The dynamics of phosphodiesterase activation in rods and cones

Rhodopsin, light-sensor of vision

The light sensor of vertebrate scotopic (low-light) vision, rhodopsin, is a G-protein-coupled receptor comprising a polypeptide chain with bound chromophore, 11-cis-retinal, that exhibits remarkable physicochemical properties. This photopigment is extremely stable in the dark, yet its chromophore isomerises upon photon absorption with 70% efficiency, enabling the activation of its G-protein, transducin, with high efficiency. Rhodopsin's photochemical and biochemical activities occur over very different time-scales: the energy of retinaldehyde's excited state is stored in <1 ps in retinal-protein interactions, but it takes milliseconds for the catalytically active state to form, and many tens of minutes for the resting state to be restored. In this review, we describe the properties of rhodopsin and its role in rod phototransduction. We first introduce rhodopsin's gross structural features, its evolution, and the basic mechanisms of its activation. We then discuss light absorption and spectral sensitivity, photoreceptor electrical responses that result from the activity of individual rhodopsin molecules, and recovery of rhodopsin and the visual system from intense bleaching exposures. We then provide a detailed examination of rhodopsin's molecular structure and function, first in its dark state, and then in the active Meta states that govern its interactions with transducin, rhodopsin kinase and arrestin. While it is clear that rhodopsin's molecular properties are exquisitely honed for phototransduction, from starlight to dawn/dusk intensity levels, our understanding of how its molecular interactions determine the properties of scotopic vision remains incomplete. We describe potential future directions of research, and outline several major problems that remain to be solved.

Photoreceptor physiology and evolution: cellular and molecular basis of rod and cone phototransduction

The detection of light in the vertebrate retina utilizes a duplex system of closely related rod and cone photoreceptors: cones respond extremely rapidly, and operate at 'photopic' levels of illumination, from moonlight upwards; rods respond much more slowly, thereby obtaining greater sensitivity, and function effectively only at 'scotopic' levels of moonlight and lower. Rods and cones employ distinct isoforms of many of the proteins in the phototransduction cascade, and they thereby represent a unique evolutionary system, whereby the same process (the detection of light) uses a distinct set of genes in two classes of cell. The molecular mechanisms of phototransduction activation are described, and the classical quantitative predictions for the onset phase of the electrical response to light are developed. Recent work predicting the recovery phase of the rod's response to intense flashes is then presented, that provides an accurate account of the time that the response spends in saturation. Importantly, this also provides a new estimate for the rate at which a single rhodopsin activates molecules of the G-protein, transducin, that is substantially higher than other estimates in the literature. Finally, the evolutionary origin of the phototransduction proteins in rods and cones is examined, and it is shown that most of the rod/cone differences were established at the first of the two rounds of whole-genome duplication more than 500 million years ago.

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.

Light responses of mammalian cones

Cone photoreceptors provide the foundation of most of human visual experience, but because they are smaller and less numerous than rods in most mammalian retinas, much less is known about their physiology. We describe new techniques and approaches which are helping to provide a better understanding of cone function. We focus on several outstanding issues, including the identification of the features of the phototransduction cascade that are responsible for the more rapid kinetics and decreased sensitivity of the cone response, the roles of inner-segment voltage-gated and Ca²⁺-activated channels, the means by which cones remain responsive even in the brightest illumination, mechanisms of cone visual pigment regeneration in constant light, and energy consumption of cones in comparison to that of rods.

A kinetic analysis of mouse rod and cone photoreceptor responses

KEY POINTS

Most vertebrate eyes have rods for dim-light vision and cones for brighter light and higher temporal sensitivity. Rods evolved from cone-like precursors through expression of different transduction genes or the same genes at different expression levels, but we do not know which molecular differences were most important. We approached this problem by analysing rod and cone responses with the same model but with different values for model parameters. We showed that, in addition to outer-segment volume, the most important differences between rods and cones are: (1) decreased transduction gain, reflecting smaller amplification in the G-protein cascade; (2) a faster rate of turnover of the second messenger cGMP in darkness; and (3) an accelerated rate of decay of the effector enzyme phosphodiesterase and perhaps also of activated visual pigment. We believe our analysis has identified the principal alterations during evolution responsible for the duplex retina.

ABSTRACT

Most vertebrates have rod and cone photoreceptors, which differ in their sensitivity and response kinetics. We know that rods evolved from cone-like precursors through the expression of different transduction genes or the same genes at different levels, but we do not know which molecular differences were most important. We have approached this problem in mouse retina by analysing the kinetic differences between rod flash responses and recent voltage-clamp recordings of cone flash responses, using a model incorporating the principal features of photoreceptor transduction. We apply a novel method of analysis using the log-transform of the current, and we ask which of the model's dynamic parameters need be changed to transform the flash response of a rod into that of a cone. The most important changes are a decrease in the gain of the response, reflecting a reduction in amplification of the transduction cascade; an increase in the rate of turnover of cGMP in darkness; and an increase in the rate of decay of activated phosphodiesterase, with perhaps also an increase in the rate of decay of light-activated visual pigment. Although we cannot exclude other differences, and in particular alterations in the Ca2+ economy of the photoreceptors, we believe that we have identified the kinetic parameters principally responsible for the differences in the flash responses of the two kinds of photoreceptors, which were likely during evolution to have resulted in the duplex retina.

Quantitative modeling of the molecular steps underlying shut-off of rhodopsin activity in rod phototransduction

PURPOSE

To examine the predictions of alternative models for the stochastic shut-off of activated rhodopsin (R*) and their implications for the interpretation of experimentally recorded single-photon responses (SPRs) in mammalian rods.

THEORY

We analyze the transitions that an activated R* molecule undergoes as a result of successive phosphorylation steps and arrestin binding. We consider certain simplifying cases for the relative magnitudes of the reaction rate constants and derive the probability distributions for the time to arrestin binding. In addition to the conventional model in which R* catalytic activity declines in a graded manner with successive phosphorylations, we analyze two cases in which the activity is assumed to occur not via multiple small steps upon each phosphorylation but via a single large step. We refer to these latter two cases as the binary R* shut-off and three-state R* shut-off models.

METHODS

We simulate R*'s stochastic reactions numerically for the three models. In the simplifying cases for the ratio of rate constants in the binary and three-state models, we show that the probability distribution of the time to arrestin binding is accurately predicted. To simulate SPRs, we then integrate the differential equations for the downstream reactions using a standard model of the rod outer segment that includes longitudinal diffusion of cGMP and Ca(2+).

RESULTS

Our simulations of SPRs in the conventional model of graded shut-off of R* conform closely to the simulations in a recent study. However, the gain factor required to account for the observed mean SPR amplitude is higher than can be accounted for from biochemical experiments. In addition, a substantial minority of the simulated SPRs exhibit features that have not been reported in published experiments. Our simulations of SPRs using the model of binary R* shut-off appear to conform closely to experimental results for wild type (WT) mouse rods, and the required gain factor conforms to biochemical expectations. However, for the arrestin knockout (Arr(-/-)) phenotype, the predictions deviated from experimental findings and led us to invoke a low-activity state that R* enters before arrestin binding. Our simulations of this three-state R* shut-off model are very similar to those of the binary model in the WT case but are preferred because they appear to accurately predict the mean SPRs for four mutant phenotypes, Arr(+/-), Arr(-/-), GRK1(+/-), and GRK1(-/-), in addition to the WT phenotype. When we additionally treated the formation and shut-off of activated phosphodiesterase (E*) as stochastic, the simulated SPRs appeared even more similar to real SPRs, and there was very little change in the ensemble mean and standard deviation or in the amplitude distribution.

CONCLUSIONS

We conclude that the conventional model of graded reduction in R* activity through successive phosphorylation steps appears to be inconsistent with experimental results. Instead, we find that two variants of a model in which R* activity initially remains high and then declines abruptly after several phosphorylation steps appears capable of providing a better description of experimentally measured SPRs.

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.

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.

Speed, adaptation, and stability of the response to light in cone photoreceptors: the functional role of Ca-dependent modulation of ligand sensitivity in cGMP-gated ion channels

The response of cone photoreceptors to light is stable and reproducible because of the exceptional regulation of the cascade of enzymatic reactions that link visual pigment (VP) excitation to the gating of cyclic GMP (cGMP)-gated ion channels (cyclic nucleotide–gated [CNG]) in the outer segment plasma membrane. Regulation is achieved in part through negative feedback control of some of these reactions by cytoplasmic free Ca²⁺. As part of the control process, Ca²⁺ regulates the phosphorylation of excited VP, the activity of guanylate cyclase, and the ligand sensitivity of the CNG ion channels. We measured photocurrents elicited by stimuli in the form of flashes, steps, and flashes superimposed on steps in voltage-clamped single bass cones isolated from striped bass retina. We also developed a computational model that comprises all the known molecular events of cone phototransduction, including all Ca-dependent controls. Constrained by available experimental data in bass cones and cone transduction biochemistry, we achieved an excellent match between experimental photocurrents and those simulated by the model. We used the model to explore the physiological role of CNG ion channel modulation. Control of CNG channel activity by both cGMP and Ca²⁺ causes the time course of the light-dependent currents to be faster than if only cGMP controlled their activity. Channel modulation also plays a critical role in the regulation of the light sensitivity and light adaptation of the cone photoresponse. In the absence of ion channel modulation, cone photocurrents would be unstable, oscillating during and at the offset of light stimuli.

Speed, sensitivity, and stability of the light response in rod and cone photoreceptors: facts and models

The light responses of rod and cone photoreceptors in the vertebrate retina are quantitatively different, yet extremely stable and reproducible because of the extraordinary regulation of the cascade of enzymatic reactions that link photon absorption and visual pigment excitation to the gating of cGMP-gated ion channels in the outer segment plasma membrane. While the molecular scheme of the phototransduction pathway is essentially the same in rods and cones, the enzymes and protein regulators that constitute the pathway are distinct. These enzymes and regulators can differ in the quantitative features of their functions or in concentration if their functions are similar or both can be true. The molecular identity and distinct function of the molecules of the transduction cascade in rods and cones are summarized. The functional significance of these molecular differences is examined with a mathematical model of the signal-transducing enzymatic cascade. Constrained by available electrophysiological, biochemical and biophysical data, the model simulates photocurrents that match well the electrical photoresponses measured in both rods and cones. Using simulation computed with the mathematical model, the time course of light-dependent changes in enzymatic activities and second messenger concentrations in non-mammalian rods and cones are compared side by side.

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.

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.