2,330 research outputs found
Stability Analysis of Asynchronous States in Neuronal Networks with Conductance-Based Inhibition
Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations
How adaptation currents change threshold, gain and variability of neuronal spiking
Many types of neurons exhibit spike rate adaptation, mediated by intrinsic
slow -currents, which effectively inhibit neuronal responses. How
these adaptation currents change the relationship between in-vivo like
fluctuating synaptic input, spike rate output and the spike train statistics,
however, is not well understood. In this computational study we show that an
adaptation current which primarily depends on the subthreshold membrane voltage
changes the neuronal input-output relationship (I-O curve) subtractively,
thereby increasing the response threshold. A spike-dependent adaptation current
alters the I-O curve divisively, thus reducing the response gain. Both types of
adaptation currents naturally increase the mean inter-spike interval (ISI), but
they can affect ISI variability in opposite ways. A subthreshold current always
causes an increase of variability while a spike-triggered current decreases
high variability caused by fluctuation-dominated inputs and increases low
variability when the average input is large. The effects on I-O curves match
those caused by synaptic inhibition in networks with asynchronous irregular
activity, for which we find subtractive and divisive changes caused by external
and recurrent inhibition, respectively. Synaptic inhibition, however, always
increases the ISI variability. We analytically derive expressions for the I-O
curve and ISI variability, which demonstrate the robustness of our results.
Furthermore, we show how the biophysical parameters of slow
-conductances contribute to the two different types of adaptation
currents and find that -activated -currents are
effectively captured by a simple spike-dependent description, while
muscarine-sensitive or -activated -currents show a
dominant subthreshold component.Comment: 20 pages, 8 figures; Journal of Neurophysiology (in press
Conductance-Based Refractory Density Approach for a Population of Bursting Neurons
The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modeling interact- ing populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting popula- tion model makes use of slow-fast analysis, which leads to a novel method- ology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explo- rations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).Russian Science Foundation grant (project 16-15- 10201)
Spanish grant MINECO-FEDER-UE MTM-2015-71509-C2-2-R
Catalan Grant number 2017SGR104
Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses
We investigate the effect of electric synapses (gap junctions) on collective
neuronal dynamics and spike statistics in a conductance-based
Integrate-and-Fire neural network, driven by a Brownian noise, where
conductances depend upon spike history. We compute explicitly the time
evolution operator and show that, given the spike-history of the network and
the membrane potentials at a given time, the further dynamical evolution can be
written in a closed form. We show that spike train statistics is described by a
Gibbs distribution whose potential can be approximated with an explicit
formula, when the noise is weak. This potential form encompasses existing
models for spike trains statistics analysis such as maximum entropy models or
Generalized Linear Models (GLM). We also discuss the different types of
correlations: those induced by a shared stimulus and those induced by neurons
interactions.Comment: 42 pages, 1 figure, submitte
A mean-field model for conductance-based networks of adaptive exponential integrate-and-fire neurons
Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of
neocortical processing at mesoscopic scales. Since VSDi signals report the
average membrane potential, it seems natural to use a mean-field formalism to
model such signals. Here, we investigate a mean-field model of networks of
Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based
synaptic interactions. The AdEx model can capture the spiking response of
different cell types, such as regular-spiking (RS) excitatory neurons and
fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism,
together with a semi-analytic approach to the transfer function of AdEx
neurons. We compare the predictions of this mean-field model to simulated
networks of RS-FS cells, first at the level of the spontaneous activity of the
network, which is well predicted by the mean-field model. Second, we
investigate the response of the network to time-varying external input, and
show that the mean-field model accurately predicts the response time course of
the population. One notable exception was that the "tail" of the response at
long times was not well predicted, because the mean-field does not include
adaptation mechanisms. We conclude that the Master Equation formalism can yield
mean-field models that predict well the behavior of nonlinear networks with
conductance-based interactions and various electrophysiolgical properties, and
should be a good candidate to model VSDi signals where both excitatory and
inhibitory neurons contribute.Comment: 21 pages, 7 figure
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
Stochastic dynamics of a finite-size spiking neural network
We present a simple Markov model of spiking neural dynamics that can be
analytically solved to characterize the stochastic dynamics of a finite-size
spiking neural network. We give closed-form estimates for the equilibrium
distribution, mean rate, variance and autocorrelation function of the network
activity. The model is applicable to any network where the probability of
firing of a neuron in the network only depends on the number of neurons that
fired in a previous temporal epoch. Networks with statistically homogeneous
connectivity and membrane and synaptic time constants that are not excessively
long could satisfy these conditions. Our model completely accounts for the size
of the network and correlations in the firing activity. It also allows us to
examine how the network dynamics can deviate from mean-field theory. We show
that the model and solutions are applicable to spiking neural networks in
biophysically plausible parameter regimes
The effect of heterogeneity on decorrelation mechanisms in spiking neural networks: a neuromorphic-hardware study
High-level brain function such as memory, classification or reasoning can be
realized by means of recurrent networks of simplified model neurons. Analog
neuromorphic hardware constitutes a fast and energy efficient substrate for the
implementation of such neural computing architectures in technical applications
and neuroscientific research. The functional performance of neural networks is
often critically dependent on the level of correlations in the neural activity.
In finite networks, correlations are typically inevitable due to shared
presynaptic input. Recent theoretical studies have shown that inhibitory
feedback, abundant in biological neural networks, can actively suppress these
shared-input correlations and thereby enable neurons to fire nearly
independently. For networks of spiking neurons, the decorrelating effect of
inhibitory feedback has so far been explicitly demonstrated only for
homogeneous networks of neurons with linear sub-threshold dynamics. Theory,
however, suggests that the effect is a general phenomenon, present in any
system with sufficient inhibitory feedback, irrespective of the details of the
network structure or the neuronal and synaptic properties. Here, we investigate
the effect of network heterogeneity on correlations in sparse, random networks
of inhibitory neurons with non-linear, conductance-based synapses. Emulations
of these networks on the analog neuromorphic hardware system Spikey allow us to
test the efficiency of decorrelation by inhibitory feedback in the presence of
hardware-specific heterogeneities. The configurability of the hardware
substrate enables us to modulate the extent of heterogeneity in a systematic
manner. We selectively study the effects of shared input and recurrent
connections on correlations in membrane potentials and spike trains. Our
results confirm ...Comment: 20 pages, 10 figures, supplement
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