Developments in understanding neuronal spike trains and functional specializations in brain regions.

Understanding information processing at the neuronal level would provide valuable insights to computational intelligence research and computational neuroscience. In particular, understanding constraints on neuronal spike trains would provide indication about the type of syntactic rules used by neurons when processing information. A recent discovery, reported here, was made through analyzing microelectrode recordings (MER) made during surgical procedure in humans. Analysis of MERs of extracellular neuronal activity has gained increasing interest due to potential improvements to surgical techniques involving ablation or placement of deep brain stimulators, done in the treatment of advanced Parkinson's disease. Important to these procedures is the identification of different brain structures such as the globus pallidus internus from the spike train being recorded from the intracranial probe tip during surgery. Spike train data gathered during surgical procedure from multiple patients were processed using a novel feature extraction method reported here. Distinct structures within the spike trains were identified and used to build an effective brain region classifier. The extracted features upon analysis provide some insight into the 'syntactic' constraint on spike trains.     

Testing a neural coding hypothesis using surrogate data

Determining how a particular neuron, or population of neurons, encodes information in their spike trains is not a trivial problem, because multiple coding schemes exist and are not necessarily mutually exclusive. Coding schemes generally fall into one of two broad categories, which we refer to as rate and temporal coding. In rate coding schemes, information is encoded in the variations of the average firing rate of the spike train. In contrast, in temporal coding schemes, information is encoded in the specific timing of the individual spikes that comprise the train. Here, we describe a method for testing the presence of temporal encoding of information. Suppose that a set of original spike trains is given. First, surrogate spike trains are generated by randomizing each of the original spike trains subject to the following constraints: the local average firing rate is approximately preserved, while the overall average firing rate and the distribution of primary interspike intervals are perfectly preserved. These constraints ensure that any rate coding of information present in the original spike trains is preserved in the members of the surrogate population. The null-hypothesis is rejected when additional information is found to be present in the original spike trains, implying that temporal coding is present. The method is validated using artificial data, and then demonstrated using real neuronal data.     

A nonparametric approach for detection of bursts in spike trains

In spike-train data, bursts are considered as a unit of neural information and are of potential interest in studies of responses to any sensory stimulus. Consequently, burst detection appears to be a critical problem for which the Poisson-surprise (PS) method has been widely used for 20 years. However, this method has faced some recurrent criticism about the underlying assumptions regarding the interspike interval (ISI) distributions. In this paper, we avoid such assumptions by using a nonparametric approach for burst detection based on the ranks of ISI in the entire spike train. Similar to the PS statistic, a “Rank surprise” (RS) statistic is extracted. A new algorithm performing an exhaustive search of bursts in the spike trains is also presented. Compared to the performances of the PS method on realizations of gamma renewal processes and spike trains recorded in cat auditory cortex, we show that the RS method is very robust for any type of ISI distribution and is based on an elementary formalization of the definition of a burst. It presents an alternative to the PS method for non-Poisson spike trains and is simple to implement.     

Catchlike property of skeletal muscle: recent findings and clinical implications

The catchlike property of skeletal muscle is the force augmentation produced by the inclusion of an initial, brief, high-frequency burst of two to four pulses at the start of a subtetanic low-frequency stimulation train. Catchlike-inducing trains take advantage of the catchlike property of skeletal muscle and augment muscle performance compared with constant-frequency trains, especially in the fatigued state. Literature spanning more than 30 years has provided comprehensive information about the catchlike property of skeletal muscle. The pattern of the catchlike-inducing train that maximizes muscle performance is fairly similar across different muscles of different species and under various stimulation conditions. This review summarizes the mechanisms of the catchlike property, factors affecting force augmentation, techniques used to identify patterns of catchlike-inducing trains that maximize muscle performance, and potential clinical applications to provide a historical and current perspective of our understanding of the catchlike property.     

Statistical technique for analysing functional connectivity of multiple spike trains

A new statistical technique, the Cox method, used for analysing functional connectivity of simultaneously recorded multiple spike trains is presented. This method is based on the theory of modulated renewal processes and it estimates a vector of influence strengths from multiple spike trains (called reference trains) to the selected (target) spike train. Selecting another target spike train and repeating the calculation of the influence strengths from the reference spike trains enables researchers to find all functional connections among multiple spike trains. In order to study functional connectivity an "influence function" is identified. This function recognises the specificity of neuronal interactions and reflects the dynamics of postsynaptic potential. In comparison to existing techniques, the Cox method has the following advantages: it does not use bins (binless method); it is applicable to cases where the sample size is small; it is sufficiently sensitive such that it estimates weak influences; it supports the simultaneous analysis of multiple influences; it is able to identify a correct connectivity scheme in difficult cases of "common source" or "indirect" connectivity. The Cox method has been thoroughly tested using multiple sets of data generated by the neural network model of the leaky integrate and fire neurons with a prescribed architecture of connections. The results suggest that this method is highly successful for analysing functional connectivity of simultaneously recorded multiple spike trains.     

Effects of collateral inhibition in a model of the immature rat cerebellar cortex: multineuron correlations

A model of the immature rat cerebellar cortex is used to simulate the effect of the inhibitory recurrent collateral axons of the Purkinje cells on the spike trains in the network. Inhibition induces an important overall change in the statistical characteristics of individual spike trains. It is also instrumental in producing a strong cooperativity between the different neurons. Moreover, a functional spatial anisotropy appears. A specific entropy index is used to analyze levels of information transfer between clustered and faraway neurons in the network. The formatting effect of recurrent collateral inhibition on spike trains and on network functional dynamics is studied by means of a model of the newborn rat cerebellar cortex. This immature structure has simpler morphological characteristics and fewer physiological parameters than the adult one. It is thus a good candidate for the comparison between experimental and theoretical data. The model network is made of 256 formal neurons (FN), arranged in a square lattice. Each neuron is coupled to its eight nearest neighbors by inhibitory links. All the parameters of the different elements of the model — in particular integration of inhibitory and excitatory inputs — are given anatomical and physiological values derived from biological data. Activities of single FNs and correlations between spatially distant ones are analyzed with classical statistical techniques as well as with a specific informational entropy method we introduce. Simulation results indicate that inhibition is instrumental in: (1) the transformation of the spike train characteristics. This includes a lengthening of the mean interspike interval as well as an overall change in the statistical distribution of intervals, with an emergence of long-lasting ones; (2) the functional structuration of the network. Inhibitory connections between nearest neighbors induce a strong cooperativity between FNs. Furthermore a clear spatial anisotropy occurs in the functioning of the network, with inhibitory effects extending beyond local connectivity in preferential directions. We propose an interpretation of this functional structuration in terms of the various routes followed by the inhibition, including relay effects. The parameters of the model (levels of activities, inhibition rules and connectivities) were varied in order to test the robustness of the above results. Finally, the results are compared with those obtained in an experimental situation.     

Measuring spike train synchrony

Estimating the degree of synchrony or reliability between two or more spike trains is a frequent task in both experimental and computational neuroscience. In recent years, many different methods have been proposed that typically compare the timing of spikes on a certain time scale to be optimized by the analyst. Here, we propose the ISI-distance, a simple complementary approach that extracts information from the interspike intervals by evaluating the ratio of the instantaneous firing rates. The method is parameter free, time scale independent and easy to visualize as illustrated by an application to real neuronal spike trains obtained in vitro from rat slices. In a comparison with existing approaches on spike trains extracted from a simulated Hindemarsh-Rose network, the ISI-distance performs as well as the best time-scale-optimized measure based on spike timing.     

A cascade model of information processing and encoding for retinal prosthesis

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases. Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue. Some retinal models have been presented, ranking from structural models inspired by the layered architecture to functional models originated from a set of speciifc physiological phenomena. However, Most of these focus on stimulus image com-pression, edge detection and reconstruction, but do not generate spike trains corresponding to visual image. In this study, based on state-of-the-art retinal physiological mechanism, including effective visual information extraction, static nonlinear rectiifcation of biological systems and neurons Poisson coding, a cascade model of the retina including the out plexiform layer for information processing and the inner plexiform layer for information encoding was brought forward, which integrates both anatomic connections and functional com-putations of retina. Using MATLAB software, spike trains corresponding to stimulus image were numerically computed by four steps:linear spatiotemporal ifltering, static nonlinear rectiifcation, radial sampling and then Poisson spike generation. The simulated results suggested that such a cascade model could recreate visual information processing and encoding functionalities of the retina, which is helpful in developing artiifcial retina for the retinally blind.     

Single unit analysis of the human ventral thalamic nuclear group: correlation of thalamic "tremor cells" with the 3-6 Hz component of parkinsonian tremor

Although cells firing at tremor frequency, called "tremor cells" (Guiot et al., 1962), have often been recorded in the thalamus of parkinsonian patients, the extent of correlation between these spike trains and tremor has rarely been assessed quantitatively. This paper describes spectral cross-correlation functions calculated between the activity of "tremor cells" and electromyogram (EMG) signals recorded from several muscles in the contralateral arm. The power occurring in the spike train at tremor frequency was described in absolute terms by the spike autopower, and in relation to the average for all spectral components by the spike autopower signal-to-noise ratio (spike autopower SNR). The probability of significant cross-correlation between the thalamic spike train and EMG at tremor frequency was assessed by the coherence at tremor frequency. Autopower spectra of the activity of many of these cells exhibited a concentration of power at tremor frequency, indicated by spike autopower SNRs as high as 18. Of the EMG signals studied, signals recorded from finger flexors were most often significantly correlated at tremor frequency. Significant correlation between the thalamic spike train and finger flexor EMG activity was found in 34% of cells analyzed. Tremor frequency coherence was significantly correlated with tremor frequency spike autopower (r = 0.46, p less than 0.0001) and spike autopower SNR (r = 0.533, p less than 0.0001). The proportion of cells with a spike autopower SNR greater than 2 that were significantly correlated with finger flexor EMG activity was greater than that of cells with a spike autopower SNR of less than 2 (p less than 0.001; chi-square). Therefore, cells exhibiting a large amount of power at tremor frequency were those best correlated with EMG activity during tremor. Some of these cells may be involved in the generation of tremor.     

Temporal coupling between subicular and hippocampal neurons underlies retention of trial-specific events

The subiculum receives the majority of efferent outflow of neural information from the CA1 region of the hippocampus. As such it occupies a strategic position in which to integrate, transfer and resolve activity from the hippocampus relating to memory and performance. We have previously demonstrated that each structure has complementary ensemble firing patterns that together allow information to be represented continuously over the time course of a trial in a delayed-non-match-to-sample (DNMS) task. Here, we extend this analysis to show the precise manner in which specific neurons in both structures are coupled temporally across the delay interval on a single trial. Neurons in both structures encode position-specific information related to the sample lever press, but only subicular neurons continue to fire during the early portion of the subsequent variable delay interval. However, cross-correlation analysis of multiple spike trains showed that as the delay increased in duration other subicular neurons were temporally coupled to the subicular neurons that fired in the initial part of the delay. This latter population of subicular neurons showed strong cross-correlated firing with other initially activated subicular neurons until midway through the delay (<15s), but on longer delay intervals were coupled to a specific type of hippocampal neuron whose firing was critical for correct performance. Subicular neurons, therefore, play a critical role in bringing the hippocampus "back online" when trial delays exceed the minimum duration thus allowing both structures to cooperatively bridge relevant information across longer time intervals than would not otherwise be possible.     

Spike trains in rat periaqueductal gray depend on the stochastic properties of interacting electrical stimulation trains

Spike trains flowing into the periaqueductal gray (PAG) might be discriminated from one another by PAG neurons on the basis of the distribution or sequence of their respective interspike intervals. The various sequences of interspike intervals characteristic of spontaneous PAG unit activities were assessed in a preliminary experiment. These sequences were then simulated by means of appropriate mathematical functions. These functions allowed the production of stimulation trains that were applied to two PAG sites to induce spike trains with similar sequences in order to reveal the sensitivity of PAG neurons to the stochastic structure of afferent spike trains. We placed emphasis on parameters of the spike train that proved to be altered independently of any alteration of the corresponding parameters in the stimulation train. The mean pulse rate is the simplest example of such a parameter as it was never altered in the stimulation train. Alterations of either the distribution or sequence of pulses in the stimulation train were found to affect the mean discharge rate in a number of cases (30-40% of the cases). Despite their moderate degree (20-30% mean rate alteration) such differential effects could correspond to stimulation-induced differential behavioral effects as was shown in a previous study. Furthermore, a specific dependence of the generated spike trains on the sequential structure of the stimulation train was observed in some cases when appropriate stimulation trains were simultaneously applied to another PAG stimulation site. This fact is worth considering in relation to the integrative function of the PAG neuronal network.     

Discharge of neurons in the parabrachial pons related to the cardiac cycle: Changes during different sleep-waking states

Neuronal activity in the nucleus parabrachialis medialis (NPBM) was examined in unanesthetized, unrestrained cats during each sleep-waking state. Discharge related to the cardiac cycle was assessed by calculating cross-correlation functions between neuronal and cardiac events (using the peak of the EKG ‘R’ wave as a reference). Of the 60 NPBM neurons examined, the activity of 20 cells showed discharge relationships to the cardiac cycle. Firing of NPBM neurons in phase with the cardiac cycle was observed during each sleep-waking state, but was most apparent during awake (AW) and rapid eye movement (REM) sleep states. State-related changes in the correlation of NPBM neuronal discharge to the cardiac cycle included variations in the extent of rhythmic modulation of activity, and shifts in the phase relationship to the cardiac reference. The predominant phase relationship of NPBM neuronal activity to the cardiac cycle was an increased probability of discharge during a period ranging from 50 msec preceding to 50 msec following the peak of the EKG ‘R’ wave.     

Absence of light-dark entrainment on the sleep-waking cycle in mice with intact visual perception

The influence of the light-dark schedule (12 h –12 h) on the sleep-waking cycle has been studied in anophthalmic mice: the ‘eyeless’ ZRDCT/An strain.The complete anophthalmic mice or the heterozygotous mice of the same strain with unilateral or bilateral eyeballs present a circadian organization of the sleep-waking cycle which is not dependent on the light-dark cycle.These results are different from sleep rhythms of C57Br mice recorded under the same experimental conditions. They indicate that the structures responsible for the circadian rhythmicity of sleep exist in all the ‘eyeless’ ZRDCT/An mice, but are not functionally linked with the visual system even in the mice with unilateral and bilateral eyeballs.     

Towards statistical summaries of spike train data

Statistical inference has an important role in analysis of neural spike trains. While current approaches are mostly model-based, and designed for capturing the temporal evolution of the underlying stochastic processes, we focus on a data-driven approach where statistics are defined and computed in function spaces where individual spike trains are viewed as points. The first contribution of this paper is to endow spike train space with a parameterized family of metrics that takes into account different time warpings and generalizes several currently used metrics. These metrics are essentially penalized L(p) norms, involving appropriate functions of spike trains, with penalties associated with time-warpings. The second contribution of this paper is to derive a notion of a mean spike train in the case when p=2. We present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains. The proposed metrics as well as the mean computations are demonstrated using an experimental recording from the motor cortex.     

Symmetric temporal patterns in cortical spike trains during performance of a short-term memory task

Abstract

The trion model is a highly structured representation of cortical organization_l which predicts families of symmetric spatial-temporal firing patterns inherent in cortical activity. The symmetries of these inherent firing patterns are used by the brain in short-term memory to perform higher level computations. In the present study, symmetric temporal patterns were searched for in spike trains recorded from cells in parietal cortex of a monkey performing a short-term memory task. A new method of analysis was used to map neuronal firing into sequences of integers representing relative levels of firing rate about the mean (i.e. -1, 0 and 1). The results of this analysis show families of patterns related by symmetry operations. These operations are: i. the interchanging of all the + l’s and -l’s in a given pattern sequence (CT symmetry), ii. the inverting of the temporal sequence of the mapping (T symmetry)1 and iii. the combination of the two previous operations (CT symmetry). Patterns of a given family are found across cells especially in the memory periods of the task; in most cases they reoccur within a given spike train. The pattern families predicted by the model and reported here should be further investigated in multiple microelectrode and EEG recordings. [Neural Res 1997; 19: 509-514]     

Less Segregated Processing of Visual Information in V2 than in V1 of the Monkey Visual Cortex

To test the possibility of cross-talk between parallel pathways dealing with different aspects of visual information, such as orientation, direction of motion and colour in cortical area V2, we quantitatively analysed visual responses of 121 V2 cells recorded from anaesthetized and paralysed macaques and compared them with those of 147 V1 cells. A selectivity index of visual responses was calculated for each neuron, which was then classified as selective or not to a particular attribute of visual stimuli. Twenty-one percent of the V2 neurons had dual selectivity to both colour and direction of stimulus motion (C&D cells). In V1, only 5% of the cells were C&D cells. Thus, the proportion of C&D cells significantly increased from V1 to V2. We also carried out cross-correlation analysis of spike trains recorded simultaneously from pairs of V2 neurons or pairs of V1 neurons. In V2, correlated firings could be observed between cells with completely different optimal orientation, such as orthogonal, while it was never observed in V1. The cross-correlation analysis further indicated that functional interactions in V2 were more widespread than those in V1. These results suggest that neurons which have different functional properties become less segregated, and that functional interactions become more widespread in V2 than in V1.     

A mathematical model that predicts the force-frequency relationship of human skeletal muscle

In previous work we developed and validated a mathematical model that predicted force output from skeletal muscles subjected to six-pulse stimulation trains under isometric condition. The current study investigated the model's ability to predict force responses to longer stimulation trains under both nonfatigued and fatigued conditions. Using the six-pulse train model to predict the force produced by longer stimulation trains showed that the model was successful, but a modified parameter identification scheme was required. For most of the trains tested the model accounted for 95% of the variance in the experimental forces produced by stimulation trains, with mean frequencies from 12.5 to 100 HZ, train durations from 485 to 1000 ms, and number of pulses from 14 to 50 for both nonfatigued and fatigued muscles. The success of our mathematical model in predicting forces produced by stimulations with a wide range of frequencies, durations, and number of pulses implies great potential of the model for the identification of optimal activation patterns that should be used during functional electrical stimulation.     

Cross-correlation measures of unresolved multi-neuron recordings

An increasing number of laboratories are studying population properties of the nervous system using data where the spike activity of more than one neuron is recorded on each electrode and where, accidentally or deliberately, these activities are not resolved into single unit spike trains. We have previously examined the consequences for measurement of cross-correlation between two such electrodes in the limited case where all individual distant (between electrode) correlations are the same and all individual close (on a single electrode) correlations are the same [Bedenbaugh, P.H., and Gerstein, G.L. (1997). Multiunit normalized cross correlation differs from the average single-unit normalized correlation. Neural Computation 9, 1265–1275]. Here, we lift these unrealistic restrictions to allow all values of individual correlation, and examine explicitly the cases of two or three unresolved neurons on each electrode. In these situations, the cross-correlation coefficient measured between the electrodes is a linear sum of the distant correlations, divided by a non-linear function of the close correlations. We then examine in detail the case of a single direct distant correlation and take account of all relevant indirect correlations. The measured interelectrode correlation shows a reduction of this actual distant correlation by a non-linear function of the close correlations on each electrode over most of their possible values. Finally, we examine the consequences of poor waveform sorting for correlation measures; here a supposedly isolated spike train is contaminated by some fraction of the activity of another train, a situation that unfortunately is all too common in experiments. All these distortions become far more serious in the more realistic situation of dynamic firing rates and correlations. This paper is intended as a cautionary note for those who want to draw inferences about neuronal organization and/or coding or representation by using cross-correlation analysis of unresolved recordings.     

Detecting connectivity changes in neuronal networks

We develop a method from semiparametric statistics (Cox, 1972) for the purpose of tracking links and connection strengths over time in a neuronal network from spike train data. We consider application of the method as implemented in Masud and Borisyuk (2011), and evaluate its use on data generated independently of the Cox model hypothesis, in particular from a spiking model of Izhikevich in four different dynamical regimes. Then, we show how the Cox method can be used to determine statistically significant changes in network connectivity over time. Our methodology is demonstrated using spike trains from multi-electrode array measurements of networks of cultured mammalian spinal cord cells.     

Synaptic plasticity in the hippocampus is modulated by behavioral state

The possible influence of the sleep-waking cycle on evoked neurotransmission and on the induction of long-term potentiation (LTP) and depression (LTD) was studied in the perforant path-granule cell system. Freely moving rats received a high-frequency stimulus train (8 bursts at 400 Hz) during slow-wave sleep (SWS), rapid eye movement (REM) sleep, and a still-alert (SAL) behavioral state. Trains applied during SAL and REM reliably elicited LTP of the excitatory postsynaptic potential (EPSP) slope, population spike height, and spike onset latency. Granule cell excitability was also enhanced, as indicated by a leftward shift of the EPSP-population spike (E-S) relation. In contrast, tetanization in SWS rarely produced 'classical' LTP and often failed to elicit any lasting change in field potentials. Furthermore, the following types of E-S change occurred almost exclusively after tetanization in SWS: (1) LTP of the EPSP accompanied by depression of the population spike, and (2) E-S potentiation without a change in EPSP. When LTP occurred, however, its magnitude was independent of the animal's behavioral state at the time of the train. In agreement with previous reports, the efficacy of low-frequency neurotransmission varied with behavioral state. A modulation index (MI) was introduced to quantify the difference between field potentials evoked in SAL and SWS. Interestingly, both the occurrence and magnitude of LTP were related to the strength of the MI, as determined in each rat before the train. After trains, the state-dependent modulation of transmission was maintained and was superimposed on LTP and LTD. The results suggest that synaptic plasticity is dynamically modulated during the sleep-wakefulness cycle.