STDP allows fast rate-modulated coding with Poisson-like spike trains

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (~10-20 ms) for sufficiently many inputs (~100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.     

Analysis of neural spike trains with interspike interval reconstruction

As a method for the analysis of neural spike trains, we examine fundamental characteristics of interspike interval (ISI) reconstruction theoretically with a leaky-integrator neuron model and experimentally with cricket wind receptor cells. Both the input to the leaky integrator and the stimulus to the wind receptor cells are the time series generated from the Rossler system. By numerical analysis of the leaky integrator, it is shown that, even if ISI reconstruction is possible, sometimes the entire structure of the R?ssler attractor may not be reconstructed with ISI reconstruction. For analysis of the in vivo physiological responses of cricket wind receptor cells, we apply ISI reconstruction, nonlinear prediction and the surrogate data method to the experimental data. As a result of the analysis, it is found that there is a significant deterministic structure in the spike trains. By this analysis of physiological data, it is also shown that, even if ISI reconstruction is possible, the entire attractor may not be reconstructed.     

Balanced synaptic input shapes the correlation between neural spike trains

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Analysis,classification, and coding of multielectrode spike trains with hidden Markov models

It is shown that hidden Markov models (HMMs) are a powerful tool in the analysis of multielectrode data. This is demonstrated for a 30-electrode measurement of neuronal spike activity in the monkey's visual cortex during the application of different visual stimuli. HMMs with optimized parameters code the information contained in the spatiotemporal discharge patterns as a probabilistic function of a Markov process and thus provide abstract dynamical models of the pattern-generating process. We compare HMMs obtained from vector-quantized data with models in which parametrized output processes such as multivariate Poisson or binomial distributions are assumed. In the latter cases the visual stimuli are recognized at rates of more than 90% from the neuronal spike patterns. An analysis of the models obtained reveals important aspects of the coding of information in the brain. For example, we identify relevant time scales and characterize the degree and nature of the spatiotemporal variations on these scales.     

Differential coding of humoral stimuli by timing and amplitude of intracellular calcium spike trains

The ubiquitous Ca2(+)-phosphoinositide pathway transduces extracellular signals to cellular effectors. Using a mathematical model, we simulated intracellular Ca2+ fluctuations in hepatocytes upon humoral stimulation. We estimated the information encoded about random humoral stimuli in these Ca2+ spike trains using an information-theoretic approach based on stimulus estimation methods. We demonstrate accurate transfer of information about random humoral signals with low temporal cutoff frequencies. In contrast, our results suggest that high-frequency stimuli are poorly transduced by the transmembrane machinery. We found that humoral signals are encoded in both the timing and amplitude of intracellular Ca2+ spikes. The information transmitted per spike is similar to that of sensory neuronal systems, in spite of several orders of magnitude difference in firing rate.     

Note on the estimation of the correlation function of neural spike trains

The use of time-bins in the estimation of the correlation function of neural spike trains has a filtering effect on the estimate and results in distortion and aliasing. Prior low-pass filtering of the spike trains, on the other hand, and computation of the correlation function of the emerging waveforms in the standard way result in an estimate that is also a filtered version of the original function but distortion- and alias-free. In addition, the correlation function so computed can be normalized. An analogous definition of the correlation coefficient for the first technique enables the comparison of these various correlation estimates and clarifies their properties.     

A unifying theory on the relationship between spike trains,EEG, and ERP based on the noise shaping/predictive neural coding hypothesis

Cracking the neural code has long been a central issue in neuroscience. However, it has been proved difficult because there logically exist an infinite number of other models and interpretations that could account for the same data and phenomena (i.e. the problem of underdetermination). Therefore, I suggest that applying biologically realistic multiple constraints from ion-channel level to system level (e.g. cognitive neuroscience and human brain disorders) can only solve the problem of underdetermination. Here I have explored whether the noise shaping/predictive neural coding hypothesis can provide a unified view on following realistic multiple constraints: (1) cortical gain control mechanisms in vivo; (2) the relationships between acetylcholine, nicotine, dopamine, calcium-activated potassium ion-channel, and cognitive functions; (3) oscillations and synchrony; (4) why should spontaneous activity be irregular; (5) whether the cortical neurons in vivo are coincidence detectors or integrators; and (6) the causal relationship between theta oscillation, gamma band fluctuation, and P3 (or P300) ERP responses. Finally, recent experimental results supporting the unified view shall be discussed.     

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.     

Alias-free sampling of neuronal spike trains

Summary Spectral analysis provides powerful techniques for describing the lower order moments of a stochastic process and interactions between two or more stochastic processes. A major problem in the application of spectral analysis to neuronal spike trains is how to obtain equispaced samples of the spike trains which will give unbiased and alias-free spectral estimates. Various sampling methods, which treat the spike train as a continuous signal, a point process and as a series of Dirac delta-functions, are reviewed and their limitations discussed. A new sampling technique, which gives unbiased and alias-free estimates, is described. This technique treats the spike train as a series of delta functions and generates samples by digital filtering. Implementation of this technique on a small computer is simple and virtually on-line.     

Recurrence plots of neuronal spike trains

The recently developed qualitative method of diagnosis of dynamical systems — recurrence plots has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.     

Recurring discharge patterns in multiple spike trains

Simultaneously recorded spike trains were obtained using microwire bundles from unrestrained, drug-free cats during different sleep-waking states in forebrain areas associated with cardiac and respiratory activity. Cardiac and respiratory activity was simultaneously recorded with the spike trains. We applied the recurring discharge patterns detection procedure described in a companion paper (Frostig et al. 1990) to the spike and cardiorespiratory trains. The pattern detection procedure was applied to detect only precise (in time and structure) recurring patterns. Recurring discharge patterns were detected in all simultaneously recorded groups. Recurring discharge patterns were composed of up to ten spikes per pattern and involved up to four simultaneously recorded spike trains. Fourty-two percent of the recurring patterns contained cardiac and/or respiratory events in addition to neuronal spikes. When patterns were compared over different sleep-waking states it was found the the same units produced different patterns in different states, that patterns were significantly more compact in time during quiet sleep, and that changes in the discharge rates accompanying changes in sleep-waking states were not correlated with changes in pattern rate.     

Recurring discharge patterns in multiple spike trains

Neural networks are parallel processing structures that provide the capability to perform various pattern recognition tasks. A network is typically trained over a set of exemplars by adjusting the weights of the interconnections using a back propagation algorithm. This gradient search converges to locally optimal solutions which may be far removed from the global optimum. In this paper, evolutionary programming is analyzed as a technique for training a general neural network. This approach can yield faster, more efficient yet robust training procedures that accommodate arbitrary interconnections and neurons possessing additional processing capabilities.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

Neuronal spike trains and stochastic point processes. I. The single spike train

In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.     

Visualisation of synchronous firing in multi-dimensional spike trains

The gravity transform algorithm is used to study the dependencies in firing of multi-dimensional spike trains. The pros and cons of this algorithm are discussed and the necessity for improved representation of output data is demonstrated. Parallel coordinates are introduced to visualise the results of the gravity transform and principal component analysis (PCA) is used to reduce the quantity of data represented whilst minimising loss of information.     

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.     

Chaos game representation of human pallidal spike trains

Many studies have demonstrated the presence of scale invariance and long-range correlation in animal and human neuronal spike trains. The methodologies to extract the fractal or scale-invariant properties, however, do not address the issue as to the existence within the train of fine temporal structures embedded in the global fractal organisation. The present study addresses this question in human spike trains by the chaos game representation (CGR) approach, a graphical analysis with which specific temporal sequences reveal themselves as geometric structures in the graphical representation. The neuronal spike train data were obtained from patients whilst undergoing pallidotomy. Using this approach, we observed highly structured regions in the representation, indicating the presence of specific preferred sequences of interspike intervals within the train. Furthermore, we observed that for a given spike train, the higher the magnitude of its scaling exponent, the more pronounced the geometric patterns in the representation and, hence, higher probability of occurrence of specific subsequences. Given its ability to detect and specify in detail the preferred sequences of interspike intervals, we believe that CGR is a useful adjunct to the existing set of methodologies for spike train analysis.     

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.