Design of a Neuronal Array

Abstract

Retinal ganglion cells of a given type overlap their dendritic fields such that every point in space is covered by three to four cells. We investigated what function is served by such extensive overlap. Recording from pairs of ON or OFF brisk-transient ganglion cells at photopic intensities, we confirmed that this overlap causes the Gaussian receptive field centers to be spaced at ϳ2 SDs (). This, together with response nonlinearities and variability, was just sufficient to provide an ideal observer with uniform contrast sensitivity across the retina for both threshold and suprathreshold stimuli. We hypothesized that overlap might maximize the information represented from natural images, thereby optimizing retinal performance for many tasks. Indeed, tested with natural images (which contain statistical correlations), a model ganglion cell array maximized information represented in its population responses with ϳ2 spacing, i.e., the overlap observed in the retina. Yet, tested with white noise (which lacks statistical correlations), an array maximized its information by minimizing overlap. In both cases, optimal overlap balanced greater signal-to-noise ratio (from larger receptive fields) against greater redundancy (because of larger receptive field overlap). Thus, dendritic overlap improves vision by taking optimal advantage of the statistical correlations of natural scenes.

Predictable irregularities in retinal receptive fields

“…As might be expected, the mean-square error ( Over the range of ⌬L/L values typical of experimental mosaics, the predictions vary within a narrow range centered at Ϸ0.45L. The narrow width of this range explains why predictions made by using various optimization criteria assuming a regular lattice are in such good agreement with experimental data (10,(18)(19)(20) (Fig. 1 A).…”

“…Here, our goals are to find the optimal size of individual RFs based on minimizing the meansquare error or maximizing the number of distinct regions, and to compare the optimal RF size with previous predictions made according to a number of other optimization criteria (10,(18)(19)(20). Next, we will analyze how the retinal performance is affected by lattice irregularities alone, with no asymmetries or variations in RF shapes across neurons.…”

“…The predicted optimal RF size is also advantageous according to a number of other computational measures, such as achieving maximally uniform contrast sensitivity (2), equal accuracy in detecting light whether it falls near a RF center or at an intermediate position (10), and maximizing information about scenes from the natural environment (10,(18)(19)(20). In summary then, even though all of the above analyses ignore irregularities present in real retinal arrays, they all can account for the experimentally observed increase in the average RF size with lattice spacing L, indicating that such a scaling relationship might be functionally advantageous from multiple computational perspectives.…”

“…S1 for how it is derived. If RFs are described as Gaussians, then the width of the Gaussian is found to be ϷL/2 in different species and types of retinal ganglion cells (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) (Fig. 1A), with the exception of some cell types in the salamander retina (5).…”

Local statistics in natural scenes predict the saliency of synthetic textures

“…Examples include: (i) the center-surround receptive field of the retinal ganglion cell, which removes spatial correlations in natural images and decreases retinal redundancy (1-3), (ii) the twofold excess of retinal OFF pathways (encoding negative contrasts) as compared to ON pathways (encoding positive contrasts), which matches the asymmetric contrast structure of natural scenes (4), (iii) cone spectral sensitivities and color opponency in ganglion cells, which maximize chromatic information from natural scenes (5-7), (iv) overlaps of ganglion cell receptive fields within the retinal mosaic, which balance redundancy reduction against signal-to-noise ratio improvement (8,9), and (v) the shapes of the nonlinear response functions of early sensory neurons, and their adaptation to stimulus variance, which have been related to the skewed intensity distributions that occur in natural stimuli (10,11). In all cases, physiological and anatomical characteristics of the visual system are accounted for by a simple efficient coding principle: sensory systems invest their resources in relation to the expected gain in information (4).…”