A kinetic analysis of mouse rod and cone photoreceptor responses

Genetic manipulation of rod-cone differences in mouse retina

Though rod and cone photoreceptors use similar phototransduction mechanisms, previous model calculations have indicated that the most important differences in their light responses are likely to be differences in amplification of the G-protein cascade, different decay rates of phosphodiesterase (PDE) and pigment phosphorylation, and different rates of turnover of cGMP in darkness. To test this hypothesis, we constructed TrUx;GapOx rods by crossing mice with decreased transduction gain from decreased transducin expression, with mice displaying an increased rate of PDE decay from increased expression of GTPase-activating proteins (GAPs). These two manipulations brought the sensitivity of TrUx;GapOx rods to within a factor of 2 of WT cone sensitivity, after correcting for outer-segment dimensions. These alterations did not, however, change photoreceptor adaptation: rods continued to show increment saturation though at a higher background intensity. These experiments confirm model calculations that rod responses can mimic some (though not all) of the features of cone responses after only a few changes in the properties of transduction proteins.

A dynamical adaptation model of visual spatiotemporal processing in cones and horizontal cells

In this work, we introduce a phenomenological model for the cone-horizontal cell assembly, including spatial integration and formation of receptive field-like structures. The model extends our previous dynamical adaptation description with gain control accounting for processes in single cones, valid in severe nonlinear regimes. Here, a spatially extended feedback mechanism is introduced from horizontal cells to cones to account for experimental evidence, contributing thus to the development of a center-surround receptive field in cones and downstream bipolar cells. Feedback gain is defined on different spatial scales by weighting spatial filters: a short scale accounting for cone input to the feedback mechanism and a large scale driven by the syncytium characteristics of horizontal cells. A third spatial scale improves the description, mimicking neighboring cone-cone coupling. This overall spatial integration couples to temporal signal processing, thus obtaining a spatiotemporal model of outer retina responses capable of reproducing nonlinear features in both dimensions (space and time). The model was tested and validated using measurements on horizontal cells from different studies, with excellent performance. By its phenomenological nature, signal processing properties are inferred from model parameters. The model can be used in arrays of processing units with more complex incoming patterns of visual stimuli.

Direct comparison reveals algorithmic similarities in fly and mouse visual motion detection

Evolution has equipped vertebrates and invertebrates with neural circuits that selectively encode visual motion. While similarities in the computations performed by these circuits in mouse and fruit fly have been noted, direct experimental comparisons have been lacking. Because molecular mechanisms and neuronal morphology in the two species are distinct, we directly compared motion encoding in these two species at the algorithmic level, using matched stimuli and focusing on a pair of analogous neurons, the mouse ON starburst amacrine cell (ON SAC) and Drosophila T4 neurons. We find that the cells share similar spatiotemporal receptive field structures, sensitivity to spatiotemporal correlations, and tuning to sinusoidal drifting gratings, but differ in their responses to apparent motion stimuli. Both neuron types showed a response to summed sinusoids that deviates from models for motion processing in these cells, underscoring the similarities in their processing and identifying response features that remain to be explained.

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.

Pepperberg plot: Modeling flash response saturation in retinal rods of mouse

Retinal rods evolved to be able to detect single photons. Despite their exquisite sensitivity, rods operate over many log units of light intensity. Several processes inside photoreceptor cells make this incredible light adaptation possible. Here, we added to our previously developed, fully space resolved biophysical model of rod phototransduction, some of the mechanisms that play significant roles in shaping the rod response under high illumination levels: the function of RGS9 in shutting off G protein transducin, and calcium dependences of the phosphorylation rates of activated rhodopsin, of the binding of cGMP to the light-regulated ion channel, and of two membrane guanylate cyclase activities. A well stirred version of this model captured the responses to bright, saturating flashes in WT and mutant mouse rods and was used to explain "Pepperberg plots," that graph the time during which the response is saturated against the natural logarithm of flash strength for bright flashes. At the lower end of the range, saturation time increases linearly with the natural logarithm of flash strength. The slope of the relation (τ_D) is dictated by the time constant of the rate-limiting (slowest) step in the shutoff of the phototransduction cascade, which is the hydrolysis of GTP by transducin. We characterized mathematically the X-intercept ( Φ o ) which is the number of photoisomerizations that just saturates the rod response. It has been observed that for flash strengths exceeding a few thousand photoisomerizations, the curves depart from linearity. Modeling showed that the "upward bend" for very bright flash intensities could be explained by the dynamics of RGS9 complex and further predicted that there would be a plateau at flash strengths giving rise to more than ~10⁷ photoisomerizations due to activation of all available PDE. The model accurately described alterations in saturation behavior of mutant murine rods resulting from transgenic perturbations of the cascade targeting membrane guanylate cyclase activity, and expression levels of GRK, RGS9, and PDE. Experimental results from rods expressing a mutant light-regulated channel purported to lack calmodulin regulation deviated from model predictions, suggesting that there were other factors at play.

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.

Low signaling efficiency from receptor to effector in olfactory transduction: A quantified ligand-triggered GPCR pathway

G protein-coupled receptor (GPCR) signaling is ubiquitous. As an archetype of this signaling motif, rod phototransduction has provided many fundamental, quantitative details, including a dogma that one active GPCR molecule activates a substantial number of downstream G protein/enzyme effector complexes. However, rod phototransduction is light-activated, whereas GPCR pathways are predominantly ligand-activated. Here, we report a detailed study of the ligand-triggered GPCR pathway in mammalian olfactory transduction, finding that an odorant-receptor molecule when (one-time) complexed with its most effective odorants produces on average much less than one downstream effector. Further experiments gave a nominal success probability of tentatively ∼10-4 (more conservatively, ∼10-2 to ∼10-5). This picture is potentially more generally representative of GPCR signaling than is rod phototransduction, constituting a paradigm shift.

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.

Photoreceptor phosphodiesterase (PDE6): activation and inactivation mechanisms during visual transduction in rods and cones

Rod and cone photoreceptors of the vertebrate retina utilize cGMP as the primary intracellular messenger for the visual signaling pathway that converts a light stimulus into an electrical response. cGMP metabolism in the signal-transducing photoreceptor outer segment reflects the balance of cGMP synthesis (catalyzed by guanylyl cyclase) and degradation (catalyzed by the photoreceptor phosphodiesterase, PDE6). Upon light stimulation, rapid activation of PDE6 by the heterotrimeric G-protein (transducin) triggers a dramatic drop in cGMP levels that lead to cell hyperpolarization. Following cessation of the light stimulus, the lifetime of activated PDE6 is also precisely regulated by additional processes. This review summarizes recent advances in the structural characterization of the rod and cone PDE6 catalytic and regulatory subunits in the context of previous biochemical studies of the enzymological properties and allosteric regulation of PDE6. Emphasis is given to recent advances in understanding the structural and conformational changes underlying the mechanism by which the activated transducin α-subunit binds to-and relieves inhibition of-PDE6 catalysis that is controlled by its intrinsically disordered, inhibitory γ-subunit. The role of the regulator of G-protein signaling 9-1 (RGS9-1) in regulating the lifetime of the transducin-PDE6 is also briefly covered. The therapeutic potential of pharmacological compounds acting as inhibitors or activators targeting PDE6 is discussed in the context of inherited retinal diseases resulting from mutations in rod and cone PDE6 genes as well as other inherited defects that arise from excessive cGMP accumulation in retinal photoreceptor cells.

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.