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 Ca²⁺. 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.This work was supported by award number R01EY023603 from the US National Eye Institute

Spectra of human L cones

AbstractVariations in the amino acid sequences of the human cone opsins give rise to spectrally variant subtypes of L and M cone pigments even in the population with normal color vision. In vitro mutagenesis studies have shown that a limited number of amino acid substitutions produce shifts in the wavelength sensitivity. Presented here are results comparing electrophysiological measurements of single human cones with the expressed cone pigment gene sequences from the same retina. In a sample of eight long-wavelength sensitive cone (L cone) spectra obtained from five donors the precise spectral sensitivities, measured in situ, of the two most commonly occurring spectral variants were determined. The peak sensitivity of the Lser180 cone was 563 nm while that of the Lala180 cone was 559 nm

A quantitative account of mammalian rod phototransduction with PDE6 dimeric activation: Responses to bright flashes

We develop an improved quantitative model of mammalian rod phototransduction, and we apply it to the prediction of responses to bright flashes of light. We take account of the recently characterized dimeric nature of PDE6 activation, where the configuration of primary importance has two transducin molecules bound. We simulate the stochastic nature of the activation and shut-off reactions to generate the predicted kinetics of the active molecular species on the disc membrane surfaces, and then we integrate the differential equations for the downstream cytoplasmic reactions to obtain the predicted electrical responses. The simulated responses recover the qualitative form of bright-flash response families recorded from mammalian rod photoreceptors. Furthermore, they provide an accurate description of the relationship between the time spent in saturation and flash intensity, predicting the transition between first and second ‘dominant time constants’ to occur at an intensity around 5000 isomerizations per flash, when the rate of transducin activation is taken to be 1250 transducins s−1 per activated rhodopsin. This rate is consistent with estimates from light-scattering experiments, but is around fourfold higher than has typically been assumed in other studies. We conclude that our model and parameters provide a compelling description of rod photoreceptor bright-flash responses.This work was supported by award no. R01EY023603 from the US National Eye Institute

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.This work was supported by award no. R01EY023603 fromthe US National Eye Institut

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

Exome-Wide Association Study of Endometrial Cancer in a Multiethnic Population

Endometrial cancer (EC) contributes substantially to total burden of cancer morbidity and mortality in the United States. Family history is a known risk factor for EC, thus genetic factors may play a role in EC pathogenesis. Three previous genome-wide association studies (GWAS) have found only one locus associated with EC, suggesting that common variants with large effects may not contribute greatly to EC risk. Alternatively, we hypothesize that rare variants may contribute to EC risk. We conducted an exome-wide association study (EXWAS) of EC using the Infinium HumanExome BeadChip in order to identify rare variants associated with EC risk. We successfully genotyped 177,139 variants in a multiethnic population of 1,055 cases and 1,778 controls from four studies that were part of the Epidemiology of Endometrial Cancer Consortium (E2C2). No variants reached global significance in the study, suggesting that more power is needed to detect modest associations between rare genetic variants and risk of EC

Infrared High-Resolution Integrated Light Spectral Analyses of M31 Globular Clusters From Apogee

Chemical abundances are presented for 25 M31 globular clusters (GCs), based on moderately high resolution (R = 22,500) H-band integrated light (IL) spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Infrared (IR) spectra offer lines from new elements, lines of different strengths, and lines at higher excitation potentials compared to the optical. Integrated abundances of C, N, and O are derived from CO, CN, and OH molecular features, while Fe, Na, Mg, Al, Si, K, Ca, and Ti abundances are derived from atomic features. These abundances are compared to previous results from the optical, demonstrating the validity and value of IR IL analyses. The CNO abundances are consistent with typical tip of the red giant branch stellar abundances but are systematically offset from optical Lick index abundances. With a few exceptions, the other abundances agree between the optical and the IR within the 1σ uncertainties. The first integrated K abundances are also presented and demonstrate that K tracks the α elements. The combination of IR and optical abundances allows better determinations of GC properties and enables probes of the multiple populations in extragalactic GCs. In particular, the integrated effects of the Na/O anticorrelation can be directly examined for the first time

Systematic Single-Cell Analysis of Pichia pastoris Reveals Secretory Capacity Limits Productivity

Biopharmaceuticals represent the fastest growing sector of the global pharmaceutical industry. Cost-efficient production of these biologic drugs requires a robust host organism for generating high titers of protein during fermentation. Understanding key cellular processes that limit protein production and secretion is, therefore, essential for rational strain engineering. Here, with single-cell resolution, we systematically analysed the productivity of a series of Pichia pastoris strains that produce different proteins both constitutively and inducibly. We characterized each strain by qPCR, RT-qPCR, microengraving, and imaging cytometry. We then developed a simple mathematical model describing the flux of folded protein through the ER. This combination of single-cell measurements and computational modelling shows that protein trafficking through the secretory machinery is often the rate-limiting step in single-cell production, and strategies to enhance the overall capacity of protein secretion within hosts for the production of heterologous proteins may improve productivity