The limit of photoreceptor sensitivity: molecular mechanisms of dark noise in retinal cones

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.

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.

Apo-Opsin and Its Dark Constitutive Activity across Retinal Cone Subtypes

Retinal rod and cone photoreceptors mediate vision in dim and bright light, respectively, by transducing absorbed photons into neural electrical signals. Their phototransduction mechanisms are essentially identical. However, one difference is that, whereas a rod visual pigment remains stable in darkness, a cone pigment has some tendency to dissociate spontaneously into apo-opsin and retinal (the chromophore) without isomerization. This cone-pigment property is long known but has mostly been overlooked. Importantly, because apo-opsin has weak constitutive activity, it triggers transduction to produce electrical noise even in darkness. Currently, the precise dark apo-opsin contents across cone subtypes are mostly unknown, as are their dark activities. We report here a study of goldfish red (L), green (M), and blue (S) cones, finding with microspectrophotometry widely different apo-opsin percentages in darkness, being ∼30% in L cones, ∼3% in M cones, and negligible in S cones. L and M cones also had higher dark apo-opsin noise than holo-pigment thermal isomerization activity. As such, given the most likely low signal amplification at the pigment-to-transducin/phosphodiesterase phototransduction step, especially in L cones, apo-opsin noise may not be easily distinguishable from light responses and thus may affect cone vision near threshold.

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

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

Light exposure during embryonic and yolk-sac alevin development of Chinook salmon Oncorhynchus tshawytscha does not alter the spectral phenotype of photoreceptors

Colour vision is mediated by the expression of different visual pigments in photoreceptors of the vertebrate retina. Each visual pigment is a complex of a protein (opsin) and a vitamin A chromophore; alterations to either component affects visual pigment absorbance and, potentially, the visual capabilities of an animal. Many species of fish undergo changes in opsin expression during retinal development. In the case of salmonid fishes the single cone photoreceptors undergo a switch in opsin expression from SWS1 (ultraviolet sensitive) to SWS2 (blue-light sensitive) starting at the yolk-sac alevin stage, around the time when they first experience light. Whether light may initiate this event or produce a plastic response in the various photoreceptors is unknown. In this study, Chinook salmon Oncorhynchus tshawytscha were exposed to light from the embryonic (5 days prior to hatching) into the yolk sac alevin (25 days post hatching) stage and the spectral phenotype of photoreceptors assessed with respect to that of unexposed controls by in situ hybridization with opsin riboprobes. Light exposure did not change the spectral phenotype of photoreceptors, their overall morphology or spatial arrangement. These results concur with those from a variety of fish species and suggest that plasticity in photoreceptor spectral phenotype via changes in opsin expression may not be a widespread occurrence among teleosts.

A novel mechanism of cone photoreceptor adaptation

An animal’s ability to survive depends on its sensory systems being able to adapt to a wide range of environmental conditions, by maximizing the information extracted and reducing the noise transmitted. The visual system does this by adapting to luminance and contrast. While luminance adaptation can begin at the retinal photoreceptors, contrast adaptation has been shown to start at later stages in the retina. Photoreceptors adapt to changes in luminance over multiple time scales ranging from tens of milliseconds to minutes, with the adaptive changes arising from processes within the phototransduction cascade. Here we show a new form of adaptation in cones that is independent of the phototransduction process. Rather, it is mediated by voltage-gated ion channels in the cone membrane and acts by changing the frequency response of cones such that their responses speed up as the membrane potential modulation depth increases and slow down as the membrane potential modulation depth decreases. This mechanism is effectively activated by high-contrast stimuli dominated by low frequencies such as natural stimuli. However, the more generally used Gaussian white noise stimuli were not effective since they did not modulate the cone membrane potential to the same extent. This new adaptive process had a time constant of less than a second. A critical component of the underlying mechanism is the hyperpolarization-activated current, I_h, as pharmacologically blocking it prevented the long- and mid- wavelength sensitive cone photoreceptors (L- and M-cones) from adapting. Consistent with this, short- wavelength sensitive cone photoreceptors (S-cones) did not show the adaptive response, and we found they also lacked a prominent I_h. The adaptive filtering mechanism identified here improves the information flow by removing higher-frequency noise during lower signal-to-noise ratio conditions, as occurs when contrast levels are low. Although this new adaptive mechanism can be driven by contrast, it is not a contrast adaptation mechanism in its strictest sense, as will be argued in the Discussion.

An animal’s ability to survive depends on its ability to adapt to a wide range of light conditions, by maximizing the information flow through the retina. Here, we show a new form of adaptation in cone photoreceptors that helps them optimize the information they transmit by adjusting their response kinetics to better match the visual conditions. The adaptive mechanism we describe is independent of the cone phototransduction process and is instead mediated by membrane processes in which the hyperpolarization-activated current, I_h, plays a critical role. Consistent with the critical role of this current, we also found that cones sensitive to short wavelengths lacked a prominent I_h current and did not show this new form of adaptation. As voltage-dependent processes underlie the adaptational mechanism, it is only apparent when the stimuli are able to sufficiently modulate the membrane potential of cones. This happens with natural stimuli, which are able to deliver high levels of “effective” contrast. However, even though this new adaptive mechanism can be driven by contrast, we argue in the Discussion that in its strictest sense it is not a contrast adaptation mechanism per se.

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.

How lateral inhibition and fast retinogeniculo-cortical oscillations create vision: A new hypothesis

The role of the physiological processes involved in human vision escapes clarification in current literature. Many unanswered questions about vision include: 1) whether there is more to lateral inhibition than previously proposed, 2) the role of the discs in rods and cones, 3) how inverted images on the retina are converted to erect images for visual perception, 4) what portion of the image formed on the retina is actually processed in the brain, 5) the reason we have an after-image with antagonistic colors, and 6) how we remember space. This theoretical article attempts to clarify some of the physiological processes involved with human vision. The global integration of visual information is conceptual; therefore, we include illustrations to present our theory. Universally, the eyeball is 2.4cm and works together with membrane potential, correspondingly representing the retinal layers, photoreceptors, and cortex. Images formed within the photoreceptors must first be converted into chemical signals on the photoreceptors' individual discs and the signals at each disc are transduced from light photons into electrical signals. We contend that the discs code the electrical signals into accurate distances and are shown in our figures. The pre-existing oscillations among the various cortices including the striate and parietal cortex, and the retina work in unison to create an infrastructure of visual space that functionally "places" the objects within this "neural" space. The horizontal layers integrate all discs accurately to create a retina that is pre-coded for distance. Our theory suggests image inversion never takes place on the retina, but rather images fall onto the retina as compressed and coiled, then amplified through lateral inhibition through intensification and amplification on the OFF-center cones. The intensified and amplified images are decompressed and expanded in the brain, which become the images we perceive as external vision.

SUMMARY

This is a theoretical article presenting a novel hypothesis about the physiological processes in vision, and expounds upon the visual aspect of two of our previously published articles, "A unified 3D default space consciousness model combining neurological and physiological processes that underlie conscious experience", and "Functional representation of vision within the mind: A visual consciousness model based in 3D default space." Currently, neuroscience teaches that visual images are initially inverted on the retina, processed in the brain, and then conscious perception of vision happens in the visual cortex. Here, we propose that inversion of visual images never takes place because images enter the retina as coiled and compressed graded potentials that are intensified and amplified in OFF-center photoreceptors. Once they reach the brain, they are decompressed and expanded to the original size of the image, which is perceived by the brain as the external image. We adduce that pre-existing oscillations (alpha, beta, and gamma) among the various cortices in the brain (including the striate and parietal cortex) and the retina, work together in unison to create an infrastructure of visual space thatfunctionally "places" the objects within a "neural" space. These fast oscillations "bring" the faculties of the cortical activity to the retina, creating the infrastructure of the space within the eye where visual information can be immediately recognized by the brain. By this we mean that the visual (striate) cortex synchronizes the information with the photoreceptors in the retina, and the brain instantaneously receives the already processed visual image, thereby relinquishing the eye from being required to send the information to the brain to be interpreted before it can rise to consciousness. The visual system is a heavily studied area of neuroscience yet very little is known about how vision occurs. We believe that our novel hypothesis provides new insights into how vision becomes part of consciousness, helps to reconcile various previously proposed models, and further elucidates current questions in vision based on our unified 3D default space model. Illustrations are provided to aid in explaining our theory.

Calcium dynamics change in degenerating cone photoreceptors

Cone photoreceptors (cones) are essential for high-resolution daylight vision and colour perception. Loss of cones in hereditary retinal diseases has a dramatic impact on human vision. The mechanisms underlying cone death are poorly understood, and consequently, there are no treatments available. Previous studies suggest a central role for calcium (Ca²⁺) homeostasis deficits in photoreceptor degeneration; however, direct evidence for this is scarce and physiological measurements of Ca²⁺in degenerating mammalian cones are lacking.Here, we took advantage of the transgenic HR2.1:TN-XL mouse line that expresses a genetically encoded Ca²⁺biosensor exclusively in cones. We cross-bred this line with mouse models for primary ("cone photoreceptor function loss-1", cpfl1) and secondary ("retinal degeneration-1", rd1) cone degeneration, respectively, and assessed resting Ca²⁺levels and light-evoked Ca²⁺responses in cones using two-photon imaging. We found that Ca²⁺dynamics were altered in cpfl1 cones, showing higher noise and variable Ca²⁺levels, with significantly wider distribution than for wild-type and rd1 cones. Unexpectedly, up to 21% of cpfl1 cones still displayed light-evoked Ca²⁺responses, which were larger and slower than wild-type responses. In contrast, genetically intact rd1 cones were characterized by lower noise and complete lack of visual function.Our study demonstrates alterations in cone Ca²⁺dynamics in both primary and secondary cone degeneration. Our results are consistent with the view that higher (fluctuating) cone Ca²⁺levels are involved in photoreceptor cell death in primary (cpfl1) but not in secondary (rd1) cone degeneration. These findings may guide the future development of therapies targeting photoreceptor Ca²⁺homeostasis.

Biophotons Contribute to Retinal Dark Noise

The discovery of dark noise in retinal photoreceptors resulted in a long-lasting controversy over its origin and the underlying mechanisms. Here, we used a novel ultra-weak biophoton imaging system (UBIS) to detect biophotonic activity (emission) under dark conditions in rat and bullfrog (Rana catesbeiana) retinas in vitro. We found a significant temperature-dependent increase in biophotonic activity that was completely blocked either by removing intracellular and extracellular Ca(2+) together or inhibiting phosphodiesterase 6. These findings suggest that the photon-like component of discrete dark noise may not be caused by a direct contribution of the thermal activation of rhodopsin, but rather by an indirect thermal induction of biophotonic activity, which then activates the retinal chromophore of rhodopsin. Therefore, this study suggests a possible solution regarding the thermal activation energy barrier for discrete dark noise, which has been debated for almost half a century.

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.

Kinetics of thermal activation of an ultraviolet cone pigment

Visual pigments can be thermally activated via isomerization of the retinyl chromophore and hydrolysis of the Schiff base (SB) through which the retinyl chromophore is bound to the opsin protein. Here, we present the first combined experimental and theoretical study of the thermal activation of a Siberian hamster ultraviolet (SHUV) pigment. We measured the rates of thermal isomerization and hydrolysis in the SHUV pigment and bovine rhodopsin. We found that these rates were significantly faster in the UV pigment than in rhodopsin due to the difference in the structural and electrostatic effects surrounding the unprotonated Schiff base (USB) retinyl chromophore in the UV pigment. Theoretical (DFT-QM/MM) calculations of the cis-trans thermal isomerization revealed a barrier of ∼23 kcal/mol for the USB retinyl chromophore in SHUV compared to ∼40 kcal/mol for protonated Schiff base (PSB) chromophore in rhodopsin. The lower barrier for thermal isomerization in the SHUV pigment is attributed to the (i) lessening of the steric restraints near the β-ionone ring and SB ends of the chromophore, (ii) displacement of the transmembrane helix 6 (TM6) away from the binding pocket toward TM5 due to absence of the salt bridge between the USB and the protonated E113 residue, and (iii) change in orientation of the hydrogen-bonding networks (HBNs) in the extracellular loop 2 (EII). The results in comparing thermal stability of UV cone pigment and rhodopsin provide insight into molecular evolution of vertebrate visual pigments in achieving low discrete dark noise and high photosensitivity in rod pigments for dim-light vision.

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.

Origin and effect of phototransduction noise in primate cone photoreceptors

Noise in the responses of cone photoreceptors sets a fundamental limit to visual sensitivity, yet the origin of noise in mammalian cones and its relation to behavioral sensitivity are poorly understood. Our work here on primate cones improves understanding of these issues in three ways. First, we find that cone noise is not dominated by spontaneous photopigment activation or by quantal fluctuations in photon absorption but instead by other sources, namely channel noise and fluctuations in cGMP. Second, we find that adaptation in cones, unlike that in rods, affects signals and noise differently. This difference helps explain why thresholds for rod- and cone-mediated signals have different dependencies on background light level. Third, past estimates of noise in mammalian cones are too high to explain behavioral sensitivity. Our measurements indicate a lower level of cone noise, and thus help reconcile physiological and behavioral estimates of cone noise and sensitivity.

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

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

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

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

Functional significance of the taper of vertebrate cone photoreceptors

Vertebrate photoreceptors are commonly distinguished based on the shape of their outer segments: those of cones taper, whereas the ones from rods do not. The functional advantages of cone taper, a common occurrence in vertebrate retinas, remain elusive. In this study, we investigate this topic using theoretical analyses aimed at revealing structure–function relationships in photoreceptors. Geometrical optics combined with spectrophotometric and morphological data are used to support the analyses and to test predictions. Three functions are considered for correlations between taper and functionality. The first function proposes that outer segment taper serves to compensate for self-screening of the visual pigment contained within. The second function links outer segment taper to compensation for a signal-to-noise ratio decline along the longitudinal dimension. Both functions are supported by the data: real cones taper more than required for these compensatory roles. The third function relates outer segment taper to the optical properties of the inner compartment whereby the primary determinant is the inner segment’s ability to concentrate light via its ellipsoid. In support of this idea, the rod/cone ratios of primarily diurnal animals are predicted based on a principle of equal light flux gathering between photoreceptors. In addition, ellipsoid concentration factor, a measure of ellipsoid ability to concentrate light onto the outer segment, correlates positively with outer segment taper expressed as a ratio of characteristic lengths, where critical taper is the yardstick. Depending on a light-funneling property and the presence of focusing organelles such as oil droplets, cone outer segments can be reduced in size to various degrees. We conclude that outer segment taper is but one component of a miniaturization process that reduces metabolic costs while improving signal detection. Compromise solutions in the various retinas and retinal regions occur between ellipsoid size and acuity, on the one hand, and faster response time and reduced light sensitivity, on the other.

Binding by asynchrony: the neuronal phase code

Neurons display continuous subthreshold oscillations and discrete action potentials (APs). When APs are phase-locked to the subthreshold oscillation, we hypothesize they represent two types of information: the presence/absence of a sensory feature and the phase of subthreshold oscillation. If subthreshold oscillation phases are neuron-specific, then the sources of APs can be recovered based on the AP times. If the spatial information about the stimulus is converted to AP phases, then APs from multiple neurons can be combined into a single axon and the spatial configuration reconstructed elsewhere. For the reconstruction to be successful, we introduce two assumptions: that a subthreshold oscillation field has a constant phase gradient and that coincidences between APs and intracellular subthreshold oscillations are neuron-specific as defined by the "interference principle." Under these assumptions, a phase-coding model enables information transfer between structures and reproduces experimental phenomenons such as phase precession, grid cell architecture, and phase modulation of cortical spikes. This article reviews a recently proposed neuronal algorithm for information encoding and decoding from the phase of APs (Nadasdy, 2009). The focus is given to the principles common across different systems instead of emphasizing system specific differences.

Photopigment quenching is Ca2+ dependent and controls response duration in salamander L-cone photoreceptors

The time scale of the photoresponse in photoreceptor cells is set by the slowest of the steps that quench the light-induced activity of the phototransduction cascade. In vertebrate photoreceptor cells, this rate-limiting reaction is thought to be either shutoff of catalytic activity in the photopigment or shutoff of the pigment's effector, the transducin-GTP–phosphodiesterase complex. In suction pipette recordings from isolated salamander L-cones, we found that preventing changes in internal [Ca²⁺] delayed the recovery of the light response and prolonged the dominant time constant for recovery. Evidence that the Ca²⁺-sensitive step involved the pigment itself was provided by the observation that removal of Cl⁻ from the pigment's anion-binding site accelerated the dominant time constant for response recovery. Collectively, these observations indicate that in L-cones, unlike amphibian rods where the dominant time constant is insensitive to [Ca²⁺], pigment quenching rate limits recovery and provides an additional mechanism for modulating the cone response during light adaptation.

Inhibition of nitric oxide synthase desensitizes retinal ganglion cells to light by diminishing their excitatory synaptic currents under light adaptation

The effect of inhibiting nitric oxide synthase (NOS) on the visual responses of mouse retinal ganglion cells (RGCs) was studied under light adaptation by using patch-clamp recordings. The results demonstrated that NOS inhibitor, l-NAME, reduced the sensitivity of RGCs to light under light adaptation at different ambient light conditions. These observations were seen in all cells that recordings were made from. l-NAME diminished the excitatory synaptic currents (EPSCs), rather than increasing the inhibitory synaptic currents, of RGCs to reduce the sensitivity of RGCs to light. Cones may be the sites that l-NAME acted to diminish the EPSCs of RGCs.

Diffusion in narrow domains and application to phototransduction

The mean time for a Brownian particle to find a small target inside a narrow domain is a key parameter for many chemical reactions occurring in cellular microstructures. Although current estimations are given for a large class of domains, they cannot be used for narrow domains often encountered in cellular biology, such as the synaptic cleft, narrow compartments in the outer segment of vertebrate photoreceptors, or neuron-glia contact. We compute here the mean time for a Brownian particle to hit a small target placed on the surface of a narrow cylinder. We then use this result to estimate the rate constant of cyclic-GMP (cGMP) hydrolysis by the activated enzyme phosphodiesterase (PDE) in the narrow microdomains that build up the outer segment of a rod photoreceptor. By controlling the cGMP concentration, PDE activity is at the basis of the early photoresponse chemical reaction cascade. Our approach allows us to compute the cGMP rate constant as a function of biophysical parameters.

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.

Quantal noise from human red cone pigment

The rod pigment, rhodopsin, shows spontaneous isomerization activity. This quantal noise produces a dark light of approximately 0.01 photons s(-1) rod(-1) in human, setting the threshold for rod vision. The spontaneous isomerization activity of human cone pigments has long remained a mystery because the effect of a single isomerized pigment molecule in cones, unlike that in rods, is small and beyond measurement. We have now overcome this problem by expressing human red cone pigment transgenically in mouse rods in order to exploit their large single-photon response, especially after genetic removal of a key negative-feedback regulation. Extrapolating the measured quantal noise of transgenic cone pigment to native human red cones, we obtained a dark rate of approximately 10 false events s(-1) cone(-1), almost 10(3)-fold lower than the overall dark transduction noise previously reported in primate cones. Our measurements provide a rationale for why mammalian red, green and blue cones have comparable sensitivities, unlike their amphibian counterparts.

The dynamics of phosphodiesterase activation in rods and cones

Phototransduction starts with the activation of a rhodopsin (respectively, coneopsin) molecule, located in the outer segment of rod (respectively, cone) photoreceptors. The subsequent amplification pathway proceeds via the G-protein transducin to the activation of phosphodiesterase (PDE), a G-protein coupled effector enzyme. In this article, we study the dynamics of PDE activation by constructing a Markov model that is based on the underlying chemical reactions including multiple rhodopsin phosphorylations. We derive explicit equations for the mean and the variance of activated PDE. Our analysis reveals that a low rhodopsin lifetime variance is neither necessary nor sufficient to achieve reliable PDE activation. The numerical simulations show that during the rising phase the variability of PDE activation is much lower compared to the recovery phase, and this property depends crucially on the transducin activation rates. Furthermore, we find that the dynamics of the activation process greatly differs depending on whether rhodopsin or PDE deactivation limits the recovery of the photoresponse. Finally, our simulations for cones show that only very few PDEs are activated by an excited photopigment, which might explain why in S-cones no single photon response can be observed.

Chromophore switch from 11-cis-dehydroretinal (A2) to 11-cis-retinal (A1) decreases dark noise in salamander red rods

Dark noise, light-induced noise and responses to brief flashes of light were recorded in the membrane current of isolated rods from larval tiger salamander retina before and after bleaching most of the native visual pigment, which mainly has the 11-cis-3,4-dehydroretinal (A2) chromophore, and regenerating with the 11-cis-retinal (A1) chromophore in the same isolated rods. The purpose was to test the hypothesis that blue-shifting the pigment by switching from A2 to A1 will decrease the rate of spontaneous thermal activations and thus intrinsic light-like noise in the rod. Complete recordings were obtained in five cells (21 degrees C). Based on the wavelength of maximum absorbance, lambda max,A1 = 502 nm and lambda max,A2 = 528 nm, the average A2 : A1 ratio determined from rod spectral sensitivities and absorbances was approximately 0.74 : 0.26 in the native state and approximately 0.09 : 0.91 in the final state. In the native (A2) state, the single-quantum response (SQR) had an amplitude of 0.41 +/- 0.03 pA and an integration time of 3.16 +/- 0.15 s (mean +/- s.e.m.). The low-frequency branch of the dark noise power spectrum was consistent with discrete SQR-like events occurring at a rate of 0.238 +/- 0.026 rod(-1) s(-1). The corresponding values in the final state were 0.57 +/- 0.07 pA (SQR amplitude), 3.47 +/- 0.26 s (SQR integration time), and 0.030 +/- 0.006 rod(-1) s(-1) (rate of dark events). Thus the rate of dark events per rod and the fraction of A2 pigment both changed by ca 8-fold between the native and final states, indicating that the dark events originated mainly in A2 molecules even in the final state. By extrapolating the linear relation between event rates and A2 fraction to 0% A2 (100% A1) and 100% A2 (0% A1), we estimated that the A1 pigment is at least 36 times more stable than the A2 pigment. The noise component attributed to discrete dark events accounted for 73% of the total dark current variance in the native (A2) state and 46% in the final state. The power spectrum of the remaining 'continuous' noise component did not differ between the two states. The smaller and faster SQR in the native (A2) state is consistent with the idea that the rod behaves as if light-adapted by dark events that occur at a rate of nearly one per integration time. Both the decreased level of dark noise and the increased SQR amplitude must significantly improve the reliability of photon detection in dim light in the presence of the A1 chromophore compared to the native (A2) state in salamander rods.

Physiological properties of rod photoreceptor cells in green-sensitive cone pigment knock-in mice

Rod and cone photoreceptor cells that are responsible for scotopic and photopic vision, respectively, exhibit photoresponses different from each other and contain similar phototransduction proteins with distinctive molecular properties. To investigate the contribution of the different molecular properties of visual pigments to the responses of the photoreceptor cells, we have generated knock-in mice in which rod visual pigment (rhodopsin) was replaced with mouse green-sensitive cone visual pigment (mouse green). The mouse green was successfully transported to the rod outer segments, though the expression of mouse green in homozygous retina was approximately 11% of rhodopsin in wild-type retina. Single-cell recordings of wild-type and homozygous rods suggested that the flash sensitivity and the single-photon responses from mouse green were three to fourfold lower than those from rhodopsin after correction for the differences in cell volume and levels of several signal transduction proteins. Subsequent measurements using heterozygous rods expressing both mouse green and rhodopsin E122Q mutant, where these pigments in the same rod cells can be selectively irradiated due to their distinctive absorption maxima, clearly showed that the photoresponse of mouse green was threefold lower than that of rhodopsin. Noise analysis indicated that the rate of thermal activations of mouse green was 1.7 x 10(-7) s(-1), about 860-fold higher than that of rhodopsin. The increase in thermal activation of mouse green relative to that of rhodopsin results in only 4% reduction of rod photosensitivity for bright lights, but would instead be expected to severely affect the visual threshold under dim-light conditions. Therefore, the abilities of rhodopsin to generate a large single photon response and to retain high thermal stability in darkness are factors that have been necessary for the evolution of scotopic vision.

Transgenic mice carrying the H258N mutation in the gene encoding the beta-subunit of phosphodiesterase-6 (PDE6B) provide a model for human congenital stationary night blindness

Mutations in the beta-subunit of cGMP-phosphodiesterase (PDE6beta) can lead to either progressive retinal disease, such as human retinitis pigmentosa (RP), or stationary disease, such as congenital stationary night blindness (CSNB). Individuals with CSNB in the Rambusch pedigree were found to carry the H258N allele of PDE6B (MIM# 180072); a similar mutation was not found in RP patients. This report describes an individual carrying the H258N allele, who presented with generalized retinal dysfunction affecting the rod system and a locus of dysfunction at the rod-bipolar interface. Also described are preclinical studies in which transgenic mice with the H258N allele were generated to study the pathophysiological mechanisms of CSNB. While Pde6b(rd1)/Pde6b(rd1) mice have severe photoreceptor degeneration, as in human RP, the H258N transgene rescued these cells. The cGMP-PDE6 activity of dark-adapted H258N mice showed an approximate three-fold increase in the rate of retinal cGMP hydrolysis: from 130.1 nmol x min(-1) x nmol(-1) rhodopsin in wild-type controls to 319.2 nmol x min(-1) x nmol(-1) rhodopsin in mutants, consistent with the hypothesis that inhibition of the PDE6beta activity by the regulatory PDE6gamma subunit is blocked by this mutation. In the albino (B6CBA x FVB) F2 hybrid background, electroretinograms (ERG) from H258N mice were similar to those obtained from affected Rambusch family members, as well as humans with the most common form of CSNB (X-linked), demonstrating a selective loss of the b-wave with relatively normal a-waves. When the H258N allele was introduced into the DBA background, there was no evidence of selective reduction in b-wave amplitudes; rather a- and b-wave amplitudes were both reduced. Thus, factors other than the PDE6B mutation itself could contribute to the variance of an electrophysiological response. Therefore, caution is advisable when interpreting physiological phenotypes associated with the same allele on different genetic backgrounds. Nevertheless, such animals should be of considerable value in further studies of the molecular pathology of CSNB.

Response variability of marmoset parvocellular neurons

This study concerns the properties of neurons carrying signals for colour vision in primates. We investigated the variability of responses of individual parvocellular lateral geniculate neurons of dichromatic and trichromatic marmosets to drifting sinusoidal luminance and chromatic gratings. Response variability was quantified by the cycle-to-cycle variation in Fourier components of the response. Averaged across the population, the variability at low contrasts was greater than predicted by a Poisson process, and at high contrasts the responses were approximately 40% more variable than responses at low contrasts. The contrast-dependent increase in variability was nevertheless below that expected from the increase in firing rate. Variability falls below the Poisson prediction at high contrast, and intrinsic variability of the spike train decreases as contrast increases. Thus, while deeply modulated responses in parvocellular cells have a larger absolute variability than weakly modulated ones, they have a more favourable signal: noise ratio than predicted by a Poisson process. Similar results were obtained from a small sample of magnocellular and koniocellular ('blue-on') neurons. For parvocellular neurons with pronounced colour opponency, chromatic responses were, on average, less variable (10-15%, p<0.01) than luminance responses of equal magnitude. Conversely, non-opponent parvocellular neurons showed the opposite tendency. This is consistent with a supra-additive noise source prior to combination of cone signals. In summary, though variability of parvocellular neurons is largely independent of the way in which they combine cone signals, the noise characteristics of retinal circuitry may augment specialization of parvocellular neurons to signal luminance or chromatic contrast.

The glutamic acid-rich protein-2 (GARP2) is a high affinity rod photoreceptor phosphodiesterase (PDE6)-binding protein that modulates its catalytic properties

The glutamic acid-rich protein-2 (GARP2) is a splice variant of the beta-subunit of the cGMP-gated ion channel of rod photoreceptors. GARP2 is believed to interact with several membrane-associated phototransduction proteins in rod photoreceptors. In this study, we demonstrated that GARP2 is a high affinity PDE6-binding protein and that PDE6 co-purifies with GARP2 during several stages of chromatographic purification. We found that hydrophobic interaction chromatography succeeds in quantitatively separating GARP2 from the PDE6 holoenzyme. Furthermore, the 17-kDa prenyl-binding protein, abundant in retinal cells, selectively released PDE6 (but not GARP2) from rod outer segment membranes, demonstrating the specificity of the interaction between GARP2 and PDE6. Purified GARP2 was able to suppress 80% of the basal activity of the nonactivated, membrane-bound PDE6 holoenzyme at concentrations equivalent to its endogenous concentration in rod outer segment membranes. However, GARP2 was unable to reverse the transducin activation of PDE6 (in contrast to a previous study) nor did it significantly alter catalysis of the fully activated PDE6 catalytic dimer. The high binding affinity of GARP2 for PDE6 and its ability to regulate PDE6 activity in its dark-adapted state suggest a novel role for GARP2 as a regulator of spontaneous activation of rod PDE6, thereby serving to lower rod photoreceptor "dark noise" and allowing these sensory cells to operate at the single photon detection limit.