1,321 research outputs found
Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory
instantaneous post-synaptic potentials. In particular, we report exact results
for the firing rate, the coefficient of variation and the spike train spectrum
for various synaptic weight distributions. Our results are not limited to
stimulations of infinitesimal amplitude, but they apply as well to finite
amplitude post-synaptic potentials, thus being able to capture the effect of
rare and large spikes. The developed methods are able to reproduce also the
average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
A unique method for stochastic models in computational and cognitive neuroscience
We review applications of the FokkerâPlanck equation for the description of systems with event trains in computational and cognitive neuroscience. The most prominent example is the spike trains generated by integrate-and-fire neurons when driven by correlated (colored) fluctuations, by adaptation currents and/or by other neurons in a recurrent network. We discuss how for a general Gaussian colored noise and an adaptation current can be incorporated into a multidimensional FokkerâPlanck equation by Markovian embedding for systems with a fire-and-reset condition and how in particular the spike-train power spectrum can be determined by this equation. We then review how this framework can be used to determine the self-consistent correlation statistics in a recurrent network in which the colored fluctuations arise from the spike trains of statistically similar neurons. We then turn to the popular drift-diffusion models for binary decisions in cognitive neuroscience and demonstrate that very similar FokkerâPlanck equations (with two instead of only one threshold) can be used to study the statistics of sequences of decisions. Specifically, we present a novel two-dimensional model that includes an evidence variable and an expectancy variable that can reproduce salient features of key experiments in sequential decision making.Humboldt-UniversitĂ€t zu Berlin (1034)Peer Reviewe
Intrinsically-generated fluctuating activity in excitatory-inhibitory networks
Recurrent networks of non-linear units display a variety of dynamical regimes
depending on the structure of their synaptic connectivity. A particularly
remarkable phenomenon is the appearance of strongly fluctuating, chaotic
activity in networks of deterministic, but randomly connected rate units. How
this type of intrinsi- cally generated fluctuations appears in more realistic
networks of spiking neurons has been a long standing question. To ease the
comparison between rate and spiking networks, recent works investigated the
dynami- cal regimes of randomly-connected rate networks with segregated
excitatory and inhibitory populations, and firing rates constrained to be
positive. These works derived general dynamical mean field (DMF) equations
describing the fluctuating dynamics, but solved these equations only in the
case of purely inhibitory networks. Using a simplified excitatory-inhibitory
architecture in which DMF equations are more easily tractable, here we show
that the presence of excitation qualitatively modifies the fluctuating activity
compared to purely inhibitory networks. In presence of excitation,
intrinsically generated fluctuations induce a strong increase in mean firing
rates, a phenomenon that is much weaker in purely inhibitory networks.
Excitation moreover induces two different fluctuating regimes: for moderate
overall coupling, recurrent inhibition is sufficient to stabilize fluctuations,
for strong coupling, firing rates are stabilized solely by the upper bound
imposed on activity, even if inhibition is stronger than excitation. These
results extend to more general network architectures, and to rate networks
receiving noisy inputs mimicking spiking activity. Finally, we show that
signatures of the second dynamical regime appear in networks of
integrate-and-fire neurons
Revealing Spectrum Features of Stochastic Neuron Spike Trains
none4noopenOrcioni, Simone; Paffi, Alessandra; Apollonio, Francesca; Liberti, MicaelaOrcioni, Simone; Paffi, Alessandra; Apollonio, Francesca; Liberti, Micael
Revealing spectrum features of stochastic neuron spike trains
Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra
Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space
Chronic and acute implants of multi-electrode arrays that cover several
mm of neural tissue provide simultaneous access to population signals like
extracellular potentials and the spiking activity of 100 or more individual
neurons. While the recorded data may uncover principles of brain function, its
interpretation calls for multiscale computational models with corresponding
spatial dimensions and signal predictions. Such models can facilitate the
search of mechanisms underlying observed spatiotemporal activity patterns in
cortex. Multi-layer spiking neuron network models of local cortical circuits
covering ~1 mm have been developed, integrating experimentally obtained
neuron-type specific connectivity data and reproducing features of in-vivo
spiking statistics. With forward models, local field potentials (LFPs) can be
computed from the simulated spiking activity. To account for the spatial scale
of common neural recordings, we extend a local network and LFP model to 4x4
mm. The upscaling preserves the neuron densities, and introduces
distance-dependent connection probabilities and delays. As detailed
experimental connectivity data is partially lacking, we address this
uncertainty in model parameters by testing parameter combinations within
biologically plausible bounds. Based on model predictions of spiking activity
and LFPs, we find that the upscaling procedure preserves the overall spiking
statistics of the original model and reproduces asynchronous irregular spiking
across populations and weak pairwise spike-train correlations observed in
sensory cortex. In contrast with the weak spike-train correlations, the
correlation of LFP signals is strong and distance-dependent, compatible with
experimental observations. Enhanced spatial coherence in the low-gamma band may
explain the recent experimental report of an apparent band-pass filter effect
in the spatial reach of the LFP.Comment: 44 pages, 9 figures, 5 table
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