Spike Train Metrics Research Articles

Multisensory Neurons in the Primate Amygdala.

Animals identify, interpret, and respond to complex, natural signals that are often multisensory. The ability to integrate signals across sensory modalities depends on the convergence of sensory inputs at the level of single neurons. Neurons in the amygdala are expected to be multisensory because they respond to complex, natural stimuli, and the amygdala receives inputs from multiple sensory areas. We recorded activity from the amygdala of 2 male monkeys (Macaca mulatta) in response to visual, tactile, and auditory stimuli. Although the stimuli were devoid of inherent emotional or social significance and were not paired with rewards or punishments, the majority of neurons that responded to these stimuli were multisensory. Selectivity for sensory modality was stronger and emerged earlier than selectivity for individual items within a sensory modality. Modality and item selectivity were expressed via three main spike-train metrics: (1) response magnitude, (2) response polarity, and (3) response duration. None of these metrics were unique to a particular sensory modality; rather, each neuron responded with distinct combinations of spike-train metrics to discriminate sensory modalities and items within a modality. The relative proportion of multisensory neurons was similar across the nuclei of the amygdala. The convergence of inputs of multiple sensory modalities at the level of single neurons in the amygdala rests at the foundation for multisensory integration. The integration of visual, auditory, and tactile inputs in the amygdala may serve social communication by binding together social signals carried by facial expressions, vocalizations, and social grooming.SIGNIFICANCE STATEMENT Our brain continuously decodes information detected by multiple sensory systems. The emotional and social significance of the incoming signals is likely extracted by the amygdala, which receives input from all sensory domains. Here we show that a large portion of neurons in the amygdala respond to stimuli from two or more sensory modalities. The convergence of visual, tactile, and auditory signals at the level of individual neurons in the amygdala establishes a foundation for multisensory integration within this structure. The ability to integrate signals across sensory modalities is critical for social communication and other high-level cognitive functions.

Decoding of naturalistic textures from spike patterns of neuromorphic artificial mechanoreceptors

Significant advances were recently achieved in the bidirectional control of upper limb neuroprostheses [1], however implementing a realistic tactile feedback on artificial hands is still an open challenge [2]. We target this ambition with a neuromorphic approach. Towards this direction we integrated MEMS tactile sensors with a realistic spatial arrangement on the distal phalanx of artificial fingers [3] and we converted the sensor readouts into spike trains mimicking the neural firing properties of glabrous skin mechanoreceptors [4]. The neuromorphic approach presents several advantages [5], among which the most relevant for neuroprosthetics is that a sufficiently realistic tactile feedback is expected to reduce drastically the time the brain needs to adapt to the prosthesis and to each single new task, leading to enhanced quality of life of the subjects. Since the long term goal is to implement a hardware version of the neuromorphic neurons, we modeled the mechanoreceptors as Izhikevich neurons, a model which at the same time is computationally lean and takes into account the effects of firing rate adaptation that are particularly relevant in mechanoreceptors. Parameters were tuned so to achieve a match with Slowly Adapting (SA) mechanoreceptors dynamics in primates [4]. The output of each tactile sensor was normalized and injected as an excitatory input current into a single neuron model [6]. To reproduce the features of Fast Adapting (FA) mechanoreceptors responsible for edge detection [7], we injected in a second set of neuron models the smoothed derivative of the pressure sensors outputs. The fingertip was then repeatedly presented with ten different daily-life textures such as textiles, polymeric tissues, glass or paper. FA spike trains were used to identify onset and offset of contact between fingertip and stimuli, whereas SA spike trains were used to decode the stimulus presented. We applied two decoding procedures: one based on the combination of firing rate and inter-spike interval Fano factor, and the other one based on Victor-Purpura distance [8]. Error rate was close to 20% in the first case and to 5% in the second, reflecting the relevance for decoding of the fine temporal structure of the neuromorphic sensor outputs. Finally, we introduced a normalization in the cost of the Victor-Purpura spike train metrics thanks to which the above level of correct classification was maintained even if sensing conditions varied across trials. These results support a possible future evaluation of the biomimetic fingertip endowed with neuromorphic artificial mechanoreceptors in clinical trials with human subjects.

Neural Decoding with Kernel-Based Metric Learning

In studies of the nervous system, the choice of metric for the neural responses is a pivotal assumption. For instance, a well-suited distance metric enables us to gauge the similarity of neural responses to various stimuli and assess the variability of responses to a repeated stimulus-exploratory steps in understanding how the stimuli are encoded neurally. Here we introduce an approach where the metric is tuned for a particular neural decoding task. Neural spike train metrics have been used to quantify the information content carried by the timing of action potentials. While a number of metrics for individual neurons exist, a method to optimally combine single-neuron metrics into multineuron, or population-based, metrics is lacking. We pose the problem of optimizing multineuron metrics and other metrics using centered alignment, a kernel-based dependence measure. The approach is demonstrated on invasively recorded neural data consisting of both spike trains and local field potentials. The experimental paradigm consists of decoding the location of tactile stimulation on the forepaws of anesthetized rats. We show that the optimized metrics highlight the distinguishing dimensions of the neural response, significantly increase the decoding accuracy, and improve nonlinear dimensionality reduction methods for exploratory neural analysis.

A New Class of Metrics for Spike Trains

The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance, and compare them with existing metrics. Some of our new metrics (the modulus-metric and the max-metric) have characteristics that are qualitatively different from those of classical metrics like the van Rossum distance or the Victor and Purpura distance. The modulus-metric and the max-metric are particularly suitable for measuring distances between spike trains where information is encoded in bursts, but the number and the timing of spikes inside a burst do not carry information. The modulus-metric does not depend on any parameters and can be computed using a fast algorithm whose time depends linearly on the number of spikes in the two spike trains. We also introduce localized versions of the new metrics, which could have the biologically relevant interpretation of measuring the differences between spike trains as they are perceived at a particular moment in time by a neuron receiving these spike trains.

Modulation of a decision-making process by spatiotemporal spike patterns decoding: evidence from spike-train metrics analysis and spiking neural network modeling

While monkeys perform a task alternating between behavioral adaptation --relying on feedback monitoring and memory of previous choices-- and repetition of previous actions, firing rates in dorsal Anterior Cingulate Cortex (dACC) modulate with cognitive control levels [1]. Further, it has been hypothesized that dorsolateral Prefrontal Cortex (dlPFC) could make use of dACC signals to take the adapted decision [2]. However, little is known about whether dACC spike timing may participate to behavioral adaptation signaling, and how multiple unit activities may be jointly decoded by dlPFC. We tested the hypothesis that temporal (or spatiotemporal) pattern matching mediate information transmission by dACC. We used spike-train metrics [3] to decode dACC activity recorded in a problem solving task [1] (336 cells, 2 monkeys). We computed a similarity measure between every spike train and the activity patterns in different task epochs for classification. When computing the similarity, we explored different degrees of (i) timing sensitivity and (ii) distinction between spikes from different neurons, which led to different classification performances. We found that timing sensitivity could improve behavioral adaptation vs. repetition classification of single unit spike trains. Optimal decoding occurred when accounting for spike times at a resolution <= 200 ms. Furthermore, spike-train metrics decoding of unitary discharges was related to the monkeys' response time. A downstream neural decoder could exploit this temporal information through coincidence detection determined by synaptic and membrane time constants. In addition, when decoding two units jointly, we found that each pair had a specific optimal distinction degree between spikes coming from the two different neurons. In a realistic neural decoder, the tuning of this distinction degree might occur through non-linear dendritic integration. To further investigate the computational properties of temporal decoding in the context of decision-making, we are implementing a recurrent spiking neural network with connectivity leading to attractor dynamics. In this framework, each decision is mapped to a state in which a corresponding neural subpopulation shows elevated activity, as observed experimentally in dlPFC [4]. In addition, neurons will undergo membrane properties adaptation [5] and short-term plasticity, leading to history-of-choices dependent temporal spike patterns. We will investigate how this temporal-spike-patterns memory of past choices could interact with dACC feedback-specific temporal patterns to lead to adapted decision. The feasibility and putative advantages of spike-timing-dependent-plasticity-based learning of response selectivity to the appropriate dACC-dlPFC temporal correlations will be considered.

Identifying Temporal Codes in Spontaneously Active Sensory Neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.

Improved Similarity Measures for Small Sets of Spike Trains

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in neuroprosthetic devices and electrophysiological experiments. Frequently only a few spike trains are available in each class. We derive analytical expressions for the small-sample bias present when comparing estimators of the time-dependent firing intensity. We then exploit analogies between the comparison of firing intensities and previously used spike train metrics and show that improved spike train measures can be successfully used for fitting neuron models to experimental data, for comparisons of spike trains, and classification of spike train data. In classification tasks, the improved similarity measures can increase the recovered information. We demonstrate that when similarity measures are used for fitting mathematical models, all previous methods systematically underestimate the noise. Finally, we show a striking implication of this deterministic bias by reevaluating the results of the single-neuron prediction challenge.

Quantifying Neurotransmission Reliability Through Metrics-Based Information Analysis

We set forth an information-theoretical measure to quantify neurotransmission reliability while taking into full account the metrical properties of the spike train space. This parametric information analysis relies on similarity measures induced by the metrical relations between neural responses as spikes flow in. Thus, in order to assess the entropy, the conditional entropy, and the overall information transfer, this method does not require any a priori decoding algorithm to partition the space into equivalence classes. It therefore allows the optimal parameters of a class of distances to be determined with respect to information transmission. To validate the proposed information-theoretical approach, we study precise temporal decoding of human somatosensory signals recorded using microneurography experiments. For this analysis, we employ a similarity measure based on the Victor-Purpura spike train metrics. We show that with appropriate parameters of this distance, the relative spike times of the mechanoreceptors' responses convey enough information to perform optimal discrimination--defined as maximum metrical information and zero conditional entropy--of 81 distinct stimuli within 40 ms of the first afferent spike. The proposed information-theoretical measure proves to be a suitable generalization of Shannon mutual information in order to consider the metrics of temporal codes explicitly. It allows neurotransmission reliability to be assessed in the presence of large spike train spaces (e.g., neural population codes) with high temporal precision.

A new spike train metric

The theoretical and practical importance of quantifying the degree of similarity between pairs of spike trains has resulted in a plethora of spike train metrics. Some are based on cost functions [1,2] while others use smoothing kernels [3] or binning techniques [4] and then rely on spike intervals or precise spike timings to compute the distance. Spike metrics are especially important as they enable the analysis of the neural code, a fundamental and heavily debated issue in neuroscience. Here, we introduce a new class of spike train metrics dependent on smooth kernels. They compute the distance between pairs of spike trains and yield a result that is non-linearly dependent on the precise timing of the differences across the two spike trains. In this situation, the actual position of a spike outweighs the importance of the inter-spike interval. In the exchange of information between two neurons each spike may be as important as the spike train itself [5] and therefore, metrics based on the specific timing of differences are desirable. The introduced spike train metrics, which will be referred to as max-metrics, are similar to the Hausdorff distance between two non-empty compact sets. They are given in two distinct forms: one that uses a convolution kernel to filter each spike train and, the other that uses the raw spike times. Because the latter does not rely on a smoothing kernel and uses the spike train directly, it does not introduce additional time constants and therefore has the advantage that it is more general. From a mathematical point of view the kernels can be just about any function because the generated metrics are commensurable. Some, however, will have a lesser physiological interpretation than others. The space of spike trains endowed with either form of the max-metric is compact. The implication for learning is that any learning rule based on the metric will eventually converge to a point in the spike train space. Because the max-metric generates the same topology regardless of the choice of kernels, topological properties such as compactness are common to all spike train spaces. The metrics are benchmarked against a simple spike count distance and against the original and a modified version of the van Rossum metric [3].

Statistical Analysis of a Spike Train Distance in Poisson Models

Several spike train metrics have been proposed in the last years for the evaluation of neural responses. In this letter, we perform deep statistical analysis on an important metric. This metric evaluates the dissimilarity between spike trains by applying a linear filter on the trains and then integrating the squared difference of the result. The statistical analysis is made when the metric is used to evaluate spike trains originated from nonhomogenous Poisson processes. Contrary to previous works, the analytical results have been obtained for the general case and not only for particular limiting conditions. By computing the expected value of the metric, insightful information is retrieved; it allows for the proposal of a normalization factor which addresses several deficiencies when comparing neural responses.

Measuring spike train synchrony and reliability

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 fixed beforehand. In this study [1], we propose the ISI-distance, a simple complementary approach that extracts information from the interspike intervals by evaluating the ratio of the instantaneous frequencies. 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 (cf. [2]). We compare the method with six existing approaches (two spike train metrics [3,4], a correlation measure [2,5], a similarity measure [6], and event synchronization [7]) using spike trains extracted from a simulated Hindemarsh-Rose network [8]. In this comparison the ISI-distance performs as well as the best time-scale-optimized measure based on spike timing, without requiring an externally determined time scale for interaction or comparison.

Linking non-binned spike train kernels to several existing spike train metrics

This work presents three kernel functions that can be used as inner product operators on non-binned spike trains, allowing the use of state-of-the-art classification techniques. One of the main advantages is that this approach does not require the spike trains to be binned. Thus a high temporal resolution is preserved which is needed when temporal coding is used. The kernels are closely related to several recent and often-used spike train metrics which take into account the biological variability of spike trains. It follows that the different existing metrics are unified by the spike train kernels presented. As a test of the classification potential of the new kernel functions, a jittered spike train template classification problem is solved.

Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons

Spike train metrics quantify the notion of dissimilarity, or distance, between spike trains and between multineuronal responses (J. Neurophysiol. 76 (1996) 1310, Network 8 (1997) 127). We present a new algorithm for the implementation of a metric based on the timing of individual spikes and on their neurons of origin. This algorithm surpasses the earlier approach in speed by a factor that grows exponentially with the number of neurons, substantially extending the applicability of metric space methods to the study of coding in larger neuronal populations.