The neuronal refractory period causes a short-term peak in the autocorrelation function

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Abstract

Autocorrelation functions are a major tool for the understanding of single-cell firing patterns. Short-term peaks in autocorrelation functions have previously been interpreted as a tendency towards bursting activity or elevated probability to emit spikes in a short time-scale. These peaks can actually be a result of the firing of a neuron with a refractory period followed by a period of constant firing probability. Analytic studies and simulations of such neurons replicate the autocorrelation functions of real-world neurons. The relative size of the peak increases with the refractory period and with the firing rate of the cell. This phenomenon is therefore more notable in areas such as the globus pallidus and cerebellum and less clear in the cerebral cortex. We describe here a compensation factor that can be calculated from the neuron's hazard function. This factor can be removed from the original autocorrelation function to reveal the underlying firing pattern of the cell.

Introduction

Spike train analysis – the heart of the analysis in most studies of extracellular recordings – is based on the timing of action potentials, while neglecting sub-threshold phenomena and changes in spike shape and amplitude. Computing the autocorrelation function (Perkel et al., 1967a) is a common first step toward revealing a spike train's internal structure. This function describes the probability that a neuron will emit a spike as a function of the time elapsed from another firing of a spike by that neuron.

A prominent feature of all neuronal autocorrelation functions is the refractory period caused by the inability of neurons to emit two spikes in close proximity. Neuronal autocorrelation functions (also known as autocorrelograms) are often categorized as flat, oscillatory or bursty according to the shape of the function following the refractory period (Wilson and Groves, 1981, Munemori et al., 1984, Wichmann et al., 1994). Early simulation studies (Segundo et al., 1968) have demonstrated a continuous spectrum of firing patterns ranging from random (flat autocorrelogram), to early mode types (autocorrelograms with a single short peak), and finally to periodic correlograms. This continuous gradation was achieved simply by changing the number or the pattern of the inputs to the simulated neuron. However, later studies have usually assumed a more discrete classification of the firing patterns of neurons. In the canonical interpretation, flat autocorrelation functions reflect neurons with a constant probability for firing a spike (Abeles, 1982a); oscillatory autocorrelation functions reflect periodic oscillations in the neurons’ firing probability (Filion, 1979, Engel et al., 1991, Bergman et al., 1994a); and a peak in the autocorrelation functions reflects the cells’ tendency to fire several action potentials in rapid succession, called bursting (Wichmann et al., 1994).

Bursting activity can be caused by intrinsic properties of the neurons, such as elevated calcium or calcium conductance levels, or by extrinsic input, such as prolonged synchronous synaptic activity. Bursts may have a special role in synaptic plasticity and information processing in the brain (Lisman, 1997). The definition of bursting activity varies according to the research field. Intracellular/computational researchers use the definition of firing dynamics on multiple time-scales (Rinzel, 1987). Researchers using extracellular recording methods in behaving animals use the functional definition of enhanced firing probability on a short time-scale following the emission of spikes (Abeles, 1982b). The area of the peak in the autocorrelation function is used for estimating the average burst size, that is, the number of spikes within a burst is approximately twice the size of the area (Abeles, 1982b, Bergman et al., 1994a, Colder et al., 1996).

In this manuscript we show that short peaks in the autocorrelation function may be the result of the refractory period of cells with high firing rate and not of the elevated firing probability (bursting activity). We further demonstrate how this effect can be compensated by calculation of an equivalent renewal process using parameters extracted from the hazard function of the cell.

Section snippets

Electrophysiological data

Electrophysiological examples were obtained from various physiological recordings made previously in our laboratory (Wichmann et al., 1994, Wichmann et al., 1999, Nini et al., 1995). We used standard physiological techniques for extracellular recording of spiking activity of neurons in behaving primates (Nini et al., 1995). Stability and recording quality were evaluated off-line, and only well-isolated and stable spike trains — those with stable spike waveforms, stable firing rate and

Short-term peaks in electrophysiological studies

Neurons in many areas of the nervous system display short-term ‘bursty’ autocorrelation functions. Some of the autocorrelation functions of such cells are shown in Fig. 1: a neuron from the globus pallidus external segment (1a) and from the internal segment (1b), a neuron from the substantia nigra pars reticulata (1c) and a subthalamic nucleus neuron (1d). Other examples from the literature include spinothalamic tract neurons in the spinal cord (Surmeier et al., 1989, Figs. 6c and 7c), neurons

Discussion

The major points emphasized in this article are:

  • Short-term peaks in the autocorrelation function do not necessarily reflect bursting activity of the neuron.

  • The peaks are significant in neurons featuring high firing rates and/or long refractory periods.

  • The underlying firing pattern can be revealed by the compensation method described above.

Acknowledgements

This study was supported in part by the Israeli Academy of Science, AFIRST and the US–Israel Bi-national Science Foundation. We thank Moshe Abeles, Opher Donchin and Genela Morris for their critical reading and helpful suggestions. We thank Thomas Wichmann, Gali Havazelet-Heimer, Joshua A. Goldberg and Sharon Maraton for sharing their data with us.

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