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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Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons simultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.     

Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons

The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI), which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously) and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE) solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates) at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.     

Measuring Information-Transfer Delays

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.     

Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected—if dependence is attributed to the trains—the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.     

Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks

The analysis of cortical and subcortical networks requires the identification of their nodes, and of the topology and dynamics of their interactions. Exploratory tools for the identification of nodes are available, e.g. magnetoencephalography (MEG) in combination with beamformer source analysis. Competing network topologies and interaction models can be investigated using dynamic causal modelling. However, we lack a method for the exploratory investigation of network topologies to choose from the very large number of possible network graphs. Ideally, this method should not require a pre-specified model of the interaction. Transfer entropy--an information theoretic implementation of Wiener-type causality--is a method for the investigation of causal interactions (or information flow) that is independent of a pre-specified interaction model. We analysed MEG data from an auditory short-term memory experiment to assess whether the reconfiguration of networks implied in this task can be detected using transfer entropy. Transfer entropy analysis of MEG source-level signals detected changes in the network between the different task types. These changes prominently involved the left temporal pole and cerebellum--structures that have previously been implied in auditory short-term or working memory. Thus, the analysis of information flow with transfer entropy at the source-level may be used to derive hypotheses for further model-based testing.     

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.     

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。     

Detection of mutual determinism between a pair of spike trains

 A method for detecting mutual deterministic dependence between a pair of spike trains is proposed. When it is assumed that a cell assembly, which is a subgroup of neurons processing a common task, is constituted as a dynamical system, then the mutual determinism between constituent neurons may be directly reflected in functional connectivity in the assembly. The deterministic dependence between two spike trains can be measured with statistical significance using a method of nonlinear prediction. Some examples of simulations are demonstrated in both deterministic and stochastic cases. Received: 8 August 1999 / Accepted in revised form: 29 March 2001     

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.     

Model based decoding of spike trains

Reliably decoding neuronal responses requires knowing what aspects of neuronal responses are stimulus related, and which aspects act as noise. Recent work shows that spike trains can be viewed as stochastic samples from the rate variation function, as estimated by the time dependent spike density function (or normalized peristimulus time histogram). Such spike trains are exactly described by order statistics, and can be decoded millisecond-by-millisecond by iterative application of order statistics.     

Effects of Isoflurane Anesthesia on Ensemble Patterns of Ca2+ Activity in Mouse V1: Reduced Direction Selectivity Independent of Increased Correlations in Cellular Activity

Anesthesia affects brain activity at the molecular, neuronal and network level, but it is not well-understood how tuning properties of sensory neurons and network connectivity change under its influence. Using in vivo two-photon calcium imaging we matched neuron identity across episodes of wakefulness and anesthesia in the same mouse and recorded spontaneous and visually evoked activity patterns of neuronal ensembles in these two states. Correlations in spontaneous patterns of calcium activity between pairs of neurons were increased under anesthesia. While orientation selectivity remained unaffected by anesthesia, this treatment reduced direction selectivity, which was attributable to an increased response to the null-direction. As compared to anesthesia, populations of V1 neurons coded more mutual information on opposite stimulus directions during wakefulness, whereas information on stimulus orientation differences was lower. Increases in correlations of calcium activity during visual stimulation were correlated with poorer population coding, which raised the hypothesis that the anesthesia-induced increase in correlations may be causal to degrading directional coding. Visual stimulation under anesthesia, however, decorrelated ongoing activity patterns to a level comparable to wakefulness. Because visual stimulation thus appears to ‘break’ the strength of pairwise correlations normally found in spontaneous activity under anesthesia, the changes in correlational structure cannot explain the awake-anesthesia difference in direction coding. The population-wide decrease in coding for stimulus direction thus occurs independently of anesthesia-induced increments in correlations of spontaneous activity.     

The stochastic properties of input spike trains control neuronal arithmetic

In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains.     

Investigation of a monosynaptic excitatory connection by means of a biomathematical model of neuronal interaction

A biomathematical model of neuronal interaction, including real mollusk neurons and mathematical models of functioning of deficient synaptic connections between these neurons and synaptic endings of other neurons, was created on the basis of a computer and an experimental arrangement for investigating molluscan ganglia. The effect of the properties of a monosynaptic excitatory connection of the statistical characteristics of spike trains of interacting pacemaker neurons was investigated.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 12, No. 4, pp. 413–420, July–August, 1980.     

Scale-Free Topology of the CA3 Hippocampal Network: A Novel Method to Analyze Functional Neuronal Assemblies

Cognitive mapping functions of the hippocampus critically depend on the recurrent network of the CA3 pyramidal cells. However, it is still not known in detail how network activity patterns emerge, or how they encode information. By using functional multineuron calcium imaging, we simultaneously recorded the activity of >100 neurons in the CA3 region of hippocampal slice cultures. We utilized a novel computational method to analyze the multichannel spike trains and to depict functional neuronal assemblies. By means of event synchronization and the correlation matrix analysis method, we found that: 1), the average functional neuronal cluster consists of 23 neurons, and neurons could be part of multiple assemblies; 2), the clustering strength, size, and mean distance among cells in neuronal assemblies follow a power-law-like distribution; 3), the clustering strength and size of neuronal assemblies are not correlated with the total number of neurons and their physical distance; and 4), the clustering distance of neuronal assemblies is weakly correlated with the total number of neurons and their physical distance. These findings suggest that the functional organization of the spontaneously firing CA3 hippocampal network is a scale-free structure in slice culture.     

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na⁺ and K⁺ channels, with generator potential and graded potential models lacking voltage-gated Na⁺ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na⁺ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.     

A Granger causality measure for point process models of ensemble neural spiking activity

The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the directional interactions between multiple sets of continuous-valued data, but cannot be applied to neural spike train recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood function to relate a neuron's spiking probability to possible covariates, such as its own spiking history and the concurrent activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process data, and has the potential to provide unique physiological insights when applied to neural spike trains.     

Organization of neocortical neuronal networks

Multiple unit activity in deep layers of the frontal and motor cortices was recorded by chronically implanted semimicroelectrodes in waking cats with different levels of food motivation. From four to seven neuronal spike trains were selected from the recorded multiunit activity. Interactions between neighbouring neurons in the motor and frontal areas of the neocortex (within the local neuronal networks) and between the neurons of these areas (distributed neuronal networks) were estimated by means of statistical crosscorrelation analysis of spike trains within the range of delays from 0 to 100 ms. Neurons in the local networks were divided in two subgroups: the neurons with higher spike amplitudes with the dominance of divergent connections and neurons with lower spike amplitudes with the dominance of convergent connections. Strong monosynaptic connections (discharges with a delay of less than 2 ms) between the neurons with high- and low-amplitude spikes formed the background of the local networks. Connections between low-amplitude neurons in the frontal cortex and high-amplitude neurons in the motor cortex dominated in the distributed networks. A 24-hour food deprivation predominantly altered the late interneuronal crosscorrelations with time delays within the range of 2-100 ms in both local and distributed networks.     

The influence of the astrocyte field on neuronal dynamics and synchronization

Astrocytes can sense local synaptic release of glutamate by metabotropic glutamate receptors. Receptor activation in turn can mediate transient increases of astrocytic intracellular calcium concentration through inositol 1,4,5-trisphosphate production. Notably, the perturbation of calcium concentration can propagate to other adjacent astrocytes. Astrocytic calcium signaling can therefore be linked to synaptic information transfer between neurons. On the other hand, astrocytes can also modulate neuronal activity by feeding back onto synaptic terminals in a fashion that depends on their intracellular calcium concentration. Thus, astrocytes can also be active partners in neuronal network activity. The aim of our study is to provide a computationally simple network model of mutual neuron–astrocyte interactions, in order to investigate the possible roles of astrocytes in neuronal network dynamics. In particular, we focus on the information entropy of neuronal firing of the whole network, considering how it could be affected by neuron–glial interactions.