Activity-dependent enhancement in the reliability of correlated spike timings in cultured cortical neurons

To study the use-dependent modification of activity in neural networks, we investigated the spike timing by simultaneously recording activity at multiple sites in a network of cultured cortical neurons. We used dynamical analysis to study the temporal structure of spike trains and the activity-dependent changes in the reliability and reproducibility of spike patterns evoked by a stimulus. We also used cross-correlation analysis to evaluate the interactions of neuron pairs. Our main conclusions are that even when no obvious change in spike numbers can be seen, use-dependent modification occurs, either enhancing or reducing in the reliability and reproducibility of spike trains evoked by a stimulus, and the fine temporal structure of stimulus-evoked spike trains and interactions between neurons are also modified by tetanic stimulation. Received: 25 February 1998 / Accepted in revised form: 24 August 1998     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998     

大鼠初级传入纤维与脊髓背角神经元间的动作电序列的突触传递

外周感觉神经元通过动作电位序列对信号进行编码,这些动作电位序列经过突触传递最终到达脑部。但是各种脉冲序列如何通过神经元之间的化学突触进行传递依然是一个悬而未决的问题。研究了初级传入A6纤维与背角神经元之间各种动作电位序列的突触传递过程。用于刺激的规则,周期、随机脉冲序列由短簇脉冲或单个脉冲构成。定义“事件”(event)为峰峰问期(intefspike interval)小于或等于规定阈值的最长动作电位串,然后从脉冲序列中提取事件间间期(interevent interval,IEI)。用时间,IEI图与回归映射的方法分析IEI序列,结果表明在突触后输出脉冲序列中可以检测到突触前脉冲序列的主要时间结构特征,特别是在短簇脉冲作为刺激单位时。通过计算输入与输出脉冲序列的互信息,发现短簇脉冲可以更可靠地跨突触传递由输入序列携带的神经信息。这些结果表明外周输入脉冲序列的主要时间结构特征可以跨突触传递,在突触传递神经信息的过程中短簇脉冲更为有效。这一研究在从突触传递角度探索神经信息编码方面迈出了一步。     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

 Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses. Received: 3 April 1995/Accepted in revised form: 11 July 1995     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

The spike trains generated by a neuron model are studied by the methods of nonlinear time series analysis. The results show that the spike trains are chaotic. To investigate effect of noise on transmission of chaotic spike trains, this chaotic spike trains are used as a discrete subthreshold input signal to the integrate-and-fire neuronal model and the FitzHugh-Nagumo(FHN) neuronal model working in noisy environment. The mutual information between the input spike trains and the output spike trains is calculated, the result shows that the transformation of information encoded by the chaotic spike trains is optimized by some level of noise, and stochastic resonance(SR) measured by mutual information is a property available for neurons to transmit chaotic spike trains.     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

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Use of `relative-phase' analysis to assess correlation between neuronal spike trains

 We propose a new method of studying the correlation between neuronal spike trains. This technique is based on the analysis of relative phase between two point processes. Relative phase here is defined as the relative timing difference between two spike trains normalized by the associated interspike interval of one cell. This phase measurement is intended to reveal the relative timing relationship between spike trains atdifferent firing rates. We apply this method to a numerical example and an example from two cerebellar neuronal spike trains of a behaving rat. The results are compared with classical cross-correlation analysis. We show that the technique can avoid some of the limitations of cross-correlation methods, reveal certain statistical dependencies that cannot be shown by cross correlation, and provide information as to the direction of influence between two spike trains. Received: 8 November 2001 / Accepted: 30 September 2002 / Published online: 24 January 2003 Correspondence to: Y. Chen (e-mail: chen@nsi.edu, Fax: + 1-858-626-2099) Acknowledgements. Research for this paper was supported by the Alafi Family Foundation and the Neurosciences Research Foundation.     

A metric space approach to the information channel capacity of spike trains

A novel method is presented for calculating the information channel capacity of spike trains. This method works by fitting a χ-distribution to the distribution of distances between responses to the same stimulus: the χ-distribution is the length distribution for a vector of Gaussian variables. The dimension of this vector defines an effective dimension for the noise and by rephrasing the problem in terms of distance based quantities, this allows the channel capacity to be calculated. As an example, the capacity is calculated for a data set recorded from auditory neurons in zebra finch.     

Exact digital simulation of time-invariant linear systems with applications to neuronal modeling

An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as models for neuronal systems, or as submodules of such systems. The matrix exponential is used to construct a matrix iteration, which propagates the dynamic state of the system step by step on a regular time grid. A large and general class of dynamic inputs to the system, including trains of δ-pulses, can be incorporated into the exact simulation scheme. An extension of the proposed scheme presents an attractive alternative for the approximate simulation of networks of integrate-and-fire neurons with linear sub-threshold integration and non-linear spike generation. The performance of the proposed method is analyzed in comparison with a number of multi-purpose solvers. In simulations of integrate-and-fire neurons, Exact Integration systematically generates the smallest error with respect to both sub-threshold dynamics and spike timing. For the simulation of systems where precise spike timing is important, this results in a practical advantage in particular at moderate integration step sizes. Received: 3 October 1998 / Accepted in revised form: 19 March 1999     

Estimating Temporal Causal Interaction between Spike Trains with Permutation and Transfer Entropy

Estimating the causal interaction between neurons is very important for better understanding the functional connectivity in neuronal networks. We propose a method called normalized permutation transfer entropy (NPTE) to evaluate the temporal causal interaction between spike trains, which quantifies the fraction of ordinal information in a neuron that has presented in another one. The performance of this method is evaluated with the spike trains generated by an Izhikevich’s neuronal model. Results show that the NPTE method can effectively estimate the causal interaction between two neurons without influence of data length. Considering both the precision of time delay estimated and the robustness of information flow estimated against neuronal firing rate, the NPTE method is superior to other information theoretic method including normalized transfer entropy, symbolic transfer entropy and permutation conditional mutual information. To test the performance of NPTE on analyzing simulated biophysically realistic synapses, an Izhikevich’s cortical network that based on the neuronal model is employed. It is found that the NPTE method is able to characterize mutual interactions and identify spurious causality in a network of three neurons exactly. We conclude that the proposed method can obtain more reliable comparison of interactions between different pairs of neurons and is a promising tool to uncover more details on the neural coding.     

Spatial and temporal stochastic interaction in neuronal assemblies

Summary The observation of various types of spatio-temporal correlations in spike-patterns of multiple cortical neurons has shifted attention from rate coding paradigms to computational processes based on the precise timing of spikes in neuronal ensembles. In the present work we develop the notion of “spatial” and “temporal interaction” which provides measures for statistical dependences in coupled stochastic processes like multiple unit spike trains. We show that the classical Willshaw network and Abeles’ synfire chain model both reveal a moderate spatial interaction, but only the synfire chain model reveals a positive temporal interaction, too. Systems that maximize temporal interaction are shown to be almost deterministic globally, but posses almost unpredictable firing behavior on the single unit level.     

A stochastic model and a functional central limit theorem for information processing in large systems of neurons

The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1≤i≤N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.     

Stochasticity,spikes and decoding: sufficiency and utility of order statistics

For over 75 years it has been clear that the number of spikes in a neural response is an important part of the neuronal code. Starting as early as the 1950’s with MacKay and McCullough, there has been speculation over whether each spike and its exact time of occurrence carry information. Although it is obvious that the firing rate carries information it has been less clear as to whether there is information in exactly timed patterns, when they arise from the dynamics of the neurons and networks, as opposed to when they represent some strong external drive that entrains them. One strong null hypothesis that can be applied is that spike trains arise from stochastic sampling of an underlying deterministic temporally modulated rate function, that is, there is a time-varying rate function. In this view, order statistics seem to provide a sufficient theoretical construct to both generate simulated spike trains that are indistinguishable from those observed experimentally, and to evaluate (decode) the data recovered from experiments. It remains to learn whether there are physiologically important signals that are not described by such a null hypothesis. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a “small-world” network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity. Action Editor: Xiao-Jing Wang     

Elimination of response latency variability in neuronal spike trains

 Neuronal activity in the mammalian cortex exhibits a considerable amount of trial-by-trial variability. This may be reflected by the magnitude of the activity as well as by the response latency with respect to an external event, such as the onset of a sensory stimulus, or a behavioral event. Here we present a novel nonparametric method for estimating trial-by-trial differences in response latency from neuronal spike trains. The method makes use of the dynamic rate profile for each single trial and maximizes their total pairwise correlation by appropriately shifting all trials in time. The result is a new alignment of trials that largely eliminates the variability in response latency and provides a new internal trigger that is independent of experiment time. To calibrate the method, we simulated spike trains based on stochastic point processes using a parametric model for phasic response profiles. We illustrate the method by an application to simultaneous recordings from a pair of neurons in the motor cortex of a behaving monkey. It is demonstrated how the method can be used to study the temporal relation of the neuronal response to the experiment, to investigate whether neurons share the same dynamics, and to improve spike correlation analysis. Differences between this and other previously published methods are discussed. Received: 8 April 2002 / Accepted: 26 November 2002 / Published online: 7 April 2003 Correspondence to: Stefan Rotter (e-mail: rotter@biologie.uni-freiburg.de), Tel.: +49-761-2032862, Fax: +49-761-2032860 Acknowledgements. We are grateful to Alexa Riehle for providing us with the monkey data and for valuable discussions. We also thank Felix Kümmell, Hiroyuki Nakahara, and Shun-ichi Amari for helpful discussions. Partial funding was received by the Deutsche Forschungsgemeinschaft (DFG, SFB 505) and the German-Israeli Foundation (GIF). Additional support was provided by the RIKEN Brain Science Institute.     

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long—potentially redundant—past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.     

Mutual information and redundancy in spontaneous communication between cortical neurons

An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior characterized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates—in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals.     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.