Estimating the amount of information conveyed by a population of neurons

Abstract

Recent technological advances have made the simultaneous recording of the activity of many neurons common. However, estimating the amount of information conveyed by the discharge of a neural population remains a significant challenge. Here we describe our recently published analysis method that assists in such estimates. We describe the key concepts and assumptions on which the method is based, illustrate its use with data from both simulated and real neurons recorded from the lateral geniculate nucleus of a monkey, and show how it can be used to calculate redundancy and synergy among neuronal groups.

Keywords: frequency analysis; information; neural population; redundancy.

Figure 1

The three steps that are required for calculating the information carried by a neural population: Fourier representation of each spike train; variance estimation, and entropy-information calculation.

Figure 2

Left: the two cells (A and B) fire independently; a two-dimensional distribution is the product of two one-dimensional distributions. Right: the two cells (C and D) are correlated in this bi-variate Gaussian distribution; when new coordinates (red axes) are chosen, the distribution becomes a product of two one-dimensional Gaussian distributions.

Figure 3

Cumulative information rates as a function of frequency for single cells and for a neural population. Colored lines near the bottom indicate the cumulative information for each of the eight simulated cells (A) and eight LGN cells (B). In simulated cells, the sum total information of all individual cells exceeds the information conveyed by the group together, indicating redundancy. In the monkey LGN cells, the sum total exceeds the group information until approximately half the stimulus frequency, after which synergy dominates.

Figure 4

Redundancy and Synergy among groups of neurons in a population. Information rates from simulated Poisson spike trains (A), created to match the firing rates of monkey LGN neurons (B). In both panels the eight cells were split into two groups, matched approximately for firing rates. The total group information is shown in a dashed blue line, and the summed information from two groups is shown in a solid red line. For the LGN cells, but not for the simulated cells, the curves cross around 30 Hz: below 30 Hz we see redundancy, while above it we see synergy.