Multiple steps of phosphorylation of activated rhodopsin can account for the reproducibility of vertebrate rod single-photon responses

UVR and RPE - The Good, the Bad and the degenerate Macula

Ultraviolet Radiation (UVR) has a well-established causative influence within the aetiology of conditions of the skin and the anterior segment of the eye. However, a grounded assessment of the role of UVR within conditions of the retina has been hampered by a historical lack of quantitative, and spectrally resolved, assessment of how UVR impacts upon the retina in terms congruent with contemporary theories of ageing. In this review, we sought to summarise the key findings of research investigating the connection between UVR exposure in retinal cytopathology while identifying necessary avenues for future research which can deliver a deeper understanding of UVR's place within the retinal risk landscape.

Analysis of dim-light responses in rod and cone photoreceptors with altered calcium kinetics

Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical current using a signal transduction pathway that depends on Ca[Formula: see text] feedback. It is known that manipulating the Ca[Formula: see text] kinetics affects the response shape and the photoreceptor sensitivity, but a precise quantification of these effects remains unclear. We have approached this task in mouse retina by combining numerical simulations with mathematical analysis. We consider a parsimonious phototransduction model that incorporates negative Ca[Formula: see text] feedback onto the synthesis of cyclic GMP, and fast buffering reactions to alter the Ca[Formula: see text] kinetics. We derive analytic results for the photoreceptor functioning in sufficiently dim light conditions depending on the photoreceptor type. We exploit these results to obtain conceptual and quantitative insight into how response waveform and amplitude depend on the underlying biophysical processes and the Ca[Formula: see text] feedback. With a low amount of buffering, the Ca[Formula: see text] concentration changes in proportion to the current, and responses to flashes of light are monophasic. With more buffering, the change in the Ca[Formula: see text] concentration becomes delayed with respect to the current, which gives rise to a damped oscillation and a biphasic waveform. This shows that biphasic responses are not necessarily a manifestation of slow buffering reactions. We obtain analytic approximations for the peak flash amplitude as a function of the light intensity, which shows how the photoreceptor sensitivity depends on the biophysical parameters. Finally, we study how changing the extracellular Ca[Formula: see text] concentration affects the response.

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.

Kinetics of cone specific G-protein signaling in avian photoreceptor cells

Cone photoreceptor cells of night-migratory songbirds seem to process the primary steps of two different senses, vision and magnetoreception. The molecular basis of phototransduction is a prototypical G protein-coupled receptor pathway starting with the photoexcitation of rhodopsin or cone opsin thereby activating a heterotrimeric G protein named transducin. This interaction is well understood in vertebrate rod cells, but parameter describing protein-protein interactions of cone specific proteins are rare and not available for migratory birds. European robin is a model organism for studying the orientation of birds in the earth magnetic field. Recent findings showed a link between the putative magnetoreceptor cryptochrome 4a and the cone specific G-protein of European robin. In the present work, we investigated the interaction of European robin cone specific G protein and cytoplasmic regions of long wavelength opsin. We identified the second loop in opsin connecting transmembrane regions three and four as a critical binding interface. Surface plasmon resonance studies using a synthetic peptide representing the second cytoplasmic loop and purified G protein α-subunit showed a high affinity interaction with a K _D value of 21 nM. Truncation of the G protein α-subunit at the C-terminus by six amino acids slightly decreased the affinity. Our results suggest that binding of the G protein to cryptochrome can compete with the interaction of G protein and non-photoexcited long wavelength opsin. Thus, the parallel presence of two different sensory pathways in bird cone photoreceptors is reasonable under dark-adapted conditions or during illumination with short wavelengths.

Mathematical analysis of phototransduction reaction parameters in rods and cones

Retinal photoreceptor cells, rods and cones, convert photons of light into chemical and electrical signals as the first step of the visual transduction cascade. Although the chemical processes in the phototransduction system are very similar to each other in these photoreceptors, the light sensitivity and time resolution of the photoresponse in rods are functionally different than those in the photoresponses of cones. To systematically investigate how photoresponses are divergently regulated in rods and cones, we have developed a detailed mathematical model on the basis of the Hamer model. The current model successfully reconstructed light intensity-, ATP- and GTP-dependent changes in concentrations of phosphorylated visual pigments (VPs), activated transducins (Tr*s) and phosphodiesterases (PDEs) in rods and cones. In comparison to rods, the lower light sensitivity of cones was attributed not only to the lower affinity of activated VPs for Trs but also to the faster desensitization of the VPs. The assumption of an intermediate inactive state, MIIⁱ, in the thermal decay of activated VPs was essential for inducing faster inactivation of VPs in rods, and possibly also in cones.

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.

A hybrid stochastic/deterministic model of single photon response and light adaptation in mouse rods

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A hybrid stochastic/deterministic model of mouse rod phototransduction is presented.

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Rod photocurrent to photovoltage conversion in darkness is accurately characterized.

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Photoresponses to dim and bright stimuli and in various mutants are well reproduced.

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Recently debated molecular mechanisms of the phototransduction cascade are examined.

The phototransduction cascade is paradigmatic for signaling pathways initiated by G protein-coupled receptors and is characterized by a fine regulation of photoreceptor sensitivity and electrical response to a broad range of light stimuli. Here, we present a biochemically comprehensive model of phototransduction in mouse rods based on a hybrid stochastic and deterministic mathematical framework, and a quantitatively accurate description of the rod impedance in the dark. The latter, combined with novel patch clamp recordings from rod outer segments, enables the interconversion of dim flash responses between photovoltage and photocurrent and thus direct comparison with the simulations. The model reproduces the salient features of the experimental photoresponses at very dim and bright stimuli, for both normal photoreceptors and those with genetically modified cascade components. Our modelling approach recapitulates a number of recent findings in vertebrate phototransduction. First, our results are in line with the recently established requirement of dimeric activation of PDE6 by transducin and further show that such conditions can be fulfilled at the expense of a significant excess of G protein activated by rhodopsin. Secondly, simulations suggest a crucial role of the recoverin-mediated Ca²⁺-feedback on rhodopsin kinase in accelerating the shutoff, when light flashes are delivered in the presence of a light background. Finally, stochastic simulations suggest that transient complexes between dark rhodopsin and transducin formed prior to light stimulation increase the reproducibility of single photon responses. Current limitations of the model are likely associated with the yet unknown mechanisms governing the shutoff of the cascade.

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.

Functional modulation of phosphodiesterase-6 by calcium in mouse rod photoreceptors

Phosphodiesterase-6 (PDE6) is a key protein in the G-protein cascade converting photon information to bioelectrical signals in vertebrate photoreceptor cells. Here, we demonstrate that PDE6 is regulated by calcium, contrary to the common view that PDE1 is the unique PDE class whose activity is modulated by intracellular Ca²⁺. To broaden the operating range of photoreceptors, mammalian rod photoresponse recovery is accelerated mainly by two calcium sensor proteins: recoverin, modulating the lifetime of activated rhodopsin, and guanylate cyclase-activating proteins (GCAPs), regulating the cGMP synthesis. We found that decreasing rod intracellular Ca²⁺ concentration accelerates the flash response recovery and increases the basal PDE6 activity (β_dark) maximally by ~ 30% when recording local electroretinography across the rod outer segment layer from GCAPs^-/- recoverin^-/- mice. Our modeling shows that a similar elevation in β_dark can fully explain the observed acceleration of flash response recovery in low Ca²⁺. Additionally, a reduction of the free Ca²⁺ in GCAPs^-/- recoverin^-/- rods shifted the inhibition constants of competitive PDE inhibitor 3-isobutyl-1-methylxanthine (IBMX) against the thermally activated and light-activated forms of PDE6 to opposite directions, indicating a complex interaction between IBMX, PDE6, and calcium. The discovered regulation of PDE6 is a previously unknown mechanism in the Ca²⁺-mediated modulation of rod light sensitivity.

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.

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.

Implications of dimeric activation of PDE6 for rod phototransduction

We examine the implications of a recent report providing evidence that two transducins must bind to the rod phosphodiesterase to elicit significant hydrolytic activity. To predict the rod photoreceptor's electrical response, we use numerical simulation of the two-dimensional diffusional contact of interacting molecules at the surface of the disc membrane, and then we use the simulated PDE activity as the driving function for the downstream reaction cascade. The results account for a number of aspects of rod phototransduction that have previously been puzzling. For example, they explain the existence of a greater initial delay in rods than in cones. Furthermore, our analysis suggests that the 'continuous' noise recorded in rods in darkness is likely to arise from spontaneous activation of individual molecules of PDE at a rate of a few tens per second per rod, probably as a consequence of spontaneous activation of transducins at a rate of thousands per second per rod. Hence, the dimeric activation of PDE in rods provides immunity against spontaneous transducin activation, thereby reducing the continuous noise. Our analysis also provides a coherent quantitative explanation of the amplification underlying the single photon response. Overall, numerical analysis of the dimeric activation of PDE places rod phototransduction in a new light.

Determination of basal phosphodiesterase activity in mouse rod photoreceptors with cGMP clamp

Light regulates cGMP concentration in the photoreceptor cytoplasm by activating phosphodiesterase (PDE) molecules through a G-protein signalling cascade. Spontaneous PDE activity is present in rod outer segments even in darkness. This basal PDE activity (β_dark) has not been determined in wild type mammalian photoreceptor cells although it plays a key role in setting the sensitivity and recovery kinetics of rod responses. We present a novel method for determination of β_dark using local electroretinography (LERG) from isolated mouse retinas. The method is based on the ability of PDE inhibitors to decrease β_dark, which can be counterbalanced by increasing PDE activity with light. This procedure clamps cytoplasmic cGMP to its dark value. β_dark can be calculated based on the amount of light needed for the "cGMP clamp" and information extracted from the registered rod photoresponses. Here we apply this method to determine β_dark values for the first time in the mammalian rods and obtain the following estimates for different mouse models: 3.9 s^-1 for wild type, 4.5 s^-1 for guanylate cyclase activating proteins (GCAPs) knockout, and 4.4 s^-1 for GCAPs and recoverin double knockout mice. Our results suggest that depletion of GCAPs or recoverin do not affect β_dark.

Temporal resolution of single-photon responses in primate rod photoreceptors and limits imposed by cellular noise

Sensory receptor noise corrupts sensory signals, contributing to imperfect perception and dictating central processing strategies. For example, noise in rod phototransduction limits our ability to detect light, and minimizing the impact of this noise requires precisely tuned nonlinear processing by the retina. But detection sensitivity is only one aspect of night vision: prompt and accurate behavior also requires that rods reliably encode the timing of photon arrivals. We show here that the temporal resolution of responses of primate rods is much finer than the duration of the light response and identify the key limiting sources of transduction noise. We also find that the thermal activation rate of rhodopsin is lower than previous estimates, implying that other noise sources are more important than previously appreciated. A model of rod single-photon responses reveals that the limiting noise relevant for behavior depends critically on how rod signals are pooled by downstream neurons. NEW & NOTEWORTHY Many studies have focused on the visual system's ability to detect photons, but not on its ability to encode the relative timing of detected photons. Timing is essential for computations such as determining the velocity of moving objects. Here we examine the timing precision of primate rod photoreceptor responses and show that it is more precise than previously appreciated. This motivates an evaluation of whether scotopic vision approaches limits imposed by rod temporal resolution.

A neurociência computacional no estudo dos processos cognitivos

Resumo Nas últimas décadas o estudo de processos cognitivos vem sendo influenciado por duas tendências: a legitimação de diversas formas e níveis de estudo e a tentativa de integração multidisciplinar. A primeira teve grande importância na segunda metade do século XX, quando linhas de pesquisa na psicologia cognitiva e nas neurociências fortaleceram-se. Nesse sentido, destacam-se os três níveis de Marr (computacional, algorítmico e implementacional) como forma de estruturar o estudo dos processos cognitivos. A segunda tendência é mais recente e busca, apoiada na primeira, aprofundar o entendimento dos processos cognitivos em suas diversas escalas e integrar diversos paradigmas de estudos, buscando consiliência teórica. O intento deste artigo é apresentar a neurociência computacional e suas possíveis contribuições para a psicologia cognitiva, articulando, por meio dos três níveis de Marr, uma base teórica que explicite o papel de cada uma das disciplinas e as suas possíveis interações.

Processing of single-photon responses in the mammalian On and Off retinal pathways at the sensitivity limit of vision

Visually guided behaviour at its sensitivity limit relies on single-photon responses originating in a small number of rod photoreceptors. For decades, researchers have debated the neural mechanisms and noise sources that underlie this striking sensitivity. To address this question, we need to understand the constraints arising from the retinal output signals provided by distinct retinal ganglion cell types. It has recently been shown in the primate retina that On and Off parasol ganglion cells, the cell types likely to underlie light detection at the absolute visual threshold, differ fundamentally not only in response polarity, but also in the way they handle single-photon responses originating in rods. The On pathway provides the brain with a thresholded, low-noise readout and the Off pathway with a noisy, linear readout. We outline the mechanistic basis of these different coding strategies and analyse their implications for detecting the weakest light signals. We show that high-fidelity, nonlinear signal processing in the On pathway comes with costs: more single-photon responses are lost and their propagation is delayed compared with the Off pathway. On the other hand, the responses of On ganglion cells allow better intensity discrimination compared with the Off ganglion cell responses near visual threshold.

This article is part of the themed issue ‘Vision in dim light’.

Phototransduction early steps model based on Beer-Lambert optical law

The amount of available rhodopsin on the photoreceptor outer segment and its change over time is not considered in classic models of phototransduction. Thus, those models do not take into account the absorptance variation of the outer segment under different brightness conditions. The relationship between the light absorbed by a medium and its absorptance is well described by the Beer-Lambert law. This newly proposed model implements the absorptance variation phenomenon in a set of equations that admit photons per second as input and results in active rhodopsins per second as output. This study compares the classic model of phototransduction developed by Forti et al. (1989) to this new model by using different light stimuli to measure active rhodopsin and photocurrent. The results show a linear relationship between light stimulus and active rhodopsin in the Forti model and an exponential saturation in the new model. Further, photocurrent values have shown that the new model behaves equivalently to the experimental and theoretical data as published by Forti in dark-adapted rods, but fits significantly better under light-adapted conditions. The new model successfully introduced a physics optical law to the standard model of phototransduction adding a new processing layer that had not been mathematically implemented before. In addition, it describes the physiological concept of saturation and delivers outputs in concordance to input magnitudes.

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.

Human Visual System as a Double-Slit Single Photon Interference Sensor: A Comparison between Modellistic and Biophysical Tests

This paper describes a computational approach to the theoretical problems involved in the Young's single-photon double-slit experiment, focusing on a simulation of this experiment in the absence of measuring devices. Specifically, the human visual system is used in place of a photomultiplier or similar apparatus. Beginning with the assumption that the human eye perceives light in the presence of very few photons, we measure human eye performance as a sensor in a double-slit one-photon-at-a-time experimental setup. To interpret the results, we implement a simulation algorithm and compare its results with those of human subjects under identical experimental conditions. In order to evaluate the perceptive parameters exactly, which vary depending on the light conditions and on the subject's sensitivity, we first review the existing literature on the biophysics of the human eye in the presence of a dim light source, and then use the known values of the experimental variables to set the parameters of the computational simulation. The results of the simulation and their comparison with the experiment involving human subjects are reported and discussed. It is found that, while the computer simulation indicates that the human eye has the capacity to detect the corpuscular nature of photons under these conditions, this was not observed in practice. The possible reasons for the difference between theoretical prediction and experimental results are discussed.

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.

C-terminal threonines and serines play distinct roles in the desensitization of rhodopsin, a G protein-coupled receptor

Rod photoreceptors generate measurable responses to single-photon activation of individual molecules of the G protein-coupled receptor (GPCR), rhodopsin. Timely rhodopsin desensitization depends on phosphorylation and arrestin binding, which quenches G protein activation. Rhodopsin phosphorylation has been measured biochemically at C-terminal serine residues, suggesting that these residues are critical for producing fast, low-noise responses. The role of native threonine residues is unclear. We compared single-photon responses from rhodopsin lacking native serine or threonine phosphorylation sites. Contrary to expectation, serine-only rhodopsin generated prolonged step-like single-photon responses that terminated abruptly and randomly, whereas threonine-only rhodopsin generated responses that were only modestly slower than normal. We show that the step-like responses of serine-only rhodopsin reflect slow and stochastic arrestin binding. Thus, threonine sites play a privileged role in promoting timely arrestin binding and rhodopsin desensitization. Similar coordination of phosphorylation and arrestin binding may more generally permit tight control of the duration of GPCR activity.

DOI:http://dx.doi.org/10.7554/eLife.05981.001

‘Rod’ cells in the eye enable us to see in starlight. Inside these cells, a protein called rhodopsin is activated by light, which leads to an electrical signal being produced that travels to the brain. The duration of the electrical signal depends on the time it takes for the rhodopsin to be deactivated. Rhodopsin is a member of a large class of receptor proteins known as G protein-coupled receptors that regulate many processes throughout the body.

Previous studies have shown that rhodopsin is deactivated by the attachment of phosphate groups to the protein. This allows another protein called arrestin to bind to rhodopsin. The phosphates can be attached to particular amino acids—the building blocks of proteins—at one end of rhodopsin. Three of these are a type of amino acid called serine. Previous work has shown that light increases the speed at which phosphate groups are added to these serines, suggesting that they are important for producing rapid electrical signals. The other three amino acids are of a different type—called threonine—but it is less clear what role they play in deactivating rhodopsin.

Here, Azevedo et al. studied mutant forms of rhodopsin that were missing the serines or threonines in mice. The experiments show that loss of the serines only slightly slowed the electrical signals. However, loss of the threonines resulted in much slower electrical signals that ended at random times. This was due to rhodopsin being less able to bind to arrestin.

Azevedo et al. propose a new model for how rhodopsin is deactivated. Once light activates the protein, phosphate groups are rapidly added to the serines, which begins to lower the activity of rhodopsin. However, it is the slower addition of phosphates to the threonines that is essential to promote arrestin binding and fully deactivate the protein. Other proteins belonging to the G protein-coupled receptor family also have these serines and threonines, and thus, may be regulated in a similar way.

DOI:http://dx.doi.org/10.7554/eLife.05981.002

cGMP in mouse rods: the spatiotemporal dynamics underlying single photon responses

Vertebrate vision begins when retinal photoreceptors transduce photons into electrical signals that are then relayed to other neurons in the eye, and ultimately to the brain. In rod photoreceptors, transduction of single photons is achieved by a well-understood G-protein cascade that modulates cGMP levels, and in turn, cGMP-sensitive inward current. The spatial extent and depth of the decline in cGMP during the single photon response (SPR) have been major issues in phototransduction research since the discovery that single photons elicit substantial and reproducible changes in membrane current. The spatial profile of cGMP decline during the SPR affects signal gain, and thus may contribute to reduction of trial-to-trial fluctuations in the SPR. Here we summarize the general principles of rod phototransduction, emphasizing recent advances in resolving the spatiotemporal dynamics of cGMP during the SPR.

A comprehensive model of the phototransduction cascade in mouse rod cells

Vertebrate visual phototransduction is perhaps the most well-studied G-protein signaling pathway. A wealth of available biochemical and electrophysiological data has resulted in a rich history of mathematical modeling of the system. However, while the most comprehensive models have relied upon amphibian biochemical and electrophysiological data, modern research typically employs mammalian species, particularly mice, which exhibit significantly faster signaling dynamics. In this work, we present an adaptation of a previously published, comprehensive model of amphibian phototransduction that can produce quantitatively accurate simulations of the murine photoresponse. We demonstrate the ability of the model to predict responses to a wide range of stimuli and under a variety of mutant conditions. Finally, we employ the model to highlight a likely unknown mechanism related to the interaction between rhodopsin and rhodopsin kinase.

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.

Fluorescence spectroscopy of rhodopsins: insights and approaches

Fluorescence spectroscopy has become an established tool at the interface of biology, chemistry and physics because of its exquisite sensitivity and recent technical advancements. However, rhodopsin proteins present the fluorescence spectroscopist with a unique set of challenges and opportunities due to the presence of the light-sensitive retinal chromophore. This review briefly summarizes some approaches that have successfully met these challenges and the novel insights they have yielded about rhodopsin structure and function. We start with a brief overview of fluorescence fundamentals and experimental methodologies, followed by more specific discussions of technical challenges rhodopsin proteins present to fluorescence studies. Finally, we end by discussing some of the unique insights that have been gained specifically about visual rhodopsin and its interactions with affiliate proteins through the use of fluorescence spectroscopy. This article is part of a Special Issue entitled: Retinal Proteins - You can teach an old dog new tricks.

Exploring the rate-limiting steps in visual phototransduction recovery by bottom-up kinetic modeling

Background

Phototransduction in vertebrate photoreceptor cells represents a paradigm of signaling pathways mediated by G-protein-coupled receptors (GPCRs), which share common modules linking the initiation of the cascade to the final response of the cell. In this work, we focused on the recovery phase of the visual photoresponse, which is comprised of several interacting mechanisms.

Results

We employed current biochemical knowledge to investigate the response mechanisms of a comprehensive model of the visual phototransduction pathway. In particular, we have improved the model by implementing a more detailed representation of the recoverin (Rec)-mediated calcium feedback on rhodopsin kinase and including a dynamic arrestin (Arr) oligomerization mechanism. The model was successfully employed to investigate the rate limiting steps in the recovery of the rod photoreceptor cell after illumination. Simulation of experimental conditions in which the expression levels of rhodospin kinase (RK), of the regulator of the G-protein signaling (RGS), of Arr and of Rec were altered individually or in combination revealed severe kinetic constraints to the dynamics of the overall network.

Conclusions

Our simulations confirm that RGS-mediated effector shutdown is the rate-limiting step in the recovery of the photoreceptor and show that the dynamic formation and dissociation of Arr homodimers and homotetramers at different light intensities significantly affect the timing of rhodopsin shutdown. The transition of Arr from its oligomeric storage forms to its monomeric form serves to temper its availability in the functional state. Our results may explain the puzzling evidence that overexpressing RK does not influence the saturation time of rod cells at bright light stimuli. The approach presented here could be extended to the study of other GPCR signaling pathways.

Calcium feedback to cGMP synthesis strongly attenuates single-photon responses driven by long rhodopsin lifetimes

Rod photoreceptors generate amplified, reproducible responses to single photons via a G protein signaling cascade. Surprisingly, genetic perturbations that dramatically alter the deactivation of the principal signal amplifier, the GPCR rhodopsin (R∗), do not much alter the amplitude of single-photon responses (SPRs). These same perturbations, when crossed into a line lacking calcium feedback regulation of cGMP synthesis, produced much larger alterations in SPR amplitudes. Analysis of SPRs from rods with and without feedback reveal that the consequences of trial-to-trial fluctuations in R∗ lifetime in normal rods are also dampened by feedback regulation of cGMP synthesis. Thus, calcium feedback trumps the mechanisms of R∗ deactivation in determining the SPR amplitude, attenuating responses arising from longer R∗ lifetimes to a greater extent than those arising from shorter ones. As a result, rod SPRs achieve a more stereotyped amplitude, a characteristic considered important for reliable transmission through the visual system.

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.

Cone photoreceptor contributions to noise and correlations in the retinal output

Transduction and synaptic noise generated in retinal cone photoreceptors determine the fidelity with which light inputs are encoded, and the readout of cone signals by downstream circuits determines whether this fidelity is used for vision. We examined the effect of cone noise on visual signals by measuring its contribution to correlated noise in primate retinal ganglion cells. Correlated noise was strong in the responses of dissimilar cell types with shared cone inputs. The dynamics of cone noise could account for rapid correlations in ganglion cell activity, and the extent of shared cone input could explain correlation strength. Furthermore, correlated noise limited the fidelity with which visual signals were encoded by populations of ganglion cells. Thus, a simple picture emerges: cone noise, traversing the retina through diverse pathways, accounts for most of the noise and correlations in the retinal output and constrains how higher centers exploit signals carried by parallel visual pathways.

G-protein betagamma-complex is crucial for efficient signal amplification in vision

A fundamental question of cell signaling biology is how faint external signals produce robust physiological responses. One universal mechanism relies on signal amplification via intracellular cascades mediated by heterotrimeric G-proteins. This high amplification system allows retinal rod photoreceptors to detect single photons of light. Although much is now known about the role of the α-subunit of the rod-specific G-protein transducin in phototransduction, the physiological function of the auxiliary βγ-complex in this process remains a mystery. Here, we show that elimination of the transducin γ-subunit drastically reduces signal amplification in intact mouse rods. The consequence is a striking decline in rod visual sensitivity and severe impairment of nocturnal vision. Our findings demonstrate that transducin βγ-complex controls signal amplification of the rod phototransduction cascade and is critical for the ability of rod photoreceptors to function in low light conditions.

Activation and molecular recognition of the GPCR rhodopsin--insights from time-resolved fluorescence depolarisation and single molecule experiments

The cytoplasmic surface of the G-protein coupled receptor (GPCR) rhodopsin is a key element in membrane receptor activation, molecular recognition by signalling molecules, and receptor deactivation. Understanding of the coupling between conformational changes in the intramembrane domain and the membrane-exposed surface of the photoreceptor rhodopsin is crucial for the elucidation of the molecular mechanism in GPCR activation. As little is known about protein dynamics, particularly the conformational dynamics of the cytoplasmic surface elements on the nanoseconds timescale, we utilised time-resolved fluorescence anisotropy experiments and site-directed fluorescence labelling to provide information on both, conformational space and motion. We summarise our recent advances in understanding rhodopsin dynamics and function using time-resolved fluorescence depolarisation and single molecule fluorescence experiments, with particular focus on the amphipathic helix 8, lying parallel to the cytoplasmic membrane surface and connecting transmembrane helix 7 with the long C-terminal tail.

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.

Visual threshold is set by linear and nonlinear mechanisms in the retina that mitigate noise: how neural circuits in the retina improve the signal-to-noise ratio of the single-photon response

In sensory biology, a major outstanding question is how sensory receptor cells minimize noise while maximizing signal to set the detection threshold. This optimization could be problematic because the origin of both the signals and the limiting noise in most sensory systems is believed to lie in stimulus transduction. Signal processing in receptor cells can improve the signal-to-noise ratio. However, neural circuits can further optimize the detection threshold by pooling signals from sensory receptor cells and processing them using a combination of linear and nonlinear filtering mechanisms. In the visual system, noise limiting light detection has been assumed to arise from stimulus transduction in rod photoreceptors. In this context, the evolutionary optimization of the signal-to-noise ratio in the retina has proven critical in allowing visual sensitivity to approach the limits set by the quantal nature of light. Here, we discuss how noise in the mammalian retina is mitigated to allow for highly sensitive night vision.

Ectopic expression of cone-specific G-protein-coupled receptor kinase GRK7 in zebrafish rods leads to lower photosensitivity and altered responses

To investigate the roles of G-protein receptor kinases (GRKs) in the light responses of vertebrate photoreceptors, we generated transgenic zebrafish lines, the rods of which express either cone GRK (GRK7) or rod GRK (GRK1) in addition to the endogenous GRK1, and we then measured the electrophysiological characteristics of single-cell responses and the behavioural responses of intact animals. Our study establishes the zebrafish expression system as a convenient platform for the investigation of specific components of the phototransduction cascade. The addition of GRK1 led to minor changes in rod responses. However, exogenous GRK7 in GRK7-tg animals led to lowered rod sensitivity, as occurs in cones, but surprisingly to slower response kinetics. Examination of responses to long series of very dim flashes suggested the possibility that the GRK7-tg rods generated two classes of single-photon response, perhaps corresponding to the interaction of activated rhodopsin with GRK1 (giving a standard response) or with GRK7(giving a very small response). Behavioural measurement of optokinetic responses (OKR) in intact GRK7-tg zebrafish larvae showed that the overall rod visual pathway was less sensitive, in accord with the lowered sensitivity of the rods. These results help provide an understanding for the molecular basis of the electrophysiological differences between cones and rods.

Channel modulation and the mechanism of light adaptation in mouse rods

Vertebrate photoreceptors are thought to adapt to light by a change in Ca(2+), which is postulated to mediate modulation of (1) excited rhodopsin (Rh*) by Ca(2+)-dependent binding of recoverin, (2) guanylyl cyclase activity via Ca(2+)-dependent GCAP proteins, and (3) cyclic nucleotide-gated channels by binding of Ca(2+)-calmodulin. Previous experiments genetically deleted recoverin and the GCAPs and showed that significant regulation of sensitivity survives removal of (1) and (2). We genetically deleted the channel Ca(2+)-calmodulin binding site in the mouse Mus musculus and found that removal of (3) alters response waveform, but removal of (3) or of (2) and (3) together still leaves much of adaptation intact. These experiments demonstrate that an important additional mechanism is required, which other experiments indicate may be regulation of phosphodiesterase 6 (PDE6). We therefore constructed a kinetic model in which light produces a Ca(2+)-mediated decrease in PDE6 decay rate, with the novel feature that both spontaneously activated and light-activated PDE6 are modulated. This model, together with Ca(2+)-dependent acceleration of guanylyl cyclase, can successfully account for changes in sensitivity and response waveform in background light.

Systems biochemistry approaches to vertebrate phototransduction: towards a molecular understanding of disease

Phototransduction in vertebrates represents a paradigm of signalling pathways, in particular those mediated by G-protein-coupled receptors. The variety of protein-protein, protein-ion and protein-nucleotide interactions makes up an intricate network which is finely regulated by activating-deactivating molecules and chemical modifications. The holistic systems properties of the network allow for typical adaptation mechanisms, which ultimately result in fine adjustments of sensitivity and electrical response of the photoreceptor cells to the broad range of light stimuli. In the present article, we discuss a novel bottom-up strategy to study the phototransduction cascade in rod cells starting from the underlying biochemistry. The resulting network model can be simulated and the predicted dynamic behaviour directly compared with data from electrophysiological experiments performed on a wide range of illumination conditions. The advantage of applying procedures typical of systems theory to a well-studied signalling pathway is also discussed. Finally, the potential application to the study of the molecular basis of retinal diseases is highlighted through a practical example, namely the simulation of conditions related to Leber congenital amaurosis.

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.

Lessons from photoreceptors: turning off g-protein signaling in living cells

Phototransduction in retinal rods is one of the most extensively studied G-protein signaling systems. In recent years, our understanding of the biochemical steps that regulate the deactivation of the rod's response to light has greatly improved. Here, we summarize recent advances and highlight some of the remaining puzzles in this model signaling system.

Phototransduction and the evolution of photoreceptors

Photoreceptors in metazoans can be grouped into two classes, with their photoreceptive membrane derived either from cilia or microvilli. Both classes use some form of the visual pigment protein opsin, which together with 11-cis retinaldehyde absorbs light and activates a G-protein cascade, resulting in the opening or closing of ion channels. Considerable attention has recently been given to the molecular evolution of the opsins and other photoreceptor proteins; much is also known about transduction in the various photoreceptor types. Here we combine this knowledge in an attempt to understand why certain photoreceptors might have conferred particular selective advantages during evolution. We suggest that microvillar photoreceptors became predominant in most invertebrate species because of their single-photon sensitivity, high temporal resolution, and large dynamic range, and that rods and a duplex retina provided primitive chordates and vertebrates with similar sensitivity and dynamic range, but with a smaller expenditure of ATP.

Rhodopsin: the functional significance of asn-linked glycosylation and other post-translational modifications

Rhodopsin, the G-protein coupled receptor in retinal rod photoreceptors, is a highly conserved protein that undergoes several types of post-translational modifications. These modifications are essential to maintain the protein's structure as well as its proper function in the visual transduction cycle. Rhodopsin is N-glycosylated at Asn-2 and Asn-15 in its extracellular N-terminal domain. Mutations within the glycosylation consensus sequences of rhodopsin cause autosomal dominant retinitis pigmentosa, a disease that leads to blindness. Several groups have studied the role of rhodopsin's N-linked glycan chains in protein structure and function using a variety of approaches. These include the generation of a transgenic mouse model, study of a naturally occurring mutant animal model, in vivo pharmacological inhibition of glycosylation, and in vitro analyses using transfected COS-1 cells. These studies have provided insights into the possible role of rhodopsin glycosylation, but have yielded conflicting results.

Quantitative modeling of GRK-mediated beta2AR regulation

We developed a unified model of the GRK-mediated β2 adrenergic receptor (β2AR) regulation that simultaneously accounts for six different biochemical measurements of the system obtained over a wide range of agonist concentrations. Using a single deterministic model we accounted for (1) GRK phosphorylation in response to various full and partial agonists; (2) dephosphorylation of the GRK site on the β2AR; (3) β2AR internalization; (4) recycling of the β2AR post isoproterenol treatment; (5) β2AR desensitization; and (6) β2AR resensitization. Simulations of our model show that plasma membrane dephosphorylation and recycling of the phosphorylated receptor are necessary to adequately account for the measured dephosphorylation kinetics. We further used the model to predict the consequences of (1) modifying rates such as GRK phosphorylation of the receptor, arrestin binding and dissociation from the receptor, and receptor dephosphorylation that should reflect effects of knockdowns and overexpressions of these components; and (2) varying concentration and frequency of agonist stimulation “seen” by the β2AR to better mimic hormonal, neurophysiological and pharmacological stimulations of the β2AR. Exploring the consequences of rapid pulsatile agonist stimulation, we found that although resensitization was rapid, the β2AR system retained the memory of the previous stimuli and desensitized faster and much more strongly in response to subsequent stimuli. The latent memory that we predict is due to slower membrane dephosphorylation, which allows for progressive accumulation of phosphorylated receptor on the surface. This primes the receptor for faster arrestin binding on subsequent agonist activation leading to a greater extent of desensitization. In summary, the model is unique in accounting for the behavior of the β2AR system across multiple types of biochemical measurements using a single set of experimentally constrained parameters. It also provides insight into how the signaling machinery can retain memory of prior stimulation long after near complete resensitization has been achieved.

The β2 adrenergic receptor (β2AR) is involved in regulating many cellular processes such as smooth muscle relaxation in the airways and the vasculature. Drugs that activate the β2AR are used in treating asthma and chronic obstructive pulmonary disorder (COPD), and prolonged use of these drugs leads to the loss of their effects. Thus, a dynamic model of how the β2AR responds to different drugs is fundamental to their rational use. In this study a consensus model of G protein coupled receptor kinase (GRK)-mediated receptor regulation was formulated based on quantitative measures of six processes involved in β2AR regulation. This model was then used to simulate the consequences of manipulating key rates associated with the GRK-mediated β2AR regulation, leading to predictions which will provide a useful framework for further tests and elaborations of the model in basic and clinical research.

Functional interaction structures of the photochromic retinal protein rhodopsin

We studied functional interaction structures of the vertebrate membrane photoreceptor rhodopsin containing retinal as a chromophore. Using time-resolved fluorescence depolarization we analyzed real-time dynamics and conformational changes of the cytoplasmic helix 8 (H8) preceding the long C-terminal tail of rhodopsin. H8 runs parallel to the membrane surface and extends from transmembrane helix 7 whose highly conserved NPxxY(x)F motif connects that region of rhodopsin with the retinal binding pocket. Our measurements indicate that photo-induced retinal isomerization from 11-cis to all-trans provokes conformational changes of H8, including slower motion and reduced flexibility, that are specific for the active metarhodopsin-II photo-intermediate. These conformational changes are absent in the retinal-devoid state opsin and in the phosphorylated metarhodopsin-II state upon receptor deactivation. Furthermore we show that membrane rim effects can influence interfacial reactions at the cytoplasmic rhodopsin surface such as proton transfer reactions between surface and aqueous bulk phase or binding of the signaling protein transducin visualized with single-molecule widefield microscopy. These findings are important for an understanding of the effects of membrane structure on the photo-transduction mechanism.

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.

Arrestin competition influences the kinetics and variability of the single-photon responses of mammalian rod photoreceptors

Reliable signal transduction via G-protein-coupled receptors requires proper receptor inactivation. For example, signals originating from single rhodopsin molecules vary little from one to the next, requiring reproducible inactivation of rhodopsin by phosphorylation and arrestin binding. We determined how reduced concentrations of rhodopsin kinase (GRK1) and/or arrestin1 influenced the kinetics and variability of the single-photon responses of mouse rod photoreceptors. These experiments revealed that arrestin, in addition to its role in quenching the activity of rhodopsin, can tune the kinetics of rhodopsin phosphorylation by competing with GRK1. This competition influenced the variability of the active lifetime of rhodopsin. Biasing the competition in favor of GRK1 revealed that rhodopsin remained active through much of the single-photon response under the conditions of our experiments. This long-lasting rhodopsin activity can explain the characteristic time course of single-photon response variability. Indeed, explaining the late time-to-peak of the variance required an active lifetime of rhodopsin approximately twice that of the G-protein transducin. Competition between arrestins and kinases may be a general means of influencing signals mediated by G-protein-coupled receptors, particularly when activation of a few receptors produces signals of functional importance.

Maximally reliable Markov chains under energy constraints

Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.

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.

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.