Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Proposed mechanisms for coincidence detection in the auditory brainstem

Sound localization in mammals uses two distinct neural circuits, one for low- and one for high-frequency bands. Recent experiments call for revision of the theory explaining how the direction of incoming sound is calculated. We propose such a revised theory. Our theory is based on probabilistic spiking and probabilistic delay of spikes from both sides. We have applied the mechanism originally proposed as an operation on spike trains resulting in multiplication of firing rates. We have adapted this mechanism for the case of synchronous spike trains. The mechanism has to detect spikes from both sides within a short time window. Therefore, in both circuits neurons act as coincidence detectors. In the excitatory low-frequency circuit we call the mechanism the excitatory coincidence detection, to distinguish it from the mechanism of the inhibitory coincidence detection in the high-frequency circuit. The times to first spike and gains of the two mechanisms are calculated. We show how the output gains of the mechanisms predict the dip within the human frequency sensitivity range. This dip has been described in human psychophysical experiments.     

An Efficient Supervised Training Algorithm for Multilayer Spiking Neural Networks

The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.     

龙虾胃肠神经系统的数值分析

利用抑制神经系统的WinnerLess Competition(WLC)模型,通过数值方法分析Mulloney型龙虾胃肠神经系统神经元的电位发放,得到胃研磨囊和幽门神经系统中各个神经元的电位发放和系统的节律变化。结果表明,胃研磨系统内神经元的发放规律显示两侧牙齿和中间牙齿出现切断、挤压和研磨食物等状态,幽门系统内神经元的发放规律显示幽门节律出现依次发放的三个部分。两个神经系统的数值结果,不仅解释了龙虾胃肠神经系统中神经元电位发放与肌肉运动的关系,而且理论再现了龙虾胃肠神经系统的节律变化和实验结果。     

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Deltat) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (6 ms) triggered spikes at lower temporal precision (>or=6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Bursts and isolated spikes code for opposite movement directions in midbrain electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases.     

Timing Precision in Population Coding of Natural Scenes in the Early Visual System

The timing of spiking activity across neurons is a fundamental aspect of the neural population code. Individual neurons in the retina, thalamus, and cortex can have very precise and repeatable responses but exhibit degraded temporal precision in response to suboptimal stimuli. To investigate the functional implications for neural populations in natural conditions, we recorded in vivo the simultaneous responses, to movies of natural scenes, of multiple thalamic neurons likely converging to a common neuronal target in primary visual cortex. We show that the response of individual neurons is less precise at lower contrast, but that spike timing precision across neurons is relatively insensitive to global changes in visual contrast. Overall, spike timing precision within and across cells is on the order of 10 ms. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary to represent the more slowly varying natural environment, we argue that preserving relative spike timing at a ~10-ms resolution is a crucial property of the neural code entering cortex.     

多通道神经元锋电位检测和分类的新方法

大脑神经元胞外单细胞动作电位(即锋电位)的检测和分类是提取神经元脉冲序列、研究神经系统信息处理机制的关键．为了提高锋电位的检出率和分类的正确性,设计了一种处理多通道锋电位记录信号的算法,用于分析微电极阵列记录的大鼠海马神经元锋电位信号,电极阵列上的测量点排列紧密,4个通道可以同时记录到来自相同神经元的信号．该算法首先利用一种多通道阈值检测法检出四通道记录信号中的锋电位,然后利用一种基于复合锋电位的主成分特征参数分类法将锋电位分类．仿真数据和实验记录信号的检验结果表明：与相应的单通道算法相比,该算法的锋电位检出率和分类的正确性显著提高,并且可以增加单次实验测得的神经元数目．因此,该算法为实现神经元锋电位的自动检测提供了一种简单有效的新 方法．     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

A proposed mechanism for multiplication of neural signals

The probability of the joint occurrence of two statistically independent events is the product of the probabilities of the individual events. This fact is used to show that a neuron which detects coincident arrivals of spikes from two input neurons can function as a multiplier, i.e. its average output spike frequency is proportional to the product of the average input spike frequencies. The theoretical analysis is checked in two ways: (a) Computer simulations confirm the derived expressions for the output frequency and show that increasing the jitter in the input spike trains improves the operation of the multiplier by making the output spike train more regular (b) Experimentally recorded spike trains are used to demonstrate that the type and amount of jitter present in real spike trains is adequate for satisfactory operation of the proposed scheme for multiplication. The operating characteristics of the proposed multiplier make it an attractive candidate for the multiplicative mechanism that is involved in the optomotor response of insects.     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

Optical Recording of Suprathreshold Neural Activity with Single-cell and Single-spike Resolution

Signaling of information in the vertebrate central nervous system is often carried by populations of neurons rather than individual neurons. Also propagation of suprathreshold spiking activity involves populations of neurons. Empirical studies addressing cortical function directly thus require recordings from populations of neurons with high resolution. Here we describe an optical method and a deconvolution algorithm to record neural activity from up to 100 neurons with single-cell and single-spike resolution. This method relies on detection of the transient increases in intracellular somatic calcium concentration associated with suprathreshold electrical spikes (action potentials) in cortical neurons. High temporal resolution of the optical recordings is achieved by a fast random-access scanning technique using acousto-optical deflectors (AODs)¹. Two-photon excitation of the calcium-sensitive dye results in high spatial resolution in opaque brain tissue². Reconstruction of spikes from the fluorescence calcium recordings is achieved by a maximum-likelihood method. Simultaneous electrophysiological and optical recordings indicate that our method reliably detects spikes (>97% spike detection efficiency), has a low rate of false positive spike detection (< 0.003 spikes/sec), and a high temporal precision (about 3 msec) ³. This optical method of spike detection can be used to record neural activity in vitro and in anesthetized animals in vivo^3,4.     

Cross-intensity functions and the estimate of spike-time jitter

Correlation measures are important tools for the analysis of simultaneously recorded spike trains. A well-known measure with probabilistic interpretation is the cross-intensity function (CIF), which is an estimate of the conditional probability that a neuron spikes as a function of the time lag to spikes in another neuron. The non-commutative nature of the CIF is particularly useful when different neuron classes are studied that can be distinguished based on their anatomy or physiology. Here we explore the utility of the CIF for estimating spike-time jitter in synaptic interactions between neuron pairs of connected classes. When applied to spike train pairs from sleeping songbirds, we are able to distinguish fast synaptic interactions mediated primarily by AMPA receptors from slower interactions mediated by NMDA receptors. We also find that spike jitter increases with the time lag between spikes, reflecting the accumulation of noise in neural activity sequences, such as in synfire chains. In conclusion, we demonstrate some new utility of the CIF as a spike-train measure.     

Spike-sorting analysis of neural electrical signals evoked by acupuncture based on model

Acupuncturing the Zusanli (ST 36) point with different types of manual acupuncture manipulations (MAs) and different frequencies can evoke a lot of neural response activities in spinal dorsal root neurons. The action potential is the basic unit of communication in the neural response process. With the rapid development of the electrode acquisition technology, we can simultaneously obtain neural electrical signals of multiple neurons in the target area. So it is crucial to extract spike trains of each neuron from raw recorded data. To solve the problem of variability of the spike waveform, this paper adopts a optimization algorithm based on model to improve the wave-cluster algorithm, which can provide higher accuracy and reliability. Further, through this optimization algorithm, we make a statistical analysis on spike events evoked by different MAs. Results suggest that numbers of response spikes under reinforcing manipulations are far more than reducing manipulations, which mainly embody in synchronous spike activities.     

BDNF boosts spike fidelity in chaotic neural oscillations

Oscillatory activity and its nonlinear dynamics are of fundamental importance for information processing in the central nervous system. Here we show that in aperiodic oscillations, brain-derived neurotrophic factor (BDNF), a member of the neurotrophin family, enhances the accuracy of action potentials in terms of spike reliability and temporal precision. Cultured hippocampal neurons displayed irregular oscillations of membrane potential in response to sinusoidal 20-Hz somatic current injection, yielding wobbly orbits in the phase space, i.e., a strange attractor. Brief application of BDNF suppressed this unpredictable dynamics and stabilized membrane potential fluctuations, leading to rhythmical firing. Even in complex oscillations induced by external stimuli of 40 Hz (gamma) on a 5-Hz (theta) carrier, BDNF-treated neurons generated more precisely timed spikes, i.e., phase-locked firing, coupled with theta-phase precession. These phenomena were sensitive to K252a, an inhibitor of tyrosine receptor kinases and appeared attributable to BDNF-evoked Na(+) current. The data are the first indication of pharmacological control of endogenous chaos. BDNF diminishes the ambiguity of spike time jitter and thereby might assure neural encoding, such as spike timing-dependent synaptic plasticity.