Modeling the role of incisures in vertebrate phototransduction

Photoreceptor disc incisures form as an adaptive mechanism ensuring the completion of disc enclosure

The first steps of vision take place within a stack of tightly packed disc-shaped membranes, or 'discs', located in the outer segment compartment of photoreceptor cells. In rod photoreceptors, discs are enclosed inside the outer segment and contain deep indentations in their rims called 'incisures'. The presence of incisures has been documented in a variety of species, yet their role remains elusive. In this study, we combined traditional electron microscopy with three-dimensional electron tomography to demonstrate that incisures are formed only after discs become completely enclosed. We also observed that, at the earliest stage of their formation, discs are not round as typically depicted but rather are highly irregular in shape and resemble expanding lamellipodia. Using genetically manipulated mice and frogs and measuring outer segment protein abundances by quantitative mass spectrometry, we further found that incisure size is determined by the molar ratio between peripherin-2, a disc rim protein critical for the process of disc enclosure, and rhodopsin, the major structural component of disc membranes. While a high perpherin-2 to rhodopsin ratio causes an increase in incisure size and structural complexity, a low ratio precludes incisure formation. Based on these data, we propose a model whereby normal rods express a modest excess of peripherin-2 over the amount required for complete disc enclosure in order to ensure that this important step of disc formation is accomplished. Once the disc is enclosed, the excess peripherin-2 incorporates into the rim to form an incisure.

Photoreceptor disc incisures form as an adaptive mechanism ensuring the completion of disc enclosure

The first steps of vision take place within a stack of tightly packed disc-shaped membranes, or "discs", located in the outer segment compartment of photoreceptor cells. In rod photoreceptors, discs are enclosed inside the outer segment and contain deep indentations in their rims called "incisures". The presence of incisures has been documented in a variety of species, yet their role remains elusive. In this study, we combined traditional electron microscopy with three-dimensional electron tomography to demonstrate that incisures are formed only after discs become completely enclosed. We also observed that, at the earliest stage of their formation, discs are not round as typically depicted but rather are highly irregular in shape and resemble expanding lamellipodia. Using genetically manipulated mice and frogs and measuring outer segment protein abundances by quantitative mass spectrometry, we further found that incisure size is determined by the molar ratio between peripherin-2, a disc rim protein critical for the process of disc enclosure, and rhodopsin, the major structural component of disc membranes. While a high perpherin-2 to rhodopsin ratio causes an increase in incisure size and structural complexity, a low ratio precludes incisure formation. Based on these data, we propose a model whereby normal rods express a modest excess of peripherin-2 over the amount required for complete disc enclosure in order to ensure that this important step of disc formation is accomplished. Once the disc is enclosed, the excess peripherin-2 incorporates into the rim to form an incisure.

Effects of cell size and bicarbonate on single photon response variability in retinal rods

Accurate photon counting requires that rods generate highly amplified, reproducible single photon responses (SPRs). The SPR is generated within the rod outer segment (ROS), a multilayered structure built from membranous disks that house rhodopsin. Photoisomerization of rhodopsin at the disk rim causes a local depletion of cGMP that closes ion channels in the plasmalemma located nearby with relative rapidity. In contrast, a photoisomerization at the disk center, distant from the plasmalemma, has a delayed impact on the ion channels due to the time required for cGMP redistribution. Radial differences should be greatest in large diameter rods. By affecting membrane guanylate cyclase activity, bicarbonate could impact spatial inhomogeneity in cGMP content. It was previously known that in the absence of bicarbonate, SPRs are larger and faster at the base of a toad ROS (where the ROS attaches to the rest of the cell) than at the distal tip. Given that bicarbonate enters the ROS at the base and diffuses to the tip and that it expedites flash response recovery, there should be an axial concentration gradient for bicarbonate that would accentuate the base-to-tip SPR differences. Seeking to understand how ROS geometry and bicarbonate affect SPR variability, we used mathematical modeling and made electrophysiological recordings of single rods. Modeling predicted and our experiments confirmed minor radial SPR variability in large diameter, salamander rods that was essentially unchanged by bicarbonate. SPRs elicited at the base and tip of salamander rods were similar in the absence of bicarbonate, but when treated with 30 mM bicarbonate, SPRs at the base became slightly faster than those at the tip, verifying the existence of an axial gradient for bicarbonate. The differences were small and unlikely to undermine visual signaling. However, in toad rods with longer ROSs, bicarbonate somehow suppressed the substantial, axial SPR variability that is naturally present in the absence of bicarbonate. Modeling suggested that the axial gradient of bicarbonate might dampen the primary phototransduction cascade at the base of the ROS. This novel effect of bicarbonate solves a mystery as to how toad vision is able to function effectively in extremely dim light.

Phototransduction in retinal cones: Analysis of parameter importance

In daylight, cone photoreceptors in the retina are responsible for the bulk of visual perception, yet compared to rods, far less is known quantitatively about their biochemistry. This is partly because it is hard to isolate and purify cone proteins. The issue is also complicated by the synergistic interaction of these parameters in producing systems biology outputs, such as photoresponse. Using a 3-D resolved, finite element model of cone outer segments, here we conducted a study of parameter significance using global sensitivity analysis, by Sobol indices, which was contextualized within the uncertainty surrounding these parameters in the available literature. The analysis showed that a subset of the parameters influencing the circulating dark current, such as the turnover rate of cGMP in the dark, may be most influential for variance with experimental flash response, while the shut-off rates of photoexcited rhodopsin and phosphodiesterase also exerted sizable effect. The activation rate of transducin by rhodopsin and the light-induced hydrolysis rate of cGMP exerted measurable effects as well but were estimated as relatively less significant. The results of this study depend on experimental ranges currently described in the literature and should be revised as these become better established. To that end, these findings may be used to prioritize parameters for measurement in future investigations.

Analysis of waveform and amplitude of mouse rod and cone flash responses

KEY POINTS

Most vertebrate eyes have rod and cone photoreceptors, which use a signal transduction pathway consisting of many biological processes to transform light into an electrical response. We dissect and quantify the contribution of each of these processes to the photoreceptor light response by using a novel method of analysis that provides an analytical solution for the entire time course of the dim-flash light response. We find that the shape of the light response is exclusively controlled by deactivation parameters. Activation parameters scale this shape and alter the response amplitude. We show that the rising phase of the response depends on Ca²⁺ feedback, and we identify the deactivation parameters that control the recovery phase of the response. We devise new methods to extract values for deactivation and activation parameters from a separate analysis of response shape and response amplitude.

ABSTRACT

Vertebrate eyes have rod and cone photoreceptors, which use a complex transduction pathway comprising many biological processes to transform the absorption of light into an electrical response. A fundamental question in sensory transduction is how these processes contribute to the response. To study this question, we use a well-accepted phototransduction model, which we analyse with a novel method based on the log transform of the current. We derive an analytical solution that describes the entire time course of the photoreceptor response to dim flashes of light. We use this solution to dissect and quantify the contribution of each process to the response. We find that the entire dim-flash response is proportional to the flash intensity. By normalizing responses to unit amplitude, we define a waveform that is independent of the light intensity and characterizes the invariant shape of dim-flash responses. We show that this waveform is exclusively determined by deactivation rates; activation rates only scale the waveform and affect the amplitude. This analysis corrects a previous assumption that the rising phase is determined entirely by activation rates. We further show that the rising phase depends on Ca²⁺ feedback to the cyclase, contrary to current belief. We identify the deactivation rates that control the recovery phase of the response, and we devise new methods to extract activation and deactivation rates from an analysis of response shape and response amplitude. In summary, we provide a comprehensive understanding of how the various transduction processes produce the cellular response.

Position of rhodopsin photoisomerization on the disk surface confers variability to the rising phase of the single photon response in vertebrate rod photoreceptors

Retinal rods function as accurate photon counters to provide for vision under very dim light. To do so, rods must generate highly amplified, reproducible responses to single photons, yet outer segment architecture and randomness in the location of rhodopsin photoisomerization on the surface of an internal disk introduce variability to the rising phase of the photon response. Soon after a photoisomerization at a disk rim, depletion of cGMP near the plasma membrane closes ion channels and hyperpolarizes the rod. But with a photoisomerization in the center of a disk, local depletion of cGMP is distant from the channels in the plasma membrane. Thus, channel closure is delayed by the time required for the reduction of cGMP concentration to reach the plasma membrane. Moreover, the local fall in cGMP dissipates over a larger volume before affecting the channels, so response amplitude is reduced. This source of variability increases with disk radius. Using a fully space-resolved biophysical model of rod phototransduction, we quantified the variability attributable to randomness in the location of photoisomerization as a function of disk structure. In mouse rods that have small disks bearing a single incisure, this variability was negligible in the absence of the incisure. Variability was increased slightly by the incisure, but randomness in the shutoff of rhodopsin emerged as the main source of single photon response variability at all but the earliest times. Variability arising from randomness in the transverse location of photoisomerization increased in magnitude and persisted over a longer period in the photon response of large salamander rods. A symmetric arrangement of multiple incisures in the disks of salamander rods greatly reduced this variability during the rising phase, but the incisures had the opposite effect on variability arising from randomness in rhodopsin shutoff at later times.

Local, nonlinear effects of cGMP and Ca2+ reduce single photon response variability in retinal rods

The single photon response (SPR) in vertebrate photoreceptors is inherently variable due to several stochastic events in the phototransduction cascade, the main one being the shutoff of photoactivated rhodopsin. Deactivation is driven by a random number of steps, each of random duration with final quenching occurring after a random delay. Nevertheless, variability of the SPR is relatively low, making the signal highly reliable. Several biophysical and mathematical mechanisms contributing to variability suppression have been examined by the authors. Here we investigate the contribution of local depletion of cGMP by PDE*, the non linear dependence of the photocurrent on cGMP, Ca²⁺ feedback by making use of a fully space resolved (FSR) mathematical model, applied to two species (mouse and salamander), by varying the cGMP diffusion rate severalfold and rod outer segment diameter by an order of magnitude, and by introducing new, more refined, and time dependent variability functionals. Globally well stirred (GWS) models, and to a lesser extent transversally well stirred models (TWS), underestimate the role of nonlinearities and local cGMP depletion in quenching the variability of the circulating current with respect to fully space resolved models (FSR). These distortions minimize the true extent to which SPR is stabilized by locality in cGMP depletion, nonlinear effects linking cGMP to current, and Ca²⁺ feedback arising from the physical separation of E* from the ion channels located on the outer shell, and the diffusion of these second messengers in the cytoplasm.

Multi-scale, numerical modeling of spatio-temporal signaling in cone phototransduction

Mammals have two types of photoreceptors, rods and cones. While rods are exceptionally sensitive and mediate vision at very low illumination levels, cones operate in daylight and are responsible for the bulk of visual perception in most diurnal animals, including humans. Yet the mechanisms of phototransduction in cones is understudied, largely due to unavailability of pure cone outer segment (COS) preparations. Here we present a novel mathematical model of cone phototransduction that explicitly takes into account complex cone geometry and its multiple physical scales, faithfully reproduces features of the cone response, and is orders of magnitude more efficient than the standard 3D diffusion model. This is accomplished through the mathematical techniques of homogenization and concentrated capacity. The homogenized model is then computationally implemented by finite element method. This homogenized model permits one to analyze the effects of COS geometry on visual transduction and lends itself to performing large numbers of numerical trials, as required for parameter analysis and the stochasticity of rod and cone signal transduction. Agreement between the nonhomogenized, (i.e., standard 3D), and homogenized diffusion models is reported along with their simulation times and memory costs. Virtual expression of rod biochemistry on cone morphology is also presented for understanding some of the characteristic differences between rods and cones. These simulations evidence that 3D cone morphology and ion channel localization contribute to biphasic flash response, i.e undershoot. The 3D nonhomogenized and homogenized models are contrasted with more traditional and coarser well-stirred and 1D longitudinal diffusion models. The latter are single-scale and do not explicitly account for the multi-scale geometry of the COS, unlike the 3D homogenized model. We show that simpler models exaggerate the magnitude of the current suppression, yield accelerated time to peak, and do not predict the local concentration of cGMP at the ionic channels.

Protein Sorting in Healthy and Diseased Photoreceptors

Rods and cones are retinal photoreceptor neurons required for our visual sensation. Because of their highly polarized structures and well-characterized processes of G protein-coupled receptor-mediated phototransduction signaling, these photoreceptors have been excellent models for studying the compartmentalization and sorting of proteins. Rods and cones have a modified ciliary compartment called the outer segment (OS) as well as non-OS compartments. The distinct membrane protein compositions between OS and non-OS compartments suggest that the OS is separated from the rest of the cellular compartments by multiple barriers or gates that are selectively permissive to specific cargoes. This review discusses the mechanisms of protein sorting and compartmentalization in photoreceptor neurons. Proper sorting and compartmentalization of membrane proteins are required for signal transduction and transmission. This review also discusses the roles of compartmentalized signaling, which is compromised in various retinal ciliopathies.

Origins of the phototransduction delay as inferred from stochastic and deterministic simulation of the amplification cascade

PURPOSE

To identify steps of the phototransduction cascade responsible for the delay of the photoresponse.

METHODS

Electrical responses of fish (Carassius) cones and Rana ridibunda frog rods and cones were recorded with a suction pipette technique and as an aspartate-isolated mass receptor potential from isolated perfused retinas. Special attention was paid to sufficiently high temporal resolution (1-ms flash, 700 Hz amplification bandpass). Stochastic simulation of the activation steps from photon absorption to the formation of catalytically active phosphodiesterase (PDE) was performed. In addition, a deterministic mathematical model was fit to the experimental responses. The model included a detailed description of the activation steps of the cascade that enabled identification of the role of individual transduction stages in shaping the initial part of the response.

RESULTS

We found that the apparent delay of the photoresponse gets shorter with increasing stimulus intensity and reaches an asymptotic value of approximately 3 ms in cones and greater than or equal to 10 ms in rods. The result seems paradoxical since it is suggested that the delay occurs in the chain of steps from photon absorption to the formation of active transducin (T*) which in cones is, on average, slower than in rods. Stochastic simulation shows that actually the steps from photon absorption to T* may not contribute perceptibly to the delay. Instead, the delay occurs at the stage that couples the cycle of repetitive activation of T by rhodopsin (R*) with the activation of PDE. These steps include formation of T* (= T _α GTP) out of T _αβγ GTP released from the activation cycle and the subsequent interaction of T* with PDE. This poses a problem. The duration of an average cycle of activation of T in rods is approximately 5 ms and is determined by the frequency of collisions between R* and T in the photoreceptor membrane. The frequency is roughly proportional to the surface packing density of T in the membrane. As the packing density of PDE is approximately 12 times lower than that of T, it could be expected that the rate of the T*-PDE interaction were an order of magnitude slower than that of R* and T. As modeling shows, this is the case in rods. However, the delay in cones is approximately 3 ms which could be achieved only at a T*-PDE interaction time of less than or equal to 5 ms. This means that either the frequency of the collisions of T* and PDE, or the efficiency of collisions, or both in cones are approximately ten times higher than in rods. This may be a challenge to the present model of the molecular organization of the photoreceptor membrane.

CONCLUSIONS

The delay of the photoresponse is mainly set by the rate of interaction of T* with PDE. In cones, the delay is shorter than in rods and, moreover, shorter than the duration of the cycle of repetitive activation of T by R*. This poses a problem for the present model of diffusion interaction of phototransduction proteins in the photoreceptor membrane.

Molecular basis for photoreceptor outer segment architecture

To serve vision, vertebrate rod and cone photoreceptors must detect photons, convert the light stimuli into cellular signals, and then convey the encoded information to downstream neurons. Rods and cones are sensory neurons that each rely on specialized ciliary organelles to detect light. These organelles, called outer segments, possess elaborate architectures that include many hundreds of light-sensitive membranous disks arrayed one atop another in precise register. These stacked disks capture light and initiate the chain of molecular and cellular events that underlie normal vision. Outer segment organization is challenged by an inherently dynamic nature; these organelles are subject to a renewal process that replaces a significant fraction of their disks (up to ∼10%) on a daily basis. In addition, a broad range of environmental and genetic insults can disrupt outer segment morphology to impair photoreceptor function and viability. In this chapter, we survey the major progress that has been made for understanding the molecular basis of outer segment architecture. We also discuss key aspects of organelle lipid and protein composition, and highlight distributions, interactions, and potential structural functions of key OS-resident molecules, including: kinesin-2, actin, RP1, prominin-1, protocadherin 21, peripherin-2/rds, rom-1, glutamic acid-rich proteins, and rhodopsin. Finally, we identify key knowledge gaps and challenges that remain for understanding how normal outer segment architecture is established and maintained.

How rods respond to single photons: Key adaptations of a G-protein cascade that enable vision at the physical limit of perception

Rod photoreceptors are among the most sensitive light detectors in nature. They achieve their remarkable sensitivity across a wide variety of species through a number of essential adaptations: a specialized cellular geometry, a G-protein cascade with an unusually stable receptor molecule, a low-noise transduction mechanism, a nearly perfect effector enzyme, and highly evolved mechanisms of feedback control and receptor deactivation. Practically any change in protein expression, enzyme activity, or feedback control can be shown to impair photon detection, either by decreasing sensitivity or signal-to-noise ratio, or by reducing temporal resolution. Comparison of mammals to amphibians suggests that rod outer-segment morphology and the molecules and mechanism of transduction may have evolved together to optimize light sensitivity in darkness, which culminates in the extraordinary ability of these cells to respond to single photons at the ultimate limit of visual perception.

Explicit spatiotemporal simulation of receptor-G protein coupling in rod cell disk membranes

Dim-light vision is mediated by retinal rod cells. Rhodopsin (R), a G-protein-coupled receptor, switches to its active form (R(∗)) in response to absorbing a single photon and activates multiple copies of the G-protein transducin (G) that trigger further downstream reactions of the phototransduction cascade. The classical assumption is that R and G are uniformly distributed and freely diffusing on disk membranes. Recent experimental findings have challenged this view by showing specific R architectures, including RG precomplexes, nonuniform R density, specific R arrangements, and immobile fractions of R. Here, we derive a physical model that describes the first steps of the photoactivation cascade in spatiotemporal detail and single-molecule resolution. The model was implemented in the ReaDDy software for particle-based reaction-diffusion simulations. Detailed kinetic in vitro experiments are used to parametrize the reaction rates and diffusion constants of R and G. Particle diffusion and G activation are then studied under different conditions of R-R interaction. It is found that the classical free-diffusion model is consistent with the available kinetic data. The existence of precomplexes between inactive R and G is only consistent with the data if these precomplexes are weak, with much larger dissociation rates than suggested elsewhere. Microarchitectures of R, such as dimer racks, would effectively immobilize R but have little impact on the diffusivity of G and on the overall amplification of the cascade at the level of the G protein.

Submembrane assembly and renewal of rod photoreceptor cGMP-gated channel: insight into the actin-dependent process of outer segment morphogenesis

The photoreceptor outer segment (OS) is comprised of two compartments: plasma membrane (PM) and disk membranes. It is unknown how the PM renewal is coordinated with that of the disk membranes. Here we visualized the localization and trafficking process of rod cyclic nucleotide-gated channel α-subunit (CNGA1), a PM component essential for phototransduction. The localization was visualized by fusing CNGA1 to a fluorescent protein Dendra2 and expressing in Xenopus laevis rod photoreceptors. Dendra2 allowed us to label CNGA1 in a spatiotemporal manner and therefore discriminate between old and newly trafficked CNGA1-Dendra2 in the OS PM. Newly synthesized CNGA1 was preferentially trafficked to the basal region of the lateral OS PM where newly formed and matured disks are also added. Unique trafficking pattern and diffusion barrier excluded CNGA1 from the PM domains, which are the proposed site of disk membrane maturation. Such distinct compartmentalization allows the confinement of cyclic nucleotide-gated channel in the PM, while preventing the disk membrane incorporation. Cytochalasin D and latrunculin A treatments, which are known to disrupt F-actin-dependent disk membrane morphogenesis, prevented the entrance of newly synthesized CNGA1 to the OS PM, but did not prevent the entrance of rhodopsin and peripherin/rds to the membrane evaginations believed to be disk membrane precursors. Uptake of rhodopsin and peripherin/rds coincided with the overgrowth of the evaginations at the base of the OS. Thus F-actin is essential for the trafficking of CNGA1 to the ciliary PM, and coordinates the formations of disk membrane rim region and OS PM.

Detection of single photons by toad and mouse rods

Amphibian and mammalian rods can both detect single photons of light even though they differ greatly in physical dimensions, mammalian rods being much smaller in diameter than amphibian rods. To understand the changes in physiology and biochemistry required by such large differences in outer segment geometry, we developed a computational approach, taking into account the spatial organization of the outer segment divided into compartments, together with molecular dynamics simulations of the signaling cascade. We generated simulations of the single-photon response together with intrinsic background fluctuations in toad and mouse rods. Combining this computational approach with electrophysiological data from mouse rods, we determined key biochemical parameters. On average around one phosphodiesterase (PDE) molecule is spontaneously active per mouse compartment, similar to the value for toad, which is unexpected due to the much smaller diameter in mouse. A larger number of spontaneously active PDEs decreases dark noise, thereby improving detection of single photons; it also increases cGMP turnover, which accelerates the decay of the light response. These constraints explain the higher PDE density in mammalian compared with amphibian rods that compensates for the much smaller diameter of mammalian disks. We further find that the rate of cGMP hydrolysis by light-activated PDE is diffusion limited, which is not the case for spontaneously activated PDE. As a consequence, in the small outer segment of a mouse rod only a few activated PDEs are sufficient to generate a signal that overcomes noise, which permits a shorter lifetime of activated rhodopsin and greater temporal resolution.

17β-estradiol eye drops protect the retinal ganglion cell layer and preserve visual function in an in vivo model of glaucoma

Neuroprotection in glaucoma as a curative strategy complementary to current therapies to lower intraocular pressure (IOP) is highly desirable. This study was designed to investigate neuroprotection by 17β-estradiol (E2) to prevent retinal ganglion cell (RGC) death in a glaucoma model of surgically elevated IOP in rats. We found that daily treatment with E2-containing eye drops resulted in significant E2 concentration in the retina with concomitant profound neuroprotective therapeutic benefits, even in the presence of continually elevated IOP. The number of apoptotic cells in the RGC layer was significantly decreased in the E2-treated group, when compared to the vehicle-treated controls. Deterioration in visual acuity in these animals was also markedly prevented. Using mass spectrometry-based proteomics, beneficial changes in the expression of several proteins implicated in the maintenance of retinal health were also found in the retina of E2-treated animals. On the other hand, systemic side effects could not be avoided with the eye drops, as confirmed by the measured high circulating estrogen levels and through the assessment of the uterus representing a typical hormone-sensitive peripheral organ. Collectively, the demonstrated significant neuroprotective effect of topical E2 in the selected animal model of glaucoma provides a clear rationale for further studies aiming at targeting E2 into the eye while avoiding systemic E2 exposure to diminish undesirable off-target side effects.

The photovoltage of rods and cones in the dark-adapted mouse retina

Research on photoreceptors has led to important insights into how light signals are detected and processed in the outer retina. Most information about photoreceptor function, however, comes from lower vertebrates. The large majority of mammalian studies are based on suction pipette recordings of outer segment currents, a technique that doesn't allow examination of phenomena occurring downstream of phototransduction. Only a small number of whole-cell recordings have been made, mainly in the macaque. Due to the growing importance of the mouse in vision research, we have optimized a retinal slice preparation that allows the reliable collection of perforated-patch recordings from light responding rods and cones. Unexpectedly, the frequency of cone recordings was much higher than their numeric proportion of ∼3%. This allowed us to obtain direct functional evidence suggestive of rod–cone coupling in the mouse. Moreover, rods had considerably larger single photon responses than previously published for mammals (3.44 mV, SD 1.37, n = 19 at 24°C; 2.46 mV, SD 1.08, n = 10 at 36°C), and a relatively high signal/noise ratio (6.4, SD 1.8 at 24°C; 6.8, SD 2.8 at 36°C). Both findings imply a more favourable transmission at the rod–rod bipolar cell synapse. Accordingly, relatively few photoisomerizations were sufficient to elicit a half-maximal response (6.7, SD 2.7, n = 5 at 24°C; 10.6, SD 1.7, n = 3 at 36°C), leading to a narrow linear response range. Our study demonstrates new features of mammalian photoreceptors and opens the way for further investigations into photoreceptor function using retinas from mutant mouse models.

Rhodopsin expression level affects rod outer segment morphology and photoresponse kinetics

BACKGROUND

The retinal rod outer segment is a sensory cilium that is specialized for the conversion of light into an electrical signal. Within the cilium, up to several thousand membranous disks contain as many as a billion copies of rhodopsin for efficient photon capture. Disks are continually turned over, requiring the daily synthesis of a prodigious amount of rhodopsin. To promote axial diffusion in the aqueous cytoplasm, the disks have one or more incisures. Across vertebrates, the range of disk diameters spans an order of magnitude, and the number and length of the incisures vary considerably, but the mechanisms controlling disk architecture are not well understood. The finding that transgenic mice overexpressing rhodopsin have enlarged disks lacking an incisure prompted us to test whether lowered rhodopsin levels constrain disk assembly.

METHODOLOGY/PRINCIPAL FINDINGS

The structure and function of rods from hemizygous rhodopsin knockout (R+/-) mice with decreased rhodopsin expression were analyzed by transmission electron microscopy and single cell recording. R+/- rods were structurally altered in three ways: disk shape changed from circular to elliptical, disk surface area decreased, and the single incisure lengthened to divide the disk into two sections. Photocurrent responses to flashes recovered more rapidly than normal. A spatially resolved model of phototransduction indicated that changes in the packing densities of rhodopsin and other transduction proteins were responsible. The decrease in aqueous outer segment volume and the lengthened incisure had only minor effects on photon response amplitude and kinetics.

CONCLUSIONS/SIGNIFICANCE

Rhodopsin availability limits disk assembly and outer segment girth in normal rods. The incisure may buffer the supply of structural proteins needed to form larger disks. Decreased rhodopsin level accelerated photoresponse kinetics by increasing the rates of molecular collisions on the membrane. Faster responses, together with fewer rhodopsins, combine to lower overall sensitivity of R+/- rods to light.

Identification of key factors that reduce the variability of the single photon response

Rod photoreceptors mediate vision in dim light. Their biological function is to discriminate between distinct, very low levels of illumination, i.e., they serve as reliable photon counters. This role requires high reproducibility of the response to a particular number of photons. Indeed, single photon responses demonstrate unexpected low variability, despite the stochastic nature of the individual steps in the transduction cascade. We analyzed individual system mechanisms to identify their contribution to variability suppression. These include: (i) cooperativity of the regulation of the second messengers; (ii) diffusion of cGMP and Ca(2+) in the cytoplasm; and (iii) the effect of highly localized cGMP hydrolysis by activated phosphodiesterase resulting in local saturation. We find that (i) the nonlinear relationships between second messengers and current at the plasma membrane, and the cGMP hydrolysis saturation effects, play a major role in stabilizing the system; (ii) the presence of a physical space where the second messengers move by Brownian motion contributes to stabilization of the photoresponse; and (iii) keeping Ca(2+) at its dark level has only a minor effect on the variability of the system. The effects of diffusion, nonlinearity, and saturation synergize in reducing variability, supporting the notion that the observed high fidelity of the photoresponse is the result of global system function of phototransduction.

Kinetics of rhodopsin deactivation and its role in regulating recovery and reproducibility of rod photoresponse

The single photon response (SPR) in vertebrate phototransduction is regulated by the dynamics of R* during its lifetime, including the random number of phosphorylations, the catalytic activity and the random sojourn time at each phosphorylation level. Because of this randomness the electrical responses are expected to be inherently variable. However the SPR is highly reproducible. The mechanisms that confer to the SPR such a low variability are not completely understood. The kinetics of rhodopsin deactivation is investigated by a Continuous Time Markov Chain (CTMC) based on the biochemistry of rhodopsin activation and deactivation, interfaced with a spatio-temporal model of phototransduction. The model parameters are extracted from the photoresponse data of both wild type and mutant mice, having variable numbers of phosphorylation sites and, with the same set of parameters, the model reproduces both WT and mutant responses. The sources of variability are dissected into its components, by asking whether a random number of turnoff steps, a random sojourn time between steps, or both, give rise to the known variability. The model shows that only the randomness of the sojourn times in each of the phosphorylated states contributes to the Coefficient of Variation (CV) of the response, whereas the randomness of the number of R* turnoff steps has a negligible effect. These results counter the view that the larger the number of decay steps of R*, the more stable the photoresponse is. Our results indicate that R* shutoff is responsible for the variability of the photoresponse, while the diffusion of the second messengers acts as a variability suppressor.

Dynamics of mouse rod phototransduction and its sensitivity to variation of key parameters

The deep understanding of the biochemical and biophysical basis of visual transduction, makes it ideal for systems-level analysis. A sensitivity analysis is presented for a self-consistent set of parameters involved in mouse phototransduction. The organising framework is a spatio-temporal mathematical model, which includes the geometry of the rod outer segment (ROS), the layered array of the discs, the incisures, the biochemistry of the activation/deactivation cascade and the biophysics of the diffusion of the second messengers in the cytoplasm and the closing of the cyclic guanosine monophosphate (cGMP) gated cationic channels. These modules include essentially all the relevant geometrical, biochemical and biophysical parameters. The parameters are selected from within experimental ranges, to obey basic first principles such as conservation of mass and energy fluxes. By means of the model they are compared to a large set of experimental data, providing a strikingly close match. Following isomerisation of a single rhodopsin R * (single photon response), the sensitivity analysis was carried out on the photo-response, measured both in terms of number of effector molecules produced, and photocurrent suppression, at peak time and the activation and recovery phases of the cascade. The current suppression is found to be very sensitive to variations of the catalytic activities, Hill's coefficients and hydrolysis rates and the geometry of the ROS, including size and shape of the incisures. The activated effector phosphodiesterase (PDE *) is very sensitive to variations of catalytic activity of G-protein activation and the average lifetimes of activated rhodopsin R * and PDE *; however, they are insensitive to geometry and variations of the transduction parameters. Thus the system is separated into two functional modules, activation/deactivation and transduction, each confined in different geometrical domains, communicating through the hydrolysis of cGMP by PDE *, and each sensitive to variations of parameters only in its own module.

Network-level analysis of light adaptation in rod cells under normal and altered conditions

Photoreceptor cells finely adjust their sensitivity and electrical response according to changes in light stimuli as a direct consequence of the feedback and regulation mechanisms in the phototransduction cascade. In this study, we employed a systems biology approach to develop a dynamic model of vertebrate rod phototransduction that accounts for the details of the underlying biochemistry. Following a bottom-up strategy, we first reproduced the results of a robust model developed by Hamer et al. (Vis. Neurosci., 2005, 22(4), 417), and then added a number of additional cascade reactions including: (a) explicit reactions to simulate the interaction between the activated effector and the regulator of G-protein signalling (RGS); (b) a reaction for the reformation of the G-protein from separate subunits; (c) a reaction for rhodopsin (R) reconstitution from the association of the opsin apoprotein with the 11-cis-retinal chromophore; (d) reactions for the slow activation of the cascade by opsin. The extended network structure successfully reproduced a number of experimental conditions that were inaccessible to prior models. With a single set of parameters the model was able to predict qualitative and quantitative features of rod photoresponses to light stimuli ranging over five orders of magnitude, in normal and altered conditions, including genetic manipulations of the cascade components. In particular, the model reproduced the salient dynamic features of the rod from Rpe65(-/-) animals, a well established model for Leber congenital amaurosis and vitamin A deficiency. The results of this study suggest that a systems-level approach can help to unravel the adaptation mechanisms in normal and in disease-associated conditions on a molecular basis.

Overexpression of rhodopsin alters the structure and photoresponse of rod photoreceptors

Rhodopsins are densely packed in rod outer-segment membranes to maximize photon absorption, but this arrangement interferes with transducin activation by restricting the mobility of both proteins. We attempted to explore this phenomenon in transgenic mice that overexpressed rhodopsin in their rods. Photon capture was improved, and, for a given number of photoisomerizations, bright-flash responses rose more gradually with a reduction in amplification--but not because rhodopsins were more tightly packed in the membrane. Instead, rods increased their outer-segment diameters, accommodating the extra rhodopsins without changing the rhodopsin packing density. Because the expression of other phototransduction proteins did not increase, transducin and its effector phosphodiesterase were distributed over a larger surface area. That feature, as well as an increase in cytosolic volume, was responsible for delaying the onset of the photoresponse and for attenuating its amplification.

Kinetics of turn-offs of frog rod phototransduction cascade

The time course of the light-induced activity of phototrandsuction effector enzyme cGMP-phosphodiesterase (PDE) is shaped by kinetics of rhodopsin and transducin shut-offs. The two processes are among the key factors that set the speed and sensitivity of the photoresponse and whose regulation contributes to light adaptation. The aim of this study was to determine time courses of flash-induced PDE activity in frog rods that were dark adapted or subjected to nonsaturating steady background illumination. PDE activity was computed from the responses recorded from solitary rods with the suction pipette technique in Ca²⁺-clamping solution.

A flash applied in the dark-adapted state elicits a wave of PDE activity whose rising and decaying phases have characteristic times near 0.5 and 2 seconds, respectively. Nonsaturating steady background shortens both phases roughly to the same extent. The acceleration may exceed fivefold at the backgrounds that suppress ≈70% of the dark current.

The time constant of the process that controls the recovery from super-saturating flashes (so-called dominant time constant) is adaptation independent and, hence, cannot be attributed to either of the processes that shape the main part of the PDE wave. We hypothesize that the dominant time constant in frog rods characterizes arrestin binding to rhodopsin partially inactivated by phosphorylation. A mathematical model of the cascade that considers two-stage rhodopsin quenching and transducin inactivation can mimic experimental PDE activity quite well. The effect of light adaptation on the PDE kinetics can be reproduced in the model by concomitant acceleration on both rhodopsin phosphorylation and transducin turn-off, but not by accelerated arrestin binding. This suggests that not only rhodopsin but also transducin shut-off is under adaptation control.

Estimating the rate constant of cyclic GMP hydrolysis by activated phosphodiesterase in photoreceptors

The early steps of light response occur in the outer segment of rod and cone photoreceptor. They involve the hydrolysis of cGMP, a soluble cyclic nucleotide, that gates ionic channels located in the outer segment membrane. We shall study here the rate by which cGMP is hydrolyzed by activated phosphodiesterase (PDE). This process has been characterized experimentally by two different rate constants beta(d) and beta(sub): beta(d) accounts for the effect of all spontaneously active PDE in the outer segment, and beta(sub) characterizes cGMP hydrolysis induced by a single light-activated PDE. So far, no attempt has been made to derive the experimental values of beta(d) and beta(sub) from a theoretical model, which is the goal of this work. Using a model of diffusion in the confined rod geometry, we derive analytical expressions for beta(d) and beta(sub) by calculating the flux of cGMP molecules to an activated PDE site. We obtain the dependency of these rate constants as a function of the outer segment geometry, the PDE activation and deactivation rates and the aqueous cGMP diffusion constant. Our formulas show good agreement with experimental measurements. Finally, we use our derivation to model the time course of the cGMP concentration in a transversally well-stirred outer segment.

Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction

The single photon response in vertebrate phototransduction is highly reproducible despite a number of random components of the activation cascade, including the random activation site, the random walk of an activated receptor, and its quenching in a random number of steps. Here we use a previously generated and tested spatiotemporal mathematical and computational model to identify possible mechanisms of variability reduction. The model permits one to separate the process into modules, and to analyze their impact separately. We show that the activation cascade is responsible for generation of variability, whereas diffusion of the second messengers is responsible for its suppression. Randomness of the activation site contributes at early times to the coefficient of variation of the photoresponse, whereas the Brownian path of a photoisomerized rhodopsin (Rh*) has a negligible effect. The major driver of variability is the turnoff mechanism of Rh*, which occurs essentially within the first 2-4 phosphorylated states of Rh*. Theoretically increasing the number of steps to quenching does not significantly decrease the corresponding coefficient of variation of the effector, in agreement with the biochemical limitations on the phosphorylated states of the receptor. Diffusion of the second messengers in the cytosol acts as a suppressor of the variability generated by the activation cascade. Calcium feedback has a negligible regulatory effect on the photocurrent variability. A comparative variability analysis has been conducted for the phototransduction in mouse and salamander, including a study of the effects of their anatomical differences such as incisures and photoreceptors geometry on variability generation and suppression.