Network Amplification of Local Fluctuations Causes HighSpike Rate Variability, Fractal Firing Patterns andOscillatory Local Field Potentials (original) (raw)
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Noise in Attractor Networks in the Brain Produced by Graded Firing Rate Representations
PLoS ONE, 2011
Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry.
Correlated noise and memory effects in neural firing statistics
This paper discusses two problems at the forefront of neurobiology and of noise research. They arise from non-renewal firing processes in nerve cells, due to various forms of memory. The combination of short and long-term correlations between firing intervals has been shown to enhance information transfer, namely by causing a minimal variability in the spike count distribution at a specific counting time. The first problem concerns first passage time calculations in a model that combines these two forms of correlations. It is a two-dimensional leaky integrate-and-fire (LIF) model in which the threshold is also a dynamical variable. The second problem concerns the effect of long-range correlations on neuron firing statistics. We show new results on the interspike interval densities as well as the spike count Fano factor for the perfect integrate-and-fire (PIF) model forced by a slow (long-correlation time) Ornstein-Uhlenbeck process, which is a simplification of the previous model. These theoretical results are obtained using a quasi-static noise approximation. There remain, however, many exciting challenges in relating correlations with signal detection in neurobiological systems, some of which are highlighted in our paper.
Physical Review E, 2009
The activity of spiking neurons is frequently described by renewal point process models that assume the statistical independence and identical distribution of the intervals between action potentials. However, the assumption of independent intervals must be questioned for many different types of neurons. We review experimental studies that reported the feature of a negative serial correlation of neighboring intervals, commonly observed in neurons in the sensory periphery as well as in central neurons, notably in the mammalian cortex. In our experiments we observed the same short-lived negative serial dependence of intervals in the spontaneous activity of mushroom body extrinsic neurons in the honeybee. To model serial interval correlations of arbitrary lags, we suggest a family of autoregressive point processes. Its marginal interval distribution is described by the generalized gamma model, which includes as special cases the log-normal and gamma distributions, which have been widely used to characterize regular spiking neurons. In numeric simulations we investigated how serial correlation affects the variance of the neural spike count. We show that the experimentally confirmed negative correlation reduces single-neuron variability, as quantified by the Fano factor, by up to 50%, which favors the transmission of a rate code. We argue that the feature of a negative serial correlation is likely to be common to the class of spike-frequency-adapting neurons and that it might have been largely overlooked in extracellular single-unit recordings due to spike sorting errors.
Frontiers in Computational Neuroscience, 2008
The activity of spiking neurons is frequently described by renewal point process models that assume the statistical independence and identical distribution of the intervals between action potentials. However, the assumption of independent intervals must be questioned for many different types of neurons. We review experimental studies that reported the feature of a negative serial correlation of neighboring intervals, commonly observed in neurons in the sensory periphery as well as in central neurons, notably in the mammalian cortex. In our experiments we observed the same short-lived negative serial dependence of intervals in the spontaneous activity of mushroom body extrinsic neurons in the honeybee. To model serial interval correlations of arbitrary lags, we suggest a family of autoregressive point processes. Its marginal interval distribution is described by the generalized gamma model, which includes as special cases the log-normal and gamma distributions, which have been widely used to characterize regular spiking neurons. In numeric simulations we investigated how serial correlation affects the variance of the neural spike count. We show that the experimentally confirmed negative correlation reduces single-neuron variability, as quantified by the Fano factor, by up to 50%, which favors the transmission of a rate code. We argue that the feature of a negative serial correlation is likely to be common to the class of spike-frequency-adapting neurons and that it might have been largely overlooked in extracellular single-unit recordings due to spike sorting errors.
Journal of Neurophysiology, 2003
When the local field potential of a cortical network displays coherent fast oscillations (∼40-Hz gamma or ∼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 depen...
Physical Review E, 2014
First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network reveals irregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior.
Journal of Computational Neuroscience, 2009
Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f-I curve. We introduce a novel classification of neurons into Types A, B−, and B+ according to how f-I curves are modulated by input fluctuations. In Type A neurons, the f-I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B− neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple "energy barrier" model.
Correlation between neural spike trains increases with firing rate
Nature, 2007
Populations of neurons in the retina 1-3 , olfactory system 4 , visual 5 and somatosensory 6 thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding 9 , attention 11 , stimulus discrimination 4 , and motor behaviour 12 . Nevertheless, the mechanisms underlying correlated spiking are poorly understood 2,3,13-20 , and its coding implications are still debated . It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using 'integrate-and-fire' neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.