Image Anal Stereo l 2009;28:1-10 Review Paper 1 STEREOLOGY AND SOME STRUCTURAL CORRELATES OF RETINAL AND PHOTORECEPTOR CELL FUNCTION TERRY M MAYHEW Centre for Integrated Systems Biology and Medicine , School of Biomedical Sciences, University of Nottingham, Queen's Medical Cent re, Nottingham NG7 2UH, UK e-mail: terry.mayhew@nottingham.ac.uk (Accepted March 3, 2009) ABSTRACT The retina is the part of the eye which detects light, tr ansduces it into nerve impulses and plays a significant role in visual perception. Sensitivity to light is multi -factorial and depends on the properties of photopigment molecules, their synthesis and incorporation into photoreceptor membranes and the neural circuitry between photoreceptor cells, bipolar neurons and ganglion neurons. In addition, it depends on structural factors such as the absolute and relative numbers of different types of photoreceptor neurons, their subcellular morphology, their distribu tion across the retina and the physical di mensions (especially surface areas) and spatial arrangements of their photoreceptor membranes. At the molecular level, these membranes harbour photosensitive pigment molecules comprising transmembrane glycoproteins (opsins, which vary between photoreceptor cells) and a non-protein chromophore. Phototransduction involves a conformational change in the chromophore and activation of an opsin. A transducer G protein, tran sducin, lowers levels of cGMP and triggers changes in membrane ion permeability including the closure of Na + channels. This causes the plasmalemma to become less depolarized and the relative hyperpolarization stimulates ganglion cells whose axons form the optic nerve. Phosducin is a light-regulated phosphoprotein located in inner and outer segments of rod photoreceptor cells. It modulates phot otransduction by binding to beta and gamma subunits of transducin. This review briefly illustrates ways in wh ich stereology can contribute to our understanding of these processes by providing quantitative data on phot oreceptor number, disk membrane surface area and the subcellular immunolocalisation of key molecules. Keywords: immunogold quantification, membrane surface area, number, photoreceptor neurons, retina, stereology. INTRODUCTION In adult humans, the eye has a diameter of about 20 mm and about 70% of its internal surface is occupied by the retina. It has been estim ated that there are about 120 million photoreceptor neurons (114 million rods and 6 million cones) within the retina and about 1.1 million fibres within the optic nerve (Kupfer et al., 1967; Williams et al., 1989). This represents an overall photoreceptor:fibre convergence ratio of 110:1 but the ratio varies across the retina from centrally to peripherally and between r ods and cones. The fovea centralis contains only cones and displays the greatest visual acuity and the cone:fibre convergence ratio is 1:1. By contrast, the periphery is rod-dominated, there is greater sensitivity and reduced acuity and many rods converge on each bipolar neuron and many bipolar neurons converge on a single ganglion cell. In the vertebrate neural retina, light sensitivity is multi-factorial and depends on the properties of photo-pigment molecules, their synthesis and incorporation into photoreceptor membranes and the neuronal circuitry between photorecepto r, bipolar and ganglion neurons. In turn, pigment incorporation and light-responsiveness are influenced by structural factors, e.g. the number and subcellular morphology of photoreceptor cells (PRCs), their spatial distribution and the physical dimensi ons and arrangements of their photoreceptor membranes. PRCs are arranged radially through several layers of the retina and show differences in morphology, function and behaviour which distinguish them as rods or cones. Despite the differences, each PRC possesses well-defined subcellular domains concerned with particular functions in cluding phototransduction, aerobic metabolism, gene expression and transmitter release. Phototransduction, the conversion of incident light into nerve impulses (Wassle and Boycott, 1991), occurs in the outer segment (OS) domain in which photoreceptor membranes are arranged as stacks of MAYHEW TM: Photoreceptor cells and the retina 2 disks, the sizes and numbers of which vary according to species and PRC type and position. Photoreceptor membranes are renewed in a circadian rhythm following shedding at the OS tips and subsequent endocytosis by cells of the retinal pigment epithelium, RPE (Goldman et al., 1980; Lavail, 1980; Cahill and Besharse, 1995). Rods and cones differ not only in terms of the shape of the OS domain but also in the mechanisms of renewal of photoreceptor membranes (Steinberg et al., 1980; Eckmiller, 1987; 1990). PRCs also vary in their responses to lighting conditions by changes in length (Burnside and Dearry, 1986; Rey and Burnside, 1999). Photoreceptor disk membranes harbour photo- sensitive pigment molecules comprising one of a number of transmembrane glycoproteins (opsins) and a non-protein chromophore (11-cis-retinal). Opsins vary between PRCs and between cones. In darkness, the rod cell plasmalemma is depolarized and the rods secrete neurotransmitters. Channels are kept open by cyclic GMP (cGMP). Phototransduction involves a conformational change in the chromophore and activation of an opsin. Phosducin, a light-regulated phosphoprotein, binds to subunits of transducin, a transducer G protein (Lee et al., 1987; Savage et al., 2000), and this lowers levels of cGMP and triggers changes in ionic permeability (including the closure of Na + channels). The PRC plasmalemma becomes less depolarized and the relative hyperpolarization ultimately leads to ganglion cell stimulation (Grusser, 1983; Liebman et al., 1987). While phototransduction o ccurs in the OS domain of PRCs, aerobic metabolism occurs in the ellipsoid domain which is rich in mitochondria (55-85% of ellipsoid volume in macaques, Hoang et al ., 2002). Gene expression and protein synthesis occur in the cell body of PRCs. Another domain, the myoid, lies between the OS and cell body and it is in this domain that PRC elongation/contraction occur in response to changes in light conditions (Rey and Burnside, 1999). These movements help to optimise the position of OS segments: rods elongate in bright light whereas cones elongate in dim light or darkness. Finally, transmitter release by exocytosis takes place in the synaptic terminal. From the latter site, impulses are transmitted to bipolar neurons and, from them, to ganglion neurons whose axons form the optic nerve. Here, we illustrate some ways in which stereology can contribute to our understanding of these processes, in particular visual phototrans duction. This is illustrated by taking examples from studies on the numbers of PRCs and their disk membrane surface areas and on the subcellular distribution of immunolabelled phosducin within PRC domains. EXAMPLE 1: THE RETINA AND ITS PHOTORECEPTORS This example draws on a stereological study of rat retina (Mayhew and Astle, 1997) designed in order to characterise PRCs at w hole organ and average cell levels. To this end, eyeballs were removed from inbred rats, immersed in cold fixative solution (2% glutaral- dehyde, 1% paraformaldehyde, 3 mM calcium chloride and 1% sucrose in 0.1 M cacodylate Millonig's buffer, pH 7.4) and, after fixation, trimmed of excess fat. Subsequently, they were postfixed with 1% osmium tetroxide in Millonig's buffer, washed in cacodylate buffer plus 6% sucrose (pH 7.2) and block-stained in 2% uranyl acetate in distilled water. Following dehy-dration, pieces of tissue from each eye were embedded in Transmit resin at a standard orientation. Sampling The aim of sampling was to accord all regions (and all PRCs) an equal chance of being selected. The sampling was multistage (Mayhew and Astle, 1997) and, consequently, it was important to aim for consistency of definition of tissue compartments when moving from one stage to another (Cruz-Orive and Weibel, 1981). The design provided three primary outcome measures: [a] total retinal volume, V ret; [b] total number of PRCs per retina, N prc, and [c] total surface area of disk membranes per retina, S dm. Stage 1 sampling. The aim here was to obtain macroscopic estimates of retinal surface area, S ret. Under a binocular dissecting microscope, two mutually perpendicular lengths across the eyeball (the distances between tangents to its outer surface) were measured using the parallel lines of an eyepiece graticule. This was superimposed on the projected image of each eyeball so as to be random in position and orientation. After measurement, the eyeball was rotated and the exercise repeated. The average length was then taken to correspond to eyeball mean projected height and used to obtain rough estimates, assuming sphericity, of eyeball volume and outer surface area. To calculate S ret, each eyeball was cut along its visual axis. After removing the lens and cornea, the remaining tissue was cut into several pieces and flattened under a glass coverslip by gentle pressure. Stage 2 sampling. The aim here was to derive light microscopic (LM) estimates of mean retinal Image Anal Stereo l 2009;28:1-10 3 thickness, T ret, and the volumes of the retina and its outer nuclear and outer segment layers (V ret, V onl and Vosl respectively). Pieces of retina were positioned and oriented in resin blocks so that full-depth (vertical) slices could be cut. Blocks selected for microtomy by the lottery method were rotated about their long axis in order to satisfy sampling conditions for estimation of surface areas from vertical sections (Baddeley et al., 1986). Sections approximately 1 μm thick were mounted on glass slides and stained with toluidine blue. Sectional images were projected onto white paper at a final magnification of x 1550 which was calibrated using a stage micrometer scale as an external standard. By means of two step-motors, LM fields of view were selected in a system atic uniform random fashion (Gundersen and Jensen, 1987; Mayhew, 2007). Tracings were made of the boundaries of the entire retina (extending from the outer segment/RPE interface to the internal limiting membrane), the outer segment layer and outer nuclear layer. Stages 3 and 4 sampling. Stage 3 provided low- power transmission electron microscopic (TEM) estimates of the volume-weighted mean volume, ν Vnuc, of PRC nuclei within the outer nuclear layer, and the volume density of nuclei in the layer, Vnuc/Vonl. At stage 4, high-power TEM estimates of the packing density of PRC disk membrane surface area, S dm, within the volume of the OS layer (Sdm/Vosl) were derived. Ultrathin sections (thickness ca. 70 nm) were cut from the same blocks, mounted on copper support grids, and stained with lead citrate. TEM fields were recorded and printed at x 2216 (outer nuclear layer) or x 26860 (outer segment layer) with the aid of grating replicas as external calibration standards. Montages were made so that the vertical direction could be monitored within each layer. Stereological estimations Stage 1 estimates. Retinal surface area was estimated by test point counting using the relation est S ret = ΣPret x a(p), where a(p) is the area associated with one test point. Retinal area, divided by the outer area for the eyeball, gave an estimate of the fractional surface occupied by retina. Stage 2 estimates . Projected images of full-depth vertical slices were used to obtain estimates of the arithmetic mean thickness of the retina, T ret, which was taken to be the mean distance from the inner aspect of the RPE to the internal limiting membrane. The volume of the retina was estimated as est V ret = S ret x T ret. In addition, the thicknesses of the outer nuclear and OS layers were recorded and the relative thicknesses used as estimators of relative volumes. Stage 3 estimates. Micrographs of the outer nuclear layer provided estimates of the volume-weighted mean volumes of PRC nuclei and the fractional volume of the layer occupied by those nuclei. Estimates of νVnuc were obtained by measuring point-sampled intercept lengths (Gundersen and Jensen, 1985) using test lines superimposed at sine-weighted angles with respect to the vertical axis on the sections (Baddeley et al ., 1986; Cruz-Orive and Hunziker, 1986). A sine- weighted angle between 0 o and 97o was chosen at random for the first montage and subsequent montages from the same retina were analysed by rotating the lines systematically at an angle of 37o. When a test point fell on a nuclear profile, the length of line passing through the point in the specified direction and intercepting the nuclear profile was measured. The estimate of νVnuc was calculated from the mean of the cubed intercept lengths (l3) using the equation est νVnuc = (π/3) x (l3)/M3, where M is the final linear magnification. This volume overestimates the number-weighted mean volume, ν Nnuc, of nuclei and the relative bias was estimated using the selector (Cruz-Oriv e, 1987). The coefficient of variation (CV) of the distribution of nuclear volumes within a retina averaged 57 %. Therefore, the relative bias was about 33% and nuclear volume and number estimates were corrected for this degree of bias: est N prc = V onl x (V nuc/Vonl) x 1/νNnuc, where νVnuc represents the number-weighted mean volume of PRC nuclei. Stage 4 estimates. Micrographs of the outer segment layer were sampled in order to estimate the surface density of disk membranes in PRC outer segments and the fractional volume of the layer occupied by those segment s. Again, the latter was estimated by test point counting. Disk membrane surface densities within outer segments were estimated by counting intersections usin g cycloid test arc lattices (Baddeley et al., 1986) and the formula est S dm/Vos = 2 x ΣIdm/ΣPos x (l/M), where ΣPos x (l/M) is the total length of cycloid arcs on the specimen scale. Micrographs were sampled only where OS membrane images were clear so as to avoid errors due to image loss by oblique sectioning (Mayhew and Reith, 1988). MAYHEW TM: Photoreceptor cells and the retina 4 The surface density of disk membranes in the OS was multiplied by the fractional volumes of outer segments in order to calculate the membrane surface density in the complete layer, S dm/Vosl, and then the total membrane surface per retina was estimated as est S dm = V osl x (S dm/Vosl). Findings Key outcome measures are summarised in Table 1. The retina possessed a volume of roughly 16 mm3 and a total surface area of 80 mm2. The latter represents about 56% of the external eyeball surface but this slightly underestimates the fraction of the internal surface occupied by retina because it does not take into account the thickness of the eyeball. The retina also contained 30 million PRCs each possessing, on average, about 700 disks per stack and 2600 μm 2 of disk membrane surface area. Collectively this equates to a global surface area of approximately 770 cm2 per retina. EXAMPLE 2: THE IMMUNOLOCALIZATION OF PHOSDUCIN IN RODS This example illustrates an application of recently- developed immunogold coun ting methods for high- resolution subcellular localization of interesting mole- cules (Mayhew, 2007; Mayhew and Lucocq, 2008a;b). In particular, their practical utility is illustrated by analysis of gold particle s labelling the phosphoprotein, phosducin, in subcellular domains of rod photoreceptors in the retinas of light- and dark-adapted groups of rats (Chen et al., 2005). Each domain represents a volume- occupying compartment. Four rats per group were examined. Following enucleation, eyeballs were fixed with 2% paraformal-dehyde and 2% glutaralde hyde in 0.1 M phosphate buffer at room temperature. After a buffer wash, retinas were cut into smaller fragments, dehydrated in increasing concentrations of ethanol and block-embedded in LR White embedding medium. From a random selection of blocks, ultrathin sections (50-100 nm thickness) running vertically through the retina were cut and collected on copper support grids for TEM analysis. Post-embedding immunogold labelling was under- taken (Chen et al., 2005). Sections were incubated in buffer containing 10% donkey serum followed sequen- tially by glycine, buffer wash and overnight incubation with phosducin primary antibody diluted 1:1000 in buffer containing bovine serum albumin. Grids were subsequently washed again prior to incubation with the secondary antibody (donkey anti -rabbit IgG) conjugated with 12-nm colloidal gold particles. Following rinses in deionized water, randomly-chosen sections were contrasted with 1% uranyl acetate and randomly-chosen fields of view were recorded for purposes of gold counting. Stereological estimations Gold particles were counted in rod PRCs and assigned to one of five compartments, each of which constituted a subcellular dom ain. The selected domains were the OS, ellipsoid, myoid, nucleus and synaptic terminal. In the original study (Chen et al ., 2005), percentage frequencies of gold particle distributions were presented for each domain together with labelling densities expressed as gold particles per μm2. In practice, a simpler and more efficient estimator of labelling density is gold particles per test point where points are randomly superimposed on TEM images (Mayhew et al ., 2003). For present purposes, the original data were used to estimate gold and point counts and these were normalised to roughly 200 per group to represent a reasonable workload in terms of overall precision of estimation (Lucocq et al., 2004). Table 1. Stereological estimates for the entire retina and aver age PRC. Values are means (CVs) for n=6 rats (data based on Mayhew and Astle, 1997). Variable Quantity per eyeball Volume of retina, mm3 15.9 (8%) Volume of outer segment layer, mm3 1.6 (14%) Volume of outer segments, mm3 1.1 (14%) Surface area of eyeball exterior, mm2 144 (3%) Surface area of retina, mm2 80.4 (4%) Surface area of disk membranes, mm2 76700 (24%) Number of PRCs (rods and cones), millions 30 (18%) Disk membrane area per PRC, μm2 2610 (27%) Number of disks per stack 704 (25%) Image Anal Stereo l 2009;28:1-10 5 The observed gold particles falling on different domains in light- and dark-adapted retinas were used to test the null hypothesis of no difference in phosducin labelling distributions between the two study groups. For within-group comparisons, the observed gold particles and predicted distributions (obtained from point counts) were used to test the null hypothesis of no difference in labelling between compartments. The between-group comparisons of labelling patterns were undertaken using the raw gold counts on each subcellular domain followed by a c x r contingency table analysis with c = 2 columns (= photo- adaptation groups) and r = 5 rows (= subcellular domains). The total chi-squared, χ 2, for 4 degrees of freedom (2-1 columns x 5-1 rows) was used to decide whether the group labelling di stributions were different. For within-group comparisons of labelling distributions, a two-sample χ2 analysis was applied with c = 2 columns (= observed and expected distributions) and r = 5 rows (= subcellular domains). From observed (N o) and expected (N e) gold counts, relative labelling indices (RLI = N o/Ne) were calculated for each PRC domain. Each RLI value indicates the degree to which a subcellular domain is labelled in comparison to random labelling. The distribution of expected (‘randomly-distributed’) gold gold particles is simulated simply by randomly superimposing lattices of test points (Mayhew et al., 2002). If a domain is preferentially labelled, RLI > 1 but it is necessary to confirm this by monitoring the corresponding partial χ 2 values for each domain. The total χ2 for 4 degrees of freedom (2-1 columns x 5-1 rows) indicates whether any of the domains are preferentially labelled. This required that two criteria were met: (i) the domain RLI had to be > 1 and (ii) its partial χ2 value had to account for 10% or more of total χ2 (Mayhew, 2007; Mayhew and Lucocq, 2008b). Findings Results of TEM analysis of gold particle probes localising phosducin in the selected domains of light- and dark-adapted groups are summarised in Tables 2-4. For the between-group comparison (Table 2), total χ 2 amounted to 4.74 and, with 4 degrees of freedom (df), this corresponded to a probability level of P = 0.315. Consequently, the null hypothesis of no difference between groups was accepted. The distribution of phosducin labelling did not shift between compartments as a result of photo-adaptation. Two within-group comparisons were drawn, the one for domains in light-adapted eyes and the other for those in dark-adapted eyes. In the light-adapted group, χ 2 analysis yielded a total value of 226.6 and, for df = 4, this corresponded to P < 0.001 (Table 3). The null hypothesis was rejected and we conclude that the distribution of phosducin is not random. Analysis of RLI values indicated three cell domains with RLI > 1. However, only the myoid and synapse domains showed partial χ 2 values which made substantial contributions to the total. These amounted to roughly 27% (myoid) and 49% (synaptic terminal) of total χ2. We conclude that the synapse domain showed almost 4-fold higher labelling, and the myoid domain almost 3-fold higher labelling, than might be predicted on the basis of random labelling. Similar conclusions were drawn when domain labelling patterns were compared in the dark-adapted group (Table 4, P < 0.001). In this case, myoid and synapse domains had RLI values of 2.10 and 3.88 and partial χ 2 values accounting for 14% and 68% respectively of total χ2. Table 2. Subcellular localization of gold-labelled phosducin in light- and dark-adapted groups of rod cells. Values are observed (expected) numbers of gold particles in each domain (based on data in Chen et al., 2005). Contingency table analysis reveals that labelling distributions in light- and dark-adapted groups are not significantly different (total χ2 = 4.74, degrees of freedom = 4, P = 0.315). Rod Cell Domains Light-adapted Gr oup Dark-adapted Group Row Totals χ2 values Outer segment 30 (33.5) 34 (30.5) 64 0.37, 0.41 Ellipsoid 55 (51.3) 43 (46.7) 98 0.26, 0.29 Myoid 52 (46.1) 36 (41.9) 88 0.76, 0.83 Nucleus 32 (37.7) 40 (34.3) 72 0.87, 0.95 Synaptic terminal 51 (51.3) 47 (46.7) 98 0.00, 0.00 Column Totals 220 (220) 200 (200) 420 4.74 MAYHEW TM: Photoreceptor cells and the retina 6 DISCUSSION EXAMPLE 1: THE RETINA AND ITS PHOTORECEPTORS This example was based on a study prompted by the desire to establish stereological baseline data on the number of PRCs and the surfaces of their disk membranes (Mayhew and Astle, 1997). These structural quantities are important correlates of retinal function. The findings revealed the substantial extent of disk membrane area (770 cm 2) created by densely packing 30 million PRCs on a retinal surface of only 80 mm2. Volume-weighted mean volumes (Gundersen and Jensen, 1985; Baddeley et al., 1986) were converted to number-weighted volumes using correction factors obtained using the selector (Cruz-Orive, 1987). These correction factors cannot be transferred uncritically to other species, or even to retinas in other experimental groups from the same species, because the distribution of nuclear volumes may vary with experimental manipulation. Instead, it would be preferable to adopt a direct approach to estimating PRC number (and separate numbers for rods and cones) using some variant of the disector or fra ctionator principles (Sterio, 1984; Gundersen, 1986; 2002). Resolving rods and cones would need to be undertaken using morphological or other criteria. Because of the dense packing of PRC nuclei within the outer nuclear layer, such estimates are probably best obtained using the optical rather than the physical disector. In the original study (Mayhew and Astle, 1997), this would have been more technically demanding since combined LM and TEM was required in order to estimate disk membrane areas. A practical benefit of using volume-weighted mean is that it can be estimated without knowing section thickness or making assumptio ns about nuclear shape. The bias arising from assuming that each PRC has one nucleus is likely to be negligible and biases arising from the presence of cone nuclei (which appeared to be bigger) are also likely to be trivial since there is a consensus that cones account for a tiny proportion (< 4%) of all PRCs (Lavail, 1976; Carter-Dawson and Lavail, 1979; Mayhew and Astle, 1997). Previous studies on primates have indicated that there are 700-1300 disks per OS (Young, 1967; Williams et al., 1989). The figure for rat retina, 700 Table 3. Subcellular localization of gold-labelled phosducin in light-adapted rod cells (based on data in Chen et al., 2005). Two-sample chi-squared analysis reveals that the labelling distribution is not random (total χ 2 = 226.6, degrees of freedom = 4, P < 0.001). Three domains appear to be preferentially labelled on the basis of their relative labelling index (RLI > 1) but only the myoid and synapse domains can be regarded as preferentially labelled because their partial χ2 values make substantial contributions to total χ2 (accounting for about 27% and 49% respectively). Rod Cell Domains Observed Golds, N o Test Points, P Expected Golds, N e RLI = N o/Ne χ2 values Outer segment 30 65 70.10 0.43 22.9 Ellipsoid 55 39 42.06 1.31 4.0 Myoid 52 17 18.33 2.84 61.8 Nucleus 32 71 76.57 0.42 25.9 Synaptic terminal 51 12 12.94 3.94 111.9 Column Totals 220 204 220 1.00 226.6 Table 4. Subcellular localization of gold-labelled phosducin in dark-adapted rod cells (based on data in Chen et al., 2005). Chi-squared analysis reveals that the labelling distribution is not random (total χ2 = 147.4, degrees of freedom = 4, P < 0.001). Three domains appear to be preferentially labelled (RLI > 1) but only the myoid and synapse domains can be regarded as preferentially labelled because their partial χ2 values make substantial contributions to total χ2 (accounting for about 14% and 68% respectively). Rod Cell Domains Observed Golds, N o Test Points, P Expected Golds, N e RLI = N o/Ne χ2 values Outer segment 34 61 61.62 0.55 12.4 Ellipsoid 43 38 38.38 1.12 0.6 Myoid 36 17 17.17 2.10 20.7 Nucleus 40 70 70.70 0.57 13.3 Synaptic terminal 47 12 12.12 3.88 100.4 Column Totals 200 198 200 1.00 147.4 Image Anal Stereo l 2009;28:1-10 7 disks per OS, is at the lower end of this range. For the mouse retina, samples taken from areas of high disk packing density suggest values of 500 (cones) to 980 (rods) disks per cell (Carter-Dawson and Lavail, 1979). These comparisons imply that the membrane amplification factor within PCRs (roughly equal to twice the disk number per cell) is smaller in rats than primates. Since OS diameters (1-2 μm in primates and 1.4 μm in rats) and disk thicknesses (ca. 20 nm) seem to be similar between species, the figure of 120 million PRCs for the human retina suggests a total disk membrane area of 6000 cm 2 and this area is roughly 8 times more extensive than in the rat retina. Whilst the observed coeffi cient of variation between rats was relatively low (2-14%) for several variables, it was greater (18-27%) for the PRCs and their disk membranes. The higher CVs for the latter variables probably reflect the fact that the numbers and sizes of PRCs vary across the retina and that disk membrane loss and renewal vary through the day (Steinberg et al., 1973; Goldman et al., 1980; Lavail, 1980; Cahill and Besharse, 1995). The disk membrane surface area (ca. 770 cm2) represents a substantial substrate on which to incorporate photopigment molecules. This area is associated with a stack of 700 disks and, if the phagocytosis of disk membranes by RPE cells operates at a comparable rate in the rat to that in humans (turnover every 10 days, see Young, 1967), each PRC would have to renew 70 disks every day. At the cellular level, this is equivalent to about 260 μm 2 of photoreceptor membrane but, for the retina as a whole, 77 cm2 of membrane per day. It is worth noting that the latter is almost 54-fold greater than the surface area of the eyeball exterior. Morphometric studies on the rat optic nerve have established its fibre content at 100,000 to 140,000 (Treff et al ., 1972; Mayhew, 1990; Fukui et al ., 1991). With the present estimate of 30 million PRCs, this equates to a convergence ratio of roughly 260:1. This is higher than the va lue of 110:1 suggested for human retina (Kupfer et al ., 1967; Williams et al ., 1989) and is consistent with the greater sensitivity of the scotopic retina of the rat. EXAMPLE 2: THE IMMUNOLOCALIZATION OF PHOSDUCIN IN RODS Based on data presented in Chen et al. (2005), the findings illustrate the value of a portfolio of new methods for comparing the immunogold labelling distributions of different compartments within a cell group and of the same set of compartments in different groups of cells (Mayhew and Lucocq, 2008b). Provided properly-randomised sampling is conducted at each stage of the multistage selection process, the methods provide unbiased estimates of the numbers of gold particles associated with interesting subcellular do mains. Another advantage of the between-group method is its ability to permit analysis of sets of compartments which are mixtures of organelles, membranes a nd filaments rather than compartments belonging solely to a single class. A further attraction is the possibility to alter the final magnification between experimental groups of cells provided that this does not compromise the ability to recognise or resolve compartments. The method is well-suited to between-group comparisons but comparing labelling patterns between compartments within a group of cells requires an a lternative approach (Mayhew et al ., 2002; 2003). Although operating under more constraints, the latter does provide information related to the intensity of compartment labelling and these quantities will assist in interpreting effects, interactions and translocation pathways within cells. Quantifying gold labelling distributions in volume- occupying compartments requires a sampling scheme which randomises only the location of items, particularly the spatial encounters between section planes and compartments. By contrast, quantifying distributions involving surface-occupying and linear compartments requires a scheme that also randomises spatial orientation. It follows that the latter is required when the study aim is to quantify mixtures of organelles, membranes and filaments. Systematic uniform random sampling schemes for meeting these demands are described elsewhere (Baddeley et al. 1986; Mattfeldt et al . 1990; Nyengaard and Gundersen, 1992; Gundersen et al., 1999; Howard and Reed, 2005; Mayhew, 2008). Here, the immunogold quantification methods were applied to examine the distributions of phosducin in retinas from light- and dark-adapted eyes. They confirmed the main findings of the earlier study (Chen et al ., 2005) although present sample sizes were created artificially and standardised to approximately 200 gold particles and 200 test points per group. The reason for decreasing the gold particle counts was to reduce workloads to acceptable levels: counts of roughly 200 golds on each of two sections have been found to yield reasonabl y precise estimates (Mayhew et al., 2002; Lucocq et al., 2004). Another consideration is that, for statistical testing by contingency table analysis, it is recommended that no expected number (of gold particles) should be smaller than five. Observed MAYHEW TM: Photoreceptor cells and the retina 8 numbers of gold particles may be less than this. Clearly, this recommendation may influence the choice of compartments. For example, it may be possible to achieve the target minimum of expected gold particles by the simple expedient of creating composite or portmanteau compartments. Phosducin is a light-regulated phosphoprotein which binds to subunits of transducin (Lee et al ., 1987; Savage et al ., 2000). Phosducin expression in the retina appears to be confined to PRCs. In an earlier study (Chen et al ., 2005), high immunogold labelling densities were found in the synaptic terminal, lower densities in the ellipsoid and myoid domains and minimal labelling in the rod OS and nucleus. These patterns were seen in both light- and dark-adapted groups. The present study has confirmed these findings and shown that, in terms of numbers of gold particles, the synaptic terminal contains roughly 4 times the amount of phosducin than might be predicted on the basis of a random distribution of molecules throughout the rod cell. Expressed in the same way, the myoid domain exhibits 2-3 times the amount whilst the OS and nucleus have l ess phosducin than might be predicted on the same basis. The high concentration of phosducin in the synaptic terminal is consistent with the notion of a regulatory role in synaptic functioning whilst that in the nucleus might suggest a role in regulating transcription (Yusim et al., 2000; Zhu and Craft, 2000; Nakano et al., 2001). CONCLUDING REMARKS It is anticipated that these simple and efficient sampling and stereological estimation procedures will contribute to future studies involving quantitative structural analysis and immunoelectron microscopy of the retina to complement those undertaken on other regions of the nervous system. The methods should complement biochemical, physiological and other studies to facilitate our understanding of retinal function. From a molecular perspective, the recently-introduced immunolabelling methods offer convenient and effective ways of comparing labelling distributions between groups and of making mechanistic interpretations of observed shifts in labelling patterns. 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