Stochastic Spiking Research Articles

Spikes in Mammalian Bipolar Cells Support Temporal Layering of the Inner Retina

In the mammalian retina, 10-12 different cone bipolar cell (BC) types decompose the photoreceptor signal into parallel channels, providing the basis for the functional diversity of retinal ganglion cells (RGCs). BCs differing in their temporal properties appear to project to different strata of the retina's inner synaptic layer, based on somatic recordings of BCs and excitatory synaptic currents measured in RGCs. However, postsynaptic currents in RGCs are influenced by dendritic morphology and receptor types, and the BC signal can be transformed at the axon terminals both through interactions with amacrine cells and through the generation of all-or-nothing spikes. Therefore, the temporal properties of the BC output have not been analyzed systematically across different types of mammalian BCs. We recorded calcium signals directly within axon terminals using two-photon imaging and show that BCs can be divided into ≥eight functional clusters. The temporal properties of the BC output were directly reflected in their anatomical organization within the retina's inner synaptic layer: faster cells stratified closer to the border between ON and OFF sublamina. Moreover, ≥three fastest groups generated clear all-or-nothing spikes. Therefore, the systematic projection pattern of BCs provides distinct temporal "building blocks" for the feature extracting circuits of the inner retina.

Efficient “Communication through Coherence” Requires Oscillations Structured to Minimize Interference between Signals

The ‘communication through coherence’ (CTC) hypothesis proposes that selective communication among neural networks is achieved by coherence between firing rate oscillation in a sending region and gain modulation in a receiving region. Although this hypothesis has stimulated extensive work, it remains unclear whether the mechanism can in principle allow reliable and selective information transfer. Here we use a simple mathematical model to investigate how accurately coherent gain modulation can filter a population-coded target signal from task-irrelevant distracting inputs. We show that selective communication can indeed be achieved, although the structure of oscillatory activity in the target and distracting networks must satisfy certain previously unrecognized constraints. Firstly, the target input must be differentiated from distractors by the amplitude, phase or frequency of its oscillatory modulation. When distracting inputs oscillate incoherently in the same frequency band as the target, communication accuracy is severely degraded because of varying overlap between the firing rate oscillations of distracting inputs and the gain modulation in the receiving region. Secondly, the oscillatory modulation of the target input must be strong in order to achieve a high signal-to-noise ratio relative to stochastic spiking of individual neurons. Thus, whilst providing a quantitative demonstration of the power of coherent oscillatory gain modulation to flexibly control information flow, our results identify constraints imposed by the need to avoid interference between signals, and reveal a likely organizing principle for the structure of neural oscillations in the brain.

AN EXCITABLE ELECTRONIC CIRCUIT AS A SENSORY NEURON MODEL

An electronic circuit device, inspired on the FitzHugh–Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of the electronics quantitatively reproduces the experimental observations on the circuit, including the Hopf bifurcation at the onset of tonic spiking. Moreover, we have implemented an analog noise generator as a source to study the variability of the spike trains. When the circuit is in the excitable regime, coherence resonance is observed. At sufficiently low noise intensity the spike trains have Poisson statistics, as in many biological neurons. The transfer function of the stochastic spike trains has a dynamic range of 6 dB, close to experimental values for real olfactory receptor neurons.

Effect of Sparse Random Connectivity on the Stochastic Spiking Coherence of Inhibitory Subthreshold Neurons

Effect of Sparse Random Connectivity on the Stochastic Spiking Coherence of Inhibitory Subthreshold Neurons

Control of stochastic spike motion in an excitable system via recycled noise

The control effect of recycled noise, generated by the superposition of a primary Gaussian noise source and a secondary source with a constant delay, has been studied in an excitable FitzHugh-Nagumo system. We mainly focus on the performance of noise-induced spike and coherence resonance in a parameter region sub-threshold to supercritical Hopf bifurcation. For fixed noise intensity, simulations show that the coherence (quantitatively measured by R, which is defined as the mean value of the spike interval time T normalized to its mean square root) and the emission velocity of the noise-induced spikes exhibit damped oscillations with the variation of delay time, demonstrating a new kind of multi-resonance phenomenon. Furthermore, the optimal delay times for resonance and the fast emission velocity are related to the inherent frequency of the system. It seems that there are some synchronization effects between the dynamic character of the system and the delay time of recycled noise. Our results give clear information about how one can control the coherence and emission velocity of the noise-induced spike in a rather effective way, by deliberately adjusting the delay time and the fraction of the secondary noise.

Measuring burstiness and regularity in oscillatory spike trains

Abstract The ability of neurons to emit different firing patterns such as bursts or oscillations is important for information processing in the brain. In dopaminergic neurons, prominent patterns include repetitive, oscillatory bursts, regular pacemakers, and irregular spike trains with nonstationary properties. In order to describe and measure the variability of these patterns, we describe burstiness and regularity in a single model framework. We present a doubly stochastic spike train model in which a background oscillation with independent and normally distributed intervals gives rise to either single spikes or bursty spike events with Gaussian firing intensities. Five easily interpretable parameters allow a classification into bursty or single spike and irregularly or regularly oscillating firing patterns. This classification is based primarily on features of the autocorrelation histogram which are usually studied qualitatively by visual inspection. The present model provides a quantitative and objective classification scheme and relates these features directly to the underlying processes. In addition, confidence intervals visualize the uncertainty of parameter estimation and classification precision. We apply the model to a data set obtained from single dopaminergic substantia nigra neurons recorded extracellularly in vivo. The model is able to represent a high variety of discharge patterns observed empirically, and the classification agrees closely with visual inspection. In addition, changes in the parameters can be studied quantitatively, including also the properties related to bursting behavior. Thus, the proposed model can be used for the description of neuronal firing patterns and the investigation of their dynamical changes with cellular and experimental conditions.

Compressed sensing with stochastic spikes

Compressed Sensing (CS) refers to the mathematical finding that perfect reconstruction of a high dimensional state can be possible also from much lower dimensional samples provided the state representation is sufficiently sparse. Since neuronal activities in cortex are in fact sparse it is tempting to explain certain aspects of neuronal coding in terms of CS ([1] and [2]). The applicability of CS to neuronal structures and activities, however, critically relies on realistic assumptions about the neuronal mechanisms that could implement efficient algorithms. Here we investigated the feasibility of CS with rate coding neurons. Also, we are interested in the speed-precision tradeoff of reconstructions using spike-based algorithms similar to the one we introduced previously [3]. We find that a biologically plausible algorithm for non-negative activities can efficiently exploit the information contained in stochastic spike events and converges to close solutions for a wide range of sparsenesses and under-samplings. Figure ​Figure11 shows the root mean squared error (relative to the initial error) averaged over 10 examples depending on proportion of zeros in the representation on the abscissa and the compression ratio M/N on the ordinate, where M is number of observed neurons and N (here set to 500) is the dimension of the underlying state. Figure 1 We also investigated conditions on the generating matrix that would facilitate satisfactory reconstructions from limited numbers of spikes. Learning such structures with sparseness constraints can speed up estimations but will in general not match the 'true' generating model. Therefore the construction of sparse representations from spikes can be considered a bias favoring speed in contrast to faithfulness. In [3] we showed that learning generating matrices is possible using only spike activity. Taken together, our results underline the potential relevance of CS for understanding connectivity structures, sparseness and activity dynamics in the brain.

Stochastic Model Explains the Role of Excitation and Inhibition in Binaural Sound Localization in Mammals

Interaural time differences (ITDs), the differences of arrival time of the sound at the two ears, provide a major cue for low-frequency sound localization in the horizontal plane. The first nucleus involved in the computation of ITDs is the medial superior olive (MSO). We have modeled the neural circuit of the MSO using a stochastic description of spike timing. The inputs to the circuit are stochastic spike trains with a spike timing distribution described by a given probability density function (beta density). The outputs of the circuit reproduce the empirical firing rates found in experiment in response to the varying ITD. The outputs of the computational model are calculated numerically and these numerical simulations are also supported by analytical calculations. We formulate a simple hypothesis concerning how sound localization works in mammals. According to this hypothesis, there is no array of delay lines as in the Jeffress' model, but the inhibitory input is shifted in time as a whole. This is consistent with experimental observations in mammals.

Emergent oscillations in networks of stochastic spiking neurons.

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework.

Statistical-mechanical measure of stochastic spiking coherence in a population of inhibitory subthreshold neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure M ( s ) by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure M ( s ) is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of M ( s ), we quantitatively characterize the stochastic spiking coherence, and find that M ( s ) reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure M ( s ) may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons.

The random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling the states of ion channels nonlinearly couples continuous-time Markov chains to a differential equation for voltage. Beginning with the work of R. F. Fox and Y.-N. Lu [Phys. Rev. E 49, 3421 (1994)], there have been attempts to generate simpler models that use stochastic differential equation (SDEs) to approximate the stochastic spiking activity produced by Markov chain models. Recent numerical investigations, however, have raised doubts that SDE models can capture the stochastic dynamics of Markov chain models.We analyze three SDE models that have been proposed as approximations to the Markov chain model: one that describes the states of the ion channels and two that describe the states of the ion channel subunits. We show that the former channel-based approach can capture the distribution of channel noise and its effects on spiking in a Hodgkin-Huxley neuron model to a degree not previously demonstrated, but the latter two subunit-based approaches cannot. Our analysis provides intuitive and mathematical explanations for why this is the case. The temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels, but the subunit-based approaches do not correctly account for this structure. Our study confirms and elucidates the findings of previous numerical investigations of subunit-based SDE models. Moreover, it presents evidence that Markov chain models of the nonlinear, stochastic dynamics of neural membranes can be accurately approximated by SDEs. This finding opens a door to future modeling work using SDE techniques to further illuminate the effects of ion channel fluctuations on electrically active cells.

Generalized stochastic spiking neuron model and extended spike response model in spatial-temporal pulse pattern detection task

A generalized model of spiking neuron is proposed as a non-stationary stochastic spike sequences processing unit. The generalized spiking neuron model is described with a conditional spike generation probability distribution and with a state evolution operator. An information theory language is used for the convenient neuron's learning tasks description. The problem of spiking neuron learning with the teacher is solved using information entropy minimization algorithm. A particular implementation of generalized model using stochastic Spike Response Model with alpha-functions set is provided. A task of time delay maintenance between input and output spikes and a task of detecting of a spiking pattern in a noisy stream of pulse signals are considered using extended SRM neuron. It is shown that after the using of the proposed learning method spiking neuron became capable to detect a spatial-temporal pulse pattern and to serve as an adaptive delay unit.

A network of spiking neurons that can represent interval timing: mean field analysis.

Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.

Calcium spikes: Chance or necessity?

Calcium oscillations present one of the most important signaling mechanisms in cell biology. The standard paradigm for the origin of calcium oscillations is dynamic, i.e. fast release of calcium from intracellular stores is followed by slow inhibition. Yet, this very dynamic theory for these oscillations came recently into scrutiny since the building blocks of cellular calcium signals are spatially and temporally limited calcium release events through small, distinct cluster of ion channels. According to this new paradigm, a coherent wave of calcium release, triggered by stochastic release events from a group of clusters, sweeps the cell. Oscillations are believed to emerge through a spatial coherence resonance mechanism. In this paper we investigate the difference in stochastic spiking generated by a small periodic system and a small excitable system and compare with published experimental data.

Analytical investigation of the effects of lateral connections on the accuracy of population coding

We studied how lateral connections affect the accuracy of a population code by using a model of orientation selectivity in the primary visual cortex. Investigating the effects of lateral connections on population coding is a complex problem because these connections simultaneously change the shape of tuning curves and correlations between neurons. Both of these changes caused by lateral connections have to be taken into consideration to correctly evaluate their effects. We propose a theoretical framework for analytically computing the Fisher information, which measures the accuracy of a population code, in stochastic spiking neuron models with refractory periods. Within our framework, we accurately evaluated both the changes in tuning curves and correlations caused by lateral connections and their effects on the Fisher information. We found that their effects conflicted with each other and the answer to whether or not the lateral connections increased the Fisher information strongly depended on the intrinsic properties of the model neuron. By systematically changing the coupling strengths of excitations and inhibitions, we found the parameter regions of lateral connectivities where sharpening of tuning curves through Mexican-hat connectivities led to an increase in information, which is in contrast to some previous findings.

Fitting a stochastic spiking model to neuronal current injection data

Spiking neuron models have advanced to the stage of accurately predicting the spike times of individual biological neurons for given fluctuating current. Most of the successful models are based on deterministic mechanistic modeling. In order to describe the stochastic aspect of neuronal firing, I propose setting a deterministic model in a stochastic framework, namely, incorporating the multi-timescale adaptive threshold (MAT) model of neuronal spiking into the stochastic framework of the linear-nonlinear Poisson (LNP) model in the form of a generalized linear model (GLM). In this setting, the probability of spike occurrence is updated each time a spike is derived from the past probability. Accordingly, the model may account for nontrivial firing patterns of various neurons that cannot be realized with the inhomogeneous Poisson process. The stochastic MAT model is not only capable of characterizing firing mechanisms specific to individual neurons, but may render the statistical inference feasible for the underlying mechanisms from the data. I also examine here two plausible principles for adjusting the model parameters: maximizing the spike time coincidence between the model and data, and maximizing the likelihood. It is found that these principles bring about greatly different characteristics for an identical set of data.

Multiple routes to functionally feedforward dynamics in cortical network models.

Event Abstract Back to Event Multiple routes to functionally feedforward dynamics in cortical network models. Edward Wallace1*, Marc Benayoun2, Wim Van Drongelen3 and Jack Cowan1 1 University of Chicago, Dept. of Mathematics, United States 2 University of Chicago, CNS Graduate Program, United States 3 University of Chicago, Pediatric Neurology, United States Networks with closely balanced inhibition and excitation exhibit dynamics of particular interest to computational neuroscientists. They may respond quickly to sudden changes in afferent input, or presented with slow changes in input they may move between synchronous and asynchronous dynamics. This has been attributed to a hidden functionally feedforward structure in the network, meaning that a co-ordinate change to the dynamical variables reveals an underlying unidirectional flow of activity. It is therefore of interest to determine which combinations of feedforward structure and input obtainable under physiological constraints produce which network dynamics, and what this means for information processing. We generate random sparse matrices with strong hidden feedforward structure, by adjusting the spectral properties of sub-blocks of the connectivity matrix. This may be achieved by fixing the mean values of the sub-blocks of the matrix. Less intuitively, it may also be achieved by adjusting their variances. Then, the interplay between the connectivity matrix and the input, depending on their mutual correlations, causes the network to move between dynamical regimes. A special case of this in a stochastic spiking network is a transition from asynchronous firing to aperiodic synchronous firing, with spikes grouped into so-called neuronal avalanches. The spectral properties necessary for functionally feedforward dynamics may hold in networks with a variety of connection topologies. In particular, we show how to generate networks with small-world connectivity and underlying feedforward dynamics. This is relevant to the problem of inferring a network’s connectivity from its dynamics: experimental measurements of the dynamical repertoire obtainable from functionally feedforward networks are not enough to show that the network under observation does or does not have small-world topology. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session III Citation: Wallace E, Benayoun M, Drongelen W and Cowan J (2010). Multiple routes to functionally feedforward dynamics in cortical network models.. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00160 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: 02 Mar 2010; Published Online: 02 Mar 2010. * Correspondence: Edward Wallace, University of Chicago, Dept. of Mathematics, Chicago, United States, ewjwallace@gmail.com 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 Edward Wallace Marc Benayoun Wim Van Drongelen Jack Cowan Google Edward Wallace Marc Benayoun Wim Van Drongelen Jack Cowan Google Scholar Edward Wallace Marc Benayoun Wim Van Drongelen Jack Cowan PubMed Edward Wallace Marc Benayoun Wim Van Drongelen Jack Cowan 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.

FIND -- a unified framework for neural data analysis

The complexity of neurophysiology data has increased tremendously over the last years, especially due to the widespread availability of multi-channel recording techniques. With adequate computing power the current limit for computational neuroscience is the effort and time it takes for scientists to translate their ideas into working code. Advanced analysis methods are complex and often lack reproducibility on the basis of published descriptions. To overcome this limitation we develop FIND (Finding Information in Neural Data) as a platform-independent, open source framework for the analysis of neuronal activity data based onMatlab (Mathworks). Here, we outline the structure of the FIND framework and describe its functionality, our measures of quality control, and the policies for developers and users. Within FIND we have developed a unified data import from various proprietary formats, simplifying standardized interfacing with tools for analysis and simulation. The toolbox FIND covers a steadily increasing number of tools. These analysis tools address various types of neural activity data, including discrete series of spike events, continuous time series and imaging data. Additionally, the toolbox provides solutions for the simulation of parallel stochastic point processes tomodelmulti-channel spiking activity.We illustrate two examples of complex analyses with FIND tools: First, we present a time-resolved characterization of the spiking irregularity in an in vivo extracellular recording from a mushroom-body extrinsic neuron in the honeybee during odor stimulation. Second, we describe layer specific input dynamics in the rat primary visual cortex in vivo in response to visual flash stimulation on the basis of multi-channel spiking activity. © 2008 Elsevier Ltd. All rights reserved.

Spontaneous Activity of Auditory Nerve Fibers in the Barn Owl (Tyto alba): Analyses of Interspike Interval Distributions

In vertebrate auditory systems, the conversion from graded receptor potentials across the hair-cell membrane into stochastic spike trains of the auditory nerve (AN) fibers is performed by ribbon synapses. The statistics underlying this process constrain auditory coding but are not precisely known. Here, we examine the distributions of interspike intervals (ISIs) from spontaneous activity of AN fibers of the barn owl (Tyto alba), a nocturnal avian predator whose auditory system is specialized for precise temporal coding. The spontaneous activity of AN fibers, with the exception of those showing preferred intervals, is commonly thought to result from excitatory events generated by a homogeneous Poisson point process, which lead to spikes unless the fiber is refractory. We show that the ISI distributions in the owl are better explained as resulting from the action of a brief refractory period ( approximately 0.5 ms) on excitatory events generated by a homogeneous stochastic process where the distribution of interevent intervals is a mixture of an exponential and a gamma distribution with shape factor 2, both with the same scaling parameter. The same model was previously shown to apply to AN fibers in the cat. However, the mean proportions of exponentially versus gamma-distributed intervals in the mixture were different for cat and owl. Furthermore, those proportions were constant across fibers in the cat, whereas they covaried with mean spontaneous rate and with characteristic frequency in the owl. We hypothesize that in birds, unlike in mammals, more than one ribbon may provide excitation to most fibers, accounting for the different proportions, and that variation in the number of ribbons may underlie the variation in the proportions.