Photoreceptors are highly specialized cells essential for converting light into neural signals, the fundamental process of vision. Structurally, they consist of distinct compartments, including an inner segment (IS), which is separated from the outer segment (OS) by a short connecting stalk (cilium). The OS itself is a modified cilium. These compartments are uniquely tailored to support visual function, resulting in remarkably complex metabolic demands. The IS contains the organelles necessary for cellular maintenance and metabolic processes, while the OS houses the phototransduction machinery, crucial for capturing light and initiating visual signaling. The OS also undergoes turnover and renewal in an orderly fashion, a process first demonstrated by Young [1] and Young and Bok [2], who observed that newly synthesized protein was incorporated at the OS base, migrated along the segment, and was eventually shed from the tip and taken up by retinal pigment epithelial (RPE) cells.

A key feature of the OS is its lack of mitochondria, which is particularly striking given the high metabolic demands of phototransduction. The OS meets its energy requirements in two ways. First, ATP produced via oxidative phosphorylation in the IS diffuses into the OS. Second, glycolytic intermediates, including fructose 1,6-bisphosphate (F1,6BP), also diffuse from the IS [3, 4], where they support local glycolysis within the OS.

Aerobic glycolysis is a major energy source for photoreceptors [5]. The retina converts approximately 80% of the glucose it receives into lactate via aerobic glycolysis [5, 6], a process critical for normal photoreceptor function [5–9]. The enzymes required for glycolysis are present in the OS [10–15], although there has been some controversy regarding the presence of the final enzyme, pyruvate kinase, in the rod OS. Some studies report its presence through immunohistochemistry [13, 16], while others do not [17]. Mass spectrometry-based proteomics has confirmed the presence of glycolytic enzymes, including glyceraldehyde-3-phosphate dehydrogenase, in OS disc preparations [18, 19], and pyruvate kinase has been detected in the OS [18, 20]. Additionally, a peak in pyruvate kinase activity has been localized to the rod OS [13]. It has also been shown that glycolysis is essential for maintaining OS length [21]. The balance of evidence favors the presence of pyruvate kinase being present in the OS. Furthermore, photoreceptors express the isoenzyme lactate dehydrogenase A, characteristic of cells that export lactate, suggesting that photoreceptors are a major source of lactate production [9].

The energy demands of the OS also include maintaining asymmetry between the inner and outer leaflets of the plasma membrane, a process dependent on ATP-consuming flippases (P4-ATPases), which move phosphatidylserine (PS) from the outer to the inner leaflet, essential for preserving membrane asymmetry. Photoreceptors express the flippase ATP8A2 [22]. As flippases consume energy, we hypothesize that if the tip of the rod OS becomes energy-deficient, PS will redistribute to the outer leaflet. Rhodopsin, which is present in both the discs and the OS plasma membrane, is not only crucial for phototransduction but also functions as an efficient scramblase [23]. Scrambling is a passive process, and due to the negative charge of PS [24], the negative membrane potential will cause PS to accumulate preferentially in the outer leaflet.

The OS undergoes continual growth, balanced by the shedding of its tip in a diurnal rhythm, which occurs primarily at or shortly after dawn in many vertebrate species [25, 26]. Redistribution of PS to the outer leaflet at the tip of the OS follows light onset, preceding and promoting phagocytosis by the RPE [27]. This leads to the hypothesis that the length of the OS is determined by the distance over which energy can be effectively supplied—that is, the length over which energy production and transport mechanisms can meet consumption. In this study, we developed a simple reaction-diffusion model to test this hypothesis. We propose that the OS, lacking mitochondria, depends both on glycolysis and diffusion of ATP from the IS. Since rod OS lacks glucose transporters [28], glycolysis also depends on diffusion of glucose (or F1,6BP as a key intermediate of glycolysis) from the IS.

2.1. Model construction and reaction-diffusion equation

The compartment in the model represents the OS, with boundary conditions applied at each end of the segment. The dimensions used are summarized in table 1.

Table 1. Dimensions of rod inner and outer segments.

SegmentLength (mm)Diameter (mm)Inner segment (IS)32 [29]1.5–2 [30]Outer segment (OS)28 in human [29] and mouse (direct measurement) 50 in Xenopus [31]1.5–2 (rat and primate) [29] 7 (in Rana and Xenopus)

The model is an example of a reaction-diffusion system. Such systems are of fundamental importance in physiology [32]. The basic equation is the advection-diffusion equation, augmented with both source and consumption terms:

Cm represents the concentration of molecule m (e.g. F1,6BP or ATP), along the length of the photoreceptor (x), Dm is the diffusion coefficient, Pm is a source term, and Qm is a consumption term of the molecular species m. This equation can be simplified. Although the OS undergoes continuous growth, calculation shows that the advective contribution (the term in equation (1) to transport is negligible and can be set to zero. Additionally, under steady-state conditions term can also be set to zero. Therefore, equation (1) simplifies to:

Solving with boundary conditions (see supplementary information S1), and , results in: .

2.2. Model parameters: intracellular concentrations and diffusion coefficients

The intracellular concentrations and diffusion coefficients used are summarized in table 2. The intracellular ATP concentration in the retina has been reported to be 4.14 mM [33]. The OS is densely packed with photoreceptor discs containing the photoreceptive opsins, which significantly hinder longitudinal diffusion [34, 35]. Rather than explicitly modeling the exact geometry of stacked discs, we describe diffusion using an effective diffusion coefficient , where represents the fraction accessible in the total OS volume (porosity) and the tortuosity (a measure of increased diffusion path length due to cellular structures; i.e. OS discs). This effective-medium approximation is commonly used for diffusion in porous and crowded environments (Bruggeman approximation) [36, 37]. Typical intracellular environments are crowded and exhibit hindered diffusion relative to dilute aqueous solution [38]. Rod OSs are an especially structured environment due to dense disc stacking (approximately 85%–95% of the volume), motivating the use of small effective porosity values ( = 0.03–0.1). Typical values for tortuosity coefficients are in free solution, 1.5–3 in cytoplasm, and up to 2–5 in highly structured media [39, 40]. Combining representative values ( 0.03, results in , corresponding to an effective diffusion coefficient approximately two orders of magnitude lower than in aqueous solution.

Table 2. Estimates of molecular weights, diffusion coefficients (in water) and concentrations of metabolites.

MetaboliteMolecular weight (g mol−1)Concentration (mM)Diffusion coefficient (m2 s −1)ATP4994.143×10−10 [41] (3×10−12)Glucose1801.36 × 10−10(6 × 10−12)

Consequently, for water-soluble compounds in the OS, the diffusion coefficients were calculated by dividing the diffusion coefficients in water by 100. Oxygen, being lipid-soluble, diffuses freely through the discs, and its diffusion coefficient is unaffected.

To account for lipid membranes in the OS, the estimates were divided by 100 (in brackets).

While differences in size and charge are expected to affect diffusion, these variations are typically minor for small metabolites. Fructose-1,6-bisphosphate (F1,6BP), due to its larger size and higher charge, is expected to diffuse slightly more slowly than glucose; however, this difference is likely small. Given the uncertainty in assigning precise intracellular diffusion coefficients, we assume that the diffusion coefficient of F1,6BP is similar to that of glucose.

2.3. Model assumptions

The model is based on the following key assumptions:

(i)  

Steady-state conditions apply (see supplementary information S2);

(ii)  

ATP production occurs via glycolysis and oxidative phosphorylation with fixed ratios;

(iii)  

Diffusion is described using an effective diffusion coefficient that accounts for structural hindrance because of dense OS discs;

(iv)  

Glucose/ F1,6BP availability may act as the rate-limiting metabolite for ATP production (hypothesis tested in this study);

(v)  

All parameters are varied within ±20% to account for physiological uncertainty.

(vi)  

The system is approximated as one-dimensional along the length of the rod OS; since OS length (∼25–30 µm) greatly exceeds OS diameter (∼1–2 µm), diffusion along the length will be the dominant diffusion path.

2.4. Energy balance framework and ATP consumption estimates

Photoreceptor ATP consumption is divided into IS and OS components. Basal metabolic rates (i.e. ATP consumptions linked to housekeeping processes such as protein turnover, intracellular transport, and maintenance of ion gradients) are indicated as and , respectively. Additional ATP demand arises from the dark current () in darkness and from the phototransduction cascade () in light conditions.

The overall photoreceptor energy consumption is represented by during dark conditions () and during light conditions (). Additionally, since oxygen consumption in darkness is roughly double compared to light, we set the ratio of / to 2. This relationship is captured in the following equation:

ATP consumption rates for IS and OS photoreceptor compartments were obtained from published measurements retinal oxygen consumption and metabolic rates (see supplementary information S3). The resulting ATP fluxes under light and dark conditions are summarized in table 3, which provides the input constraints for all subsequent calculation.

Table 3. Energy balance under light and dark conditions.

Condition (region)ATP consumption (mmol l−1s−1)ATP Production (mmol l−1s−1)DARK (IS)2.522.52LIGHT (IS)1.141.17DARK (OS)0.030.03LIGHT (OS)0.1350.10

Oxidative phosphorylation requires mitochondria and the IS is densely populated with these organelles and it is assumed that all the energy demands in the IS are met by both glycolysis and oxidative phosphorylation. In contrast, the OS lacks mitochondria and depends on two key sources for energy:

Diffusion of ATP from the IS.Glycolysis, with glucose transporters and hexokinases located in the IS [14], requires the metabolites necessary for glycolysis to diffuse in from the IS.

The glycolytic rate of the OS has been measured [12], with a maximum capacity of 0.1 mmol of ATP/L/s. This allows for the generation of a simple overall energy budget, summarized in table 3.

2.5. Estimating energy production and substrate requirements

The IS contains mitochondria and supports both glycolysis and oxidative phosphorylation. In contrast, the OS lacks mitochondria and depends on (i) diffusion of ATP from the IS and (ii) glycolysis supported by metabolite diffusion from the IS. ATP production is assumed to occur via glycolysis and oxidative phosphorylation, and ATP demand is linked to substrate utilization through these pathways. A full description of ATP production rates, as well as the conversion of ATP consumption into glucose and oxygen fluxes, is provided in supplementary information S4.

2.6. Blood flow estimation and physiological constraints

To estimate the minimal blood flow required to sustain photoreceptor metabolism under light and dark conditions, we used the previously calculated rates of glucose consumption in the rod photoreceptors.

Minimal blood flow was calculated for glucose using the formula:

A typical A–V concentration difference of 0.44 mmol l−1 for glucose in both light and darkness was assumed. Full derivations of glucose and oxygen fluxes and blood flow calculations are provided in supplementary information S6.

2.7. Flippase energetics and membrane asymmetry

The model assumes that OS length is limited by the point at which ATP concentration approaches zero (at the tip of the OS). This assumption is supported by energetic estimates needed to keep membrane asymmetry, the ATP-dependent transport of PS to the inner leaflet.

Calculating the energetic cost of maintaining PS asymmetry shows that asymmetry is preserved until ATP levels are nearly completely depleted, resulting in a sharp transition at low ATP concentrations. This justifies the use of ATP depletion as a boundary condition for determining maximum OS length (see supplementary information S6).

2.8. Blood flow in choroidal circulation

Any energy model must be consistent with the energy that can be delivered by the circulation. The blood supply to the outer retina comes primarily from the choroidal circulation [42, 43]. To assess whether the theoretical minimal blood flow required to meet photoreceptor metabolic demands aligns with physiological measurements, we compared our model-derived estimates to experimentally measured choroidal blood flow. Nork et al [44] reported choroidal blood flow ranging from 1 to 10 μl min−1mm−2 depending on the region of the monkey retina. This corresponds to approximately 1.67 × 10−8–1.67 × 10−7 l s−1mm−2.

3.1. Energy supply and demand in photoreceptors under dark and light conditions

Photoreceptors exhibit remarkably high and dynamic energy demands that shift between dark and light conditions (figures 1 A and (B)). To quantify these changes, we estimated ATP consumption and production rates in both the IS and OS, integrating experimental data with physiology-based assumptions (see Methods; table 3). Energy supply in the IS was assumed to rely both on glycolysis and oxidative phosphorylation, while the OS depends on both ATP diffusion from the IS and local glycolysis, with specific assumptions regarding metabolic transport and enzyme activity.

Figure 1. Model of ATP production and consumption in photoreceptor inner and outer segments under dark and light conditions, and its link to daily RPE phagocytosis.(A) Left: Schematic of the photoreceptor IS and OS during the night, showing the dark current. Bottom: ATP availability from the IS to the OS tip. Right: ATP consumption at night in the IS and OS. (B). Left: Schematic of the photoreceptor IS and OS at dawn, showing phototransduction activation. Bottom: ATP availability from the IS to the OS tip, highlighting ATP depletion at the tip and resulting appearance of phosphatidylserine (PS) in the outer leaflet. Right: ATP consumption at dawn in the IS and OS. (C) Schematic of the photoreceptor IS, OS, and adjacent RPE cell during daytime. Each day, the OS tip is phagocytized by the RPE, digested in lysosomes (catabolism), and the resulting building blocks are recycled to the IS, where molecules are synthesized (anabolism).

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In darkness, energy demand in the IS is dominated by the Na+/K+ ATPase activity that supports the DC. Our estimates indicate an ATP requirement of approximately 1.37 mmol l−1s−1 for this process alone. We also incorporated published values of basal ATP consumption, which include processes such as protein turnover and maintenance of basal ion gradients.

In contrast, when photoreceptors are stimulated by light, the DC ceases, and the energy demand shifts to the OS. The OS then requires significant ATP for phototransduction, the process by which light is converted into electrical signals. This transition from DC in the IS to phototransduction in the OS highlights the dynamic energy needs of photoreceptors as they adapt to changing light conditions, which we explore further using a reaction-diffusion model.

3.2. Mammalian OS length supported by ATP diffusion

The equation to be solved is the steady-state equation equation (2) for ATP:

where Patp represents the production of ATP by glycolysis (0.1 mmol s−1l−1), Qatp is the consumption term (0.135 mmol s−1l−1) and Datp is the diffusion coefficient for ATP. This equation can be solved to give:

where A and B are constants of integration. The boundary conditions are a fixed concentration of ATP, at x = 0 (adjacent to the connecting stalk) and at the OS tip, where x = length of the OS (L). This results in two equations, and solving for A and B (see methods) gives:

The maximum length is determined by the point where the ATP level drops to zero, i.e. . By setting the left-hand of equation (4) to zero and solving for L, we obtain the expression:

This gives the maximum length of the OS that can be supported by ATP diffusion. Using the estimated values for , , and , we calculate a maximum value for the OS length of 26.6 μm which is close to the observed value for mammalian rods (around 28 μm) [29, 38]. To estimate the error associated with Lmax, we generated 1000 models, each with the parameters , and the net term () simultaneously and randomly varied within a ± 20% range of the original values. This resulted in Lmax = 26.6 ± 2.7 mm (figure 2 A, B).

Figure 2. Summary of photoreceptor OS length modeling.(A) Schematic representation of photoreceptor OS and parameters used to predict the maximum lengths (Lmax) using parameters C(0), D and Q−P for ATP.(B) Results of 1000 calculations for Lmax, in which all parameters (C(0), D and the net term Q−P) are simultaneously and randomly varied within ±20% of their respective baseline values.(C) Schematic representation of photoreceptor OS and parameters used to predict Lmax using parameters C(0), D and Q–P for F1,6BP.(D) Results of 1000 calculations for Lmax, in which each parameters (C(0), D and the net term Q-P) are simultaneously and randomly varied within ±20% of their respective baseline values.

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This calculation makes a key assumption: that the OS can be supported by even the smallest amount of ATP and that its length is determined by when ATP is completely consumed. We support this assumption as follows: PS, which has a net negative charge of −1 [24] and constitutes up to 15% of the plasma membrane lipid [45], is typically confined to the inner leaflet of the plasma membrane, where it comprises about 30% of the lipid present. The resting potential of a neuron is typically around −70 mV, which also applies to photoreceptors under light conditions (the photoreceptor detects darkness). Under these conditions, one would expect the PS to be distributed according to its Nernst potential with fourteen fold more PS in the outer leaflet than in the inner leaflet. However, the reverse ratio is observed, indicating that this distribution must be actively maintained.

A calculation outlined in the method section suggests that the flipping reaction is energetically highly favorable and that consumption of 99.95% of a cell’s ATP would only cause the PS content of the outer leaflet to rise to 6% (while the inner leaflet would decrease to 24%). The consumption of the remaining 0.05% would result in the PS content of the outer leaflet increasing to 28% (with the inner leaflet PS content dropping to 2%). This gradual decline in ATP leads to a sharper transition in the PS content of the outer leaflet (figure 1(B)). The appearance of PS in the outer leaflet constitutes an ‘eat me’ signal [46], which is relevant for both apoptotic bodies [47] and the tips of OS [27] (figure 1(C)).

3.3. Mammalian OS length supported by diffusion of glucose metabolites

It is important to consider the diffusion of metabolites, other than ATP, as potential determinants of the maximum OS length that can be sustained. Unlike the mammalian OS, which lacks glucose transporters [28], the IS expresses glucose transporter 1 (Glut1), which facilitates the transport of glucose into the cell. Hexokinase 2 (HK2)—which plays a key role in the initial step of glycolysis by phosphorylating glucose to form glucose-6-phosphate—is present in the IS but absent in the OS. While other enzymes involved in glycolysis are present in both segments [14], the absence of HK2 in the OS implies that glucose itself is not directly used for glycolysis in the OS. Furthermore, the phosphate needed to produce F1,6BP in the third step of glycolysis predominantly comes from oxidative phosphorylation which only occurs in the IS [48]. Instead, we propose that it is downstream glycolytic metabolites that diffuse into the OS.

Intracellular glucose concentration has been reported to vary between 0.7 and 1.3 mM, depending on the brain region [49]. The first steps of glycolysis consume two ATP to generate first glucose-6-phosphate and then F1,6BP. Reported intracellular concentrations in a mammalian cell line include1.1 mM for hexose phosphate and 1.5 mM for F1,6BP [50]. Of all glycolytic intermediates, F1,6BP is found at the highest concentration, which is why it was selected for modeling. We used equation (5), assuming the diffusion coefficient () for F1,6BP is similar to that of glucose (i.e. 6 × 10−10 m2 s −1). As in previous simulations, we assumed that this diffusion coefficient is reduced to 1% of its normal value due to the presence of rod photoreceptor discs, which limit the diffusion of water-soluble compounds within the OS.

To summarize, the following assumptions were made:

The first steps of the glycolytic pathway occur in the IS, where key early enzymes, such as glucose transporters and hexokinases are located. Glut1 is present in the IS and excluded from the rod OS [28]. Hexokinases are preferentially located to mitochondria [48], including in rod photoreceptors [14]. Furthermore, the phosphate used to generate hexose phosphates for the glycolytic pathway has been shown to come preferentially from oxidative phosphorylation [48]. Other glycolytic enzymes are found both in the IS and the OS [14].F1,6BP, being present at the highest intracellular concentration among glycolytic intermediates, is considered the most important diffusible metabolite and the main contributor to local glycolysis in the OS.F1,6BP forms in the IS, and the yield of ATP by the remainder of the glycolytic pathway in the OS is 4 ATP per molecule.The diffusion coefficient of F1,6BP is similar to that of glucose and, as in earlier steps, reduced to 1% of its normal value due to the presence of the discs in the OS.There is no production term for F1,6BP in the OS (as it lacks HK2), and the consumption rate is set at 25 μmol l−1s−1.

Using equation (5), this yielded similar results, with an Lmax of 27 ± 2.8 μm (figure 2 C, D). These calculations were performed under light-adapted conditions. Under dark conditions, the metabolic requirement for OS can be met by local glycolysis alone, supported by the diffusion of F1,6BP, which can support a length of 48.9 μm.

3.4. Effect of changes in glycolytic activity on OS length

Changes in glycolytic activity levels affect the ATP and F1,6BP concentration gradients in the OS. The measured OS length (i.e. 28 µm) is consistent with our predicted length when using experimental data from bovine OSs under light conditions, where maximal glycolytic activity corresponds to an ATP production rate of 0.1 mM s−1 [12]. Under these conditions, both ATP and F1,6BP concentration gradients predict similar OS lengths (figure 3 A,B).

Figure 3. Alterations in concentration gradients in response to glycolytic activity levels in the OS.(A–D) Concentration gradients of ATP (left panels) and F1,6BP (right panels) in the OS under light conditions are shown under maximal and low glycolytic activity in light conditions. Each plot shows concentration (C, in mM) as a function of distance from the OS base (x, in µm). Insets summarize key parameters used in the model, including diffusion coefficient (D), initial concentration (C(0)), net consumption rate (Q −P), and predicted maximal OS length (L).(E, F) Predicted ATP and F1,6BP concentration gradients in the OS under dark conditions. Each graph shows metabolite concentration (C, in mM) as a function of distance from the OS base (x, in µm). Insets display parameter values for diffusion coefficient (D), initial concentration (C(0)), net consumption rate (Q −P), and predicted OS length (L).

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To explore how reduced glycolytic activity would impact the predicted OS length, we decreased the ATP production rate (PATP) to 10% of its default value (i.e. 0.01 mM s−1). This change increased the OS length that can be supported by the F1,6BP concentration gradient from 26.8 to 84.9 µm, while the length supportable by the ATP concentration gradient decreases from 26.6 to 13.6 µm (figure 3 C,D). Ultimately, the effective OS length would be constrained by the most limiting factor.

3.5. Effect of diffusion constants and IS concentrations on OS length

We also investigated how changes in the initial concentration (C(0)) and diffusion coefficient (D), up to twice their default values, affect the predicted OS length under light conditions (figure 4). The default values for the C(0) and D occupy similar relative positions on their respective response curves for both ATP and F1,6BP, indicating a comparable influence on OS length (L) when these parameters are proportionally increased. For instance, increasing D to 1.5 times its default value results in predicted OS lengths that remain close to the observed length of human OSs—approximately 32.6 µm for ATP and 32.8 µm for F1,6BP.

Figure 4. Relationship between IS concentration, diffusion coefficient, and OS length under light conditions. The top panels show how varying IS substrate concentrations (C(0)) of ATP (left) and F1,6BP (right) affect OS length (L). Maximum C(0) values were set to twice the default: defaults were 4.1 mM for ATP and 1.5 mM for F1,6BP. The bottom panels illustrate how changes in the diffusion coefficient (D) on the OS length for ATP (left) and F1,6BP (right), with D values also ranging up to twice their defaults: 3.0 µm2 s−1 for ATP and 6.0 µm2 s−1 for F1,6BP. Boxes indicate the specific values of D, net consumption rate (Q − P), and C(0) used to generate these relationships.

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We next examined how OS length is predicted to vary in Xenopus laevis, a commonly used amphibian model organism in laboratory settings. These animals are typically maintained at ambient temperatures between 18 °C and 22 °C, whic