Elsevier

Biosystems

Volume 48, Issues 1–3, 1 November 1998, Pages 139-146
Biosystems

Cross-correlation between neurons: a source of information about the nervous system

https://doi.org/10.1016/S0303-2647(98)00059-8Get rights and content

Abstract

Impulse trains of spiking neurons are a stochastic process; however, the impulse trains of related neurons are generally not statistically independent. Cross-correlation may be due to either a common input that affects the firing of both cells, or to direct synaptic influence of the one neuron upon the other. By analyzing the distributions of intervals preceding and those following the coincident firings relative to that of all the intervals between impulses in each train, it is possible to infer restrictions upon the ways in which the correlating influence interacts with other sources of variability for each cell. This is applied to pairs of cells in two systems, one in which the coincident firing is due to an input common to the two cells, and one in which one cell is presynaptic to the other.

Introduction

Each spiking neuron in a sensory system produces an impulse train that is driven by stimuli but includes a stochastic component. Despite this component, neurons commonly show cross-correlation of their impulse trains, even in the absence of stimulation.

Cross-correlation may arise either because the two correlated neurons share a common variable input, or because one of the neurons provides synaptic input to the other. When both neurons are at the same level in the nervous system, it is often assumed that they share a common input; direct monosynaptic crosstalk can often be rejected based on a broad time window within which the probability of joint firing is affected. Conversely, the monosynaptic influence of one neuron upon another is often verified by the minimal variability in the relative timing of impulses in the two cells, at a delay consistent with an intervening synapse.

Most analyses of cross-correlation have concentrated on cells at the same level, for which there is a question of whether there are common inputs, direct crosstalk, or feedback circuits. Cross-correlation in pairs for which monosynaptic transfer is likely have concentrated on demonstrating that a relationship indeed exists. This report is an examination of how the distribution of intervals can characterize the mechanism underlying cross-correlation. The analysis is applied to one system in which the cells presumably share a common input, and to another system in which one cell is presynaptic to the other.

Section snippets

Cross-correlation of retinal ganglion cells

In the vision literature, analyses of cells at comparable levels have examined the possible interrelationships of cortical cells (Engel et al., 1992, Ghose et al., 1994, Singer and Gray, 1995), or the cross-correlation of ganglion cells in the retina (Arnett, 1978, Arnett and Spraker, 1981, Ginsburg et al., 1984, Mastronarde, 1983a, Mastronarde, 1983b, Meister et al., 1995, Meister, 1996). Retinal ganglion cells provide a particularly interesting system; these cells, which provide the sole

Transmission from retinal ganglion cells to thalamus

The preceding section considered a case in which cells at the same processing level exhibit cross-correlation, presumably due to a common variable input. Analysis of the intervals flanking coincidences constrained the models for how such an influence might affect each cell. This section considers a case in which one of the cells is a known input to the other; as before, an analysis of intervals can help reveal the underlying circuitry.

Discussion

The distributions of intervals preceding and following coincident impulses between pairs of neighboring retinal ganglion cells place constraints upon the mechanism by which cross-correlation may be realized. A model in which impulses are interjected into the two ongoing impulse trains does not satisfy these constraints; neither does a linear model in which a common source of variability adds to the variability in each ganglion cell. A nonlinear model is required; one in which the common source

Acknowledgements

I am grateful to my colleague Roger Zimmerman, and former students Kenneth Ginsburg and James Johnsen, who are responsible for collecting most of the ganglion cell data reported here. I am also grateful to Brian Cleland, who allowed me to assist him in his laboratory in Sydney, Australia, and without whom the LGN data could not have been obtained. Data collection was supported by NIH grant EY01951, the NH and MRC of Australia, and Fogarty International Center Senior International Fellowship

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