Phototransduction: modeling the primate cone flash response

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.

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.

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.

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

Detection threshold in cone photoreceptors requires the simultaneous absorption of several photons because single photon photocurrent is small in amplitude and does not exceed intrinsic fluctuations in the outer segment dark current (dark noise). To understand the mechanisms that limit light sensitivity, we characterized the molecular origin of dark noise in intact, isolated bass single cones. Dark noise is caused by continuous fluctuations in the cytoplasmic concentrations of both cGMP and Ca²⁺ that arise from the activity in darkness of both guanylate cyclase (GC), the enzyme that synthesizes cGMP, and phosphodiesterase (PDE), the enzyme that hydrolyzes it. In cones loaded with high concentration Ca²⁺ buffering agents, we demonstrate that variation in cGMP levels arise from fluctuations in the mean PDE enzymatic activity. The rates of PDE activation and inactivation determine the quantitative characteristics of the dark noise power density spectrum. We developed a mathematical model based on the dynamics of PDE activity that accurately predicts this power spectrum. Analysis of the experimental data with the theoretical model allows us to determine the rates of PDE activation and deactivation in the intact photoreceptor. In fish cones, the mean lifetime of active PDE at room temperature is ∼55 ms. In nonmammalian rods, in contrast, active PDE lifetime is ∼555 ms. This remarkable difference helps explain why cones are noisier than rods and why cone photocurrents are smaller in peak amplitude and faster in time course than those in rods. Both these features make cones less light sensitive than rods.

Imaging visual function with the multifocal m-sequence technique

The multifocal m-sequence technique is a versatile set of tools for visual electrophysiology designed to provide access to the complex dynamic interplay of converging signals in the central nervous system. Here, a number of uses for the technique are demonstrated, with examples from human electroretinography. A simple relationship between the binary kernels extracted from a single experiment permits us to distinguish local from lateral interactions in the retina. Transformation of the series of binary kernels into response sequences provides new insight into unexpected fast dynamic properties of retinal responses and facilitates future modeling of the signals as well as identification of the signal sources.

Computational analysis of vertebrate phototransduction: combined quantitative and qualitative modeling of dark- and light-adapted responses in amphibian rods

We evaluated the generality of two models of vertebrate phototransduction. The approach was to quantitatively optimize each model to the full waveform of high-quality, dark-adapted (DA), salamander rod flash responses. With the optimal parameters, each model was then used to account for signature, qualitative features of rod responses from three experimental paradigms (stimulus/response, "S/R suite"): (1) step responses; (2) the intensity dependence of the period of photocurrent saturation (Tsat vs. ln(I)); and (3) light-adapted (LA) incremental flash sensitivity as a function of background intensity. The first model was the recent successful model of Nikonov et al. (1998). The second model replaced the instantaneous Ca2+ buffering used in the Nikonov et al. model with a dynamic buffer. The results showed that, in the absence of the dynamic Ca2+ buffer, the Nikonov et al. model does not have sufficient flexibility to provide a good fit to the flash responses, and, using the same parameters, reproduce the salient features of the S/R suite--critical features at step onset and offset are absent; the Tsat function has too shallow a slope; and the model cannot generate the empirically observed I-range of Weber-Fechner LA behavior. Some features could be recovered by changing parameters, but only at the expense of the fit to the reference (Ref) data. When the dynamic buffer is added, the model is able to achieve an acceptable fit to the Ref data while reproducing several features of the S/R suite, including an empirically observed Tsat function, and an extended range of LA flash sensitivity adhering to Weber's law. The overall improved behavior of the model with a dynamic Ca2+ buffer indicates that it is an important mechanism to include in a working model of phototransduction, and that, despite the slow kinetics of amphibian rods, Ca2+ buffering should not be simulated as an instantaneous process. However, neither model was able to capture all the features with the same parameters yielding the optimal fit to the Ref data. In addition, neither model could maintain a good fit to the Ref data when five key biochemical parameters were held at their current known values. Moreover, even after optimization, a number of important parameters remained outside their empirical estimates. We conclude that other mechanisms will need to be added, including additional Ca2+-feedback mechanisms. The present research illustrates the importance of a hybrid qualitative/quantitative approach to model development, and the limitations of modeling restricted sets of data.