fig.
4c) suggest that ridge/background ratio is robust to reduced
stimulus correlation down to ?0.9 (1.44 ? 0.18, n ? 5). We
verified that MAE computation remains feasible in this regime
by modifying the stimulus paradigm from Fig. 3 to use 0.9
correlated gamma waveforms (Fig. S2).
at 2-ms temporal resolution (8, 9), but how the size of this
neuron in the population receives independent time-varying excitatory drive
(I1–I10) and a common oscillatory input (Icommon). All 10 neurons provide
synaptic input to a postsynaptic read-out neuron (R) that reports population
synchrony by generating action potentials. (b) To reproduce this model ex-
perimentally, a single L2/3 cell was injected with 10 waveforms of 10-s dura-
remain fixed at a common value for 3 s, followed by another 3.5-s interval,
during which they linearly diverge to 10 distinct levels. The time-averaged
stimulus amplitude is identical for each epoch, as illustrated by waveform
color coding: A high initial level is matched with a low final level, and vice
forms. During the experiment, a common noisy oscillatory stimulus with Fc?
by increasing initial constant current level and color-coded to match b. Stim-
ulus epochs were presented in a random order during the experiment. (d)
Spike rasters from each stimulus epoch were convolved with the EPSP kernel
(? ? 2 ms) and summed to mimic synaptic input to a coincidence detector
postsynaptic to 10 neurons. A threshold of six events was applied to detect
population synchrony. (e) Ticks indicate threshold-crossing events in d. Pop-
ulation synchrony is greatly enhanced during the time period when all firing
rates are approximately equal. (f) Average firing rate across all 10 epochs
calculated by counting spikes in sequential bins of 220 ms. Average firing rate
remains unchanged across time.
Rate-specific synchrony underlies MAE computation. (a) Model net-
Cell 1 - RMS Voltage (mV)
a t l o
R - 2 l l e
Cross-Cell Ridge/BackgroundCross-Cell Synchrogram
Synchrony Window (ms)
o i t a
Cell 1 - Rate (Hz)
( e t a
R - 2 l l e
o i t a
grams were generated by comparing stimulus epochs from two different
neurons. In this example, the horizontal and vertical axes now index-separate
a function of the rms amplitude of evoked membrane potential fluctuations
in each cell (n ? 5, all pairs). This ratio decays as the difference in stimulus
amplitude increases. When stimulus amplitudes are equal, the ratio increases
with increasing stimulus amplitude. (c) Summary of same-cell ridge/
Fc? 30 Hz, Fw? 30 Hz, and Arms? 50% (n ? 5 at all correlations) analyzed by
using a 2-ms synchrony window. In each experiment, a common gamma
waveform was corrupted by summation with an independently generated
gamma waveform during each epoch to yield a desired mean pairwise stim-
ulus correlation across epochs (see Methods). (d) Summary of same-cell ridge/
background synchrony versus synchrony window duration for all 23 experi-
ments with Fc? 30 Hz, Fw? 30 Hz, and Arms? 50%. In this analysis, EPSP time
constants ranged from 2–10 ms with a fixed threshold of 1.37.
Robustness of pairwise rate-specific synchrony. (a) Cross-cell synchro-
Markowitz et al.PNAS ?
June 17, 2008 ?
vol. 105 ?
no. 24 ?
detection window varies across brain regions remains unknown.
To explore how rate-specific synchrony measurements change
with increasing synchrony window duration, we reanalyzed the
data from our 3-s protocol (Fig. 1) by using 2- to 10-ms windows
(Fig. 4d). This analysis demonstrates that ridge/background
synchrony decays with increasing window duration, approaching
a ratio of 1.3 ? 0.17 (n ? 23) at 6 ms. We conclude that neurons
must be capable of detecting synchronous events at temporal
resolutions of ?6 ms for rate-specific synchrony to be used
computationally in the brain.
Read-out of synchrony using a biologically inspired coinci-
dence detector differs from other methods commonly used to
study correlated activity in the brain. To address whether our
results were dependent on the specific method we used, we also
analyzed our 3-s stimulus data by using correlation coefficient
(13) and spike cross-correlation as measures of synchrony. As
show a prominent diagonal ridge characteristic of rate-specific
synchrony, and both techniques estimate higher ridge/
background ratios than those obtained with our method at all
Several previous conceptual models have addressed the rela-
tionship between gamma oscillations and neural synchrony (4,
18–20). Most have focused on phase codes during sinusoidal
oscillation, in which the timing of an action potential changes
systematically with neuron depolarization (21). Notably, how-
ever, phase models based on sinusoidal drive fail to account for
Poisson-like interspike intervals commonly observed in single-
unit recordings (22, 23). Rate-specific synchrony resolves this
issue by demonstrating that noisy oscillations produce a finger-
print of irregular spike timings that changes with firing rate,
rather than simple phase precession. Although this encoding is
complex and constantly changing, the commonness of this code
across a population of neurons would permit its use in neural
information representation and computation. Fig. 3 demon-
strates that rate-specific synchrony can be used to implement
MAE computation, a powerful algorithm for scale-invariant
pattern recognition (17).
When comparing our results to in vivo electrophysiological
recordings, it is important to consider that rate-specific syn-
chrony is likely to exist only while noisy gamma oscillations are
present. This notion directly follows from our observation that
no synchrony is produced in the absence of oscillatory input (Fig.
2e). Gamma oscillations in anesthetized (15), and behaving
animals (1, 16) often show brief epochs of high power, typically
with 100- to 300-ms duration. Because rate-specific synchrony
emerges shortly after gamma onset (Fig. 2d) and degrades
rapidly after gamma offset (Fig. S4), we would expect only brief
periods of rate-specific synchrony to be associated with these
brief gamma epochs in vivo.
The evaluation of rate-specific synchrony in vivo would be best
performed by dual intracellular recording in awake animals,
which, despite experimental advances (24, 25), remains techni-
that exhibit high peak amplitudes when rates are similar and
gamma oscillations are present. By contrast, low cross-
correlation peaks would be expected when long spike trains are
compared without consideration of firing rate differences or
LFP power in the gamma band, as is typically done with in vivo
data. This expected reduction in peak amplitude can be dem-
onstrated with our own in vitro experimental data (see Fig. 1f iii
and Fig. S4f). A recent study showed that weak pairwise corre-
lations also can occur because of low input stimulus correlation
and demonstrated that spike correlations are determined by the
geometric mean of firing rates in this regime (13). Here we show
that spike correlation progressively moves to the regime of
rate-specific synchrony as common noisy input correlation
strengthens (see Fig. S5). This result would only be evident from
in vivo recordings if the data were properly parsed by rate and
the presence of gamma.
More work is required to understand how changing the
parameters of the noisy oscillation, such as its center frequency,
bandwidth, and phase relationships, changes rate-specific syn-
chrony. In addition, modulation of currents that change the
dynamic time scales of spike generation may modify or gate
rate-specific synchrony (26). Preliminary numerical simulations
using leaky integrate-and-fire and Hodgkin Huxley model neu-
rons indicate that rate-specific synchrony can be reproduced in
silico. Such studies were important in the design of our experi-
ments and, together with analytical approaches (27), should
provide a fertile testing ground for exploring this phenomenon.
Our present findings suggest that rate-specific synchrony is an
emergent property of any neural system subject to common-
mode noisy oscillations. Because MAE computation is trivially
performed under such conditions, as shown in Fig. 3, we suggest
a general role for this framework in brain areas where noisy
oscillations, highly correlated synaptic input, and neuronal syn-
chrony are observed.
Electrophysiology. All experiments were performed in compliance with the
Guide for the Care and Use of Laboratory Animals (www.nap.edu/
readingroom/books/labrats). Specific protocols were approved by the Prince-
isofluorane and decapitated, and the brain was removed under cold (?5°C)
1.25 mM NaH2PO4, 1.8 mM Dextrose, 1.8 mM MgSO4, and 1.6 mM CaCl2
continuously bubbled with 95% O2/5% CO2). Then 300-?m-thick semicoronal
somatosensory cortical slices were prepared by using a VS 1000 vibratome
(Leica) and incubated at room temperature (T ? 20–22°C) in an interface
chamber. After 1–5 h, individual slices were placed in a submerged slice
recording chamber and maintained at 32–35°C, with aCSF perfused at 2–4
ml/min flowing over both surfaces.
Blind whole-cell patch recordings were acquired from layer 2/3 cortical
neurons using 4–7 M? pipettes pulled with 1.2-mm OD/0.6-mm ID glass (FHC)
on a P2000 puller (Sutter Instruments) and filled with intracellular solution
[148 mM K-gluconate, 10 mM Hepes, 2 mM MgCl2, 3 mM ATPNa2, and 0.3 mM
headstage and digitized at 10 kHz (Digidata 1322A, Clampex software; Mo-
Stimulus Generation and Presentation. Stimulus waveforms were created in
Matlab (Mathworks) and imported as analog waveforms into Clampex (Mo-
lecular Devices). Experiments were performed in episodic stimulation mode,
with a sequence of 150 3-s stimulus epochs applied to the external command
of the BVC-700 operating in current clamp. The common oscillatory stimulus
waveforms were created in Matlab by using the inverse Fourier Transform
function operating on a 30,000-element conjugate symmetric Fourier Spec-
trum vector with a Gaussian amplitude profile and random independent
phases. The Gaussian amplitude was characterized by two parameters: center
frequency and width. The noisy oscillation was rescaled and added to 50
was a specific fraction of the maximum constant step. The 50 constant steps
were placed in random order, with each step repeated three times sequen-
tially, for a total of 150 stimulus epochs in each run. Oscillation parameters
to the maximum constant current step value. Parameter values were chosen
for consistency with published EEG and LFP power spectra (28–30). Most
commonly, experiments (n ? 23) were done with 30 Hz Fc, 30 Hz Fw, and 50%
Arms. Stimuli were offset and rescaled in amplitude for individual neurons in
Clampex so as to induce firing between 0 and ?30 Hz. A 5-s rest interval at 0
nA constant current was given between stimulus epochs. Thirty-eight runs of
150 stimuli were performed on 26 neurons in 13 preparations. Longer 10-s
stimuli involving time-varying currents (Fig. 3 and Fig. S2) were created in a
similar way. A 100,000-element Gaussian-profiled Fourier spectrum vector
www.pnas.org?cgi?doi?10.1073?pnas.0803183105Markowitz et al.
with random phases was used to create the common oscillatory drive. The Download full-text
common drive was then added to the 10 distinct current waveforms (Fig. 3b
and Fig. S2b) after being scaled such that the Armsof the common drive was
25% or 50% of the dynamic range of currents presented. For decorrelation
experiments, a frozen gamma waveform was chosen for a run, and on each
epoch, a randomly generated and rescaled gamma waveform was added to
the frozen gamma stimulus to produce the desired ensemble correlation
value. Each decorrelated stimulus waveform was then rescaled to guarantee
the desired Armsfor that epoch. Twenty-two total runs of 150 stimuli were
performed on 18 neurons in seven preparations by using this paradigm.
Synchrony Analysis. Action potential onset times were detected in Matlab by
thresholding high-pass-filtered (10-Hz cutoff) membrane voltage waveforms
to create spike rasters. Pairwise synchrony between two stimulus epochs was
calculated by convolving each raster with a synaptic kernel, S(t) ? e?t/??
defined for t ? 0 with ??? 2 ms and adding the outputs together. The
maximum value at t ? 0 was 1. A synchronous event was identified when the
resulting waveform crossed a threshold of 1.37, chosen to yield a synchrony
window duration of 2 ms. (Larger values of ??can yield the same window
duration provided a suitable threshold is chosen.) Synchrony was then calcu-
lated as the number of synchronous events divided by the minimum spike
count in either raster. This measure of synchrony defines the probability of a
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to span the desired window; otherwise, synchrograms were created using the
same procedure. On-diagonal (ridge) synchrony, ridge width, and off-
diagonal (background) synchrony were used to characterize synchrograms as
defined in the text.
for help with pilot slice experiments. This work was supported by National
Energy Computational Science Graduate Fellowship Grant DE-FG02-
97ER25308 (to D.A.M.).
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Markowitz et al. PNAS ?
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vol. 105 ?
no. 24 ?