The impact of spike timing variability on the signal-encoding performance of neural spiking models

It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance

Fractionally Predictive Spiking Neurons

Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spike-train itself can be considered as the fractional derivative, provided that the neural signal is approximated by a sum of power-law kernels. A simple standard thresholding spiking neuron suffices to carry out such an approximation, given a suitable refractory response. Empirically, we find that the online approximation of signals with a sum of power-law kernels is beneficial for encoding signals with slowly varying components, like long-memory self-similar signals. For such signals, the online power-law kernel approximation typically required less than half the number of spikes for similar SNR as compared to sums of similar but exponentially decaying kernels. As power-law kernels can be accurately approximated using sums or cascades of weighted exponentials, we demonstrate that the corresponding decoding of spike-trains by a receiving neuron allows for natural and transparent temporal signal filtering by tuning the weights of the decoding kernel.Comment: 13 pages, 5 figures, in Advances in Neural Information Processing 201

Neural activity classification with machine learning models trained on interspike interval series data

The flow of information through the brain is reflected by the activity patterns of neural cells. Indeed, these firing patterns are widely used as input data to predictive models that relate stimuli and animal behavior to the activity of a population of neurons. However, relatively little attention was paid to single neuron spike trains as predictors of cell or network properties in the brain. In this work, we introduce an approach to neuronal spike train data mining which enables effective classification and clustering of neuron types and network activity states based on single-cell spiking patterns. This approach is centered around applying state-of-the-art time series classification/clustering methods to sequences of interspike intervals recorded from single neurons. We demonstrate good performance of these methods in tasks involving classification of neuron type (e.g. excitatory vs. inhibitory cells) and/or neural circuit activity state (e.g. awake vs. REM sleep vs. nonREM sleep states) on an open-access cortical spiking activity dataset

Comparing Offline Decoding Performance in Physiologically Defined Neuronal Classes

Objective: Recently, several studies have documented the presence of a bimodal distribution of spike waveform widths in primary motor cortex. Although narrow and wide spiking neurons, corresponding to the two modes of the distribution, exhibit different response properties, it remains unknown if these differences give rise to differential decoding performance between these two classes of cells. Approach: We used a Gaussian mixture model to classify neurons into narrow and wide physiological classes. Using similar-size, random samples of neurons from these two physiological classes, we trained offline decoding models to predict a variety of movement features. We compared offline decoding performance between these two physiologically defined populations of cells. Main results: We found that narrow spiking neural ensembles decode motor parameters better than wide spiking neural ensembles including kinematics, kinetics, and muscle activity. Significance: These findings suggest that the utility of neural ensembles in brain machine interfaces may be predicted from their spike waveform widths

Spike train statistics and Gibbs distributions

This paper is based on a lecture given in the LACONEU summer school, Valparaiso, January 2012. We introduce Gibbs distribution in a general setting, including non stationary dynamics, and present then three examples of such Gibbs distributions, in the context of neural networks spike train statistics: (i) Maximum entropy model with spatio-temporal constraints; (ii) Generalized Linear Models; (iii) Conductance based Inte- grate and Fire model with chemical synapses and gap junctions.Comment: 23 pages, submitte

Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method

Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have been focusing on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In a second part, we present a new method based on Monte-Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles.Comment: 41 pages, 10 figure

Linear response for spiking neuronal networks with unbounded memory

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.Comment: 60 pages, 8 figure

Adaptive Neural Coding Dependent on the Time-Varying Statistics of the Somatic Input Current

It is generally assumed that nerve cells optimize their performance to reflect the statistics of their input. Electronic circuit analogs of neurons require similar methods of self-optimization for stable and autonomous operation. We here describe and demonstrate a biologically plausible adaptive algorithm that enables a neuron to adapt the current threshold and the slope (or gain) of its current-frequency relationship to match the mean (or dc offset) and variance (or dynamic range or contrast) of the time-varying somatic input current. The adaptation algorithm estimates the somatic current signal from the spike train by way of the intracellular somatic calcium concentration, thereby continuously adjusting the neuronś firing dynamics. This principle is shown to work in an analog VLSI-designed silicon neuron