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.     

Information trains. The technique and its uses in spike train and network analysis, with examples taken from the nucleus parabrachialis medialis during sleep-waking states

We describe an analytical procedure for assessing functional interactions between neuronal spike trains based on the outcome of cross-correlation procedures. Subsets of a reference cell spike train in a two-train recording are extracted, based on their time-locked relationship to spikes in the dependent train. Such timing relationships comprise the significant primary structures in the cross-correlogram. Different subsets can be extracted for different primary structures in the same correlogram (i.e. a subset responsible for an interaction effect, a subset responsible for a shared input effect, etc.) These new spike trains represent an information transfer process across synapses. These ‘information trains’ may be compared and correlated to different cells of the network across different functional conditions such as sleep-waking states, and may also be subjected to conventional spike train analysis techniques such as rate histogram, auto-correlation and cross-correlation procedures. We illustrate the information train procedures with a network analysis of a set of cells recorded in the nucleus parabrachialis medialis during different sleep-waking states.     

Functional connections between neurons of interpositus nucleus of the cerebellum and the red nucleus

Patterns of functional connections between individual neurons of nucleus interpositus (IP) of the cerebellum and red nucleus (RN) were examined. This was assessed by cross-correlation of spike trains characterizing interaction between simultaneously recorded neurons. Direct interpositorubral connections were always excitatory in nature: direct inhibition was only found within and not between these nuclei. Shared inputs from common sources outnumber other types of interpositorubral connections. Patterns of connection between IP RN neurons could be influenced by sensorimotor cortex.     

Corticofugal modulation of functional connectivity within the auditory thalamus of rat, guinea pig and cat revealed by cooling deactivation

Microelectrode recordings were simultaneously performed at multiple sites in the medial geniculate body (MGB) of anesthetized cats, rats and guinea pigs. We studied the effect of cortical deactivation on the association of neural activity within the thalamus during spontaneous activity. The corticofugal influence was suppressed by temporary cooling of the auditory cortex. Pairs of spike trains recorded from the same electrode were distinguished from cases where units were in MGB but recorded with different electrodes. Time domain analyses included crosscorrelations and search for precise repetition of complex spatiotemporal firing patterns of reverberating thalamic circuits. As a complementary approach we performed bispectral analyses of simultaneously recorded local field potentials in order to uncover the frequency components of their power spectra which are non linearly coupled. All results suggest that new functional neuronal circuits might appear at the thalamic level in the absence of input from the cortex. The newly active intrathalamic connections would provide the necessary input to sustain the reverberating activity of thalamic cell assemblies and generate low frequency non-linear interactions. The dynamic control exerted by the cortex over the functional segregation of information processing carried out in the thalamus conforms with theoretical neural network studies and with the functional selectivity-adaptive filtering theory of thalamic neuronal assemblies. Although this general conclusion remains valid across species, specific differences are discussed in the frame of known differences of the microcircuitry elements.     

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.     

Measuring spike pattern reliability with the Lempel-Ziv-distance

Spike train distance measures serve two purposes: to measure neuronal firing reliability, and to provide a metric with which spike trains can be classified. We introduce a novel spike train distance based on the Lempel-Ziv complexity that does not require the choice of arbitrary analysis parameters, is easy to implement, and computationally cheap. We determine firing reliability in vivo by calculating the deviation of the mean distance of spike trains obtained from multiple presentations of an identical stimulus from a Poisson reference. Using both the Lempel-Ziv-distance (LZ-distance) and a distance focussing on coincident firing, the pattern and timing reliability of neuronal firing is determined for spike data obtained along the visual information processing pathway of macaque monkey (LGN, simple and complex cells of V1, and area MT). In combination with the sequential superparamagnetic clustering algorithm, we show that the LZ-distance groups together spike trains with similar but not necessarily synchronized firing patterns. For both applications, we show how the LZ-distance gives additional insights, as it adds a new perspective on the problem of firing reliability determination and allows neuron classifications in cases, where other distance measures fail.     

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.     

Single-trial estimation of neuronal firing rates: from single-neuron spike trains to population activity

We present a method to estimate the neuronal firing rate from single-trial spike trains. The method, based on convolution of the spike train with a fixed kernel function, is calibrated by means of simulated spike trains for a representative selection of realistic dynamic rate functions. We derive rules for the optimized use and performance of the kernel method, specifically with respect to an effective choice of the shape and width of the kernel functions. An application of our technique to the on-line, single-trial reconstruction of arm movement trajectories from multiple single-unit spike trains using dynamic population vectors illustrates a possible use of the proposed method.     

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.     

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.     

Measure and statistical test for cross-correlation between paired neuronal spike trains with small sample size

Recent development of multi-unit recording techniques such as optical recording and multi-electrode arrays makes it possible to record neuronal activities from tens or hundreds of neurons simultaneously. To analyze functional connections between these neurons, cross-correlation analysis has been most commonly applied to the hundreds to thousands of pairs of these neurons. However, conventional cross-correlation data needs statistical tests for significance especially when the sample size of recorded spike trains is small. Here, a multiple hypergeometric model based on a transformation of the cross-correlogram data to a 2×J table has been suggested. The exact p value for significance can be obtained by the generalized Fisher's method with small sample size and a cross-correlation coefficient for the strength of cross-correlation can be obtained based on the R-square analogue for nominal data. For large sample size, χ² test can be applied based on the same transformation. Examples of real spike train data set and simulation show that the methods are applicable to the data of multi-unit activity with only tens of spikes. These methods are especially useful when thousands of cross-correlograms need to be screened quickly and automatically.     

S<Emphasis Type="SmallCaps">pi</Emphasis>C<Emphasis Type="SmallCaps">o</Emphasis>D<Emphasis Type="SmallCaps">yn</Emphasis>: A Toolbox for the Analysis of Neuronal Network Dynamics and Connectivity from Multi-Site Spike Signal Recordings

We implemented an automated and efficient open-source software for the analysis of multi-site neuronal spike signals. The software package, named SpiCoDyn, has been developed as a standalone windows GUI application, using C# programming language with Microsoft Visual Studio based on .NET framework 4.5 development environment. Accepted input data formats are HDF5, level 5 MAT and text files, containing recorded or generated time series spike signals data. SpiCoDyn processes such electrophysiological signals focusing on: spiking and bursting dynamics and functional-effective connectivity analysis. In particular, for inferring network connectivity, a new implementation of the transfer entropy method is presented dealing with multiple time delays (temporal extension) and with multiple binary patterns (high order extension). SpiCoDyn is specifically tailored to process data coming from different Multi-Electrode Arrays setups, guarantying, in those specific cases, automated processing. The optimized implementation of the Delayed Transfer Entropy and the High-Order Transfer Entropy algorithms, allows performing accurate and rapid analysis on multiple spike trains from thousands of electrodes.     

Analysis of phase-locked oscillations in multi-channel single-unit spike activity with wavelet cross-spectrum

Electrophysiological measures of neural activity frequently display oscillatory patterns at various frequencies. Furthermore, these oscillatory patterns can become dynamically synchronized across a wide region of the brain in a task-dependent manner. In this study, phase-locked oscillations in simultaneously recorded spike trains were analyzed using the wavelet cross-spectrum. Adaptation of the existent methods of calculating wavelet cross-spectrum to spike train data was straightforward. In contrast, new methods were needed for evaluating the statistical significance of the cross-spectrum. Although a permutation test based on a large number of re-sampled cross-spectra can provide a reliable estimate of statistical significance, this was quite time-consuming. As an alternative, statistical significance was determined with a normal probability density function estimated from a small number of re-sampled cross-spectra. When applied to neuron pairs recorded in the primate supplementary motor area, the re-sampling procedure produced a reliable outcome even when it was based on as few as ten re-sampled cross-spectra. These results suggest that the wavelet analysis in combination with a re-sampling procedure provides a useful tool to examine the dynamic patterns of temporal correlation in cortical spike trains.     

Measurement of variability dynamics in cortical spike trains

We propose a method for the time-resolved joint analysis of two related aspects of single neuron variability, the spiking irregularity measured by the squared coefficient of variation (CV(2)) of the ISIs and the trial-by-trial variability of the spike count measured by the Fano factor (FF). We provide a calibration of both estimators using the theory of renewal processes, and verify it for spike trains recorded in vitro. Both estimators exhibit a considerable bias for short observations that count less than about 5-10 spikes on average. The practical difficulty of measuring the CV(2) in rate modulated data can be overcome by a simple procedure of spike train demodulation which was tested in numerical simulations and in real spike trains. We propose to test neuronal spike trains for deviations from the null-hypothesis FF=CV(2). We show that cortical pyramidal neurons, recorded under controlled stationary input conditions in vitro, comply with this assumption. Performing a time-resolved joint analysis of CV(2) and FF of a single unit recording from the motor cortex of a behaving monkey we demonstrate how the dynamic change of their quantitative relation can be interpreted with respect to neuron intrinsic and extrinsic factors that influence cortical variability in vivo. Finally, we discuss the effect of several additional factors such as serial interval correlation and refractory period on the empiric relation of FF and CV(2).     

Multivariate receptive field mapping in marmoset auditory cortex

We describe a novel method for estimation of multivariate neuronal receptive fields that is based on least-squares (LS) regression. The method is shown to account for the relationship between the spike train of a given neuron, the activity of other neurons that are recorded simultaneously, and a variety of time-varying features of acoustic stimuli, e.g. spectral content, amplitude, and sound source direction. Vocalization-evoked neuronal responses from the marmoset auditory cortex are used to illustrate the method. Optimal predictions of single-unit activity were obtained by using the recent-time history of the target neuron and the concurrent activity of other simultaneously recorded neurons (R: 0.82 +/- 0.01, approximately 67% of variance). Predictions based on ensemble activity alone (R: 0.63 +/- 0.18) were equivalent to those based on the combination of ensemble activity and spectral features of the vocal calls (R: 0.61 +/- 0.24). This result suggests that all information derived from the spectrogram is embodied in ensemble activity and that there is a high level of redundancy in the marmoset auditory cortex. We also illustrate that the method allows for quantification of relative and shared contributions of each variable (spike train, spectral feature) to predictions of neuronal activity and describe a novel "neurolet" transform that arises from the method and that may serve as a tool for computationally efficient processing of natural sounds.     

The connectivity underlying the orientation selectivity in the infragranular layers of monkey striate cortex

The striate cortex of the monkey was studied with an array of 30 closely spaced microelectrodes. Responses to oriented light bars were recorded simultaneously, and interneuronal connectivity was inferred from spike train correlations of pairs of neurones. Between cells with parallel preferred orientations, interactions were strong at short ranges but negative or only weakly positive at separations of 0.3-0.4 mm. At these distances, the stronger correlations were observed between orthogonally oriented cells. The finding does not explain the generation of orientation selectivity, but it is in agreement with a cooperative principle explaining the spatially regular arrangement of oriented cells.     

Network‐selectivity and stimulus‐discrimination in the primary visual cortex: cell‐assembly dynamics

Visual neurons coordinate their responses in relation to the stimulus; however, the complex interplay between a stimulus and the functional dynamics of an assembly still eludes neuroscientists. To this aim, we recorded cell assemblies from multi‐electrodes in the primary visual cortex of anaesthetized cats in response to randomly presented sine‐wave drifting gratings whose orientation tilted in 22.5° steps. Cross‐correlograms revealed the functional connections at all the tested orientations. We show that a cell‐assembly discriminates between orientations by recruiting a ‘salient’ functional network at every presented orientation, wherein the connections and their strengths (peak‐probabilities in the cross‐correlogram) change from one orientation to another. Within these assemblies, closely tuned neurons exhibited increased connectivity and connection‐strengths compared with differently tuned neurons. Minimal connectivity between untuned neurons suggests the significance of neuronal selectivity in assemblies. This study reflects upon the dynamics of functional connectivity, and brings to the fore the importance of a ‘signature’ functional network in an assembly that is strictly related to a specific stimulus. It appears that an assembly is the major ‘functional unit’ of information processing in cortical circuits, rather than the individual neurons.     

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.     

An improved method for the estimation of firing rate dynamics using an optimal digital filter

In most neural systems, neurons communicate by means of sequences of action potentials or 'spikes'. Information encoded by spike trains is often quantified in terms of the firing rate which emphasizes the frequency of occurrence of action potentials rather than their exact timing. Common methods for estimating firing rates include the rate histogram, the reciprocal interspike interval, and the spike density function. In this study, we demonstrate the limitations of these aforementioned techniques and propose a simple yet more robust alternative. By convolving the spike train with an optimally designed Kaiser window, we show that more robust estimates of firing rate are obtained for both low and high-frequency inputs. We illustrate our approach by considering spike trains generated by simulated as well as experimental data obtained from single-unit recordings of first-order sensory neurons in the vestibular system. Improvements were seen in the prevention of aliasing, phase and amplitude distortion, as well as in the noise reduction for sinusoidal and more complex input profiles. We review the generality of the approach, and show that it can be adapted to describe neurons with sensory or motor responses that are characterized by marked nonlinearities. We conclude that our method permits more robust estimates of neural dynamics than conventional techniques across all stimulus conditions.     

A simple indicator of nonstationarity of firing rate in spike trains

The assessment of stationarity of firing rate in neural spike trains is important but is often performed only visually. Facing the growing amount of neural data generated by multi-electrode recording, there is a need for an automatic method to identify and disqualify spike trains with highly nonstationary firing rates. In this report, we propose a simple test of nonstationarity, associated with an indicator quantifying the degree of nonstationary in a spike train. This method is compared to the Mann-Kendall test of trend detection and the Runs test on simulated and real spike trains.