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.     

A maximum entropy test for evaluating higher-order correlations in spike counts

Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness-of-fit test, which tests--for a given divergence measure of interest--whether the experimental data lead to the rejection of the null hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.     

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.     

A new method to infer higher-order spike correlations from membrane potentials

What is the role of higher-order spike correlations for neuronal information processing? Common data analysis methods to address this question are devised for the application to spike recordings from multiple single neurons. Here, we present a new method which evaluates the subthreshold membrane potential fluctuations of one neuron, and infers higher-order correlations among the neurons that constitute its presynaptic population. This has two important advantages: Very large populations of up to several thousands of neurons can be studied, and the spike sorting is obsolete. Moreover, this new approach truly emphasizes the functional aspects of higher-order statistics, since we infer exactly those correlations which are seen by a neuron. Our approach is to represent the subthreshold membrane potential fluctuations as presynaptic activity filtered with a fixed kernel, as it would be the case for a leaky integrator neuron model. This allows us to adapt the recently proposed method CuBIC (cumulant based inference of higher-order correlations from the population spike count; Staude et al., J Comput Neurosci 29(1–2):327–350, 2010c) with which the maximal order of correlation can be inferred. By numerical simulation we show that our new method is reasonably sensitive to weak higher-order correlations, and that only short stretches of membrane potential are required for their reliable inference. Finally, we demonstrate its remarkable robustness against violations of the simplifying assumptions made for its construction, and discuss how it can be employed to analyze in vivo intracellular recordings of membrane potentials.     

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.     

Analysis of higher-order neuronal interactions based on conditional inference

 Higher-order neural interactions, i.e., interactions that cannot be reduced to interactions between pairs of cells, have received increasing attention in the context of recent attempts to understand the cooperative dynamics in cortical neural networks. Typically, likelihood-ratio tests of log-linear models are being employed for statistical inference. The parameter estimation of these models for simultaneously recorded single-neuron spiking activities is a crucial ingredient of this approach. Extending a previous investigation of a two-neuron system, we present here the general formulation of an exact test suited for the detection of positive higher-order interactions between m neurons. This procedure does not require the estimation of any interaction parameters and additionally optimizes the test power of the statistical inference. We apply the approach to a three-neuron system and show how second-order and third-order interactions can be reliably distinguished. We study the performance of the method as a function of the interaction strength. Received: 18 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 13 March 2003 RID="*" ID="*" Present address: Institute for Theoretical Biology, Humboldt University, 10115 Berlin, Germany Correspondence to: R. Gütig (e-mail: r.guetig@biologie.hu-berlin.de, Tel.: +49 30 2093 9112, Fax: +49 30 2093 8801) Acknowledgements. We thank Shun-ichi Amari and Hiro Nakahara for valuable discussions on the information geometry of the exponential family of probability distributions underlying the present approach. Supported in part by the Studienstiftung des deutschen Volkes, the German-Israeli Foundation for Scientific Research and Development (GIF), the Deutsche Forschungsgemeinschaft (DFG), and the Institut für Grenzgebiete der Psychologie, Freiburg.     

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

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.     

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.     

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.     

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.     

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.     

Review of massively parallel DNA sequencing technologies

Since the development of technologies that can determine the base-pair sequence of DNA, the ability to sequence genes has contributed much to science and medicine. However, it has remained a relatively costly and laborious process, hindering its use as a routine biomedical tool. Recent times are seeing rapid developments in this field, both in the availability of novel sequencing platforms, as well as supporting technologies involved in processes such as targeting and data analysis. This is leading to significant reductions in the cost of sequencing a human genome and the potential for its use as a routine biomedical tool. This review is a snapshot of this rapidly moving field examining the current state of the art, forthcoming developments and some of the issues still to be resolved prior to the use of new sequencing technologies in routine clinical diagnosis.     

State-space analysis of time-varying higher-order spike correlation for multiple neural spike train data

Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.     

Efficient p-value estimation in massively parallel testing problems

We present a new method to efficiently estimate very large numbers of p-values using empirically constructed null distributions of a test statistic. The need to evaluate a very large number of p-values is increasingly common with modern genomic data, and when interaction effects are of interest, the number of tests can easily run into billions. When the asymptotic distribution is not easily available, permutations are typically used to obtain p-values but these can be computationally infeasible in large problems. Our method constructs a prediction model to obtain a first approximation to the p-values and uses Bayesian methods to choose a fraction of these to be refined by permutations. We apply and evaluate our method on the study of association between 2-way interactions of genetic markers and colorectal cancer using the data from the first phase of a large, genome-wide case-control study. The results show enormous computational savings as compared to evaluating a full set of permutations, with little decrease in accuracy.     

Retention of lung distension information in pump cell spike trains

Respiratory control requires feedback signals from the viscera, including mechanoreceptors and chemoreceptors. We previously showed that typical pulmonary stretch receptor (PSR) spike trains provide the central nervous system with approximately 31% of the theoretical maximum information regarding the amplitude of lung distension. However, it is unknown whether the spatiotemporal convergence of many PSR inputs onto second-order neurons (e.g., pump cells) results in more, or less, information about the stimulus carried by second-order cell spike trains. We recorded pump cell activity in adult, anesthetized, paralyzed, artificially ventilated rabbits during continuous manipulation of ventilator rate and volume to test the hypothesis that less information is carried by spike trains of individual pump cells than PSRs. Using previously developed analytic methods, we quantified the information carried by the pump cell spike trains and compared it with the same values derived from PSR data. Our results provide evidence that rejects our hypothesis: pump cells as a group did not carry significantly less information about the lung distension stimulus than PSRs, although that trend was implied by the data. By comparing the response variances with the theoretical minimum, we discovered that the trend toward information loss depends on response strength, with higher mean responses associated with larger response variances in pump cells than in PSRs. Thus spatiotemporal integration may result in information loss within certain analytic/stimulus parameters, but this is counterbalanced by the consistency of pump cell responses during brief integration times and/or low stimulus amplitudes, resulting in retention of total information.     

Effect of cooling on spike trains from skin receptors

Quantitative characteristics of the afferent flow in a cutaneous nerve during cooling of the skin in cats were determined by the cross-correlation method. Lowering the skin temperature by 10°C with different gradients of cooling led to the appearance of activity in A-, A-, and C-fibers. The first fibers to become excited were C-fibers, followed in turn by A-fibers, a group of slowly-conducting A-fibers, and a group of fast-conducting A-fibers. The latent period of excitation of the C-fibers remained unchanged whatever the rate of skin cooling, whereas in A-fibers it increased with slowing of the rate of fall of temperature. The level of maximal activity neither in A- nor in C-fibers depended on the gradient of skin cooling, but in all the groups of fibers mentioned the time taken to reach the maximum of activity decreased with an increase in the rate of cooling.Research Institute of Applied Mathematics and Cybernetics, N. I. Lobachevskii State University, Gor'kii. Translated from Neirofiziologiya, Vol. 12, No. 4, pp. 405–412, July–August, 1980.