Design of a Trichromatic Cone Array

Abstract

Cones with peak sensitivity to light at long (L), medium (M) and short (S) wavelengths are unequal in number on the human retina: S cones are rare (<10%) while increasing in fraction from center to periphery, and the L/M cone proportions are highly variable between individuals. What optical properties of the eye, and statistical properties of natural scenes, might drive this organization? We found that the spatial-chromatic structure of natural scenes was largely symmetric between the L, M and S sensitivity bands. Given this symmetry, short wavelength attenuation by ocular media gave L/M cones a modest signal-to-noise advantage, which was amplified, especially in the denser central retina, by long-wavelength accommodation of the lens. Meanwhile, total information represented by the cone mosaic remained relatively insensitive to L/M proportions. Thus, the observed cone array design along with a long-wavelength accommodated lens provides a selective advantage: it is maximally informative.

Why Do Axons Differ in Caliber?

“…Why this difference in direction of skew? Note that cones sensitive to middle (M) and long (L) wavelengths capture information at similar rates and constitute 95% of the population (Garrigan et al, 2010). According to the hypothesis, their axon diameters should distribute narrowly and with little skew.…”

Heterogeneity and Efficiency in the Brain

“…Given the known cone spectral sensitivities and noise properties, and a measured distribution of light in different spectral bands of an ensemble of natural images [28], we can evaluate what sorts of cone mosaics will maximize chromatic information transmission. This maximization yields a surpriseVit seems that the relative proportions of L and M cones are largely irrelevant over a sevenfold range, but the fraction of S cones should be less than 10% because there is less visual information in the blue wavelengths after filtering by the medium and pigments in the eye [38]. Satisfyingly, recent anatomical measurements have shown that S cones are rare (less than 6% in most mammals) and that there is massive variability in the L=M cone ratios between humans with normal color vision [39].…”

Optimizing Neural Information Capacity through Discretization

“…The available theoretical results have yielded quantitative explanations for the experimental observation on the number and properties of neuronal sub-types in the retina, long a canonical test bed for theories of cell type specialization (Balasubramanian and Sterling, 2009; Borghuis et al, 2008; Garrigan et al, 2010; Ratliff et al, 2010; Sterling, 1983). A case in point is a recent experimental observation of adapting and sensitizing cell types of retinal ganglion cells (RGCs) that encode the same temporal modulations of light intensities within their receptive fields, but with different thresholds (Kastner and Baccus, 2011).…”

“…Overall, the theory of cell type specialization appears to have passed its first tests when applied to a set of three sub-types of retinal ganglion cells. From here, expanding the framework to describe multidimensional input signals and different metabolic constraints (Borghuis et al, 2008; Fitzgerald and Sharpee, 2009; Ganguli and Simoncelli, 2014; Garrigan et al, 2010; Tkacik et al, 2010) may allow to systematize our understanding of how neuronal types from different species relate to each to each other, for example in the retina. Other sensory systems where information maximization could account for coordinated encoding include olfactory receptor neurons in the fly (Asahina et al, 2009) and chemosensory neurons in C. elegans (Chalasani et al, 2007).…”