Functional significance of the taper of vertebrate cone photoreceptors

Abstract

Vertebrate photoreceptors are commonly distinguished based on the shape of their outer segments: those of cones taper, whereas the ones from rods do not. The functional advantages of cone taper, a common occurrence in vertebrate retinas, remain elusive. In this study, we investigate this topic using theoretical analyses aimed at revealing structure-function relationships in photoreceptors. Geometrical optics combined with spectrophotometric and morphological data are used to support the analyses and to test predictions. Three functions are considered for correlations between taper and functionality. The first function proposes that outer segment taper serves to compensate for self-screening of the visual pigment contained within. The second function links outer segment taper to compensation for a signal-to-noise ratio decline along the longitudinal dimension. Both functions are supported by the data: real cones taper more than required for these compensatory roles. The third function relates outer segment taper to the optical properties of the inner compartment whereby the primary determinant is the inner segment's ability to concentrate light via its ellipsoid. In support of this idea, the rod/cone ratios of primarily diurnal animals are predicted based on a principle of equal light flux gathering between photoreceptors. In addition, ellipsoid concentration factor, a measure of ellipsoid ability to concentrate light onto the outer segment, correlates positively with outer segment taper expressed as a ratio of characteristic lengths, where critical taper is the yardstick. Depending on a light-funneling property and the presence of focusing organelles such as oil droplets, cone outer segments can be reduced in size to various degrees. We conclude that outer segment taper is but one component of a miniaturization process that reduces metabolic costs while improving signal detection. Compromise solutions in the various retinas and retinal regions occur between ellipsoid size and acuity, on the one hand, and faster response time and reduced light sensitivity, on the other.

Figure 1.

Electron micrographs of vertebrate photoreceptors illustrating diverse outer segment tapers and ellipsoid morphologies. (A) Goldfish single cone (SC) and rod (R) flanking one member of a double cone (DC). The cone ellipsoids are packed with mitochondria (Mi). Cone outer segments (black arrows) taper, whereas those of the rods do not (white arrow; only a portion of the rod outer segment is visible). (B) Single cone, double cone, and rod of coho salmon. In this species, there is a clear gradient in the size of cone mitochondria from smaller, at the level of the myoid, to larger, at the level of the ellipsoid. (C) Double cone from a mummichog killifish showing megamitochondria (M) associated with the ellipsoid of each double cone member. This species also has ellipsosomes, which arise from megamitochondria as the cristae disappear. (D) Rod and single cone from a bullfrog. The rod mitochondria are long and compacted; the single cone exhibits an ellipsosome-like structure (E*) in the ellipsoid. (E) Two single cones among rods in the bullfrog retina; one of the cones contains an oil droplet (*). Note the large difference in size between rods and cones. (F) Single cones and rods from a Canada goose. The single cones show different types of oil droplets. As in the frog, elongated mitochondria pack rod inner segments, and the mean diameter of cone ellipsoids (entrance aperture) is similar to that of rods. (G) Single cones of the red-eared slider turtle showing large oil droplets and pronounced cone taper. (H) Rods of the mouse retina. The cones in this and similar nocturnal species are hard to identify without molecular markers. Bars, 2 µm.

Figure 2.

Drawings of single cones from fresh retinal preparations illustrating the morphological parameters measured as well as the taper angle, τ. The cellular dimensions were obtained from video images recorded via a microscope equipped with a calibrated infrared-sensitive video system. (A) Single cone from blue gill sunfish. (B) Single cone from leopard frog. (C) Cone outer segment (left) from B and an idealized representation of that of the optically equivalent rod (right). The equivalency is based on the assumption that both cells have equal entrance aperture with diameter d_i and that the cone ellipsoid funnels the incident flux to the outer segment without loss. The cellular dimensions (in µm) for these cones were as follows: (A) for the blue gill sunfish, d_i = 8.3, d_o = 5.0, d_z = 2.9, z = 18, and the inner segment length, l_i = 25.2; (B) for the leopard frog, d_i = 7.2, d_o = 2.8, d_z = 1.3, z = 6.3, and l_i = 17.5. The parameter z, in these two cases, equals the outer segment length, and d_z is the diameter at the tip of the outer segment. The asterisk in B depicts an oil droplet.

Figure 3.

Ratio of observed taper to critical taper (τ/τ′) in relation to observed taper (τ). (A) Species from which live cell measurements were obtained. (B) Species for which measurements originated from the literature. Recall that taper is defined as the angle between the axis of the cone and the inclination of the contour line, which, upon precession, describes the conical surface. Critical taper is the taper required to exactly compensate for light flux diminution by absorption (self-screening) so that flux density remains invariant throughout the outer segment. In general, taper was highest for species with focusing organelles in the ellipsoids.

Figure 4.

Regressions of expected rod/cone ratios as a function of those observed for primarily diurnal (though birythmic) species. (A) Data for species from which live cell measurements were obtained. (B) Data for species for which measurements originated from the literature.

Figure 5.

Regression of expected rod/cone ratios as a function of those observed for fully diurnal and primarily nocturnal species. Data originated from the literature.

Figure 6.

Regressions of the ratio of realistic to critical characteristic length (a_z′⁻¹/a_h1⁻¹) as a function of concentration factor (F_C). Recall that the characteristic length is the distance along the outer segment at which the light flux, Φ, falls to 0.368 of the incident light flux at the base, Φ_o. The concentration factor is the square of the ratio between ellipsoid diameter at its largest cross section and outer segment base diameter, i.e., F_C = (d_i/d_o)², and represents coupling of light flux without loss from ellipsoid to outer segment. (A) Data for species from which live cell measurements were obtained. (B) Data for species for which measurements originated from the literature.