Spike Timing Variability Research Articles

Intrinsic variability of latency to first-spike

The assessment of the variability of neuronal spike timing is fundamental to gain understanding of latency coding. Based on recent mathematical results, we investigate theoretically the impact of channel noise on latency variability. For large numbers of ion channels, we derive the asymptotic distribution of latency, together with an explicit expression for its variance. Consequences in terms of information processing are studied with Fisher information in the Morris-Lecar model. A competition between sensitivity to input and precision is responsible for favoring two distinct regimes of latencies.

Distinct signal processing properties of two populations of electrosensory neurons exhibiting different levels of spike time variability

Distinct signal processing properties of two populations of electrosensory neurons exhibiting different levels of spike time variability

Correlation transfer in neuronal populations

Event Abstract Back to Event Correlation transfer in neuronal populations Correlated activity in neural tissue can significantly impact the information carried by a population of neurons. However, there are relatively few analytical results that provide a mechanistic understanding of how correlations are generated and propagated. We start by examining this question using the integrate and fire model which has inspired many developments in theoretical neuroscience. In the second part of the presentation we demonstrate these results using new numerical methods for the simulation of networks of stochastic integrate and fire neurons. These methods are several orders of magnitude faster than typical Monte Carlo simulations. Outputs of a population of neurons are typically pooled to form the input to cells downstream. We provide simple analytical results that describe this situation and show that correlations can be propagated in a counterintuitive manner: Small correlations in the population can translate into large input correlations after such pooling. On the other hand, an increase of correlations within a populations can decrease correlations between populations. It has recently been observed that the transfer of correlations from input currents to output spike trains depends on the firing rate in neuron models and experiments in vitro. Over rapid time scales, correlation transfer increases with both spike time variability and rate; the dependence on variability disappears at large time scales. We show that the behavior of the perfect integrate and fire (PIF) model is quite different: correlations are transferred perfectly over large windows. We give a full description of correlation transfer in PIFs, and provide an intuitive understanding of how cross-correlograms are transformed in networks of such neurons. Although the PIF preserves correlations over long time windows, it tends to "smear out" the cross-correlogram, due to thresholding.This analysis shows that the decorrelation typically observed in a feedforward configuration of more realistic neurons results both from the existence of a firing threshold and "memory loss" induced by the leak. Therefore, the peculiarity of the PIF model can be used to provide an intuitive understanding of the behavior of more complex models. To examine when these results apply to more complex models requires numerical simulations. We present a fast and accurate finite volume method to approximate the solution of the Fokker-Planck equation that models the multivariate density of the subthreshold voltages of stochastic integrate and fire neurons. The discretization of the boundary conditions offers a particular challenge, as standard operator splitting approaches cannot be applied without modification. In comparison to Monte Carlo methods, the present approach offers improved accuracy, and decreases computation times by several orders of magnitude. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Correlation transfer in neuronal populations. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.311 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 04 Feb 2009; Published Online: 04 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Cellular Mechanisms Underlying Stimulus-Dependent Gain Modulation in Primary Visual Cortex Neurons In Vivo

Gain modulation is a widespread neuronal phenomenon that modifies response amplitude without changing selectivity. Computational and in vitro studies have proposed cellular mechanisms of gain modulation based on the postsynaptic effects of background synaptic activation, but these mechanisms have not been studied in vivo. Here, we used intracellular recordings from cat primary visual cortex to measure neuronal gain while changing background synaptic activity with visual stimulation. We found that increases in the membrane fluctuations associated with increases in synaptic input do not obligatorily result in gain modulation in vivo. However, visual stimuli that evoked sustained changes in resting membrane potential, input resistance, and membrane fluctuations robustly modulated neuronal gain. The magnitude of gain modulation depended critically on the spatiotemporal properties of the visual stimulus. Gain modulation in vivo may thus be determined on a moment-to-moment basis by sensory context and the consequent dynamics of synaptic activation.

Functional penetration of variability of motor neuron spike timing through a modulated neuromuscular system

Variability of the neuronal spike pattern is usually thought of in terms of the information that the different interspike intervals might be encoding. However, the very presence of the variability can have other kinds of functional significance. Here, we consider the example of the B15/B16–ARC neuromuscular system of Aplysia, a model system for the study of neuromuscular modulation and control. We show that variability of motor neuron spike timing at the input to the system penetrates throughout the system, affecting all downstream variables including modulator release, modulator concentrations, modulatory actions, and the contraction of the muscle. Furthermore, not only does the variability penetrate through the system, but also it is actually instrumental in maintaining its modulation and contractions at a robust, physiological level.

Rate Coding and Spike-Time Variability in Cortical Neurons With Two Types of Threshold Dynamics

Neurons and dynamical models of spike generation display two different classes of threshold behavior: type 1 [firing frequency vs. current (f-I) relationship is continuous at threshold] and type 2 (discontinuous f-I). With steady current or conductance stimulation, regular-spiking (RS) pyramidal neurons and fast-spiking (FS) inhibitory interneurons in layer 2/3 of somatosensory cortex exhibit type 1 and type 2 threshold behaviors, respectively. We compared the postsynaptic firing variability of type 1 RS and type 2 FS cells, during naturalistic, fluctuating conductance input. In RS neurons, increasing the level of independently random, shunting inhibition caused a monotonic increase in spike reliability, whereas in FS interneurons, there was an optimum level of shunting inhibition for achieving the most reliable spike generation and the most precise spike-time encoding. This was observed over a range of different degrees of synchrony, or correlation, in the input. RS cells displayed a progressive rise in spike jitter during natural-like transient burst inputs, whereas for FS cells, jitter was mostly kept low. Furthermore, RS cells showed encoding of the input level in the spike shape, whereas FS cells did not. These differences between the two cell types are consistent with a role of RS neurons as rate-coding integrators, and a role of FS neurons as resonators controlling the coherence of synchronous firing.

Computing with inter-spike interval codes in networks of integrate and fire neurons

Information encoding in spikes and computations performed by spiking neurons are two sides of the same coin and should be consistent with each other. This study uses this consistency requirement to derive some new results for inter-spike interval (ISI) coding in networks of integrate and fire (IF) neurons. Our analysis shows that such a model can carry out useful computations and that it does also account for variability in spike timing as observed in cortical neurons. Our general result is that IF type neurons, though highly non-linear, perform a simple linear weighted sum operation of ISI coded quantities. Further, we derive bounds on the variation of ISIs that occur in the model although the neurons are deterministic. We also derive useful estimates of the maximum processing speed in a hierarchical network.

Precision of spike trains in primate retinal ganglion cells.

Recent studies have revealed striking precision in the spike trains of retinal ganglion cells in several species and suggested that this precision could be an important aspect of visual signaling. However, the precision of spike trains has not yet been described in primate retina. The spike time and count variability of parasol (magnocellular-projecting) retinal ganglion cells was examined in isolated macaque monkey retinas stimulated with repeated presentations of high contrast, spatially uniform intensity modulation. At the onset of clearly delineated periods of firing, retinal ganglion cells fired spikes time-locked to the stimulus with a variability across trials as low as 1 ms. Spike count variance across trials was much lower than the mean and sometimes approached the minimum variance possible with discrete counts, inconsistent with Poisson statistics expected from independently generated spikes. Spike time and count variability decreased systematically with stimulus strength. These findings were consistent with a model in which firing probability was determined by a stimulus-driven free firing rate modulated by a recovery function representing the action potential absolute and relative refractory period.

Stages of spike time variability during neuronal responses to transient inputs.

In cerebral cortex, cells tend to fire in response to strong transient fluctuations in input, produced by synchronous population activity, which reset the precision of firing and erase correlations between prior and future spike times. Here, using experiments and modeling, we study the accumulation of spike time variance in response to single decaying transient stimuli. All such responses go through distinct stages in time. When the stimulus is high, variance is held low, while at low stimulus levels near threshold, variance rises dramatically, approaching a Poisson level. This behavior was reproduced in a stochastically simulated Hodgkin-Huxley model, and in two simpler models, class 1 (Morris-Lecar) and class 2 (FitzHugh-Nagumo), incorporating Ornstein-Uhlenbeck noise. Early stage variance represents perturbation of uniform limit-cycle motion of the dynamical variables. Late stage variance reflects random motion of the dynamical variables captured within the basin of the resting fixed point. We show that the two stages have different sensitivities to the amplitude and time scale of noise, and relate this to coherence resonance. This rapid breakdown in reliability during responses to transient stimuli may restrict precise signalling by spike times to brief time windows, and limit the duration of coherent synchronous responses in the cortex.

The impact of spike timing variability on the signal-encoding performance of neural spiking models.

It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance.

Jittery trains induced by synaptic-like currents in cerebellar inhibitory interneurons.

Cerebellar inhibitory interneurons respond to parallel fiber input with a characteristic train of action potentials. Here we show that the characteristics of these trains reflect the intrinsic properties of the interneurons. In in vitro cerebellar slices, the response of these neurons to synaptic-like current resembles their in vivo response to parallel fiber input-a train of action potentials characterized by a gradual increase in interspike interval and spike amplitude. A large variability in spike timing, or jitter, was observed, the last action potential emerging from a slow depolarizing wave that lasted beyond the synaptic current and was prevented by either TTX or membrane hyperpolarization. While response duration was weakly dependent on current intensity, the variability of the overall duration was closely related to the variability of the timing of the last action potential. Blocking the Ca(2+) currents or partial blockade of the delayed rectifier (TEA 2 mM) decreased the excitability, leading to a decrease in the duration and variability of the response and increasing its dependence on stimulus intensity. Increased duration and variability was observed in the presence of Cs(+) ions (5 mM) that blocked an h-like current. We conclude that a persistent Na(+) current governs the duration of the response, whereas the synaptic current and the spiking mechanism shape its pattern. The large variability between trials is due to the stochastic nature of the persistent Na(+) current. Thus unless precise timing is achieved by a network of interconnected neurons, these results vote against temporal coding as a player in the cerebellar computational processing.

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders — an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na + and K + channels obeying Hodgkin–Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.

Subthreshold voltage noise due to channel fluctuations in active neuronal membranes.

Voltage-gated ion channels in neuronal membranes fluctuate randomly between different conformational states due to thermal agitation. Fluctuations between conducting and nonconducting states give rise to noisy membrane currents and subthreshold voltage fluctuations and may contribute to variability in spike timing. Here we study subthreshold voltage fluctuations due to active voltage-gated Na+ and K+ channels as predicted by two commonly used kinetic schemes: the Mainen et al. (1995) (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (1952) (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temperatures. We contrast the results from Monte Carlo simulations of the stochastic nonlinear kinetic schemes with analytical, closed-form expressions derived using passive and quasi-active linear approximations to the kinetic schemes. For all subthreshold voltage ranges, the quasi-active linearized approximation is accurate within 8% and may thus be used in large-scale simulations of realistic neuronal geometries.

On the use of Bayesian methods for evaluating compartmental neural models.

Computational modeling is being used increasingly in neuroscience. In deriving such models, inference issues such as model selection, model complexity, and model comparison must be addressed constantly. In this article we present briefly the Bayesian approach to inference. Under a simple set of commonsense axioms, there exists essentially a unique way of reasoning under uncertainty by assigning a degree of confidence to any hypothesis or model, given the available data and prior information. Such degrees of confidence must obey all the rules governing probabilities and can be updated accordingly as more data becomes available. While the Bayesian methodology can be applied to any type of model, as an example we outline its use for an important, and increasingly standard, class of models in computational neuroscience--compartmental models of single neurons. Inference issues are particularly relevant for these models: their parameter spaces are typically very large, neurophysiological and neuroanatomical data are still sparse, and probabilistic aspects are often ignored. As a tutorial, we demonstrate the Bayesian approach on a class of one-compartment models with varying numbers of conductances. We then apply Bayesian methods on a compartmental model of a real neuron to determine the optimal amount of noise to add to the model to give it a level of spike time variability comparable to that found in the real cell.