4,800 research outputs found
Homeostatic plasticity and external input shape neural network dynamics
In vitro and in vivo spiking activity clearly differ. Whereas networks in
vitro develop strong bursts separated by periods of very little spiking
activity, in vivo cortical networks show continuous activity. This is puzzling
considering that both networks presumably share similar single-neuron dynamics
and plasticity rules. We propose that the defining difference between in vitro
and in vivo dynamics is the strength of external input. In vitro, networks are
virtually isolated, whereas in vivo every brain area receives continuous input.
We analyze a model of spiking neurons in which the input strength, mediated by
spike rate homeostasis, determines the characteristics of the dynamical state.
In more detail, our analytical and numerical results on various network
topologies show consistently that under increasing input, homeostatic
plasticity generates distinct dynamic states, from bursting, to
close-to-critical, reverberating and irregular states. This implies that the
dynamic state of a neural network is not fixed but can readily adapt to the
input strengths. Indeed, our results match experimental spike recordings in
vitro and in vivo: the in vitro bursting behavior is consistent with a state
generated by very low network input (< 0.1%), whereas in vivo activity suggests
that on the order of 1% recorded spikes are input-driven, resulting in
reverberating dynamics. Importantly, this predicts that one can abolish the
ubiquitous bursts of in vitro preparations, and instead impose dynamics
comparable to in vivo activity by exposing the system to weak long-term
stimulation, thereby opening new paths to establish an in vivo-like assay in
vitro for basic as well as neurological studies.Comment: 14 pages, 8 figures, accepted at Phys. Rev.
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Efficiency characterization of a large neuronal network: a causal information approach
When inhibitory neurons constitute about 40% of neurons they could have an
important antinociceptive role, as they would easily regulate the level of
activity of other neurons. We consider a simple network of cortical spiking
neurons with axonal conduction delays and spike timing dependent plasticity,
representative of a cortical column or hypercolumn with large proportion of
inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics
and it is interconnected randomly to other neurons. The network dynamics is
investigated estimating Bandt and Pompe probability distribution function
associated to the interspike intervals and taking different degrees of
inter-connectivity across neurons. More specifically we take into account the
fine temporal ``structures'' of the complex neuronal signals not just by using
the probability distributions associated to the inter spike intervals, but
instead considering much more subtle measures accounting for their causal
information: the Shannon permutation entropy, Fisher permutation information
and permutation statistical complexity. This allows us to investigate how the
information of the system might saturate to a finite value as the degree of
inter-connectivity across neurons grows, inferring the emergent dynamical
properties of the system.Comment: 26 pages, 3 Figures; Physica A, in pres
Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons
Networks of stochastic spiking neurons are interesting models in the area of
Theoretical Neuroscience, presenting both continuous and discontinuous phase
transitions. Here we study fully connected networks analytically, numerically
and by computational simulations. The neurons have dynamic gains that enable
the network to converge to a stationary slightly supercritical state
(self-organized supercriticality or SOSC) in the presence of the continuous
transition. We show that SOSC, which presents power laws for neuronal
avalanches plus some large events, is robust as a function of the main
parameter of the neuronal gain dynamics. We discuss the possible applications
of the idea of SOSC to biological phenomena like epilepsy and dragon king
avalanches. We also find that neuronal gains can produce collective
oscillations that coexists with neuronal avalanches, with frequencies
compatible with characteristic brain rhythms.Comment: 16 pages, 16 figures divided into 7 figures in the articl
Fluctuations and information filtering in coupled populations of spiking neurons with adaptation
Finite-sized populations of spiking elements are fundamental to brain
function, but also used in many areas of physics. Here we present a theory of
the dynamics of finite-sized populations of spiking units, based on a
quasi-renewal description of neurons with adaptation. We derive an integral
equation with colored noise that governs the stochastic dynamics of the
population activity in response to time-dependent stimulation and calculate the
spectral density in the asynchronous state. We show that systems of coupled
populations with adaptation can generate a frequency band in which sensory
information is preferentially encoded. The theory is applicable to fully as
well as randomly connected networks, and to leaky integrate-and-fire as well as
to generalized spiking neurons with adaptation on multiple time scales
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
- …