Information transmission using non-poisson regular firing

Spontaneous activity in cortical neurons is stereotyped and non-Poisson

Neurons fire even in the absence of sensory stimulation or task demands. Numerous theoretical studies have modeled this spontaneous activity as a Poisson process with uncorrelated intervals between successive spikes and a variance in firing rate equal to the mean. Experimental tests of this hypothesis have yielded variable results, though most have concluded that firing is not Poisson. However, these tests say little about the ways firing might deviate from randomness. Nor are they definitive because many different distributions can have equal means and variances. Here, we characterized spontaneous spiking patterns in extracellular recordings from monkey, cat, and mouse cerebral cortex neurons using rate-normalized spike train autocorrelation functions (ACFs) and a logarithmic timescale. If activity was Poisson, this function should be flat. This was almost never the case. Instead, ACFs had diverse shapes, often with characteristic peaks in the 1-700 ms range. Shapes were stable over time, up to the longest recording periods used (51 min). They did not fall into obvious clusters. ACFs were often unaffected by visual stimulation, though some abruptly changed during brain state shifts. These behaviors may have their origin in the intrinsic biophysics and dendritic anatomy of the cells or in the inputs they receive.

Robust transmission of rate coding in the inhibitory Purkinje cell to cerebellar nuclei pathway in awake mice

Neural coding through inhibitory projection pathways remains poorly understood. We analyze the transmission properties of the Purkinje cell (PC) to cerebellar nucleus (CN) pathway in a modeling study using a data set recorded in awake mice containing respiratory rate modulation. We find that inhibitory transmission from tonically active PCs can transmit a behavioral rate code with high fidelity. We parameterized the required population code in PC activity and determined that 20% of PC inputs to a full compartmental CN neuron model need to be rate-comodulated for transmission of a rate code. Rate covariance in PC inputs also accounts for the high coefficient of variation in CN spike trains, while the balance between excitation and inhibition determines spike rate and local spike train variability. Overall, our modeling study can fully account for observed spike train properties of cerebellar output in awake mice, and strongly supports rate coding in the cerebellum.

Detailed computer simulations of biological neurons can make an important contribution to our understanding of how the brain works. In this paper we use such a model of a neuron that represents the output from the cerebellum. We can show that the inhibition this neuron type receives from Purkinje cells in the cerebellar cortex is well suited to pass a detailed time course of movement control to the output of the cerebellum. Importantly we find that this type of coding requires a population of Purkinje cells that pass the same temporal coding of spike rate to the output neurons in the cerebellar nuclei.

On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.

Analog and digital codes in the brain

It has long been debated whether information in the brain is coded at the rate of neuronal spiking or at the precise timing of single spikes. Although this issue is essential to the understanding of neural signal processing, it is not easily resolved because the two mechanisms are not mutually exclusive. We suggest revising this coding issue so that one hypothesis is uniquely selected for a given spike train. To this end, we decide whether the spike train is likely to transmit a continuously varying analog signal or switching between active and inactive states. The coding hypothesis is selected by comparing the likelihood estimates yielded by empirical Bayes and hidden Markov models on individual data. The analysis method is applicable to generic event sequences, such as earthquakes, machine noises, and human communications, and enhances the gain in decoding signals and infers underlying activities.