How much the eye tells the brain

Abstract

In the classic "What the frog's eye tells the frog's brain," Lettvin and colleagues showed that different types of retinal ganglion cell send specific kinds of information. For example, one type responds best to a dark, convex form moving centripetally (a fly). Here we consider a complementary question: how much information does the retina send and how is it apportioned among different cell types? Recording from guinea pig retina on a multi-electrode array and presenting various types of motion in natural scenes, we measured information rates for seven types of ganglion cell. Mean rates varied across cell types (6-13 bits . s(-1)) more than across stimuli. Sluggish cells transmitted information at lower rates than brisk cells, but because of trade-offs between noise and temporal correlation, all types had the same coding efficiency. Calculating the proportions of each cell type from receptive field size and coverage factor, we conclude (assuming independence) that the approximately 10(5) ganglion cells transmit on the order of 875,000 bits . s(-1). Because sluggish cells are equally efficient but more numerous, they account for most of the information. With approximately 10(6) ganglion cells, the human retina would transmit data at roughly the rate of an Ethernet connection.

Figure 1

Statistics of Natural Stimuli Differ from Those of White NoiseNatural movies mimicked saccades, optic flow, and object motion [10]. To mimic fixational eye movements, we used Psychophysics toolbox [40, 41] to jitter van Hateren's images (http://hlab.phys.rug.nl/archive.html) randomly over the retina, with step size and velocity matched to that measured for the rabbit [9, 42]. When projected onto the retina, stimuli filled approximately 4 mm × 4 mm with mean luminance corresponding to photopic vision. The photon absorption rates were 2900 and 440 photons · s⁻¹ for the M and S cones, respectively. Each movie lasted 20–27 s and was repeated 60–100 times. Intensity distributions and amplitude spectra were obtained after averaging over all frames.

1. Intensities in white noise (gray lines) are equally represented, but in natural scenes (black lines), lower intensities are more likely.

2. Spatial frequencies in white noise have equal amplitude, but in natural scenes, amplitude declines with frequency (slope ∼ −1.5). Spectra have been separated (shifted up) for clarity.

3. Temporal frequencies in white noise have equal amplitude, but in natural motion, amplitude declines with frequency (slope ∼ −1.0). Spectra have been shifted up for clarity.

Figure 2

Four Types of Natural Motion Evoked Similar Spike Patterns within a Cell Type But Different Patterns Across Types

1. All five cells were recorded simultaneously (multi-electrode array). Each cell responded similarly to all three motion stimuli. The brisk-transient and ON-OFF direction-selective (DS) cells responded with high peak rates and low firing fractions, whereas the brisk-sustained, ON DS, and local-edge cells responded with lower peak rates and higher firing fractions. The brisk-transient and ON-OFF DS responses showed the lowest spike-time jitter across trials, whereas the brisk-sustained and local-edge responses showed the highest. As expected for sluggish types, mean firing rates were about half that of the brisk cell types [2].

2. Cells were recorded singly (loose-patch). Spike patterns to simulated fixational eye movements resembled those of the other types of motion.

Figure 3

All Cell Types Transmitted Information with Similar Efficiency Because Total Entropy and Noise Entropy were Correlated by Spike Train BurstsInformation rate (total entropy–noise entropy) was estimated by the direct method [43] with bin width (Δt) = 5 ms and spike word-lengths up to eight digits. Bin width was set by the longest refractory period (5 ms for local-edge cells). Estimates of total and noise entropy were extrapolated to infinite data size [44]. Estimated total and noise entropies were within 15% of that calculated for the longest word. A solid line shows the coding capacity of a ganglion cell assuming noiseless firing with no spike correlations (C(R, Δt); see text). A dashed line shows the fraction of coding capacity (ε that best fit information rate, total entropy, or noise entropy).

1. Information rate was 26% of coding capacity (0.26 C(R,Δt)). K² (percent of variation unexplained by coding capacity equation) was 19%.

2. Total entropy was 91% of coding capacity. K² = 4%.

3. Noise entropy was 65% of coding capacity. K² = 12%.

4. A dashed line indicates the fraction of coding capacity per spike, (0.26 * C(R,Δt))/R. Lower rates carry more bits per spike.

5. Line is least squares fit: slope = 1.2 (R² = coefficient of determination). Noise entropy is strongly correlated with total entropy.

6. Burst fraction is the fraction of spikes with interspike intervals <6 ms. Line is least squares fit: slope = −0.6. Total entropy as a fraction of capacity decreased with burst fraction.

7. Line is least squares fit; slope = −0.6. Noise entropy as a fraction of capacity decreased with burst fraction.