Temporal structure of the spike trains in the neuronal impulses of the visual and sensorimotor areas of the rabbit neocortex during conditioned reflex activity

Conjugated spikes were singled out from successions of discharges of neurones in the rabbit's visual and sensorimotor neocortical areas acting in correlation. Their temporal structure was studied at intersignal intervals in transswitching of defensive positive and inhibitory conditioned reflexes and also in pseudoconditioning. The obtained results testify that conjugated discharges appeared for the most part periodically (in the average in 85% of fragments of unit activity). At positive and inhibitory conditioned reflexes, the frequency of periodical conjugated discharges belonged in most cases to the theta-rhythm range. At pseudoconditioning, periodical conjugated discharges were in the main of frequencies of delta-range (up to 4 Hz). The obtained results testify about a great significance of cortical neurones interaction in theta-range frequency at conditioned activity.     

Neuronal impulse trains of the visual and sensorimotor areas of the rabbit neocortex in calm wakefulness and pseudoconditioning

The conjugation of unit activity in the neocortical visual and sensorimotor areas during calm wakefulness and in intersignal intervals, in two groups of rabbits at pseudoconditioning was studied. The first group was presented in a random order with flashes and electrocutaneous stimuli, the second one--with sounds and electrocutaneous stimuli. The number of neurones pairs working in correlation during calm wakefulness is significantly less (35%) than during pseudoconditioning (49 and 50% in the first and second rabbits groups, respectively). During calm wakefulness and in both groups during pseudoconditioning, the number of pairs with delays of discharges of the visual area neurones after the sensorimotor one, and of the sensorimotor after visual up to 120 ms was equal. Comparison of the data on delayed neuronal discharges during calm wakefulness and pseudoconditioning with those obtained earlier with conditioned reflexes testifies that forestalling of visual area neuronal discharges by sensorimotor discharges is characteristic only for the activity of cortical projections of conditioned and unconditioned stimuli.     

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.     

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.     

Note on the coefficient of variations of neuronal spike trains

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.     

An interpretation of 1/f fluctuations in neuronal spike trains during dream sleep

The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the cerebral cortex. We have investigated the statistical characteristics of the single neuronal activity in the MRF of cat during two activated states: paradoxical sleep (PS) and state in which the animal is watching birds (BW). 1/f-like spectra are observed for both PS and BW states, being more pronounced for PS state. For the interpretation of these findings, we have applied the clustering Poisson process, which not only gives rise to a 1/f spectrum but also suggests a generation mechanism. The MRF neuronal activities in PS and BW are closely fitted by the clustering Poisson process, both in terms of power spectral density and counting statistics. These results strongly suggest that the activities of MRF neurons in PS and BW can be interpreted as the superpositions of randomly occurring clusters which consist of various number of impulses.     

Sequential interval histogram analysis of non-stationary neuronal spike trains

The spike interval histogram, a commonly used tool for the analysis of neuronal spike trains, is evaluated as a statistical estimator of the probability density function (pdf) ofinterspike intervals. Using a mean square error criterion, it is concluded that a Parzen convolution estimate of the pdf is superior to the conventional histogram procedure. The Parzen estimate using a Gaussian weighting function reduces the number of intervals required to achieve a given error by a factor of 5–10. The Parzen estimation procedure has been implemented in the sequential interval histogram (SQIH) procedure for analysis of non-stationary spike trains. Segments of the spike train are defined using a moving window and the pdf for each segment is estimated sequentially. The procedure which we have found most practical is interactive with the user and utlizes the theoretical results of the error analysis as guidelines for the evolution of an estimation strategy. The SQIH procedure appears useful both as a criterion for stationarity and as a means to characterize non-stationary activity.Portions of this work were presented at the Symposium on Computer Technology in Neuroscience Research, West Virginia University Medical Center, Morgantown, West Virginia, USA, April, 1975.     

Counting statistics of 1/f fluctuations in neuronal spike trains

The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the celebral cortex. In this paper, the statistical features of single neuronal activities in MRF of cat during dream sleep are investigated; the neuronal spike train exhibits 1/f fluctuations. Counting statistics is applied to the neuronal spike train giving rise to a variance/mean curve which follows at-law. For an interpretation of these findings, the clustering Poisson process is applied which not only gives rise to at-law but also suggests a generation mechanism. The MRF neuronal activities are closely fitted by the clustering Poisson process and the underlying statistical parameters can be estimated. These findings strongly suggest that neuronal activities can be interpreted as superposition of randomly occuring clusters ( = bursts of spikes).     

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.     

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.     

Effect of piracetam on the neuronal activity of the neocortex and on behavior in rabbits during learning

Against the background of the action of piracetam--a cyclic derivative of GABA--in a dose of 200-400 mg/kg, no significant changes were observed of probabilities of motor reactions to inhibitory and reinforced light flashes. Piracetam in that dose did not affect inhibitory pauses in responses of neurones in the visual area and corresponding late components of the evoked potential to nonreinforced light flashes, i.e. it did not intensify inhibitory hyperpolarization processes in the cerebral cortex. Piracetam administration improved differentiation of inhibitory and reinforced light flashes judging by bioelectric parameters of the brain activity as a result of intensification of pain reinforcement action on cortical neurones. The carried-out experiments revealed significant differences in neurophysiological mechanisms of action of piracetam and fenibut--GABA linear derivate related to nootropic class.     

Dependence of different spike sequences on the mean neuronal firing rate in the neocortex in vivo and in vitro

Neuronal spikes were recorded extracellularly in rabbit visual cortex in vivo (88 cells) and in surviving slices of guinea pig sensorimotor cortex in vitro (50 cells). Spike sequences (SS) with monotonically increasing (SS+) and decreasing (SS-) interspike intervals were detected. Relative number of spikes of SS in the recording was closely associated with SS generation. The relative number of spikes was plotted against the average firing rate, this function had a biphasic character with the critical point around 7 Hz. The rate of change in interspike duration (the slope) was virtually independent of the firing rate, but was significantly different in vivo and in vitro conditions for both SS+ (325 and 180 ms/s, respectively) and SS- (270 and 160 ms/s, respectively). By and large, in vivo and in vitro the spike sequence parameters depended in the average firing rate in the same manner. The role of the spike sequences in rhythmic and information processes in neocortex is discussed.     

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.     

Space-time organization of the electrical activity of the human brain in a state of calm wakefulness and during the solution of intellectual tasks

In a series of experiments it has been shown that during solution of mental tasks of various complexity, a marked desynchronization is observed of the cortical rhythmic activity characteristic of the state of calm wakefulness. In the range of main wakefulness frequencies (alpha and beta), a significant lowering is observed of the level of spatial biopotential synchronizations. Its increase in these conditions is connected with the range of slow EEG rhythms; there exist different opinions about their functional significance in wakefulness.     

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.