%% Papers Published
@article{fds328550,
Author = {Brunel, N and Nadal, J-P and Toulouse, G},
Title = {Information capacity of a perceptron},
Journal = {Journal of Physics A: Mathematical and General},
Volume = {25},
Number = {19},
Pages = {5017-5038},
Publisher = {IOP Publishing},
Year = {1992},
Month = {December},
url = {http://dx.doi.org/10.1088/0305-4470/25/19/015},
Abstract = {The authors study the information storage capacity of a
simple perceptron in the error regime. For random unbiased
patterns the geometrical analysis gives a logarithmic
dependence for the information content in the asymptotic
limit. In this case, the statistical physics approach, when
used at the simplest level of replica theory, does not give
satisfactory results. However for perceptrons with finite
stability, the information content can be simply calculated
with statistical physics methods in a region above the
critical storage level, for biased as well as for unbiased
patterns.},
Doi = {10.1088/0305-4470/25/19/015},
Key = {fds328550}
}
@article{fds328549,
Author = {Amit, DJ and Brunel, N},
Title = {Adequate input for learning in attractor neural
networks},
Journal = {Network: Computation in Neural Systems},
Volume = {4},
Number = {2},
Pages = {177-194},
Publisher = {Informa UK Limited},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.1088/0954-898X_4_2_003},
Abstract = {In the context of learning in attractor neural networks
(ANN) the authors discuss the issue of the constraints
imposed by there requirements that the afferents arriving at
the neurons in the attractor network from the stimulus,
compete successfully with the afferents generated by the
recurrent activity inside the network, in a situation in
which both sets of synaptic efficacies are weak and
approximately equal. We simulate and analyse a two-component
network: one representing the stimulus, the other an ANN.
They show that if stimuli art correlated with the receptive
fields of neurons in the ANN, and are of sufficient
contrast, the stimulus can provide the necessary information
to the recurrent network to allow learning new stimulus,
even in the very disfavoured situation of synaptic
predominance in the recurrent part. Stimuli which are
insufficiently correlated with the receptive fields, or are
of insufficient contrast, are submerged by the recurrent
activity. © 1993 Informa UK Ltd All rights reserved:
reproduction in whole or part not permitted.},
Doi = {10.1088/0954-898X_4_2_003},
Key = {fds328549}
}
@article{fds328548,
Author = {Brunel, N},
Title = {Effect of synapse dilution on the memory retrieval in
structured attractor neural networks},
Journal = {Journal de Physique I},
Volume = {3},
Number = {8},
Pages = {1693-1715},
Publisher = {EDP Sciences},
Year = {1993},
Month = {August},
url = {http://dx.doi.org/10.1051/jp1:1993210},
Doi = {10.1051/jp1:1993210},
Key = {fds328548}
}
@article{fds328546,
Author = {Brunel, N and Zecchina, R},
Title = {Response functions improving performance in analog attractor
neural networks.},
Journal = {Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip
Topics},
Volume = {49},
Number = {3},
Pages = {R1823-R1826},
Year = {1994},
Month = {March},
url = {http://dx.doi.org/10.1103/physreve.49.r1823},
Doi = {10.1103/physreve.49.r1823},
Key = {fds328546}
}
@article{fds328543,
Author = {Brunel, N},
Title = {Dynamics of an attractor neural network converting temporal
into spatial correlations},
Journal = {Network: Computation in Neural Systems},
Volume = {5},
Number = {4},
Pages = {449-470},
Publisher = {Informa UK Limited},
Year = {1994},
Month = {November},
url = {http://dx.doi.org/10.1088/0954-898x/5/4/003},
Doi = {10.1088/0954-898x/5/4/003},
Key = {fds328543}
}
@article{fds328544,
Author = {Amit, DJ and Brunel, N and Tsodyks, MV},
Title = {Correlations of cortical Hebbian reverberations: theory
versus experiment.},
Journal = {J Neurosci},
Volume = {14},
Number = {11 Pt 1},
Pages = {6435-6445},
Year = {1994},
Month = {November},
url = {http://dx.doi.org/10.1523/JNEUROSCI.14-11-06435.1994},
Abstract = {Interpreting recent single-unit recordings of delay
activities in delayed match-to-sample experiments in
anterior ventral temporal (AVT) cortex of monkeys in terms
of reverberation dynamics, we present a model neural network
of quasi-realistic elements that reproduces the empirical
results in great detail. Information about the contiguity of
successive stimuli in the training sequence, representing
the fact that training is done on a set of uncorrelated
stimuli presented in a fixed temporal sequence, is embedded
in the synaptic structure. The model reproduces quite
accurately the correlations between delay activity
distributions corresponding to stimulation with the
uncorrelated stimuli used for training. It reproduces also
the activity distributions of spike rates on sample cells as
a function of the stimulating pattern. It is, in our view,
the first time that a computational phenomenon, represented
on the neurophysiological level, is reproduced in all its
quantitative aspects. The model is then used to make
predictions about further features of the physiology of such
experiments. Those include further properties of the
correlations, features of selective cells as discriminators
of stimuli provoking different delay activity distributions,
and activity distributions among the neurons in a delay
activity produced by a given pattern. The model has
predictive implications also for the dependence of the delay
activities on different training protocols. Finally, we
discuss the perspectives of the interplay between such
models and neurophysiology as well as its limitations and
possible extensions.},
Doi = {10.1523/JNEUROSCI.14-11-06435.1994},
Key = {fds328544}
}
@article{fds328545,
Author = {Brunel, N},
Title = {Storage capacity of neural networks: Effect of the
fluctuations of the number of active neurons per
memory},
Journal = {Journal of Physics A: Mathematical and General},
Volume = {27},
Number = {14},
Pages = {4783-4789},
Publisher = {IOP Publishing},
Year = {1994},
Month = {December},
url = {http://dx.doi.org/10.1088/0305-4470/27/14/009},
Abstract = {The storage capacity in an attractor neural network with
excitatory couplings is shown to depend not only on the
fraction of active neurons per pattern (or coding rate), but
also on the fluctuations around this value, in the
thermodynamical limit. The capacity is calculated in the
case of exactly the same number of active neurons in every
pattern. For every coding level the capacity is increased
with respect to the case of random patterns. Results are
supported by numerical simulations done with an exhaustive
search algorithm, and partly solve in the sparse coding
limit the paradox of the discrepancy of the capacity of the
Willshaw model with optimal capacity.},
Doi = {10.1088/0305-4470/27/14/009},
Key = {fds328545}
}
@article{fds328540,
Author = {Brunel, N and Amit, DJ},
Title = {Learning internal representations in an analog attractor
neural network},
Journal = {INTERNATIONAL JOURNAL OF NEURAL SYSTEMS, SUPPLEMENTARY
ISSUE, 1995},
Pages = {19-23},
Publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD},
Editor = {Amit, DJ and delGiudice, P and Denby, B and Rolls, ET and Treves,
A},
Year = {1995},
Month = {January},
ISBN = {981-02-2482-6},
Key = {fds328540}
}
@article{fds328541,
Author = {Brunel, N},
Title = {Quantitative modeling of local Hebbian reverberations in
primate cortex},
Journal = {INTERNATIONAL JOURNAL OF NEURAL SYSTEMS, SUPPLEMENTARY
ISSUE, 1995},
Pages = {13-17},
Publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD},
Editor = {Amit, DJ and delGiudice, P and Denby, B and Rolls, ET and Treves,
A},
Year = {1995},
Month = {January},
ISBN = {981-02-2482-6},
Key = {fds328541}
}
@article{fds328538,
Author = {Amit, D and Brunel, N},
Title = {Learning internal representations in an attractor neural
network with analogue neurons},
Journal = {Network: Computation in Neural Systems},
Volume = {6},
Number = {3},
Pages = {359-388},
Publisher = {Informa UK Limited},
Year = {1995},
Month = {August},
url = {http://dx.doi.org/10.1088/0954-898x/6/3/004},
Doi = {10.1088/0954-898x/6/3/004},
Key = {fds328538}
}
@article{fds328537,
Author = {Brunel, N and Zecchina, R},
Title = {A SIMPLE GEOMETRICAL BOUND FOR REPLICA SYMMETRY STABILITY IN
NEURAL NETWORKS MODELS},
Journal = {Modern Physics Letters B},
Volume = {09},
Number = {18},
Pages = {1159-1164},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {1995},
Month = {August},
url = {http://dx.doi.org/10.1142/s0217984995001157},
Doi = {10.1142/s0217984995001157},
Key = {fds328537}
}
@article{fds328536,
Author = {Ninio, J and Brunel, N},
Title = {Time to detect a single difference between two correlated
images},
Journal = {PERCEPTION},
Volume = {25},
Pages = {89-89},
Publisher = {PION LTD},
Year = {1996},
Month = {January},
Key = {fds328536}
}
@article{fds328535,
Author = {Brunel, N},
Title = {Hebbian learning of context in recurrent neural
networks.},
Journal = {Neural Comput},
Volume = {8},
Number = {8},
Pages = {1677-1710},
Year = {1996},
Month = {November},
url = {http://dx.doi.org/10.1162/neco.1996.8.8.1677},
Abstract = {Single electrode recording in the inferotemporal cortex of
monkeys during delayed visual memory tasks provide evidence
for attractor dynamics in the observed region. The
persistent elevated delay activities could be internal
representations of features of the learned visual stimuli
shown to the monkey during training. When uncorrelated
stimuli are presented during training in a fixed sequence,
these experiments display significant correlations between
the internal representations. Recently a simple model of
attractor neural network has reproduced quantitatively the
measured correlations. An underlying assumption of the model
is that the synaptic matrix formed during the training phase
contains in its efficacies information about the contiguity
of persistent stimuli in the training sequence. We present
here a simple unsupervised learning dynamics that produces
such a synaptic matrix if sequences of stimuli are
repeatedly presented to the network at fixed order. The
resulting matrix is then shown to convert temporal
correlations during training into spatial correlations
between attractors. The scenario is that, in the presence of
selective delay activity, at the presentation of each
stimulus, the activity distribution in the neural assembly
contain information of both the current stimulus and the
previous one (carried by the attractor). Thus the recurrent
synaptic matrix can code not only for each of the stimuli
presented to the network but also for their context. We
combine the idea that for learning to be effective, synaptic
modification should be stochastic, with the fact that
attractors provide learnable information about two
consecutive stimuli. We calculate explicitly the probability
distribution of synaptic efficacies as a function of
training protocol, that is, the order in which stimuli are
presented to the network. We then solve for the dynamics of
a network composed of integrate-and-fire excitatory and
inhibitory neurons with a matrix of synaptic collaterals
resulting from the learning dynamics. The network has a
stable spontaneous activity, and stable delay activity
develops after a critical learning stage. The availability
of a learning dynamics makes possible a number of
experimental predictions for the dependence of the delay
activity distributions and the correlations between them, on
the learning stage and the learning protocol. In particular
it makes specific predictions for pair-associates delay
experiments.},
Doi = {10.1162/neco.1996.8.8.1677},
Key = {fds328535}
}
@article{fds328532,
Author = {Amit, DJ and Brunel, N},
Title = {Model of global spontaneous activity and local structured
activity during delay periods in the cerebral
cortex.},
Journal = {Cereb Cortex},
Volume = {7},
Number = {3},
Pages = {237-252},
Year = {1997},
url = {http://dx.doi.org/10.1093/cercor/7.3.237},
Abstract = {We investigate self-sustaining stable states (attractors) in
networks of integrate-and-fire neurons. First, we study the
stability of spontaneous activity in an unstructured
network. It is shown that the stochastic background
activity, of 1-5 spikes/s, is unstable if all neurons are
excitatory. On the other hand, spontaneous activity becomes
self-stabilizing in presence of local inhibition, given
reasonable values of the parameters of the network. Second,
in a network sustaining physiological spontaneous rates, we
study the effect of learning in a local module, expressed in
synaptic modifications in specific populations of synapses.
We find that if the average synaptic potentiation (LTP) is
too low, no stimulus specific activity manifests itself in
the delay period. Instead, following the presentation and
removal of any stimulus there is, in the local module, a
delay activity in which all neurons selective (responding
visually) to any of the stimuli presented for learning have
rates which gradually increase with the amplitude of
synaptic potentiation. When the average LTP increases beyond
a critical value, specific local attractors (stable states)
appear abruptly against the background of the global uniform
spontaneous attractor. In this case the local module has two
available types of collective delay activity: if the
stimulus is unfamiliar, the activity is spontaneous; if it
is similar to a learned stimulus, delay activity is
selective. These new attractors reflect the synaptic
structure developed during learning. In each of them a small
population of neurons have elevated rates, which depend on
the strength of LTP. The remaining neurons of the module
have their activity at spontaneous rates. The predictions
made in this paper could be checked by single unit
recordings in delayed response experiments.},
Doi = {10.1093/cercor/7.3.237},
Key = {fds328532}
}
@article{fds328534,
Author = {Brunel, N and Nadal, J-P},
Title = {Optimal tuning curves for neurons spiking as a Poisson
process.},
Journal = {ESANN},
Publisher = {D-Facto public},
Editor = {Verleysen, M},
Year = {1997},
ISBN = {2-9600049-7-3},
Key = {fds328534}
}
@article{fds328530,
Author = {Amit, D and Brunel, N},
Title = {Dynamics of a recurrent network of spiking neurons before
and following learning},
Journal = {Network: Computation in Neural Systems},
Volume = {8},
Number = {4},
Pages = {373-404},
Publisher = {Informa UK Limited},
Year = {1997},
Month = {January},
url = {http://dx.doi.org/10.1088/0954-898X_8_4_003},
Abstract = {Extensive simulations of large recurrent networks of
integrate-and-fire excitatory and inhibitory neurons in
realistic cortical conditions (before and after Hebbian
unsupervised learning of uncorrelated stimuli) exhibit a
rich phenomenology of stochastic neural spike dynamics and,
in particular, coexistence between two types of stable
states: spontaneous activity upon stimulation by an
unlearned stimulus, and 'working memory' states strongly
correlated with learned stimuli. Firing rates have very wide
distributions, due to the variability in the connectivity
from neuron to neuron. ISI histograms are exponential,
except for small intervals. Thus the spike emission
processes are well approximated by a Poisson process. The
variability of the spike emission process is effectively
controlled by the magnitude of the post-spike reset
potential relative to the mean depolarization of the cell.
Cross-correlations (CC) exhibit a central peak near zero
delay, flanked by damped oscillations. The magnitude of the
central peak in the CCs depends both on the probability that
a spike emitted by a neuron affects another randomly chosen
neuron and on firing rates. It increases when average rates
decrease. Individual CCs depend very weakly on the synaptic
interactions between the pairs of neurons. The dependence of
individual CCs on the rates of the pair of neurons is in
agreement with experimental data. The distribution of firing
rates among neurons is in very good agreement with a simple
theory, indicating that correlations between spike emission
processes in the network are effectively small. © 1997 IOP
Publishing Ltd.},
Doi = {10.1088/0954-898X_8_4_003},
Key = {fds328530}
}
@article{fds328533,
Author = {Brunel, N},
Title = {Cross-correlations in sparsely connected recurrent networks
of spiking neurons},
Journal = {Lecture Notes in Computer Science (including subseries
Lecture Notes in Artificial Intelligence and Lecture Notes
in Bioinformatics)},
Volume = {1327},
Pages = {31-36},
Year = {1997},
Month = {January},
ISBN = {9783540636311},
url = {http://dx.doi.org/10.1007/bfb0020128},
Abstract = {We study the dynamics of sparsely connected recurrent
networks composed of excitatory and inhibitory
integrate-and-fire (IF) neurons firing at low rates, and in
particular cross-correlations (CC) between spike times of
pairs of neurons using both numerical simulations and a
recent theory. CCs exhibit damped oscillations with a
frequency which depends on synaptic time constants.
Individual CCs are shown to depend weakly on synaptic
connectivity. They depend more strongly on the firing rates
of individual neurons.},
Doi = {10.1007/bfb0020128},
Key = {fds328533}
}
@article{fds328531,
Author = {Brunel, N and Ninio, J},
Title = {Time to detect the difference between two images presented
side by side.},
Journal = {Brain Res Cogn Brain Res},
Volume = {5},
Number = {4},
Pages = {273-282},
Year = {1997},
Month = {June},
url = {http://dx.doi.org/10.1016/s0926-6410(97)00003-7},
Abstract = {The time to locate a difference between two artificial
images presented side by side on a CRT screen was studied as
a function of their complexity. The images were square
lattices of black or white squares or quadrangles, in some
cases delineated by a blue grid. Each pair differed at a
single position, chosen at random. For images of size N x N,
the median reaction time varied as cN2, from N = 3-15, with
c being around 50 ms in the absence of grid (i.e., when the
quadrangles were associated into continuous shapes). For N <
or = 9, when the lattice was made irregular, performance did
not deteriorate, up to a rather high level of irregularity.
Furthermore, the presence of uncorrelated distortions in the
left and right images did not affect performance for N < or
= 6. In the presence of a grid, the reaction times were on
average higher by 20%. The results taken together indicate
that the detection of differences does not proceed on a
point-by-point basis and must be mediated by some abstract
shape analysis, in agreement with current views on
short-term visual memory (e.g., Phillips, W.A., On the
distinction between sensory storage and short-term visual
memory, Percept. Psychophys., 16 (1974) 283-290 [13]). In
complementary experiments, the subjects had to judge whether
two images presented side by side were the same or
different, with N varying from 1 to 5. For N < 3, the same
and the different responses were similar in all their
statistical aspects. For N > or = 4, the "same" responses
took a significantly larger time than the "different"
responses and were accompanied by a significant increase in
errors. The qualitative change from N = 3 to N = 4 is
interpreted as a shift from a "single inspection" analysis
to an obligatory scanning procedure. On the whole, we
suggest that visual information in our simultaneous
comparison task is extracted by chunks of about 12 +/- 3
bits, and that the visual processing and matching tasks take
about 50 ms per couple of quadrangles. In Section 4, we
compare these values to the values obtained through other
experimental paradigms.},
Doi = {10.1016/s0926-6410(97)00003-7},
Key = {fds328531}
}
@article{fds328528,
Author = {Brunel, N and Nadal, JP},
Title = {Modeling memory: what do we learn from attractor neural
networks?},
Journal = {C R Acad Sci III},
Volume = {321},
Number = {2-3},
Pages = {249-252},
Year = {1998},
url = {http://dx.doi.org/10.1016/s0764-4469(97)89830-7},
Abstract = {In this paper we summarize some of the main contributions of
models of recurrent neural networks with associative memory
properties. We compare the behavior of these attractor
neural networks with empirical data from both physiology and
psychology. This type of network could be used in models
with more complex functions.},
Doi = {10.1016/s0764-4469(97)89830-7},
Key = {fds328528}
}
@article{fds328529,
Author = {Brunel, N and Trullier, O},
Title = {Plasticity of directional place fields in a model of rodent
CA3.},
Journal = {Hippocampus},
Volume = {8},
Number = {6},
Pages = {651-665},
Year = {1998},
url = {http://dx.doi.org/10.1002/(SICI)1098-1063(1998)8:6<651::AID-HIPO8>3.0.CO;2-L},
Abstract = {We propose a computational model of the CA3 region of the
rat hippocampus that is able to reproduce the available
experimental data concerning the dependence of directional
selectivity of the place cell discharge on the environment
and on the spatial task. The main feature of our model is a
continuous, unsupervised Hebbian learning dynamics of
recurrent connections, which is driven by the neuronal
activities imposed upon the network by the
environment-dependent external input. In our simulations,
the environment and the movements of the rat are chosen to
mimic those commonly observed in neurophysiological
experiments. The environment is represented as local views
that depend on both the position and the heading direction
of the rat. We hypothesize that place cells are
intrinsically directional, that is, they respond to local
views. We show that the synaptic dynamics in the recurrent
neural network rapidly modify the discharge correlates of
the place cells: Cells tend to become omnidirectional place
cells in open fields, while their directionality tends to
get stronger in radial-arm mazes. We also find that the
synaptic learning mechanisms account for other properties of
place cell activity, such as an increase in the place cell
peak firing rates as well as clustering of place fields
during exploration. Our model makes several experimental
predictions that can be tested using current
techniques.},
Doi = {10.1002/(SICI)1098-1063(1998)8:6<651::AID-HIPO8>3.0.CO;2-L},
Key = {fds328529}
}
@article{fds328527,
Author = {Brunel, N and Carusi, F and Fusi, S},
Title = {Slow stochastic Hebbian learning of classes of stimuli in a
recurrent neural network.},
Journal = {Network},
Volume = {9},
Number = {1},
Pages = {123-152},
Year = {1998},
Month = {February},
url = {http://dx.doi.org/10.1088/0954-898x/9/1/007},
Abstract = {We study unsupervised Hebbian learning in a recurrent
network in which synapses have a finite number of stable
states. Stimuli received by the network are drawn at random
at each presentation from a set of classes. Each class is
defined as a cluster in stimulus space, centred on the class
prototype. The presentation protocol is chosen to mimic the
protocols of visual memory experiments in which a set of
stimuli is presented repeatedly in a random way. The
statistics of the input stream may be stationary, or
changing. Each stimulus induces, in a stochastic way,
transitions between stable synaptic states. Learning
dynamics is studied analytically in the slow learning limit,
in which a given stimulus has to be presented many times
before it is memorized, i.e. before synaptic modifications
enable a pattern of activity correlated with the stimulus to
become an attractor of the recurrent network. We show that
in this limit the synaptic matrix becomes more correlated
with the class prototypes than with any of the instances of
the class. We also show that the number of classes that can
be learned increases sharply when the coding level
decreases, and determine the speeds of learning and
forgetting of classes in the case of changes in the
statistics of the input stream.},
Doi = {10.1088/0954-898x/9/1/007},
Key = {fds328527}
}
@article{fds328526,
Author = {Nadal, JP and Brunel, N and Parga, N},
Title = {Nonlinear feedforward networks with stochastic outputs:
infomax implies redundancy reduction.},
Journal = {Network},
Volume = {9},
Number = {2},
Pages = {207-217},
Year = {1998},
Month = {May},
url = {http://dx.doi.org/10.1088/0954-898x/9/2/004},
Abstract = {We prove that maximization of mutual information between the
output and the input of a feedforward neural network leads
to full redundancy reduction under the following sufficient
conditions: (i) the input signal is a (possibly nonlinear)
invertible mixture of independent components; (ii) there is
no input noise; (iii) the activity of each output neuron is
a (possibly) stochastic variable with a probability
distribution depending on the stimulus through a
deterministic function of the inputs (where both the
probability distributions and the functions can be different
from neuron to neuron); (iv) optimization of the mutual
information is performed over all these deterministic
functions. This result extends that obtained by Nadal and
Parga (1994) who considered the case of deterministic
outputs.},
Doi = {10.1088/0954-898x/9/2/004},
Key = {fds328526}
}
@article{fds328525,
Author = {Brunel, N and Nadal, JP},
Title = {Mutual information, Fisher information, and population
coding.},
Journal = {Neural Comput},
Volume = {10},
Number = {7},
Pages = {1731-1757},
Year = {1998},
Month = {October},
url = {http://dx.doi.org/10.1162/089976698300017115},
Abstract = {In the context of parameter estimation and model selection,
it is only quite recently that a direct link between the
Fisher information and information-theoretic quantities has
been exhibited. We give an interpretation of this link
within the standard framework of information theory. We show
that in the context of population coding, the mutual
information between the activity of a large array of neurons
and a stimulus to which the neurons are tuned is naturally
related to the Fisher information. In the light of this
result, we consider the optimization of the tuning curves
parameters in the case of neurons responding to a stimulus
represented by an angular variable.},
Doi = {10.1162/089976698300017115},
Key = {fds328525}
}
@article{fds328524,
Author = {Brunel, N and Sergi, S},
Title = {Firing frequency of leaky intergrate-and-fire neurons with
synaptic current dynamics.},
Journal = {J Theor Biol},
Volume = {195},
Number = {1},
Pages = {87-95},
Year = {1998},
Month = {November},
url = {http://dx.doi.org/10.1006/jtbi.1998.0782},
Abstract = {We consider a model of an integrate-and-fire neuron with
synaptic current dynamics, in which the synaptic time
constant tau' is much smaller than the membrane time
constant tau. We calculate analytically the firing frequency
of such a neuron for inputs described by a random Gaussian
process. We find that the first order correction to the
frequency due to tau' is proportional to the square root of
the ratio between these time constants radicaltau'/tau. This
implies that the correction is important even when the
synaptic time constant is small compared with that of the
potential. The frequency of a neuron with tau'>0 can be
reduced to that of the basic IF neuron (corresponding to
tau'=1) using an "effective" threshold which has a linear
dependence on radical tau'/tau. Numerical simulations show a
very good agreement with the analytical result, and permit
an extrapolation of the "effective" threshold to higher
orders in radical tau'/tau. The obtained frequency agrees
with simulation data for a wide range of
parameters.},
Doi = {10.1006/jtbi.1998.0782},
Key = {fds328524}
}
@article{fds328522,
Author = {Brunel, N and Hakim, V},
Title = {Fast global oscillations in networks of integrate-and-fire
neurons with low firing rates.},
Journal = {Neural Comput},
Volume = {11},
Number = {7},
Pages = {1621-1671},
Year = {1999},
Month = {October},
url = {http://dx.doi.org/10.1162/089976699300016179},
Abstract = {We study analytically the dynamics of a network of sparsely
connected inhibitory integrate-and-fire neurons in a regime
where individual neurons emit spikes irregularly and at a
low rate. In the limit when the number of neurons -->
infinity, the network exhibits a sharp transition between a
stationary and an oscillatory global activity regime where
neurons are weakly synchronized. The activity becomes
oscillatory when the inhibitory feedback is strong enough.
The period of the global oscillation is found to be mainly
controlled by synaptic times but depends also on the
characteristics of the external input. In large but finite
networks, the analysis shows that global oscillations of
finite coherence time generically exist both above and below
the critical inhibition threshold. Their characteristics are
determined as functions of systems parameters in these two
different regions. The results are found to be in good
agreement with numerical simulations.},
Doi = {10.1162/089976699300016179},
Key = {fds328522}
}
@article{fds328518,
Author = {Brunel, N},
Title = {Dynamics of networks of randomly connected excitatory and
inhibitory spiking neurons.},
Journal = {J Physiol Paris},
Volume = {94},
Number = {5-6},
Pages = {445-463},
Year = {2000},
url = {http://dx.doi.org/10.1016/s0928-4257(00)01084-6},
Abstract = {Recent advances in the understanding of the dynamics of
populations of spiking neurones are reviewed. These studies
shed light on how a population of neurones can follow
arbitrary variations in input stimuli, how the dynamics of
the population depends on the type of noise, and how
recurrent connections influence the dynamics. The importance
of inhibitory feedback for the generation of irregularity in
single cell behaviour is emphasized. Examples of computation
that recurrent networks with excitatory and inhibitory cells
can perform are then discussed. Maintenance of a network
state as an attractor of the system is discussed as a model
for working memory function, in both object and spatial
modalities. These models can be used to interpret and make
predictions about electrophysiological data in the awake
monkey.},
Doi = {10.1016/s0928-4257(00)01084-6},
Key = {fds328518}
}
@article{fds328520,
Author = {Brunel, N},
Title = {Dynamics of sparsely connected networks of excitatory and
inhibitory spiking neurons.},
Journal = {J Comput Neurosci},
Volume = {8},
Number = {3},
Pages = {183-208},
Year = {2000},
url = {http://dx.doi.org/10.1023/a:1008925309027},
Abstract = {The dynamics of networks of sparsely connected excitatory
and inhibitory integrate-and-fire neurons are studied
analytically. The analysis reveals a rich repertoire of
states, including synchronous states in which neurons fire
regularly; asynchronous states with stationary global
activity and very irregular individual cell activity; and
states in which the global activity oscillates but
individual cells fire irregularly, typically at rates lower
than the global oscillation frequency. The network can
switch between these states, provided the external
frequency, or the balance between excitation and inhibition,
is varied. Two types of network oscillations are observed.
In the fast oscillatory state, the network frequency is
almost fully controlled by the synaptic time scale. In the
slow oscillatory state, the network frequency depends mostly
on the membrane time constant. Finite size effects in the
asynchronous state are also discussed.},
Doi = {10.1023/a:1008925309027},
Key = {fds328520}
}
@article{fds328521,
Author = {Brunel, N and Wang, XJ},
Title = {Fast network oscillations with intermittent principal cell
firing in a model of a recurrent excitatory-inhibitory
circuit},
Journal = {EUROPEAN JOURNAL OF NEUROSCIENCE},
Volume = {12},
Pages = {79-79},
Publisher = {BLACKWELL SCIENCE LTD},
Year = {2000},
Month = {January},
Key = {fds328521}
}
@article{fds328519,
Author = {Brunel, N},
Title = {Phase diagrams of sparsely connected networks of excitatory
and inhibitory spiking neurons},
Journal = {Neurocomputing},
Volume = {32-33},
Pages = {307-312},
Publisher = {Elsevier BV},
Year = {2000},
Month = {June},
url = {http://dx.doi.org/10.1016/S0925-2312(00)00179-X},
Abstract = {The dynamics of networks of sparsely connected excitatory
and inhibitory integrate-and-fire neurons is studied
analytically. The 'phase diagrams' of such systems include:
synchronous states in which neurons fire regularly;
Asynchronous states with stationary global activity and very
irregular individual cell activity; synchronous states in
which the global activity oscillates but individual cells
fire irregularly, typically at frequencies lower than the
global oscillation frequency. The network can switch between
these states, provided the external frequency, or the
balance between excitation and inhibition, is varied. (C)
2000 Published by Elsevier Science B.V. All rights
reserved.},
Doi = {10.1016/S0925-2312(00)00179-X},
Key = {fds328519}
}
@article{fds328517,
Author = {Compte, A and Brunel, N and Goldman-Rakic, PS and Wang,
XJ},
Title = {Synaptic mechanisms and network dynamics underlying spatial
working memory in a cortical network model.},
Journal = {Cereb Cortex},
Volume = {10},
Number = {9},
Pages = {910-923},
Year = {2000},
Month = {September},
url = {http://dx.doi.org/10.1093/cercor/10.9.910},
Abstract = {Single-neuron recordings from behaving primates have
established a link between working memory processes and
information-specific neuronal persistent activity in the
prefrontal cortex. Using a network model endowed with a
columnar architecture and based on the physiological
properties of cortical neurons and synapses, we have
examined the synaptic mechanisms of selective persistent
activity underlying spatial working memory in the prefrontal
cortex. Our model reproduces the phenomenology of the
oculomotor delayed-response experiment of Funahashi et al.
(S. Funahashi, C.J. Bruce and P.S. Goldman-Rakic, Mnemonic
coding of visual space in the monkey's dorsolateral
prefrontal cortex. J Neurophysiol 61:331-349, 1989). To
observe stable spontaneous and persistent activity, we find
that recurrent synaptic excitation should be primarily
mediated by NMDA receptors, and that overall recurrent
synaptic interactions should be dominated by inhibition.
Isodirectional tuning of adjacent pyramidal cells and
interneurons can be accounted for by a structured
pyramid-to-interneuron connectivity. Robust memory storage
against random drift of the tuned persistent activity and
against distractors (intervening stimuli during the delay
period) may be enhanced by neuromodulation of recurrent
synapses. Experimentally testable predictions concerning the
neural basis of working memory are discussed.},
Doi = {10.1093/cercor/10.9.910},
Key = {fds328517}
}
@article{fds328516,
Author = {Brunel, N},
Title = {Persistent activity and the single-cell frequency-current
curve in a cortical network model.},
Journal = {Network},
Volume = {11},
Number = {4},
Pages = {261-280},
Year = {2000},
Month = {November},
url = {http://dx.doi.org/10.1088/0954-898x/11/4/302},
Abstract = {Neurophysiological experiments indicate that working memory
of an object is maintained by the persistent activity of
cells in the prefrontal cortex and infero-temporal cortex of
the monkey. This paper considers a cortical network model in
which this persistent activity appears due to recurrent
synaptic interactions. The conditions under which the
magnitude of spontaneous and persistent activity are close
to one another (as is found empirically) are investigated
using a simplified mean-field description in which firing
rates in these states are given by the intersections of a
straight line with the f-I curve of a single pyramidal cell.
The present analysis relates a network phenomenon -
persistent activity in a 'working memory' state - to
single-cell data which are accessible to experiment. It
predicts that, in networks of the cerebral cortex in which
persistent activity phenomena are observed, average synaptic
inputs in both spontaneous and persistent activity should
bring the cells close to firing threshold. Cells should be
slightly sub-threshold in spontaneous activity, and slightly
supra-threshold in persistent activity. The results are
shown to be robust to the inclusion of inhomogeneities that
produce wide distributions of firing rates, in both
spontaneous and working memory states.},
Doi = {10.1088/0954-898x/11/4/302},
Key = {fds328516}
}
@article{fds328514,
Author = {Brunel, N and Wang, XJ},
Title = {Effects of neuromodulation in a cortical network model of
object working memory dominated by recurrent
inhibition.},
Journal = {J Comput Neurosci},
Volume = {11},
Number = {1},
Pages = {63-85},
Year = {2001},
url = {http://dx.doi.org/10.1023/a:1011204814320},
Abstract = {Experimental evidence suggests that the maintenance of an
item in working memory is achieved through persistent
activity in selective neural assemblies of the cortex. To
understand the mechanisms underlying this phenomenon, it is
essential to investigate how persistent activity is affected
by external inputs or neuromodulation. We have addressed
these questions using a recurrent network model of object
working memory. Recurrence is dominated by inhibition,
although persistent activity is generated through recurrent
excitation in small subsets of excitatory neurons. Our main
findings are as follows. (1) Because of the strong feedback
inhibition, persistent activity shows an inverted U shape as
a function of increased external drive to the network. (2) A
transient external excitation can switch off a network from
a selective persistent state to its spontaneous state. (3)
The maintenance of the sample stimulus in working memory is
not affected by intervening stimuli (distractors) during the
delay period, provided the stimulation intensity is not
large. On the other hand, if stimulation intensity is large
enough, distractors disrupt sample-related persistent
activity, and the network is able to maintain a memory only
of the last shown stimulus. (4) A concerted modulation of
GABA(A) and NMDA conductances leads to a decrease of
spontaneous activity but an increase of persistent activity;
the enhanced signal-to-noise ratio is shown to increase the
resistance of the network to distractors. (5) Two mechanisms
are identified that produce an inverted U shaped dependence
of persistent activity on modulation. The present study
therefore points to several mechanisms that enhance the
signal-to-noise ratio in working memory states. These
mechanisms could be implemented in the prefrontal cortex by
dopaminergic projections from the midbrain.},
Doi = {10.1023/a:1011204814320},
Key = {fds328514}
}
@article{fds328515,
Author = {Brunel, N and Chance, FS and Fourcaud, N and Abbott,
LF},
Title = {Effects of synaptic noise and filtering on the frequency
response of spiking neurons.},
Journal = {Phys Rev Lett},
Volume = {86},
Number = {10},
Pages = {2186-2189},
Year = {2001},
Month = {March},
url = {http://dx.doi.org/10.1103/PhysRevLett.86.2186},
Abstract = {Noise can have a significant impact on the response dynamics
of a nonlinear system. For neurons, the primary source of
noise comes from background synaptic input activity. If this
is approximated as white noise, the amplitude of the
modulation of the firing rate in response to an input
current oscillating at frequency omega decreases as 1/square
root[omega] and lags the input by 45 degrees in phase.
However, if filtering due to realistic synaptic dynamics is
included, the firing rate is modulated by a finite amount
even in the limit omega-->infinity and the phase lag is
eliminated. Thus, through its effect on noise inputs,
realistic synaptic dynamics can ensure unlagged neuronal
responses to high-frequency inputs.},
Doi = {10.1103/PhysRevLett.86.2186},
Key = {fds328515}
}
@article{fds328513,
Author = {Fourcaud, N and Brunel, N},
Title = {Dynamics of the firing probability of noisy
integrate-and-fire neurons.},
Journal = {Neural Comput},
Volume = {14},
Number = {9},
Pages = {2057-2110},
Year = {2002},
Month = {September},
url = {http://dx.doi.org/10.1162/089976602320264015},
Abstract = {Cortical neurons in vivo undergo a continuous bombardment
due to synaptic activity, which acts as a major source of
noise. Here, we investigate the effects of the noise
filtering by synapses with various levels of realism on
integrate-and-fire neuron dynamics. The noise input is
modeled by white (for instantaneous synapses) or colored
(for synapses with a finite relaxation time) noise.
Analytical results for the modulation of firing probability
in response to an oscillatory input current are obtained by
expanding a Fokker-Planck equation for small parameters of
the problem - when both the amplitude of the modulation is
small compared to the background firing rate and the
synaptic time constant is small compared to the membrane
time constant. We report here the detailed calculations
showing that if a synaptic decay time constant is included
in the synaptic current model, the firing-rate modulation of
the neuron due to an oscillatory input remains finite in the
high-frequency limit with no phase lag. In addition, we
characterize the low-frequency behavior and the behavior of
the high-frequency limit for intermediate decay times. We
also characterize the effects of introducing a rise time to
the synaptic currents and the presence of several synaptic
receptors with different kinetics. In both cases, we
determine, using numerical simulations, an effective decay
time constant that describes the neuronal response
completely.},
Doi = {10.1162/089976602320264015},
Key = {fds328513}
}
@article{fds328509,
Author = {Brunel, N and Frégnac, Y and Meunier, C and Nadal,
J-P},
Title = {Neuroscience and computation.},
Journal = {J Physiol Paris},
Volume = {97},
Number = {4-6},
Pages = {387-390},
Year = {2003},
url = {http://dx.doi.org/10.1016/j.jphysparis.2004.02.001},
Doi = {10.1016/j.jphysparis.2004.02.001},
Key = {fds328509}
}
@article{fds328511,
Author = {Brunel, N and Hakim, V and Richardson, MJE},
Title = {Firing-rate resonance in a generalized integrate-and-fire
neuron with subthreshold resonance.},
Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
Volume = {67},
Number = {5 Pt 1},
Pages = {051916},
Year = {2003},
Month = {May},
url = {http://dx.doi.org/10.1103/PhysRevE.67.051916},
Abstract = {Neurons that exhibit a peak at finite frequency in their
membrane potential response to oscillatory inputs are
widespread in the nervous system. However, the influence of
this subthreshold resonance on spiking properties has not
yet been thoroughly analyzed. To this end, generalized
integrate-and-fire models are introduced that reproduce at
the linear level the subthreshold behavior of any given
conductance-based model. A detailed analysis is presented of
the simplest resonant model of this kind that has two
variables: the membrane potential and a supplementary
voltage-gated resonant variable. The firing-rate modulation
created by a noisy weak oscillatory drive, mimicking an in
vivo environment, is computed numerically and analytically
when the dynamics of the resonant variable is slow compared
to that of the membrane potential. The results show that the
firing-rate modulation is shaped by the subthreshold
resonance. For weak noise, the firing-rate modulation has a
minimum near the preferred subthreshold frequency. For
higher noise, such as that prevailing in vivo, the
firing-rate modulation peaks near the preferred subthreshold
frequency.},
Doi = {10.1103/PhysRevE.67.051916},
Key = {fds328511}
}
@article{fds328512,
Author = {Richardson, MJE and Brunel, N and Hakim, V},
Title = {From subthreshold to firing-rate resonance.},
Journal = {J Neurophysiol},
Volume = {89},
Number = {5},
Pages = {2538-2554},
Year = {2003},
Month = {May},
url = {http://dx.doi.org/10.1152/jn.00955.2002},
Abstract = {Many types of neurons exhibit subthreshold resonance.
However, little is known about whether this frequency
preference influences spike emission. Here, the link between
subthreshold resonance and firing rate is examined in the
framework of conductance-based models. A classification of
the subthreshold properties of a general class of neurons is
first provided. In particular, a class of neurons is
identified in which the input impedance exhibits a
suppression at a nonzero low frequency as well as a peak at
higher frequency. The analysis is then extended to the
effect of subthreshold resonance on the dynamics of the
firing rate. The considered input current comprises a
background noise term, mimicking the massive synaptic
bombardment in vivo. Of interest is the modulatory effect an
additional weak oscillating current has on the instantaneous
firing rate. When the noise is weak and firing regular, the
frequency most preferentially modulated is the firing rate
itself. Conversely, when the noise is strong and firing
irregular, the modulation is strongest at the subthreshold
resonance frequency. These results are demonstrated for two
specific conductance-based models and for a generalization
of the integrate-and-fire model that captures subthreshold
resonance. They suggest that resonant neurons are able to
communicate their frequency preference to postsynaptic
targets when the level of noise is comparable to that
prevailing in vivo.},
Doi = {10.1152/jn.00955.2002},
Key = {fds328512}
}
@article{fds328510,
Author = {Brunel, N and Wang, X-J},
Title = {What determines the frequency of fast network oscillations
with irregular neural discharges? I. Synaptic dynamics and
excitation-inhibition balance.},
Journal = {J Neurophysiol},
Volume = {90},
Number = {1},
Pages = {415-430},
Year = {2003},
Month = {July},
url = {http://dx.doi.org/10.1152/jn.01095.2002},
Abstract = {When the local field potential of a cortical network
displays coherent fast oscillations ( approximately 40-Hz
gamma or approximately 200-Hz sharp-wave ripples), the spike
trains of constituent neurons are typically irregular and
sparse. The dichotomy between rhythmic local field and
stochastic spike trains presents a challenge to the theory
of brain rhythms in the framework of coupled oscillators.
Previous studies have shown that when noise is large and
recurrent inhibition is strong, a coherent network rhythm
can be generated while single neurons fire intermittently at
low rates compared to the frequency of the oscillation.
However, these studies used too simplified synaptic kinetics
to allow quantitative predictions of the population rhythmic
frequency. Here we show how to derive quantitatively the
coherent oscillation frequency for a randomly connected
network of leaky integrate-and-fire neurons with realistic
synaptic parameters. In a noise-dominated interneuronal
network, the oscillation frequency depends much more on the
shortest synaptic time constants (delay and rise time) than
on the longer synaptic decay time, and approximately 200-Hz
frequency can be realized with synaptic time constants taken
from slice data. In a network composed of both interneurons
and excitatory cells, the rhythmogenesis is a compromise
between two scenarios: the fast purely interneuronal
mechanism, and the slower feedback mechanism (relying on the
excitatory-inhibitory loop). The properties of the rhythm
are determined essentially by the ratio of time scales of
excitatory and inhibitory currents and by the balance
between the mean recurrent excitation and inhibition. Faster
excitation than inhibition, or a higher excitation/inhibition
ratio, favors the feedback loop and a much slower
oscillation (typically in the gamma range).},
Doi = {10.1152/jn.01095.2002},
Key = {fds328510}
}
@article{fds328507,
Author = {Mongillo, G and Amit, DJ and Brunel, N},
Title = {Retrospective and prospective persistent activity induced by
Hebbian learning in a recurrent cortical
network.},
Journal = {Eur J Neurosci},
Volume = {18},
Number = {7},
Pages = {2011-2024},
Year = {2003},
Month = {October},
url = {http://dx.doi.org/10.1046/j.1460-9568.2003.02908.x},
Abstract = {Recordings from cells in the associative cortex of monkeys
performing visual working memory tasks link persistent
neuronal activity, long-term memory and associative memory.
In particular, delayed pair-associate tasks have revealed
neuronal correlates of long-term memory of associations
between stimuli. Here, a recurrent cortical network model
with Hebbian plastic synapses is subjected to the
pair-associate protocol. In a first stage, learning leads to
the appearance of delay activity, representing individual
images ('retrospective' activity). As learning proceeds, the
same learning mechanism uses retrospective delay activity
together with choice stimulus activity to potentiate
synapses connecting neural populations representing
associated images. As a result, the neural population
corresponding to the pair-associate of the image presented
is activated prior to its visual stimulation ('prospective'
activity). The probability of appearance of prospective
activity is governed by the strength of the inter-population
connections, which in turn depends on the frequency of
pairings during training. The time course of the transitions
from retrospective to prospective activity during the delay
period is found to depend on the fraction of slow,
N-methyl-d-aspartate-like receptors at excitatory synapses.
For fast recurrent excitation, transitions are abrupt; slow
recurrent excitation renders transitions gradual. Both
scenarios lead to a gradual rise of delay activity when
averaged over many trials, because of the stochastic nature
of the transitions. The model reproduces most of the
neuro-physiological data obtained during such tasks, makes
experimentally testable predictions and demonstrates how
persistent activity (working memory) brings about the
learning of long-term associations.},
Doi = {10.1046/j.1460-9568.2003.02908.x},
Key = {fds328507}
}
@article{fds328508,
Author = {Brunel, N and Latham, PE},
Title = {Firing rate of the noisy quadratic integrate-and-fire
neuron.},
Journal = {Neural Comput},
Volume = {15},
Number = {10},
Pages = {2281-2306},
Year = {2003},
Month = {October},
url = {http://dx.doi.org/10.1162/089976603322362365},
Abstract = {We calculate the firing rate of the quadratic
integrate-and-fire neuron in response to a colored noise
input current. Such an input current is a good approximation
to the noise due to the random bombardment of spikes, with
the correlation time of the noise corresponding to the decay
time of the synapses. The key parameter that determines the
firing rate is the ratio of the correlation time of the
colored noise, tau(s), to the neuronal time constant,
tau(m). We calculate the firing rate exactly in two limits:
when the ratio, tau(s)/tau(m), goes to zero (white noise)
and when it goes to infinity. The correction to the short
correlation time limit is O(tau(s)/tau(m)), which is qualita
tively different from that of the leaky integrate-and-fire
neuron, where the correction is O( radical tau(s)/tau(m)).
The difference is due to the different boundary conditions
of the probability density function of the membrane
potential of the neuron at firing threshold. The correction
to the long correlation time limit is O(tau(m)/tau(s)). By
combining the short and long correlation time limits, we
derive an expression that provides a good approximation to
the firing rate over the whole range of tau(s)/tau(m) in the
suprathreshold regime-that is, in a regime in which the
average current is sufficient to make the cell fire. In the
subthreshold regime, the expression breaks down somewhat
when tau(s) becomes large compared to tau(m).},
Doi = {10.1162/089976603322362365},
Key = {fds328508}
}
@article{fds328506,
Author = {Brunel, N},
Title = {Dynamics and plasticity of stimulus-selective persistent
activity in cortical network models.},
Journal = {Cereb Cortex},
Volume = {13},
Number = {11},
Pages = {1151-1161},
Year = {2003},
Month = {November},
url = {http://dx.doi.org/10.1093/cercor/bhg096},
Abstract = {Persistent neuronal activity is widespread in many areas of
the cerebral cortex of monkeys performing cognitive tasks
with a working memory component. Modeling studies have
helped understanding of the conditions under which
persistent activity can be sustained in cortical circuits.
Here, we first review several basic models of persistent
activity, including bistable models with excitation only and
multistable models for working memory of a discrete set of
pictures or objects with structured excitation and global
inhibition. In many experiments, persistent activity has
been shown to be subject to changes due to associative
learning. In cortical network models, Hebbian learning
shapes the synaptic structure and, in turn, the properties
of persistent activity when pictures are associated together
in the course of a task. It is shown how the theoretical
models can reproduce basic experimental findings of
neurophysiological recordings from inferior temporal and
perirhinal cortices obtained using the following
experimental protocols: (i) the pair-associate task; (ii)
the pair-associate task with color switch; and (iii) the
delay match to sample task with a fixed sequence of
samples.},
Doi = {10.1093/cercor/bhg096},
Key = {fds328506}
}
@article{fds328505,
Author = {Fourcaud-Trocmé, N and Hansel, D and van Vreeswijk, C and Brunel,
N},
Title = {How spike generation mechanisms determine the neuronal
response to fluctuating inputs.},
Journal = {J Neurosci},
Volume = {23},
Number = {37},
Pages = {11628-11640},
Year = {2003},
Month = {December},
url = {http://dx.doi.org/10.1523/JNEUROSCI.23-37-11628.2003},
Abstract = {This study examines the ability of neurons to track
temporally varying inputs, namely by investigating how the
instantaneous firing rate of a neuron is modulated by a
noisy input with a small sinusoidal component with frequency
(f). Using numerical simulations of conductance-based
neurons and analytical calculations of one-variable
nonlinear integrate-and-fire neurons, we characterized the
dependence of this modulation on f. For sufficiently high
noise, the neuron acts as a low-pass filter. The modulation
amplitude is approximately constant for frequencies up to a
cutoff frequency, fc, after which it decays. The cutoff
frequency increases almost linearly with the firing rate.
For higher frequencies, the modulation amplitude decays as
C/falpha, where the power alpha depends on the spike
initiation mechanism. For conductance-based models, alpha =
1, and the prefactor C depends solely on the average firing
rate and a spike "slope factor," which determines the
sharpness of the spike initiation. These results are
attributable to the fact that near threshold, the sodium
activation variable can be approximated by an exponential
function. Using this feature, we propose a simplified
one-variable model, the "exponential integrate-and-fire
neuron," as an approximation of a conductance-based model.
We show that this model reproduces the dynamics of a simple
conductance-based model extremely well. Our study shows how
an intrinsic neuronal property (the characteristics of fast
sodium channels) determines the speed with which neurons can
track changes in input.},
Doi = {10.1523/JNEUROSCI.23-37-11628.2003},
Key = {fds328505}
}
@article{fds328504,
Author = {Brunel, N and Hakim, V and Isope, P and Nadal, J-P and Barbour,
B},
Title = {Optimal information storage and the distribution of synaptic
weights: perceptron versus Purkinje cell.},
Journal = {Neuron},
Volume = {43},
Number = {5},
Pages = {745-757},
Year = {2004},
Month = {September},
url = {http://dx.doi.org/10.1016/j.neuron.2004.08.023},
Abstract = {It is widely believed that synaptic modifications underlie
learning and memory. However, few studies have examined what
can be deduced about the learning process from the
distribution of synaptic weights. We analyze the perceptron,
a prototypical feedforward neural network, and obtain the
optimal synaptic weight distribution for a perceptron with
excitatory synapses. It contains more than 50% silent
synapses, and this fraction increases with storage
reliability: silent synapses are therefore a necessary
byproduct of optimizing learning and reliability. Exploiting
the classical analogy between the perceptron and the
cerebellar Purkinje cell, we fitted the optimal weight
distribution to that measured for granule cell-Purkinje cell
synapses. The two distributions agreed well, suggesting that
the Purkinje cell can learn up to 5 kilobytes of
information, in the form of 40,000 input-output
associations.},
Doi = {10.1016/j.neuron.2004.08.023},
Key = {fds328504}
}
@article{fds328503,
Author = {Boucheny, C and Brunel, N and Arleo, A},
Title = {A continuous attractor network model without recurrent
excitation: maintenance and integration in the head
direction cell system.},
Journal = {J Comput Neurosci},
Volume = {18},
Number = {2},
Pages = {205-227},
Year = {2005},
url = {http://dx.doi.org/10.1007/s10827-005-6559-y},
Abstract = {Motivated by experimental observations of the head direction
system, we study a three population network model that
operates as a continuous attractor network. This network is
able to store in a short-term memory an angular variable
(the head direction) as a spatial profile of activity across
neurons in the absence of selective external inputs, and to
accurately update this variable on the basis of angular
velocity inputs. The network is composed of one excitatory
population and two inhibitory populations, with
inter-connections between populations but no connections
within the neurons of a same population. In particular,
there are no excitatory-to-excitatory connections. Angular
velocity signals are represented as inputs in one inhibitory
population (clockwise turns) or the other (counterclockwise
turns). The system is studied using a combination of
analytical and numerical methods. Analysis of a simplified
model composed of threshold-linear neurons gives the
conditions on the connectivity for (i) the emergence of the
spatially selective profile, (ii) reliable integration of
angular velocity inputs, and (iii) the range of angular
velocities that can be accurately integrated by the model.
Numerical simulations allow us to study the proposed
scenario in a large network of spiking neurons and compare
their dynamics with that of head direction cells recorded in
the rat limbic system. In particular, we show that the
directional representation encoded by the attractor network
can be rapidly updated by external cues, consistent with the
very short update latencies observed experimentally by
Zugaro et al. (2003) in thalamic head direction
cells.},
Doi = {10.1007/s10827-005-6559-y},
Key = {fds328503}
}
@article{fds328499,
Author = {Brunel, N},
Title = {Course 10 Network models of memory},
Volume = {80},
Number = {C},
Pages = {407-476},
Publisher = {Elsevier},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.1016/S0924-8099(05)80016-2},
Doi = {10.1016/S0924-8099(05)80016-2},
Key = {fds328499}
}
@article{fds328502,
Author = {Fourcaud-Trocmé, N and Brunel, N},
Title = {Dynamics of the instantaneous firing rate in response to
changes in input statistics.},
Journal = {J Comput Neurosci},
Volume = {18},
Number = {3},
Pages = {311-321},
Year = {2005},
Month = {June},
url = {http://dx.doi.org/10.1007/s10827-005-0337-8},
Abstract = {We review and extend recent results on the instantaneous
firing rate dynamics of simplified models of spiking neurons
in response to noisy current inputs. It has been shown
recently that the response of the instantaneous firing rate
to small amplitude oscillations in the mean inputs depends
in the large frequency limit f on the spike initiation
dynamics. A particular simplified model, the exponential
integrate-and-fire (EIF) model, has a response that decays
as 1/f in the large frequency limit and describes very well
the response of conductance-based models with a
Hodgkin-Huxley type fast sodium current. Here, we show that
the response of the EIF instantaneous firing rate also
decays as 1/f in the case of an oscillation in the variance
of the inputs for both white and colored noise. We then
compute the initial transient response of the firing rate of
the EIF model to a step change in its mean inputs and/or in
the variance of its inputs. We show that in both cases the
response speed is proportional to the neuron stationary
firing rate and inversely proportional to a 'spike slope
factor' Delta(T) that controls the sharpness of spike
initiation: as 1/Delta(T) for a step change in mean inputs,
and as 1/Delta(T) (2) for a step change in the variance in
the inputs.},
Doi = {10.1007/s10827-005-0337-8},
Key = {fds328502}
}
@article{fds328501,
Author = {Roxin, A and Brunel, N and Hansel, D},
Title = {Role of delays in shaping spatiotemporal dynamics of
neuronal activity in large networks.},
Journal = {Phys Rev Lett},
Volume = {94},
Number = {23},
Pages = {238103},
Year = {2005},
Month = {June},
url = {http://dx.doi.org/10.1103/PhysRevLett.94.238103},
Abstract = {We study the effect of delays on the dynamics of large
networks of neurons. We show that delays give rise to a
wealth of bifurcations and to a rich phase diagram, which
includes oscillatory bumps, traveling waves, lurching waves,
standing waves arising via a period-doubling bifurcation,
aperiodic regimes, and regimes of multistability. We study
the existence and the stability of the various dynamical
patterns analytically and numerically in a simplified rate
model as a function of the interaction parameters. The
results derived in that framework allow us to understand the
origin of the diversity of dynamical states observed in
large networks of spiking neurons.},
Doi = {10.1103/PhysRevLett.94.238103},
Key = {fds328501}
}
@article{fds328500,
Author = {Geisler, C and Brunel, N and Wang, X-J},
Title = {Contributions of intrinsic membrane dynamics to fast network
oscillations with irregular neuronal discharges.},
Journal = {J Neurophysiol},
Volume = {94},
Number = {6},
Pages = {4344-4361},
Year = {2005},
Month = {December},
url = {http://dx.doi.org/10.1152/jn.00510.2004},
Abstract = {During fast oscillations in the local field potential
(40-100 Hz gamma, 100-200 Hz sharp-wave ripples) single
cortical neurons typically fire irregularly at rates that
are much lower than the oscillation frequency. Recent
computational studies have provided a mathematical
description of such fast oscillations, using the leaky
integrate-and-fire (LIF) neuron model. Here, we extend this
theoretical framework to populations of more realistic
Hodgkin-Huxley-type conductance-based neurons. In a noisy
network of GABAergic neurons that are connected randomly and
sparsely by chemical synapses, coherent oscillations emerge
with a frequency that depends sensitively on the single
cell's membrane dynamics. The population frequency can be
predicted analytically from the synaptic time constants and
the preferred phase of discharge during the oscillatory
cycle of a single cell subjected to noisy sinusoidal input.
The latter depends significantly on the single cell's
membrane properties and can be understood in the context of
the simplified exponential integrate-and-fire (EIF) neuron.
We find that 200-Hz oscillations can be generated, provided
the effective input conductance of single cells is large, so
that the single neuron's phase shift is sufficiently small.
In a two-population network of excitatory pyramidal cells
and inhibitory neurons, recurrent excitation can either
decrease or increase the population rhythmic frequency,
depending on whether in a neuron the excitatory synaptic
current follows or precedes the inhibitory synaptic current
in an oscillatory cycle. Detailed single-cell properties
have a substantial impact on population oscillations, even
though rhythmicity does not originate from pacemaker neurons
and is an emergent network phenomenon.},
Doi = {10.1152/jn.00510.2004},
Key = {fds328500}
}
@article{fds328497,
Author = {Brunel, N and Hansel, D},
Title = {How noise affects the synchronization properties of
recurrent networks of inhibitory neurons.},
Journal = {Neural Comput},
Volume = {18},
Number = {5},
Pages = {1066-1110},
Year = {2006},
Month = {May},
url = {http://dx.doi.org/10.1162/089976606776241048},
Abstract = {GABAergic interneurons play a major role in the emergence of
various types of synchronous oscillatory patterns of
activity in the central nervous system. Motivated by these
experimental facts, modeling studies have investigated
mechanisms for the emergence of coherent activity in
networks of inhibitory neurons. However, most of these
studies have focused either when the noise in the network is
absent or weak or in the opposite situation when it is
strong. Hence, a full picture of how noise affects the
dynamics of such systems is still lacking. The aim of this
letter is to provide a more comprehensive understanding of
the mechanisms by which the asynchronous states in large,
fully connected networks of inhibitory neurons are
destabilized as a function of the noise level. Three types
of single neuron models are considered: the leaky
integrate-and-fire (LIF) model, the exponential
integrate-and-fire (EIF), model and conductance-based models
involving sodium and potassium Hodgkin-Huxley (HH) currents.
We show that in all models, the instabilities of the
asynchronous state can be classified in two classes. The
first one consists of clustering instabilities, which exist
in a restricted range of noise. These instabilities lead to
synchronous patterns in which the population of neurons is
broken into clusters of synchronously firing neurons. The
irregularity of the firing patterns of the neurons is weak.
The second class of instabilities, termed oscillatory firing
rate instabilities, exists at any value of noise. They lead
to cluster state at low noise. As the noise is increased,
the instability occurs at larger coupling, and the pattern
of firing that emerges becomes more irregular. In the regime
of high noise and strong coupling, these instabilities lead
to stochastic oscillations in which neurons fire in an
approximately Poisson way with a common instantaneous
probability of firing that oscillates in
time.},
Doi = {10.1162/089976606776241048},
Key = {fds328497}
}
@article{fds328498,
Author = {Roxin, A and Brunel, N and Hansel, D},
Title = {Rate models with delays and the dynamics of large networks
of spiking neurons},
Journal = {Progress of Theoretical Physics Supplement},
Volume = {161},
Pages = {68-85},
Publisher = {Oxford University Press (OUP)},
Year = {2006},
Month = {June},
url = {http://dx.doi.org/10.1143/PTPS.161.68},
Abstract = {We investigate the dynamics of a one-dimensional network of
spiking neurons with spatially modulated excitatory and
inhibitory interactions through extensive numerical
simulations. We find that the network displays a rich
repertoire of dynamical states as a function of the
interaction parameters, including homogeneous oscillations,
oscillatory bumps, traveling waves, lurching waves, standing
waves, quasi-periodic and chaotic states as well as regimes
of multistability. Combining analytical calculations and
simulations we show that similar dynamics are found in a
reduced rate model provided that the interactions are
delayed.},
Doi = {10.1143/PTPS.161.68},
Key = {fds328498}
}
@article{fds328495,
Author = {Baldassi, C and Braunstein, A and Brunel, N and Zecchina,
R},
Title = {Efficient supervised learning in networks with binary
synapses.},
Journal = {Proc. Natl. Acad. Sci. USA},
Volume = {104},
Number = {26},
Pages = {11079-11084},
Year = {2007},
url = {http://dx.doi.org/10.1073/pnas.0700324104},
Abstract = {Recent experimental studies indicate that synaptic changes
induced by neuronal activity are discrete jumps between a
small number of stable states. Learning in systems with
discrete synapses is known to be a computationally hard
problem. Here, we study a neurobiologically plausible
on-line learning algorithm that derives from belief
propagation algorithms. We show that it performs remarkably
well in a model neuron with binary synapses, and a finite
number of "hidden" states per synapse, that has to learn a
random classification task. Such a system is able to learn a
number of associations close to the theoretical limit in
time that is sublinear in system size. This is to our
knowledge the first on-line algorithm that is able to
achieve efficiently a finite number of patterns learned per
binary synapse. Furthermore, we show that performance is
optimal for a finite number of hidden states that becomes
very small for sparse coding. The algorithm is similar to
the standard "perceptron" learning algorithm, with an
additional rule for synaptic transitions that occur only if
a currently presented pattern is "barely correct." In this
case, the synaptic changes are metaplastic only (change in
hidden states and not in actual synaptic state), stabilizing
the synapse in its current state. Finally, we show that a
system with two visible states and K hidden states is much
more robust to noise than a system with K visible states. We
suggest that this rule is sufficiently simple to be easily
implemented by neurobiological systems or in
hardware.},
Doi = {10.1073/pnas.0700324104},
Key = {fds328495}
}
@article{fds328496,
Author = {Barbieri, F and Brunel, N},
Title = {Irregular persistent activity induced by synaptic excitatory
feedback.},
Journal = {Front Comput Neurosci},
Volume = {1},
Pages = {5},
Year = {2007},
url = {http://dx.doi.org/10.3389/neuro.10.005.2007},
Abstract = {Neurophysiological experiments on monkeys have reported
highly irregular persistent activity during the performance
of an oculomotor delayed-response task. These experiments
show that during the delay period the coefficient of
variation (CV) of interspike intervals (ISI) of prefrontal
neurons is above 1, on average, and larger than during the
fixation period. In the present paper, we show that this
feature can be reproduced in a network in which persistent
activity is induced by excitatory feedback, provided that
(i) the post-spike reset is close enough to threshold , (ii)
synaptic efficacies are a non-linear function of the
pre-synaptic firing rate. Non-linearity between pre-synaptic
rate and effective synaptic strength is implemented by a
standard short-term depression mechanism (STD). First, we
consider the simplest possible network with excitatory
feedback: a fully connected homogeneous network of
excitatory leaky integrate-and-fire neurons, using both
numerical simulations and analytical techniques. The results
are then confirmed in a network with selective excitatory
neurons and inhibition. In both the cases there is a large
range of values of the synaptic efficacies for which the
statistics of firing of single cells is similar to
experimental data.},
Doi = {10.3389/neuro.10.005.2007},
Key = {fds328496}
}
@article{fds328494,
Author = {Graupner, M and Brunel, N},
Title = {STDP in a bistable synapse model based on CaMKII and
associated signaling pathways.},
Journal = {PLoS Comput Biol},
Volume = {3},
Number = {11},
Pages = {e221},
Year = {2007},
Month = {November},
url = {http://dx.doi.org/10.1371/journal.pcbi.0030221},
Abstract = {The calcium/calmodulin-dependent protein kinase II (CaMKII)
plays a key role in the induction of long-term postsynaptic
modifications following calcium entry. Experiments suggest
that these long-term synaptic changes are all-or-none
switch-like events between discrete states. The biochemical
network involving CaMKII and its regulating protein
signaling cascade has been hypothesized to durably maintain
the evoked synaptic state in the form of a bistable switch.
However, it is still unclear whether experimental LTP/LTD
protocols lead to corresponding transitions between the two
states in realistic models of such a network. We present a
detailed biochemical model of the CaMKII autophosphorylation
and the protein signaling cascade governing the CaMKII
dephosphorylation. As previously shown, two stable states of
the CaMKII phosphorylation level exist at resting
intracellular calcium concentration, and high calcium
transients can switch the system from the weakly
phosphorylated (DOWN) to the highly phosphorylated (UP)
state of the CaMKII (similar to a LTP event). We show here
that increased CaMKII dephosphorylation activity at
intermediate Ca(2+) concentrations can lead to switching
from the UP to the DOWN state (similar to a LTD event). This
can be achieved if protein phosphatase activity promoting
CaMKII dephosphorylation activates at lower Ca(2+) levels
than kinase activity. Finally, it is shown that the CaMKII
system can qualitatively reproduce results of plasticity
outcomes in response to spike-timing dependent plasticity
(STDP) and presynaptic stimulation protocols. This shows
that the CaMKII protein network can account for both
induction, through LTP/LTD-like transitions, and storage,
due to its bistability, of synaptic changes.},
Doi = {10.1371/journal.pcbi.0030221},
Key = {fds328494}
}
@article{fds328492,
Author = {Barbour, B and Brunel, N and Hakim, V and Nadal, J-P},
Title = {What can we learn from synaptic weight distributions?},
Journal = {Trends Neurosci},
Volume = {30},
Number = {12},
Pages = {622-629},
Year = {2007},
Month = {December},
url = {http://dx.doi.org/10.1016/j.tins.2007.09.005},
Abstract = {Much research effort into synaptic plasticity has been
motivated by the idea that modifications of synaptic weights
(or strengths or efficacies) underlie learning and memory.
Here, we examine the possibility of exploiting the
statistics of experimentally measured synaptic weights to
deduce information about the learning process. Analysing
distributions of synaptic weights requires a theoretical
framework to interpret the experimental measurements, but
the results can be unexpectedly powerful, yielding strong
constraints on possible learning theories as well as
information that is difficult to obtain by other means, such
as the information storage capacity of a cell. We review the
available experimental and theoretical techniques as well as
important open issues.},
Doi = {10.1016/j.tins.2007.09.005},
Key = {fds328492}
}
@article{fds328493,
Author = {Brunel, N and van Rossum, MCW},
Title = {Lapicque's 1907 paper: from frogs to integrate-and-fire.},
Journal = {Biol Cybern},
Volume = {97},
Number = {5-6},
Pages = {337-339},
Year = {2007},
Month = {December},
url = {http://dx.doi.org/10.1007/s00422-007-0190-0},
Abstract = {Exactly 100 years ago, Louis Lapicque published a paper on
the excitability of nerves that is often cited in the
context of integrate-and-fire neurons. We discuss Lapicque's
contributions along with a translation of the original
publication.},
Doi = {10.1007/s00422-007-0190-0},
Key = {fds328493}
}
@article{fds328491,
Author = {Battaglia, D and Brunel, N and Hansel, D},
Title = {Temporal decorrelation of collective oscillations in neural
networks with local inhibition and long-range
excitation.},
Journal = {Phys Rev Lett},
Volume = {99},
Number = {23},
Pages = {238106},
Year = {2007},
Month = {December},
url = {http://dx.doi.org/10.1103/PhysRevLett.99.238106},
Abstract = {We consider two neuronal networks coupled by long-range
excitatory interactions. Oscillations in the gamma frequency
band are generated within each network by local inhibition.
When long-range excitation is weak, these oscillations phase
lock with a phase shift dependent on the strength of local
inhibition. Increasing the strength of long-range excitation
induces a transition to chaos via period doubling or
quasiperiodic scenarios. In the chaotic regime, oscillatory
activity undergoes fast temporal decorrelation. The
generality of these dynamical properties is assessed in
firing-rate models as well as in large networks of
conductance-based neurons.},
Doi = {10.1103/PhysRevLett.99.238106},
Key = {fds328491}
}
@article{fds328490,
Author = {Brunel, N},
Title = {Daniel Amit (1938-2007).},
Journal = {Network},
Volume = {19},
Number = {1},
Pages = {3-8},
Year = {2008},
url = {http://dx.doi.org/10.1080/09548980801915391},
Doi = {10.1080/09548980801915391},
Key = {fds328490}
}
@article{fds328489,
Author = {Brunel, N and Hakim, V},
Title = {Sparsely synchronized neuronal oscillations.},
Journal = {Chaos},
Volume = {18},
Number = {1},
Pages = {015113},
Year = {2008},
Month = {March},
url = {http://dx.doi.org/10.1063/1.2779858},
Abstract = {We discuss here the properties of fast global oscillations
that emerge in networks of neurons firing irregularly at a
low rate. We first provide a simple introduction to these
sparsely synchronized oscillations, then show how they can
be studied analytically in the simple setting of rate models
and leaky integrate-and-fire neurons, and finally describe
how various neurophysiological features can be incorporated
in this framework. We end by a comparison of experimental
data and theoretical results.},
Doi = {10.1063/1.2779858},
Key = {fds328489}
}
@article{fds328488,
Author = {de Solages, C and Szapiro, G and Brunel, N and Hakim, V and Isope, P and Buisseret, P and Rousseau, C and Barbour, B and Léna,
C},
Title = {High-frequency organization and synchrony of activity in the
purkinje cell layer of the cerebellum.},
Journal = {Neuron},
Volume = {58},
Number = {5},
Pages = {775-788},
Year = {2008},
Month = {June},
url = {http://dx.doi.org/10.1016/j.neuron.2008.05.008},
Abstract = {The cerebellum controls complex, coordinated, and rapid
movements, a function requiring precise timing abilities.
However, the network mechanisms that underlie the temporal
organization of activity in the cerebellum are largely
unexplored, because in vivo recordings have usually targeted
single units. Here, we use tetrode and multisite recordings
to demonstrate that Purkinje cell activity is synchronized
by a high-frequency (approximately 200 Hz) population
oscillation. We combine pharmacological experiments and
modeling to show how the recurrent inhibitory connections
between Purkinje cells are sufficient to generate these
oscillations. A key feature of these oscillations is a fixed
population frequency that is independent of the firing rates
of the individual cells. Convergence in the deep cerebellar
nuclei of Purkinje cell activity, synchronized by these
oscillations, likely organizes temporally the cerebellar
output.},
Doi = {10.1016/j.neuron.2008.05.008},
Key = {fds328488}
}
@article{fds328487,
Author = {Barbieri, F and Brunel, N},
Title = {Can attractor network models account for the statistics of
firing during persistent activity in prefrontal
cortex?},
Journal = {Front Neurosci},
Volume = {2},
Number = {1},
Pages = {114-122},
Year = {2008},
Month = {July},
url = {http://dx.doi.org/10.3389/neuro.01.003.2008},
Abstract = {Persistent activity observed in neurophysiological
experiments in monkeys is thought to be the neuronal
correlate of working memory. Over the last decade, network
modellers have strived to reproduce the main features of
these experiments. In particular, attractor network models
have been proposed in which there is a coexistence between a
non-selective attractor state with low background activity
with selective attractor states in which sub-groups of
neurons fire at rates which are higher (but not much higher)
than background rates. A recent detailed statistical
analysis of the data seems however to challenge such
attractor models: the data indicates that firing during
persistent activity is highly irregular (with an average CV
larger than 1), while models predict a more regular firing
process (CV smaller than 1). We discuss here recent
proposals that allow to reproduce this feature of the
experiments.},
Doi = {10.3389/neuro.01.003.2008},
Key = {fds328487}
}
@article{fds328486,
Author = {Roxin, A and Hakim, V and Brunel, N},
Title = {The statistics of repeating patterns of cortical activity
can be reproduced by a model network of stochastic binary
neurons.},
Journal = {J Neurosci},
Volume = {28},
Number = {42},
Pages = {10734-10745},
Year = {2008},
Month = {October},
url = {http://dx.doi.org/10.1523/JNEUROSCI.1016-08.2008},
Abstract = {Calcium imaging of the spontaneous activity in cortical
slices has revealed repeating spatiotemporal patterns of
transitions between so-called down states and up states
(Ikegaya et al., 2004). Here we fit a model network of
stochastic binary neurons to data from these experiments,
and in doing so reproduce the distributions of such
patterns. We use two versions of this model: (1) an
unconnected network in which neurons are activated as
independent Poisson processes; and (2) a network with an
interaction matrix, estimated from the data, representing
effective interactions between the neurons. The unconnected
model (model 1) is sufficient to account for the statistics
of repeating patterns in 11 of the 15 datasets studied.
Model 2, with interactions between neurons, is required to
account for pattern statistics of the remaining four. Three
of these four datasets are the ones that contain the largest
number of transitions, suggesting that long datasets are in
general necessary to render interactions statistically
visible. We then study the topology of the matrix of
interactions estimated for these four datasets. For three of
the four datasets, we find sparse matrices with long-tailed
degree distributions and an overrepresentation of certain
network motifs. The remaining dataset exhibits a strongly
interconnected, spatially localized subgroup of neurons. In
all cases, we find that interactions between neurons
facilitate the generation of long patterns that do not
repeat exactly.},
Doi = {10.1523/JNEUROSCI.1016-08.2008},
Key = {fds328486}
}
@article{fds328485,
Author = {Mazzoni, A and Panzeri, S and Logothetis, NK and Brunel,
N},
Title = {Encoding of naturalistic stimuli by local field potential
spectra in networks of excitatory and inhibitory
neurons.},
Journal = {PLoS Comput Biol},
Volume = {4},
Number = {12},
Pages = {e1000239},
Year = {2008},
Month = {December},
url = {http://dx.doi.org/10.1371/journal.pcbi.1000239},
Abstract = {Recordings of local field potentials (LFPs) reveal that the
sensory cortex displays rhythmic activity and fluctuations
over a wide range of frequencies and amplitudes. Yet, the
role of this kind of activity in encoding sensory
information remains largely unknown. To understand the rules
of translation between the structure of sensory stimuli and
the fluctuations of cortical responses, we simulated a
sparsely connected network of excitatory and inhibitory
neurons modeling a local cortical population, and we
determined how the LFPs generated by the network encode
information about input stimuli. We first considered simple
static and periodic stimuli and then naturalistic input
stimuli based on electrophysiological recordings from the
thalamus of anesthetized monkeys watching natural movie
scenes. We found that the simulated network produced
stimulus-related LFP changes that were in striking agreement
with the LFPs obtained from the primary visual cortex.
Moreover, our results demonstrate that the network encoded
static input spike rates into gamma-range oscillations
generated by inhibitory-excitatory neural interactions and
encoded slow dynamic features of the input into slow LFP
fluctuations mediated by stimulus-neural interactions. The
model cortical network processed dynamic stimuli with
naturalistic temporal structure by using low and high
response frequencies as independent communication channels,
again in agreement with recent reports from visual cortex
responses to naturalistic movies. One potential function of
this frequency decomposition into independent information
channels operated by the cortical network may be that of
enhancing the capacity of the cortical column to encode our
complex sensory environment.},
Doi = {10.1371/journal.pcbi.1000239},
Key = {fds328485}
}
@article{fds328484,
Author = {Brunel, N and Hakim, V},
Title = {Neuronal Dynamics},
Pages = {6099-6116},
Booktitle = {Encyclopedia of Complexity and Systems Science},
Publisher = {Springer New York},
Editor = {Meyers, RA},
Year = {2009},
ISBN = {9780387758886},
url = {http://dx.doi.org/10.1007/978-0-387-30440-3_359},
Doi = {10.1007/978-0-387-30440-3_359},
Key = {fds328484}
}
@article{fds366925,
Author = {Brunel, N},
Title = {Modeling Point Neurons: From Hodgkin-Huxley to
Integrate-and-Fire},
Pages = {161-185},
Booktitle = {COMPUTATIONAL MODELING METHODS FOR NEUROSCIENTISTS},
Year = {2009},
Key = {fds366925}
}
@article{fds328482,
Author = {Dugué, GP and Brunel, N and Hakim, V and Schwartz, E and Chat, M and Lévesque, M and Courtemanche, R and Léna, C and Dieudonné,
S},
Title = {Electrical coupling mediates tunable low-frequency
oscillations and resonance in the cerebellar Golgi cell
network.},
Journal = {Neuron},
Volume = {61},
Number = {1},
Pages = {126-139},
Year = {2009},
Month = {January},
url = {http://dx.doi.org/10.1016/j.neuron.2008.11.028},
Abstract = {Tonic motor control involves oscillatory synchronization of
activity at low frequency (5-30 Hz) throughout the
sensorimotor system, including cerebellar areas. We
investigated the mechanisms underpinning cerebellar
oscillations. We found that Golgi interneurons, which gate
information transfer in the cerebellar cortex input layer,
are extensively coupled through electrical synapses. When
depolarized in vitro, these neurons displayed low-frequency
oscillatory synchronization, imposing rhythmic inhibition
onto granule cells. Combining experiments and modeling, we
show that electrical transmission of the spike
afterhyperpolarization is the essential component for
oscillatory population synchronization. Rhythmic firing
arises in spite of strong heterogeneities, is frequency
tuned by the mean excitatory input to Golgi cells, and
displays pronounced resonance when the modeled network is
driven by oscillating inputs. In vivo, unitary Golgi cell
activity was found to synchronize with low-frequency LFP
oscillations occurring during quiet waking. These results
suggest a major role for Golgi cells in coordinating
cerebellar sensorimotor integration during oscillatory
interactions.},
Doi = {10.1016/j.neuron.2008.11.028},
Key = {fds328482}
}
@article{fds328481,
Author = {Zillmer, R and Brunel, N and Hansel, D},
Title = {Very long transients, irregular firing, and chaotic dynamics
in networks of randomly connected inhibitory
integrate-and-fire neurons.},
Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
Volume = {79},
Number = {3 Pt 1},
Pages = {031909},
Year = {2009},
Month = {March},
url = {http://dx.doi.org/10.1103/PhysRevE.79.031909},
Abstract = {We present results of an extensive numerical study of the
dynamics of networks of integrate-and-fire neurons connected
randomly through inhibitory interactions. We first consider
delayed interactions with infinitely fast rise and decay.
Depending on the parameters, the network displays transients
which are short or exponentially long in the network size.
At the end of these transients, the dynamics settle on a
periodic attractor. If the number of connections per neuron
is large ( approximately 1000) , this attractor is a cluster
state with a short period. In contrast, if the number of
connections per neuron is small ( approximately 100) , the
attractor has complex dynamics and very long period. During
the long transients the neurons fire in a highly irregular
manner. They can be viewed as quasistationary states in
which, depending on the coupling strength, the pattern of
activity is asynchronous or displays population
oscillations. In the first case, the average firing rates
and the variability of the single-neuron activity are well
described by a mean-field theory valid in the thermodynamic
limit. Bifurcations of the long transient dynamics from
asynchronous to synchronous activity are also well predicted
by this theory. The transient dynamics display features
reminiscent of stable chaos. In particular, despite being
linearly stable, the trajectories of the transient dynamics
are destabilized by finite perturbations as small as O(1/N)
. We further show that stable chaos is also observed for
postsynaptic currents with finite decay time. However, we
report in this type of network that chaotic dynamics
characterized by positive Lyapunov exponents can also be
observed. We show in fact that chaos occurs when the decay
time of the synaptic currents is long compared to the
synaptic delay, provided that the network is sufficiently
large.},
Doi = {10.1103/PhysRevE.79.031909},
Key = {fds328481}
}
@article{fds328480,
Author = {Ostojic, S and Brunel, N and Hakim, V},
Title = {Synchronization properties of networks of electrically
coupled neurons in the presence of noise and
heterogeneities.},
Journal = {J Comput Neurosci},
Volume = {26},
Number = {3},
Pages = {369-392},
Year = {2009},
Month = {June},
url = {http://dx.doi.org/10.1007/s10827-008-0117-3},
Abstract = {We investigate how synchrony can be generated or induced in
networks of electrically coupled integrate-and-fire neurons
subject to noisy and heterogeneous inputs. Using analytical
tools, we find that in a network under constant external
inputs, synchrony can appear via a Hopf bifurcation from the
asynchronous state to an oscillatory state. In a homogeneous
net work, in the oscillatory state all neurons fire in
synchrony, while in a heterogeneous network synchrony is
looser, many neurons skipping cycles of the oscillation. If
the transmission of action potentials via the electrical
synapses is effectively excitatory, the Hopf bifurcation is
supercritical, while effectively inhibitory transmission due
to pronounced hyperpolarization leads to a subcritical
bifurcation. In the latter case, the network exhibits
bistability between an asynchronous state and an oscillatory
state where all the neurons fire in synchrony. Finally we
show that for time-varying external inputs, electrical
coupling enhances the synchronization in an asynchronous
network via a resonance at the firing-rate
frequency.},
Doi = {10.1007/s10827-008-0117-3},
Key = {fds328480}
}
@article{fds328479,
Author = {Ostojic, S and Brunel, N and Hakim, V},
Title = {How connectivity, background activity, and synaptic
properties shape the cross-correlation between spike
trains.},
Journal = {J Neurosci},
Volume = {29},
Number = {33},
Pages = {10234-10253},
Year = {2009},
Month = {August},
url = {http://dx.doi.org/10.1523/JNEUROSCI.1275-09.2009},
Abstract = {Functional interactions between neurons in vivo are often
quantified by cross-correlation functions (CCFs) between
their spike trains. It is therefore essential to understand
quantitatively how CCFs are shaped by different factors,
such as connectivity, synaptic parameters, and background
activity. Here, we study the CCF between two neurons using
analytical calculations and numerical simulations. We
quantify the role of synaptic parameters, such as peak
conductance, decay time, and reversal potential, and analyze
how various patterns of connectivity influence CCF shapes.
In particular, we find that the symmetry of the CCF
distinguishes in general, but not always, the case of shared
inputs between two neurons from the case in which they are
directly synaptically connected. We systematically examine
the influence of background synaptic inputs from the
surrounding network that set the baseline firing statistics
of the neurons and modulate their response properties. We
find that variations in the background noise modify the
amplitude of the cross-correlation function as strongly as
variations of synaptic strength. In particular, we show that
the postsynaptic neuron spiking regularity has a pronounced
influence on CCF amplitude. This suggests an efficient and
flexible mechanism for modulating functional
interactions.},
Doi = {10.1523/JNEUROSCI.1275-09.2009},
Key = {fds328479}
}
@article{fds328483,
Author = {Graupner, M and Brunel, N},
Title = {A bitable synaptic model with transitions between states
induced by calcium dynamics: theory vs experiment},
Journal = {BMC Neuroscience},
Volume = {10},
Number = {S1},
Pages = {O15-O15},
Publisher = {Springer Science and Business Media LLC},
Year = {2009},
Month = {September},
url = {http://dx.doi.org/10.1186/1471-2202-10-s1-o15},
Doi = {10.1186/1471-2202-10-s1-o15},
Key = {fds328483}
}
@article{fds328478,
Author = {Brunel, N and Lavigne, F},
Title = {Semantic priming in a cortical network model.},
Journal = {J Cogn Neurosci},
Volume = {21},
Number = {12},
Pages = {2300-2319},
Year = {2009},
Month = {December},
url = {http://dx.doi.org/10.1162/jocn.2008.21156},
Abstract = {Contextual recall in humans relies on the semantic
relationships between items stored in memory. These
relationships can be probed by priming experiments. Such
experiments have revealed a rich phenomenology on how
reaction times depend on various factors such as strength
and nature of associations, time intervals between stimulus
presentations, and so forth. Experimental protocols on
humans present striking similarities with pair association
task experiments in monkeys. Electrophysiological recordings
of cortical neurons in such tasks have found two types of
task-related activity, "retrospective" (related to a
previously shown stimulus), and "prospective" (related to a
stimulus that the monkey expects to appear, due to learned
association between both stimuli). Mathematical models of
cortical networks allow theorists to understand the link
between the physiology of single neurons and synapses, and
network behavior giving rise to retrospective and/or
prospective activity. Here, we show that this type of
network model can account for a large variety of priming
effects. Furthermore, the model allows us to interpret
semantic priming differences between the two hemispheres as
depending on a single association strength
parameter.},
Doi = {10.1162/jocn.2008.21156},
Key = {fds328478}
}
@article{fds328477,
Author = {Graupner, M and Brunel, N},
Title = {Mechanisms of induction and maintenance of spike-timing
dependent plasticity in biophysical synapse
models.},
Journal = {Front Comput Neurosci},
Volume = {4},
Year = {2010},
url = {http://dx.doi.org/10.3389/fncom.2010.00136},
Abstract = {We review biophysical models of synaptic plasticity, with a
focus on spike-timing dependent plasticity (STDP). The
common property of the discussed models is that synaptic
changes depend on the dynamics of the intracellular calcium
concentration, which itself depends on pre- and postsynaptic
activity. We start by discussing simple models in which
plasticity changes are based directly on calcium amplitude
and dynamics. We then consider models in which dynamic
intracellular signaling cascades form the link between the
calcium dynamics and the plasticity changes. Both mechanisms
of induction of STDP (through the ability of
pre/postsynaptic spikes to evoke changes in the state of the
synapse) and of maintenance of the evoked changes (through
bistability) are discussed.},
Doi = {10.3389/fncom.2010.00136},
Key = {fds328477}
}
@article{fds328476,
Author = {Panzeri, S and Brunel, N and Logothetis, NK and Kayser,
C},
Title = {Sensory neural codes using multiplexed temporal
scales.},
Journal = {Trends Neurosci},
Volume = {33},
Number = {3},
Pages = {111-120},
Year = {2010},
Month = {March},
url = {http://dx.doi.org/10.1016/j.tins.2009.12.001},
Abstract = {Determining how neuronal activity represents sensory
information is central for understanding perception. Recent
work shows that neural responses at different timescales can
encode different stimulus attributes, resulting in a
temporal multiplexing of sensory information. Multiplexing
increases the encoding capacity of neural responses, enables
disambiguation of stimuli that cannot be discriminated at a
single response timescale, and makes sensory representations
stable to the presence of variability in the sensory world.
Thus, as we discuss here, temporal multiplexing could be a
key strategy used by the brain to form an information-rich
and stable representation of the environment.},
Doi = {10.1016/j.tins.2009.12.001},
Key = {fds328476}
}
@article{fds328475,
Author = {Mazzoni, A and Whittingstall, K and Brunel, N and Logothetis, NK and Panzeri, S},
Title = {Understanding the relationships between spike rate and
delta/gamma frequency bands of LFPs and EEGs using a local
cortical network model.},
Journal = {Neuroimage},
Volume = {52},
Number = {3},
Pages = {956-972},
Year = {2010},
Month = {September},
url = {http://dx.doi.org/10.1016/j.neuroimage.2009.12.040},
Abstract = {Despite the widespread use of EEGs to measure the
large-scale dynamics of the human brain, little is known on
how the dynamics of EEGs relates to that of the underlying
spike rates of cortical neurons. However, progress was made
by recent neurophysiological experiments reporting that EEG
delta-band phase and gamma-band amplitude reliably predict
some complementary aspects of the time course of spikes of
visual cortical neurons. To elucidate the mechanisms behind
these findings, here we hypothesize that the EEG delta phase
reflects shifts of local cortical excitability arising from
slow fluctuations in the network input due to entrainment to
sensory stimuli or to fluctuations in ongoing activity, and
that the resulting local excitability fluctuations modulate
both the spike rate and the engagement of
excitatory-inhibitory loops producing gamma-band
oscillations. We quantitatively tested these hypotheses by
simulating a recurrent network of excitatory and inhibitory
neurons stimulated with dynamic inputs presenting temporal
regularities similar to that of thalamic responses during
naturalistic visual stimulation and during spontaneous
activity. The network model reproduced in detail the
experimental relationships between spike rate and EEGs, and
suggested that the complementariness of the prediction of
spike rates obtained from EEG delta phase or gamma amplitude
arises from nonlinearities in the engagement of
excitatory-inhibitory loops and from temporal modulations in
the amplitude of the network input, which respectively limit
the predictability of spike rates from gamma amplitude or
delta phase alone. The model suggested also ways to improve
and extend current algorithms for online prediction of spike
rates from EEGs.},
Doi = {10.1016/j.neuroimage.2009.12.040},
Key = {fds328475}
}
@article{fds328472,
Author = {Ledoux, E and Brunel, N},
Title = {Dynamics of networks of excitatory and inhibitory neurons in
response to time-dependent inputs.},
Journal = {Front Comput Neurosci},
Volume = {5},
Pages = {25},
Year = {2011},
url = {http://dx.doi.org/10.3389/fncom.2011.00025},
Abstract = {We investigate the dynamics of recurrent networks of
excitatory (E) and inhibitory (I) neurons in the presence of
time-dependent inputs. The dynamics is characterized by the
network dynamical transfer function, i.e., how the
population firing rate is modulated by sinusoidal inputs at
arbitrary frequencies. Two types of networks are studied and
compared: (i) a Wilson-Cowan type firing rate model; and
(ii) a fully connected network of leaky integrate-and-fire
(LIF) neurons, in a strong noise regime. We first
characterize the region of stability of the "asynchronous
state" (a state in which population activity is constant in
time when external inputs are constant) in the space of
parameters characterizing the connectivity of the network.
We then systematically characterize the qualitative
behaviors of the dynamical transfer function, as a function
of the connectivity. We find that the transfer function can
be either low-pass, or with a single or double resonance,
depending on the connection strengths and synaptic time
constants. Resonances appear when the system is close to
Hopf bifurcations, that can be induced by two separate
mechanisms: the I-I connectivity and the E-I connectivity.
Double resonances can appear when excitatory delays are
larger than inhibitory delays, due to the fact that two
distinct instabilities exist with a finite gap between the
corresponding frequencies. In networks of LIF neurons,
changes in external inputs and external noise are shown to
be able to change qualitatively the network transfer
function. Firing rate models are shown to exhibit the same
diversity of transfer functions as the LIF network, provided
delays are present. They can also exhibit input-dependent
changes of the transfer function, provided a suitable static
non-linearity is incorporated.},
Doi = {10.3389/fncom.2011.00025},
Key = {fds328472}
}
@article{fds328473,
Author = {Mazzoni, A and Brunel, N and Cavallari, S and Logothetis, NK and Panzeri, S},
Title = {Cortical dynamics during naturalistic sensory stimulations:
experiments and models.},
Journal = {J Physiol Paris},
Volume = {105},
Number = {1-3},
Pages = {2-15},
Year = {2011},
url = {http://dx.doi.org/10.1016/j.jphysparis.2011.07.014},
Abstract = {We report the results of our experimental and theoretical
investigations of the neural response dynamics in primary
visual cortex (V1) during naturalistic visual stimulation.
We recorded Local Field Potentials (LFPs) and spiking
activity from V1 of anaesthetized macaques during binocular
presentation of Hollywood color movies. We analyzed these
recordings with information theoretic methods, and found
that visual information was encoded mainly by two bands of
LFP responses: the network fluctuations measured by the
phase and power of low-frequency (less than 12 Hz) LFPs; and
fast gamma-range (50-100 Hz) oscillations. Both the power
and phase of low frequency LFPs carried information largely
complementary to that carried by spikes, whereas gamma range
oscillations carried information largely redundant to that
of spikes. To interpret these results within a quantitative
theoretical framework, we then simulated a sparsely
connected recurrent network of excitatory and inhibitory
neurons receiving slowly varying naturalistic inputs, and we
determined how the LFPs generated by the network encoded
information about the inputs. We found that this simulated
recurrent network reproduced well the experimentally
observed dependency of LFP information upon frequency. This
network encoded the overall strength of the input into the
power of gamma-range oscillations generated by
inhibitory-excitatory neural interactions, and encoded slow
variations in the input by entraining the network LFP at the
corresponding frequency. This dynamical behavior accounted
quantitatively for the independent information carried by
high and low frequency LFPs, and for the experimentally
observed cross-frequency coupling between phase of slow LFPs
and the power of gamma LFPs. We also present new results
showing that the model's dynamics also accounted for the
extra visual information that the low-frequency LFP phase of
spike firing carries beyond that carried by spike rates.
Overall, our results suggest biological mechanisms by which
cortex can multiplex information about naturalistic sensory
environments.},
Doi = {10.1016/j.jphysparis.2011.07.014},
Key = {fds328473}
}
@article{fds328474,
Author = {Hamaguchi, K and Riehle, A and Brunel, N},
Title = {Estimating network parameters from combined dynamics of
firing rate and irregularity of single neurons.},
Journal = {J Neurophysiol},
Volume = {105},
Number = {1},
Pages = {487-500},
Year = {2011},
Month = {January},
url = {http://dx.doi.org/10.1152/jn.00858.2009},
Abstract = {High firing irregularity is a hallmark of cortical neurons
in vivo, and modeling studies suggest a balance of
excitation and inhibition is necessary to explain this high
irregularity. Such a balance must be generated, at least
partly, from local interconnected networks of excitatory and
inhibitory neurons, but the details of the local network
structure are largely unknown. The dynamics of the neural
activity depends on the local network structure; this in
turn suggests the possibility of estimating network
structure from the dynamics of the firing statistics. Here
we report a new method to estimate properties of the local
cortical network from the instantaneous firing rate and
irregularity (CV(2)) under the assumption that recorded
neurons are a part of a randomly connected sparse network.
The firing irregularity, measured in monkey motor cortex,
exhibits two features; many neurons show relatively stable
firing irregularity in time and across different task
conditions; the time-averaged CV(2) is widely distributed
from quasi-regular to irregular (CV(2) = 0.3-1.0). For each
recorded neuron, we estimate the three parameters of a local
network [balance of local excitation-inhibition, number of
recurrent connections per neuron, and excitatory
postsynaptic potential (EPSP) size] that best describe the
dynamics of the measured firing rates and irregularities.
Our analysis shows that optimal parameter sets form a
two-dimensional manifold in the three-dimensional parameter
space that is confined for most of the neurons to the
inhibition-dominated region. High irregularity neurons tend
to be more strongly connected to the local network, either
in terms of larger EPSP and inhibitory PSP size or larger
number of recurrent connections, compared with the low
irregularity neurons, for a given excitatory/inhibitory
balance. Incorporating either synaptic short-term depression
or conductance-based synapses leads many low CV(2) neurons
to move to the excitation-dominated region as well as to an
increase of EPSP size.},
Doi = {10.1152/jn.00858.2009},
Key = {fds328474}
}
@article{fds328471,
Author = {Ostojic, S and Brunel, N},
Title = {From spiking neuron models to linear-nonlinear
models.},
Journal = {PLoS Comput Biol},
Volume = {7},
Number = {1},
Pages = {e1001056},
Year = {2011},
Month = {January},
url = {http://dx.doi.org/10.1371/journal.pcbi.1001056},
Abstract = {Neurons transform time-varying inputs into action potentials
emitted stochastically at a time dependent rate. The mapping
from current input to output firing rate is often
represented with the help of phenomenological models such as
the linear-nonlinear (LN) cascade, in which the output
firing rate is estimated by applying to the input
successively a linear temporal filter and a static
non-linear transformation. These simplified models leave out
the biophysical details of action potential generation. It
is not a priori clear to which extent the input-output
mapping of biophysically more realistic, spiking neuron
models can be reduced to a simple linear-nonlinear cascade.
Here we investigate this question for the leaky
integrate-and-fire (LIF), exponential integrate-and-fire
(EIF) and conductance-based Wang-Buzsáki models in presence
of background synaptic activity. We exploit available
analytic results for these models to determine the
corresponding linear filter and static non-linearity in a
parameter-free form. We show that the obtained functions are
identical to the linear filter and static non-linearity
determined using standard reverse correlation analysis. We
then quantitatively compare the output of the corresponding
linear-nonlinear cascade with numerical simulations of
spiking neurons, systematically varying the parameters of
input signal and background noise. We find that the LN
cascade provides accurate estimates of the firing rates of
spiking neurons in most of parameter space. For the EIF and
Wang-Buzsáki models, we show that the LN cascade can be
reduced to a firing rate model, the timescale of which we
determine analytically. Finally we introduce an adaptive
timescale rate model in which the timescale of the linear
filter depends on the instantaneous firing rate. This model
leads to highly accurate estimates of instantaneous firing
rates.},
Doi = {10.1371/journal.pcbi.1001056},
Key = {fds328471}
}
@article{fds328470,
Author = {Roxin, A and Brunel, N and Hansel, D and Mongillo, G and van Vreeswijk,
C},
Title = {On the distribution of firing rates in networks of cortical
neurons.},
Journal = {J Neurosci},
Volume = {31},
Number = {45},
Pages = {16217-16226},
Year = {2011},
Month = {November},
url = {http://dx.doi.org/10.1523/JNEUROSCI.1677-11.2011},
Abstract = {The distribution of in vivo average firing rates within
local cortical networks has been reported to be highly
skewed and long tailed. The distribution of average
single-cell inputs, conversely, is expected to be Gaussian
by the central limit theorem. This raises the issue of how a
skewed distribution of firing rates might result from a
symmetric distribution of inputs. We argue that skewed rate
distributions are a signature of the nonlinearity of the in
vivo f-I curve. During in vivo conditions, ongoing synaptic
activity produces significant fluctuations in the membrane
potential of neurons, resulting in an expansive nonlinearity
of the f-I curve for low and moderate inputs. Here, we
investigate the effects of single-cell and network
parameters on the shape of the f-I curve and, by extension,
on the distribution of firing rates in randomly connected
networks.},
Doi = {10.1523/JNEUROSCI.1677-11.2011},
Key = {fds328470}
}
@article{fds328469,
Author = {Clopath, C and Nadal, J-P and Brunel, N},
Title = {Storage of correlated patterns in standard and bistable
Purkinje cell models.},
Journal = {PLoS Comput Biol},
Volume = {8},
Number = {4},
Pages = {e1002448},
Year = {2012},
url = {http://dx.doi.org/10.1371/journal.pcbi.1002448},
Abstract = {The cerebellum has long been considered to undergo
supervised learning, with climbing fibers acting as a
'teaching' or 'error' signal. Purkinje cells (PCs), the sole
output of the cerebellar cortex, have been considered as
analogs of perceptrons storing input/output associations. In
support of this hypothesis, a recent study found that the
distribution of synaptic weights of a perceptron at maximal
capacity is in striking agreement with experimental data in
adult rats. However, the calculation was performed using
random uncorrelated inputs and outputs. This is a clearly
unrealistic assumption since sensory inputs and motor
outputs carry a substantial degree of temporal correlations.
In this paper, we consider a binary output neuron with a
large number of inputs, which is required to store
associations between temporally correlated sequences of
binary inputs and outputs, modelled as Markov chains.
Storage capacity is found to increase with both input and
output correlations, and diverges in the limit where both go
to unity. We also investigate the capacity of a bistable
output unit, since PCs have been shown to be bistable in
some experimental conditions. Bistability is shown to
enhance storage capacity whenever the output correlation is
stronger than the input correlation. Distribution of
synaptic weights at maximal capacity is shown to be
independent on correlations, and is also unaffected by the
presence of bistability.},
Doi = {10.1371/journal.pcbi.1002448},
Key = {fds328469}
}
@article{fds328468,
Author = {Graupner, M and Brunel, N},
Title = {Calcium-based plasticity model explains sensitivity of
synaptic changes to spike pattern, rate, and dendritic
location.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {109},
Number = {10},
Pages = {3991-3996},
Year = {2012},
Month = {March},
url = {http://dx.doi.org/10.1073/pnas.1109359109},
Abstract = {Multiple stimulation protocols have been found to be
effective in changing synaptic efficacy by inducing
long-term potentiation or depression. In many of those
protocols, increases in postsynaptic calcium concentration
have been shown to play a crucial role. However, it is still
unclear whether and how the dynamics of the postsynaptic
calcium alone determine the outcome of synaptic plasticity.
Here, we propose a calcium-based model of a synapse in which
potentiation and depression are activated above calcium
thresholds. We show that this model gives rise to a large
diversity of spike timing-dependent plasticity curves, most
of which have been observed experimentally in different
systems. It accounts quantitatively for plasticity outcomes
evoked by protocols involving patterns with variable spike
timing and firing rate in hippocampus and neocortex.
Furthermore, it allows us to predict that differences in
plasticity outcomes in different studies are due to
differences in parameters defining the calcium dynamics. The
model provides a mechanistic understanding of how various
stimulation protocols provoke specific synaptic changes
through the dynamics of calcium concentration and thresholds
implementing in simplified fashion protein signaling
cascades, leading to long-term potentiation and long-term
depression. The combination of biophysical realism and
analytical tractability makes it the ideal candidate to
study plasticity at the synapse, neuron, and network
levels.},
Doi = {10.1073/pnas.1109359109},
Key = {fds328468}
}
@article{fds328466,
Author = {Brunel, N and Hakim, V},
Title = {Fokker-Planck Equation},
Pages = {1-6},
Booktitle = {Encyclopedia of Computational Neuroscience},
Publisher = {Springer New York},
Editor = {Jaeger, D and Jung, R},
Year = {2013},
ISBN = {9781461466741},
url = {http://dx.doi.org/10.1007/978-1-4614-7320-6_60-1},
Doi = {10.1007/978-1-4614-7320-6_60-1},
Key = {fds328466}
}
@article{fds328467,
Author = {Clopath, C and Brunel, N},
Title = {Optimal properties of analog perceptrons with excitatory
weights.},
Journal = {PLoS Comput Biol},
Volume = {9},
Number = {2},
Pages = {e1002919},
Year = {2013},
url = {http://dx.doi.org/10.1371/journal.pcbi.1002919},
Abstract = {The cerebellum is a brain structure which has been
traditionally devoted to supervised learning. According to
this theory, plasticity at the Parallel Fiber (PF) to
Purkinje Cell (PC) synapses is guided by the Climbing fibers
(CF), which encode an 'error signal'. Purkinje cells have
thus been modeled as perceptrons, learning input/output
binary associations. At maximal capacity, a perceptron with
excitatory weights expresses a large fraction of zero-weight
synapses, in agreement with experimental findings. However,
numerous experiments indicate that the firing rate of
Purkinje cells varies in an analog, not binary, manner. In
this paper, we study the perceptron with analog inputs and
outputs. We show that the optimal input has a sparse binary
distribution, in good agreement with the burst firing of the
Granule cells. In addition, we show that the weight
distribution consists of a large fraction of silent
synapses, as in previously studied binary perceptron models,
and as seen experimentally.},
Doi = {10.1371/journal.pcbi.1002919},
Key = {fds328467}
}
@article{fds356866,
Author = {Brunel, N and Hakim, V},
Title = {Population Density Models},
Pages = {1-24},
Booktitle = {Encyclopedia of Computational Neuroscience},
Publisher = {Springer New York},
Year = {2013},
url = {http://dx.doi.org/10.1007/978-1-4614-7320-6_74-1},
Doi = {10.1007/978-1-4614-7320-6_74-1},
Key = {fds356866}
}
@article{fds339267,
Author = {Brunel, N},
Title = {Dynamics of neural networks},
Pages = {489-512},
Booktitle = {Principles of Neural Coding},
Publisher = {CRC Press},
Year = {2013},
Month = {January},
ISBN = {9781439853313},
url = {http://dx.doi.org/10.1201/b14756},
Abstract = {© 2013 by Taylor & Francis Group, LLC. Animals are
constantly submitted to a bombardment of information through
their sensory systems. This information is transmitted to
the central nervous system (CNS) in the form of spike
trains. Traditional views of how this information is
processed by the CNS consist in a series of networks (or
layers) of neurons, connected in a predominantly feedforward
manner. However, neurons in any cortical network receive
their inputs not only from the previous layers (i.e., LGN
for V1 neurons, V1 for V2 neurons, etc.), but also from
nearby neurons that are part of the same network
(“lateral” or “recurrent " connections), and from
neurons in higher areas in the feedforward hierarchy
(“top-down” connections). In fact, anatomy shows that
feedforward inputs are typically a small minority of the
inputs received by a cortical neuron (Binzegger et al.
2004). Therefore, to understand how networks of neurons in
the CNS transmit the information that they receive, it is
not enough to understand the input/output transformation at
the single neuron level. In addition, one has to understand
how the dynamics of networks of neurons shape the response
of the population as a whole to dynamic inputs.},
Doi = {10.1201/b14756},
Key = {fds339267}
}
@article{fds328464,
Author = {Hertäg, L and Durstewitz, D and Brunel, N},
Title = {Analytical approximations of the firing rate of an adaptive
exponential integrate-and-fire neuron in the presence of
synaptic noise.},
Journal = {Front Comput Neurosci},
Volume = {8},
Pages = {116},
Year = {2014},
url = {http://dx.doi.org/10.3389/fncom.2014.00116},
Abstract = {Computational models offer a unique tool for understanding
the network-dynamical mechanisms which mediate between
physiological and biophysical properties, and behavioral
function. A traditional challenge in computational
neuroscience is, however, that simple neuronal models which
can be studied analytically fail to reproduce the diversity
of electrophysiological behaviors seen in real neurons,
while detailed neuronal models which do reproduce such
diversity are intractable analytically and computationally
expensive. A number of intermediate models have been
proposed whose aim is to capture the diversity of firing
behaviors and spike times of real neurons while entailing
the simplest possible mathematical description. One such
model is the exponential integrate-and-fire neuron with
spike rate adaptation (aEIF) which consists of two
differential equations for the membrane potential (V) and an
adaptation current (w). Despite its simplicity, it can
reproduce a wide variety of physiologically observed spiking
patterns, can be fit to physiological recordings
quantitatively, and, once done so, is able to predict spike
times on traces not used for model fitting. Here we compute
the steady-state firing rate of aEIF in the presence of
Gaussian synaptic noise, using two approaches. The first
approach is based on the 2-dimensional Fokker-Planck
equation that describes the (V,w)-probability distribution,
which is solved using an expansion in the ratio between the
time constants of the two variables. The second is based on
the firing rate of the EIF model, which is averaged over the
distribution of the w variable. These analytically derived
closed-form expressions were tested on simulations from a
large variety of model cells quantitatively fitted to in
vitro electrophysiological recordings from pyramidal cells
and interneurons. Theoretical predictions closely agreed
with the firing rate of the simulated cells fed with
in-vivo-like synaptic noise.},
Doi = {10.3389/fncom.2014.00116},
Key = {fds328464}
}
@article{fds328463,
Author = {Tartaglia, EM and Mongillo, G and Brunel, N},
Title = {On the relationship between persistent delay activity,
repetition enhancement and priming.},
Journal = {Front Psychol},
Volume = {5},
Pages = {1590},
Year = {2014},
url = {http://dx.doi.org/10.3389/fpsyg.2014.01590},
Abstract = {Human efficiency in processing incoming stimuli (in terms of
speed and/or accuracy) is typically enhanced by previous
exposure to the same, or closely related stimuli-a
phenomenon referred to as priming. In spite of the large
body of knowledge accumulated in behavioral studies about
the conditions conducive to priming, and its relationship
with other forms of memory, the underlying neuronal
correlates of priming are still under debate. The idea has
repeatedly been advanced that a major neuronal mechanism
supporting behaviorally-expressed priming is repetition
suppression, a widespread reduction of spiking activity upon
stimulus repetition which has been routinely exposed by
single-unit recordings in non-human primates performing
delayed-response, as well as passive fixation tasks. This
proposal is mainly motivated by the observation that, in
human fMRI studies, priming is associated to a significant
reduction of the BOLD signal (widely interpreted as a proxy
of the level of spiking activity) upon stimulus repetition.
Here, we critically re-examine a large part of the
electrophysiological literature on repetition suppression in
non-human primates and find that repetition suppression is
systematically accompanied by stimulus-selective delay
period activity, together with repetition enhancement, an
increase of spiking activity upon stimulus repetition in
small neuronal populations. We argue that repetition
enhancement constitutes a more viable candidate for a
putative neuronal substrate of priming, and propose a
minimal framework that links together, mechanistically and
functionally, repetition suppression, stimulus-selective
delay activity and repetition enhancement.},
Doi = {10.3389/fpsyg.2014.01590},
Key = {fds328463}
}
@article{fds356865,
Author = {Brunel, N and Hakim, V},
Title = {Fokker-Planck Equation},
Pages = {1-5},
Booktitle = {Encyclopedia of Computational Neuroscience},
Publisher = {Springer New York},
Year = {2014},
ISBN = {9781461466741},
url = {http://dx.doi.org/10.1007/978-1-4614-7320-6_60-2},
Doi = {10.1007/978-1-4614-7320-6_60-2},
Key = {fds356865}
}
@article{fds328462,
Author = {Brunel, N and Hakim, V and Richardson, MJE},
Title = {Single neuron dynamics and computation.},
Journal = {Curr Opin Neurobiol},
Volume = {25},
Pages = {149-155},
Year = {2014},
Month = {April},
url = {http://dx.doi.org/10.1016/j.conb.2014.01.005},
Abstract = {At the single neuron level, information processing involves
the transformation of input spike trains into an appropriate
output spike train. Building upon the classical view of a
neuron as a threshold device, models have been developed in
recent years that take into account the diverse
electrophysiological make-up of neurons and accurately
describe their input-output relations. Here, we review these
recent advances and survey the computational roles that they
have uncovered for various electrophysiological properties,
for dendritic arbor anatomy as well as for short-term
synaptic plasticity.},
Doi = {10.1016/j.conb.2014.01.005},
Key = {fds328462}
}
@article{fds328461,
Author = {Clopath, C and Badura, A and De Zeeuw and CI and Brunel,
N},
Title = {A cerebellar learning model of vestibulo-ocular reflex
adaptation in wild-type and mutant mice.},
Journal = {J Neurosci},
Volume = {34},
Number = {21},
Pages = {7203-7215},
Year = {2014},
Month = {May},
url = {http://dx.doi.org/10.1523/JNEUROSCI.2791-13.2014},
Abstract = {Mechanisms of cerebellar motor learning are still poorly
understood. The standard Marr-Albus-Ito theory posits that
learning involves plasticity at the parallel fiber to
Purkinje cell synapses under control of the climbing fiber
input, which provides an error signal as in classical
supervised learning paradigms. However, a growing body of
evidence challenges this theory, in that additional sites of
plasticity appear to contribute to motor adaptation. Here,
we consider phase-reversal training of the vestibulo-ocular
reflex (VOR), a simple form of motor learning for which a
large body of experimental data is available in wild-type
and mutant mice, in which the excitability of granule cells
or inhibition of Purkinje cells was affected in a
cell-specific fashion. We present novel electrophysiological
recordings of Purkinje cell activity measured in naive
wild-type mice subjected to this VOR adaptation task. We
then introduce a minimal model that consists of learning at
the parallel fibers to Purkinje cells with the help of the
climbing fibers. Although the minimal model reproduces the
behavior of the wild-type animals and is analytically
tractable, it fails at reproducing the behavior of mutant
mice and the electrophysiology data. Therefore, we build a
detailed model involving plasticity at the parallel fibers
to Purkinje cells' synapse guided by climbing fibers,
feedforward inhibition of Purkinje cells, and plasticity at
the mossy fiber to vestibular nuclei neuron synapse. The
detailed model reproduces both the behavioral and
electrophysiological data of both the wild-type and mutant
mice and allows for experimentally testable
predictions.},
Doi = {10.1523/JNEUROSCI.2791-13.2014},
Key = {fds328461}
}
@article{fds328460,
Author = {Dubreuil, AM and Amit, Y and Brunel, N},
Title = {Memory capacity of networks with stochastic binary
synapses.},
Journal = {PLoS Comput Biol},
Volume = {10},
Number = {8},
Pages = {e1003727},
Year = {2014},
Month = {August},
url = {http://dx.doi.org/10.1371/journal.pcbi.1003727},
Abstract = {In standard attractor neural network models, specific
patterns of activity are stored in the synaptic matrix, so
that they become fixed point attractors of the network
dynamics. The storage capacity of such networks has been
quantified in two ways: the maximal number of patterns that
can be stored, and the stored information measured in bits
per synapse. In this paper, we compute both quantities in
fully connected networks of N binary neurons with binary
synapses, storing patterns with coding level [Formula: see
text], in the large [Formula: see text] and sparse coding
limits ([Formula: see text]). We also derive finite-size
corrections that accurately reproduce the results of
simulations in networks of tens of thousands of neurons.
These methods are applied to three different scenarios: (1)
the classic Willshaw model, (2) networks with stochastic
learning in which patterns are shown only once (one shot
learning), (3) networks with stochastic learning in which
patterns are shown multiple times. The storage capacities
are optimized over network parameters, which allows us to
compare the performance of the different models. We show
that finite-size effects strongly reduce the capacity, even
for networks of realistic sizes. We discuss the implications
of these results for memory storage in the hippocampus and
cerebral cortex.},
Doi = {10.1371/journal.pcbi.1003727},
Key = {fds328460}
}
@article{fds328458,
Author = {Higgins, D and Graupner, M and Brunel, N},
Title = {Memory maintenance in synapses with calcium-based plasticity
in the presence of background activity.},
Journal = {PLoS Comput Biol},
Volume = {10},
Number = {10},
Pages = {e1003834},
Year = {2014},
Month = {October},
url = {http://dx.doi.org/10.1371/journal.pcbi.1003834},
Abstract = {Most models of learning and memory assume that memories are
maintained in neuronal circuits by persistent synaptic
modifications induced by specific patterns of pre- and
postsynaptic activity. For this scenario to be viable,
synaptic modifications must survive the ubiquitous ongoing
activity present in neural circuits in vivo. In this paper,
we investigate the time scales of memory maintenance in a
calcium-based synaptic plasticity model that has been shown
recently to be able to fit different experimental data-sets
from hippocampal and neocortical preparations. We find that
in the presence of background activity on the order of 1 Hz
parameters that fit pyramidal layer 5 neocortical data lead
to a very fast decay of synaptic efficacy, with time scales
of minutes. We then identify two ways in which this memory
time scale can be extended: (i) the extracellular calcium
concentration in the experiments used to fit the model are
larger than estimated concentrations in vivo. Lowering
extracellular calcium concentration to in vivo levels leads
to an increase in memory time scales of several orders of
magnitude; (ii) adding a bistability mechanism so that each
synapse has two stable states at sufficiently low background
activity leads to a further boost in memory time scale,
since memory decay is no longer described by an exponential
decay from an initial state, but by an escape from a
potential well. We argue that both features are expected to
be present in synapses in vivo. These results are obtained
first in a single synapse connecting two independent Poisson
neurons, and then in simulations of a large network of
excitatory and inhibitory integrate-and-fire neurons. Our
results emphasise the need for studying plasticity at
physiological extracellular calcium concentration, and
highlight the role of synaptic bi- or multistability in the
stability of learned synaptic structures.},
Doi = {10.1371/journal.pcbi.1003834},
Key = {fds328458}
}
@article{fds328459,
Author = {Barbieri, F and Mazzoni, A and Logothetis, NK and Panzeri, S and Brunel,
N},
Title = {Stimulus dependence of local field potential spectra:
experiment versus theory.},
Journal = {J Neurosci},
Volume = {34},
Number = {44},
Pages = {14589-14605},
Year = {2014},
Month = {October},
url = {http://dx.doi.org/10.1523/JNEUROSCI.5365-13.2014},
Abstract = {The local field potential (LFP) captures different neural
processes, including integrative synaptic dynamics that
cannot be observed by measuring only the spiking activity of
small populations. Therefore, investigating how LFP power is
modulated by external stimuli can offer important insights
into sensory neural representations. However, gaining such
insight requires developing data-driven computational models
that can identify and disambiguate the neural contributions
to the LFP. Here, we investigated how networks of excitatory
and inhibitory integrate-and-fire neurons responding to
time-dependent inputs can be used to interpret sensory
modulations of LFP spectra. We computed analytically from
such models the LFP spectra and the information that they
convey about input and used these analytical expressions to
fit the model to LFPs recorded in V1 of anesthetized
macaques (Macaca mulatta) during the presentation of color
movies. Our expressions explain 60%-98% of the variance of
the LFP spectrum shape and its dependency upon movie scenes
and we achieved this with realistic values for the best-fit
parameters. In particular, synaptic best-fit parameters were
compatible with experimental measurements and the
predictions of firing rates, based only on the fit of LFP
data, correlated with the multiunit spike rate recorded from
the same location. Moreover, the parameters characterizing
the input to the network across different movie scenes
correlated with cross-scene changes of several image
features. Our findings suggest that analytical descriptions
of spiking neuron networks may become a crucial tool for the
interpretation of field recordings.},
Doi = {10.1523/JNEUROSCI.5365-13.2014},
Key = {fds328459}
}
@article{fds328465,
Author = {Brunel, N and Hakim, V},
Title = {Population Density Model},
Pages = {2447-2465},
Booktitle = {Encyclopedia of Computational Neuroscience},
Publisher = {Springer New York},
Editor = {Jaeger, D and Jung, R},
Year = {2015},
ISBN = {9781461466741},
url = {http://dx.doi.org/10.1007/978-1-4614-6675-8_74},
Doi = {10.1007/978-1-4614-6675-8_74},
Key = {fds328465}
}
@article{fds328457,
Author = {Tartaglia, EM and Brunel, N and Mongillo, G},
Title = {Modulation of network excitability by persistent activity:
how working memory affects the response to incoming
stimuli.},
Journal = {PLoS Comput Biol},
Volume = {11},
Number = {2},
Pages = {e1004059},
Year = {2015},
Month = {February},
url = {http://dx.doi.org/10.1371/journal.pcbi.1004059},
Abstract = {Persistent activity and match effects are widely regarded as
neuronal correlates of short-term storage and manipulation
of information, with the first serving active maintenance
and the latter supporting the comparison between memory
contents and incoming sensory information. The mechanistic
and functional relationship between these two basic
neurophysiological signatures of working memory remains
elusive. We propose that match signals are generated as a
result of transient changes in local network excitability
brought about by persistent activity. Neurons more active
will be more excitable, and thus more responsive to external
inputs. Accordingly, network responses are jointly
determined by the incoming stimulus and the ongoing pattern
of persistent activity. Using a spiking model network, we
show that this mechanism is able to reproduce most of the
experimental phenomenology of match effects as exposed by
single-cell recordings during delayed-response tasks. The
model provides a unified, parsimonious mechanistic account
of the main neuronal correlates of working memory, makes
several experimentally testable predictions, and
demonstrates a new functional role for persistent
activity.},
Doi = {10.1371/journal.pcbi.1004059},
Key = {fds328457}
}
@article{fds328456,
Author = {Ostojic, S and Szapiro, G and Schwartz, E and Barbour, B and Brunel, N and Hakim, V},
Title = {Neuronal morphology generates high-frequency firing
resonance.},
Journal = {J Neurosci},
Volume = {35},
Number = {18},
Pages = {7056-7068},
Year = {2015},
Month = {May},
url = {http://dx.doi.org/10.1523/JNEUROSCI.3924-14.2015},
Abstract = {The attenuation of neuronal voltage responses to
high-frequency current inputs by the membrane capacitance is
believed to limit single-cell bandwidth. However, neuronal
populations subject to stochastic fluctuations can follow
inputs beyond this limit. We investigated this apparent
paradox theoretically and experimentally using Purkinje
cells in the cerebellum, a motor structure that benefits
from rapid information transfer. We analyzed the modulation
of firing in response to the somatic injection of sinusoidal
currents. Computational modeling suggested that, instead of
decreasing with frequency, modulation amplitude can increase
up to high frequencies because of cellular morphology.
Electrophysiological measurements in adult rat slices
confirmed this prediction and displayed a marked resonance
at 200 Hz. We elucidated the underlying mechanism, showing
that the two-compartment morphology of the Purkinje cell,
interacting with a simple spiking mechanism and dendritic
fluctuations, is sufficient to create high-frequency signal
amplification. This mechanism, which we term
morphology-induced resonance, is selective for somatic
inputs, which in the Purkinje cell are exclusively
inhibitory. The resonance sensitizes Purkinje cells in the
frequency range of population oscillations observed in
vivo.},
Doi = {10.1523/JNEUROSCI.3924-14.2015},
Key = {fds328456}
}
@article{fds328455,
Author = {Alemi, A and Baldassi, C and Brunel, N and Zecchina,
R},
Title = {A Three-Threshold Learning Rule Approaches the Maximal
Capacity of Recurrent Neural Networks.},
Journal = {PLoS Comput Biol},
Volume = {11},
Number = {8},
Pages = {e1004439},
Year = {2015},
Month = {August},
url = {http://dx.doi.org/10.1371/journal.pcbi.1004439},
Abstract = {Understanding the theoretical foundations of how memories
are encoded and retrieved in neural populations is a central
challenge in neuroscience. A popular theoretical scenario
for modeling memory function is the attractor neural network
scenario, whose prototype is the Hopfield model. The model
simplicity and the locality of the synaptic update rules
come at the cost of a poor storage capacity, compared with
the capacity achieved with perceptron learning algorithms.
Here, by transforming the perceptron learning rule, we
present an online learning rule for a recurrent neural
network that achieves near-maximal storage capacity without
an explicit supervisory error signal, relying only upon
locally accessible information. The fully-connected network
consists of excitatory binary neurons with plastic recurrent
connections and non-plastic inhibitory feedback stabilizing
the network dynamics; the memory patterns to be memorized
are presented online as strong afferent currents, producing
a bimodal distribution for the neuron synaptic inputs.
Synapses corresponding to active inputs are modified as a
function of the value of the local fields with respect to
three thresholds. Above the highest threshold, and below the
lowest threshold, no plasticity occurs. In between these two
thresholds, potentiation/depression occurs when the local
field is above/below an intermediate threshold. We simulated
and analyzed a network of binary neurons implementing this
rule and measured its storage capacity for different sizes
of the basins of attraction. The storage capacity obtained
through numerical simulations is shown to be close to the
value predicted by analytical calculations. We also measured
the dependence of capacity on the strength of external
inputs. Finally, we quantified the statistics of the
resulting synaptic connectivity matrix, and found that both
the fraction of zero weight synapses and the degree of
symmetry of the weight matrix increase with the number of
stored patterns.},
Doi = {10.1371/journal.pcbi.1004439},
Key = {fds328455}
}
@article{fds328454,
Author = {Lim, S and McKee, JL and Woloszyn, L and Amit, Y and Freedman, DJ and Sheinberg, DL and Brunel, N},
Title = {Inferring learning rules from distributions of firing rates
in cortical neurons.},
Journal = {Nat Neurosci},
Volume = {18},
Number = {12},
Pages = {1804-1810},
Year = {2015},
Month = {December},
url = {http://dx.doi.org/10.1038/nn.4158},
Abstract = {Information about external stimuli is thought to be stored
in cortical circuits through experience-dependent
modifications of synaptic connectivity. These modifications
of network connectivity should lead to changes in neuronal
activity as a particular stimulus is repeatedly encountered.
Here we ask what plasticity rules are consistent with the
differences in the statistics of the visual response to
novel and familiar stimuli in inferior temporal cortex, an
area underlying visual object recognition. We introduce a
method that allows one to infer the dependence of the
presumptive learning rule on postsynaptic firing rate, and
we show that the inferred learning rule exhibits depression
for low postsynaptic rates and potentiation for high rates.
The threshold separating depression from potentiation is
strongly correlated with both mean and s.d. of the firing
rate distribution. Finally, we show that network models
implementing a rule extracted from data show stable learning
dynamics and lead to sparser representations of
stimuli.},
Doi = {10.1038/nn.4158},
Key = {fds328454}
}
@article{fds328453,
Author = {De Pittà and M and Brunel, N},
Title = {Modulation of Synaptic Plasticity by Glutamatergic
Gliotransmission: A Modeling Study.},
Journal = {Neural Plast},
Volume = {2016},
Pages = {7607924},
Year = {2016},
url = {http://dx.doi.org/10.1155/2016/7607924},
Abstract = {Glutamatergic gliotransmission, that is, the release of
glutamate from perisynaptic astrocyte processes in an
activity-dependent manner, has emerged as a potentially
crucial signaling pathway for regulation of synaptic
plasticity, yet its modes of expression and function in vivo
remain unclear. Here, we focus on two experimentally
well-identified gliotransmitter pathways, (i) modulations of
synaptic release and (ii) postsynaptic slow inward currents
mediated by glutamate released from astrocytes, and
investigate their possible functional relevance on synaptic
plasticity in a biophysical model of an astrocyte-regulated
synapse. Our model predicts that both pathways could
profoundly affect both short- and long-term plasticity. In
particular, activity-dependent glutamate release from
astrocytes could dramatically change spike-timing-dependent
plasticity, turning potentiation into depression (and vice
versa) for the same induction protocol.},
Doi = {10.1155/2016/7607924},
Key = {fds328453}
}
@article{fds366924,
Author = {Brunel, N},
Title = {Basic Neuron and Network Models},
Pages = {73-99},
Booktitle = {FROM NEURON TO COGNITION VIA COMPUTATIONAL
NEUROSCIENCE},
Year = {2016},
Key = {fds366924}
}
@article{fds328451,
Author = {Dubreuil, AM and Brunel, N},
Title = {Storing structured sparse memories in a multi-modular
cortical network model.},
Journal = {J Comput Neurosci},
Volume = {40},
Number = {2},
Pages = {157-175},
Year = {2016},
Month = {April},
url = {http://dx.doi.org/10.1007/s10827-016-0590-z},
Abstract = {We study the memory performance of a class of modular
attractor neural networks, where modules are potentially
fully-connected networks connected to each other via diluted
long-range connections. On this anatomical architecture we
store memory patterns of activity using a Willshaw-type
learning rule. P patterns are split in categories, such that
patterns of the same category activate the same set of
modules. We first compute the maximal storage capacity of
these networks. We then investigate their error-correction
properties through an exhaustive exploration of parameter
space, and identify regions where the networks behave as an
associative memory device. The crucial parameters that
control the retrieval abilities of the network are (1) the
ratio between the number of synaptic contacts of long- and
short-range origins (2) the number of categories in which a
module is activated and (3) the amount of local inhibition.
We discuss the relationship between our model and networks
of cortical patches that have been observed in different
cortical areas.},
Doi = {10.1007/s10827-016-0590-z},
Key = {fds328451}
}
@article{fds328452,
Author = {Bouvier, G and Higgins, D and Spolidoro, M and Carrel, D and Mathieu, B and Léna, C and Dieudonné, S and Barbour, B and Brunel, N and Casado,
M},
Title = {Burst-Dependent Bidirectional Plasticity in the Cerebellum
Is Driven by Presynaptic NMDA Receptors.},
Journal = {Cell Rep},
Volume = {15},
Number = {1},
Pages = {104-116},
Year = {2016},
Month = {April},
url = {http://dx.doi.org/10.1016/j.celrep.2016.03.004},
Abstract = {Numerous studies have shown that cerebellar function is
related to the plasticity at the synapses between parallel
fibers and Purkinje cells. How specific input patterns
determine plasticity outcomes, as well as the biophysics
underlying plasticity of these synapses, remain unclear.
Here, we characterize the patterns of activity that lead to
postsynaptically expressed LTP using both in vivo and in
vitro experiments. Similar to the requirements of LTD, we
find that high-frequency bursts are necessary to trigger LTP
and that this burst-dependent plasticity depends on
presynaptic NMDA receptors and nitric oxide (NO) signaling.
We provide direct evidence for calcium entry through
presynaptic NMDA receptors in a subpopulation of parallel
fiber varicosities. Finally, we develop and experimentally
verify a mechanistic plasticity model based on NO and
calcium signaling. The model reproduces plasticity outcomes
from data and predicts the effect of arbitrary patterns of
synaptic inputs on Purkinje cells, thereby providing a
unified description of plasticity.},
Doi = {10.1016/j.celrep.2016.03.004},
Key = {fds328452}
}
@article{fds328449,
Author = {Brunel, N},
Title = {Is cortical connectivity optimized for storing
information?},
Journal = {Nat Neurosci},
Volume = {19},
Number = {5},
Pages = {749-755},
Year = {2016},
Month = {May},
url = {http://dx.doi.org/10.1038/nn.4286},
Abstract = {Cortical networks are thought to be shaped by
experience-dependent synaptic plasticity. Theoretical
studies have shown that synaptic plasticity allows a network
to store a memory of patterns of activity such that they
become attractors of the dynamics of the network. Here we
study the properties of the excitatory synaptic connectivity
in a network that maximizes the number of stored patterns of
activity in a robust fashion. We show that the resulting
synaptic connectivity matrix has the following properties:
it is sparse, with a large fraction of zero synaptic weights
('potential' synapses); bidirectionally coupled pairs of
neurons are over-represented in comparison to a random
network; and bidirectionally connected pairs have stronger
synapses on average than unidirectionally connected pairs.
All these features reproduce quantitatively available data
on connectivity in cortex. This suggests synaptic
connectivity in cortex is optimized to store a large number
of attractor states in a robust fashion.},
Doi = {10.1038/nn.4286},
Key = {fds328449}
}
@article{fds328450,
Author = {De Pittà and M and Brunel, N and Volterra, A},
Title = {Astrocytes: Orchestrating synaptic plasticity?},
Journal = {Neuroscience},
Volume = {323},
Pages = {43-61},
Year = {2016},
Month = {May},
url = {http://dx.doi.org/10.1016/j.neuroscience.2015.04.001},
Abstract = {Synaptic plasticity is the capacity of a preexisting
connection between two neurons to change in strength as a
function of neural activity. Because synaptic plasticity is
the major candidate mechanism for learning and memory, the
elucidation of its constituting mechanisms is of crucial
importance in many aspects of normal and pathological brain
function. In particular, a prominent aspect that remains
debated is how the plasticity mechanisms, that encompass a
broad spectrum of temporal and spatial scales, come to play
together in a concerted fashion. Here we review and discuss
evidence that pinpoints to a possible non-neuronal, glial
candidate for such orchestration: the regulation of synaptic
plasticity by astrocytes.},
Doi = {10.1016/j.neuroscience.2015.04.001},
Key = {fds328450}
}
@article{fds328448,
Author = {Zampini, V and Liu, JK and Diana, MA and Maldonado, PP and Brunel, N and Dieudonné, S},
Title = {Mechanisms and functional roles of glutamatergic synapse
diversity in a cerebellar circuit.},
Journal = {Elife},
Volume = {5},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.7554/eLife.15872},
Abstract = {Synaptic currents display a large degree of heterogeneity of
their temporal characteristics, but the functional role of
such heterogeneities remains unknown. We investigated in rat
cerebellar slices synaptic currents in Unipolar Brush Cells
(UBCs), which generate intrinsic mossy fibers relaying
vestibular inputs to the cerebellar cortex. We show that
UBCs respond to sinusoidal modulations of their sensory
input with heterogeneous amplitudes and phase shifts.
Experiments and modeling indicate that this variability
results both from the kinetics of synaptic glutamate
transients and from the diversity of postsynaptic receptors.
While phase inversion is produced by an mGluR2-activated
outward conductance in OFF-UBCs, the phase delay of ON UBCs
is caused by a late rebound current resulting from AMPAR
recovery from desensitization. Granular layer network
modeling indicates that phase dispersion of UBC responses
generates diverse phase coding in the granule cell
population, allowing climbing-fiber-driven Purkinje cell
learning at arbitrary phases of the vestibular
input.},
Doi = {10.7554/eLife.15872},
Key = {fds328448}
}
@article{fds328447,
Author = {Titley, HK and Brunel, N and Hansel, C},
Title = {Toward a Neurocentric View of Learning.},
Journal = {Neuron},
Volume = {95},
Number = {1},
Pages = {19-32},
Year = {2017},
Month = {July},
url = {http://dx.doi.org/10.1016/j.neuron.2017.05.021},
Abstract = {Synaptic plasticity (e.g., long-term potentiation [LTP]) is
considered the cellular correlate of learning. Recent
optogenetic studies on memory engram formation assign a
critical role in learning to suprathreshold activation of
neurons and their integration into active engrams ("engram
cells"). Here we review evidence that ensemble integration
may result from LTP but also from cell-autonomous changes in
membrane excitability. We propose that synaptic plasticity
determines synaptic connectivity maps, whereas intrinsic
plasticity-possibly separated in time-amplifies neuronal
responsiveness and acutely drives engram integration. Our
proposal marks a move away from an exclusively
synaptocentric toward a non-exclusive, neurocentric view of
learning.},
Doi = {10.1016/j.neuron.2017.05.021},
Key = {fds328447}
}
@article{fds328910,
Author = {Tartaglia, EM and Brunel, N},
Title = {Bistability and up/down state alternations in
inhibition-dominated randomly connected networks of LIF
neurons.},
Journal = {Sci Rep},
Volume = {7},
Number = {1},
Pages = {11916},
Year = {2017},
Month = {September},
url = {http://dx.doi.org/10.1038/s41598-017-12033-y},
Abstract = {Electrophysiological recordings in cortex in vivo have
revealed a rich variety of dynamical regimes ranging from
irregular asynchronous states to a diversity of synchronized
states, depending on species, anesthesia, and external
stimulation. The average population firing rate in these
states is typically low. We study analytically and
numerically a network of sparsely connected excitatory and
inhibitory integrate-and-fire neurons in the
inhibition-dominated, low firing rate regime. For
sufficiently high values of the external input, the network
exhibits an asynchronous low firing frequency state (L).
Depending on synaptic time constants, we show that two
scenarios may occur when external inputs are decreased: (1)
the L state can destabilize through a Hopf bifucation as the
external input is decreased, leading to synchronized
oscillations spanning d δ to β frequencies; (2) the
network can reach a bistable region, between the low firing
frequency network state (L) and a quiescent one (Q). Adding
an adaptation current to excitatory neurons leads to
spontaneous alternations between L and Q states, similar to
experimental observations on UP and DOWN states
alternations.},
Doi = {10.1038/s41598-017-12033-y},
Key = {fds328910}
}
@article{fds339215,
Author = {Martí, D and Brunel, N and Ostojic, S},
Title = {Correlations between synapses in pairs of neurons slow down
dynamics in randomly connected neural networks.},
Journal = {Phys Rev E},
Volume = {97},
Number = {6-1},
Pages = {062314},
Year = {2018},
Month = {June},
url = {http://dx.doi.org/10.1103/PhysRevE.97.062314},
Abstract = {Networks of randomly connected neurons are among the most
popular models in theoretical neuroscience. The connectivity
between neurons in the cortex is however not fully random,
the simplest and most prominent deviation from randomness
found in experimental data being the overrepresentation of
bidirectional connections among pyramidal cells. Using
numerical and analytical methods, we investigate the effects
of partially symmetric connectivity on the dynamics in
networks of rate units. We consider the two dynamical
regimes exhibited by random neural networks: the
weak-coupling regime, where the firing activity decays to a
single fixed point unless the network is stimulated, and the
strong-coupling or chaotic regime, characterized by
internally generated fluctuating firing rates. In the
weak-coupling regime, we compute analytically, for an
arbitrary degree of symmetry, the autocorrelation of network
activity in the presence of external noise. In the chaotic
regime, we perform simulations to determine the timescale of
the intrinsic fluctuations. In both cases, symmetry
increases the characteristic asymptotic decay time of the
autocorrelation function and therefore slows down the
dynamics in the network.},
Doi = {10.1103/PhysRevE.97.062314},
Key = {fds339215}
}
@article{fds336918,
Author = {Pereira, U and Brunel, N},
Title = {Attractor Dynamics in Networks with Learning Rules Inferred
from In Vivo Data.},
Journal = {Neuron},
Volume = {99},
Number = {1},
Pages = {227-238.e4},
Year = {2018},
Month = {July},
url = {http://dx.doi.org/10.1016/j.neuron.2018.05.038},
Abstract = {The attractor neural network scenario is a popular scenario
for memory storage in the association cortex, but there is
still a large gap between models based on this scenario and
experimental data. We study a recurrent network model in
which both learning rules and distribution of stored
patterns are inferred from distributions of visual responses
for novel and familiar images in the inferior temporal
cortex (ITC). Unlike classical attractor neural network
models, our model exhibits graded activity in retrieval
states, with distributions of firing rates that are close to
lognormal. Inferred learning rules are close to maximizing
the number of stored patterns within a family of
unsupervised Hebbian learning rules, suggesting that
learning rules in ITC are optimized to store a large number
of attractor states. Finally, we show that there exist two
types of retrieval states: one in which firing rates are
constant in time and another in which firing rates fluctuate
chaotically.},
Doi = {10.1016/j.neuron.2018.05.038},
Key = {fds336918}
}
@article{fds339859,
Author = {Bouvier, G and Aljadeff, J and Clopath, C and Bimbard, C and Ranft, J and Blot, A and Nadal, J-P and Brunel, N and Hakim, V and Barbour,
B},
Title = {Cerebellar learning using perturbations.},
Journal = {Elife},
Volume = {7},
Pages = {e31599},
Year = {2018},
Month = {November},
url = {http://dx.doi.org/10.7554/eLife.31599},
Abstract = {The cerebellum aids the learning of fast, coordinated
movements. According to current consensus, erroneously
active parallel fibre synapses are depressed by complex
spikes signalling movement errors. However, this theory
cannot solve the credit assignment problem of processing a
global movement evaluation into multiple cell-specific error
signals. We identify a possible implementation of an
algorithm solving this problem, whereby spontaneous complex
spikes perturb ongoing movements, create eligibility traces
and signal error changes guiding plasticity. Error changes
are extracted by adaptively cancelling the average error.
This framework, stochastic gradient descent with estimated
global errors (SGDEGE), predicts synaptic plasticity rules
that apparently contradict the current consensus but were
supported by plasticity experiments in slices from mice
under conditions designed to be physiological, highlighting
the sensitivity of plasticity studies to experimental
conditions. We analyse the algorithm's convergence and
capacity. Finally, we suggest SGDEGE may also operate in the
basal ganglia.},
Doi = {10.7554/eLife.31599},
Key = {fds339859}
}
@article{fds348568,
Author = {Pereira, U and Brunel, N},
Title = {Unsupervised Learning of Persistent and Sequential
Activity.},
Journal = {Front Comput Neurosci},
Volume = {13},
Pages = {97},
Year = {2019},
url = {http://dx.doi.org/10.3389/fncom.2019.00097},
Abstract = {Two strikingly distinct types of activity have been observed
in various brain structures during delay periods of delayed
response tasks: Persistent activity (PA), in which a
sub-population of neurons maintains an elevated firing rate
throughout an entire delay period; and Sequential activity
(SA), in which sub-populations of neurons are activated
sequentially in time. It has been hypothesized that both
types of dynamics can be "learned" by the relevant networks
from the statistics of their inputs, thanks to mechanisms of
synaptic plasticity. However, the necessary conditions for a
synaptic plasticity rule and input statistics to learn these
two types of dynamics in a stable fashion are still unclear.
In particular, it is unclear whether a single learning rule
is able to learn both types of activity patterns, depending
on the statistics of the inputs driving the network. Here,
we first characterize the complete bifurcation diagram of a
firing rate model of multiple excitatory populations with an
inhibitory mechanism, as a function of the parameters
characterizing its connectivity. We then investigate how an
unsupervised temporally asymmetric Hebbian plasticity rule
shapes the dynamics of the network. Consistent with previous
studies, we find that for stable learning of PA and SA, an
additional stabilization mechanism is necessary. We show
that a generalized version of the standard multiplicative
homeostatic plasticity (Renart et al., 2003; Toyoizumi et
al., 2014) stabilizes learning by effectively masking
excitatory connections during stimulation and unmasking
those connections during retrieval. Using the bifurcation
diagram derived for fixed connectivity, we study
analytically the temporal evolution and the steady state of
the learned recurrent architecture as a function of
parameters characterizing the external inputs. Slow changing
stimuli lead to PA, while fast changing stimuli lead to SA.
Our network model shows how a network with plastic synapses
can stably and flexibly learn PA and SA in an unsupervised
manner.},
Doi = {10.3389/fncom.2019.00097},
Key = {fds348568}
}
@article{fds341757,
Author = {Vaz, AP and Inati, SK and Brunel, N and Zaghloul,
KA},
Title = {Coupled ripple oscillations between the medial temporal lobe
and neocortex retrieve human memory.},
Journal = {Science},
Volume = {363},
Number = {6430},
Pages = {975-978},
Publisher = {American Association for the Advancement of Science
(AAAS)},
Year = {2019},
Month = {March},
url = {http://dx.doi.org/10.1126/science.aau8956},
Abstract = {Episodic memory retrieval relies on the recovery of neural
representations of waking experience. This process is
thought to involve a communication dynamic between the
medial temporal lobe memory system and the neocortex. How
this occurs is largely unknown, however, especially as it
pertains to awake human memory retrieval. Using intracranial
electroencephalographic recordings, we found that ripple
oscillations were dynamically coupled between the human
medial temporal lobe (MTL) and temporal association cortex.
Coupled ripples were more pronounced during successful
verbal memory retrieval and recover the cortical neural
representations of remembered items. Together, these data
provide direct evidence that coupled ripples between the MTL
and association cortex may underlie successful memory
retrieval in the human brain.},
Doi = {10.1126/science.aau8956},
Key = {fds341757}
}
@article{fds361409,
Author = {Oleskiw, TD and Bair, W and Shea-Brown, E and Brunel,
N},
Title = {Firing rate of the leaky integrate-and-fire neuron with
stochastic conductance-based synaptic inputs with short
decay times},
Year = {2020},
Month = {February},
Abstract = {We compute the firing rate of a leaky integrate-and-fire
(LIF) neuron with stochastic conductance-based inputs in the
limit when synaptic decay times are much shorter than the
membrane time constant. A comparison of our analytical
results to numeric simulations is presented for a range of
biophysically-realistic parameters.},
Key = {fds361409}
}
@article{fds349025,
Author = {Fore, TR and Taylor, BN and Brunel, N and Hull, C},
Title = {Acetylcholine Modulates Cerebellar Granule Cell Spiking by
Regulating the Balance of Synaptic Excitation and
Inhibition.},
Journal = {J Neurosci},
Volume = {40},
Number = {14},
Pages = {2882-2894},
Year = {2020},
Month = {April},
url = {http://dx.doi.org/10.1523/JNEUROSCI.2148-19.2020},
Abstract = {Sensorimotor integration in the cerebellum is essential for
refining motor output, and the first stage of this
processing occurs in the granule cell layer. Recent evidence
suggests that granule cell layer synaptic integration can be
contextually modified, although the circuit mechanisms that
could mediate such modulation remain largely unknown. Here
we investigate the role of ACh in regulating granule cell
layer synaptic integration in male rats and mice of both
sexes. We find that Golgi cells, interneurons that provide
the sole source of inhibition to the granule cell layer,
express both nicotinic and muscarinic cholinergic receptors.
While acute ACh application can modestly depolarize some
Golgi cells, the net effect of longer, optogenetically
induced ACh release is to strongly hyperpolarize Golgi
cells. Golgi cell hyperpolarization by ACh leads to a
significant reduction in both tonic and evoked granule cell
synaptic inhibition. ACh also reduces glutamate release from
mossy fibers by acting on presynaptic muscarinic receptors.
Surprisingly, despite these consistent effects on Golgi
cells and mossy fibers, ACh can either increase or decrease
the spike probability of granule cells as measured by
noninvasive cell-attached recordings. By constructing an
integrate-and-fire model of granule cell layer population
activity, we find that the direction of spike rate
modulation can be accounted for predominately by the initial
balance of excitation and inhibition onto individual granule
cells. Together, these experiments demonstrate that ACh can
modulate population-level granule cell responses by altering
the ratios of excitation and inhibition at the first stage
of cerebellar processing.SIGNIFICANCE STATEMENT The
cerebellum plays a key role in motor control and motor
learning. While it is known that behavioral context can
modify motor learning, the circuit basis of such modulation
has remained unclear. Here we find that a key
neuromodulator, ACh, can alter the balance of excitation and
inhibition at the first stage of cerebellar processing.
These results suggest that ACh could play a key role in
altering cerebellar learning by modifying how sensorimotor
input is represented at the input layer of the
cerebellum.},
Doi = {10.1523/JNEUROSCI.2148-19.2020},
Key = {fds349025}
}
@article{fds350568,
Author = {Sanzeni, A and Akitake, B and Goldbach, HC and Leedy, CE and Brunel, N and Histed, MH},
Title = {Inhibition stabilization is a widespread property of
cortical networks.},
Journal = {Elife},
Volume = {9},
Year = {2020},
Month = {June},
url = {http://dx.doi.org/10.7554/eLife.54875},
Abstract = {Many cortical network models use recurrent coupling strong
enough to require inhibition for stabilization. Yet it has
been experimentally unclear whether inhibition-stabilized
network (ISN) models describe cortical function well across
areas and states. Here, we test several ISN predictions,
including the counterintuitive (paradoxical) suppression of
inhibitory firing in response to optogenetic inhibitory
stimulation. We find clear evidence for ISN operation in
mouse visual, somatosensory, and motor cortex. Simple
two-population ISN models describe the data well and let us
quantify coupling strength. Although some models predict a
non-ISN to ISN transition with increasingly strong sensory
stimuli, we find ISN effects without sensory stimulation and
even during light anesthesia. Additionally, average
paradoxical effects result only with transgenic, not viral,
opsin expression in parvalbumin (PV)-positive neurons;
theory and expression data show this is consistent with ISN
operation. Taken together, these results show strong
coupling and inhibition stabilization are common features of
the cortex.},
Doi = {10.7554/eLife.54875},
Key = {fds350568}
}
@article{fds352530,
Author = {Sanzeni, A and Histed, MH and Brunel, N},
Title = {Response nonlinearities in networks of spiking
neurons.},
Journal = {PLoS Comput Biol},
Volume = {16},
Number = {9},
Pages = {e1008165},
Year = {2020},
Month = {September},
url = {http://dx.doi.org/10.1371/journal.pcbi.1008165},
Abstract = {Combining information from multiple sources is a fundamental
operation performed by networks of neurons in the brain,
whose general principles are still largely unknown.
Experimental evidence suggests that combination of inputs in
cortex relies on nonlinear summation. Such nonlinearities
are thought to be fundamental to perform complex
computations. However, these non-linearities are
inconsistent with the balanced-state model, one of the most
popular models of cortical dynamics, which predicts networks
have a linear response. This linearity is obtained in the
limit of very large recurrent coupling strength. We
investigate the stationary response of networks of spiking
neurons as a function of coupling strength. We show that,
while a linear transfer function emerges at strong coupling,
nonlinearities are prominent at finite coupling, both at
response onset and close to saturation. We derive a general
framework to classify nonlinear responses in these networks
and discuss which of them can be captured by rate models.
This framework could help to understand the diversity of
non-linearities observed in cortical networks.},
Doi = {10.1371/journal.pcbi.1008165},
Key = {fds352530}
}
@article{fds361500,
Author = {Sanzeni, A and Histed, MH and Brunel, N},
Title = {Emergence of irregular activity in networks of strongly
coupled conductance-based neurons},
Year = {2020},
Month = {September},
Abstract = {Cortical neurons are characterized by irregular firing and a
broad distribution of rates. The balanced state model
explains these observations with a cancellation of mean
excitatory and inhibitory currents, which makes fluctuations
drive firing. In networks of neurons with current-based
synapses, the balanced state emerges dynamically if coupling
is strong, i.e. if the mean number of synapses per neuron
$K$ is large and synaptic efficacy is of order $1/\sqrt{K}$.
When synapses are conductance-based, current fluctuations
are suppressed when coupling is strong, questioning the
applicability of the balanced state idea to biological
neural networks. We analyze networks of strongly coupled
conductance-based neurons and show that asynchronous
irregular activity and broad distributions of rates emerge
if synapses are of order $1/\log(K)$. In such networks,
unlike in the standard balanced state model, current
fluctuations are small and firing is maintained by a
drift-diffusion balance. This balance emerges dynamically,
without fine tuning, if inputs are smaller than a critical
value, which depends on synaptic time constants and coupling
strength, and is significantly more robust to connection
heterogeneities than the classical balanced state model. Our
analysis makes experimentally testable predictions of how
the network response properties should evolve as input
increases.},
Key = {fds361500}
}
@article{fds353292,
Author = {Gillett, M and Pereira, U and Brunel, N},
Title = {Characteristics of sequential activity in networks with
temporally asymmetric Hebbian learning.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {117},
Number = {47},
Pages = {29948-29958},
Year = {2020},
Month = {November},
url = {http://dx.doi.org/10.1073/pnas.1918674117},
Abstract = {Sequential activity has been observed in multiple neuronal
circuits across species, neural structures, and behaviors.
It has been hypothesized that sequences could arise from
learning processes. However, it is still unclear whether
biologically plausible synaptic plasticity rules can
organize neuronal activity to form sequences whose
statistics match experimental observations. Here, we
investigate temporally asymmetric Hebbian rules in sparsely
connected recurrent rate networks and develop a theory of
the transient sequential activity observed after learning.
These rules transform a sequence of random input patterns
into synaptic weight updates. After learning, recalled
sequential activity is reflected in the transient
correlation of network activity with each of the stored
input patterns. Using mean-field theory, we derive a
low-dimensional description of the network dynamics and
compute the storage capacity of these networks. Multiple
temporal characteristics of the recalled sequential activity
are consistent with experimental observations. We find that
the degree of sparseness of the recalled sequences can be
controlled by nonlinearities in the learning rule.
Furthermore, sequences maintain robust decoding, but display
highly labile dynamics, when synaptic connectivity is
continuously modified due to noise or storage of other
patterns, similar to recent observations in hippocampus and
parietal cortex. Finally, we demonstrate that our results
also hold in recurrent networks of spiking neurons with
separate excitatory and inhibitory populations.},
Doi = {10.1073/pnas.1918674117},
Key = {fds353292}
}
@article{fds354283,
Author = {Inglebert, Y and Aljadeff, J and Brunel, N and Debanne,
D},
Title = {Synaptic plasticity rules with physiological calcium
levels.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {117},
Number = {52},
Pages = {33639-33648},
Year = {2020},
Month = {December},
url = {http://dx.doi.org/10.1073/pnas.2013663117},
Abstract = {Spike-timing-dependent plasticity (STDP) is considered as a
primary mechanism underlying formation of new memories
during learning. Despite the growing interest in
activity-dependent plasticity, it is still unclear whether
synaptic plasticity rules inferred from in vitro experiments
are correct in physiological conditions. The abnormally high
calcium concentration used in in vitro studies of STDP
suggests that in vivo plasticity rules may differ
significantly from in vitro experiments, especially since
STDP depends strongly on calcium for induction. We therefore
studied here the influence of extracellular calcium on
synaptic plasticity. Using a combination of experimental
(patch-clamp recording and Ca2+ imaging at CA3-CA1 synapses)
and theoretical approaches, we show here that the classic
STDP rule in which pairs of single pre- and postsynaptic
action potentials induce synaptic modifications is not valid
in the physiological Ca2+ range. Rather, we found that these
pairs of single stimuli are unable to induce any synaptic
modification in 1.3 and 1.5 mM calcium and lead to
depression in 1.8 mM. Plasticity can only be recovered when
bursts of postsynaptic spikes are used, or when neurons fire
at sufficiently high frequency. In conclusion, the STDP rule
is profoundly altered in physiological Ca2+, but specific
activity regimes restore a classical STDP
profile.},
Doi = {10.1073/pnas.2013663117},
Key = {fds354283}
}
@article{fds361689,
Author = {Goldt, S and Krzakala, F and Zdeborová, L and Brunel,
N},
Title = {Bayesian reconstruction of memories stored in neural
networks from their connectivity},
Journal = {PLOS Computational Biology 19(1): e1010813
2023},
Year = {2021},
Month = {May},
Abstract = {The advent of comprehensive synaptic wiring diagrams of
large neural circuits has created the field of connectomics
and given rise to a number of open research questions. One
such question is whether it is possible to reconstruct the
information stored in a recurrent network of neurons, given
its synaptic connectivity matrix. Here, we address this
question by determining when solving such an inference
problem is theoretically possible in specific attractor
network models and by providing a practical algorithm to do
so. The algorithm builds on ideas from statistical physics
to perform approximate Bayesian inference and is amenable to
exact analysis. We study its performance on three different
models, compare the algorithm to standard algorithms such as
PCA, and explore the limitations of reconstructing stored
patterns from synaptic connectivity.},
Key = {fds361689}
}
@article{fds357513,
Author = {Aljadeff, J and Gillett, M and Pereira Obilinovic and U and Brunel,
N},
Title = {From synapse to network: models of information storage and
retrieval in neural circuits.},
Journal = {Curr Opin Neurobiol},
Volume = {70},
Pages = {24-33},
Year = {2021},
Month = {October},
url = {http://dx.doi.org/10.1016/j.conb.2021.05.005},
Abstract = {The mechanisms of information storage and retrieval in brain
circuits are still the subject of debate. It is widely
believed that information is stored at least in part through
changes in synaptic connectivity in networks that encode
this information and that these changes lead in turn to
modifications of network dynamics, such that the stored
information can be retrieved at a later time. Here, we
review recent progress in deriving synaptic plasticity rules
from experimental data and in understanding how plasticity
rules affect the dynamics of recurrent networks. We show
that the dynamics generated by such networks exhibit a large
degree of diversity, depending on parameters, similar to
experimental observations in vivo during delayed response
tasks.},
Doi = {10.1016/j.conb.2021.05.005},
Key = {fds357513}
}
@article{fds361499,
Author = {Pereira-Obilinovic, U and Aljadeff, J and Brunel,
N},
Title = {Forgetting leads to chaos in attractor networks},
Year = {2021},
Month = {November},
Abstract = {Attractor networks are an influential theory for memory
storage in brain systems. This theory has recently been
challenged by the observation of strong temporal variability
in neuronal recordings during memory tasks. In this work, we
study a sparsely connected attractor network where memories
are learned according to a Hebbian synaptic plasticity rule.
After recapitulating known results for the continuous,
sparsely connected Hopfield model, we investigate a model in
which new memories are learned continuously and old memories
are forgotten, using an online synaptic plasticity rule. We
show that for a forgetting time scale that optimizes storage
capacity, the qualitative features of the network's memory
retrieval dynamics are age-dependent: most recent memories
are retrieved as fixed-point attractors while older memories
are retrieved as chaotic attractors characterized by strong
heterogeneity and temporal fluctuations. Therefore,
fixed-point and chaotic attractors co-exist in the network
phase space. The network presents a continuum of
statistically distinguishable memory states, where chaotic
fluctuations appear abruptly above a critical age and then
increase gradually until the memory disappears. We develop a
dynamical mean field theory (DMFT) to analyze the
age-dependent dynamics and compare the theory with
simulations of large networks. Our numerical simulations
show that a high-degree of sparsity is necessary for the
DMFT to accurately predict the network capacity. Finally,
our theory provides specific predictions for delay response
tasks with aging memoranda. Our theory of attractor networks
that continuously learn new information at the price of
forgetting old memories can account for the observed
diversity of retrieval states in the cortex, and in
particular the strong temporal fluctuations of cortical
activity.},
Key = {fds361499}
}
@article{fds361498,
Author = {Feng, Y and Brunel, N},
Title = {Storage capacity of networks with discrete synapses and
sparsely encoded memories},
Year = {2021},
Month = {December},
Abstract = {Attractor neural networks (ANNs) are one of the leading
theoretical frameworks for the formation and retrieval of
memories in networks of biological neurons. In this
framework, a pattern imposed by external inputs to the
network is said to be learned when this pattern becomes a
fixed point attractor of the network dynamics. The storage
capacity is the maximum number of patterns that can be
learned by the network. In this paper, we study the storage
capacity of fully-connected and sparsely-connected networks
with a binarized Hebbian rule, for arbitrary coding levels.
Our results show that a network with discrete synapses has a
similar storage capacity as the model with continuous
synapses, and that this capacity tends asymptotically
towards the optimal capacity, in the space of all possible
binary connectivity matrices, in the sparse coding limit. We
also derive finite coding level corrections for the
asymptotic solution in the sparse coding limit. The result
indicates the capacity of network with Hebbian learning
rules converges to the optimal capacity extremely slowly
when the coding level becomes small. Our results also show
that in networks with sparse binary connectivity matrices,
the information capacity per synapse is larger than in the
fully connected case, and thus such networks store
information more efficiently.},
Key = {fds361498}
}
@article{fds363004,
Author = {Sanzeni, A and Histed, MH and Brunel, N},
Title = {Emergence of Irregular Activity in Networks of Strongly
Coupled Conductance-Based Neurons.},
Journal = {Phys Rev X},
Volume = {12},
Number = {1},
Year = {2022},
url = {http://dx.doi.org/10.1103/physrevx.12.011044},
Abstract = {Cortical neurons are characterized by irregular firing and a
broad distribution of rates. The balanced state model
explains these observations with a cancellation of mean
excitatory and inhibitory currents, which makes fluctuations
drive firing. In networks of neurons with current-based
synapses, the balanced state emerges dynamically if coupling
is strong, i.e., if the mean number of synapses per neuron K
is large and synaptic efficacy is of the order of 1 / K .
When synapses are conductance-based, current fluctuations
are suppressed when coupling is strong, questioning the
applicability of the balanced state idea to biological
neural networks. We analyze networks of strongly coupled
conductance-based neurons and show that asynchronous
irregular activity and broad distributions of rates emerge
if synaptic efficacy is of the order of 1/ log(K). In such
networks, unlike in the standard balanced state model,
current fluctuations are small and firing is maintained by a
drift-diffusion balance. This balance emerges dynamically,
without fine-tuning, if inputs are smaller than a critical
value, which depends on synaptic time constants and coupling
strength, and is significantly more robust to connection
heterogeneities than the classical balanced state model. Our
analysis makes experimentally testable predictions of how
the network response properties should evolve as input
increases.},
Doi = {10.1103/physrevx.12.011044},
Key = {fds363004}
}
@article{fds363900,
Author = {Feng, Y and Brunel, N},
Title = {Storage capacity of networks with discrete synapses and
sparsely encoded memories.},
Journal = {Phys Rev E},
Volume = {105},
Number = {5-1},
Pages = {054408},
Year = {2022},
Month = {May},
url = {http://dx.doi.org/10.1103/PhysRevE.105.054408},
Abstract = {Attractor neural networks are one of the leading theoretical
frameworks for the formation and retrieval of memories in
networks of biological neurons. In this framework, a pattern
imposed by external inputs to the network is said to be
learned when this pattern becomes a fixed point attractor of
the network dynamics. The storage capacity is the maximum
number of patterns that can be learned by the network. In
this paper, we study the storage capacity of fully connected
and sparsely connected networks with a binarized Hebbian
rule, for arbitrary coding levels. Our results show that a
network with discrete synapses has a similar storage
capacity as the model with continuous synapses, and that
this capacity tends asymptotically towards the optimal
capacity, in the space of all possible binary connectivity
matrices, in the sparse coding limit. We also derive finite
coding level corrections for the asymptotic solution in the
sparse coding limit. The result indicates the capacity of
networks with Hebbian learning rules converges to the
optimal capacity extremely slowly when the coding level
becomes small. Our results also show that in networks with
sparse binary connectivity matrices, the information
capacity per synapse is larger than in the fully connected
case, and thus such networks store information more
efficiently.},
Doi = {10.1103/PhysRevE.105.054408},
Key = {fds363900}
}
@article{fds363743,
Author = {Abed Zadeh and A and Turner, BD and Calakos, N and Brunel,
N},
Title = {Non-monotonic effects of GABAergic synaptic inputs on
neuronal firing.},
Journal = {PLoS Comput Biol},
Volume = {18},
Number = {6},
Pages = {e1010226},
Year = {2022},
Month = {June},
url = {http://dx.doi.org/10.1371/journal.pcbi.1010226},
Abstract = {GABA is generally known as the principal inhibitory
neurotransmitter in the nervous system, usually acting by
hyperpolarizing membrane potential. However, GABAergic
currents sometimes exhibit non-inhibitory effects, depending
on the brain region, developmental stage or pathological
condition. Here, we investigate the diverse effects of GABA
on the firing rate of several single neuron models, using
both analytical calculations and numerical simulations. We
find that GABAergic synaptic conductance and output firing
rate exhibit three qualitatively different regimes as a
function of GABA reversal potential, EGABA: monotonically
decreasing for sufficiently low EGABA (inhibitory),
monotonically increasing for EGABA above firing threshold
(excitatory); and a non-monotonic region for intermediate
values of EGABA. In the non-monotonic regime, small GABA
conductances have an excitatory effect while large GABA
conductances show an inhibitory effect. We provide a phase
diagram of different GABAergic effects as a function of GABA
reversal potential and glutamate conductance. We find that
noisy inputs increase the range of EGABA for which the
non-monotonic effect can be observed. We also construct a
micro-circuit model of striatum to explain observed effects
of GABAergic fast spiking interneurons on spiny projection
neurons, including non-monotonicity, as well as the
heterogeneity of the effects. Our work provides a
mechanistic explanation of paradoxical effects of GABAergic
synaptic inputs, with implications for understanding the
effects of GABA in neural computation and
development.},
Doi = {10.1371/journal.pcbi.1010226},
Key = {fds363743}
}
@article{fds367466,
Author = {De Pittà and M and Brunel, N},
Title = {Multiple forms of working memory emerge from
synapse-astrocyte interactions in a neuron-glia network
model.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {119},
Number = {43},
Pages = {e2207912119},
Year = {2022},
Month = {October},
url = {http://dx.doi.org/10.1073/pnas.2207912119},
Abstract = {Persistent activity in populations of neurons, time-varying
activity across a neural population, or activity-silent
mechanisms carried out by hidden internal states of the
neural population have been proposed as different mechanisms
of working memory (WM). Whether these mechanisms could be
mutually exclusive or occur in the same neuronal circuit
remains, however, elusive, and so do their biophysical
underpinnings. While WM is traditionally regarded to depend
purely on neuronal mechanisms, cortical networks also
include astrocytes that can modulate neural activity. We
propose and investigate a network model that includes both
neurons and glia and show that glia-synapse interactions can
lead to multiple stable states of synaptic transmission.
Depending on parameters, these interactions can lead in turn
to distinct patterns of network activity that can serve as
substrates for WM.},
Doi = {10.1073/pnas.2207912119},
Key = {fds367466}
}
@article{fds369113,
Author = {Goldt, S and Krzakala, F and Zdeborová, L and Brunel,
N},
Title = {Bayesian reconstruction of memories stored in neural
networks from their connectivity.},
Journal = {PLoS Comput Biol},
Volume = {19},
Number = {1},
Pages = {e1010813},
Year = {2023},
Month = {January},
url = {https://arxiv.org/abs/2105.07416},
Abstract = {The advent of comprehensive synaptic wiring diagrams of
large neural circuits has created the field of connectomics
and given rise to a number of open research questions. One
such question is whether it is possible to reconstruct the
information stored in a recurrent network of neurons, given
its synaptic connectivity matrix. Here, we address this
question by determining when solving such an inference
problem is theoretically possible in specific attractor
network models and by providing a practical algorithm to do
so. The algorithm builds on ideas from statistical physics
to perform approximate Bayesian inference and is amenable to
exact analysis. We study its performance on three different
models, compare the algorithm to standard algorithms such as
PCA, and explore the limitations of reconstructing stored
patterns from synaptic connectivity.},
Doi = {10.1371/journal.pcbi.1010813},
Key = {fds369113}
}
@article{fds369744,
Author = {Pereira-Obilinovic, U and Aljadeff, J and Brunel,
N},
Title = {Forgetting Leads to Chaos in Attractor Networks},
Journal = {Physical Review X},
Volume = {13},
Number = {1},
Year = {2023},
Month = {January},
url = {https://arxiv.org/abs/2112.00119},
Abstract = {Attractor networks are an influential theory for memory
storage in brain systems. This theory has recently been
challenged by the observation of strong temporal variability
in neuronal recordings during memory tasks. In this work, we
study a sparsely connected attractor network where memories
are learned according to a Hebbian synaptic plasticity rule.
After recapitulating known results for the continuous,
sparsely connected Hopfield model, we investigate a model in
which new memories are learned continuously and old memories
are forgotten, using an online synaptic plasticity rule. We
show that for a forgetting timescale that optimizes storage
capacity, the qualitative features of the network's memory
retrieval dynamics are age dependent: most recent memories
are retrieved as fixed-point attractors while older memories
are retrieved as chaotic attractors characterized by strong
heterogeneity and temporal fluctuations. Therefore,
fixed-point and chaotic attractors coexist in the network
phase space. The network presents a continuum of
statistically distinguishable memory states, where chaotic
fluctuations appear abruptly above a critical age and then
increase gradually until the memory disappears. We develop a
dynamical mean field theory to analyze the age-dependent
dynamics and compare the theory with simulations of large
networks. We compute the optimal forgetting timescale for
which the number of stored memories is maximized. We found
that the maximum age at which memories can be retrieved is
given by an instability at which old memories destabilize
and the network converges instead to a more recent one. Our
numerical simulations show that a high degree of sparsity is
necessary for the dynamical mean field theory to accurately
predict the network capacity. To test the robustness and
biological plausibility of our results, we study numerically
the dynamics of a network with learning rules and transfer
function inferred from in vivo data in the online learning
scenario. We found that all aspects of the network's
dynamics characterized analytically in the simpler model
also hold in this model. These results are highly robust to
noise. Finally, our theory provides specific predictions for
delay response tasks with aging memoranda. In particular, it
predicts a higher degree of temporal fluctuations in
retrieval states associated with older memories, and it also
predicts fluctuations should be faster in older memories.
Overall, our theory of attractor networks that continuously
learn new information at the price of forgetting old
memories can account for the observed diversity of retrieval
states in the cortex, and in particular, the strong temporal
fluctuations of cortical activity.},
Doi = {10.1103/PhysRevX.13.011009},
Key = {fds369744}
}
@article{fds373502,
Author = {Brunel, N and Monasson, R and Sompolinsky, H and Leo van Hemmen,
J},
Title = {From the Statistical Physics of Disordered Systems to
Neuroscience},
Pages = {499-521},
Booktitle = {Spin Glass Theory and Far Beyond: Replica Symmetry Breaking
after 40 Years},
Year = {2023},
Month = {January},
ISBN = {9789811273919},
url = {http://dx.doi.org/10.1142/9789811273926_0025},
Abstract = {This chapter studies the bridges and differences between the
statistical physics of disordered systems, as developed
notably in the context of spin glass theory, and problems in
neuroscience. In a first contribution (Sec. 25.1), Nicolas
Brunel, Rémi Monasson and Haim Sompolinsky first recall the
main lines of the statistical physics approach to neural
networks models as developed in the 1980s and 1990s. They
then survey more recent developments at the interface
between statistical physics and neuroscience, including the
inference of synaptic plasticity rules and the statistics of
synaptic connectivity. Finally they present the Tempotron
model for learning temporal patterns. In a second
contribution (Sec. 25.2), Leo van Hemmen discusses the
difference between real spin glasses, neuronal networks (of
real biological neurons) and neural networks (of artificial
neurons); with illustrations ranging from site-disorder
models of spin glasses to temporal coding in neuronal
networks and unlearning.},
Doi = {10.1142/9789811273926_0025},
Key = {fds373502}
}
@article{fds370618,
Author = {Bachschmid-Romano, L and Hatsopoulos, NG and Brunel,
N},
Title = {Interplay between external inputs and recurrent dynamics
during movement preparation and execution in a network model
of motor cortex.},
Journal = {Elife},
Volume = {12},
Year = {2023},
Month = {May},
url = {https://www.biorxiv.org/content/10.1101/2022.02.19.481140v1},
Abstract = {The primary motor cortex has been shown to coordinate
movement preparation and execution through computations in
approximately orthogonal subspaces. The underlying network
mechanisms, and the roles played by external and recurrent
connectivity, are central open questions that need to be
answered to understand the neural substrates of motor
control. We develop a recurrent neural network model that
recapitulates the temporal evolution of neuronal activity
recorded from the primary motor cortex of a macaque monkey
during an instructed delayed-reach task. In particular, it
reproduces the observed dynamic patterns of covariation
between neural activity and the direction of motion. We
explore the hypothesis that the observed dynamics emerges
from a synaptic connectivity structure that depends on the
preferred directions of neurons in both preparatory and
movement-related epochs, and we constrain the strength of
both synaptic connectivity and external input parameters
from data. While the model can reproduce neural activity for
multiple combinations of the feedforward and recurrent
connections, the solution that requires minimum external
inputs is one where the observed patterns of covariance are
shaped by external inputs during movement preparation, while
they are dominated by strong direction-specific recurrent
connectivity during movement execution. Our model also
demonstrates that the way in which single-neuron tuning
properties change over time can explain the level of
orthogonality of preparatory and movement-related
subspaces.},
Doi = {10.7554/eLife.77690},
Key = {fds370618}
}
@article{fds373674,
Author = {Sanzeni, A and Palmigiano, A and Nguyen, TH and Luo, J and Nassi, JJ and Reynolds, JH and Histed, MH and Miller, KD and Brunel,
N},
Title = {Mechanisms underlying reshuffling of visual responses by
optogenetic stimulation in mice and monkeys.},
Journal = {Neuron},
Volume = {111},
Number = {24},
Pages = {4102-4115.e9},
Year = {2023},
Month = {December},
url = {https://www.biorxiv.org/content/10.1101/2022.07.13.499597v1},
Abstract = {The ability to optogenetically perturb neural circuits opens
an unprecedented window into mechanisms governing circuit
function. We analyzed and theoretically modeled neuronal
responses to visual and optogenetic inputs in mouse and
monkey V1. In both species, optogenetic stimulation of
excitatory neurons strongly modulated the activity of single
neurons yet had weak or no effects on the distribution of
firing rates across the population. Thus, the optogenetic
inputs reshuffled firing rates across the network. Key
statistics of mouse and monkey responses lay on a continuum,
with mice/monkeys occupying the low-/high-rate regions,
respectively. We show that neuronal reshuffling emerges
generically in randomly connected excitatory/inhibitory
networks, provided the coupling strength (combination of
recurrent coupling and external input) is sufficient that
powerful inhibitory feedback cancels the mean optogenetic
input. A more realistic model, distinguishing tuned visual
vs. untuned optogenetic input in a structured network,
reduces the coupling strength needed to explain
reshuffling.},
Doi = {10.1016/j.neuron.2023.09.018},
Key = {fds373674}
}
@article{fds375962,
Author = {Feng, Y and Brunel, N},
Title = {Attractor neural networks with double well
synapses.},
Journal = {PLoS Comput Biol},
Volume = {20},
Number = {2},
Pages = {e1011354},
Year = {2024},
Month = {February},
url = {http://dx.doi.org/10.1371/journal.pcbi.1011354},
Abstract = {It is widely believed that memory storage depends on
activity-dependent synaptic modifications. Classical studies
of learning and memory in neural networks describe synaptic
efficacy either as continuous or discrete. However, recent
results suggest an intermediate scenario in which synaptic
efficacy can be described by a continuous variable, but
whose distribution is peaked around a small set of discrete
values. Motivated by these results, we explored a model in
which each synapse is described by a continuous variable
that evolves in a potential with multiple minima. External
inputs to the network can switch synapses from one potential
well to another. Our analytical and numerical results show
that this model can interpolate between models with discrete
synapses which correspond to the deep potential limit, and
models in which synapses evolve in a single quadratic
potential. We find that the storage capacity of the network
with double well synapses exhibits a power law dependence on
the network size, rather than the logarithmic dependence
observed in models with single well synapses. In addition,
synapses with deeper potential wells lead to more robust
information storage in the presence of noise. When memories
are sparsely encoded, the scaling of the capacity with
network size is similar to previously studied network models
in the sparse coding limit.},
Doi = {10.1371/journal.pcbi.1011354},
Key = {fds375962}
}
%% Papers Submitted
@article{fds360702,
Author = {A Sanzeni and M Histed and N Brunel},
Title = {Emergence of irregular states in networks with
conductance-based synapses},
Journal = {Phys Rev X},
Year = {2021},
Key = {fds360702}
}
%% Preprints
@article{fds374524,
Author = {Li, Y and An, X and Qian, Y and Xu, XH and Zhao, S and Mohan, H and Bachschmid-Romano, L and Brunel, N and Whishaw, IQ and Huang,
ZJ},
Title = {Cortical network and projection neuron types that articulate
serial order in a skilled motor behavior.},
Year = {2023},
Month = {October},
url = {http://dx.doi.org/10.1101/2023.10.25.563871},
Doi = {10.1101/2023.10.25.563871},
Key = {fds374524}
}