Mechanisms that modulate the transfer of spiking correlations

Correlations between neuronal spike trains affect network dynamics and population coding. Overlapping afferent populations and correlations between presynaptic spike trains introduce correlations between the inputs to downstream cells. To understand network activity and population coding, it is therefore important to understand how these input correlations are transferred to output correlations.Recent studies have addressed this question in the limit of many inputs with infinitesimal postsynaptic response amplitudes, where the total input can be approximated by gaussian noise. In contrast, we address the problem of correlation transfer by representing input spike trains as point processes, with each input spike eliciting a finite postsynaptic response. This approach allows us to naturally model synaptic noise and recurrent coupling and to treat excitatory and inhibitory inputs separately.We derive several new results that provide intuitive insights into the fundamental mechanisms that modulate the transfer of spiking correlations.     

Higher-order statistics of input ensembles and the response of simple model neurons

Pairwise correlations among spike trains recorded in vivo have been frequently reported. It has been argued that correlated activity could play an important role in the brain, because it efficiently modulates the response of a postsynaptic neuron. We show here that a neuron's output firing rate critically depends on the higher-order statistics of the input ensemble. We constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations, but differed with regard to the higher-order interactions within the population. The first ensemble was characterized by clusters of spikes synchronized over the whole population. In the second ensemble, the size of spike clusters was, on average, proportional to the pairwise correlation. For both input models, we assessed the role of the size of the population, the firing rate, and the pairwise correlation on the output rate of two simple model neurons: a continuous firing-rate model and a conductance-based leaky integrate-and-fire neuron. An approximation to the mean output rate of the firing-rate neuron could be derived analytically with the help of shot noise theory. Interestingly, the essential features of the mean response of the two neuron models were similar. For both neuron models, the three input parameters played radically different roles with respect to the postsynaptic firing rate, depending on the interaction structure of the input. For instance, in the case of an ensemble with small and distributed spike clusters, the output firing rate was efficiently controlled by the size of the input population. In addition to the interaction structure, the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate.     

Information encoding and computation with spikes and bursts

Neurons compute and communicate by transforming synaptic input patterns into output spike trains. The nature of this transformation depends crucially on the properties of voltage-gated conductances in neuronal membranes. These intrinsic membrane conductances can enable neurons to generate different spike patterns including brief, high-frequency bursts that are commonly observed in a variety of brain regions. Here we examine how the membrane conductances that generate bursts affect neural computation and encoding. We simulated a bursting neuron model driven by random current input signal and superposed noise. We consider two issues: the timing reliability of different spike patterns and the computation performed by the neuron. Statistical analysis of the simulated spike trains shows that the timing of bursts is much more precise than the timing of single spikes. Furthermore, the number of spikes per burst is highly robust to noise. Next we considered the computation performed by the neuron: how different features of the input current are mapped into specific output spike patterns. Dimensional reduction and statistical classification techniques were used to determine the stimulus features triggering different firing patterns. Our main result is that spikes, and bursts of different durations, code for different stimulus features, which can be quantified without a priori assumptions about those features. These findings lead us to propose that the biophysical mechanisms of spike generation enables individual neurons to encode different stimulus features into distinct spike patterns.     

Integrate-and-fire neurons driven by correlated stochastic input

Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron's response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.     

Dependence of neuronal correlations on filter characteristics and marginal spike train statistics

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.     

The effects of pair-wise and higher order correlations on the firing rate of a post-synaptic neuron

Coincident firing of neurons projecting to a common target cell is likely to raise the probability of firing of this postsynaptic cell. Therefore, synchronized firing constitutes a significant event for postsynaptic neurons and is likely to play a role in neuronal information processing. Physiological data on synchronized firing in cortical networks are based primarily on paired recordings and cross-correlation analysis. However, pair-wise correlations among all inputs onto a postsynaptic neuron do not uniquely determine the distribution of simultaneous postsynaptic events. We develop a framework in order to calculate the amount of synchronous firing that, based on maximum entropy, should exist in a homogeneous neural network in which the neurons have known pair-wise correlations and higher-order structure is absent. According to the distribution of maximal entropy, synchronous events in which a large proportion of the neurons participates should exist even in the case of weak pair-wise correlations. Network simulations also exhibit these highly synchronous events in the case of weak pair-wise correlations. If such a group of neurons provides input to a common postsynaptic target, these network bursts may enhance the impact of this input, especially in the case of a high postsynaptic threshold. The proportion of neurons participating in synchronous bursts can be approximated by our method under restricted conditions. When these conditions are not fulfilled, the spike trains have less than maximal entropy, which is indicative of the presence of higher-order structure. In this situation, the degree of synchronicity cannot be derived from the pair-wise correlations.     

Short-term synaptic plasticity can enhance weak signal detectability in nonrenewal spike trains

We study the encoding of weak signals in spike trains with interspike interval (ISI) correlations and the signals' subsequent detection in sensory neurons. Motivated by the observation of negative ISI correlations in auditory and electrosensory afferents, we assess the theoretical performance limits of an individual detector neuron receiving a weak signal distributed across multiple afferent inputs. We assess the functional role of ISI correlations in the detection process using statistical detection theory and derive two sequential likelihood ratio detector models: one for afferents with renewal statistics; the other for afferents with negatively correlated ISIs. We suggest a mechanism that might enable sensory neurons to implicitly compute conditional probabilities of presynaptic spikes by means of short-term synaptic plasticity. We demonstrate how this mechanism can enhance a postsynaptic neuron's sensitivity to weak signals by exploiting the correlation structure of the input spike trains. Our model not only captures fundamental aspects of early electrosensory signal processing in weakly electric fish, but may also bear relevance to the mammalian auditory system and other sensory modalities.     

A unified approach to the study of temporal, correlational, and rate coding

We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each reflecting something about potential coding mechanisms. This is possible in the coding regime in which few spikes are emitted in the relevant time window. This approach allows us to study the additional information contributed by spike timing beyond that present in the spike counts and to examine the contributions to the whole information of different statistical properties of spike trains, such as firing rates and correlation functions. It thus forms the basis for a new quantitative procedure for analyzing simultaneous multiple neuron recordings and provides theoretical constraints on neural coding strategies. We find a transition between two coding regimes, depending on the size of the relevant observation timescale. For time windows shorter than the timescale of the stimulus-induced response fluctuations, there exists a spike count coding phase, in which the purely temporal information is of third order in time. For time windows much longer than the characteristic timescale, there can be additional timing information of first order, leading to a temporal coding phase in which timing information may affect the instantaneous information rate. In this new framework, we study the relative contributions of the dynamic firing rate and correlation variables to the full temporal information, the interaction of signal and noise correlations in temporal coding, synergy between spikes and between cells, and the effect of refractoriness. We illustrate the utility of the technique by analyzing a few cells from the rat barrel cortex.     

Spatiotemporal spike encoding of a continuous external signal

Interspike intervals of spikes emitted from an integrator neuron model of sensory neurons can encode input information represented as a continuous signal from a deterministic system. If a real brain uses spike timing as a means of information processing, other neurons receiving spatiotemporal spikes from such sensory neurons must also be capable of treating information included in deterministic interspike intervals. In this article, we examine functions of neurons modeling cortical neurons receiving spatiotemporal spikes from many sensory neurons. We show that such neuron models can encode stimulus information passed from the sensory model neurons in the form of interspike intervals. Each sensory neuron connected to the cortical neuron contributes equally to the information collection by the cortical neuron. Although the incident spike train to the cortical neuron is a superimposition of spike trains from many sensory neurons, it need not be decomposed into spike trains according to the input neurons. These results are also preserved for generalizations of sensory neurons such as a small amount of leak, noise, inhomogeneity in firing rates, or biases introduced in the phase distributions.     

Intrinsic stabilization of output rates by spike-based Hebbian learning.

We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quantified by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed if the integral of the learning window is negative. A negative integral corresponds to anti-Hebbian learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and anti-Hebbian rules is questionable since learning is driven by correlations on the timescale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.     

Finding the event structure of neuronal spike trains

Neurons in sensory systems convey information about physical stimuli in their spike trains. In vitro, single neurons respond precisely and reliably to the repeated injection of the same fluctuating current, producing regions of elevated firing rate, termed events. Analysis of these spike trains reveals that multiple distinct spike patterns can be identified as trial-to-trial correlations between spike times (Fellous, Tiesinga, Thomas, & Sejnowski, 2004 ). Finding events in data with realistic spiking statistics is challenging because events belonging to different spike patterns may overlap. We propose a method for finding spiking events that uses contextual information to disambiguate which pattern a trial belongs to. The procedure can be applied to spike trains of the same neuron across multiple trials to detect and separate responses obtained during different brain states. The procedure can also be applied to spike trains from multiple simultaneously recorded neurons in order to identify volleys of near-synchronous activity or to distinguish between excitatory and inhibitory neurons. The procedure was tested using artificial data as well as recordings in vitro in response to fluctuating current waveforms.     

Analytical model for the effects of learning on spike count distributions

The spike count distribution observed when recording from a variety of neurons in many different conditions has a fairly stereotypical shape, with a single mode at zero or close to a low average count, and a long, quasi-exponential tail to high counts. Such a distribution has been suggested to be the direct result of three simple facts: the firing frequency of a typical cortical neuron is close to linear in the summed input current entering the soma, above a threshold; the input current varies on several timescales, both faster and slower than the window used to count spikes; and the input distribution at any timescale can be taken to be approximately normal. The third assumption is violated by associative learning, which generates correlations between the synaptic weight vector on the dendritic tree of a neuron, and the input activity vectors it is repeatedly subject to. We show analytically that for a simple feed-forward model, the normal distribution of the slow components of the input current becomes the sum of two quasi-normal terms. The term important below threshold shifts with learning, while the term important above threshold does not shift but grows in width. These deviations from the standard distribution may be observable in appropriate recording experiments.     

Quantifying variability in neural responses and its application for the validation of model predictions

A rate code assumes that a neuron's response is completely characterized by its time-varying mean firing rate. This assumption has successfully described neural responses in many systems. The noise in rate coding neurons can be quantified by the coherence function or the correlation coefficient between the neuron's deterministic time-varying mean rate and noise corrupted single spike trains. Because of the finite data size, the mean rate cannot be known exactly and must be approximated. We introduce novel unbiased estimators for the measures of coherence and correlation which are based on the extrapolation of the signal to noise ratio in the neural response to infinite data size. We then describe the application of these estimates to the validation of the class of stimulus-response models that assume that the mean firing rate captures all the information embedded in the neural response. We explain how these quantifiers can be used to separate response prediction errors that are due to inaccurate model assumptions from errors due to noise inherent in neuronal spike trains.     

An algorithm for modifying neurotransmitter release probability based on pre- and postsynaptic spike timing

The precise times of occurrence of individual pre- and postsynaptic action potentials are known to play a key role in the modification of synaptic efficacy. Based on stimulation protocols of two synaptically connected neurons, we infer an algorithm that reproduces the experimental data by modifying the probability of vesicle discharge as a function of the relative timing of spikes in the pre- and postsynaptic neurons. The primary feature of this algorithm is an asymmetry with respect to the direction of synaptic modification depending on whether the presynaptic spikes precede or follow the postsynaptic spike. Specifically, if the presynaptic spike occurs up to 50 ms before the postsynaptic spike, the probability of vesicle discharge is upregulated, while the probability of vesicle discharge is downregulated if the presynaptic spike occurs up to 50 ms after the postsynaptic spike. When neurons fire irregularly with Poisson spike trains at constant mean firing rates, the probability of vesicle discharge converges toward a characteristic value determined by the pre- and postsynaptic firing rates. On the other hand, if the mean rates of the Poisson spike trains slowly change with time, our algorithm predicts modifications in the probability of release that generalize Hebbian and Bienenstock-Cooper-Munro rules. We conclude that the proposed spike-based synaptic learning algorithm provides a general framework for regulating neurotransmitter release probability.     

Improved similarity measures for small sets of spike trains

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in neuroprosthetic devices and electrophysiological experiments. Frequently only a few spike trains are available in each class. We derive analytical expressions for the small-sample bias present when comparing estimators of the time-dependent firing intensity. We then exploit analogies between the comparison of firing intensities and previously used spike train metrics and show that improved spike train measures can be successfully used for fitting neuron models to experimental data, for comparisons of spike trains, and classification of spike train data. In classification tasks, the improved similarity measures can increase the recovered information. We demonstrate that when similarity measures are used for fitting mathematical models, all previous methods systematically underestimate the noise. Finally, we show a striking implication of this deterministic bias by reevaluating the results of the single-neuron prediction challenge.     

Assessing neuronal coherence with single-unit, multi-unit, and local field potentials

The purpose of this study was to obtain a better understanding of neuronal responses to correlated input, in particular focusing on the aspect of synchronization of neuronal activity. The first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input. For Poisson neurons, we could derive that the peak of the coherence between the correlated input and multi-unit activity increases proportionally with the square root of the number of neurons in the multi-unit recording. The coherence between two typical multi-unit recordings (2 to 10 single units) with partially correlated input increases proportionally with the number of units in the multi-unit recordings. The second aim of this study was to investigate to what extent the amplitude and signal-to-noise ratio of the coherence between input and output varied for single-unit versus multi-unit activity and how they are affected by the duration of the recording. The same problem was addressed for the coherence between two single-unit spike series and between two multi-unit spike series. The analytical results for the Poisson neuron and numerical simulations for the conductance-based leaky integrate-and-fire neuron and for the conductance-based Hodgkin-Huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording. The only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function. The results of analytical derivations and computer simulations for model neurons show that the coherence for multi-unit activity is larger than that for single-unit activity. This is in agreement with the results of experimental data obtained from monkey visual cortex (V4). Finally, we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate.     

基于脉冲神经网络的红外目标提取

模拟生物信息处理机制,设计了一种用于红外目标提取的脉冲神经网络(SNN)。首先,利用输入层脉冲神经元将激励图像转化为脉冲序列;其次,采用中间层脉冲神经元输出脉冲的密度编码红外图像目标的轮廓像素和非目标轮廓像素;最后,根据输出层神经元输出脉冲的密度是否超过阈值提取红外目标。实验结果表明,设计的脉冲神经网络具有较好的红外目标提取性能,并且符合生物视觉信息处理机制。     

神经元膜电位对信息的编码

神经元膜电位的放电活动是神经编码的基础。然而,目前对于神经元电活动对神经信息的编码方式,至今尚未形成一个完整的认识。传统的编码理论认为神经系统以离散的动作电位放电序列进行信息的表达和传递,主要研究动作电位的发放频率和放电活动的时间模式。基于该理论,对神经元放电序列所携带的信息已经出现了一些定量的计算方法,但这些方法还很难应用到大规模神经元网络的计算当中。本研究以神经元的膜电位为研究对象,展示了如何量化膜电位序列所携带的信息,并将该计算结果与传统放电序列方沣的计算结果进行了对比分析,其结果取得了很好的一致性。本研究为神经活动信息量的定量计算提供了一种新的思路和方法。     

Correlated firing improves stimulus discrimination in a retinal model

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.