A Model for the Study of the Increase in Stimulus and Change Point Detection with Small and Variable Spiking Delays

Precise timing of spikes between different neurons has been found to convey reliable information beyond the spike count. In contrast, the role of small and variable spiking delays, as reported, for example, in the visual cortex, remains largely unclear. This issue becomes particularly important considering the high speed of neuronal information processing, which is assumed to be based on only a few milliseconds within each processing step. We investigate the role of small and variable spiking delays with a parsimonious stochastic spiking model that is strongly motivated by experimental observations. The model contains only two parameters for the response of a neuron to one stimulus, describing directly the rate and the delay, or phase. Within the theoretical model, we specifically investigate two quantities, the probability of correct stimulus detection and the probability of correct change point detection, as a function of these parameters and within short periods of time. Optimal combinations of the two parameters across stimuli are derived that maximize these probabilities and enable comparison of pure rate, pure phase, and combined codes. In particular, the gain in correct detection probability when adding small and variable spiking delays to pure rate coding increases with the number of stimuli. More interesting, small and variable spiking delays can considerably improve the process of detecting changes in the stimulus, while also decreasing the probability of false alarms and thus increasing robustness and speed of change point detection. The results are compared to empirical spike train recordings of neurons in the visual cortex reported earlier in response to a number of visual stimuli. The results suggest that near-optimal combinations of rate and phase parameters may be implemented in the brain and that adding phase information could particularly increase the quality of change point detection in cases of highly similar stimuli.

Detecting joint pausiness in parallel spike trains

BACKGROUND

Transient periods with reduced neuronal discharge - called 'pauses' - have recently gained increasing attention. In dopamine neurons, pauses are considered important teaching signals, encoding negative reward prediction errors. Particularly simultaneous pauses are likely to have increased impact on information processing.

COMPARISON WITH EXISTING METHODS

Available methods for detecting joint pausing analyze temporal overlap of pauses across spike trains. Such techniques are threshold dependent and can fail to identify joint pauses that are easily detectable by eye, particularly in spike trains with different firing rates.

NEW METHOD

We introduce a new statistic called pausiness that measures the degree of synchronous pausing in spike train pairs and avoids threshold-dependent identification of specific pauses. A new graphic termed the cross-pauseogram compares the joint pausiness of two spike trains with its time shifted analogue, such that a (pausiness) peak indicates joint pausing. When assessing significance of pausiness peaks, we use a stochastic model with synchronous spikes to disentangle joint pausiness arising from synchronous spikes from additional 'joint excess pausiness' (JEP). Parameter estimates are obtained from auto- and cross-correlograms, and statistical significance is assessed by comparison to simulated cross-pauseograms.

RESULTS

Our new method was applied to dopamine neuron pairs recorded in the ventral tegmental area of awake behaving mice. Significant JEP was detected in about 20% of the pairs.

CONCLUSION

Given the neurophysiological importance of pauses and the fact that neurons integrate multiple inputs, our findings suggest that the analysis of JEP can reveal interesting aspects in the activity of simultaneously recorded neurons.

Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.

Measuring burstiness and regularity in oscillatory spike trains

The ability of neurons to emit different firing patterns such as bursts or oscillations is important for information processing in the brain. In dopaminergic neurons, prominent patterns include repetitive, oscillatory bursts, regular pacemakers, and irregular spike trains with nonstationary properties. In order to describe and measure the variability of these patterns, we describe burstiness and regularity in a single model framework. We present a doubly stochastic spike train model in which a background oscillation with independent and normally distributed intervals gives rise to either single spikes or bursty spike events with Gaussian firing intensities. Five easily interpretable parameters allow a classification into bursty or single spike and irregularly or regularly oscillating firing patterns. This classification is based primarily on features of the autocorrelation histogram which are usually studied qualitatively by visual inspection. The present model provides a quantitative and objective classification scheme and relates these features directly to the underlying processes. In addition, confidence intervals visualize the uncertainty of parameter estimation and classification precision. We apply the model to a data set obtained from single dopaminergic substantia nigra neurons recorded extracellularly in vivo. The model is able to represent a high variety of discharge patterns observed empirically, and the classification agrees closely with visual inspection. In addition, changes in the parameters can be studied quantitatively, including also the properties related to bursting behavior. Thus, the proposed model can be used for the description of neuronal firing patterns and the investigation of their dynamical changes with cellular and experimental conditions.