Synaptic convergence regulates synchronization-dependent spike transfer in feedforward neural networks
Synaptic convergence regulates synchronization-dependent spike transfer in feedforward neural networks
Pachaya Sailamul 0 1
Jaeson Jang 0 1
Se-Bum Paik 0 1
Action Editor: Maxim Bazhenov 0 1
0 Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology , Daejeon , Republic of Korea
1 Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology , Daejeon , Republic of Korea
Correlated neural activities such as synchronizations can significantly alter the characteristics of spike transfer between neural layers. However, it is not clear how this synchronization-dependent spike transfer can be affected by the structure of convergent feedforward wiring. To address this question, we implemented computer simulations of model neural networks: a source and a target layer connected with different types of convergent wiring rules. In the Gaussian-Gaussian (GG) model, both the connection probability and the strength are given as Gaussian distribution as a function of spatial distance. In the Uniform-Constant (UC) and Uniform-Exponential (UE) models, the connection probability density is a uniform constant within a certain range, but the connection strength is set as a constant value or an exponentially decaying function, respectively. Then we examined how the spike transfer function is modulated under these conditions, while static or synchronized input patterns were introduced to simulate different levels of feedforward spike synchronization. We observed that the synchronization-dependent modulation of the transfer function appeared noticeably different for each convergence condition. The modulation of the spike transfer function was largest in the UC model, and smallest in the UE model. Our analysis showed that this difference was induced by the different spike weight distributions that was generated from convergent synapses in each model. Our results suggest that, the structure of the feedforward convergence is a crucial factor for correlation-dependent spike control, thus must be considered important to understand the mechanism of information transfer in the brain.
Spike transfer function; Feedforward networks; Synaptic convergence; Spike synchrony; Neural oscillation
Pachaya Sailamul and Jaeson Jang contributed equally to this work.
Correlated neural activities are commonly found in the brain
(Salinas and Sejnowski 2001)
. In a large neural network, mutual
interaction between individual neurons often induces correlated
neural activities such as periodic oscillations in firing rate, as
reported in both experimental
(Buzsáki et al. 1992; Buzsáki
and Draguhn 2004; Courtemanche et al. 2003; Donoghue et al.
1998; Engel and Singer 2001; Klimesch 1996; Singer and Gray
and computational studies
(Engel and Singer 2001; Fries
. In general, correlated neural spike activities appear as
various forms of spike synchronization
(Gray and McCormick
1996; Salinas and Sejnowski 2001; Varela et al. 2001; Ward
and may play an important role in the information
processing in the brain
(Engel et al. 2001; Fries et al. 2001; Ward
2003; Womelsdorf et al. 2007)
. A number of studies have
reported that disruption of neural synchronization can result in a
cognitive dysfunction (
Başar and Güntekin 2008
Dinstein et al.
Grice et al. 2001
Hammond et al. 2007
Uhlhaas and Singer 2006
, 2010). In particular,
previous studies have reported that correlated neural activities can
alter spike transfer functions between neural layers
2009; Ratté et al. 2013; Wang et al. 2010)
, implying that varying
spike transfer may play a role in modulating the dynamics of a
neural network. However, it is not clear yet, if this
synchronization-dependent spike transfer, which might work as
a mechanism of dynamic control of spike transfer, can be
achieved conditionally on a specific feedforward pathway
structure, or rather, be achieved independent of underlying circuitry.
Here we address this question by performing computer
simulations of feedforward neural networks with different types of
convergent synaptic connections.
A feedforward network is generally composed of
unidirectional interlayer connections from the lower (source) to the
higher (target) level neural layers
(Felleman and Van Essen
1991; Kumar et al. 2010)
. In most cases, each cell in the target
layer receives input from more than one source cell through
convergent synaptic connections, as observed in the
thalamocortical connections in the visual system (Hubel and
Wiesel 1962). Here we hypothesize that the achievement of
synchronization-dependence of spike transfer is reliant on
convergent wiring in the feedforward pathway.
To test our idea, we developed a model simulation of three
convergence rules that have different spatial distributions of
synaptic connection probability and strength. This included one
where the connection probability and the strength were
independent of the spatial distance between source and target cells, and
one where all the connection parameters systemically changed as
a function of neural distance. Then we examined how the spike
transfer function changes under these conditions, while we varied
the synchronization level of input spikes.
We first confirmed that the spike transfer function of the
model neural network alters depending on the level of input
synchronization. In addition, we found that the modulation of
spike transfer function strongly depends on the
convergencewiring rule, because the synchronization-dependency of
transfer function appeared significantly different in each
convergence model. We observed that the spike transfer function of
the target neuron was sensitively altered by the convergence
structure, because the weight distribution of input spikes were
significantly different in each convergence condition, even for
identical input sources.
This result suggests that feedforward convergence is a
crucial factor for achieving the correlation-dependent spike
transfer in neural systems, and may provide insight about the
mechanism of information processing in the brain.
2 Materials and methods
2.1 Development of cell mosaics
To decide the spatial distribution of cells in source and target
layers, we used an adapted version of a pairwise interaction
point process (PIPP) model, which is a computational model
of cell mosaic development
(Eglen et al. 2005)
, where each
cell is relocated until the new position satisfies the designed
mosaic statistics (Fig. 1a,b). As a modification of the PIPP
model, we introduced a local repulsive interaction between
the nearby cells that induces a gradual shift of each cell
position. Source and target layers were developed independently
from an initial random distribution of cells. To avoid the
sampling bias in the boundary area, the target layer was designed
smaller than the source layer, with different unit distances for
source (ds) and target (dT) layers, dS ¼ 2:2dT .
For the local repulsive interaction, we used a sigmoidal
function !F !r , so that the strength of repulsion increases
as two cells at !x1 and !x2 get closer.
¼ < 1−exph−n
!r −δ .ϕo i
δ < !r < 2d
where !r ¼ !x1− !x2, the coefficient a = 10−5, !u ¼ !!r and
the parameters for sigmoidal function were α=1.6, ϕ=5.7d
At each time t, velocity of a cell !vt is decided by the sum
of all repulsive interactions between the target and other cells,
!vt ¼ !vt−1 þ !Fnet;t
!Fnet;t ¼ ∑i !Fi;t−c !vt−1
To prevent too fast movement of cells, c !vt−1 !vt−1 was
added as a friction term, where c = 0.1. We allowed 5000
iterations for the development of each mosaic.
2.2 Single model neuron
We developed a single model neuron in the target layer using
(Carnevale and Hines 2006)
, based on
the Hodgkin-Huxley model
(Hodgkin and Huxley 1952)
C dt ¼ −gLðv−V LÞ−GNaðv−V NaÞ−GK ðv−V K Þ−GCaT ðv−V CaT Þ
where C is membrane capacitance, gL is leakage conductance,
gE is excitatory synaptic conductance from input spikes, GX is
conductance for X ion channel, and VX is reversal potential for
the X ion channel. We included a sodium channel (Na), a
potassium channel (K), a T-type calcium channel (CaT), and
an excitatory synaptic input channel (E). The ion channel
conductance terms GNa, GK, and GCaT are functions of membrane
potential v, and take the general form as in previous studies
(Hodgkin and Huxley 1952)
. The parameter values were
determined from previous studies
(Hodgkin and Huxley 1952)
as GNa = 120 mS/cm2, GK = 36 mS/cm2, GL = 0.4 mS/cm2, GCaT
= 2 mS/cm2, ENa = 55 mV, EK = −80 mV, EL = −65 mV, ECaT =
126.1 mV . A single neuron was designed as a point model of
cylindrical shape with both height and diameter equal to 28 μm.
The membrane capacitance was set to 1 μF/cm2 and resistance to
200 ohm· cm. All the synaptic interactions, or excitatory
distance between source and target cells. (d–e) Uniform-Constant (UC)
and Uniform-Exponential (UE) models: The connection probability is
uniform within a certain range and the connection strength is set as a
constant (UC) or an exponentially decaying function (UE), respectively.
The dotted lines indicate the range of allowed variation of connection
strength across target neurons. (f) Sum of connection strength (Σw) for
different conditions of convergence: Σw increases as rc or wc increases.
P22 was selected for further analysis. (g-h) Amplitude of oscillation in
mean firing rate of source neurons modulates the level of synchronization
in source activity: (g) Static (Af = 0) input generated by source cells, (h)
Synchronized input (Af = 1). Top, Instantaneous firing rate of source cells.
Bottom, Raster plot of spikes in 100 source cells. Synchronization in spike
timings is observed for synchronized input
postsynaptic conductance (EPSC) were modeled as
twoparameter alpha function, gE(t) = w · [exp(−t/τ2) − exp(−t/τ1)],
where τ1= 1 ms and τ2= 3 ms are the rise and decay time
constants, and w is a synaptic-strength weight factor
. The activities of neurons in the network were
simulated for five seconds in each trial, and were repeated for 10
2.3 Model feedforward networks of different convergence rules
To build up a simple feedforward network, we first developed
cell mosaics of source and target layers of network, using an
adapted version of a pairwise interaction point process (PIPP)
(Eglen et al. 2005)
, which assumes a local repulsive
interaction between neighboring cells (Fig. 1a, see Methods
2.1 for detailed model design). The source and target layers
included 1150 and 166 cells, respectively. For simplicity, all
the neurons were assumed to be excitatory and all the spatial
length units were normalized with the expected unit distance
(dS ) between two cells in the source layer when every cell is
distributed in a perfectly hexagonal lattice pattern. To develop
various convergent connections between the source and target
layers (Fig. 1b), we designed three wiring rules that consider
only two variables: connection probability and connection
strength (Fig. 1c,d, and e).
First, in the Gaussian-Gaussian (GG) model, which is
conventionally used for inter-neural connectivity in network
(Paik et al. 2009; Paik and Glaser 2010; Ringach
, the synaptic connection probability and connection
strength follow the 2D Gaussian as a function of distance
between the source and target cells: y ¼ A exp − 2dσ22 , where
d is distance between cells, A is the maximum probability at
d = 0, and σ is the standard deviation, which controls the width
of the Gaussian curve (Fig. 1c, left). For connection
probability in our model, A was set to 0.85 within the range of
connection rc= 3σ, and to 0 outside this range
(McLaughlin et al.
2000; Reid and Alonso 1995)
. Under this condition, we could
estimate the expected number of convergent connections per
target neuron, n, from the area below the connection
probability distribution (Fig. 1c, middle). Using this number n in the
GG model, we made a calibration between convergence
models so that the actual number of connections was about
the same in all models. Next, the connection strength for the
GG model was defined similarly, by the same Gaussian
function where the maximum strength of connection wc was set as
a variable to determine the strength level of synaptic
connections (Fig. 1c, right).
For the other two convergence rules, Uniform-Constant
(UC) and Uniform-Exponential (UE) models, the connection
probability does not depend on the distance between the
source and target cells. This connection probability is set as
a uniform distribution within the range rc estimated in the GG
model (Fig. 1d and e, middle), and the constant value of this
connection probability is calculated so that the expected
number of connections per target neuron becomes the same as n in
the GG model.
The connection strength for each target cell in the UC and
UE models were also normalized so that the expected value of
total connection strength ( ∑ w) for each target cell was the
same in all models. In the UC model, the connection strength
of every synapse connected to a specific target cell was set to a
constant, wc' (Fig. 1d, right), which is the mean of connection
strength connected to that target cell in the GG model. In the
U E m o d e l , w hi c h is b a s ed on t h e o b s e r v at i o n o f
(Jin et al. 2011)
, the strength of each
connection was randomly sampled from an exponentially
decaying probability distribution, p(w) = λ exp(−λw),
independent of the distance between the source and target cell
(Fig. 1e, right). Also in this case, the value of λ was properly
chosen so that the sum of connection strength was always
equal to that in GG model. Due to the stochastic process in
connection wiring, the value of wc' and λ slightly vary for each
2.4 Variation of convergence parameters and total synaptic weight
In our convergence models described above, the sum of all
convergent synaptic connection weight for a target neuron can
be represented by two parameters in the GG model:
range of connection, rc and strength of connection, wc
(Fig. 1c). This is because the other two models are set
to have the same amount of total synaptic weight as the
GG model. In general, rc decides how many source
cells will be connected to a target cell, and wc
determines how strong the connections will be. As each
parameter increases, the total feedforward connection
strength ∑w increases. To test various cases of
convergence parameters and connection strength ∑w within
each model, we simulated the activity of a model
network for 36 parameter sets (P1–P36, Fig. 1f).
2.5 Static and synchronized input spike patterns
To simulate different conditions of input spike correlation, two
types of input pattern (static and synchronized (Sync) inputs)
were designed to provide a source activity for the feedforward
network (Fig. 1g, h). The static input pattern of a source cell
was generated by a Poisson spike generator with constant
mean firing rate, fc= 20 Hz (Fig. 1g, top). On the other hand,
for synchronized input, mean firing rate f(t) of the spike
generator of each cell was given as a sinusoidal function (Fig. 1h,
f ðtÞ ¼ f c 1 þ A f sinð2π f OSCtÞ
Because the phase of the oscillation is identical for all the
source neurons, this oscillation induces synchronized activity
in the input spikes of source neurons (Fig. 1g, h, bottom). For
the synchronized input pattern, we simulated different levels
of oscillation by varying Af from 0 (no synchronization, or
static; Fig. 1g) to 1 (Strong synchronization; Fig. 1h). The
frequency of oscillation fosc was set to 40 Hz to model a
gamma band oscillation.
3.1 Synchronization-dependent response modulation in a feedforward network
We investigated the synchronization-dependent spike transfer
of the three different convergent feedforward model networks.
We measured the response of target neurons while varying the
spike patterns of the source neurons, from static to strongly
synchronized (Af= 0 to 1), as different levels of synchronized
To investigate the response activity of the target
layer, the Bspike transfer function^ of a network was
estimated by measuring the firing rate of the target layer as
the response (R) to a given input of fixed spike counts.
Furthermore, Bsynchronization-dependent spike transfer^
was defined as the ratio between spike transfer for
synchronized input and for static input (RSync/RStatic), to
examine the effect of input synchronization more
First, we compared the spike transfer between the
convergence models. For a fixed parameter set, we observed that
spike transfer increased as the input synchronization became
stronger (Fig. 2a). Interestingly, we noted that the mean firing
rate of the target neurons appeared different across the
convergence models for each type of given input. Because our
main interest was not the spike transfer itself, but how
much the response increased for the synchronized input,
we measured the Bsynchronization-dependent spike
transfer^, the ratio between the responses for static and
synchronized input patterns (RSync/RStatic) (Fig. 2b).
Although the response itself was greatest in the UE
model for all the input, the ratio of increase of firing
rate for synchronized input was greatest in the UC
model. For further statistical analysis, we selected three
conditions of synchronization Af= 0 (static), 0.5 (weak
Sync), 1 (strong Sync), and confirmed that both the
mean firing rate and the ratio between the static and
synchronized conditions were significantly different across
convergence models in all cases (* p = 5.7×10−6, ** p = 9.2×10−10,
*** p = 1.1×10−10, one-way ANOVA followed by post hoc
Bonferroni analysis; Fig. 2c and * p = 4.8×10−9, **
p = 1.7×10−14, one-way ANOVA followed by post hoc
Bonferroni analysis; Fig. 2d).
Next, to confirm the difference between the models for the
other convergence conditions, we observed that the mean
firing rate of target neurons increased as the total feedforward
connection strength (Σw) increased in the 36 different
conditions of parameter sets (P1-P36) we tested (Fig. 2e). This
relationship between the sum of synaptic weight Σw and the
firing rate of response was well fitted to a linear function. We
found that the slope of this linear fit noticeably varied as we
varied the input spike correlation from static to synchronized
patterns (Fig. 2e). In all three convergence models (GG, UC,
and UE), the slope increased as the correlation level in the
input increased (* p = 7.2×10−17, ** p = 1.0×10−22, ***
p = 1.4×10−24, one-way ANOVA followed by post hoc
Bonferroni analysis; Fig. 2f). This result confirms that
synchronized or temporally correlated inputs can transfer more
spikes than uncorrelated inputs in a feedforward network. In
other words, even when the number of input spikes is the
same, the number of transferred spikes can significantly vary
depending on the level of input synchronization. This
suggests a synchronization-dependent modulation of
spike transfer. Interestingly, we observed that the
modulation of spike transfer by input correlation appeared
different across the convergence models (* p = 4.2×10−22,
one-way ANOVA followed by post hoc Bonferroni analysis;
Fig. 2g). We found that the change of the slope in the response
function induced by input synchronization was significantly
larger in the UC convergence model than in the GG or UE
models. In other words, the spike-transfer function of the
network with UC-type convergence was more susceptible to the
change of synchronization level than that with the other two
To examine this further, we compared the response firing
rates of the system to static input and to strongly synchronized
input, for each condition of Σw (Fig. 2h). We confirmed that
the response activity to synchronized input was always higher
than that to static input, because the slope of the
Response(Static) vs. Response(Sync) graph was always
greater than 1. More importantly, we found that this slope is larger
in UC model than in the other two models for both weak and
strong synchronization-input conditions (* p = 3.9×10−14, **
p = 2.4×10−21, one-way ANOVA followed by post hoc
Bonferroni analysis; Fig. 2i). This result shows that
the modulation of spike transfer by synchronization is
the most significant in UC-type convergence, and
suggests that the structure of the feedforward convergence
is a critical factor for achieving a synchronization-dependent
We performed additional simulations to investigate the
effect of heterogeneous oscillation phase of each individual
source neuron activity (Supplementary Fig. S1). We
observed, in all three models, that the response increased
as the oscillating phase of each individual neuron was
more sharply synchronized, similar to the result where
synchronization was modulated by the amplitude of
oscillation (Fig. 2a, b). We were also able to estimate the
response dependence on the phase synchronization by
calculating the response change ratio (Supplementary
Fig. S1c). Again, the response of the UC model was
most dependent on the degree of phase synchronization,
similar to the oscillation strength dependence in Fig. 2.
3.2 Synchronization-dependent spike transfer for a single spike input
Next, we tested to see if the convergence-dependent
modulation of the spike transfer is also observed in response to a
single spike input. In each simulation condition above, we
examined the average response per single input spike in each
neuron (Fig. 3a). Specifically, in each target neuron, we
estimated the average number of induced spikes (N) after every
value of linear fitting for every input pattern are shown. (Pearson
correlation coefficient, r = 0.94, 0.96, 0.98 and p = 2.2×10−16, 2.3×10−20,
2.2×10−26 for static, weakly and strongly synchronized input,
respectively) Responses of the UC and UE models are not shown. (f) Slope between
response and Σw in each model (One-way ANOVA followed by post hoc
Bonferroni analysis, * p = 7.2×10−17, ** p = 1.0×10−22, ***
p = 1.4×10−24). In every model, slope increases as the input pattern is
better synchronized. (g) Ratio of slope for strong synchronization over
static input in each model (One-way ANOVA followed by post hoc
Bonferroni analysis, * p = 4.2×10−22). Increase of slope for synchronized
input is greatest in the UC model. (h) Responses of three models for static
and strongly synchronized input. Pearson correlation coefficient (r) and
pvalue of linear fitting are shown for every model. (Pearson correlation
coefficient r = 0.95, 0.95, 0.95 and p = 1.6×10−17, 1.9×10−19, 3.6×10−23
for UC, GG, UE model, respectively) The plot between static and weakly
synchronized input is not shown. (i) Slope between response for strongly/
weakly synchronized input and static input (One-way ANOVA followed
by post hoc Bonferroni analysis, * p = 3.9×10−14, ** p = 2.4×10−21). The
ratio of response for synchronized input over response for static input is
greatest in the UC model
single input spike was received. Here, N is defined as the area
above the mean response level in the histogram of output
spikes, after each input spike to the cell (Fig. 3a). For example,
in the UC model at P22, N = 0.11 for static input, and N = 0.48
for strong synchronization. To investigate the dependency on
the input synchronization, the ratio of N between
synchronized and static input patterns are compared in each model
(* p = 1.4×10−3, n.s. p = 0.094, one-way ANOVA followed
by post hoc Bonferroni analysis; Fig. 3b). We found
that this ratio was highest in the UC model and that
the ratios of different convergence models were
This result reveals that every single input spike may have a
different probability of inducing a spike response, depending on
change in the correlation level of inputs. Moreover, this
correlation-dependent response modulation appeared strongest
in UC-type feedforward convergence, compared to UE and GG
types. From these results, we confirmed that the
synchronizationdependent spike transfer is most significant in the UC model,
from both population and single-spike level analysis.
Although N was different across static and synchronized
input, the peak of output spike chance was consistently at 6 ms
of delay from an input spike for different levels of
synchronization. Considering that an identical set of rise and decay time
constants in EPSC was used in all models, the length of delay
is expected to mainly depend on the form of EPSC, rather than
the degree of oscillation or the convergence structure. The
dynamics of delay was not investigated further, because our
main interest was the varying part of the network originated
by the different convergence structures.
synchronization is normalized by response for static input during one
period of oscillation at P22. Ψ is amplitude and δ is full width at half
maximum of tuning curve. Dotted line at ‘1’ indicates the average
response level for static input. (d) Phase tuning between output response
and oscillation of input spike pattern (Ψ/δ) (One-way ANOVA followed
by post hoc Bonferroni analysis, * p = 1.3×10−3, n.s. p = 0.26). The
degree of tuning between input and output for strong synchronization is
greatest in the UC model
3.3 Oscillation phase-dependent spike transfer
Next, to test if the convergence-dependent response
modulation we found could be instantaneously controlled by the
temporal correlation of input spikes, we investigated the
phasedependency of spike transfer in each cycle of input oscillation
(Fig. 3c). In a period of input oscillation (1/40 Hz = 25 ms), we
counted the average number of induced spikes as a function of
the oscillation phase (colored solid lines), and compared this
with the spike responses to static input (black dashed line). We
observed that the spike responses in synchronized inputs are
phase-locked to different degrees, depending on the
oscillation strength in all convergence conditions. To analyze this
quantitatively, we measured the amplitude (Ψ) and the width
(δ, full width at half maximum) of the spike response curve
and calculated Ψ/δ as the index of sharpness of phase tuning.
We found that the value of Ψ/δ appears noticeably different
across convergence types, and is higher in UC model than in
the other two (* p = 1.3×10−3, n.s. p = 0.26, one-way ANOVA
followed by post hoc Bonferroni analysis; Fig. 3d),
suggesting that UC-type convergence can best perform a
synchronization-dependent spike filter, or transfer
control, among the models we tested.
Our results show that the types of feedforward convergence
circuits may determine the effectiveness of synchronized input
spikes in a way that the network becomes either a very
dynamic synchronization-dependent spike filter, or just a robust
relay station that is independent of input spike correlation.
Among those convergence models we tested, we found that
UC-type feedforward convergence could work as an effective
control of spike transfer that modulates spike transfer
depending on the instantaneous change of spike correlation in the
3.4 Convergence structure regulates input spike profiles towards a target cell
Having observed that the spike transfer function and the
synchronization dependency of each model network varied
significantly, we then examined whether this observed difference
between the models could be explained by their feedforward
convergence circuit structures.
In our model network, we confirmed that the distributions
of individual connection weights toward a target cell were
noticeably different across models (Fig. 4a), even though the
total synaptic connection weights were set to be consistent in
all models (area under each plot, Fig. 4a). Thus, we expected
these disparities would induce different input spike profiles for
each target neuron and result in dissimilar target cell activities.
To investigate how the identical source neuron activity is
converted into different input patterns for a target cell by each
convergence structure, we measured the number (N) and the
connection-weight sum (∑w) of input spikes within a
temporal window (5 ms) before every input spike (t0, Fig. 4b) that a
target cell received. We assumed that the strength and
synchrony of input spikes can be simply described with these
two parameters (N , ∑ w). Based on this assumption, we
determined whether each input pattern of a parameter set (N , ∑
w) could induce a spike in a target cell after each onset spike
(Fig. 4c). As a result, we observed that the 2D profiles of input
patterns appear noticeably different across convergence types
(Fig. 4d), indicating that different synaptic convergence
conditions induce dissimilar input spike patterns onto a target cell,
even from identical input sources.
On the other hand, the spike probability for each condition
of (N, ∑w) appears fairly similar across models (Fig. 4e, See
Supplementary Fig. S2 for details). This is understandable
because this result is dependent on the target cell response
function only, which is identical in all models. This
observation shows that we can use the same spike probability function
to estimate output activity level for all models, for a given
input profile. Using this result, we evaluated the expected
number of target spikes (Fig. 4f) by multiplying the target
spike probability (Fig. 4e) and the measured input profile of
(N, ∑w) in each model (Fig. 4d). Then, we compared the
estimated target cell firing, Φ with the simulated result in
Fig. 2c, d. The estimated response, Φ, in the UC, GG, and
UE models for both static and synchronized input patterns
were noticeably different from each other (* p = 3.7×10−4,
** p = 1.1×10−5, *** p = 8.9×10−6, one-way ANOVA
followed by post hoc Bonferroni analysis; Fig. 4g), and well agreed
with the observed result in Fig. 2c. In addition, we calculated
the expected synchronization-dependency of network
activities, from the Φ ratio for static and synchronized input patterns
in each model. The observed result showed significant
difference across the models (* p = 1.8×10−4, ** p = 2.5×10−10,
one-way ANOVA followed by post hoc Bonferroni analysis;
Fig. 4h), and agreed fairly well with the simulation result in
Fig. 2d. This indicated that the convergence-dependent input
pattern variation could explain the dissimilar
synchronizationdependency character between the models.
3.5 Functional implications across different convergence types and ranges
In the neural system, it has been observed that the range of
convergence in feedforward networks is not fixed but varies
widely across the regions. For example, between the retina
and the lateral geniculate nucleus (LGN) in thalamus, the
feedforward pathway relies on a very simple wiring rule, a
nearly one-to-one connection between source and target
(Usrey et al. 1999)
, while the wiring from the LGN to the
visual cortex follows a much more complicated convergent
(Jin et al. 2011)
(Fig. 5a). This implies that the wiring
rule of the convergence circuit may be one of the crucial
factors for understanding information processing in the visual
system. Having shown that each model of the feedforward
convergence circuit structure can induce different features of
synchronization-specific spike transfer, here we investigated
the functional implication of convergence by comparing it to
the response of the network from a very small range of
convergence (as a model of feedforward wiring from retina to
LGN) to large range (from LGN to visual cortex).
To investigate the way how the source signals are
transmitted in each convergence condition, we examined the number
of source spikes that induce an output spike in the target
neuron (Fig. 5b). We implemented the source neuron as a Poisson
spike generator with constant mean firing rate of 20 Hz, as in
Fig. 1, and then varied the convergence range of the model
neural network from 0.5 to 1.25, where ‘1’ is the connection
range used in Figs. 2 and 3, and the total connection
strength (∑w) was kept the same across all the
convergence conditions, as before.
We first observed that, in small convergence (range = 0.5),
only around two input spikes within 10 ms could induce a target
spike in all models (* p = 2.2×10−10, ** p = 2.4×10−13, ***
p = 8.3×10−14, n.s. p = 1, One-way ANOVA followed by post
hoc Bonferroni analysis; Fig. 5c), which works as a consistent
spike relay (Fig. 5c). On the other hand, as the convergence range
became larger, it required a larger number of input spikes within
was counted for each model. (e) Averaged target spike probability of all
three models combined. See Supplementary Fig. S2 for details (f)
Estimated target response in each model obtained by multiplying the
input spike distribution in (d) and the target spike probability in (e). (g)
Target cell firing (Φ) was estimated by summing all the response matrix
components in (f). They appeared significantly different across models
(One-way ANOVA followed by post hoc Bonferroni analysis, *
p = 3.7×10−4, ** p = 1.1×10−5, *** p = 8.9×10−6), and the difference
was consistent with the result simulated in Fig. 2c (h) The Φ ratios of
static to synchronized input patterns were significantly different across
models, corresponding to the observed result in Fig. 2d (One-way
ANOVA followed by post hoc Bonferroni analysis, * p = 1.8×10−4, **
p = 2.5×10−10). For (g)–(h), the observed results in Fig. 2c-d were
indicated as orange solid lines for comparison
10 ms to generate an output spike, which was more likely to
occur when source spikes were synchronized. This suggests that
the network with large convergence would be silent for static
input but respond only to synchronized inputs, operating as a
spike synchrony detector.
In addition, when the convergence range was small, we
found that all three models (UC, GG, UE) operated similarly
Fig. 5 Network with large convergence sensitively responds to input
synchronization, while network with small convergence stably relays
source activity. (a) Illustration of convergence circuits in visual
pathway; a small convergence between the retina and the LGN, and a
large convergence between the LGN and the visual cortex. (b)
Characteristic of spike transfer. The number of source spikes (N) within
10 ms before a target spike indicates how many source spikes are required
to produce a target spike. Larger N implies that more spikes are needed to
provide a target spike. (c) The number of source spikes N across different
conditions of convergence. As the range becomes larger, N in each model
as a spike relay. However, as the convergence range
became larger, we observed a noticeable difference of
spike transfer between the models (Fig. 5c). Thus, we
found that the spike transfer function of the circuit can
vary greatly by both the range and type of convergence
wiring in sensory information processing, such as in the
From the perspective of functional implications, a
feedforward network with a small range of convergence could
be specialized for relaying information, as the thalamic receptive
field has a structure similar to that observed in the retina
et al. 1999)
. On the other hand, a network with a large
convergence could play a role as a coincidence detector. Revisiting our
main results, a network with a large convergence could modulate
the sensitivity to synchronization, depending on how the synaptic
strength is distributed across the connections. As the range
increases, the difference between the convergence types becomes
important, implying functional diversity in the feedforward
network. As observed in experimental studies
(Jin et al. 2011; Smith
and Häusser 2010)
, feedforward networks between layers may
generally increases, implying that the network needs more input spikes
within a short time to generate a target spike. This condition makes the
network with large convergence respond only to synchronized inputs, as a
coincidence detector. Note that the difference between the models
becomes larger as convergence range increases. This implies that spike transfer
function of a large convergence strongly depends on the structure of
convergence circuits. (One-way ANOVA followed by post hoc Bonferroni analysis,
* p = 2.2×10−10, ** p = 2.4×10−13, *** p = 8.3×10−14, n.s. p = 1). The
average number of connections for a target cell at each range is 4.4, 9.8,
17.5, and 27.2, respectively
provide a basic circuit for information processing through
4.1 Oscillation of firing rate and spike synchronization
Correlations in neural spike activities have been studied
extensively in both experimental and theoretical research and a
number of studies have reported that synchronized neural
spikes might be crucial to information processing in the brain
(Buzsáki et al. 1992; Buzsáki and Draguhn 2004;
Courtemanche et al. 2003; Donoghue et al. 1998; Engel
et al. 2001; Engel and Singer 2001; Fries 2005; Gray and
McCormick 1996; Klimesch 1996; Salinas and Sejnowski
2001; Singer and Gray 1995; Varela et al. 2001; Ward 2003;
Womelsdorf et al. 2007)
. In accordance with the view that the
spike transfer between neural layers may control the network
dynamics, it also has been suggested that the brain may
process information selectively through
synchronizationdependent modulation of response function or gain of the
(Paik et al. 2009; Paik and Glaser 2010)
Although the appearance of neural selectivity originated by
the convergence between neural layers has been studied in
(Huerta-Ocampo et al. 2014; Morgan et al. 2016;
Wang et al. 2010)
, there has been little study of whether this
synchronization-dependent modulation of spike activity is
dependent on the structure of the convergent circuit, or if there is
any crucial factor in the convergent structure to control it.
In the current study, first we found that oscillations in the
input firing rate could control the synchronization of spike
trains. This is consistent with the general idea that various
kinds of neural oscillations observed in brain may work as
dynamic controllers of neural correlation (
Başar et al. 2000
Bastos et al. 2014
; Fries et al. 2001;
Koepsell et al. 2009
et al. 2009; Paik and Glaser 2010; Salinas and Sejnowski
2001; Uhlhaas and Singer 2010;
van Kerkoerle et al. 2014
Wang et al. 2010; Ward 2003). Next, we found that the
response of feedforward neural networks is, in general, altered
by the level of input synchronization to a certain degree. This
suggests that synchronization-dependent neural activity
modulation is a generally applicable mechanism for the control of
neural response function, even without any changes in the
neural circuit such as the number or strength of synaptic
4.2 Synchronization-dependent activity depends on the convergent connection rules
More importantly, we found that synchronization-dependent
spike transfer modulation is strongly influenced by the
structure of a circuit, in relation to the convergent rule of
feedforward wiring. In previous anatomical studies, it was
observed that there exist various types of convergent wiring
in feedforward neural networks
(Felleman and Van Essen
1991; Hubel and Wiesel 1962)
. For example, in visual
systems the feedforward pathway from the retina to the thalamus
relies on a very simple wiring rule, close to the one-to-one
connection between source and target neurons, while wiring
from the thalamus to the visual cortex follows a much more
complicated convergent form
(Jin et al. 2011; Usrey et al.
. This reveals that even in the same feedforward
pathway, the structure of feedforward wiring between different
layers may have different convergent structures.
Our results suggest that the different convergence
structures may work as a different type of
synchronizationdependent spike transfer modulator. As we showed in our
result, one type of convergence rule may more dynamically
modulate the system’s transfer function as the input
synchronization increases or decreases, while another type of
convergent circuit is relatively insensitive to the change of input
correlation. As a result, two types of feedforward circuit may
be able to work as a type of information filter or gate, and the
brain may develop a different type of convergence structure in
different regions of the neural system, as needed for optimal
The next question to ask is how these various convergent
structures develop in the brain. For example, one possible
mechanism that could account for this synaptic wiring could
be activity-dependent refinement of neural structure
et al. 2007; Chedotal and Richards 2010; Soto-Treviño et al.
. It also might be relevant to a common notion that
neurons seek optimal wiring rules that minimize the cost of
wiring under particular functional constraints
Sporns 2012; Chen et al. 2006; Chklovskii and Koulakov
2004; Kaiser and Hilgetag 2006; Young and Scannell 1996)
In general, it is possible that the optimal wiring rule may vary
under different developmental constraints, or by functional
structures that should be achieved during development.
In addition, a number of studies suggest that feedback from
cortex to subcortical layer, or top-down processing, could
contribute to the modulation of feedforward neural activity
(Buschman and Miller 2007; Buzsáki and Draguhn 2004;
Engel et al. 2001; Moldakarimov et al. 2015; Romei et al.
2010; Saalmann et al. 2007)
. Our result implies that one
possible way to achieve top-down control of the incoming input is
to affect the feedforward convergent connection by changing
the synaptic weight distribution so that it modulates the
synchronization-dependency of the circuits. Further
developmental study might be helpful to validate this scenario.
4.3 Various frequency bands of neural oscillation and spike transfer modulation
Among the known brain rhythms, gamma frequency
oscillations are considered one of the most interesting features of
brain activity and a large number of studies have reported
the possible relationship between gamma oscillations and
various brain functions
(Engel and Singer 2001; Fries 2009; Fries
et al. 2007; Paik and Glaser 2010; Sohal et al. 2009; Tiesinga
and Sejnowski 2009; Uhlhaas and Singer 2010; Zheng and
. Here we designed our simulation of the
oscillating input at 40 Hz, to mimic a gamma-band oscillation.
Thus, our results could be interpreted as a mechanism by
which the neural system responds to the synchronization
induced by gamma band oscillations. This may provide insight
into related problems, such as the modulation of sensory
information by variation of gamma band power or frequency.
Even though we focused on synchronization at gamma
frequency, the mechanism we found here may not be limited
to that case. Our findings about the relationship between the
feedforward convergence and synchronization could
generally be applicable to various conditions of neural networks with
gamma or beta frequency oscillations. They might also be
applicable to even more complicated cases, such as those in
which multiple components of oscillations exist together (e.g.,
theta and gamma, or beta and gamma). Therefore, our findings
here may reveal a general and fundamental mechanism for
how the neural system could make use of temporal correlation
of inputs to achieve a proper control of its response function.
In summary, we conducted a simulation study on the
modulation of information transfer for different level of
synchronization of convergent inputs in feedforward networks
connected by various convergent rules. Overall, we found that the
synchronization-dependent spike transfer strongly depends on
the feedforward convergence circuit of a neural network. Our
results suggest that, not only the correlation of input spikes,
but also the convergent synaptic connectivity patterns in a
network, need to be considered to understand the mechanism
of information transfer in the brain.
Funding This work was supported by Basic Science Research Program
through the National Research Foundation of Korea (NRF) funded by the
M i n i s t r y o f S c i e n c e , I C T & F u t u r e P l a n n i n g ( N R F
2013R1A1A1058415, NRF-2016R1C1B2016039) and the Future
Systems Healthcare Project of KAIST.
Compliance with ethical standards
Conflict of interest The authors declare that they have no competing
Open Access This article is distributed under the terms of the Creative
C o m m o n s A t t r i b u t i o n 4 . 0 I n t e r n a t i o n a l L i c e n s e ( h t t p : / /
creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a link
to the Creative Commons license, and indicate if changes were made.
Başar , E. , & Güntekin , B. ( 2008 ). A review of brain oscillations in cognitive disorders and the role of neurotransmitters . Brain Research , 1235 , 172 - 193 . https://doi.org/10.1016/j.brainres. 2008 . 06 .103.
Başar , E. , Başar-Eroğlu , C. , Karakaş , S. , & Schürmann , M. ( 2000 ). Brain oscillations in perception and memory . International journal of psychophysiology : official journal of the International Organization of Psychophysiology , 35 ( 2-3 ), 95 - 124 . https://doi.org/10.1016/S0167- 8760 ( 99 ) 00047 - 1 .
Bastos , A. M. , Briggs , F. , Alitto , H. J. , Mangun , G. R. , & Usrey , W. M. ( 2014 ). Simultaneous recordings from the primary visual cortex and lateral geniculate nucleus reveal rhythmic interactions and a cortical source for gamma-band oscillations . Journal of Neuroscience , 34 ( 22 ), 7639 - 7644 . https://doi.org/10.1523/JNEUROSCI.4216- 13 . 2014 .
Bullmore , E. , & Sporns , O. ( 2012 ). The economy of brain network organization . Nature Reviews. Neuroscience , 13 ( 5 ), 336 - 349 . https://doi. org/10.1038/nrn3214.
Buschman , T. J. , & Miller , E. K. ( 2007 ). Top-down versus bottom-up control of attention in the prefrontal and posterior parietal cortices . Science , 315 ( 5820 ), 1860 - 1862 . https://doi.org/10.1126/science. 1138071.
Butts , D. A. , Kanold , P. O. , & Shatz , C. J. ( 2007 ). A burst-based BHebbian^ learning rule at retinogeniculate synapses links retinal waves to activity-dependent refinement . PLoS Biology , 5 ( 3 ), e61 . https://doi.org/10.1371/journal.pbio. 0050061 .
Buzsáki , G. , & Draguhn , A. ( 2004 ). Neuronal oscillations in cortical networks . Science (New York, N.Y.), 304 ( 5679 ), 1926 - 1929 . https://doi.org/10.1126/science.1099745.
Buzsáki , G. , Horvath , Z. , Urioste , R. , Hetke , J. , & Wise , K. ( 1992 ). Highfrequency network oscillation in the hippocampus . Science (New York, N.Y.), 256 ( 5059 ), 1025 - 1027 . https://doi.org/10.1126/ science.1589772.
Carnevale , N. T. , & Hines , M. L. ( 2006 ). The NEURON book (1st ed.) . Cambridge: Cambridge University Press. https://doi.org/10.1017/ CBO9780511541612.
Chedotal , A. , & Richards , L. J. ( 2010 ). Wiring the brain: The biology of neuronal guidance . Cold Spring Harbor Perspectives in Biology , 2 ( 6 ), a001917 - a001917 . https://doi.org/10.1101/cshperspect. a001917.
Chen , B. L. , Hall , D. H. , & Chklovskii , D. B. ( 2006 ). Wiring optimization can relate neuronal structure and function . Proceedings of the National Academy of Sciences , 103 ( 12 ), 4723 - 4728 . https://doi. org/10.1073/pnas.0506806103.
Chklovskii , D. B. , & Koulakov , A. A. ( 2004 ). MAPS IN THE BRAIN: What can we learn from them? Annual Review of Neuroscience , 27 ( 1 ), 369 - 392 . https://doi.org/10.1146/annurev.neuro. 27 .070203. 144226.
Courtemanche , R. , Fujii , N. , & Graybiel , A. M. ( 2003 ). Synchronous, focally modulated beta-band oscillations characterize local field potential activity in the striatum of awake behaving monkeys . The Journal of neuroscience : the official journal of the Society for Neuroscience , 23 ( 37 ), 11741 -11752 http://www.ncbi.nlm.nih.gov/ pubmed/14684876.
Dinstein , I. , Pierce , K. , Eyler , L. , Solso , S. , Malach , R. , Behrmann , M. , & Courchesne , E. ( 2011 ). Disrupted neural synchronization in toddlers with autism . Neuron , 70 ( 6 ), 1218 - 1225 . https://doi.org/10.1016/j. neuron. 2011 . 04 .018.
Donoghue , J. P. , Sanes , J. N. , Hatsopoulos , N. G. , & Gaál , G. ( 1998 ). Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements . Journal of Neurophysiology , 79 ( 1 ), 159 - 173 .
Eglen , S. J. , Diggle , P. J. , & Troy , J. B. ( 2005 ). Homotypic constraints dominate positioning of on- and off-center beta retinal ganglion cells . Visual Neuroscience , 22 ( 6 ), 859 - 871 . https://doi.org/10. 1017/S0952523805226147.
Engel , A. K. , & Singer , W. ( 2001 ). Temporal binding and the neural correlates of sensory awareness . Trends in Cognitive Sciences , 5 ( 1 ), 16 - 25 . https://doi.org/10.1016/S1364- 6613 ( 00 ) 01568 - 0 .
Engel , A. K. , Fries , P. , & Singer , W. ( 2001 ). Dynamic predictions: Oscillations and synchrony in top-down processing . Nature Reviews. Neuroscience , 2 ( 10 ), 704 - 716 . https://doi.org/10.1038/ 35094565.
Felleman , D. J. , & Van Essen , D. C. ( 1991 ). Distributed hierarchical processing in the primate cerebral cortex . Cerebral cortex (New York, N.Y. : 1991 ), 1 ( 1 ), 1 - 47 . https://doi.org/10.1093/cercor/1.1.1.
Fries , P. ( 2005 ). A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence . Trends in Cognitive Sciences , 9 ( 10 ), 474 - 480 . https://doi.org/10.1016/j.tics. 2005 . 08 . 011.
Fries , P. ( 2009 ). Neuronal gamma-band synchronization as a fundamental process in cortical computation . Annual Review of Neuroscience , 32 , 209 - 224 . https://doi.org/10.1146/annurev.neuro. 051508 .135603.
Fries , P. , Reynolds , J. H. , Rorie , A. E. , & Desimone , R. ( 2001 ). Modulation of oscillatory neuronal synchronization by selective visual attention . Science (New York, N.Y.), 291 ( 5508 ), 1560 - 1563 . https://doi.org/10.1126/science.1055465.
Fries , P. , Nikolić , D. , & Singer , W. ( 2007 ). The gamma cycle . Trends in Neurosciences , 30 ( 7 ), 309 - 316 . https://doi.org/10.1016/j.tins. 2007 . 05 .005.
Gray , C. M. , & McCormick , D. A. ( 1996 ). Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex . Science (New York, N.Y.), 274 ( 5284 ), 109 - 113 . https://doi.org/10.1126/science.274.5284.109.
Grice , S. J. , Spratling , M. W. , Karmiloff-Smith , A. , Halit , H. , Csibra , G., de Haan, M. , & Johnson , M. H. ( 2001 ). Disordered visual processing and oscillatory brain activity in autism and Williams syndrome . Neuroreport , 12 ( 12 ), 2697 - 2700 . https://doi.org/10.1097/ 00001756 -200108280-00021.
Hammond , C. , Bergman , H. , & Brown , P. ( 2007 ). Pathological synchronization in Parkinson's disease: Networks, models and treatments . Trends in Neurosciences , 30 ( 7 ), 357 - 364 . https://doi.org/10.1016/j. tins. 2007 . 05 .004.
Hodgkin , A. L. , & Huxley , A. F. ( 1952 ). A quantitative description of membrane current and its application to conduction and excitation in nerve . The Journal of Physiology , 117 ( 4 ), 500 - 544 . https://doi.org/ 10.1113/jphysiol. 1952 .sp004764.
Hubel , D. H. , & Wiesel , T. N. ( 1962 ). Receptive fields, binocular interaction and functional architecture in the cat's visual cortex . The Journal of Physiology , 160 ( 1 ), 106 - 154 . https://doi.org/10.1113/ jphysiol. 1962 .sp006837.
Huerta-Ocampo , I. , Mena-Segovia , J. , & Bolam , J. P. ( 2014 ). Convergence of cortical and thalamic input to direct and indirect pathway medium spiny neurons in the striatum . Brain Structure & Function , 219 ( 5 ), 1787 - 1800 . https://doi.org/10.1007/s00429-013- 0601-z.
Jin , J. , Wang , Y. , Swadlow , H. a. , & Alonso , J. M. ( 2011 ). Population receptive fields of ON and OFF thalamic inputs to an orientation column in visual cortex . Nature Neuroscience , 14 ( 2 ), 232 - 238 . https://doi.org/10.1038/nn.2729.
Kaiser , M. , & Hilgetag , C. C. ( 2006 ). Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems . PLoS Computational Biology , 2 ( 7 ), 0805 - 0815 . https:// doi.org/10.1371/journal.pcbi. 0020095 .
van Kerkoerle , T. , Self , M. W. , Dagnino , B. , Gariel-Mathis , M.-A. , Poort , J., van der Togt, C. , & Roelfsema , P. R. ( 2014 ). Alpha and gamma oscillations characterize feedback and feedforward processing in monkey visual cortex . Proceedings of the National Academy of Sciences of the United States of America , 111 ( 40 ), 14332 - 14341 . https://doi.org/10.1073/pnas.1402773111.
Klimesch , W. ( 1996 ). Memory processes, brain oscillations and EEG synchronization . International Journal of Psychophysiology , 24 ( 1- 2 ), 61 - 100 . https://doi.org/10.1016/S0167- 8760 ( 96 ) 00057 - 8 .
Koepsell , K. , Wang , X. , Vaingankar , V. , Wei , Y. , Wang , Q. , Rathbun , D. L. , et al. ( 2009 ). Retinal oscillations carry visual information to cortex. Frontiers in Systems Neuroscience, 3(April), 4 . https://doi. org/10.3389/neuro.06.004. 2009 .
Kumar , A. , Rotter , S. , & Aertsen , A. ( 2010 ). Spiking activity propagation in neuronal networks: Reconciling different perspectives on neural coding . Nature Reviews Neuroscience , 11 ( 9 ), 615 - 627 . https://doi. org/10.1038/nrn2886.
McLaughlin , D. , Shapley , R. , Shelley , M. , & Wielaard , D. J. ( 2000 ). A neuronal network model of macaque primary visual cortex (V1): Orientation selectivity and dynamics in the input layer 4Cα . Proceedings of the National Academy of Sciences of the United States of America , 97 ( 14 ), 8087 - 8092 . https://doi.org/10.1073/ pnas.110135097.
Moldakarimov , S. , Bazhenov , M. , & Sejnowski, T. J. ( 2015 ). Feedback stabilizes propagation of synchronous spiking in cortical neural networks . Proceedings of the National Academy of Sciences of the United States of America , 112 ( 8 ), 2545 - 2550 . https://doi.org/10. 1073/pnas.1500643112.
Morgan , J. L. , Berger , D. R. , Wetzel , A. W. , & Lichtman , J. W. ( 2016 ). The fuzzy logic of network connectivity in mouse visual thalamus . Cell , 165 ( 1 ), 192 - 206 . https://doi.org/10.1016/j.cell. 2016 . 02 .033.
Paik , S. B. , & Glaser , D. A. ( 2010 ). Synaptic plasticity controls sensory responses through frequency-dependent gamma oscillation resonance . PLoS Computational Biology , 6 ( 9 ), e1000927 . https://doi. org/10.1371/journal.pcbi. 1000927 .
Paik , S. B. , Kumar , T. , & Glaser , D. A. ( 2009 ). Spontaneous local gamma oscillation selectively enhances neural network responsiveness . PLoS Computational Biology , 5 ( 4 ), e1000342 . https://doi.org/10. 1371/journal.pcbi. 1000342 .
Ratté , S. , Hong , S. , De Schutter , E. , & Prescott , S. A. ( 2013 ). Impact of neuronal properties on network coding: Roles of spike initiation dynamics and robust synchrony transfer . Neuron , 78 ( 5 ), 758 - 772 . https://doi.org/10.1016/j.neuron. 2013 . 05 .030.
Reid , R. C. , & Alonso , J. M. ( 1995 ). Specificity of monosynaptic connections from thalamus to visual cortex . Nature , 378 ( 6554 ), 281 - 284 . https://doi.org/10.1038/378281a0.
Ringach , D. L. ( 2004 ). Haphazard wiring of simple receptive fields and orientation columns in visual cortex . Journal of Neurophysiology , 92 ( 1 ), 468 - 476 . https://doi.org/10.1152/jn.01202. 2003 .
Romei , V. , Gross , J. , & Thut , G. ( 2010 ). On the role of prestimulus alpha rhythms over occipito-parietal areas in visual input regulation: Correlation or causation? The Journal of neuroscience : the official journal of the Society for Neuroscience , 30 ( 25 ), 8692 - 8697 . https:// doi.org/10.1523/JNEUROSCI.0160- 10 . 2010 .
Saalmann , Y. B. , Pigarev , I. N. , & Vidyasagar , T. R. ( 2007 ). Neural mechanisms of visual attention: How top-down feedback highlights relevant locations . Science , 316 ( 5831 ), 1612 - 1615 . https://doi.org/ 10.1126/science.1139140.
Salinas , E. , & Sejnowski, T. J. ( 2001 ). Correlated neuronal activity and the flow of neural information . Nature Reviews. Neuroscience , 2 ( 8 ), 539 - 550 . https://doi.org/10.1038/35086012.
Schnitzler , A. , & Gross , J. ( 2005 ). Normal and pathological oscillatory communication in the brain . Nature Reviews. Neuroscience , 6 ( 4 ), 285 - 296 . https://doi.org/10.1038/nrn1650.
Singer , W. , & Gray , C. M. ( 1995 ). Visual feature integration and the temporal correlation hypothesis . Annual Review of Neuroscience , 18 , 555 - 586 . https://doi.org/10.1146/annurev.ne. 18 .030195. 003011.
Smith , S. L. , & Häusser , M. ( 2010 ). Parallel processing of visual space by neighboring neurons in mouse visual cortex . Nature Neuroscience , 13 ( 9 ), 1144 - 1149 . https://doi.org/10.1038/nn. 2620.
Sohal , V. S. , Zhang , F. , Yizhar , O. , & Deisseroth , K. ( 2009 ). Parvalbumin neurons and gamma rhythms enhance cortical circuit performance . Nature , 459 ( 7247 ), 698 - 702 . https://doi.org/10.1038/nature07991.
Soto-Treviño , C. , Thoroughman , K. a ., Marder , E. , & Abbott , L. F. ( 2001 ). Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks . Nature Neuroscience , 4 ( 3 ), 297 - 303 . https://doi.org/10.1038/85147.
Tiesinga , P. , & Sejnowski, T. J. ( 2009 ). Cortical enlightenment: Are attentional gamma oscillations driven by ING or PING? Neuron , 63 ( 6 ), 727 - 732 . https://doi.org/10.1016/j.neuron. 2009 . 09 .009.
Uhlhaas , P. J. , & Singer , W. ( 2006 ). Neural synchrony in brain disorders: Relevance for cognitive dysfunctions and pathophysiology . Neuron , 52 ( 1 ), 155 - 168 . https://doi.org/10.1016/ j.neuron. 2006 . 09 .020.
Uhlhaas , P. J. , & Singer , W. ( 2010 ). Abnormal neural oscillations and synchrony in schizophrenia . Nature Reviews. Neuroscience , 11 ( 2 ), 100 - 113 . https://doi.org/10.1038/nrn2774.
Usrey , W. M. , Reppas , J. B. , & Reid , R. C. ( 1999 ). Specificity and s t r e n g t h o f r e t i n o g e n i c u l a t e c o n n e c t i o n s . J o u r n a l o f Neurophysiology , 82 ( 6 ), 3527 - 3540 .
Varela , F. , Lachaux , J. P. , Rodriguez , E. , & Martinerie , J. ( 2001 ). The brainweb: Phase synchronization and large-scale integration . Nature Reviews. Neuroscience , 2 ( 4 ), 229 - 239 . https://doi.org/10.1038/ 35067550.
Wang , H. P. , Spencer , D. , Fellous , J. M. , & Sejnowski, T. J. ( 2010 ). Synchrony of Thalamocortical inputs maximizes cortical reliability . Science , 328 ( 5974 ), 106 - 109 . https://doi.org/10.1126/science. 1183108.
Ward , L. M. ( 2003 ). Synchronous neural oscillations and cognitive processes . Trends in Cognitive Sciences , 7 ( 12 ), 553 - 559 . https://doi. org/10.1016/j.tics. 2003 . 10 .012.
Womelsdorf , T. , Schoffelen , J.-M. , Oostenveld , R. , Singer , W. , Desimone , R. , Engel , A. K. , & Fries , P. ( 2007 ). Modulation of neuronal interactions through neuronal synchronization . Science (New York, N.Y.), 316 ( 5831 ), 1609 - 1612 . https://doi.org/10.1126/ science.1139597.
Young , M. P. , & Scannell , J. W. ( 1996 ). Component-placement optimization in the brain . Trends in Neurosciences , 19 ( 10 ), 413 - 415 . https://doi.org/10.1016/ 0166 - 2236 ( 96 ) 84416 - X .
Zheng , C. , & Colgin , L. L. ( 2015 ). Beta and Gamma rhythms go with the flow . Neuron , 85 ( 2 ), 236 - 237 . https://doi.org/10.1016/j.neuron. 2014 . 12 .067.