Quantification and statistical verification of neuronal stimulus responses from noisy spike train data

Usually neuronal responses to short-lasting stimuli are displayed as peri-stimulus time histogram. The function estimated by such a histogram allows to obtain informations about stimulus-induced postsynaptic events as long as the interpretation is restricted to the first response component after the stimulus. The interpretation of secondary response components is much more difficult, as they may be either due to stimulus effects or represent an echo of the primary response. In the present paper two output functions are developed that do not show such an echoing of responses. The first one, the interspike interval change function, represents an ideal way to quantify a neuronal stimulus response as its amplitude was found to be almost independent of the stimulation strategy used during acquisition of the spike train data. The other function, the displaced impulses function, allows to verify the statistical significance of an observed response component. Both functions may be estimated from stimulus-correlated spike train data, even if the neuron under investigation shows considerable interspike-interval variability in the absence of stimulation. The concepts underlying these neuronal output functions are developed on simulated responses of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature that is exposed to a transient excitatory conductance increase. Additionally, estimation of these output functions is also demonstrated on responses of human soleus motoneurons that were exposed to electrical stimuli of the tibial nerve in the popliteal fossa.     

Fourier analysis of spike train data

A formal representation of nerve spike trains in the form of a sum of rectangular functions is proposed. This formal instantaneous frequency function can be Fourier analyzed. The resulting algorithm has the useful properties of spike by spike calculations and an insensitivity to the mean (carrier) spike rate. The technique is also useful for producing a smooth (filtered) reconstruction of a spike train.     

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.     

Nonlinear principal components analysis of neuronal spike train data

Many recent approaches to decoding neural spike trains depend critically on the assumption that for low-pass filtered spike trains, the temporal structure is optimally represented by a small number of linear projections onto the data. We therefore tested this assumption of linearity by comparing a linear factor analysis technique (principal components analysis) with a nonlinear neural network based method. It is first shown that the nonlinear technique can reliably identify a neuronally plausible nonlinearity in synthetic spike trains. However, when applied to the outputs from primary visual cortical neurons, this method shows no evidence for significant temporal nonlinearities. The implications of this are discussed. Received: 29 November 1996 / Accepted in revised form: 1 July 1997     

Analytical reconstruction of the neuronal input current from spike train data

The time course of the current driving action potential generation at a neuron investigated experimentally is in general not measurable directly. In this paper an indirect method is introduced that allows estimation of this unknown current time course using only spike train data. Assuming the leaky integrator model as valid for the action potential encoding site of the investigated neuron, the unknown input current is obtained by determining (analytically) a current time course that upon injection into the leaky integrator model evokes action potential sequences identical to those observed experimentally. Applications of this current-reconstruction procedure to neuronal output data obtained from a leaky integrator model showed that the procedure allows a good estimation of the underlying input current even if the membrane time constant of the investigated neuron is not known exactly. Additionally, an application of current reconstruction to experimental data obtained from a cat muscle spindle primary afferent subject to repeated -stimuli is demonstrated.     

Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data

Recent advancements in miniaturized fluorescence microscopy have made it possible to investigate neuronal responses to external stimuli in awake behaving animals through the analysis of intracellular calcium signals. An ongoing challenge is deconvolving the temporal signals to extract the spike trains from the noisy calcium signals' time series. In this article, we propose a nested Bayesian finite mixture specification that allows the estimation of spiking activity and, simultaneously, reconstructing the distributions of the calcium transient spikes' amplitudes under different experimental conditions. The proposed model leverages two nested layers of random discrete mixture priors to borrow information between experiments and discover similarities in the distributional patterns of neuronal responses to different stimuli. Furthermore, the spikes' intensity values are also clustered within and between experimental conditions to determine the existence of common (recurring) response amplitudes. Simulation studies and the analysis of a dataset from the Allen Brain Observatory show the effectiveness of the method in clustering and detecting neuronal activities.     

Causal pattern recovery from neural spike train data using the Snap Shot Score

We present a new approach to learning directed information flow networks from multi-channel spike train data. A novel scoring function, the Snap Shot Score, is used to assess potential networks with respect to their quality of causal explanation for the data. Additionally, we suggest a generic concept of plausibility in order to assess network learning techniques under partial observability conditions. Examples demonstrate the assessment of networks with the Snap Shot Score, and neural network simulations show its performance in complex situations with partial observability. We discuss the application of the new score to real data and indicate how it can be modified to suit other neural data types.     

Criteria for excitation and inhibition in peristimulus spike train activity

1) Five possibilities of defining a coefficient of facilitation and inhibition are described. 2) It is shown that the application of these definition to the same spike train activity eventually leads to considerably different results, e.g., a response which is inhibitory according to one definition sometimes is facilitatory according to another definition. 3) To find the most reliable definition the theoretical differences between the five alternatives are examined, whereby a coefficient is considered reliable if it is reproducible and independent of external experimental parameters, such as the record length. 4) As an experimental example spike trains were recorded from mitral cells in the olfactory bulb of the goldfish. We divide every response into two sections: an initial reaction and a steady state reaction. In this way each response can be uniquely classified. 5) The most reliable definition of a coefficient of facilitation turns out to be based on the steady state levels of an averaged peristimulus time histogramme. Under certain conditions this corresponds to considering the means of the sample mean rates of a stochastic point process before and after the stimulus application, whereby the initial reactions are neglected. These should be classified by other methods and notions.     

An information-geometric framework for statistical inferences in the neural spike train space

Statistical inferences are essentially important in analyzing neural spike trains in computational neuroscience. Current approaches have followed a general inference paradigm where a parametric probability model is often used to characterize the temporal evolution of the underlying stochastic processes. To directly capture the overall variability and distribution in the space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in the function space in which spike trains are viewed as individual points. To this end, we at first develop a parametrized family of metrics that takes into account different warpings in the time domain and generalizes several currently used spike train distances. These new metrics are essentially penalized L ^p norms, involving appropriate functions of spike trains, with penalties associated with time-warping. The notions of means and variances of spike trains are then defined based on the new metrics when p = 2 (corresponding to the “Euclidean distance”). Using some restrictive conditions, we present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains with arbitrary numbers of spikes. The proposed metrics as well as the mean spike trains are demonstrated using simulations as well as an experimental recording from the motor cortex. It is found that all these methods achieve desirable performance and the results support the success of this novel framework.     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

A quantitative method for the detection of edges in noisy time-series

A modification of the edge detector of Chung & Kennedy is proposed in which the output provides confidence limits for the presence or absence of sharp edges (steps) in the input waveform. Their switching method with forward and backward averaging windows is retained, but the output approximates an ideal output function equal to the difference in these averages divided by the standard deviation of the noise. Steps are associated with peak output above a pre-set threshold. Formulae for the efficiency and reliability of this ideal detector are derived for input waveforms with Gaussian white noise and sharp edges, and serve as benchmarks for the switching edge detector. Efficiency is kept high if the threshold is a fixed fraction of the step size of interest relative to noise, and reliability is improved by increasing the window width W to reduce false output. For different steps sizes D, the window width for fixed efficiency and reliability scales as 1/D2. Versions with weighted averaging (flat, ramp, triangular) or median averaging but the same window width perform similarly. Binned above-threshold output is used to predict the locations and signs of detected steps, and simulations show that efficiency and reliability are close to ideal. Location times are accurate to order square root of W. Short pulses generate reduced output if the number of data points in the pulse is less than W. They are optimally detected by choosing W as above and collecting data at a rate such that the pulse contains approximately W data points. A Fortran program is supplied.     

The correlation grid: analysis of synchronous spiking in multi-dimensional spike train data and identification of feasible connection architectures

This paper presents a visualization technique specifically designed to support the analysis of synchronous firings in multiple, simultaneously recorded, spike trains. This technique, called the correlation grid, enables investigators to identify groups of spike trains, where each pair of spike trains has a high probability of generating spikes approximately simultaneously or within a constant time shift. Moreover, the correlation grid was developed to help solve the following reverse problem: identification of the connection architecture between spike train generating units, which may produce a spike train dataset similar to the one under analysis. To demonstrate the efficacy of this approach, results are presented from a study of three simulated, noisy, spike train datasets. The parameters of the simulated neurons were chosen to reflect the typical characteristics of cortical pyramidal neurons. The schemes of neuronal connections were not known to the analysts. Nevertheless, the correlation grid enabled the analysts to find the correct connection architecture for each of these three data sets.     

The evolution of alternative adaptive strategies for effective communication in noisy environments

Animals communicating socially are expected to produce signals that are conspicuous within the habitats in which they live. The particular way in which a species adapts to its environment will depend on its ancestral condition and evolutionary history. At this point, it is unclear how properties of the environment and historical factors interact to shape communication. Tropical Anolis lizards advertise territorial ownership using visual displays in habitats where visual motion or "noise" from windblown vegetation poses an acute problem for the detection of display movements. We studied eight Anolis species that live in similar noise environments but belong to separate island radiations with divergent evolutionary histories. We found that species on Puerto Rico displayed at times when their signals were more likely to be detected by neighboring males and females (during periods of low noise). In contrast, species on Jamaica displayed irrespective of the level of environmental motion, apparently because these species have a display that is effective in a range of viewing conditions. Our findings appear to reflect a case of species originating from different evolutionary starting points evolving different signal strategies for effective communication in noisy environments.     

Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation

Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects between noisy and nonlinear dynamics. Often, this is achieved by a simple noise term in the membrane equation (current noise). However, there are ongoing discussions whether such current noise is justified or whether rather conductance noise should be introduced because it is closer to the natural origin of noise. Therefore, we have compared the effects of current and conductance noise in a neuronal model for subthreshold oscillations and action potential generation. We did not see any significant differences in the model behavior with respect to voltage traces, tuning curves of interspike intervals, interval distributions or frequency responses when the noise strength is adjusted. These findings indicate that simple current noise can give reasonable results in neuronal simulations with regard to physiological relevant noise effects.     

Bifurcations in the decremental propagation of a spike train in the Hodgkin-Huxley model of low excitability

Response of a nerve fiber of low excitability to periodic stimulus pulses is studied with computer simulation of the Hodgkin-Huxley model. The excitability of the Hodgkin-Huxley model is reduced by decreasing the equilibrium potential for the sodium ion and by increasing the temperature, so that the decremental propagation of spikes occurs in the refractory period. It is shown that, as the period of stimulus pulses is decreased, the propagation length of the spikes is continuously changed, and period-doubling bifurcations occur. The response of a nerve fiber of low excitability is then qualitatively different from that of a normal fiber. Received: 6 December 1996 / Accepted in revised form: 12 June 1998     

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures—most of which are variants of Granger causality—with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger’s original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.